river morphology - garde - india

This pageintentionally left

blank

Copyright © 2006, New Age International (P) Ltd., PublishersPublished by New Age International (P) Ltd., Publishers

All rights reserved.No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography,or any other means, or incorporated into any information retrieval system, electronic ormechanical, without the written permission of the publisher. All inquiries should beemailed to [email protected]

ISBN (13) : 978-81-224-2841-4

PUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS4835/24, Ansari Road, Daryaganj, New Delhi - 110002Visit us at www.newagepublishers.com

Preface

Rivers have been the focus of human activity since the early civilizations. Even in modern times alarge number of activities of the engineers such as water supply, irrigation, water quality control,power generation, flood control, river regulation, navigation and recreation are centered aroundrivers. Hence considerable interest has been evinced in the society about various aspects of riverssuch as their formation, hydraulics and sediment transport, erosion and sedimentation, and effect ofnatural and human interferences on rivers.

Books have been written on rivers by geologists, geomorphologists, hydraulic engineers,hydrologists and geographers. Even though all of them have attempted to understand the behaviourof rivers that have carved their channels through the material deposited by them, the emphasis ofeach one of them is different from that of the other depending on his background, objectives ofwriting the book and the targeted readership. Yet fewer attempts seem to have been made tosynthesize the contributions of these scientists into a coherent text that takes a balanced view of thesubject of river morphology. To fill this gap is the objective in writing this book. Hence, the textcovers history of fluvial hydraulics and geomorphology, drainage basin characteristics, erosion,fluvial morphology, hydraulics of alluvial and gravel-bed rivers, river bed and channel changes,fluvial palaeo hydrology, analytical and numerical modeling of fluvial processes, morphology ofsome Indian rivers, rivers and environment, and data needs for morphological studies. The text canbe used for teaching a course on river morphology to graduate and undergraduate students in civilengineering and geology, and as a reference material for engineers engaged in planning andmanagement of rivers.

My interest and involvement in the study of alluvial rivers and associated problems started withlate Prof. E.W. Lane, and Profs. M.L. Albertson, D.B. Simons and E.V. Richardson of the ColoradoState University, Fort Collins (U.S.A.). Over four decades of teaching and research in fluvialhydraulics, and association with colleagues at the University of Roorkee (now I.I.T. Roorkee) India,have helped me in looking at rivers in a much broader perspective. My association with CentralWater and Power Research Station at Pune over the last decade further enriched my associationwith the rivers problems.

While preparing the manuscript of the book, valuable assistance has been rendered by myformer colleagues Profs. K.G. Ranga Raju and U.C. Kothyari who have gone through the draft ofthe book and given valuable suggestions for its improvement; most of these have been incorporated.I am indebted to Profs. Rajiv Sinha of I.I.T. Kanpur, Brahma Parkash and Pradeep Kumar of I.I.T.Roorkee, and V.S. Kale of the University of Poona for making their publications available to me. I

am thankful to Dr. Z.S. Tarapore and subsequent directors of CWPRS for allowing me to work at theresearch station for the past thirteen years. I am particularly thankful to M.S. Shitole, Joint Director,D.N. Deshmukh, J.D. Prayag, R.A. Oak, Hradaya Prakash, Pradeep Kumar, Mukund Deshpande,Y.N. Karanjikar and others whose assistance has been valuable in finalizing the manuscript of thebook. Lastly, I am thankful to my wife Vidya and daughter Rashmi for the patience shown by themwhile I was preparing the manuscript.

December 2005 R. J. Garde

R-1 Sankul CondominiumNear Deenanath HospitalEvandavane, Pune-411004

Prefacevi

a1,a2,a3 coefficients/exponents

A area of cross-section, area of basinAb area at bankful stage, area corresponding to bedAf area of fanAu area of basin of order u

Au mean area of basin of order uAw area of corresponding to wallb exponent

B width of rectangular channelBI Brice braiding indexC Chezy’s coefficient, suspended sediment concentration at a point, climate indexCa reference suspended sediment concentration

CD drag coefficientCL lift coefficient

C CB, bed material concentration in ppm by wt., total load concentration

d* dimensionless sediment size

d, d50 median size of bed material, rain drop sized16, d50, d84, d90 sediment size such that 16,50,84,90 percent material is finer than this size respectivelyda arithmetic mean sizedi any size fraction

dmax maximum size of sedimentD depth of flow (WD=A)DC depth at the centreDd drainage density

Dmax maximum depthE kinetic energy of stormER entrenchment ratiof Darcy-Weisbach resistance coefficient

List of Symbols

f ¢ friction factor corresponding to grain roughnessf ¢¢ friction factor corresponding to form roughness

f1 Lacey’s silt factorF stream frequencyFb Blench’s bed factorFbo value of Fb when bed load is negligible

FD drag forceFe erosion factorFL lift force

Fr Froude number (= U/ gD )

Fs Blench’s side factorg gravitational accelerationG transport rate of any section

Ge equilibrium transport rateG¥ sediment transport rate at infinityDG change in Ghb head loss in bend

hs saltation heightH average height at ripple or dunes, bars; reliefi indexI intensity of rain fall

I30 maximum 30 minute intensity during stormj indexks roughness parameterK erodibility index, diffusion coefficient, wave number (= 2pD/L)

Ko theoretical diffusion coefficientl length, distance, length of aggradationL average length of ripples or dunes, length of stream up to drainage dividels saltation length

Lu total length of streams of order u

Lu mean length of streams of order u

m exponent

M percent of silt-clay in perimeter, Kramer’s uniformity coefficient, dimensionlessvelocity bed or water wave

Mb meander beltML meander lengthMW meander width (MB-W)

River Morphologyviii

n index, exponent, Manning’s n

nb Manning’s n with respect to bed

ns Strickler’s nNu number of streams of order u

nw Manning’s n with respect to wallpi per cent

P perimeter, annual rainfallPmax average monthly maximum precipitationq discharge per unit widthqb bed load transport rate in weight/width

qBv volumetric bed load transport rate per unit widthqc critical water discharge per unit widthqs suspended load transport rate per unit widthqT total sediment transport rate in volume per unit width

qTv total volumetric sediment transport rate per unit width

q* dimensionless discharge (= q/ gd3 )

q¢ lateral inflow per unit length on both sides

Q, Qw water discharge

Q1 = Qb/d2 gd

Q2 = QbS/d2 gd

Q3 = Qb/d2 gdS

Q2.33 flood discharge of return period 2.33 years

Qb bankful dischargeQB bed-load dischargeQma mean annual dischargeQmaf mean annual flood discharge

Qr runoff rate per unit areaQS suspended load dischargeQT total sediment transport rate in weight or volumer radius

rc centre line radius of bendri, ro inner and outer radius of bendR hydraulic radius, annul run off, run off parameterRA area ratio

Rb hydraulic radius corresponding to bed, bifurcation ratio

List of Symbols ix

Rb¢,Rb¢¢ Rb with respect to grain and form roughness respectivelyRe Reynolds number

RL length ratio of HortonRm mean radius of meander bends

Ro*2 = Dg sd f

3 2/r n

Rs bifurcation ratio for slopeRW hydraulic radius corresponding to wallsR* particle Reynolds number u* d/vS, So slope, bed slope, slope at x = o

S¢ slope corresponding to grain roughnessS¢¢ slope corresponding to form roughnessSa annual erosion rate in cm (absolute)Sf energy slope, fan slope

Si sinuositySW water surface slope

S average catchment slope

Su average slope of segments of order uSDR sediment delivery ratioSE super-elevation

tp time to peak

T number of years, also dimensionless excess shear {= ( ' /)t t t- 0 0c c}

TE trap efficiency of reservoirs

u local velocity in x direction, order of stream

¢u 2 r.m.s. value of velocity function in x direction

ud velocity at the top of particle

udcr critical velocity at particle level

u* shear velocity (= t r0 / f )

u*¢ shear velocity corresponding to grain roughnessu*¢¢ shear velocity corresponding to form roughness

U average velocityUcr average critical velocityUg average velocity of particle moving as bed loadUW average velocity of bed form or wave

v local velocity in y direction

River Morphologyx

¢v 2 r.m.s. value of velocity fluctuations in y direction

vq velocity in q directionvmax maximum velocity at any verticalvr velocity in r directionVcp average velocity in the vertical

w local velocity in z direction, mean width of rib

¢w 2 r.m.s. value of velocity fluctuations in z direction

W average width (WD = A); weight of the particleWav average unit weight over T years

Wb bankful widthWo unit weight value of sedimentWs water surface widthx distance in x direction, a dimensionless coefficient

y distance from the wallY1 hydraulic mean depth (=A/Ws)z lateral distance from the origin,Z actual slope of suspended sediment distribution curve, elevation of bed at given x and

t; side slope of channel (Z hor.: 1 vert.)

Zo theoretical value of suspended distribution curve; bed elevation at x = 0a energy correction coefficienta1, a2, a3 exponentsb es/em ratio of sediment transfer coefficient to the momentum transfer coefficient

gs, gf specific weights of sediment and fluidd lag distanced¢ thickness of laminar sub-layerDgs difference in specific weights of sediment and fluid

Îm momentum transfer coefficientÎs sediment transfer coefficienth dimensionless distance in the verticalq angle

k Karman constant (actual)k0 Karman constant (clear water)l porosity, wave lengthm dynamic viscosity of fluid

n kinematic viscosity of fluidx sheltering coefficient

List of Symbols xi

rf mass density of fluidrs mass density of sediment

s arithmetic standard deviationsg geometric standard deviationt shear stressto average shear stress on the bed

t0c critical shear stress for sedimenttr, tq components of shear stress on the bed along r and q directiont* dimensionless shear stresst*c dimensionless critical shear stress

j angle of reposejB, jS, jT dimensionless bed-load, suspended load and total load transport rate respectivelyy = Dgsd35/t0

y¢ = Dgsd35/t0¢w fall velocityw0 fall velocity under ideal conditions

Subscripts and superscriptsSubscripts* dimensionless quantity

c pertaining to critical condition

1, 2 pertaining to section 1, 2.Superscripts' corresponding to grain roughness

'' corresponding to form roughness

River Morphologyxii

Below is given meaning of some terms occurring in the text. (adapted from Easterbrook 1969)Abrasion: wearing away of particle due to frictionAggradation: rise in bed level of the stream over large lengthAlluvium: unconsolidated sediment deposited by river; sediment deposited in river bed, floodplains,

lakes, alluvial fans etc.

Alluvial fan: cone shaped accumulation of debris or sediment deposited by the stream as it descendsfrom steep slope to a plain where the material deposits in the form of a fan

Avalanche: mass of snow sliding down the mountainAvulsion: shifting of a river course

Base level: the level below which a land surface cannot be reduced by running waterBed-load: material moved on or near the bed due to tractive force of the flowBed-forms: features developed on the bed of the river due to interaction between flowing water and

river bed sediments

Bed-load: material moved on or near the bed due to tractive force of the flowBed material load: material transported by the stream which has the stream bed or banks as its originBeheaded stream: lower portion of the stream from which water has been diverted due to stream piracyBraided stream: a stream divided into a number of channels by island formation, which may join and

bifurcate again and again

Cirque: a deep steep walled recess in a mountain caused by erosion due to glaciersColluvium: unconsolidated deposits, usually at the foot hills or cliff, brought down by gravity

Creep: slow down-slope movement of rock fragments and soilCrevasse: a fissure formed in glacial ice due to various strains

Degradation: general lowering of stream bed over large length due to deficiency of sediment load ascompared to its sediment transport capacity

Delta: a triangular shaped alluvial deposit formed when a stream enters lake or seaDiastrophism: the process or processes by which the crust of the earth’s surface is deformed

Glossary of Some Terms inRiver Morphology

Divide: a ridge between the streams; a line of separation between drainage basinsDrainage basin: the area drained by a system of rivers

Eolian: deposits which are due to transporting action of the wind

Ephemeral stream: the stream which flows only in direct response to precipitation; it receives no waterfrom ground water

Escarpment: relatively steep slope or cliff separating gently sloping tractsEustatic: pertaining to simultaneous world wide changes in sea level

Floodplain: relatively flat land strip on one or both sides of a stream built by sediment deposits duringflooding. It is sometimes called active flood plain

Fluvial: produced by the action of rivers

Geomorphic cycle: erosion cycle during which land forms are evolved which change from youth tomaturity to old, each of which is characterized by distinctive features

Geologic structure: it includes not only folding, faulting and uplift of the crust but also includes otherfactors related to the physical and chemical characteristics of rocks, relative resistance toweathering, dip, strike, jointing, stratification etc.

Glacial drift: material transported by glaciers

Glacial trough: U-shaped valley produced by glacial erosion

Hanging valley: a tributary valley whose floor is higher than that of the main valley at the junction dueto degradation of the main valley

Incised meander or entrenched meander: a deep sinuous valley cut by a rejuvenated stream

Levee: natural or man-made embankment above the general level of floodplain which confines thestream channel

Loess: fine sized particles deposited by wind

Mass-wasting: the down-slope movement of rock debris under the influence of gravity

Meander scar: crescent-shaped cut in a valley side made by lateral planation of the outer part of ameander

Meandering stream: a stream that follows sinuous or crooked pathMisfit stream: a stream whose meanders are either too small or too large, compared to valley widthMonadnock: a residual hill or mountain standing above a peneplain

Oxbow: a crescent-shaped lake formed in an abandoned river bend by a meander cutoff

Palaeosol: a buried soilPeneplain: a landscape of low relief formed by long continued erosion

Periglacial: region beyond the margin of a glacierPiracy: diversion of one stream by the otherPleistocene: the last Ice Age

River Morphologyxiv

Regimes of flow: characteristics of bed and water surface produced by water flowing on a loose alluvialbed

Rejuvenation: activation of erosion of a stream by uplift, climatic changes or change in base level

Relief: the difference between high and low points of the land surface

Saltation load: material bouncing along the bed or moved directly or indirectly by the impact ofbouncing particles

Scour: local lowering of the bed of the stream usually due to presence of a hydraulic structure in thestream

Suspended load: that part of the sediment load carried by the stream that is kept in suspension byturbulent fluctuations

Talus: an accumulation of loose rock mass at the base of a cliffTerrace: a flat or gently sloping surface bordered by an escarpment, it is composed of alluvium or bed

rock. It is flooded so rarely that it does not grow by sediment deposition

Underfit stream: a stream which is too small for the valley through which it flows

Glossary of Some Terms in River Morphology xv


blank

Contents

Preface v

List of Symbols vii

Glossary xiii

1. INTRODUCTION 11.1 Introduction 1

1.2 Some Problems in River Morphology 21.3 Historical Developments in Fluvial Hydraulics 41.4 Historical Developments in Geomorphology 71.5 Scope 9

References 10

2. DRAINAGE BASINS AND CHANNEL NETWORKS 112.1 Introduction 112.2 Drainage Patterns and Texture 122.3 Stream Order 14

2.4 Horton’s Laws of Stream Numbers and Stream Lengths 162.5 Areas of Drainage Basins 192.6 Basin Shape 212.7 Lithology 21

2.8 Vegetation 222.9 Drainage Densities and Stream Frequency 24

2.10 Relief Aspects 262.11 Drainage Basin Characteristics and Hydrology 29

2.12 Random Walk Model 292.13 Concluding Remarks 31

References 31

3. SOIL EROSION AND SEDIMENT YIELD 343.1 Introduction 34

3.2 Global Erosion Rates 35

3.3 Types of Erosion 393.4 Factors Affecting Erosion 41

3.5 Mechanics of Sheet Erosion 443.6 Equations for Predicting Soil Loss from Agricultural Lands 483.7 Measurement of Sediment Yield 503.8 Sediment Delivery Ratio 56

3.9 Process Based Modelling of Erosion 603.10 Erosion Rates from Indian Catchments 64

References 67

4. FLUVIAL MORPHOLOGY 714.1 Geomorphology and Fluvial Morphology 71

4.2 Geomorphic Cycle (or Cycle of Erosion) 724.3 Rejuvenation of Erosion Cycle 744.4 Criticism of Geomorphic Cycle 744.5 Noncyclic Concept of Landscape Evolution 76

4.6 Geological Time Scale 774.7 Glaciation 804.8 Fluvial Morphology 824.9 Topography Produced by Streams 94

4.10 Variables in River Morphology 1044.11 Neotectonics and Earthquakes 105

References 107

5. HYDRAULICS OF ALLUVIAL STREAMS 1105.1 Introduction 110

5.2 Incipient Motion 1105.3 Modes of Sediment Transport 1205.4 Bed-Forms in Unidirectional Flow 1245.5 Resistance to Flow in Alluvial Streams 137

5.6 Bed-Load Transport 1455.7 Suspended Load Transport 1505.8 Total Load Transport 158

References 164

6. HYDRAULIC GEOMETRY AND PLAN FORMS OF ALLUVIAL RIVERS 1696.1 Introduction 169

6.2 Stable Channels Carrying Sediment 1706.3 Hydraulic Geometry of Alluvial Streams 1766.4 Empirical Relationships for Hydraulic Geometry 180

River Morphologyxviii

6.5 Non-Dimensional Relations for Hydraulic Geometry 1866.6 Flow Around Bends with Rigid and Alluvial Beds 189

6.7 Shear Direction Near Curved Stream Bed and Bed Topography 1946.8 Braided Rivers 1986.9 Meandering 202

6.10 Stability Analysis and Criteria for Plan-Forms 212

References 223

7. GRAVEL-BED RIVERS 2297.1 Introduction 2297.2 Data for Gravel-Bed Rivers 2307.3 Bed Material 230

7.4 Pavement 2337.5 Hydraulic Geometry 2337.6 Bed Features in Gravel-Bed Rivers 2377.7 Resistance to Flow in Gravel-Bed Rivers 241

7.8 Sediment Transport in Gravel-Bed Rivers 246References 253

8. FLUVIAL PALAEO HYDROLOGY 2568.1 Introduction 2568.2 Objectives of Palaeo Hydrologic Studies 257

8.3 Basis of Analysis 2588.4 Climatic Changes: Past and Future 2608.5 Palaeo Hydrologic Estimates of Discharge and Velocity 2628.6 Palaeo Hydrologic Studies in India 267

8.7 Fluvial Palaeo Hydrologic Studies in India 271References 273

9. BED LEVEL VARIATION IN STREAMS 2759.1 Introduction 275

Degradation 2779.2 Types of Degradation 277

9.3 Downstream Progression Degradation 2829.4 Upstream Progression Degradation 2859.5 Effects of Degradation 2859.6 Prediction of Depth of Degradation 286

9.7 Control of Degradation 286Local Scour Around Bridge Piers 286

9.8 Factors Affecting Scour 288

Contents xix

9.9 Equations for Predicting Scour Depth 2919.10 Verification of Equations for Scour Depth 293

9.11 Scour in Gravelly Material 2959.12 Scour in Cohesive Soils 2969.13 Protection of Scour Around Bridge Piers 296

Aggradation 2969.14 Occurrence of Aggradation 297

Reservoir Sedimentation 3019.15 Sediment Inflow and Trap Efficiency 3029.16 Movement and Sediment Deposition in Reservoirs 304

9.17 Modeling of Sediment Deposition 3069.18 Methods for Preserving and Restoring Reservoir Capacity 310

References 311

10. RIVER CHANNEL CHANGES 31510.1 Introduction 315

10.2 Avulsion 31510.3 Stream Capture 32110.4 Erosion at Bends 32310.5 Natural and Artificial Cut-Offs 326

10.6 Channel Pattern Changes 32910.7 Longitudinal Grain Sorting 331

References 334

11. ANALYTICAL MODELS OF RIVER MORPHOLOGY 33711.1 Introduction 337

11.2 Basic One-Dimensional Equations 33811.3 Analysis of Water Surfaces and Bed Waves 34211.4 Analytical Models 34311.5 Some Applications of Linear Models 346

References 357

12. NUMERICAL MODELS FOR MORPHOLOGICAL STUDIES 35912.1 Introduction 35912.2 One-Dimensional Equations 36012.3 Numerical Schemes of Solution 36212.4 Classification of One-Dimensional Models 363

12.5 Convergence and Stability 36612.6 Boundary Conditions 367

River Morphologyxx

12.7 Channel Cross-Sections and Method of Erosion or Deposition 36812.8 Modeling of Armouring 369

12.9 HEC – 6 37212.10 CRARIMA 37612.11 Applications of HEC – 6 378

References 383

13. MORPHOLOGY OF SOME INDIAN RIVERS 38613.1 River Systems in North India 386

Kosi 38813.2 Introduction 38813.3 Catchment Characteristics and Geology 391

13.4 Geotectonics 39213.5 Hydrology 39313.6 Sediment Size and Slope 39513.7 Morphology of the Kosi 396

13.8 Management of the Kosi 39813.9 Present Day Problems of the Kosi 402

Brahmaputra 40213.10 Introduction 402

13.11 River Characteristics 40713.12 Seismicity and Landslides 41013.13 Climate and Hydrology 41113.14 Resistance to Flow and Sediment Transport 414

13.15 Plan-Forms 41613.16 Flooding and Flood Protection 41913.17 Drainage of Hinter Lands 42013.18 River Bed Changes in Brahmaputra 422

13.19 Development Plans 42313.20 Role of Dredging 424

References 424

14. RIVERS AND ENVIRONMENT 42714.1 Introduction 427

14.2 Actions Causing Disturbance in Stream System and Their Impacts 42914.3 Environmental Effects of Hydraulic Structures 42914.4 Dams and Reservoirs 43014.5 Water Quality in Reservoirs 433

14.6 Thermal and Hydro-Power Plants 436

Contents xxi

14.7 Recreation 43714.8 Stream Pollution 437

14.9 River Action Plans 43814.10 Stream Restoration 439

References 440

15. DATA REQUIREMENTS FOR MORPHOLOGICAL STUDIES 44215.1 Introduction 44215.2 Maps, Air-Photos, Satellite Imageries 44215.3 Lithology and Tectonics 44515.4 Vegetal Cover 446

15.5 Geomorphic Map 44615.6 Basin Characteristics and Morphometry 44915.7 Sea-Level Fluctuations, Climatic and Other Changes 45015.8 Cross-Sections, Longitudinal Section and Plan-Form 451

15.9 Bed and Bank Material 45315.10 Hydrologic Data 45415.11 Sediment Load Data 45515.12 Stratigraphic Studies 456

15.13 Water Quality Related Data 45815.14 Catalogue of Information on Morphological Studies 459

References 459

Appendix A 462

Author Index 463

Subject Index 473

River Morphologyxxii

1C H A P T E R

Introduction

1.1 INTRODUCTION

A river carries water, sediment and solute from the drainage area to the sea and is thus of interest tohydraulic engineers, geomorphologists and sedimentologists. This is important to engineers becausewater is used for a variety of purposes by humanity; water courses are used as navigation channels, andalso erosion, transportation and deposition of sediment cause a number of problems in the river and inthe catchment that must be solved pragmatically. The direct effect of transportation of sediment andwater from the geologist’s and geomorphologist’s point of view is that the structure and form of the riverand adjoining areas are continually changed due to erosion and sedimentation. The rates of this changeare variable. While geologists and geomorphologists are concerned about changes taking place in 103 to106 years or more, engineers are concerned with changes in a river during a relatively short period, say10–20 years to probably 50–100 years. These channel changes can be in the form of size, shape,composition of bed material, slope and plan-form. The engineer’s primary objective is to understand thebasic mechanisms of erosion, transportation and deposition of sediment by flow in the river and developqualitative and quantitative methods for prediction of river behaviour. The approach followed byengineers is called fluvial hydraulics or river dynamics and this approach has been developed during thepast 200–300 years.

The other approach taken by geologists and geomorphologists is primarily qualitative even though,in recent years some quantitative methods have been used. Morphology is defined as the science ofstructure or form. Hence according to Worcester (1948) geomorphology is the science of landforms; it isthe interpretive description of the relief features of the earth. It thus describes the surface of thelithosphere, explains its origin and interprets its history. To understand geomorphology one shouldknow in detail the composition and structure of the rocks of the earth and the processes which act on it.Geomorphology recognises that the earth’s surface has changed in the past and is changing at presentdue to internal and external processes. The internal processes are those, which originate within the earthitself and include diastrophism and volcanism. External processes shaping the earth’s surface includerunning water, weathering, waves and shore currents, glaciers, avalanches, and plant, animal and human

River Morphology2

activities. It may be mentioned that most of the changes taking place in the earth’s surface are slow, eventhough a few may be catastrophic. Conventional texts in geomorphology would deal in detail about theinternal and external processes which cause changes in the landform and then deal with the topographyproduced by streams in humid regions, by winds in arid and semiarid regions, glaciers, shore processes,ground water, volcanoes etc. Geomorphology is sometimes called physiography. This latter term, asused particularly in Europe, includes climatology, meteorology, oceanography and mathematicalgeography. Inasmuch as these are not addressed in this book, the term geomorphology is preferred tophysiography.

The word “fluvial” means produced by river action. Hence fluvial morphology means the science oflandforms as produced by river action. It can also be called river morphology; it is a branch ofgeomorphology and it would deal with form of the streams and adjoining areas as brought about byerosion, transportation and deposition of sediment by the running water. Both river morphology andgeomorphology are descriptive sciences based mainly on careful observation and interpretation ofnatural phenomena. In the last century hydraulic engineers, hydrologists and geographers have alsomade contributions to river morphology.

1.2 SOME PROBLEMS IN RIVER MORPHOLOGY

Since the dawn of civilization, mankind has used rivers for supporting and sustaining life. This has beendone by harnessing and controlling rivers for the benefit of people. In doing so the regime or stability ofthe river is invariably disturbed. In discussing these problems caused by disturbance in the stability ofrivers, it is desirable to define what geomorphologists call a graded stream (Mackin 1948). A gradedstream, poised stream, balanced stream or a stream in equilibrium is defined by Mackin as the one inwhich channel dimensions and slope are so adjusted over a period of time that it carries incomingsediment load and water without appreciable erosion or deposition.

In geologic time frame no river can be graded because of the natural tendency of land mass andrivers to erode gradually towards sea level. In a true dynamic sense also no river can be in trueequilibrium since the discharge changes continuously. However, it may be mentioned that the changesrelated to geomorphic erosion are very slow and hence if one considers a time period of a few years tosome decades, most of the streams can be considered to be in equilibrium, except a few rivers such as theKosi, the Brahmaputra and the Yellow river which are truly unstable.

This equilibrium of the stream is disturbed by natural or man-made interferences in one or more ofthe conditions that maintain the equilibrium. A few of these instances are discussed below.

i. When a large dam is constructed across the river to store water for irrigation, water supply,flood control, generation of water power, navigation or recreation, the sediment transportcapacity upstream of the dam is reduced thereby causing aggradation in the main reservoir andalso in the tributaries on the upstream. This has many undesirable effects including depletion ofreservoir capacity and flooding of the upstream areas. In some cases such as the Imperial damon the Colorado river and Bhakra dam on the Sutlej in India sediment deposition has beenfound to occur 70-80 km upstream of the dam.The water released from the reservoir is almost sediment free and hence it picks up sedimentfrom the bed and banks of the stream causing degradation over long reaches of the stream. It

Introduction 3

may also lead to channel widening or change in the planform of the river. Needless toemphasise, degradation has many undesirable effects.

ii. It has long been recognized that water transport is comparatively much cheaper than road or railtransport and hence many streams such as the Danube, the Volga, the Rhine, the Mississippi,the Yangtze, the Ganga, the Brahmaputra and the Nile have been used for navigation sinceancient times. Making the river navigable year around involves construction of dams, locks,channel widening, channel straightening and channel contraction using spurs or jetties andbank stabilization. It may also involve dredging and releasing additional water during lowflows. These changes affect the stability of the river and hence executions of such changes needconsideration from hydraulic and morphologic points of view.

iii. Barrages, canal head works, sediment excluders and extractors in irrigation canals areconstructed for withdrawing relatively sediment free water for irrigation and water supplypurposes. This disturbs the equilibrium of the stream causing aggradation in the downstreamreaches. Similarly, aggradation takes place when rivers are used for dumping mining wasteshoping that the stream will safely carry the dumped material downstream. However, the streamcan carry this excess load only with increased slope, which is achieved by aggradation. Thishappened, for example, on the Yuba river in California (U.S.A.) during gold-rush period in thelatter half of the 19th century.

iv. Similarly, when sand and gravel are mined from the river bed to meet the ever increasingdemand of the construction industry, the river downstream is found to degrade creating manyproblems in that reach. Such degradation in the river causes similar effects in the tributaries andsub-tributaries on the downstream side.

v. In order to have equitable distribution of water throughout the country large scale transfer ofwater from one basin to the other is either contemplated or is being executed. This is likely todisturb the equilibrium of the streams because the balance between water distribution andsediment load distribution is likely to be disturbed.

vi. Construction of flood control works such as embankments, reservoirs, channel straightening,meander cut-offs and channel improvement also tend to disturb the equilibrium of the streamand needs careful study.

vii. Large scale dredging carried out along the river for navigation purposes also disturbs thesediment balance and hence the stream equilibrium.There are other less obvious factors that affect the stability of the stream, i.e., they affectchannel slope, plan-form, cross-section, and alignment. Some of these are the following:

viii. Change in drainage basin characteristics due to change in land use such as deforestation,reforestation, agricultural land development, road construction, urbanization, and building ofdams and check-dams disturb the river equilibrium by changing runoff and sediment load andtrigger changes in the channel characteristics.Ruhe (1971) has described the case where straightening of a channel had repercussionsthroughout the basin. In the Willow river (Crawford County, Iowa, USA) straightening led tochannel deepening and widening. In addition, new deeply entrenched gullies extended formany kilometres up the tributary system and developed hill slides, disrupting agricultural landsand public roads.

River Morphology4

When urbanization takes place large-scale changes are induced in the catchment, itshydrological characteristics and the sediment yield. Because of breaking of new grounds,removing of vegetation, and use of construction equipment, the runoff and storm flow increasesand hence land erosion is accelerated. As a result the sediment load of the streams is oftenincreased dramatically. Wolman and Schick (1967) recorded up to 50,000 tons/km2/yr sedimentload at one site, as compared to 80-200 tons/km2/yr under normal conditions.After the urban area is developed, infiltration is reduced and ground water levels may belowered. Untreated waste including sewage may be discharged into the streams causingpollution, which in turn, may be lethal for the aquatic life and detrimental to the use of the waterin downstream reaches for drinking and recreational purposes. Due to urbanization there is anencroachment on the flood plain and hence channels are confined resulting in higher floodlevels.

ix. Long term changes in the climate or hydrologic regime lead to significant changes in discharge,type of sediment load and its quality which lead to change in channel dimensions, change inriver course and/or change in plan-form or meander characteristics. In extreme case the rivercan cease to exist.

x. Earthquakes and active tectonic movement such as subsidence or upheaval are found toinfluence the river stability.

Earthquake of magnitude greater than 4 on Richter scale can trigger a number of landslides throughout the region and earthquake of magnitude 8 or larger is capable of triggering tens of thousands of landslides throughout the region that extends to more than 400 km from the fault (Wilson and Keefer 1985).Heavy rainfall following such landslides can bring enormous amount of material in the stream and canchange its regime. Gee (1951) has reported the damage caused by 15 August 1950 earthquake inBrahmaputra valley that was of 8.6 intensity on Richter scale. He found that 75 percent of hills in 4 3000km2 area were mutilated by landslides. Small and large rivers became blocked by material that fell inthem and some even ceased to flow. Flood following the earthquake burst these dams and large quantityof sediment and rock material was carried downstream. The rivers Dibang and Subansiri twice changedtheir courses. The Brahmaputra got considerably silted up near Dibrugarh, and the bed level rose by afew metres; it took several years for the excess sediment to move downstream.

In engineering literature little attention has been paid to active neo-tectonic movement as a factorinfluencing river morphology. The rates of surficial deformation in certain region may vary from lessthan 10 mm/yr to more than 10 mm/yr for seismic deformation. When considered over a few decadessuch deformation can affect valley slope enough to affect the river morphology. If at a particular sectionalong the river there is uplift there is aggradation on upstream and downstream side while in betweenthere is degradation.

1.3 HISTORICAL DEVELOPMENTS IN FLUVIAL HYDRAULICS(GARDE 1995)

Even though mankind has been living with sediment problems for the past several centuries, relativelylittle progress was made in our knowledge about sediment movement up to 16th century A.D. Earliercivilizations in the valleys of the Indus, the Tigris, the Euphrates, the Nile and the Yellow rivers were

Introduction 5

using canals for supplying water for irrigation through unlined channels. These canals either took offfrom a weir or they were inundation canals. The common problem with these canals was silting andhence frequent sediment removal was necessary. Locating the canals on the outer side of the bend of astream to reduce sediment entry into canal seems to have been practised. The Chinese had madeconsiderable progress in controlling large rivers, flood diversion, and similar other problems. TheRomans had made progress in water supply and sewerage. The Greeks knew about the fall velocity ofdifferent sediment particles.

During 1600–1800 A.D. relatively more progress was made in understanding the physics of flow inopen channels. The basic equations governing the flow, viz. the continuity equation and the equations ofmotion were developed during this period. d¢ Alembert (1717–1783) gave the differential equation forcontinuity of flow which was generalized by Leonard Euler (1707–1783). It was also during this periodthat the equations of motion, commonly known as Euler’s equations were established. The French

engineer Chezy (1718–1798) gave the resistance equation U C RS= where U is the average velocity,R the hydraulic radius, S the channel slope and C is Chezy coefficient. Some basic ideas about riverhydraulics were initiated by Dominico Guglielmini (1655–1710) and Paul Frizi; both wrote books onrivers. Du Buat (1734–1809) gave scouring velocities for materials of different sizes.

Much more progress was made during 19th century. Bouniceau, Grass, Lechalas, Suchier andDeacon conducted studies and critical velocities for different sized materials were recommended.Brahm showed that the critical velocity is proportional to (submerged particle weight)1/6. D.F. duBoys(1847-1924) gave a simple model for bed-load transport and reached the conclusion that qB ~to (to – toc) were qB is the rate of bed-load transport, and to and toc are the average bed shear stress andcritical shear stress for given size of bed material respectively. During this period two new resistanceequations, which are now commonly used, were proposed. These are

Darcy-Weisbach equation: hf = f L

D

U

g

2

2

and

Manning’s equation U = 1 2 3 1 2

nR S/ / ...(1.1)

Here hf is the head loss in length L of pipe diameter D, R is the hydraulic radius, S is the slope andf and n are friction factor and Manning’s roughness coefficient respectively. In the latter half of 19thcentury O. Fargue (1827–1910) who was closely associated with the developmental work of the riverGaronne, gave what are popularly known as “Fargue’s rules” of river behaviour. Finally equations ofmotion for laminar flow and turbulent flow, commonly known as Navier-Stokes equations and Reynoldsequations were developed. Similarly Sternberg gave his law for the reduction of sediment size along theriver by the combined action of grinding and sorting. It was also at the fag end of 19th century thatKennedy proposed the method for design of stable channels based on canal data from India that waslater modified by Lacey and others.

The first half of the twentieth century witnessed all round progress in fluvial hydraulics. G.K.Gilbert (1843–1918) performed extensive laboratory experiments and studied modes of sediment

River Morphology6

transport, and observed various bed-forms. Different investigators later used the hydraulic datacollected by Gilbert to study resistance and sediment transport in channels. As regards channelresistance, Strickler analysed Swiss river data and for plane beds with coarse material proposed theequation

n = d 501 6/ /21 ...(1.2)

where d50 is expressed in metres. Exner tried to explain formation of bed undulations using theequations of motion. During this period a number of investigators conducted experiments in thelaboratory and developed empirical equations for critical shear stress (i.e., shear stress at whichsediment of a given size just starts moving) as a function of sediment size d and the difference in specificweight between sediment and water Dgs. However, the credit for developing the rational criterion forincipient motion that is based on sound principles of fluid mechanics goes to A.F. Shields (1908–1974).Using sediments of different relative densities and sizes, he obtained a unique curve between toc/Dgsd

and t r noc f d/ . / . Here toc is critical shear stress for sediment of size d and n is the kinematic viscosity

of fluid. The term t roc f/ = u*c is known as critical shear velocity.

In a similar manner a number of empirical equations were developed by different investigatorsrelating rate of bed-load transport to (to – toc), (q – qc) or (U – Uc) where q is the discharge per unitwidth, U is the average velocity of flow, and quantities with subscript c refer to their values at incipientmotion conditions. However, these equations were of limited use. In 1948 E. Meyer-Peter and R. Müllerproposed an empirical equation for bed-load transport which is based on a wide range of sediment sizesand flow conditions and which is used often even today. A. Kalinske and H.A. Einstein developed bed-load equations using statistical nature of sediment movement.

Simultaneously progress was made in developing the theory of suspended sediment transport. TheGerman meteorologist Schmidt gave the equation

wo sCdC

dy+ Î = 0 ...(1.3)

for distribution of suspended sediment in the vertical. Here C is the concentration of sediment of fallvelocity wo at a distance y from the bed and Îs is sediment transfer coefficient. This equation wasintegrated independently by Rouse and by Ippen using equation for velocity distribution obtained byKarman and Prandtl, and the integrated form was verified by Vanoni and Ismail. Simultaneously, bed-load and suspended load samplers were developed and tested in Europe and U.S.A., which greatlyhelped in collecting valuable data on sediment transport by rivers.

As regards the resistance to flow, Karman and Prandtl’s equations for velocity distribution forturbulent flow in pipes were adapted to open channel flow and velocity distribution laws forhydrodynamically smooth and rough surfaces were established. Einstein (1904–1963) suggested amethod for separating grain resistance and form resistance of bed undulations while Einstein andBarbarossa proposed a method for predicting resistance to flow in alluvial streams.

Lastly on the basis of a large volume of data from stable mobile bed alluvial channels and buildingon the advances made by Kennedy, Lindley, King and others, G. Lacey (1887–1980) proposed a methodof channel design according to which for given Q and bed material size, the channel depth, width and

Introduction 7

slope are uniquely fixed. Also data were collected about the geometry of alluvial rivers and equationshave been developed to predict width and depth as a function of bankful discharge and sediment size.

The last half of the twentieth century has seen considerable progress in fluvial hydraulics. Thecharacteristics of different bed-forms have been studied and criteria for their prediction established. Anumber of equations have been developed to predict the resistance and sediment transport rates ofuniform and non-uniform sediments.

Kennedy, Engelund, Hansen and Fredsoe, have studied stability of mobile bed subjected to smalldisturbances to explain the formation of dunes, antidunes and plane bed. Similarly, Hansen, Callander,Parker, Hayaski and Ozaki, Engelund and Skovgaard and others have carried out stability analysis todetermine the conditions under which streams meander.

And finally, with the availability of high speed computers the equations of motion in alluvialstreams have been solved to develop methods of prediction of bed levels in unsteady non-uniform flowssuch as silting of reservoirs, aggradation caused by increase in sediment load or decrease in dischargeand degradation caused by increase in flow. Simultaneously field data are being collected to test varioussoftwares developed for solving such problems. Also experimental data are being collected to studysome basic problems such as armouring and pickup function.

There has also seen considerable activity in understanding the hydraulics of gravel-bed rivers, theirhydraulic geometry and sediment transport and scour.

1.4 HISTORICAL DEVELOPMENTS IN GEOMORPHOLOGY(Tinkler, 1985)

From the Greek writings one can extract three basic principles regarding the rational investigations oflandforms; these are (i) the concept of infinite time, (ii) reality of denudation i.e., loss of mass ormaterial from the landscape and (iii) acceptance of the principle of conservation of mass. Herodotus(485–425 B.C.) recognized the importance of yearly increments of silt and clay deposition by the Nile.He also anticipated the idea of changing sea levels that is of great significance in geomorphology.Aristotle (384–322 B.C.) thought that rainfall might produce a temporary torrent, but doubted that itcould maintain flow in a river. Strabo (54 B.C.–25 A.D.) noted examples of local sinking and rise of theland. He also mentioned about the effect of ebbs and tides on the growth of delta. Both Strabo andSeneca (B.C.–65 A.D.) recognized the role played by volcanic activity and earthquakes on thelandforms.

During the many centuries that followed the decline of the Roman Empire, there was little or noprogress of scientific thought in Europe; however, some learning process continued in Arabia. During941–982 A.D. there is reference to erosion and transportation of sediment by the streams and wind andweathering in the four-volume tretise on discourses of the Brothers of Purity.

Little progress was made in Europe between the first century and beginning of the 16th century.During the fifteenth, sixteenth and seventeenth centuries landforms were explained by the philosophy ofcatastrophism, according to which the features of the earth were created as a result of violentcatastrophic actions. Leonardo da Vinci (1452–1519 A.D.) had very advanced ideas about geologicthinking for his time. He recognized that streams cut the valleys and that the streams carried sedimentfrom one part of the earth and deposited at other places. The Frenchman Baffon (1707–1788) thought

River Morphology8

that erosion by streams would eventually reduce the land to the sea level. He was also the first to suggestthat the age of the earth was not to be measured in terms of a few thousand years. Another FrenchmanGuetthard (1715–1786) also discussed about the degradation of mountains by streams and emphasizedthat not all the material removed by the stream would immediately be carried to the sea but a part wouldalso deposit on the flood plains. The Swiss De Saussure (1740–1799) recognized the ability of glaciersto carry out erosional work.

James Hutton (1726–1797) who entered the university at the age of 14 to study humanities wasmore interested in chemistry and geology. Finally, he was educated as a physician. However, instead ofpractising medicine he gradually switched over to agriculture and travelled through Southern Englandduring which time he developed his interest in geology. Hutton is known for propounding the conceptthat “the present is the key to the past”, thus establishing the doctrine of uniformitarianism. His writingsclearly express the concept of a river system and its geomorphic significance. Some other importantconcepts introduced by Hutton are:

i. A vast portion of the present rocks is composed of bodies, animals, vegetables and minerals ofmore ancient formation.

ii. All present rocks are going to decay and their material going to deposit in the sea.iii. The morphological process requires indefinitely long geological time.iv. There is a conceptual possibility of relative change between land and sea levels leading to

upheaval.

Hutton’s friend John Playfair (1748–1819) who was Professor of Mathematics and Philosophy atEdinburgh was in contact with Hutton, Joseph Black, and Adam Smith. After the death of Hutton in1797 Playfair published “Illustrations of Huttonian Theory of Earth” in 1802 for he had realized howconfused and repetitive were the writings of Hutton; Playfair’s work was smaller, cheaper, and precisewith great clarity and beauty of expression. Playfair presented Hutton’s ideas and conclusions clearly.Playfair also proclaimed the ability of glaciers to erode their valleys deeply.

Sir Charles Lyell (1797–1875) wrote a number of textbooks to spread the geologic knowledge. Hewas somewhat doubtful about the immense ability of running water to carve the valleys. It was during19th century that there was recognition of an ice age during which much of North Europe was coveredwith ice sheets. Playfair had sensed the possibility of large boulders being transported by glaciers. LouisAgassiz (1807-1873), Venetz of Switzerland in 1821, Bernardi of Germany in 1832 and Jean deCharpentier in 1836 supported this concept of glaciation in Europe. In the later part of 19th centurybooks were written to describe the principles of landform development. These were by Peschel,Richthofen and A. Penck.

The basic foundation of geomorphology was laid in America in the later half of 19th century byMajor J.W. Powell (1834-1902), G.K. Gilbert (1843-1918) and C.E. Dutton (1841-1912). Powell’sstudies of Unita Mountains emphasized the importance of geologic structure in the classification oflandforms. He also introduced the concept of the limiting level to which the land-level would reduce andcalled it the base level. Col. George Greenwood earlier used this concept in Europe in 1857. Powellrecognized that the process of erosion, if carried undisturbed on land, would reduce it eventually to alevel little above sea level. He was able to correctly interpret that various unconformities in rocks in theGrand Canyon, Colorado (U.S.A.) correspond to ancient periods of land erosion.

Introduction 9

G.K. Gilbert’s contribution in experimental work carried out in California has already beendescribed. He was a pioneer in studying hydraulic mining and its effect on stream morphology. His othercontributions include recognizing the importance of lateral planation by streams in the development ofvalleys and his explanation of Henry Mountains of Utah (U.S.A.) as the result of erosion of intrusivebodies. Dutton gave a penetrating analysis of individual landforms. Gilbert and Dutton are given creditfor initiating the concept of erosional unloading of the earth’s crest technically known as isostasy. W.M.Davis (1850–1934) had greater impact on the development of geomorphology than any one else. Of allthe contributions to geomorphology, Davis is remembered for introducing the concept of geomorphiccycle. According to this concept in the evolution of landscapes there is a systematic sequence thatenables one to recognize the stages of development of landforms. This sequence is called by him asyouth, maturity and old age. These landsforms are explainable in terms of differences in geologicstructure, geomorphic processes and the stage of development. In the development of the idea ofgeomorphic cycle Davis had assumed that there is a relatively rapid uplift due to diastrophism which isfollowed by a relatively long period of standstill which permits the erosion cycle to run its course. W.Penck and his followers questioned Davis’ idea of geomorphic cycle during 1920’s and 30’s. In spite ofthese objections the Davisian geomorphic cycle is still considered a reasonable model primarily becauseof the absence of a plausible reasonable alternative.

Recent ContributionsSince the end of the Second World War a large number of aspects about river morphology have been orare being studied. These include channel geometry, mathematical modelling, effect of neo-tectonics andmass movements on channels, fluvial systems, experimental fluvial morphology, palaeo climatic andpalaeo hydrologic effects and gravel-bed rivers. Scientists working at U.S. Geological Survey havestudied short-term morphology of river channels; they include W.B. Langbein, L.B. Leopold and M.G.Wolman. S.A. Schumm, M.P. Mosley and W.E. Weaver studied fluvial systems and performedexperiments in the laboratory to study river morphology. J.R.L. Allen from U.K. has done extensivework on the character and classification of bed forms and sedimentary structures with respect to deltas,meanders and floodplains. Many investigators including K.J. Gregory, J. Lewin, V.R. Baker and L.Starkel have studied Palaeo climatic and palaeo hydrologic effects on river channels. Geographers inU.K. have given impetus to the research in gravel-bed rivers and this work is now continued in Canada,U.S.A. and New Zealand.

1.5 SCOPE

The text takes a balanced view of the contributions made by engineers, geologists, geomorphologistsand geographers to fluvial morphology.

Introduction, morphologic problems, and history of fluvial hydraulics and geomorphology arediscussed in the first chapter. The second chapter is devoted to the discussion about drainage basin andchannel networks. The third chapter deals with erosion from the catchment in humid regions whereerosion due to water action predominates. The fourth chapter presents basic concepts fromgeomorphology such as geomorphic cycle, stages of landform and rivers and discusses the erosional anddepositional features developed by rivers. Chapter five deals with the hydraulics of alluvial rivers whilechapter six deals with the hydraulic geometry and plan-forms in alluvial streams. The seventh chapter

River Morphology10

deals with gravel-bed rivers. Chapter eight deals with fluvial paleo hydrology while chapters nine andten are devoted to changes in bed level and plan-form. Chapters eleven and twelve deal with analyticaland numerical models used in studying the transient flows in rivers. Chapter thirteen is devoted to thediscussion of morphology of the Kosi and the Brahmaputra rivers in India. Chapter fourteen deals withrivers and environment, and the fifteenth chapter dicusses the data requirements for morphologicalstudies.

References

Garde, R.J. (1995) History of Fluvial Hydraulics. New Age International (P) Ltd., Publishers, New Delhi.

Gee, G.P. (1951) The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629–638.

Mackin, J.H. (1948) Concept of the Graded River. Bul. Geological Society of America, Vol. 59, pp. 463–512.

Ouchi, S. (1985) Response of Alluvial Rivers to Slow Active Tectonic Movement. Bul. Geological Society ofAmerica, Vol. 96, Apr, pp. 504–513.

Ruhe, R.V. (1971) Stream Region and Man’s Manipulation - in Environmental Geomorphology (Ed. D.R. Coates).Publication in Geomorphology, State University of New York, Binghamton, U.S.A.

Thornbury, W.D. (1969) Principles of Geomorphology. John Wiley and Sons Inc., New York, 2nd Ed. Chapter 1.

Tinkler, K.J. (1985) A Short History of Geomorphology. Croom Helm (P) Ltd., U.K., 1st Edition.

Wilson, R.C. and Keefer, D.K. (1985) Predicting Areal Limits of Earthquake–Induced Land Sliding. In EvaluatingEarthquake Hazards in the Los Angeles Region (Ed. Ziony, J.I.). USGS Professional Paper 1360, pp 317–345

Wolman, M.G. and Schick A.P. (1967) Effects of Construction on Fluvial Sediment Urban and Sub-urban Areas ofMaryland. Water Resources Research, Vol. 3, pp. 451–464.

Worcester, P.G. (1948) A Text Book of Geomorphology. D. Van Nostrand Co. Inc., New York, U.S.A., 2nd Edition.

2C H A P T E R

Drainage Basins and ChannelNetworks

2.1 INTRODUCTION

Drainage basin is an area drained by the stream and its tributaries. It is bounded by a divide. Drainagebasin is also sometimes called watershed or catchment area. It can be thought of as an open system thatreceives energy or input from the atmosphere and sun over the basin and loses energy or output throughthe water and sediment mainly through the basin mouth or outlet (Strahler 1964). The present form ofany drainage basin is the result of the processes that have operated in the past on the material availablelocally. These processes at the basin level are the precipitation and runoff, sediment yield and rate oferosion. However, these processes in the past may not be the same in their relative importance as theones that operate in the drainage basin at present. The importance of studying the drainage basincharacteristics derives from the need of studying forms of channels and channel networks as they arerelated to physical characteristics of the drainage basin, and also from the need of relating physicalcharacteristics of the basin to flow characteristics and sediment yield.

The drainage pattern is the arrangement and length of small, medium and large streams in the basin.Two aspects of the development of drainage basins have been studied. In earlier years, the drainagepattern development in relation to the structure and lithology of the underlying rocks was studied. Thiswas essentially qualitative in nature. In the recent times drainage patterns have been treated more asgeometric patterns and attempts have been made to derive relationships for them (Horton 1945). Thedrainage pattern acquired at any time is the result of the combined effect of lithology, precipitationpattern and climate, and their variation with respect to space and time. Since the sediment eroded fromthe drainage basin along with water causing erosion, flows through the tributaries and the main stream,the drainage net is intimately associated with the hydraulic geometry of the stream channels and theirlongitudinal profile. As suggested by Schumm (1977) the drainage basin is primarily a sedimentproduction area where climate, diastrophism and land use act as the upstream controls.

River Morphology12

Glock (1932) assumed that the drainage pattern is initiated on an essentially smooth plane due to theuplift. According to him the drainage pattern goes through the following developmental stages:initiation, elongation (headward growth of the main stream), elaboration (filling in of the previouslyundissected areas by small tributaries), maximum extension (the maximum development of the drainagepattern) and abstraction (loss of tributaries as the elevation is reduced through time). This sequencetakes a long time in geologic sense. During this sequence the sediment yield first increases to amaximum and then decreases. However, such erosional development cannot be observed. Hence severaldrainage basins in different stages of development are studied at a given time. Thus what is to beobserved in time domain is studied in space domain assuming the process to be ergodic.

The topographic characteristics of the drainage basin can be visualised either for the basin or for thedrainage network. The most important topographic characteristics for the basin are its area, length,shape and relief. The corresponding characteristics for the drainage network are area tributary to streamchannels, drainage density, stream length, network shape or drainage pattern, and network relief.

2.2 DRAINAGE PATTERNS AND TEXTURE

Drainage pattern is the general arrangement of channels in a drainage basin. Drainage patterns reflectthe influence of such factors as initial slope, inequalities in rock hardness, structural controls, recentdiastrophism, and recent geomorphic and geologic history of the drainage basin. Because drainagepatterns are influenced by many factors, they are quite useful in the interpretation of geomorphicfeatures and their study represents one of the more practical approaches to the understanding of thestructural and lithologic controls on landform evolution. Looking at them in the most general manner,one can classify drainage patterns into the following categories:

Figure 2.1 (a) shows dendritic or branch-like pattern that is probably the most common drainagepattern. This is characterised by irregular branching of tributary streams in many directions and atalmost any angle usually less than 90o. Dendritic patterns develop on rocks of uniform resistance andindicate a complete lack of structural control. This pattern is more likely to be found on nearlyhorizontal sedimentary rocks or on areas of massive igneous rocks. They may also be seen on complexmetamorphosed rocks.

Trellised or lattice-like pattern shown in Fig. 2.1 (b) displays a system of sub-parallel streams,usually along the strike of the rock formations or between parallel or nearly parallel topographicfeatures recently deposited by wind or ice.

Radial pattern shown in Fig. 2.1 (c) is usually found on the flanks of domes or volcanoes andvarious other types of isolated conical and sub conical hills.

Parallel drainage pattern shown in Fig. 2.1 (d) is usually found in regions of pronounced slope orstructural controls that lead to regular spacing of parallel or near parallel streams.

Rectangular drainage pattern shown in Fig. 2.1 (e) has the main stream and its tributariesdisplaying right-angled bends. This is common in areas where joints and faults intersect at right angle.The streams are thus adjusted to the underlying structure.

Deranged drainage pattern, see Fig. 2.1 (f) indicates a complete lack of structural or bed rockcontrol. Here the preglacial drainage has been affected by glaciation and new drainage has not hadenough time to develop any significant degree of integration. It is marked by irregular stream coursesthat flow into and out of lakes and swamps and have only a few short tributaries.

Drainage Basins and Channel Networks 13

Centripetal pattern shown in Fig. 2.1 (g) is encountered locally. Here the drainage lines convergeinto a central depression. These are found on sinkholes, craters and other basin like depressions.

Highly violent pattern shown in Fig. 2.1 (h) is characteristic of areas of complex geology.The complex drainage patterns observed in nature are a result of differing lithology, regional slopes,

presence of joints and faults, and geologic activities such as glaciation, volcanism and limestonesolution. Zernitz (1932), Howard (1967) and Thornbury (1969) have given full description ofcommonly occurring drainage patterns and their interpretation.

Drainage TextureAn important geomorphic concept about the drainage pattern is the drainage texture by which onemeans relative spacing of drainage lines. Drainage texture is commonly expressed as fine, medium orcoarse. Climate affects the drainage texture both directly and indirectly. The amount and type ofprecipitation influence directly the quantity and character of runoff. In areas where the precipitation

Fig. 2.1 Various drainage pattern

b) Trellis or lattice like patterna) Dendritic pattern

f) Deranged patterne) Rectangular pattern

d) Parallel patternc) Radial or concentric pattern

h) Highly violent patterng) Centripetal pattern

b) Trellied or lattice like pattern

River Morphology14

occurs primarily in the form of thunder showers, a larger percentage of rainfall will result in runoffimmediately and hence, other factors remaining the same, there will be more surface drainage lines. Theclimate affects the drainage texture indirectly by its control on the amount and types of vegetationpresent which, in turn, influences the amount and rate of surface runoff. With similar conditions oflithology and geologic structure, semiarid regions have finer drainage structure than humid regions,even though major streams may be more widely spaced in semiarid than in humid regions. It is alsonoticed that drainage lines are more numerous over impermeable materials than over permeable areas.The initial relief also affects drainage structure; drainage lines develop in larger number upon anirregular surface than on the one that lacks conspicuous relief.

Bad-land topography promotes fine drainage structure. Impermeable clays and shales, sparsevegetation and existence of thundershowers are responsible for very fine drainage structure. Coarsedrainage structure is in particular found on sand and gravel outwash plains. Gravel plains have fewerdrainage lines on them than adjacent till plains underlain by relatively impermeable clay till.

The drainage structure can be qualitatively related to a parameter known as drainage density (seesection 2.9) first defined by Horton (1932) as total length of streams per unit of drainage area. Drainagedensity varies from about 0.93 km/km2 on steep impervious areas to nearly zero for highly permeablebasins. It varies from about 2.0 to 0.60 km/km2 in humid regions. As indicated by Smith (1950) andStrahler (1957), coarse drainage structure corresponds to drainage density less than 5.0 km/km2,medium drainage structure to drainage density value between 5 and 15 km/km2 and fine drainagestructure to drainage density between 15 and 150 km/km2.

2.3 STREAM ORDER

A stream net or river net is the interrelated drainage pattern formed by a set of streams in a certain area.A junction is the point where two channels meet. A link is any unbroken stretch of the river between twojunctions; this is then known as the interior link. If it is between the source and first junction, it is calledthe exterior link.

Quantitative analysis of the stream network really started with Horton (1945). This analysis hasbeen developed to facilitate comparison between different drainage basins, to help obtain relationsbetween various aspects of drainage patterns, and to define certain useful properties of drainage basinsin significant terms.

According to Horton (1945) the main stream in the river net should be denoted by the same ordernumber all the way from its mouth to its headwaters. Thus, at every junction where the order changes,one of the lower order streams is renumbered to the higher order and the process repeated. Thus in Fig.2.2 (a) the main stream is shown as the fourth order stream right back to its source. The third orderstreams which are tributary to the fourth order stream are also extended back to their farthest source asthe third order streams and so on. The streams joining the third order stream are second order stream andthey can be extended backward. It can be immediately realized that a certain amount of subjectivity isinvolved in the ordering of streams according to Horton’s method.

In Strahler’s (1952) system, see Fig. 2.2 (b), the headwater streams that receive no tributary arecalled first order streams. Two first order streams unite to give a second order stream. Two second orderstreams unite to give a third order stream and so on. When two streams of different order unite, thecombined stream retains the order of the higher order stream. A combination of two streams of lower


order, say (u – 1), with a stream of given order u increases the order of the latter by one integer, that is(u + 1). The result of this system of ordering is that it does not reflect any increments exceptapproximately doubling the discharge if one assumes that streams of the same order in the samedrainage basin carry approximately equal discharges.

Scheideggar (1965) defines the order x after two streams of order u1 and u2 by

x = log2 2 21 2u u´d i ...(2.1)

His system of ordering is shown in Fig. 2.2 (c).

Shreve (1967) has suggested a system of ordering streams in which, the order numbers of twostreams contributing to the junction are added to arrive at the order number below the junction, see Fig.2.2 (d). Thus each exterior link or head tributary has a magnitude 1. If links of magnitude u1 and u2 join,then the resultant downstream link has the order (u1 + u2). If we assume that the first order streams areapproximately of the same magnitude and that the discharge is neither lost nor gained from any sourceother than the tributaries (which is not completely true) then Shreve number is roughly proportional tothe discharge in the segment of the stream. It may be mentioned that Strahler’s system of ordering hasbeen more commonly used than the other methods and the same is utilised herein. The analysis ofdrainage basin considering stream orders is often known as morphometry.

The morphometric analysis of drainage basins carried out by Horton (1945), Strahler (1952),Rzhanitsyn (1960) and others is based on the premise that for the given conditions of lithology, climate,rainfall, and other relevant parameters in the basin, the river net, the slope and the surface relief tend toreach a steady state in which the morphology is adjusted to transmit the sediment and excess flowproduced. If there are any major climatic or hydrologic changes in the region, the steady state

c) Scheideggar (1965) d) Shreve (1967)

Fig. 2.2 Systems of stream ordering

a) Horton (1945) b) Strahler (1952)

River Morphology16

morphologic characteristics will naturally be modified. In other words, the river net is the definiteresponse of the drainage basin to the complex physical processes taking place over the drainage basin.

2.4 HORTON�S LAWS OF STREAM NUMBERS AND STREAM LENGTHS

Consider a river net in a drainage basin in which the highest order of the stream is K. Let u represent theorder of any segment and Nu represent the number of streams of the order u. It has been found by Hortonand other investigators that if log (Nu) is plotted against u for any river net the data fall on a singlestraight line with Nu decreasing for increasing u, see Fig. 2.3. Hence the relation between Nu and u canbe expressed as

Fig. 2.3 Variation of log Nu with u (Horton’s ordering system)

log Nu = a – bu

Also log N(u + 1) = a – b (u + 1) ...(2.2)

or log N

Nu

u( )+1

= b from which one gets ...(2.3)

N

Nu

u( )+1

= 10b = Rb

Here a and b are constants. The constant Rb is known as the bifurcation ratio. It is defined as thenumber of streams of order u divided by number of streams of order (u – 1). Since Nk = 1

N(k – 1)/Nk = Rb or N(k – 1) = Rb

N(k – 2) = N(k – 1) ´ Rb = Rb2

Nu = Rb(k – u) ...(2.4)

u0 1 2 3 4 5 6 7

R = 4.07b

R = 4.12b

R = 4.34b

0

1

2

3

4

log

Nu

- Daddy's creek- Alleghney river

- Sher river (India)


It may be mentioned that for small drainage basins the relation between log Nu and u has been foundto be slightly concave upwards thus deviating from the linear relationship expressed by Eq. (2.2);however the deviation becomes smaller as u increases, see Smart (1967). Horton (1945) found that thevalue of Rb varied from 2 to 4 for the river nets investigated by him, whereas Strahler (1964) found thisrange to be from 3 to 5 for the drainage basins in which geologic structures do not distort the drainagepattern. Mittal et al. (1974) found Rb to lie between 4.4 and 5.0 for sixty-two third order drainage basinsin Garhwal, Himalaya (India), where lithologic conditions were represented by limestones, quartzites,phyllites, sand-shales and alluvium. This value ranged between 3.5 and 4.5 for sixth and seventh ordersub basins of the Narmada, see NIH (1995).

It has been found by some investigators that the bifurcation ratio Rb is not independent of the orderof stream, and hence in a particular drainage basin Rb should be calculated between streams of 1 orderlag with those of 2 order lag in order to reduce the difficulties introduced by order and the size of areaanalysed. Schumm (1956) recommends the use of weighted Rb designated as WRb

WRb = S

S

R N N

N

b u u u u( , )+ ++1 1d i

where Nu is the number of streams of u th order.

The principle embodied in Eqs. (2.2) and (2.3) is commonly known as Horton’s Law of StreamNumbers which states that

“The number of streams of different order in a given drainage basin tends closely toapproximate an inverse geometric series in which the first term is unity and the ratio is thebifurcation ratio”. (Horton 1945).The fact that the bifurcation ratio remains fairly constant is interpreted to mean that the drainage

basins in homogenous materials tend to show geometric similarity. Strahler (1964) has emphasized thatthere is a close relationship between the shape of the drainage basin, bifurcation ratio and the shape ofthe unit hydrograph. A very elongated basin will have a very high value of Rb (of the order of 15 or so)and will give a sustained unit graph with low peak. On the other hand a near circular drainage basin willhave a low Rb value (around 2.4 or so) and would yield a unit graph with high peak and small baselength.

It can be seen from Eq. (2.4) that

i

n

u k

bK

bK

bK

bK

b

N N N N N

R R R

R R

=

- - -

-

-

å = + + +

= + + + +

=

U

V

|||

W

|||

11 2 3

1 2 3

11

1

.....

.....

( ) .....d i

...(2.5)

If one measures the total length of streams of a given order u in a drainage basin and designates it Lu,

the mean length of the streams of order u, Lu will be

River Morphology18

Lu = Lu/Nu ...(2.6)

If in any given basin log Lu is plotted against u one gets log Lu increasing linearly with u, thusyielding a straight line, see Fig. 2.4. This means that

Lu /Lu – 1 = constant RL ...(2.7)

where RL is known as the Horton’s length ratio. It follows from Eq. (2.7) that

L2 = L1 RL, L3 = L2 RL = L1 RL2 ...(2.8)

and Lu = L1 RLu -1

The principle embodied in Eqs. (2.7) and (2.8) is known as Horton’s Second Law of StreamLengths, which states that

“The average lengths of the streams of each of the different orders in a drainage basin tendclosely to approximate a direct geometric series in which the first term is the average length ofstreams of first order”. (Horton 1945).Morisawa (1962) has found that RL values ranged from 2 to 3 in Applachian Plateau Province

(U.S.A.), while its value ranged between 1.50 and 2.40 for four sub basins of Narmada.

These two laws of drainage composition have been substantiated by several investigatorsirrespective of whether Horton’s or Strahler’s method of stream ordering is used. They include Chorely(1957), Morisawa (1962) and Gregory (1966).

The total length of streams of order u will be Lu Nu. Substituting the value of Nu from Eq. (2.4) andusing Eq. (2.8) one gets

Fig. 2.4 Variation of Nu, Au , Lu with u

u Order

6

106

105

104

103

102

101

100

10–1

105

104

103

102

101

100

10–1

10–2

Na

nd

km

u}

2

u

}u

Lukm

Nu

øu

Sessquehannariver basin (U.S.A.)

426 8 10


Lu = Total length of streams of order u = Nu Lu

= L1 RL(u–1)Rb

(k–u)

Hence total length of the streams of Kth order basin will be

1

K

uLå = L R L R R L R R L R R L Rbk

L bK

L bK

LK

b LK

11

12

12 3

12

11- - - - -

+ + + +...

= L1 RbK -1 1

2 3 2 1

+ +

FHGIKJ

+

FHGIKJ

+ +

FHGIKJ

+

FHGIKJ

RS|

T|

UV|

W|

- -

R

R

R

R

R

R

R

R

R

RL

b

L

b

L

b

L

b

K

L

b

K

... ...(2.9)

Substituting RL/Rb = RLB one can simplify the above equation to the form

1

K

uLå= L1 Rb

K -1R

R

LBIK

LBK

-

-

1

1

d id i

...(2.9)

Another length parameter introduced by Horton (1945) is the length of overland flow Lo which isthe length of flow path, projected to the horizontal, of non channel flow from the point of drainagedivide to the point on the adjacent stream channel. Length of overland flow is one of the most importantvariables affecting the hydrologic and physiographic development of the drainage basin. Duringevolution of the drainage basin Lo is approximately equal to half the reciprocal of the drainage density.

2.5 AREAS OF DRAINAGE BASINS

Basin area is hydrologically important because it directly affects the size of the storm hydrograph, andthe magnitude of mean and peak flows. Amount of sediment eroded from the drainage basin is alsorelated to the basin area. In fact, since almost every watershed characteristic is correlated with area, thearea is the most important parameter in the description of form and processes of the drainage basin.

The area Au of a basin of given order u is defined as the total area projected upon a horizontal plane,which contributes overland flow to the channel segment of a given order and all the tributaries of thelower order. Thus area of the basin of the third order, A3 will be the sum of areas of first and second orderbasins, plus all additional areas, known as inter-basin areas, contributing directly to channels of orderhigher than the first. Thus

A2 = SN1 A1 + SN

1 Ao2

where Ao2 is the inter-basin area contributing to second order segments. In general one can write

Au = {SN1 A1 + SN

1 A2 + SN1 A3 + ... SN

1 Au–1} ...(2.10)

+ {SN1 Ao1 + SN

1 Ao2 + ... SN1 Aou}

Law of areas has been inferred by Horton (1945) and stated by Schumm (1956), according to whichthe mean basin areas of stream of each order tend closely to approximate a direct geometric sequence inwhich the first term is the mean area of the first order basin. Hence if log Au is plotted against u, astraight line is obtained as shown in Fig. 2.4. From this one can deduce that

River Morphology20

Au = A RAu

11- ...(2.11)

where Au is the mean area of basin of order u, A1 is mean area of first order basins, and RA is known asthe area ratio.

Some attempts have been made to relate stream lengths to basin areas. It is argued that according tothe laws of stream lengths and basin areas, both these parameters are related to the stream order. Hencea relation of the type L ~ An should relate basin length to the basin area. On the basis of over 300measurements made by Langbein (1947), Hack (1957) found that this relation is of the type

L = 1.16 A0.60 ...(2.12)

where L is the stream length in km measured up to the drainage divide and A is basin area in km2. Forgeometrically similar basins one would expect L ~ A0.50. Since according to Hack L ~ A0.60, it means thatdrainage basin changes its shape in the downstream direction; it tends to become longer and narrower asit changes. Figure 2.5 shows variation of L with A for different regions as well as the enveloping curves.

Fig. 2.5 Variation of total stream length with basin area

Müller (see Gregory and Walling (1976)) defines three lengths to describe the stream length. Theseare the length of the stream channel Le, the length of valley Lv and shortest distance between the mouthand the source of stream Lm.

Hack has also shown that

Au = A RR

RAu LB

u

LB1

1 1

1-

-

-

( )

( )...(2.13)

A km2

102

101

100

101

102

103

103

10–1

100

101

102

103

Lkm

Envelope curves

1. W. Malaysia

2. Deron

3. W. USA

4. Uganda

5. Wales

6. Australia

7. Nebraska (USA)

8. E. USA


The circularity and elongation ratios can be of practical utility in predicting certain hydrologicalcharacteristics of the drainage basin. Elongation ratio has been used in the studies of sediment erodedfrom the basins. In general drainage basins tend to become more elongated with strong relief and steepslopes. Available data indicate that the drainage basin gets relatively elongated as its size increases.

2.7 LITHOLOGY

The lithology and rock structure in the basin play an important role in influencing the hydrologic,erosional and other characteristics of the basin. The rock type and soil mantle affect the infiltrationcapacity. Permeable soil or rock allows water to percolate into the ground which later may be dischargedinto the stream. Hence the surface runoff is reduced. Basins with bed rock or soil which is relativelyimpermeable produce high volume of surface runoff and very little ground water flow.

Rock type governs the character and rate weathering, the weathering products obtained and hencethe nature of sediment and solutes supplied to the stream. The nature and effect of vegetation is alsopartly governed by rock type, which in turn governs the sediment supply. Hence sediment load vs waterdischarge relationship would depend on rock type. Similarly alluvial fan area vs drainage arearelationship also depends on rock type.

The rock type also influences the shape of the valley and stream because it controls resistance toerosion and also the runoff as discussed above. Morisawa (1968) found that valleys cut inunconsolidated beach sands and gravels were V-shaped, while those cut in silts and muds were flatbottomed. In the same manner Brush and Hack have found that the correlation between channel gradientS and its length L depends on the lithology and rock type. If S = a Lb the slope decreased with increasein L for all the rock types i.e., b was negative, but the rate of decrease varied with rock type. Lastly,

Table 2.1 Form factors for basins

S.No. Notation Definition Reference Comments

1. Form factor Rf Basin area Au/(Basin Horton Reciprocal of this is used by Corps oflength)2 (1932) Engineers (U.S.A.) in Hydrograph analysis

2. Circularity Basin area Au/Area of circle Miller C = 0.6 to 0.7 for homogeneous basins of 1st andratio C with the same perimeter (1953) 2nd order. For non-homogenous basin C = 0.4 to

0.503. Elongation (Diameter of a circle with Schumm E = 0.6 to 1.0; lower value for areas with strong

ratio E area of basin)/(Maximum (1956) relief and steep slopebasin length)

4. Lamniscate (Basin length)2/4 (basin Chorely et al. —ratio K area) (1957)

2.6 BASIN SHAPE

Basin shape affects the hydrologic characteristics of the basin, namely hydrograph shape. As mentionedearlier a long narrow basin having high bifurcation ratio gives a low but sustained peak whereas roundbasins with low bifurcation ratio would give a sharply peaked hydrograph. Several shape factors havebeen suggested to describe the shape of the basins, some of which are listed below:

River Morphology22

lithology and rock structure also affect the morphometry and geometry of the drainage basins. A flat-lying resistant bed will cause increase in stream length and decrease in stream slope. Where thesediments are folded, stream cutting across resistant strata will be short and steep with small drainageareas. Similarly drainage pattern is also influenced by lithology. For flat and homogenous rock surfacedrainage net tends to form at random and streams flowing in all directions i.e. dendritic pattern. In thecase of jointed or folded rocks streams tend to erode the channel along a weakness. If joints are theweakness, their orientation determines the stream pattern. In tilted or folded strata streams tend todevelop along linear bands of outcropping weak rock. Therefore, a full understanding of lithology isessential for the study of river morphology.

2.8 VEGETATION

Vegetation including grass, shrubs, and forests plays an important role in the hydrologic cycle andcatchment erosion. Hence, its effect is of prime importance to those working on river morphology andriver dynamics. Studies by various investigators have shown that water and sediment yield, flood peaksand the time of their occurrence, and the velocity of travel of the flow peak are strongly influenced bythe nature and extent of vegetation.

When the pressure on the land, because of increase in the population and human activity, was notheavy, there were marginal changes in the forests, and minor disturbances in their coverage were soonmade up naturally. However, because of increase in the population and industrial growth andconsequent increase in food, space and energy requirements of nations, there has been indiscriminatedeforestation in some parts of the world. In the early eighties, most of the tropical forests were estimatedas being altered by man at around 12 million hectares per year, see Bruijnzeel (1990). Manyinvestigators consider this as an underestimate. Deforestation includes cutting of trees for fuel, timberand other industrial uses, deforestation caused by great and small forest fires, shifting of zoomcultivation, construction activity related to logging such as creation of access roads, skid tracks andlandings, clearing areas for habitation and developing industry, surface mining and similar activities.Generally speaking, a forest subjected to some of the above mentioned disturbances may recover to itsprevious state if left alone for a sufficiently long period. However, this is not the case when the forest isconverted to permanent agriculture such as grazing, cropping or extractive tree crops.

The effects of partial or complete removal of forest on climate, water yield and its seasonaldistribution and on sediment production have been studied by many investigators. Below are given thesalient features of these effects, (see Bruijnzeel (1990)).

Rainfall and Water Yield1. Tropical forests reflect about 12 percent of the incident short wave radiation while agricultural

crops reflect 15 to 20 percent. Hence a different partitioning of energy between warming up ofthe boundary layer and evaporation is to be expected when tropical forests are converted tograss lands or agricultural crops.

2. As a result of extensive studies during the past four decades, it is found that the extent of forestshas definite effect on rainfall.

3. It has been found that in humid tropics removal of natural forests cover may result inconsiderable initial increase in water yield, the increase depending on the amount of rainreceived.


4. The initial increase in water yield, after removal of the forest cover, gradually decreases withthe passage of years and may return to pre cut flows in about eight years in case of naturalregrowth.

Stream Flow Regime1. Geological, topographical and vegetative cover play an important role on floods and hence

isolation of effect of vegetation becomes rather difficult.2. If geology is favourable, cutting vegetation shifts infiltration flow to surface flow and therefore

peaks will enhance.3. Also in the absence of retarding effect, the peak is likely to occur earlier.

4. Change in evapo-transpiration and infiltration opportunities associated with change in forestcover will govern the dry season flows. If infiltration opportunities after forest removal havedecreased to the extent that the increase in amount of water leaving the area as stream flowexceeds the gain in base flow associated with reduced evapo-transpiration, then the dry seasonflow is reduced. If on the other hand, the surface infiltration characteristics are maintained overmost of the area by deliberate soil conservation practices or by some other method, then theeffect of reduced evapo-transpiration after clearing will show up as increased base flow or dryseasonal flow.

Sediment Production and YieldWhen dealing with the effect of change in forest cover on erosion and sedimentation it is helpful todistinguish between surface erosion (i.e., splash, sheet and rill erosion), gully erosion, and massmovements because the ability of vegetation cover to control the various forms of erosion is ratherdifferent. It is well known that only part of the material eroded from hill side will enter drainagenetwork, the rest may move into temporary storage such as depressions, foot slopes, small alluvial fansor in small tributaries, behind debris basins or flood plains. The stored material may be released duringlarge storms or caught by vegetation, or form stable topographic elements. Since these storageopportunities tend to increase with increase in area, sediment delivery ratio, which is defined as theamount of sediment passing a given section during a given time divided by amount of sediment erodedfrom upstream in the same time, is found to decrease with increase in catchment area. It may be yearsbefore sediment stored in temporary storages is released and its effect felt several kilometersdownstream from the region of erosion. Sediment yield, which is rate of sediment passing a givensection, is discussed in detail, in Chapter–III. This was found to be the case on the Brahmaputra river inAssam (India) after 1950 strong earthquake, see Goswami (1985). During August 1950 earthquake,apparently one of the most severe ever recorded, massive landslides occurred which temporarilyblocked many major tributaries. Bursting of these dams after several days not only produced devastatingfloods downstream, but also brought down enormous volume of sediment thereby raising the beds ofthese rivers considerably. The mean annual suspended load and water discharge between 1955–1963were 750 000 m3 and 16 530 m3/s as against 130 000 m3 and 14 850 m3/s during 1969–1976. Alsoduring the former period the river reach upstream of Pandu was aggrading, whilst it was degradingduring 1969–1976.

River Morphology24

Surface and Gully ErosionStudies by Wiersum (1984) have indicated that erosion is minimum (0.10 to 0.60 tonnes/km2/year) inthose areas where soil surface is adequately protected by a well developed litter and herb layer. Whenthis layer is destroyed or removed, erosion rates rise dramatically to 500 to 5000 tonnes/km2/year. Henceprotection from tree stands lays not so much in the ability of tree canopy to break the power of rain dropsbut rather in developing and maintaining a litter layer. When rills are formed and they grow into gullies,their lateral and head ward extension through scouring, undercutting and subsequent collapse of wallscause a large increase in sediment production.

Mass WastingSome of the highest reported natural erosion rates from rain-forested areas have been related to intensemass wasting under conditions of steep topography, tectonic activity, and intense rainfall. In masswasting, steep slopes in combination with geological and climatic factors are more important than landuse. Prasad (1975) after ten years of observations of seismic activity, rainfall and occurrence of landslides in eastern Nepal concluded that intense precipitation and associated saturation of soil wereapparently more important than seismic shocks. Starkel (1972) has opined that the role of vegetation inpreventing shallow slope failures (less than 3 m) is very important; Manandhar and Khanal (1988) haveconfirmed this in south of Khatmandu. As regards the influence of tall vegetation on slope stability, thenet effect is considered positive, the major factor being the mechanical reinforcement of the soil by treeroots.

2.9 DRAINAGE DENSITIES AND STREAM FREQUENCY

Drainage density is defined as the total length of streams in a basin divided by its area. Hence thedrainage density Dd is given by

Dd = 1

Kå 1

N

å Lu/A ...(2.14)

and will have dimension of km–1. Here N is the number of streams of order u and K is the order of theriver basin. Greater drainage density means more channels per unit area or more closeness of channelspacing. Drainage density varies over a wide range from 2 km–1 to 800 km–1 or even more depending onthe character of subsoil material, vegetation and relief. Climate is equally important in determining thedrainage density since it controls discharge and indirectly the vegetation. Table 2.2 illustrates the effectof these factors, namely lithology, climate and vegetation on the drainage density.

Drainage density does not seem to change regularly with stream order within basins. Investigationsby Morisawa (1968) indicate that drainage density of the whole basin tends to approximate the meandrainage density of the 1st order basins in the watershed. Langbein appreciated the significance ofdrainage density as a factor determining the time of travel of water. Since water and sediment flowthrough the stream channels, annual sediment yield from the catchment is found to increase withincrease in drainage as sediment yield ~ Dd

0.1 (Garde and Kothyari 1987). Osborn has found that meanannual flood Q2.33 is proportional to Dd

2.0 . Gregory and Walling (1976) have plotted total stream lengthagainst drainage area for a large number of catchments and found that L ~ A0.378 up to 100 km2 area andbeyond that the exponent of A somewhat increases, see Fig. 2.5. Hence one can conclude that L/A i.e. Ddwould decrease as A increases.


Obtaining drainage density can be a tricky problem because a lot would depend on the scale of themap used. Hence uniform scale needs to be used in the comparison of drainage densities of differentbasins. Carlson and Langbein (1960) have recommended a more rapid method of estimation of thedrainage density. Draw a line of known length L on the contour map and count the number of streams nwhich intersect this line. A minimum of 50 contour crossings is advocated to provide an adequatesample. Then drainage density equals 1.41 n/L.

Strahler (1964) considered the drainage density Dd to be a variable dependent on runoff rate per unitarea Qr, erosion proportionately factor K (which is mass rate of erosion per unit area per unit erodingforce), relief H, mass density of fluid rf, dynamic viscosity m, and g.

\ Dd = f (Qr, K H, rf , m, g)

The above equation can be written in dimensionless form as

Dd H = f KQQ H Q

g Hrr f r, ,r

m

2FHG

IKJ

The first term (Dd H) is known as the ruggedness number, (Qr K) is known as Horton number,which expresses the relative intensity of erosion processes in the drainage basin, (Qr rf H/m) is Reynoldsnumber and (Qr

2/g H) is Froude number.Schumm (1956) has introduced a parameter called constant of channel maintenance C that

represents the area in km2 necessary to develop and maintain one kilometer of drainage channel. If Au isplotted against Su

1Lu it is found that the two are related linearly as

Table 2.2 Effect of lithology, climate and vegetation on drainage density[Adapted from Selby 1967, NIH 1993]

Location Lithology Climate Vegetation Dd km–1

Pennsilvania Horizontal resistant Humid, Deciduous forest 2–2.5(U.S.A.) sand stone Continental

Colorado (U.S.A.) Granite, gneiss and schist Humid, montane Montane forest 2.5–5.6

Maryland (U.S.A.) Shale Humid, Continental Coniferous and 4.4deciduous forest

Volcanic Plateau Pumice and ignimbrite Temperate, Scrub and grass 5.4(New Zealand) maritime

South Auckland Graywacke overlain Temperate, Formerly green forest, 15.7(New Zealand) by volcanic ash maritime now pasture grass

South Dakota Clay and shale Semiarid Sparse bunch grasses 50–160(U.S.A.) or none

Arizona (U.S.A.) Horizontally bedded shale Hot desert None 106–220

New Jersey (U.S.A.) Clay and sand fill Humid continental None 344-825

Bihar (India) Alluvium to Granite, Humid 59 per cent agriculture 0.377Gneiss and 41 percent forest etc.

River Morphology26

Au = a + C Su1Lu ...(2.15)

C being the constant of channel maintenance.A basin with relatively impermeable strata requires a smaller drainage area to maintain a permanent

channel as compared to the basin with permeable strata. The constant of channel maintenance is taken asa measure of erodibility of the basin.

Horton (1932) defines the stream frequency F as the number of stream segments of all orders withina given basin of order K, divided by the basin area; or

F = Su1 Nu/Ak ...(2.16)

From the analysis of worldwide data Peltier (1962) found that for areas of comparable averageslope, stream frequency is greater in semi-arid regions; it is least in the arid regions and intermediate inhumid regions. High drainage densities or stream frequencies are a reflection of increased channeldevelopment and hence should give high sediment yield, which is really the case. Melton (1958) hasanalysed in detail the relationship between stream frequency and drainage density both of whichmeasure the texture of the drainage net, yet each treats the different aspect of it. According to him it ispossible to construct two hypothetical drainage basins having the same drainage density but differentstream frequency, and vice versa. However, in nature there is a good correlation between the two. Fromthe analysis of 156 drainage basins covering a wide range of climatic and lithological conditions,Melton found the following relation

F = 0.434 Dd2 ...(2.17)

where F is in km–2 and Dd is in km–1

2.10 RELIEF ASPECTS

The relief is the difference in elevation between given points. Maximum basin relief is the difference inelevation between the basin mouth and the highest point on the basin perimeter. Alternative definition ofmaximum relief is the basin relief along the longest dimension of the basin parallel to the principaldrainage line. Relief ratio Rk is the ratio of maximum basin relief to the horizontal distance along thelongest dimension of basin parallel to the principal drainage line (Schumm 1956). Melton (1958)defines the relative relief as the maximum relief H divided by the basin perimeter P while Maxwelldefines the relative relief as H divided to basin diameter. Use of the perimeter as the horizontal lengthdimension solves the difficulty of locating a suitable axial line in the basin. Two other parametersinvolving maximum relief have been defined by Strahler (1957). The ruggedness number is the productof maximum relief H and the drainage density Dd i.e. (H Dd). The geometry number is defined as(H Dd/S) where S is the ground slope. Both these parameters are dimensionless. Observed values ofruggedness number vary from 0.05 to about 1. Strahler (1964) found that the geometry number variesover a relatively narrow range viz. 0.40 to 1.0.

Schumm (1954) found that for six small drainage basins in Colorado Plateau Province (U.S.A.) therelief ratio Rh correlated well with annual sediment loss giving a relationship of the form

log (annual sediment loss) ~ Rh


Admittedly, relief ratio strongly influences the sediment loss since the force exerted on the surfaceis directly related to Rh. However, climatic factors such as rainfall and vegetal cover also affect sedimentloss. Schumm’s data shown in Fig. 2.6 are taken from catchments in the same region; hence climaticconditions were similar even though the lithology changed somewhat.

Fig. 2.6 Relation between annual sediment loss and Rh (Schumm 1954)

Hypsometric CurvesLet “a” be the horizontal projected area of a drainage basin at an elevation h (see Fig. 2.7) and A be thetotal projected area. Then one can prepare a curve between relative height h/H and relative area a/A asshown in the Figure 2.7. Such a curve is known as hypsometric curve. The analysis of large drainagebasins using such curves was first done by Langbein (1947) and later used by Strahler and others. Thehypsometric curve, in general, will change with time because of the gradual erosion of areas at higherlevels and hence the relative position of the hypsometric curve on a/H vs h/H graph gives an idea aboutthe stage of development of the basin landscape. Figure 2.7 shows young and mature stages oftopography. This figure also shows monadnock phase in which the resistant rock in the basin may formprominent hills at isolated places giving a distorted hypsometric curve. Sometimes the integral

o

1

z f (x) dx where f (x) = h/H and x = a/A is used as an index of evolution of the topography of the basin.

This integral represents the rock mass that is still to be eroded. Young phase would correspond to a highvalue of the integral while mature phase would correspond to a relatively small value. Strahler (1964)has indicated that most of the hypsometric curves can be represented by an equation of the form

Rh

0.30.20.10 0.4 0.5 0.6

8

10–1

100

8

6

4

2

An

nu

alse

dim

en

tlo

ss

Ha

.m/k

m2

Conglomeratesandstone

Friablesandstone

ShaleSchumm's data

Res

ista

ntto

wea

kro

ck

54

81

2

3

River Morphology28

y = d x

x

a

d a

z-

-

FHG

IKJ

...(2.18)

Here y and x are as shown in Fig 2.7. The exponent z increases as the topography becomes moremature. Hypsometric curves are also related to hydrologic characteristics of the drainage basin. Thusdistribution of elevation in a drainage basin is closely related to the amount of flood storage available,the effect of which is to make the rising limb of hydrograph less steep, increase the time lag and makethe peak lower and less pronounced. Knowledge of hypsometric curve is also useful in better estimatesof rainfall, snowfall and evaporation in the basin.

Channel SlopesA composite stream profile in a drainage basin can be prepared in the following way. For each first orderstreams vertical drop and horizontal length of the segment is determined. From these data mean dropand mean horizontal length are determined. This procedure is followed for streams of all orders. Thetriangles for each order are connected in sequence to produce a composite profile. Since each segmentslope is governed by the average discharge and average sediment load, a segmented profile looks logical

even though we tend to draw a continuous curve through these points. If Su is the average slope of the

segments of order u, Horton (1945) expressed variation of Su by the law of stream slopes according towhich

Su = S1 RsK u- ...(2.19)

where Rs is ratio similar to bifurcation ratio and can be called slope ratio.

Fig. 2.7 Hypsometric curve

y

a/A

0 0.2

0

a

0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

hH

y

Monadnock(Prominent hills)

(x, y)

Mature(Equilibrium)

Young

Original land surface

Base plane

Summitplane

Entire basinarea A

Divide

Area a

h

H


2.11 DRAINAGE BASIN CHARACTERISTICS AND HYDROLOGY

Many times a need is felt to have hydrologic data at sites where gauging station data are not available.Since there is a lack of data about precipitation (input) and stream flow (output), there is great difficultyin testing input-output models unless severe simplifying assumptions are made. Hence, scientists haveworked on the premise that fluvial activity and form of the land must be related. This was reflected inStrahler’s dimensional analysis presented earlier where runoff per unit area was related to erosion, reliefand drainage density. Bodhaine and Thomas (see Osborn 1980) obtained the following expression formean annual flood Q

Q = 0.638 A0.889 L– 0.037 R1.135 G ...(2.20)

where L is ratio of lake area to catchment area expressed in percent, G is the geologic factor and R is theaverage annual runoff.

A number of studies conducted in the U.S.A. and other countries have shown that basic drainageparameters such as stream length, basin length, basin relief area, drainage density, and slope areadequate to obtain correlations with different flows from the basin. The ungauged flows for which themethods have been developed are 7 day low flows of 2-yr and 20-yr return periods Q2 and Q20respectively, average annual flow Qaa, two year and 50 year peak flows Q2p and Q50p and sediment flowQs. One flow is considered to be functionally related to another flow of same type of different returnperiod. Thus

Q2p = f (Q50p) ...(2.21)

For low flows this general relationship is

Q1L = f (Q2L)–n ...(2.22)

where n is positive. Some of the successful geomorphic parameters used are (L1 . H) (LT . H), (LT H0.5)

and (Dd . L1) L1, where L1 is the length of first order perennial streams, H is the relief, LT is the totallength of streams and Dd is the drainage density (Osborn, 1971). It may be noted that all theseparameters are dimensional.

Work done on the geomorphological instantaneous unit hydrograph has been summarised byRodriguez-Iturbe (1993). GIUH is defined as the probability density function for the time of arrival of arandomly chosen drop to the gauging site and is related to Horton’s Rb, RL, RA, average velocity of thestream flow v and length of the channel of highest order LW. The peak flow qp and time to peak tp aregiven as

qp = 1.31 RL0.43 ULW

– 1 ...(2.23)

tp = 0.44 R

RB

A

FHGIKJ

0 55.

RL–0.38 LW

U–1...(2.24)

Here qp is in hr–1, U in m/s, tp in hr and LW in km.

2.12 RANDOM WALK MODEL

The precipitation falling on a uniformly sloping plain develops an incipient set of rills near thewatershed divide; these are generally oriented downhill. As the rills deepen with time, cross grading

River Morphology30

begins owing to overflow of shallow rills. The direction that the cross grading takes place and the micropiracy of the incipient rills are postulated to be a matter of chance until the rills deepen sufficiently. Thisrandomness in the first stages of development of stream has led to formulation of random walk modelfor drainage network.

To illustrate the basic ideas behind random walk model assume a row of equally spaced points onthe boundary of the drainage basin say at 1.5 cm apart; eight such points are shown in Fig. 2.8. They canbe considered as source of first order streams. Assume each point can move to the right, left or in theforward direction through a fixed distance so that the motion is downhill. As a result, a series ofstaggering paths will be generated and junctions may occur after which the joint path will be extended asa single unit, see Leopold and Langbein (1962), Shreve (1966 and 1967). Such artificial networks haveproperties and relationships closely approximating Horton’s laws. As a consequence, it has beensuggested that some of these relationships are attributes common to all systems of randomly developednetworks and are not really laws of orderly stream development. Of course it does not follow that streamnetworks are generated at random, even though random walk models approximate to them in manyaspects. Some may even argue that streams do not develop from head downwards but do so from mouthupwards. Leopold and Langbein found that for such a random walk model constructed, Lu + 1/Lu cameout to be 2.8, a figure which lies between 2.5 and 3.7 the range obtained by Horton (1945). Similarly,from random walk model it is found that Lu ~ A0.64 which agrees well with Hack’s relation L = 1.16 A0.60

as given in Eq. (2.13).One may argue that the development of drainage network is not so much a matter of chance but it is

influenced by lithology, climate, vegetation and antecedent conditions. The present streams may reflectthe effects of sequences of beds that have been eradicated by erosion during geologic past. Sincerandom walk model ignores all these factors one must view such a model with caution.

Fig. 2.8 Random walk model for stream network

Uniform spacing at origin


2.13 CONCLUDING REMARKS

At the end it is pertinent to mention that most of the generalities developed in this chapter have beenobtained from the data on small basins in weak rocks in U.S.A. Such basins adjust rapidly to thechanging conditions. Therefore one may assume that some present property or properties are controllingthe stream geometry and slope which can be measured and statistical relations obtained. If variation inlithology is great and erosional history complex, the drainage net analysis may become more involved(Sparks 1972).

References

Bruijnzeel, L.A.(1990) Hydrology of Moist Tropical Forests and Effects of Conservation. A State of KnowledgeReview. Division of Water Sciences, IHP, UNESCO, Paris (France). 224 p.

Carlson, C.W. and Langbein, W.B. (1960). Rapid Approximation of Drainage Density: Line Intersection Method.USGS Water Resources Division, Bull. 11, February 10.

Chorely, R.J. (1957). Illustrating the Laws of Morphometry. Geo. Mag. Vol. 94.

Chorely, R.J., Malm, D.E.G. and Pogorzelski, H.A. (1957) A New Standard for Estimating Basin Shape, Am. Jour.Sci., Vol. 255, pp. 138–141.

Garde, R.J. and Kothyari, U.C. (1987) Sediment Yield Estimation. JIP, CBIP, India, Vol. 44, No. 3.

Garde, R.J. and Kothyari, U.C. (1990) Flood Estimation in Indian Catchments. Jour. of Hydrology, ElsevierScience Publications, Amsterdam, Netherlands, Vol. 113, pp. 135–146.

Goswami, D.C. (1985) Brahmaputra River, Assam, India: Physiography, Basin Denudation and ChannelAggradation. WR Research, Vol. 21.

Gregory, K.J. (1966) Dry Valleys and Composition of the Drainage Net. Jour. Hydro. Vol. 4, pp. 327–340.

Gregory, K.J. and Walling, D.E. (1976) Drainage Basin Form and Processes:A Geomorphological Approach.Edward Arnold (Publishers) Ltd., London, Paper-Back Edition, 458 p.

Glock, W.S. (1932) Available Relief as a Factor of Control in the Profile of Land Form. Jour. Geol., Vol. 40, pp.74–83.

Hack, J.T. (1957) Studies of Longitudinal Stream Profiles in Virginia and Maryland. USGS Professional Paper294 – B,. 53 p.

Horton, R.E. (1932) Drainage Basin Characteristics. Trans. AGU, Vol. 13, pp. 350–361.

Horton, R.E. (1945) Erosional Development of Stream Their Drainage Basins:Hydrological Approach toQuantitative Morphology. Bull. Geol. Soc. Am. Vol. 50, pp. 275–370.

Howard, A.D. (1967) Drainage Analysis in Geologic Interpretation:A Summation. Am. Soc. Petroleum GeologistsBull. Vol. 51, pp. 2246–2259.

Langbein, W.B. et al. (1947) Topographic Characteristics of Drainage Basins. USGS Water Supply Paper 968C.

Leopold, L.B. and Langbein, W.B. (1962) the Concept of Entropy in Landscape Evolution. Theoretical Papers inHydrologic and Geomorphic Sciences. USGS Professional Paper 500A. 20 p.

Manandhar, I.N. and Khanal, N.R. (1988) Study of Landscape Processes with Special Reference to Landslides inLele Watershed, Central Nepal. Unpublished Report, Dept. of Geology, Tribhuvan University, Khatmandu(Nepal).

Melton, M.A. (1958) Geometrical Properties of Mature Drainage Systems and Their Representation in an E4Phase. Jour. Geol. Vol. 66, pp. 35–54.

River Morphology32

Miller, V.C. (1953) A Quantitative Geomorphic Study of Drainage Basin Characteristics in the Clinch MountainArea, Verginia and Tennessee, Project NR 389-042, Tech. Rept. No. 3, Columbia University, New York(U.S.A.).

Mittal, R.S., Parkash, B. and Bajpai, I.P. (1974) Drainage Basin Morphometric Study of the Part of GarhwalHimalaya. Himalayan Geology, Wadia Institute of Himalayan Geology.

Morisawa, M.E. (1962) Quantitative Geomorphology of Some Watersheds in Appalachian Plateau. Geol. Soc.Am. Bull. Vol. 73, No. 9, pp. 1025–1046.

Morisawa, M.E. (1968) Streams–Their Dynamics and Morphology. Earth and Planetary Science Series, McGrawHill Book Company, N.Y. 175 pp

National Institute of Hydrology (1993) Geomorphological Characteristics of Punpun Basin of Ganga RiverSystem, Roorkee (India), CS (AR) - 125.

National Institute of Hydrology (1995) Fluvial Geomorphological Characteristics of Four Sub-basins of UpperNarmada, Roorkee (India), CS(AR) - 159.

Osborn, J.F. (1980) Drainage Basin Characteristics Applied to Hydraulic Design and Water ResourcesManagement, Chapter 8, In Geomorphology and Engineering (Ed. Coates, D.R.), George Allen and Unwin,London, 1980, pp. 141–172.

Peltier, L.C. (1962) Area Sampling for Terrain Analysis. Prof. Geogr. Vol. 14, pp. 24–28.

Prasad, R.C. (1975) The Landslide and Erosion Problems with Special Reference to the Kosi Catchment. Proc. ofthe Seminar on Landslides and Toe Erosion Problems with Special Reference to Himalayan Region. Gangtok,Sikkim.

Rodriguez - Iturbe, I. (1993) The Geomorphological Unit Hydrograph, Chapter 3 in Channel Network Hydrology(Ed. Beven, K. and Kirkby, M.J.), John Willey and sons, New York, pp. 43–68.

Rzhanitsyn, N.A. (1960) Morphological and Hydrological Regularities of the Structure of the River Net.Published by Gidrameterizdat, Leningrad (Translated into English by P.B. Kimgold, USDA, ARS, U.S.A.)

Scheideggar, A.E. (1965) The Algebra of Stream Order Numbers, USGS Prof. Paper 5258, pp. 187–189.

Schumm, S.A. (1954) The Relation of Drainage Basin Relief to Sediment Loss. International Union of Geodesyand Geophysics; 10th General Assembly, Rome, IASH Publ. 36, Vol. 1, pp. 216–219.

Schumm, S.A. (1956) Evolution of Drainage Systems and Slopes in Badlands at Perth Amboy, New Jersey, Geol.Soc. Am. Bulletin. 67, pp. 597–646.

Schumm, S.A. (1977) The Fluvial System. Wiley Interscience Publication. John Wiley and Sons., New York. 338p.

Selby, M.J. (1967) Morphometry of Drainage Basins in Areas of Pumice Lithology. Proc. 5th New ZealandGeography Conference, New Zealand Geogr. Soc., Auckland (N.Z.), pp. 169–174.

Shreve, R.L. (1966) Statistical Laws of Stream Numbers. Jour. Geo. Vol. 74, pp. 17–37.

Shreve, R.L. (1967) Infinite Topological Random Channel Networks. Jour. Geol. Vol. 75, No. 2, pp. 178–186.

Smart, J.S. (1967) A Comment on Horton’s Law of Stream Numbers. WR Research, Vol. 3, pp. 773–776.

Smith, K.G. (1950) Standards for Grading Texture of Erosional Topography. Am. Jour. Sci. Vol. 248, pp. 655–658.

Sparks, B.W. (1972) Geomorphology, Longman Group Ltd., London, Chapter 6, 2nd Ed.

Strahler, A.N. (1952) Dynamic Basins of Geomorphology, Bull. Geol. Soc. Am., Vol. 63, pp. 923–938.

Strahler, A.N. (1957) Quantitative Analysis of Watershed Geomorphology. Trans. AGU, Vol. 38, pp. 913–920.

Strahler, A.N. (1964) Quantitative Geomorphology of Drainage Basins and Channel Networks. Section 4-II inHandbook of Applied Hydrology (Ed. V.T. Chow ) McGraw Hill Book Company Ltd., New York, pp. 4–39 to4–76.


Thornbury, W.D. (1969) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons, Inc.,2nd Edition.

Wiersum, K.F. (1984) Surface Erosion under Various Tropical Agroforestry Systems, in Proceedings Symposiumon Effects of Forest. Land use on Erosion and Slope Stability (Eds C.L. D’Loughlin and A.J. Pearce.).IUFRO, Vienna and East-West Centre, Honolulu, (Hawaii).

Zernitz, E.R. (1932) Drainage Patterns and Their Significance. Jour. of Geol., Vol. 40, pp. 498–521.

3C H A P T E R

Soil Erosion and Sediment Yield

3.1 INTRODUCTION

Soil can be eroded from its present state by the action of water, wind and glaciers; however in thecontext of the theme of this book, attention is concentrated on soil erosion by water, which is by far themost important in humid and semi-humid areas. Soil erosion by water is the process of detachment ofsoil particles by the impact of rainfall and runoff, and its transport down the slope. Erosion frommountainous areas and agricultural lands is the major source of sediment transported by the streams andthat deposited in reservoirs, flood plains, and deltas. Sediment load is also generated by erosion of bedand banks of the streams, by the mass movements of sediment such as land slides, rockslides and mudflows, and because of construction activity related to roads, buildings and dams. Part of the sedimentfrom the above-mentioned sources, which is carried by the stream, is stored in the valley bottom and onflood plains and released later. Hence, erosion of sediment is discontinuous with time and it displays ahigh degree of spatial variability.

Since part of the sediment eroded from an area can deposit in the lower reaches, the rate of erosionis usually greater than the rate at which sediment is carried downstream at any section; the latter isknows as the sediment yield. It may be mentioned that since landscape formation and changes in it aredue to differential erosion and deposition of sediment, erosion, sediment yield and landscape formationare closely interrelated; therefore study of soil erosion and sediment yield assumes great importance inriver morphology. Excessive erosion rates in the catchments of the rivers Kosi and Brahmaputra in Indiaare responsible for the severe migration of the Kosi and change of river regime of the Brahmaputra.Similar problems are also encountered in China on the Yellow river. Reservoirs constructed on streamscarrying sediment lose their capacity due to deposition of sediment in the reservoir. On an averageIndian reservoirs are losing their storage capacity between 0.05 to 5.0 percent per year. In Pakistan,Mangla reservoir, which was planned to last 100 years, is now expected to last only 57 years due toexcessive sediment deposition (El-Swaify et al. 1982). Dendy (1968) opined that if the present rates ofsedimentation continue a large per cent of small reservoirs would lose about fifty percent capacity in thenext three decades.

Soil Erosion and Sediment Yield 35

Soil erosion is found to reduce crop productivity and large tracts of land are made unproductiveevery year. Brown (1984) estimated that about 23 billion tons of soil from croplands in the world isbeing lost every year. Accordingly to UNEP (1980), about 20 million-hectare areas in the world becomeuneconomical for cropping each year due to soil erosion and erosion induced degradation.

3.2 GLOBAL EROSION RATES

Sediment going out of the catchment every year i.e., sediment yield gives a valuable idea about rates oferosion and soil loss from the drainage basin. This information is also very useful in studying thesediment problems and river behaviour. The sediment yield is made of suspended load and bed-load.Except when the depth is small and material is coarse, it is rather difficult to measure the bed-load.Hence most of available data on erosion rates only include suspended load, which is normally expressedin tons/km2/year or tons/year.

The mean annual suspended sediment yield expressed as tons/km2/year varies over a very widerange. Low sediment yield is generally associated with lowland areas or areas underlain by rocks thatare highly resistant to weathering and erosion, e.g., 1.0 ton/km2/year for many rivers in Poland, and 1.7tons/km2/year for a river draining the Southern Table Lands and Highlands of New South Wales, seeWalling (1988). Some of the high values of sediment yield obtained are from highly erodible loessregion. Table 3.1 adapted from Walling (1988) lists some of the high sediment yield values.

Table 3.1 Maximum values of specific suspended sediment yield (Walling 1988)

Country River Drainage area Suspended sediment yieldkm2 tons/km2/year

China Huangfuchuan 3199 55 500Dali 187 21 700 —Taiwan Tsengwen 1000 28 000

Kenya Perkerra 1310 19 520North Island Waiapu 1378 19 970New Zealand Waingaromia 175 17 340

High values of suspended sediment yield can be attributed to various factors such as underlyinggeology, topography, climatic conditions, high erodibility of soils and land use. Steep slopes and highintensity of rainfall can also cause high values of sediment yield. Holeman (1968) has given valuableinformation on the sediment yield of major rivers of the world. Table 3.2 gives such data for some riversin the world, which discharge more than 104 tons of sediment each year into the sea.

Some idea about erosion rates observed in various continents would also be helpful in knowingwhich regions contribute the highest and the lowest sediment load to the oceans. Table 3.3 is based onthe synthesis of data given by Strakov, and Milliman and Meade (1983).

Table 3.3 indicates that the highest sediment load is fed to the oceans every year by Asia and thenext in line would be South America and North and Central America. On the basis of whatever data thatwere then available some investigators have produced maps of global suspended sediment yield. Onesuch map prepared by Walling (1988) is shown in Fig. 3.1. From the analysis of such data estimates are

River Morphology36

Table 3.2 Some rivers of the world discharging more than 104 tons/year sedimentto the sea (Holeman, Ref. p. 68 (1982)

S.No River Location Total drainage Average annual Average waterarea 103 km2 sediment load discharge 103 m3/s

103 tons tons/km2

1. Yellow China 666 2080 000 2945 1.50

2. Ganga India 945 1600 000 1563 11.80

3. Brahmaputra Bangladesh 658 800 000 1445 12.20

4. Yangtze China 1920 550 000 547 21.80

5. Indus Pakistan 957 480 000 508 5.60

6. Ching (tributary of China 56 450 000 8008 0.057Yellow)

7. Amazon Brazil 5709 400 000 67 181.40

8. Mississippi U.S.A. 3185 344 000 109 17.90

9. Irrawaddy Mynamar 425 330 000 914 15.60

10. Missouri U.S.A. (Missouri) 1354 240 000 176 2.00

11. Lo (tributary of China 26 210 000 7890 —Yellow)

12. Kosi India 61 190 000 3117 1.80

13. Mekong Thailand 786 187 000 484 11.10

14. Colorado U.S.A. 630 149 000 422 0.16

15. Red Vietnam 118 143 000 1207 3.90

16. Nile Egypt 2944 122 000 39 2.80

Table 3.3 Mean erosion rates in different continents

Continent Area 106 km2 Erosion rate tons/km2/year

Africa 29.81 35 - 72

Asia 44.89 208 - 229

Australia 7.86 43

North and Central America 20.44 84 - 113

South America 17.9 100 - 148

Europe 9.7 50 - 75

made of the total suspended sediment load transported to the ocean every year. Some of the estimates ofmean annual sediment load are given in Table 3.4.

The earlier data base was meagre whereas in the estimates made in 80 have been based on data fromover 2000 rivers spread over all the continents. Hence, these recent estimates are likely to be moreaccurate than the older ones.

Soil E

rosion and Sedim

ent Yield

37

Fig. 3.1 Suspended sediment yield on global basis (Walling 1988)

1000

750

500

250

100

50

Deserts andpermanent ice

Sediment Yield

t.km yr�1�2

River Morphology38

According to the concept of geomorphic cycle, material is continually eroded from higher elevationareas and brought down to the low-lying areas and sea thereby reducing the slope of the terrain. Naturalagents such as rainfall and runoff, wind and glaciers cause this erosion. Geologists have made estimatesof such erosion. The time required to reduce the uplifted land surface to a gently undulating plain wasestimated by Davis to be 20–200 million years. Geomorphologists use four types of evidences toestimate the rate of loss of material from the land. These are: (i) Method based on estimates ofsuspended and dissolved material transported by rivers; this is obtained by sampling the sediment loadand discharge measurements. (ii) Measurement of sediment accumulated in reservoirs. (iii)Measurement of surface processes on slopes including rates of soil creep, surface wash and landslides.(iv) Comparison of known geological or radiocarbon dates with landform changes identified assubsequent to them. Because of the different techniques used and also because of the fact that erosion

Table 3.4 Some estimates of the yearly-suspended sediment transport to oceans

Author Year Estimated mean annual load in 106 tons

Keunen 1950 32 500

Pechinov 1959 24 200

Fournier 1960 51 100

Mackenzie & Garrels 1966 8300

Holeman 1968 15 700

USSR National Committee for IHD 1974 15 000

Walling and Webb 1983 15 000

Fig. 3.2 Ranges of rates of lowering of land surfaces (Young 1969)

R G S PRPS G

2.5

1.5

10

20

50

100

200

500

1000

2000

Gro

un

dlo

ss

(mm

/10

00

yr)

Normal Relief Steep relief

No

rma

lre

lief

Ste

ep

relie

f


rates are governed by rock type, climate, vegetation, basin area, relative relief and steepness of slope thereported erosion rates in different environments are not rigorously comparable.

Young (1969) has examined the then-available data on erosion rates and found it necessary to dividethe results into two classes of relief: normal relief including plains moderately dissected areas and gentleto moderate slopes, and steep relief including mountainous areas and individual steep slopes. His resultsare shown in Fig. 3.2. All data have been converted into mm/1000 years and are plotted on logarithmicscale. For large variations the extreme limits are shown on the ordinate and on abscissa the method usedfor measurement is indicated viz. R river load, S reservoir sedimentation, P surface processmeasurements and G geological evidence. His analysis gives an average erosion rate of 500 mm/1000years for steep relief and 46 mm/1000 years for normal relief. He has also mentioned that with respect torock type there are no marked differences in rates of erosion between igneous and metamorphic rocks,siliceous sedimentaries and lime stones; unconsolidated rocks are eroded 10–1000 times faster thanconsolidated rocks.

Schumm (1963) suggests that denudation rate of about 900 mm/1000 years be considered as anaverage maximum rate for drainage basins of the order of 4000 km2. On the basis of suspended sedimentyield of the Kosi as reported by Khosla (1953), Schumm obtains nearly the same rate as quoted above.On the other hand, he reports data by Zeuner, Gilluly, Stone and Gutenberg, which indicate that thepresent maximum rates of uplift or orogeny are far in excess of rates of denudation in many areas. Theseare 76 m/10 000 years in California, 30 m/10 000 years in Russia, 45 m/10 000 years in Japan and 100m/10 000 years in the Gulf area. Even though average uplift rates may be 1/3 or 1/4 of the maximumrates and further it is not known that uplift will continue at this rate, it does indicate that time-independent landforms may not be obtained in some cases because the rates of denudation and uplift areso different.

3.3 TYPES OF EROSION

Major types of soil erosion due to the action of water include sheet erosion, rill and inter-rill erosion,concentrated flow erosion on gully erosion, and stream channel erosion. Sheet erosion is the erosion ofland surface caused by the impact of raindrops and transport of soil by overland flow. Sheet erosion ismore or less uniform removal of soil without development of water channels. Rill and inter-rill erosioncaused by surface runoff results in numerous small-eroded channels across the landscape. Rills are

Fig. 3.3 Formation of gullies

River Morphology40

defined as eroded channels so small that tillage operations obliterate them every year. Both sheet erosionand rill erosion are widespread over a field and according to Foster (1988) can exceed 20 000 tons/km2

in severe cases.The topography of most fields causes surface runoff in a few major natural waterways before

leaving the fields. Erosion that occurs in these areas is called concentrated flow erosion; the impact ofthis erosion is localized in and around the waterways.

When eroded channels in concentrated flow areas become so large that they cannot be easilycrossed they are called gullies. Gullies are steep sided water channels, which carry ephemeral flowduring storms. Formation of gullies is shown in Fig. 3.3. Gullies are associated with accelerated erosionand hence with landscape instability. Gullies may not normally develop from rills; their development isa complex process, which is not fully understood. Some observations indicate that small depressionscaused by weakening of vegetal cover get enlarged; several such depressions coalesce and form achannel, which develops into a gully. Some gully action is found to occur due to subsidence of pipes ortunnels formed underground due to subsurface flow. This normally happens in high sodium soils. In afew cases gully action has been initiated where linear landslides leave deep steep sided scars, which maybe occupied by running water in subsequent storms (Morgan 1979). Discontinuous gullies representyouthful stage while fused gullies are an early mature stage of development. The sediment removedfrom the landscape due to formation, widening or deepening of gullies is known as gully erosion (Heede1975, and Piest et al. 1975). Very little is known about rates of gully erosion.

It may be added that ephemeral streams are those streams, which do not flow continuously. Theyrespond only to the occurrence of precipitation. Other times they are almost dry. Perennial streams arethose streams which flow continuously, their water supply coming from rainfall, snow melt and groundwater. Stream channel erosion includes stream bank erosion, valley trenching, streambed lowering andflood plain scour. It can also include the material carried by streams such as that from mine wastes andconstruction activities (such as dams, tunnels and roads) along the banks of the channel.

In general, sheet erosion is the prime offender in humid regions, whereas in more arid parts wherethe rainfall is experienced in short high intensity storms, channel erosion is more predominant. Materialderived from sheet erosion source is fine-grained material swept from fields and carried in suspension toand through the conveyance system. Channel type erosion is a source of coarser material and thismaterial is obtained from the areas, which are already a part of the transportation system. In generalsheet erosion forms a major part of total erosion from a given area. Thus Roehl (1963) found that in4300 km2 of well scattered area in South Eastern U.S.A. sheet erosion accounted for 66 to 100 percentof the total erosion.

Mass movement includes large-scale erosion due to tectonic activity, landslides, creep rock flow ormud flows; the eroded material is ultimately fed to the stream thereby increasing the sedimentconcentration substantially. Gross Ventre landslide South of Yellow Stone Park U.S.A., which occurredin 1925, produced 50 Mm3 rock materials forming a 68 m high dam in the valley. The lake formed bythis dam was 8.0 km long. Rockslide at Frank (B.C. Canada) in 1903 brought down 35 Mm3 rock debris.Such landslides are a common occurrence in the valleys of Himalaya in India.

Relative importance of sheet erosion, gully erosion, channel erosion, mass movement, andaccelerated erosion due to construction of roads etc. varies from one catchment to the other since itdepends on various factors. Robinson (1977) has given data on sediment sources and their totalcontribution to the sediment in streams in U.S.A., (see Table 3.5).


3.4 FACTORS AFFECTING EROSION

Factors affecting erosion are briefly discussed below.

Rainfall and TemperatureRainfall is the most important factor affecting erosion because of its power to detach the soil particlesand its ability to produce runoff, which causes erosion and transportation of the eroded material. Erosioncan be produced by a short duration high intensity storm during which the infiltration capacity isexceeded. Prolonged low intensity storms can also cause erosion. In the case of erosion due to water, theantecedent conditions of the soil with regard to soil moisture play an important role. If the soil is alreadywell soaked by previous storm a low intensity short duration storm can also cause significant erosion.For each area one would expect a critical or threshold value of rainfall intensity above which significanterosion would take place. Depending on geologic conditions this value varies from 10 mm/hr to 30 mm/hr. The erosive ability of rainfall depends upon its intensity and duration and velocity and diameter ofthe rain drops. For the same mean annual precipitation the annual erosion would depend on how thisprecipitation is distributed over the year. Fournier (1949) found that the ratio (maximum monthlyrainfall/annual rainfall) is a better rainfall parameter for the study of erosion. Garde and Kothyari (1987)have utilised this parameter in their analysis of erosion from the Indian catchments.

Temperature plays an important role in the process of weathering, especially mechanicalweathering, which leads to the disintegration of rocks. Alternate freezing and thawing, and alternateheating and cooling are the processes involved in this disintegration. Rainfall is responsible forchemical weathering as well as for transportation and deposition of the eroded material. Considering theimportance of rainfall and temperature in the process of erosion it is natural that mean annualtemperature and mean annual rainfall be used as the criteria for classifying modes of weathering andtransportation as done by Leopold, Wolman and Miller (1964), (see Fig. 3.4). For any given temperaturethe erosion rate first increases with increase in precipitation, reaches a maximum and then significantlyreduces. This reduction is due to the growth of vegetation which protects the soil surface from directimpact of rain drops, increases infiltration and gives direct protection from erosion due to foliage lyingon the ground. This is shown in Fig. 3.5.

Table 3.5 Sediment sources and their total contribution to sediment in streams in U.S.A. (Robinson 1977)

Sediment source Total sediment in 106 tons/years Percent of total

Agricultural lands 680 40

Stream bank erosion 450 26

Pasture and range land 210 12

Forest lands 130 7

Other federal lands 115 6

Urban 73 4

Roads 51 3

Mining 18 1

Other 14 1

River Morphology42

Fig. 3.5 Sediment yield as related to precipitation and vegetation (Leopold et al. 1964)

Soil CharacteristicsThe erodibility of soil depends on its texture, aggregate stability, shear strength, infiltration capacity,and organic and chemical contents. Coarser the particles smaller will be their erodibility. Similarlygreater the relative density less will be the erodibility. The clay content combines with organic matterand forms clods of soil. The stability of the clods determines the resistance to erosion. The shearstrength parameter is more useful in the study of mass movements such as landslides. The erodibilityindex of the soil designated as K is used in the Universal Soil Loss Equation USLE for agricultural landsdiscussed in section 3.6. It can be determined for the known values of per cent of silt and clay, per centof sand (0.10 mm to 0.20 mm), percent of organic matter, soil structure and permeability. Figure 3.6shows the monograph for determining the value of K for the known characteristics as given byWischmeir et al. (1971). If all the details of soil are not available one can use the following averagevalues given in Table 3.6.

Fig. 3.4 Hypothetical morphogenic regions

Mean annual rainfall, cm.

200180160140120100806040200�20

�10

0

10

20

30

Me

an

an

nu

alte

mp

.°C

Wind

Mechanical weatheringmass movement

running water

Mechanical andchemical weathering

running watermass movement

Chemical weatheringmass movement

running water

Mechanicalweatheringwindrunningwater

Sediment yield tons/Km . yr2

400

160

140

120

100

80

60

40

20

0

Effective

pre

cip

itation

cm

3002001000

Desert shrub

Grassland

Forest

Mean annual temp. 10°C


Fig. 3.6 Monograph for computing soil erodibility factor K in Universal Soil Loss Equation(Weischmeir et al. 1971)

Table 3.6 Average value of erodibility Factor K

Soil Range of K

Soil loams 0.40 to 0.70

Clay loams 0.30 to 0.40

Sandy loams 0.10 to 0.30

Gravely loams 0.03 to 0.10

Slope GeometryErosion is found to increase with increase in slope and length of the slope; this is due to correspondingincrease in the velocity and volume of surface runoff. Erosion rate per unit area can be expressed as

Erosion

Area~ S Lm n ...(3.1)

where the values of m and n are found to be different by different investigators. Values of m and nobtained by various investigators as given by Morgan (1979) are listed in Table 3.7. It can be seen that mand n are functions of process of erosion, magnitude of slope, steepness, length and vegetal cover.

VegetationVegetation or plant cover reduces erosion of soil, its effectiveness depending on the height andcontinuity of canopy, density of ground cover and the root density. For a given temperature, as theprecipitation increases the sediment yield in tons/km2 increases and reaches a maximum value. If the

Example given 65% Silt + V.F. sand

20% Sand (0.1 = 0.2 mm)

3% Organic matter

Soil structure � Fine granular

Permeability � slow to moderate

K = 0.38

90

100

80

70

60

50

40

30

20

10

0

Silt

+very

fine

sand

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Soil

ero

dib

ility

facto

rK

Percent sand(0.1 � 0.2 mm)

0

20

40

60

80

12

3

4

%OM = 0

1 2 3 4

1 Very fine granular2 Fine granular3 Coarse granular4 Blocky massive

Soil strucuture

654321 Permeability

6 Very slow5 Slow4 Slow to mod3 Moderate2 Mode-rapid1 Rapid

River Morphology44

canopy is near the ground it dissipates the kinetic energy of rain. Canopy on the ground also increasesroughness and reduces the velocity of surface flow. Roots play an important role in reducing erosionrate. Roots create easy passages for water to infiltrate thereby increasing the infiltration rate andreducing the surface runoff. Small roots also bind the soil mass thereby increasing its resistance toerosion. Generally forests are the most effective in reducing erosion because of their canopy; densegrass is equally effective.

Experimental evidence indicates that the erosion-cover relationship is non-linear. As vegetal coverincreases from zero there is a rapid decreases in soil loss; however beyond 60 percent cover, furtherincrease in vegetal cover reduces the soil loss marginally. Table 3.8 shows the erosion-cover relationshipgeneralised after Elwell (1980) and Elwell and Stocking (1974). It can be seen from Table 3.8 that foradequate erosion protection at least 60–70 percent of the ground should be covered by vegetation.

Table 3.8 Relationship between percent vegetal cover and percent reduction in soil loss

Mean seasonal vegetal cover % 100 80 60 40 20 10 5Soil loss as a % of bare plot soil loss 0.5 1.5 5 10 32 60 70

It may be mentioned that there is an interaction betweenrainfall and vegetation in controlling erosion rates. Langbein andSchumm (1958) have found that vegetation bulk in kg/m2 varies asthe annual precipitation raised to a power greater than unity. Withincreasing precipitation the vegetation changes from desert shrubsto grassland to forest. As a result, when vegetation intensitybecomes adequate it inhibits erosion. Hence, on a regional scaleinitially erosion rate increases with increase in annualprecipitation, reaches a maximum and then decreases with furtherincrease in precipitation. Schumm (1977) expressed the effect of

Table 3.7 Values of m and n in Eq. 3.1(Robinson 1977)

Investigator m n Conditions/Comments

Zingg 1.40 0.60 From five experimental stations in U.S.A.Hudson and Jackson 2.0 — From experimental stations in Zimbabwe

Hovarth and Erodi 1.60 to 0.70 — m decreased with increase in slope in laboratorystudies

Quinn, Morgan and Smith 0.70 to 1.0 — m increased as grass cover decreasedKirkby 1.0 to 2.0 — For soil creep and splash erosion

1.3 to 2.0 0.3 – 0.7 For erosion by overland flow— 1.0 – 2.0 For erosion with rilling

Fig. 3.7 Variation of sediment yieldwith mean annual precipitation and

temperature (Schumm 1977)mean annual temperature and annual precipitation on sedimentyield as shown in Fig. 3.7. It can be seen that as the annualtemperature increases the peak of the sediment yield occurs athigher value of annual precipitation. This is so because at higher

Mean annual precipitation cm

Mean

annualsed.yie

ldto

ns/k

m2 400

0

300

200

100

0 40 80 120 160

5°C

10°C

15°C

20°C


temperature there is greater evapo-transpiration; hence less amount of precipitation is available forcausing runoff. As a result, peak rate of sediment yield shifts to the right. However, studies by Wallingand Kleo for 1296 measuring stations all over the world, by Sharma and Chatterji for small reservoirs inRajasthan (India), by Dunne in Kenya, by Griffiths in New Zealand, and by Duglas in Australia do notsupport the universality of Fig. 3.7. (Tiwari 1993).

3.5 MECHANICS OF SHEET EROSION

As the rainfall occurs the overland flow normally occurs at shallow depth for a short distance withoutforming any small depressions or furrows called rills. The pre-rill flow is many times called inter-rillflow and associated erosion is known as inter-rill erosion. In this area the depth of flow and thecorresponding shear on the surface are very small. Here the dominating factor influencing the surfaceerosion is rainfall impact. On the other hand, once the flow enters the rills and is concentrated, the depthof flow is large. Therefore erosion in rill-flow is related to the runoff characteristics; this erosion issometimes called rill-erosion.

It may be mentioned that rills are not a permanent feature. Rills formed from one storm are oftenobliterated before the next storm of sufficient intensity, which can cause rilling. Most rill systems arediscontinuous i.e., they have no connection with the main stream. Rills are usually initiated at a criticaldistance down the slope where overland flow becomes canalised. It may also be emphasized that rillerosion accounts for majority of erosion from the hillside. Mutchler and Young (1975) found that on a4.5 m slope plots in U.S.A., over eight percent of material was transported in rills. Relative importanceof rill erosion depends on the rill spacing. Smaller the spacing between rills greater will be the rillerosion.

Four processes associated with inter-rill and rill erosion can be identified as:Soil detachment by rainfall;Soil transport by rainfall;Soil detachment by runoff;

Soil transport by runoff.Mutchler and Young (1975) have summarised the mechanism of soil detachment by raindrops.

Raindrop sizes usually range from 7.0 mm to fine mist size and in any rainfall there are raindrops ofvarious sizes. A normal or Gaussian distribution based on the raindrop volumes is usually assumed.Hence median raindrop diameter d is that diameter for which equal amounts of volume are contained inlarger and smaller drops than d. Laws and Parsons (1943) have found a relationship between intensity ofrainfall I in mm/hour and d in mm as

d = 1.24 I 0.182 ...(3.2)

The raindrops attain a terminal fall velocity, which depends on their size, air density andtemperature. Terminal fall velocity can be obtained from CD versus Reynolds number diagram for asphere, given in all textbooks on Fluid Mechanics. The terminal fall velocity for 5 mm drop will beabout 9.0 m/s and it will be 1.0 m/s for 0.25 mm drop. Presence of strong wind has two effects onterminal fall velocity. Firstly it can increase the velocity of drops striking the land surface and secondlyit causes raindrops to strike the surface at an angle to the vertical. The ability of rain to cause soil erosionis attributed to its rate and the distribution of drop size, both of which affect the energy load of arainstorm. The erosivity of a rainstorm is attributed to its kinetic energy or momentum; both these

River Morphology46

parameters can be related to rainfall intensity or total amount of rainfall. Rose (1960), Williams (1969)and Kinnell (1973) have related the erosivity rate to momentum of rainfall. Williams and Kinnell havegiven the following equations for momentum M:

log M = 0.711 log I – 1.461M = 0.0213 I – 1.62

UVW

...(3.3)

Here M is in dynes cm–2 s–1 and I is in mm/hour.The kinetic energy of the rainfall is a major factor initiating soil detachment. Kinetic energy of

rainfall can be either measured or can be computed if one knows the rain drop size distribution andcorresponding terminal fall velocities. Investigators have used the following three forms of equations torelate kinetic energy E of rainfall expended per unit quantity of rainfall to the rainfall intensity I.

E a b I

E c b a I

E b I a

= +

= + -

= -

U

V|

W|

-

log ( )

( )1 ...(3.4)

Where a, b, c are empirical constants. Wischmeir and Smith (1958) gave the following equation

E = 13.32 + 9.78 log I ...(3.5)

where E is in J/m2 .mm and I is the rainfall intensity in mm/hour. Hudson (1965) has given the followingequation

E = 29.8 – 127 5.

I...(3.6)

There are a large number of equations developed for E which are based on data from differentregions such as Nigeria, Zimbabwe and U.S.A. It may be mentioned that for a given choice of equationfor E, the kinetic energy for a storm having non-uniform rainfall intensity is computed by

(i) dividing the storm into small time increments in which the rainfall intensity can be assumed tothe uniform;

(ii) determining the rainfall intensity in mm/hour for each time increment;(iii) computing Ei for each intensity Ii using the chosen relationship between E and I;

(iv) determining E = SEi.When the raindrop hits the soil surface there is a splash of water and its shape is as shown in

Fig. 3.8. The splash shape parameters, which define its geometry, are crater width W, splash height H,splash angle b, sheet angle a and sheet radius r. These quantities change with respect to time and theirvariation with time as recorded by a high-speed camera is also shown in Fig. 3.8. The erosive action ofraindrop is effective very early after the impact and in the vicinity of the centre of impact. Evidenceindicates that the raindrop impact is most erosive where a thin layer of water about one fifth the dropdiameter is present. If the surface water depth is about three drop diameters, it protects the soil fromraindrop impact. As the splash height reduces and the crater width increases a horizontal flow velocityaway from the splash is caused. This velocity among other parameters also depends on the ratio of waterdepth to drop diameter and is maximum when this ratio is 0.33, this horizontal component of velocitygreatly increases the potential of this surface flow to transport detached soil particles.


It must also be mentioned that as the raindrop hits a thin water layer surface, a large number ofsmaller water droplets are produced. Mutchler (1971) found that one drop of 5.67 mm diameter on0.10 mm water depth on a smooth glass produced as many as 4000 droplets which would eventually hitthe soil surface, generate turbulence and throw additional material in suspension.

Raindrop impact effects are present in rills also; but because of relatively larger water depthcompared to the size of drops, the impact effect is not so pronounced.

Erosivity IndicesIn developing equations for predicting sheet erosion some investigators have developed erosivityindices, which depend on rainfall intensity, kinetic energy and other characteristics of rainfall. Some ofthese indices are described below:

Wischmeier and Smith (1958) use the rainfall parameter R = EI30 where E is the total kinetic energyof the storm and I30 is the maximum 30 minute intensity of rainfall during the storm. They found that soilloss correlates well with EI30. The term I30 is computed as twice the greatest amount of rain falling inany 30 consecutive minutes; E is calculated using Eq. (3.5). The parameter R is used in Universal SoilLoss Equation (see below).

Fournier (1960) developed an erosivity index for river basins on the basis of relationship betweensuspended load in rivers and climatic data and relief characteristics. The index called climate index C isdefined as

C = p2/P

where p is the rainfall amount in wettest month and P is the annual rainfall. This index was subsequentlymodified by FAO (1977) as follows:

C1 = S112p2

i /P

Fig. 3.8 Changes in splash parameters with time

Time after Impact s

0.01 0.02 0.030

0.01 0.02 0.030

0

1

2

3

4

50

60

70

80

90

Hand

Win

cm

aand

in°

bSplash height H

Crater width W

Splash angle b

Sheet angle a

a

b

W

Hr

Sheetradius

River Morphology48

where pi is rainfall in ith month. It is also found that the index C1 is linearly related to the index R i.e. EI30as

R = a + b C1 ...(3.7)

where a and b vary widely from region to region having different climatic conditions.

3.6 EQUATIONS FOR PREDICTING SOIL LOSS FROM AGRICULTURALLANDS

Since about 1940 considerable research on soil erosion from agricultural lands has been carried out inU.S.A. and other countries. Often laboratory and field plots have been used to obtain experimental datafor predicting and evaluating soil erosion. Laboratory plots are of area about 1.0 m2 or less and manytimes rainfall simulators are used on them. These are used to study basic erosion phases that are difficultto study on larger plots, for example, surface sealing, aggregate stability, raindrop detachment, andsplash transport. In such experiments one must be careful in minimising the edge effects in such plots.The plots used in the development of Universal Soil Loss Equation are large enough to represent thecomplete process of rill and inter-rill erosion. These are of such size that their sediment delivery ratio isvery high.

There are various empirical equations, which give the rate of sheet erosion. However, because oftheir empirical nature the equations would be strictly valid in the region where they are developed.Hence only the functional relationships are mentioned to emphasize the variables to which soil erosionhas been related. According to Ellison (1945) the soil dislodged E1 in weight per unit area per unit timecan be expressed as

E1 = K wo4.33 d1.07 I0.65 ...(3.8)

where wo is the terminal fall velocity, d is the raindrop diameter, I is the intensity of rainfall, and K is aconstant. Musgrave and his associates in the Soil Conservation Service in U.S.A. made observationsand analysed rates of sheet erosion. As a result an empirical equation of the form

Ei ~ F Ri So1.35 L1

0.35 P1.75 ...(3.9)

was proposed in which Ei is the soil loss in weight per unit area per year, F is the soil factor based theerodibility of soil and other physical factors, Ri is the factor which is related to the land use, So is thesteepness of slope in percent, L1 is the length of the slope and P is the maximum 30 minute rainfallexpected in the locality with a 2 years return period. The constant of proportionality in this equationdepends on the units used to describe these variables.

Universal Soil Loss Equation (USLE)Soil erosion rates from cultivated lands in U.S.A. are predicted by using the Universal Soil LossEquation (USLE) developed by Wischmeier and Smith (1962, 1965) on the basis of statistical analysisof a large number of plot-years of data from 47 locations in 24 states. The equation takes into accountthe effect of rainfall, soil characteristics, slope and length factor for the land, and crop and managementpractices on soil erosion. This equation is an improvement over the earlier methods in that the above-mentioned factors have been quantified and used in the equation. The Universal Soil Loss Equation is

E = R K L S C P ...(3.10)


where E is the computed soil loss either in tons/acre year or tons/ha year. R is the rainfall factor inhundred of foot-ton-inches per acre-hour-year or in MJ. mm/ha h yr. It is the combined erosivity due torainfall and runoff. It is the average number of erosion index units in a year of rain.

K is the soil erodibility factor in tons-acre-hours per hundreds of foot-ton-inches-acres or tons-ha-hour-ha-MJ-mm. (see Fig. 3.6)

L is the slope length factor

S is the slope steepness factorC is the cropping management factorP is the erosion control practice factorErosion index is a measure of erosive force of the rainfall and is computed as the product of the total

kinetic energy of the rainstorm and its maximum 30 minutes intensity. This is summed for a period ofrecord and divided by the number of years to get its average value. This product correlates well with thesoil erosion. Wischmeier and Smith (1965) have prepared a map of U.S.A. indicating Iso-R value lines;R-value varies from 0 to 600 in U.S.A.

Soil erodibility factor K has been discussed earlier. It is defined as the erosion rate per unit oferosion index on 72.6 feet long and nine percent slope of cultivated soil. K values give an integratedeffect of the characteristics of the soil which influence its permeability and ability to resist detachmentand transport by rainfall and runoff. In central and eastern U.S.A. K values range from 0.03 to 0.70.

The slope length factor L accounts for the fact that as the length of slope increases, there isincreased runoff. It is defined as the ratio of soil loss for a given slope length to the soil loss from 72.6feet length, other factors remaining the same. If l is the slope length it is found that the soil loss~ l1.3 to 1.6 and hence soil loss per unit length will be approximately proportional to l0.50.

Slope steepness factor S takes into account the increase in the velocity of runoff as slope increases.Taking nine percent slope as standard, S is defined as the ratio of soil loss for a given slope to that froma nine percent slope. If So is the slope steepness in percent, S is related to So as

S = 0.0076 + 0.0053 So + 0.000 776 So2 ...(3.11)

Hence the combined effect of slope length and slope steepness in USLE is given as

LS = l0.50 (0.0076 + 0.0053 So + 0.000 776 So2) ...(3.12)

Cropping management factor C accounts for the crop rotation, used tillage method, crop residuetreatment, productivity level and other cultural practices. Its value is the ratio of soil loss from a fieldwith given cropping and management practices to the soil loss from the fallow conditions used toevaluate the K factor. The C factor for individual crops varies with the stage of crop growth and has beenevaluated. Erosion control practice factor P accounts for the effect of conservation practices such ascontouring strip cropping, and terracing on the resulting erosion (see Blakely et al. (1955) and Meyerand Mannering (1967)). Its value is the ratio of soil loss with one of these practices to the soil loss withstraight row farming.

Earlier USLE is revised and updated by the Agricultural Research Service and some universities inU.S.A., (see Foster (1988)). This is done

i. to incorporate recently collected data for conservation tillage and range lands into the equation;ii. to improve the applicability of USLE to other climatic regions;

River Morphology50

iii. to improve the performance of USLE for conditions where no data exist; andiv. to estimate values of the factor C.

Attempts are also made to use USLE to estimate soil loss from isolated storm events. Otherimprovement being attempted is to evaluate sediment yield by using USLE equation. However thiswould require use of the concept of sediment delivery ratio. At present effect of topographic features onsediment delivery ratio is not known; hence this method of estimating sediment yield is not accurate.

The Universal Soil Loss Equation is used for a number of purposes. Commonly it is used to find outthe soil loss under a given condition. If an acceptable value of soil loss E is chosen the slope length Lrequired to bring down the soil loss to the chosen value can be calculated. In this way appropriate terracespacing can be determined. Alternatively the value of C can be predicted and appropriate croppingpractice is specified. It may however be mentioned that the data on which USLE is based are from eastof Rocky Mountains in U.S.A. Hence values of C pertain to this region only. As mentioned by Morgan(1979), Hudson and Roose have applied this equation in Zimbabwe and Ivory Coast respectively.Morgan (1979) has pointed out that there is considerable interdependence between the variables used inUSLE and some are counted twice. For example, rainfall affects both R and C factors, and terracing theL and P factors. It is also pointed out that one important factor to which soil loss is closely relatednamely runoff has not been included in USLE. This has been overcome by Foster, Meyer, and Onstadwho have suggested replacement of rainfall factor R by R1, which depends on R, the storm runoff Q ininches and qp the storm peak runoff in in/hr. R1 is given by

R1 = 0.50 R + 15 Q qp1/3 ...(3.13)

However this needs further verification.McCool and Rendard (1990) have reported the efforts made in U.S.A. to revise USLE to estimate

more accurately the soil loss from both crop and range land areas. The modified equation is known asRevised Universal Soil Loss Equation (RUSLE). All the factors R, K, LS, C and P have receivedattention. McCool and Rendard have discussed major changes incorporated in RUSLE. Thus R-valuesare related to (El15). Further R equivalent approach is used to reflect the combined effect of drain andsnowmelt.

3.7 MEASUREMENT OF SEDIMENT YIELD

Sediment yield is the amount of sediment passing through a given section in unit time. It can beexpressed in tons/km2/yr. Two most common methods of determining sediment yield from river basinsare by measurement of suspended load, and from reservoir sedimentation surveys. These methods andassociated problems are briefly discussed below:

Suspended Sediment MeasurementsDetermining the average suspended sediment concentration and multiplying it by the discharge canmeasure suspended sediment. Average suspended sediment concentration in a vertical can be obtainedby first taking a number of samples at different locations in the vertical and then taking the average.However, since this is time-consuming and expensive, the following procedures are adopted.

A single sample at water surface or 0.6 times the depth below water surface is taken. Sampling atwater surface is easier and can give reasonably good results if suspended sediment is very fine. Forslightly coarser materials, an empirical coefficient can be used to get average concentration from the


known surface concentration. However, it may be mentioned that the coefficient would really depend onsuspended sediment size and flow conditions. Sampling at 0.60 depths has been used in India and someparts of U.S.A. in the hope that it gives the average concentration, presumably because the meanvelocity occurs approximately at this level. Analysis of wide range of data indicates that, for reasonableaccuracy, one-point measurements should be made between 0.6 and 0.8 depths, the larger value beingsuitable for coarser sediment. A better method would be to take concentrations at 0.2D and 0.8D andobtain the average concentration as

C = 3

8

5

80 2 0 8C C. .D D+FH

IK ...(3.14)

as suggested by Straub. The three point method involves measurement of concentration at surface, middepth and bottom; the mean concentration can then be obtained either by giving equal weightage to allthe three samples or by giving a weightage of two to the mid-depth sample and one to the other twosamples.

If the stream cross-section is non-rectangular the average concentration in the vertical will bedifferent for different verticals; hence sampling verticals have to be chosen. The following methods areavailable:

i. single vertical at the midstream;ii. single vertical at the point of greatest depth;iii. verticals at 1/4, 1/2, 3/4 width;iv. verticals at 1/6, 1/2, 5/6 width;

v. four or more verticals spaced equally across the stream;vi. verticals at middles of sections of equal discharge.The final choice of the number of verticals depends on the availability of man power, funds, cross-

sectional shape and accuracy desired. The suspended load carried by the stream can then be determinedfrom

Qs = 1

N

å qi Ci ...(3.15)

where N is the number of verticals, qi is discharge at the centre of each vertical and Ci is the averageconcentration.

A brief comment about the frequency of sampling is in order. In reality, samples must be collected atsuch a frequency which is satisfactory both from the point of view of accuracy needed and the expensesinvolved. Variations of sediment load occur due to variations in storm characteristics; size, shape,geological and topographical features of the drainage area, and characteristics of the stream. Out ofthese, the size of the drainage area appears to be the single most important factor. For smaller drainageareas water and sediment discharges are greatly dependent on local storm characteristics. For largerdrainage areas, where the runoff accrues from different storms and sub-watersheds, the variation inwater and sediment discharge with time is smaller. Therefore, as a rule, larger the drainage area smallercan be the frequency; however during a flood when discharge and sediment concentration vary rapidly,frequent sampling is required. For example, in the case of the Coon Creek, Wisconsin (U.S.A.), havinga drainage area of 200 km2, it was found that 90 percent of the total sediment load for 15 months was

River Morphology52

discharged within ten days or 2.2 percent of the time, (see TCPSM (1969)). Sampling frequencies varywidely depending on agency conducting the sampling, purpose of collection of data, nature of streamand funds available. Sampling interval during low flows can vary from a day to a week. During therising stage of a flood, intervals varying from 30 minutes to 12 hours have been utilised.

After collecting such data the suspended load Qs is related to the corresponding water discharge Q;or alternately suspended load per unit width qs is related to discharge per unit width q. Several fieldengineers have reported a relationship between qs and q in the form

qs = a qb ...(3.16)

where b is found to vary between 1.9 and 2.2 and can be taken as 2.0 as an approximation. However,Leopold and Maddock (1953) found that b varies between 2.0 and 3.0 for many American rivers. Thevalue of ‘a’ would depend on the units used. The usual practice is to develop such a relationship fromdata for a few years and then use it to compute suspended load for other years where only waterdischarge variation is known.

Certain limitations of qs vs q relation need to be discussed. The qs vs q relations do not take intoaccount such factors as sediment size, river slope, watershed characteristics, and pattern of dischargevariation. Experience has shown that such relationships can be different for the rising and falling stagesof the streams. In fact, these can be different for different seasons for the same stream. Significantvariations can also be obtained because the peak of sediment discharge and that of water discharge maynot coincide. For these reasons qs vs q or Qs vs Q relation can only be an approximate guide to theamount of suspended load and should be used with caution.

To the suspended load must be added the bed-load carried by stream to get the total load. Asmentioned earlier except in the case of shallow streams flowing through relatively coarse material, it israther difficult to measure the bed-load. Lane and Borland (1951) cite the following classification ofMaddock, in which percentage of unmeasured load (i.e. bed-load plus unmeasured suspended load) isrelated to the concentration of measured suspended load, type of bed material and the texture ofsuspended material, see Table 3.9.

Table 3.9 Maddock’s classification to determine unmeasured load

Concentration of Type of material Texture of the suspended Unmeasured load asmeasured suspended forming the channel sediment a percentagesediment in ppm

Less than 1000 Sand Similar to bed material 25 to 150

Less than 1000 Gravel, rock or consolidated clay Small amount of sand 5 to 121000 to 7500 Sand Similar to bed material 10 to 351000 to 7500 Gravel, rock or consolidated clay 25 percent sand or clay 5 to 12

Over 7500 Sand Similar to bed material 10 to 15Over 7500 Gravel, rock or consolidated clay 25 percent sand or less 2 to 8

The average values of qS/qT as obtained from actual measurements or otherwise are available forsome natural streams. Here qT is the total load. These are listed in Table 3.10.

Dekov and Mozzherin (1984) found the ratio of bed-load to suspended load for large streams to be0.08 for rivers in plain and 0.23 for mountain rivers.


Tricart (1962) has highlighted the dangers in determining the average erosion rates caused by thetemporal and spatial variation in erosion. His main argument is that there are different types ofdiscontinuities in the time domain. We have already seen that Qs vs Q relation is not truly unique. Timelags between flow and sediment are much greater for less mobile material such as coarse sand, graveland boulders than for colloids, silts and clays, because while the former move slowly and intermittentlyas bed-load the latter move as suspended load and with nearly the same velocity as the flow.

Then there are seasonal discontinuities, which cease more or less for long periods but recur nearlyevery year. Sporadic phenomena are caused by floods of large return periods. Catastrophic phenomenacaused by landslides and earthquakes bring in a very large amount of sediment over a short period andonly once in a while. Since the material in transport moves at different speeds, is stopped and is stored inlocation dictated by geomorphic evolution, the temporal discontinuities and spatial discontinuities areclosely interlinked. On micro scale, the erosion-taking place from hill slopes caused by rainfall may notbe uniform over the whole slope because of spatial changes in vegetation, roughness and erodibility ofthe material. Then as the material moves to the foot of the slope, coarse material may get deposited dueto reduction in slope. This is also assisted due to reduction in flow caused by the high permeability of thefan. Further, material brought down by avalanches, land slides and source chutes is also discontinuousand sporadic in variation. Lastly, in the main river sediment is trapped by vegetation, on flood plain, inthe riverbed, and at places where currents are weak. It may take years before the material is mobilisedagain and deposited elsewhere. This seems to be too complex a phenomenon to utilise deterministicmodel and hence Tricart thought that a statistical approach needs to be used.

Reservoir SurveysWhen a large capacity dam is constructed across a stream, a backwater is caused on the upstream side ofthe dam, which reduces the energy gradient, and velocity of flow. This effect is felt for severalkilometers in the upstream direction. As a result, the ability of the stream to transport sediment load isprogressively reduced from beginning of backwater curve towards the dam and the excess sediment getsdeposited. If the reservoir capacity to the annual inflow ratio is about or greater than unity, most of thesediment gets deposited upstream of the dam and only a small percent of finer material may pass overthe dam and through the sluices. Since such deposition over a period of years reduces the valuablecapacity of the reservoir to store water, reservoirs are periodically surveyed to determine the amount of

Table 3.10 Typical values of qS /qT for natural streams in U.S.A.

River Sediment size in mm Average qS / qT

Mississippi river at mouth 0.14 0.90Colorado river at Yuma 0.10 0.80Niobrara river near Cody 0.30 0.49

Niobrara river near Valentine 0.27 0.47Snake river near Burge 0.29 0.67Five mile creek near Riverton 0.24 0.81

Middle Loup river near Dunning 0.33 0.53Biose river near Twin Springs 0.10 0.65Moore Creek above Granite Creek 0.25 0.75

River Morphology54

sediment deposited in the reservoir. Hence such surveys provide valuable data on sediment load carriedby the stream.

There are two general methods of conducting reservoir surveys. These are the range-line survey,and contour survey. The general procedure of carrying out reservoir surveys has changed little in thepast four or five decades; however significant advances have taken place in the equipment available forcarrying out the surveys. Choice of the method depends on availability and character of previousmapping or survey records, the size of reservoir, degree of accuracy needed, and scope of studyobjectives. The range-line method is more widely used for medium and large reservoirs. In this methoda number of cross sections of the reservoir are surveyed before the reservoir is first filled and thenperiodically resurveyed. These cross sections are called ranges. From known data for the consecutivesurveys at each range line, one can determine area of sediment deposition, from which total volume ofsediment deposited on the upstream side of the dam can be determined.

Contour method is used for small reservoirs, which are occasionally empty, or at low stage. Thecontour method uses essentially the topographic mapping procedures. To apply this method first a goodcontour map of the reservoir is prepared before its filling. Similar contour map can be obtainedperiodically many times by aerial survey. The contour interval is 1.5 m to 0.5 m. From such consecutivecontour maps the sediment volume deposited during certain period can be ascertained. New techniquesof reservoir surveys are being used at present and these are discussed by Bruk (1985).

Now a days reservoir surveys are carried out using Global Positioning System (GPS). GPS(GARMIN 2000 and Chatterjee et al. 2001) is a satellite-based navigation system made up of a networkof 24 satellites placed into orbit by U.S. Department of Defence; this system is now available for civilianuse. It works in any weather condition, 24 hours a day.

These satellites circle the earth twice a day in a precise orbit and transmit signal information to theearth. Using signal information from three or more satellites at the same time, the receivers on the earthuse triangulation techniques to calculate the exact location of the reservoir. The GPS receivers have anumber of potential errors, but if Differential Global Positioning System (DGPS), is used by having twoidentical receivers, they provide an accurate means of surveying. The basic principle of DGPS is thaterrors calculated by two receivers in a local area will have common errors. Here one GPS receiver at thebase station is located on the surveyed point, and the second one called the rover station is located on themotorised boat, which collects bathymetric data for reservoirs. The reference station GPS receiverknows the position of its antenna and can determine the errors in satellite signals. The error betweenmeasured and calculated is the total error. The range errors for each satellite are formatted into messagesand the modular encodes these data. In an amplified form these data are radiated through antenna toroving GPS Station for real time position correction. Hence, when the two receivers are operatedconcurrently, by comparing and processing of signals of both the stations, the position of roving stationcan be obtained with adequate accuracy. The depth measuring unit consists of sonic soundingequipment, which comprises recorder, transmitting and recovering transducers and a power supply. Thisequipment needs frequent calibration. With such equipment depths can be measured with an error lessthan one percent.

Once the volume of sediment deposited in a given period is known, it can be converted intocorresponding weight if the average unit weight of sediment Wav over a period of T years is known.Miller (1953) has given the following equation for Wav.


Wav = Wo + 0.434K T

TT

--

L

NM

O

QP1

1ln ( ) ...(3.17)

where Wav and Wo are the average unit weight and initial unit weight in kN/m3 of the deposited sedimentin T years and the coefficient K depends on the sediment size and method of reservoir operation. Valuesof K as recommended by Lane and Koelzer are given in Table 3.11.

Table 3.11 Recommended values of K in Eq. 3.17 (U.S. Govt. and IIHR 1943)

S. No. Reservoir operation Deposited sedimentBoulders, gravel sand Silt Clays

1. Sediment always submerged or nearly submerged 0 0.90 2.512. Normally a moderate reservoir draw down 0 0.42 1.683. Normally considerable reservoir 0 0.16 0.94

4. Reservoir normally empty 0 0 0

Knowing the percentages of the individual fractions in the deposited sediment Wo can be

determined as Wo = S iN=1Woi pi/100. In the same way weighted K value can be determined and used in

Eq. (3.17).To determine initial unit weight Table 3.12 can be used:

Table 3.12 Initial unit weights of sediment

Material kN/m3

Clays 7.5Silts 9.5

Sands 16Gravel 20Boulders 22

As has been already mentioned, some material flows over and through the dam; therefore sedimentdeposited in the reservoir during a given time will be less than sediment flowing into the reservoirduring the same time. This ratio expressed in percent is commonly known as the trap efficiency Te of thereservoir, which will vary between 0 and 100 percent. If the trap efficiency of the reservoir is known,yearly quantity of sediment deposited in the reservoir can be converted into sediment yield using therelation:

Sediment yield =

Annual quantity of sediment

deposited in the reservoir

(Trap efficiency/100)

FHG

IKJ

...(3.18)

River Morphology56

In general, the trap efficiency of a reservoir depends on the ratio of storage capacity to annualinflow, age of the reservoir, shape of the reservoir, method of reservoir operation, sediment size and itsdistribution and type and location of outlets. There is no general method available for the determinationof trap efficiency, which takes into account all these factors. What is being used at present is the trapefficiency versus (capacity/inflow) ratio curve proposed by Brune (1953) on the basis of record of 44normally ponded reservoirs in U.S.A., (see Fig. 3.9). On the same figure are also plotted some data fromreservoirs in China, India and South Africa. At present this curve is used in most of the countries fornormally ponded reservoirs.

Sediment Yield ComputationsTheoretically one can use the equations for bed-load and suspended load computations given in ChapterV and determine the bed material load carried by the stream at a given discharge, which will be the sumof bed-load and suspended load. To this should be added an estimated quantity of wash load i.e.,material that is washed into the stream from the drainage basin and which is usually finer than thematerial found in the bed and banks of the stream. If such calculations are made for various discharges,one can prepare the sediment discharge vs water discharge curve from which average annual sedimentdischarge can be computed. However, it may be pointed out that what is obtained from such calculationsis really the sediment transport capacity; and it may be quite different from measured sediment yieldespecially in the upper reaches of the river. Hence this method is inferior to the other two methodsdiscussed above.

3.8 SEDIMENT DELIVERY RATIO

As mentioned earlier, sediment delivery ratio is defined as the ratio between amount of sediment loadpassing a given section during a certain period and the total amount of erosion from the upstreamcatchment during the same period. It can be either expressed as a mere ratio or as a percentage. For plotsof area less than 1.0 km2, the sediment delivery ratio SDR is almost 100 percent, and it decreases as the

Fig. 3.9 Trap efficiency of normally ponded reservoirs

100

Capacity/Inflow

80

60

40

20

0

Tra

pe

ffic

ien

cy,

T(%

)o

0.001 0.01 0.1 1.0 10.0

Reservoirs in ChinaReservoirs in USAReservoirs in S. AfricaReservoirs in India

Envelopes


catchment area increases. SDR for a particular basin is influenced by a wide range of geomorphologicaland environmental factors including the nature, extent and location of sediment sources, relief and slopecharacteristics, drainage pattern and channel conditions, vegetation cover, land use, and soil structure.Basin area is probably the most important variable with which SDR is related. As the catchment areaincreases, the catchment slope as well as the channel gradient decreases and hence there is an increasingopportunity for sediment deposition on flood plain and in channels. Therefore, SDR decreases as Aincreases. Other variables used to study variation of SDR are basin relief, annual runoff and gullydensity. Figure 3.10 shows the band of scatter of variation of SDR with A for some regions in U.S.A.and former U.S.S.R. This figure also shows the curve proposed by Soil Conservation Service of U.S.A.It may be mentioned that for some catchments in China, SDR is found to be 100 percent even up tocatchment area of 1000 km2. This may probably be due to very fine material such as loess that is erodedand transported without any deposition.

It needs to be mentioned that there are some serious difficulties in the estimation of SDR, (seeWalling (1988)). Firstly, correct estimation of gross erosion must be made. This is done by estimatingsheet erosion based on soil loss equation and correcting it to take into account the channel and gullyerosion. This procedure has a certain amount of uncertainty. Another problem in the determination ofSDR is the temporal discontinuity that may be involved in the sediment delivery as pointed out byTricart. Sediment eroded at one location may be temporarily stored and subsequently remobilised manytimes before reaching the outlet of the basin. The third difficulty in relating sediment yield downstreamto the soil erosion upstream is from the fact that the sediment transported by a river represents thematerial derived from a number of sources other than upland erosion, e.g., channel and gully erosionand mass movement etc. Their estimation is very difficult.

A study by FAO (1979) has compared the sediment yield with estimate of contemporary soil erosionrates from a number of African river basins having catchment areas between 150 km2 and 157 400 km2.This comparison indicates that the soil erosion rates are about one order of magnitude greater than thereported sediment yields.

One of the equations, which take into account three variables in estimating SDR, is that by Roehl(1962) which is based on the data from south eastern U.S.A. It is

Fig. 3.10 Relation between SDR and A

Central and easternCorn waste lands W. Iawa, U.S.A.Blackland Prairle, Texsas, U.S.A.Mule creek, Iowa, U.S.A.South-Eastern Piedmant, U.S.A.Missouri basin loess hills, U.S.A.Pasture waste lands, Iowa, U.S.A.USSR

U.S.A.

Enveloping lines

Curve proposed bySCS, U.S.A.

0.01 0.10 1.0 10 100 10001.0

10

100

SD

R

A k2

m

River Morphology58

SDR = 231.7 Steepnessa f0 51

0 23 2 79

.

. .A B...(3.19)

where steepness is defined as the ratio of the maximum difference in elevation in m and basin lengthalong the main waterway in m, A is the catchment area in km2, and B is the bifurcation ratio. Bifurcationratio is the weighted mean ratio of a number of streams of given order to the number of streams in thenext higher order (see Chapter II). For the average value of B = 4.37 for Roehl’s data one gets

SDR = 3 792

0 51

0 23

..

.

Steepnessa fA

...(3.20)

Walling (1988) lists a few more equations developed for different states in U.S.A. and China.A more rational and probably a more rigorous approach to defining and investigating the sediment

delivery characteristics of the drainage basin is provided by the sediment budget concept, originallyadvocated by Dietrich and Dunne (1978) and developed by Lehre (1982) and others. Here varioussediment sources within the basin are defined and the sediment mobilised from these sources is routed toand through the channel system by considering various sinks. A typical representation of such a budgetfor the Coon Creek in U.S.A. for the period 1938–1975 is shown in Fig. 3.11. Walling (1988) hasrepresented similar data for the Lone Tree Creek (California), and the Oka river in U.S.S.R. It was foundthat in all the cases the proportion of the eroded sediment delivered to the basin outlet is very small.However, it may be mentioned that presently the availability of techniques for quantifying the varioussources and sinks involved in budgeting the sediment is very limited, and as such mean SDR vs A curveis often used to obtain erosion rate from observed sediment yield.

Since there is always a gain or loss of sediment storage in the system, the input from slopes andcatchment rarely equals the sediment yield. The sediment storages in the catchment include slopestorage (i.e., colluvium) and stream valley storage (i.e., alluvium). Colluvium when transported bygravity or by water may partly remain colluvium, or become alluvium, or become sediment yield i.e.

Fig. 3.11 Sediment budget for the Coon Creek, Wisconsin (USA) (Area 360 km2)

Sources Sinks

76.7%

11.9%

Upland sheet and tillerosion

11.4%

Upland gullyerosion

Channelerosion

6.7%

Area = 360 km2

Lower main valley

Upper main valley

Upland valleys

Colluvial deposits

25.6%

4.9%

77.0%

55.7%


efflux. Similarly alluvium can be eroded from the channel or flood plain and redeposited as alluvium orbecome sediment yield. Limiting the discussion about valley storage, the most important process invalley storage gain is vertical accretion from overbank stream flow; other important storage zones arealluvial fans of small tributaries and colluvial deposits from adjacent slopes. In sediment budget a steadystate would imply input equals output, and upland erosion equals sediment yield. Since steady state is avery rare, one would like to study gain or loss of sediment from the valley as a function of time, andrelate the nature of variation to the external factors, which influence the gain, or loss of storage; Trimble(1995) has done this and identified five conceptual models of valley storage fluxes, which are shown inFig. 3.12 and briefly described below.

Model-1 (Quasi steady state) is applicable to humid regions where adequate vegetation can developand stabilise the landscape. There will be very little upland erosion and hence very little sediment load.Lateral erosion of one bank would cause lateral deposition on the opposite bank. The perturbations inthe vertical accretion of floodplain would be a few centimetres per millennium at most. This situationexisted in eastern U.S.A. before European settlement.

Fig. 3.12 Conceptual models of valley storage fluxes (Trimble 1995)

Se

dim

en

tg

ain

+

Se

dim

en

tlo

ss

�

Se

dim

en

tlo

ss

�

Se

dim

en

tg

ain

+

Se

dim

en

tg

ain

+

Se

dim

en

tlo

ss

�

Se

dim

en

tlo

ss

�

Se

dim

en

tg

ain

+

Se

dim

en

tg

ain

+

Se

dim

en

tlo

ss

�

Vertical accretion

Vertical accretion

Vertical erosion

Lateral erosion

Paving of channels

Moderate control

Uncontrolled

Colluviumaccretion

Mass movements

Flushing 20-100 yrs

20 yrs

100 yrs

100 yrs

100 yrsLateralerosion

Model-1 (Quasi-steady)

Model-1

Steady-state

(Vertical accretionwith lateral erosion)

Model-3 (Valley trenching)

Model-4 (Urban stream)

Model-5 (High energyinstability, mountainsand arid streams)

River Morphology60

Model-2 (Perturbation of humid area quasi steady state) is applicable in humid area where sedimentload in excess of transport capacity is generated by strong climatic or natural forces (e.g., mining orlarge construction activity). This causes vertical accretion of floodplain and the channel. When theactivity in the upland area stops, this deposited sediment is gradually eroded and transporteddownstream. This removal of deposited sediment shows exponential decrease. If the sediment supplyfrom the upland is low, lateral erosion of channel may take place later.

Model–3 (Valley trenching and arroyo cutting) is applicable when the climate or human inducedperturbations cause an incremental increase in discharge greater than incremental increase in sedimentdischarge. This can result in trenching or gullying. The example of this model is found in semi arid southwestern U.S.A. In such areas the fragile grasslands were overgrazed, the vegetation was thinneddrastically and the soil compacted resulting in greater stream flows and arroyo cutting.

In Model–4 (Urban streams), a brief rapid increase in erosion occurs while urbanisation inunderway, but when it is stabilised due to increasing imperviousness of the area the runoff increases anderosion decreases. This initiates arroyo cutting. In order to save valuable land, if arroyos are stabilisedby paving the Model-4 results, otherwise Model-3 results.

Model-5 (High energy instability, mounting and arid streams) is applicable to streams with a verynarrow floodplain and very steep valley sides. The sediment budget in this case is much more episodicthan cyclic in nature. Net storage gain can come from vertical accretion coming from fans of smalltributaries and mass movement from valley sides. Sediment loss comes from large events, which flushsediment downstream. This model shows a period of accretion followed by flushing events, and theprocess is repeated at uneven time intervals.

Identifying the sediment budget model enhances our understanding of the fluvial processes workingin the system and throws light on the magnitude and time scales of sediment storage fluxes under thegiven environmental conditions and natural and man made perturbations.

3.9 PROCESS BASED MODELLING OF EROSION

Even though USLE summarises a vast body of regionally derived data and expresses it in the equationform, the researchers are aware of its empirical nature and its limitation that it is not universallyapplicable. Further, it is also recognised that USLE does not explicitly represent the processes involvedin soil erosion. As a result USLE gives only an average annual soil loss. Therefore, several attemptshave been made to develop methodology for prediction of erosion by modelling the basic processesinvolved. These are discussed by Rose (1988).

Overland FlowConsider flow on a planar land surface on a slope. Let L be the length of slope. Then the sediment fluxflowing out of a unit width is

qs = q C ...(3.21)

where qs is in mass of sediment/time, width, q is volume rate of water in m3/s m, and C is the sedimentconcentration in oven dry mass of sediment per volume of suspension. One must now obtain expressionfor overland flow q. One can write


R = P – I ...(3.22)

where R is the excess rainfall, P is the precipitation and I is the rate of infiltration all being function oftime. If Q represents runoff per unit area

Q = q/(L) ...(3.23)

One can then see that R = Q ...(3.24)However, if L is large and R varies with time, it will be seen that changes in Q will lag behind those

in R. Thus in general R ¹ Q. It can be shown that

R » Q + Kp ¶

¶

Q

t...(3.25)

where Kp depends on length, slope and roughness of the plane, Q, and on whether the overland flow islaminar or turbulent. The flux q(x) at any distance is given by

q(x) = Qx ...(3.26)

Erosion and Deposition ProcessesThe following three processes affect the sediment concentration:

1. Rainfall detachment in which raindrops splash sediment from the soil surface into the water ofoverland flow.

2. Sediment deposition, which is the result of sediment settling out under the action of gravity; and3. Entrainment of sediment from the soil surface in which sediment is picked up from rills, inter-

rills and in sheet flow.Rate of raindrop detachment e is expressed as

e = a Ce P ...(3.27)

where e is in kg/m2s, a is the measure of detachability of soil by rainfall rate P and Ce is the fraction ofsoil surface exposed to the rain drops. The rate of sediment deposition di for a given size class i of fallvelocity wi is expressed as

di = wi Ci ...(3.28)

where Ci is the sediment concentration of size class i. The rate of sediment entrainment can be related toexcess stream power over its critical value. Let the rate of sediment entrainment for a given size class begi. Then conservation of mass principle applied to a given size class i yields

¶

¶x(qCi) +

¶

¶t(DCi) = ei + gi – di ...(3.29)

where D is the depth of overland flow at any time. Making certain approximations, Eq. (3.29) can bereduced to ordinary first order differential equation, which can be solved to yield

C(L, t) = ac p

QIe

iIF

HGIKJ =S 1(gi) + r f gSKCg (1 – x*/L) ...(3.30)

River Morphology62

for L > xi . Here I is the number of sediment class ranges, gi = 1+FHG

IKJ

w i

Q rf is mass density of water, S is

the land slope, K = (1 + 0.2677h), where h is the efficiency of net sediment entrainment and transport, Cris the fraction of soil surface unprotected from entrainment by overland flow, and x* is the distance downslope from the top of the plane beyond which sediment entrainment commences. The accumulated massof sediment Ms from a plane of width W is thus given by

Ms = WL0

t

z R C(L, t)QDt ...(3.31)

where tR is the duration of runoff. Equation (3.30) can be written as

C (L, t) = A + B ...(3.32)

where A is the net contribution to sediment concentration of rainfall detachment over deposition, and Bis the net contribution of entrainment over deposition. Assuming A to be negligible and taking time

average values of x*, Q and h, as x Q* , and h, C (L) can be expressed as

C(L) = 2700ShCr 1-FHIK

x

L* ...(3.33)

Dynamic Simulation ModelsA more elaborate model is given by Negev (1969), which is commonly known as Stanford SedimentModel. In this model, the rainfall impinging on the land surface is divided into two parts, that falling onthe impervious surfaces and that falling on the pervious surfaces. The sediment supply from impervioussurface is determined by a power function relationship taking hourly rainfall as the independentvariable. Rain falling on the soil is assumed to loosen the material by raindrop splash. This loosenedmaterial, called soil splash is then considered as potential sediment for the stream. If overland flowoccurs, as computed by Stanford Watershed Model, then all the soil splash material in previous storagesis transported together with the current soil splash material. Overland flow is also used to compute therate of rill and gully erosion using power function relationship. Rill and gully erosion is then dividedinto inter load and bed material storage.

The input to this model consists of hourly and daily recorded rainfall, daily recorded flow andsediment load, hourly overland flow, a translation histogram for routing the sediment through the streamsystem, information on the sediment rating curve for use in adjusting the material assigned to inter loadand bed material load from rill and gully process, and set of parameters and exponents for use in thevarious power functions by which the sediment erosion processes are estimated. These are adjustedduring the runs to calibrate the model. Use of this model to the Napa river, St. Helena, California(U.S.A.) and the river Clyde in Scotland has given good results.

Other dynamic models developed include the one developed by Simons et al., (1975). The variousprocesses modelled in this program include, interception, infiltration, overland flow from rainfallexcess, sediment detachment due to raindrop impact, sheet erosion by overland flow, channel erosionand the routing of water and sediment through the channel system. The sediment detachment iscalculated during a specific time increment as a function of rainfall intensity and provision is made for


calculating the detachment of different size fractions and for the development of surface armouring.Sediment supply for the transport depends on the initial depth of loose soil remaining from the previousstorms, the amount of soil detachment by rain drop impact and the amount of soil detached by surfacerunoff. Sediment transported by overland flow is calculated using Meyer-Peter and Müller’s formula forbed-load transport. Similar procedure is used to route the wash load and the bed material load throughthe channel system using continuity equation to determine occurrence of aggradation or degradation.Figure 3.13 shows flow chart for this model. It may be mentioned that in recent times several suchmodels have been developed. Morgan et al. (1990) describe the European Soil Erosion Model(EUROSEM) developed as a collaborative project by seven European countries.

Two more models can be briefly discussed. Kothyari et al. (1997) have developed a method forestimation of temporal variation of sediment yield for a single storm in small catchments. The method isbased on numerical solution of kinematic wave equation for simulation of overland flow, continuityequation for sediment and expressions for sediment detachment and transport. The model is calibratedand verified using twelve experimental catchments ranging in size from 0.002 km2 to 92.5 km2. Forsingle storm events sediment yield varied from 0.003 tons to 800 tons.

Julien and Rojas (2002) have discussed a physically based model simulating hydrologic response ofa watershed to distributed rainfall field, considering time-dependent processes such as precipitation,interception, infiltration, surface runoff and channel routing, and upland erosion, transport andsedimentation, the model predicts, flood and sediment load variations with time. The model was appliedto 21 km2 Goodwin Creek catchment in U.S.A.

Fig. 3.13 Flow chart for water and sediment routing model developed at Colorado State University (Simons et al. 1975)

Soil detachment by overlandflow considering sizewisetransport capacity and supplyof loose soil

Bed materialload hydrograph

Total sedimentyield

Wash loadhydrograph

Channel flowwash loadrouting

Loose soil erosionOverland flowbed materialrouting

Soil detachment bychannel erosion

Channel flow

data

Overland flowbed materialrouting

Loose soil storageOverland flowwash loadrouting

Overland flowrouting

Overlandflow

data

Waterrouting

Sizewise soil detachment byraindrop impact with provisionfor amounting

Loose soilstorage

Antecedentcharacteristics

Basincharacteristics

Stormcharacteristics

River Morphology64

Stochastic ModelsLack of detailed long duration record of erosion rates has hampered the application of various stochasticand time series modelling procedures to the erosion process. Yet some attempts have been made in theapplication of Autoregressive Moving Average (ARMA) Models to the records of Suspended Sedimentconcentration. Sharma et al. (1979) describe the use of a simple system model of this type to model themonthly and daily sediment yield of several catchments in Ontario, Canada. The model used to describedaily erosion rates explained 95 percent of the variation in the erosion process of the Thames river atIngersol, while the monthly model accounted for more than 81 percent of short-term values of sedimentconcentration recorded during individual storm events.

3.10 EROSION RATES FROM INDIAN CATCHMENTS

In India the approaches used for prediction of erosion rates have been essentially empirical involvingregression method. This is primarily so because of the lack of availability of extensive data needed foruse of physically based and simulation models. Earlier Khosla (1953) analysed the then available datafrom Indian reservoirs and reservoirs from abroad and found that the annual sediment yield in Mm3 isproportional to A0.72 where A is the catchment area in km2. However, Garde and Kothyari (1987) foundlarge variations from this relationship when it was tested with recently collected Indian data. DhruvaNarayan et al. (1983) used the data from seventeen catchments in India and obtained the followingrelations for annual sediment yield T1 in metric tons.

T1 = 5.5 + 1.1 Q ...(3.34)

where Q is the annual runoff in M ham. This equation was further modified to

T1 = 5.3 + 12.7 QW1 ...(3.35)

where W1 = T1/A, A being in M ha. Average value of W1 was found to be 1.25 M tons/M ha. Anotherrelationship proposed by them involved use of EI30.

T1 = (0.342 ́10–6)A0.84 (EI30)1.65 ...(3.36)

where EI30 is the product of average annual value of the sum of maximum 30 minute rainfall intensity incm/hr and kinetic energy value E given by

E = 210 + 89 log I30 ...(3.37)

E being in tons/ha m. However, these equations need to be verified with additional data before thesecan be used with confidence.

By far the most detailed analysis of Indian data has been carried out by Garde and Kothyari (1987,1990). They analysed the average annual sediment yield data from 50 catchments in India having areasvarying from 43 km2 to 83 880 km2. These data were obtained from the surveys of small, medium andlarge reservoirs with sedimentation period of at least ten years. Analysis of data indicated that theaverage annual erosion rate Sa in cm is a function of average annual rainfall P in cm, the average

catchment slope defined as SA

n=

11S AiSi, the drainage density D in km–1, the ratio (Pmax /P) where Pmax

is the average monthly maximum rainfall in cm, and the erosion factor Fe which gives an integratedeffect of vegetation on erosion. The erosion factor Fe was defined as


Fe = 1

A[0.8AA + 0.6AG + 0.3AF + 0.1AW] ...(3.38)

where AA is the arable area, AG scrub and grass covered area, AF is protected forest area, and AW is thewaste land area all in km2. A map showing lines of constant Fe values was prepared from available dataand this is shown as Fig. 3.14. The range of variables used by Garde and Kothyari are given below:

P 63.77 cm – 381.11 cm Pmax9.0 cm – 108.3 cm

Fe 0.28 – 1.00 S 0.001 – 0.200A 43 km2 – 82 880 km2 D 0.002 km–1 – 0.31 km–1

The regression analysis of the data gave the following equation for Sa

Sa = 0.02 P0.60 Fe1.70 S0.25 Dd

0.10 (Pmax/P)0.19 ...(3.39)

This relationship was then used on ungauged catchments for which all other data except Sa valueswere available. Sa was then computed from which sediment yield was expressed in tons/km2/year. Thususing data from 154 catchments an iso-erosion rate map was prepared which is shown in Fig. 3.15. It canbe seen that the erosion rates in India vary from about 350 tons/km2/year to 2500 tons/km2/year. Higherosion rates in North eastern region, parts of U.P., Bihar and Punjab, and in certain areas in AndhraPradesh are partly due to high rainfall in these regions and partly due to geologic conditions and landusages.

Considering that out of the variables affecting the erosion rate, only the annual rainfall changesfrom year to year, the following equation was proposed by Garde and Kothyari (1987) for the estimationof annual erosion rates.

Pa = 0.02Pam Fe

1.70 S–0.25 Dd0.10(Pmax/P)0.19 ...(3.40)

where Pa is the annual precipitation in cm. Here m is the exponent, which was found to be related tocoefficient of variation of annual precipitation. It may be seen from comparing Eqs. (3.39) and (3.40)that

P0.6 = 1

n

i

n

å Paim

where n is the number of years. Analysis of rainfall data from 100 rainfall stations indicated that ascoefficient of variation changed from 0.1 to 0.70, m, value of the exponent increased from 0.600 to0.607. This variation is shown in the following table:

Cv 0.10 0.20 0.30 0.40 0.50 0.70m in Eq. (3.40) 0.600 0.601 0.602 0.603 0.605 0.607

Thus for annual sediment yield computation Eq. 3.40 with table for m can be utilised. For futureyear wise prediction of sediment yield, one must generate annual rainfall series for known P and Cv andthen compute the sediment yield. The annual series in India are found to follow normal distribution. Itmay be mentioned that with the passage of time land use pattern as well as extent of forest and othervegetation is bound to change and hence Fig. 3.11 need to be modified at regular time intervals and soalso Fig. 3.12. However Eqs. (3.39) and (3.40) will not change.

River Morphology66

Fig. 3.14 Lines of constant Fe superimposed on the geological map of India (Garde and Kothyari 1987)

Geologic boundaries

Iso-erosion factor lines

Other ign ous andmetamorphic rocks

e

Khondalite

Unclassified crystallines

Sedimentary consolidated

Metamorphic (Schists)

Igneous intrusive rocks

Sedimentary unconsolidated(Recent alluviums)

Notations

SriLanka

0.5

0.45

0.55

0.55

0.55

0.54

0.45

0.54

0.45

0.5 0.50.5

0.60.6

0.6

0.6 0.6

0.6

0.55 0.55

0.55

0.55

0.50.55

0.6

0.6

0.55

0.5

0.4

0.4

Bangladesh

Bhutan

Nepal

0.4


Fig. 3.15 Iso-erosion rate lines in tons/km2 yr (Garde and Kothyari 1987)

River Morphology68

References

Blakely, B.D., Coyle, J.J. and Steele, J.G. (1955) Erosion on Cultivated Land. Soil- The 1957 USDA Year Book ofAgriculture.

Brown, L.R. (1984) Conserving Soils. In State of the World 1984, (Ed. Brown L.R.) Norton, New York.

Bruk, S. (1985) Methods of Computing Sedimentation in Lakes and Reservoirs. A Contribution to the IHP-IIProject, A. 2.6.1. Panel, UNESCO, Paris, pp. 224.

Brune, G.M. (1953) Trap Efficiency of Reservoirs. Trans. AGU, Vol. 34, No. 3, July, pp. 407-418.

Chatterjee, P.K., Bathija, T.S. and Sangeet, S. (2001) Methods of Reservoir Sedimentation surveys. Proc. OfC.B.I.P. Seminar on Reservoir Sedimentation, Ooty, Tamil Nadu, India, pp. 33-41.

Dekov, A.P. and Mozzherin, V.I. (1984) Eroziya I Stok Nanosov na Zemle. Izadatolstvo Karzanskogo Universiteta.

Dendy, F.E. (1968) Sedimentation in Nation’s Reservoirs. Jour. Soil and Water Conservation, Vol. 23, No. 4.

Dietrich, W.B. and Dunne, T. (1978) Sediment Budget for a Small Catchment in Mountain Terrain. Zeitschrift furGeomorphologie. Supplementband, 29, pp. 191-206.

Dhruva Narayana and Ram Babu (1983) Estimates of soil Erosion from India. JIDD, Proc. ASCE, Vol. 109, No. 4.

Ellison, W.D. (1945) Some Effects of Rainfall and Surface on Erosion and Infiltration. Trans. AGU, Vol. 26, No. 3.

El-Swaify, S.A., Dangler, E.W. and Armstrong, C.L., (1982) Soil Erosion by Water in the Tropics. University ofHawaii Research Extension Series No. 024.

Elwell, H.A. (1980) Design of Safe Rotational Systems. Department of Conservation and Extension, Harare(Zimbabwe).

Elwell, H.A. and Stocking M.A. (1974) Rainfall Parameter and a Cover Model to Predict Runoff and Soil Lossfrom Grazing Trails in the Rhodesian Sandveld. Proc. of the Grassland Society of South Africa, Vol. 9.

FAO, U.N. (1977) Assessing Soil Degradation. Soils Bulletin 34, Rome, Italy.

FAO, U.N. (1979) A Provisional Methodology of Soil Degradation Assessment, Rome, Italy.

Foster, G.R. (1988) Modelling Soil Erosion and Sediment Yield. In Soil Erosion Research Methods (Ed. Lal R.)Soil Water Conservation Society, Ankeny, Iowa (U.S.A.), pp. 97-118.

Fournier, F. (1949) Les Facteurs Climatiques de l ‘Erosion du Sol. Assoc. Geo’graphes Francais, Bull. Vol. 203.

Fournier, F. (1960) Climat et Erosion: la Relation entre l ‘Erosion du Sol par l ‘Eau et les PrecipitationsAtmospheriques. Presses Universitaires de France, Paris.

Garde, R.J. and Dattatri, J. (1961) Investigation of the Total Sediment discharge of Alluvial Streams. RoorkeeUniversity of Research Journal (India), Vol. No. pp. 65-78.

Garde, R.J. and Kothyari U.C. (1987) Sediment Yield Estimation. Journal of Irrigation and Power (India), CBIP,Vol. 44, No. 3.

Garde, R.J. and Kothyari U.C. (1990) Erosion Prediction Models for Large Catchments. International Symposiumon Water Erosion, Sedimentation and Resources Conservation. CSWCRTI, Dehradun, Oct. pp 89-102

GARMIN (2000) G.P.S. Guide for Beginners. Garmin Intl. Inc. Olathe, Kansas (U.S.A.)

Heede, B.H. (1975) Stages of Development of Gullies in the West. Proc. of the Sediment Yield Workshop, USDA,Oxford (Mississippi), ARS-S-40.

Holeman, J.N. (1968) The Sediment Yield of Major Rivers of the World. W.R. Research, Vol. 4, pp. 737-747.

Hudson, N.W. (1965) The Influence of Rainfall on Mechanics of Soil Erosion with Particular Reference toNorthern Rhodesia. M.S. Thesis, University of Cape Town, South Africa.

Janda, T. Dunne and Swanson, D.N. General Tech. Report PNW 141, Forest Service USDA Portland, Oregon,U.S.A.


Julien, P. and Rojas, R. (2002) Computer Modeling of Upland Erosion. Proc. Of 12 APD Intl. Congress,Singapore, Vol. 1, pp. 475-483.

Kinnell, P.I.A. (1973) The Problem of Assessing the Erosive Power of Rainfall from Meteorological Observations.Proc. Soil Science Society of America, Vol. 37, pp. 617-621.

Khosla, A.N. (1953) Silting of Reservoirs. CBIP Publication No. 51, New Delhi (India).

Kothyari, U.C., Tiwari, A.K. and Singh, R. (1997) Estimation of Temporal Variation of Sediment Yield from SmallCatchments through the Kinematic Method. Jour. Of Hydrology, Vol. 203, pp. 39-57.

Kuenen, P.H. (1950) Marine Geology. John Wiley and Sons, Inc., New York.

Lane, E.W. and Borland, W.M. (1951) Estimating Bed Load. Trans. AGU, Vol. 32, No. 1, February.

Langbein, W.B. and Schumm, S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans.AGU, Vol. 39.

Laws, J.O. and Parsons, D.A. (1943) The Relation of Raindrop Size to Intensity. Trans. AGU., Vol. 24.

Lehre, A.K. (1982) Sediment Budget in a Small Coast Range Drainage Basin in North Central California. InSediment Budget and Routing in Forest Drainage Basins (Ed Swanson, R.J.)

Leopold, L.B. and Wolman, M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman andCo., San Francisco, U.S.A.

Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Steam Channel and Some PhysiographicImplications. USGS Professional Paper 252.

Mackenzie, F.T. and Garrel, R.M. (1966) Chemical Mass Balance Between Rivers and Oceans. Am. Jour. Sci.,Vol. 264, pp. 507-525.

McCool, D.K. and Rendard, K.G. (1990) The Revised Universal Soil Loss Equation. Proc. of Int. Symposium onWater Erosion Sedimentation and Resource conservation, Dehradun (India), Oct., pp. 60-70.

Meyer, L.D. and Mannering, J.V. (1967) Tillage and Land Modification for Water Erosion Control. ASAE-ASA-SCSA Tillage Conference Proc. pp. 58-62.

Miller, C.R. (1953) Determination of Unit Weight of Sediment for Use in Sediment Volume Computations. USBR,Denver, U.S.A..

Milliman, J.D. and Meade, R.H. (1983) Worldwide Delivery of River Sediments to Oceans. Jour. Geology Vol. 91,pp. 1-21.

Morgan, R.P.C. (1979) Soil Erosion. Longman Group Ltd., London.

Morgan, R.P.C., Quinton, J.N. and Rikson, R.J. (1990) Structure of Soil Erosion Prediction Model for theEuropean Community. International Symposium on Water Erosion, Sedimentation and ResourceConservation - CSWCRTI, Dehradun, Oct., pp. 49-59.

Mutchler, C.K. (1971) Splash Production by Water Drop Impact. Water Resources Research, Vol. 7.

Mutchler, C.K. and Young, R.A. (1975) Soil Detachment by Raindrops. Proc. of the Sediment Yield Workshop,USDA, Oxford (Mississippi), U.S.A., ARS-S-40, pp. 113-117.

Negev, M. (1969) A Sediment Model on Digital Computer. Stanford University, U.S.A., Civil Engg. Deptt., Tech.Rep. No. 76.

Pechinov, D. (1959) Vodna Eroziya I To’rd Ottok. Priroda, Vol. 8, pp. 49-52.

Piest R.F., Bradford, J.M. and Spomer, R.G. (1975) Mechanism of Erosion and Sediment Movement from Gullies.Proc. of the Sediment Yield Workshop. USDA, Oxford, Mississippi, ARS-S-40, pp. 162-176.

Robinson, A.R. (1977) Relationship Between Soil Erosion and Sediment Delivery. Symposium on Erosion andSolid Matter Transport in Inland Waters, IASH, No. 122, July, pp. 159-167.

Roehl, J.E. (1963) Sediment Source Areas, Delivery Areas and Influencing Morphological Factors. IASHPublication No. 59.

River Morphology70

Rose, C.W. (1960) Soil Detachment Caused by Rainfall. Soil Science, Vol. 89, pp. 28-35.

Rose, C.W. (1988) Research Progress on Soil Erosion Processes and a Basis for Soil Conservation Practices. InSoil Erosion Research Methods (Ed. R. Lal. ) Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp.119-140.

Schumm, S.A. (1963) Disparity Between Present Rates of Denudation and Orogeny. U.S. Geological Survey,Professional Pape 454-H, pp. 13

Schumm, S.A. (1977) The Fluvial System A Wiley Interscience Publication, John Wiley and Sons Inc.

Sharma, T.C., Hines, W.G.S. and Dickinson, W.T. (1979) Input-Output Model for Runoff Sediment YieldProcesses. J. of Hydrology, Vol. 40.

Simons, D.B., Li, R.M. and Stevens, M.A. (1975) Development of Models for Predicting Water and SedimentRouting and Sediment Yield from Storms on Small Watersheds. CSU Report No. CER-74-75, DBS-RML-MAS-24.

TCPSM (1969) Sediment Measurement Techniques: A Fluvial Sediment Task Force Committee on thePreparation of Sediment Manual Report, JHD, Proc. ASCE. Vol. 95, No. HY-5, September.

Tiwari, A.K. (1993) Temporal variation of Sediment Yield from Small Catchments. Ph.D Thesis, University ofRoorkee.

Tricart, J. (1962) Les Discontinuities dan les Phenomenes d’ Erosion. Int. Assoc. Sci. Hydro., Vol. 59.

Trimble, S.W. (1995) Catchment Sediment Budgets and Change. In chaning River channels (Eds. Gruznell, A andPetts, G.) John Wiley and Sons, Chicester, pp. 210-215.

U.N.E.P. (1980) Annual Review. United Nations Environmental Program, Nairobi, Kenya.

U.S. Govt. and IIHR (1943) A Study of Measurement and Analysis of Sediment Loads in Streams. Density ofSediments Deposited in Reservoirs, Rep. No. 9.

U.S.S.R. National Committee for I.H.D. (1974) Mirovoi Vodnyi Balans I Vodnye Resursy Zemli. Gidrometerozat,Leningrad.

Van Rijn, L.C. (1982) Sediment Transport, Part II: Suspended Load Transport. JHE, Proc. ASCE, Vol. 110, No. 11,November, pp. 1613-1641.

Walling, D.E. (1988) Measuring Sediment Yield from River Basin In Soil Erosion Research Methods (Ed) R.Lal.Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp. 39-74.

Walling, D.E. and Webb, B.W. (1983) Patterns of Sediment Yield. In Background to Palaeohydrology (Ed GregoryK.J.) John Wiley and Sons, Chichester, U.K., pp. 69-100.

Williams, M.A. (1969) Prediction of Rainfall Splash Erosion in the Seasonaly Wet Tropics. Nature, Vol. 222, pp.763-765.

Wischmeier, W.H. and Smith, D.D. (1958) Rainfall Energy and its Relationship to Soil Loss. Trans. AGU, Vol. 39,pp. 285-291.

Wischmeier, W.H. and Smith, D.D. (1962) Soil Loss Estimation as a Tool in Water Management Planning. Int.Assoc. For Sci. Hydro. Pub. No.59, pp. 148-159.

Wischmeier, W.H. and Smith, D.D. (1978) Predicting Rainfall Erosion Losses: A Guide to Conservation Planning.USDA Agricultural Handbook No. 537, pp. 58.

Wischmeier, W.H., Jhonson, C.B. and Cross, B.V. (1971) A Soil Erodibility Monograph for Farmland andConstruction Sites. Jour. Soil and Water Conservation, Vol. 26, pp. 189-192.

Young, A. (1969) Present Rate of Land Erosion. Nature, Vol. 224, pp. 851-852.

4C H A P T E R

Fluvial Morphology

4.1 GEOMORPHOLOGY AND FLUVIAL MORPHOLOGY

The name geomorphology originates from the Greek terms geo meaning earth, morphe meaning formand logos meaning discourse. Hence, geomorphology is the science of the origin and evolution oftopographic features caused by physical and chemical processes operating at or near the earth’s surface.

The landforms may result or may be modified by denudational processes, depositional processes ora combination of the two. Denudational or degradational processes are sometimes called exogenousprocesses while the depositional processes are known as endogenous processes. Together they areknown as geomorphic processes. Among the agents and processes which shape the configuration ofearth’s surface, the important ones are: (i) Running water, (ii) Glaciers, (iii) Ground water, (iv) Wavesand currents, (v) Wind, (vi) Weathering, (vii) Volcanism and (viii) Diastrophism.

Running water is that part of rainfall or snows melt which flows on earth’s surface after infiltrationrequirement is satisfied; this is known as surface runoff. It collects in streams, which continually erodethe land and deposit the material elsewhere. Landforms produced by glaciers are markedly differentbecause glaciers move slowly and are capable of carrying large quantities of coarse material with them.Groundwater, while in contact with rocks, promotes solution and other types of chemical weathering.This leads to unique landforms, especially in the areas of rapidly soluble rocks, such as limestone.

Waves beating against the shorelines of seas and large lakes modify shorelines by their erosiveaction and subsequent deposition of the eroded material elsewhere. In arid and semi-arid regions and inregions having abundant supply of loose sand, wind is an effective agent of erosion and deposition.Weathering action loosens the rocks and breaks them into smaller pieces, which can be transported bydifferent agencies. Mechanical weathering produces angular hill-slopes whereas chemical weatheringpromotes smooth rounded slopes. Volcanic eruptions produce distinctive landforms such as volcaniccones and lava flows. A sudden change in land surface or part of it due to tensile or compressive forcesis known as diastrophism. It can be seen that volcanism and diastrophism are endogenous processes.

Since the word fluvial means produced by rivers, the term fluvial morphology can be defined as ascience dealing with forms as those produced by river action. Fluvial morphology is of great interest to

River Morphology72

hydraulic engineers, geologists, geo-morphologists, geographers and environmental engineers, sincemany of the complex problems they have to deal with are due to the form of the streams created by theerosion, transportation and deposition of sediment carried by them.

Even though several scientists have contributed to the development of the science of geo-morphology, W.M. Davis in the early 20th century was primarily responsible for synthesising many ofthe earlier developments and presenting them in the form of a unified system for the study of landforms.Certain basic concepts developed by geo-morphologists are of significance to hydraulic engineers andthese are discussed here in brief.

4.2 GEOMORPHIC CYCLE (OR CYCLE OF EROSION)

The basic idea underlying the concept of geomorphic cycle or the cycle of erosion is that the topographyof a stable region evolves through a continuous sequence of landforms having distinctive characteristicsat successive stages of development. The process starts with the initial uplift of landmass throughdiastrophism. This initial uplift is tacitly assumed to take place without appreciable erosion. Since inmost regions the current uplift rates are much greater than the denudation rates, the above assumption isa reasonable one. Later the cycle of erosion proceeds under prolonged tectonic stability producingvarious types of topography, which are characteristic of the various lengths of time for which the waterhas acted on it; the material is continually eroded from the land surface and deposited in the sea. Theelevation of the land surface is thus gradually lowered and land surface flattened until after a very longtime the whole surface is reduced to a gently sloping plain called peneplain. This is the end of the cycleand an upheaval will start a new cycle (Davis 1909, Lane 1955). Davis introduced the word peneplain todescribe landscapes that have undergone long continued weathering and erosion in humid climate. Inthe geographical context the word plain connotes a surface of very low relief. Realising that the ultimatebase level is the limit of sub-aerial erosion, which like a mathematical limit, may be approachedasymptotically but never reached, Davis prefixed the word “plain” by the Latin word “pene” meaningalmost. This peneplain is a surface of regional extent, resulting from long continued fluvial erosion.

Another concept introduced by the geo-morphologists and which is useful in discussion of fluvialmorphology in general and the cycle of erosion in particular is that of base level first formulated byPowell in 1875. In fact he wrote (Esterbrook 1969),

“We may consider the level of sea to be a grand base level, below which the dry lands cannot beeroded; but we may also have, for local and temporary purposes, other base levels of erosion, which arethe levels of the beds of the principal streams which carry away the products of erosion. The base levelwould in fact, be an imaginary surface inclining slightly in all parts towards the lower end of principalstream”.

Powell’s definition of base level, thus includes three basic ideas; namely(i) The ultimate limit of sub-aerial erosion of the continent is the base level of the sea.

(ii) Locally resistant rocks in the path of the stream, lakes in the stream path, or other obstacles canproduce temporary base level.

(iii) Tributaries may not erode below that of the main stream, and since mainstream will alwayshave some slope, the base level need not always be a flat surface.

Fluvial Morphology 73

Thus, sea level may be considered as a general, permanent base level which fluctuates from time totime but which remains normally within a range of a few metres. Local base levels such as rock outcropsand lakes are temporary; changes in base level cause changes in the mainstream, tributaries and sub-tributaries.

The geomorphic cycle is subdivided into parts of unequal duration, each part being characterised bythe degree and the variety of relief and by the rate of change, as well as by the amount of change that hasbeen accomplished since the initiation of the cycle. The various stages in the geomorphic cycle aredescribed in terms of age beginning with youth, which passes into maturity and then into old age. Thetopographic features of the first stage are spoken of as young or youthful, later ones as mature and thoseof the last stage as old, with further subdivisions when desirable such as, for example, early and latematurity. It may also be mentioned that each of these stages need not be of the same duration. Davisconsidered youth a relatively brief phase and thought old age involved a tremendously longer period oftime than either of the two stages.

It should also be noted that the blending of types of topographies is the rule rather than an exception.Thus in a region of general youthful characteristics, some streams and valleys may be mature. Similarlyin mature plateaus there will be some youthful streams actively engaged in deepening their valleys. Thespan of time involved in a complete transformation of landscape may run into millions of years.Consequently during a period of scientific observation the changes in topography may be unnoticeable.

Youthful TopographyYouthful topography is characterised by comparatively few streams but usually they have highgradients. Drainage may be poor with lakes and swamps on the divides between the streams. Streamsflow in deep walled canyons or V-shaped valleys; these will be shallow or deep depending on the heightof the region above sea level. Usually streams are actively engaged in cutting their valleys deeper.Youthful topography also possesses rapids and falls. There will be general lack of development of floodplain except along trunk streams.

Mature TopographyWhen the region advances from youth to maturity in the cycle of erosion, the drainage is betterdeveloped with the number of streams increasing. The streams cut their valleys to lowermost levels,their tributaries are well established and lakes, swamps and rapids disappear. Meanders may exist. Sincestreams start eroding laterally, valleys are flat but the widths of the valley floors do not greatly exceedthe width of the meander belt. If streams flow through homogenous rocks, tree-like drainage patternknown as dendritic pattern is developed during maturity of topography. In the regions of folded beds thedrainage pattern is rectangular i.e. tributaries meet their main streams at right angles.

Old TopographyIn old topography, all main streams have very flat slope and are meandering back and forth over theirflood plains. Valleys are extremely broad and slope gently both laterally and longitudinally; valleywidths are considerably greater than the widths of meander belts. Their velocities are low andtransporting power for sediment very limited. The whole landscape is gently rolling. Occasionallyerosional remnants stand above the general land surface. Lakes, swamps and marshes may be presentbut they are on flood plains and not in inter-stream tracts as in youth. The topography tends towards the

River Morphology74

ultimate form namely peneplain which is a large land area of low relief that has been reduced to nearlybase level by the combined action of weathering and streams. As a rule, surfaces of peneplains are notflat but gently rolling with low hills standing island-like erosion remnants in the general surface of lands(Worcester 1948).

Geomorphic cycle discussed above is for humid region. An arid region is deficient in rainfall andalso in vegetation. The groundwater table is also low. As a result deep subsurface chemical weatheringis light, but surface chemical weathering does take place. Strong winds that blow carry dust fromwherever it is found. As a result of these differences, the landforms obtained in the youth, mature andold ages in arid region are different from those in humid region. Worcester (1948) has discussed these indetail.

4.3 REJUVENATION OF EROSION CYCLE

Once initiated the erosion cycle does not always proceed to completion without interruption. Worldwidechanges in sea level, tectonic uplifts of the earth’s crust and climatic changes are the three principalcauses of rejuvenation. Changes in sea level are brought about by subsidence of portions of oceanbasins. The lowering of base level will cause streams to cut into the valley and form incised channelswhereas rise of sea levels will force streams to deposit their sediment load in channels and aggrade.Tectonic down warping or uplifting of land produces the same effects as lowering or rising of sea level.Changes in morphology due to change in climate are discussed in detail by Schumm (1969). Climaticchanges affect the precipitation, which in turn affects the vegetation and surface runoff. The latter two,in turn, change the discharge in the stream, erosion pattern and sediment load. Thus climatic changesinduce significant changes in drainage pattern and stream behaviour. In general, typical topographyformed due to rejuvenation includes uplifted peneplains, incised meanders, stream terraces and hangingvalleys. If rejuvenation takes place in this manner, the first erosion cycle remains incomplete and a newone starts. It may happen that before the new cycle completes, rejuvenation may be effected. It is,therefore, believed that partial erosion cycles may be more common than the complete ones.

4.4 CRITICISM OF GEOMORPHIC CYCLE

For the purpose of exposition, Davis made several simplifying assumptions, which have become thetarget of critical comment (Rice 1977); one of the most important was the separation of uplift anderosion into two distinct episodes. He thereby envisaged initial uplift taking place without appreciableerosion and then erosion under prolonged tectonic stability. However, current rates of uplift so exceedthose for denudation that it is clear erosion does not normally constitute a limit of continued surfaceelevation.

It is also argued, as partly discussed under rejuvenation, that stability is unlikely to stay long enoughto permit reduction of an upland area to peneplain because of persistent tectonic activity. It is thusargued that the only stage in the Davisian cycle not represented on the earth’s surface at the present dayis the peneplain.

It is also worth recalling that periodicity of major climatic oscillations during the Pleistocene epoch(see Sect. 4.6) seem to have been of the order of 105 years. On the basis of known denudation rates thelength of time required for an erosion cycle to run its full course cannot be less than 106 years. This


means that any area will almost certainly have experienced many climatic fluctuations in the course of asingle cycle with consequent changes in erosional processes.

Penck (Penck 1924, Bloom 1978) differed fundamentally from Davis. Even though he accepted theidea that landscapes could be reduced to the end forms of low relief, he maintained that these end formsnever became the initial forms of new episode of dissection. According to him the uplift was not rapidand then zero as Davis supposed, but always began slowly, reached a maximum and then wanedgradually to a stop. During the long stage of initial slow uplift, all prior forms were destroyed, and a newsurface of low relief, adjusted to a balance between uplift and degradation developed. This initialsurface of low relief was called Primärrumpf by Penck. He argued that the rate of crustal movementvaries greatly from time to time. Hence according to him, depending on whether rate of uplift is equal to,less than or greater than down cutting, the slope profile will be straight, convex upwards or concaveupwards.

No erosional sequence of forms was allowed by Penck’s scheme, because each morphologicassemblage was related to certain tectonic condition. Penck also denied any climatic control ofgeomorphic processes other than glaciations, believing that tectonics alone determined landformassemblages.

For many years, the ideas of Penck received little support from English speaking geo-morphologists. However, these have attracted attention since then and found them thought provokingeven though at times contradictory.

King (1962) a geo-morphologist from South Africa, formulated his ideas in a predominantly semi-arid region where very little geological deformation had taken place in recent times. King believes in thesupremacy of cyclic erosion in the development of continental landscapes and argues that the chiefdefect of Davisian concept is the absence of parallel slope retreat. King’s concept of changes in valleyslope is that the chief means of landscape change is the migration of valley side slopes away from therivers without significant change of angle as shown in Fig. 4.1 (a). On the other hand, Davis concludedthat during youthful stream incision, valley sides would be steep. Once rapid valley deepening hasceased, the slope processes almost solely influence the form leading to a gradual decline in the angle,(see Fig. 4.1 (b)).

Fig. 4.1 Valley slope evolution according to King and Davis

Both King and Davis argue that their models of landscape evolution could be adapted to a widevariety of climatic environment with only minor modifications. However, in 1909 Davis was convinced

Stream incision

b Davis

a King

Stream incision

Slopereducing

Almost parallelslope receding

River Morphology76

of the need to formulate a separate cycle for arid region because of (i) absence of the normal base levelcontrol in areas without perennial streams draining to the coast; (ii) increasing importance of windaction; and (iii) belief that a unique combination of the processes might lead to slope retreat withoutangular decline. Since then many writers such as Peltier have proposed variety of the original Davisiancycle, believed to be more appropriate to specific climatic zones. It is shown that climatic zone in whichthe cycle of erosion has been deemed to be significantly different from those outlined by Davis and Kingis the humid tropics, where chemical weathering significantly affects the development of landforms.Another climatic zone for which a distinctive cycle of erosion has been proposed is peri-glacial.

4.5 NON-CYCLIC CONCEPT OF LANDSCAPE EVOLUTION

Reactions against the limitations of the Davisian cycle of erosion have led to reassessments more radicalthan those discussed so far. Hack (1960) views landscape as the product of competition between theresistance of crustal materials to erosion and the forces of denudation. He argues that the orderliness ofstream organization first discerned by Horton (1945) will naturally lead to regularity in the overallpattern of relief. Within a single climatic region where stream and slope profiles are both controlled bythe nature of bedrock, similar geologic conditions should produce similar topography. Thus Hack putforward the concept of non-cyclic approach in the form of dynamic equilibrium. He does not probablyquestion the existence of a very long period of land form evolution, but argues that its details are nowlost beyond reconstruction; hence he is more concerned about the relationship between form andprocesses and adopts an attitude of ignorance towards land form history. Thus, Hacks’s argumentimplies that landforms adapt easily to changing environmental controls; however if this logic werestretched too far it would preclude, for instance, the identification of formerly glaciated areas.

It may be mentioned (Craig 1982) that during the past the geo-morphologists have developedmathematical models for slope erosion. Three models can be mentioned in this respect. The first is

¶

¶

Z

t= –b

¶

¶

Z

x...(4.1)

where Z is the elevation, t is the time, x is the distance from the divide and b is a positive constant calledrecession coefficient. Thus the rate of denudation is proportional to the slope. Where the denudation isproportional to convex curvature, the equation used is

¶

¶

Z

t= a

¶

¶

2

2

Z

x...(4.2)

where a is called debris diffusion coefficient. These two equations have been brought together byHirano (see Craig 1982) in a form, which describes the combined effects of weathering (Eq. 4.1) andcreep (Eq. 4.2). The equation is

¶

¶

Z

t= a

¶

¶

2

2

Z

x + b

¶

¶

Z

x...(4.3)

There is considerable difficulty in determining which equation should be used for a particularsituation and hence only a few areas are subjected to this type of analysis.


Hence, in spite of all the limitations of Davisian erosion cycle, it is still considered as the bestbecause no other viable alternative meeting all the objections to Davisian cycle is available.

4.6 GEOLOGICAL TIME SCALE

Historical or stratigraphical geology is mainly concerned with the description and classification of rockswith a view to arranging them in chronological order in which they were laid down on the surface of theearth. Of the three groups of rocks – sedimentary, igneous and metamorphic – only the sedimentaryrocks are amenable to such an arrangement since they have been deposited layer by layer and contain theremains of organisms which flourished while they were formed.

The time scales used by the hydraulic engineer and the geologist are quite different. The hydraulicengineer uses seconds or days as the unit of time when dealing with transport rates of water or sediment.When he is dealing with the morphological changes such as aggradation or degradation of the riverbedhe is concerned with bed level changes occurring in a few years or a few decades at the most. As againstthis in stratigraphy the unit time used is million years. Thus Lord Kelvin (Rice 1977) assumed that earthstarted as a molten body, and applying the theory of cooling to this mass he estimated that to attain thepresent day temperature the earth must have taken 20 to 40 million years.

For arranging the various geologic formations in the order of increasing antiquity, the geologist usesvarious means at his disposal. The first is the fundamental principle of superposition in which the upperbeds in an un-inverted succession are dated as younger than the lower ones. The second means is thepalaentological dating depending on the fossil content of the formation. Each formation encloses afossil assemblage, which is characteristic and different from that of the underlying or over lyingformations. The animal and vegetable organisms of each geological age bear special characters notfound in those of other ages. It needs to be emphasised that the fossils present in a series of formationsare not only a function of the period when the formation was laid down but are also a function of (i) thegeological period when rocks were formed; (ii) the zoological or botanical provinces in which thelocality was situated; and (iii) the physical conditions prevalent at the time, e.g. depth, salinity,muddiness of water, temperature, character of sea bottom and currents. The geological formations arenamed in such a manner that they indicate the stage of development of the organisms. Thus the Azoicera is completely devoid of organisms, while Proterozoic era shows traces of the most primitive life. ThePalaeozoic era contains the remains of ancient plants and animals, and so on to the recent time. The thirdmeans used for determining the age of formation is the lithology. Each lithology unit may comprise anumber of individual beds having more or less the same characters, when it is spoken of as a formation,and given a local or specific name to distinguish it from a similar formation of different age or belongingto a different area. Lithology is many times useful in the determination of chronology.

With the discovery of radioactive elements uranium and thorium at the end of 19th and beginning of20th century a more powerful means was available for determining the chronology of rocks and otherformations. It was found that uranium and thorium emit alpha and beta radiations; alpha radiationconsists of positively charged helium nuclei with two positive charges while beta radiation consists ofnegatively charged electrons. Depending on the nature of radioactive elements half the atoms of theelement will disintegrate in this manner in a period known as half-life of the element concerned. As aresult of such emission of alpha and beta radiation a new element or daughter element is formed. If thequantity of the parent element to the daughter element is known at any time, the period during which the

River Morphology78

radioactive decay has taken place can be calculated. Uranium and thorium, as a result of radioactivedecay are finally converted to lead Pb206, Pb207, or Pb208 isotopes. The isotopic analysis of the mineralsis carried out using the technique of mass spectroscopy. Using radioactive dating techniques, it isestimated that the age of crustal material of the earth is about 4,500 million years while the age of lunarrock ranges from 3,000 to 4,500 million years.

Table 4.1 gives the era, group, system or formation or rocks, and the chief fossils found in theseformations. Even though geologists are interested in all the eras from Quaternary to Azoic or Archaen,geo-morphologists consider Quaternary and Tertiary periods as of primary significance to them; this isso because it is believed that the majority of landforms are about a million years old, and the remainingnot more than 20 to 30 million years old. Hence, from the geo-morphologist’s point of view it becomescrucial that the dating between Quaternary and Tertiary periods is done carefully. This aspect has beendiscussed in detail by Rice (1977) and the following discussion is based on his comments. The dating ofCenozoic era has become complicated because of various reasons. Earlier stratigraphic column wasconstructed on the basis of marine sediments and faunas raised above the modern sea level. Suchcontinuous marine successions are rare in the late Cenozoic age, and the contemporary terrestrial bedstend to be fragmentary, of short duration and local. The second difficulty arises because of the relativelybrief duration of Cenozoic era because of which the biological evolution during this period was notadequate to delimit the era. Then there were at least eight or probably even more environmental changesduring this period, which have complicated building up of the chronological sequence. Lastly, asregards methods of estimating the age of the formation, K/Ar dating is most suitable for Cenozoic era;however because of the very small amount of Ar present in the formations the accuracy of the method isdoubtful.

Sufficient light has been thrown on the chronology of Cenozoic era by obtaining cores of materialsdeposited on the beds of deep seas. These deposits contain fossils of marine organisms such asforaminiferal, globorotalia menardii and diatoms in large numbers. Since these organisms have differentenvironmental requirements, their fossils give information on the changing temperature of seawater.The change in the ratio O18/O16 of the isotopes of oxygen in the shells also indicates the temperaturechanges. Shells formed in the cold climate are relatively richer in O18. Such evidences have helped infixing the chronology of later Cenozoic era.

Some investigators argue that the most distinctive characteristic of Pleistocene epoch is thedevelopment of large continental ice sheets in Europe and North America. Hence the beginning ofPleistocene should be equated with dramatic fall in temperature. However, glaciation in different partsof the world leads to a very large variation in the onset of Pleistocene. Therefore many argue that it isunwise to relate glaciation to Pleistocene.

Similar uncertainty prevails in fixing the Pleistocene–Holocene boundary. The term Holocene wasoriginally intended to designate the post glaciation period. However, the melting of ice sheets beingtransgressive of time, the post glaciation period in one region could be glaciation period in anotherregion. Therefore, this criterion was difficult to use. Hence the boundary between Pleistocene andHolocene is fixed arbitrarily. The most accepted boundary is that first proposed by Scandinavianworkers using pollen analysis. Using this technique the period of rapid warming indicating the onset ofHolocene has been fixed at about 10,000 years ago.

It is necessary to emphasize that during the Pleistocene era some areas were covered by ice sheetswhile some were not. In glaciated areas the attention was focussed on till sheets laid down one over the


Table 4.1 Geological time scale [Adapted from Wadia (1961), and Krishnan (1982)]

Era Period Epoch Duration Years before Chief fossilsM years present

M years (Ma)

Cenozoic Quaternary Holocene 0.01 0.01 Living animals

(present)Pleistocene 1 1 Man appears; many animals dies(Glacial) off during glaciation

Tertiary Pliocene 7 8

Miocene 17 25Oligocene 13 38Eocene 27 65

Cretaceons 75 140

Mesozoic Secondary Jurassic 60 200

Triassic 40 240

Permian 50 290Carboni-ferous 60 350

Devonian 60 410Silurian

Ordovician 35 445

Cambrion 60 505

100 605

Proterozoic Precambrian Precambrian 2500 Soft bodied animals and plants

Azoic Archaen Archaen 3600 Lifeless

Mamals, mollusca, and floweringplants dominate. Divisian largelybased on proportion of living toextinct species of mollusca and thepresence of mammal species

Giant reptiles and ammonitesdisappear at the end. Floweringplants become numerous

Ammonites abundant. First birds,flowering plants and sea urchinsAmmonites, reptiles, amphibiaabundant. Arid climate

Palaezoic Primary

Trilobites disappear at the endMany non-flowering plants, firstreptiles appear

Abundance of corals, branchiopoda,first amphibious and lung-fishes

Graptolites disappear at the end;first fishes; probably first land plantsAbundance of trilobites andgraptolitesAbundance of trilobites

other as a result of multiple glacial advances. Equal attention was given to the pollen analysis ofbiogenic materials entrapped within the tills. Similarly a thorough study was made of non-marinemolluscs and beetles. However, it has been found that the record of terrestrial sediments in glaciatedregions is small and is confined to the later part of Pleistocene era. In the unglaciated regions, at alimited number of places pollen analysis has been used. Some deep core samples have also beenobtained from the desert areas where earlier lakes existed. Another technique used to determine thechronology of continental land surfaces in Pleistocene era is the carbon C14 dating which is very usefulfor dating of Pleistocene and Holocene eras because of short half-life of 5730 years of C14.

This method depends on the fact that the atmosphere and the hydrosphere represent reservoirs ofradioactive carbon C14, which are tapped by animals and plants to build up their structures and tissues.The source of radioactive carbon lies in the cosmic ray bombardment of nitrogen in the atmosphere,which converts it into C14. Carbon has three isotopes C12, C13 and C14 and it is present in the atmosphere

River Morphology80

in the form of CO2. Out of the three isotopes C14 is the only unstable isotope with half-life of 5730 years.In historical times a balance was reached between new C14 received from cosmic radiation and thatdisintegrated due to radioactive decay. Since living organisms absorb CO2, each organism absorbs afixed proportion of C14 of the total carbon absorbed during the lifetime. After the death of the livingorganism, the replenishment of C14 ceases and C14 content declines due to radioactive decay. The ratioof radioactive to the total carbon present at any time is, therefore, a measure of the age of the organicmaterials such as bones, tusks, grains, wood, hide, peat etc. The method is suitable for dating up to50,000 years.

4.7 GLACIATION

Glacier is a slow moving mass of ice formed by accumulation of snow in mountain valleys and otherplaces. Area of the continents that is covered by ice at present is close to 15 M km2, the largest part ofwhich is concentrated in Antarctica (12.5 M km2) and in Greenland (1.7 M km2). Glaciers today, exceptat high altitudes and in high latitudes, are of minor importance in shaping landforms; but those thatexisted during the Pleistocene epoch have left their imprints on many millions of square kilometres ofthe earth’s surface. About 10 M km2 of the North America, 5 M km2 of Europe, 4 M km2 of Siberia andlarge parts of the Himalayas were glaciated. Pleistocene epoch consisted of four major glacial agesseparated by interglacial ages of probably far greater duration than the glacial ones. The latest glaciationhas left the most obvious imprints on the topography. Glaciers are classified into ice caps, valleyglaciers, ice-streams and glacier ice.

Glaciers that are continuous sheets of snow from which ice may move in all directions are known asice caps. Glaciers that are confined to courses, which direct their movement, are called valley-glaciersand ice-streams. Glacier, which spreads in cake-like sheets over level ground at the base of glaciatedareas, is known as glacier ice.

Glaciation in India (Wadia 1961, Krishnan 1982)Majority of the present Himalayan glaciers are three to five km in lengths, however there are some giantglaciers of forty km or more in length such as the Milam and Gangotri glaciers of Kumon and Zemuglacier draining Kanchanjunga group of peaks in Sikkim. The latest glaciers of the Indian subcontinentare those of Karakoram discharging into the Indus river; these are Hispar and Batura of the Hunzavalley, and Biafo and Baltora of the Shigar, a tributary of the Indus. These are about 50 km in length and130 to 330 m in thickness. These are the latest survivors of the last Ice Age of the Himalayas. Presenceof terminal moraines covered, many times by grass, seen in Pir Panjal moraines at the snouts of existingglaciers at low level hills of Punjab lead to the conclusion that at least this part of India experiencedglacial age in Pleistocene epoch. Parts of India lying to the south of Himalayas experienced cold pluvialepochs during this period. The evidence leading to this conclusion is derived from the fauna and flora ofthe hills and mountains in India and Sri Lanka.

According to Wadia (1961) indications of extensive glaciation in the immediate past and in thepresent glaciers are: (i) presence of enormous heaps of terminal moraine covered by grass and trees; (ii)presence of ice transported blocks; and (iii) smoothed or striated hummocky rock surfaces. According togeologists the Kashmir area of the Himalayas underwent four distinct glaciations separated by theinterglacial warm periods; the last of the glaciations occurred about ten to twenty thousand years back.


Glacial Movement and ErosionGlaciers move slowly showing erratic and sudden advances of their fronts. Glaciers reduce in size by thecombined action of melting and evaporation/sublimation, a process known as ablation. Glaciers mayalso get nourishment and thus increase in size. Depending on whether a glacier gets nourishment or notthe glacier is called an active or inactive glacier. Active glacier will have an advancing front whereas aninactive glacier will have a receding front. Abundant striations, polished and grooved rock surfaces giveevidence of effective glacial erosion. The bottom topography of bedrock floor may show irregularityand over deepening which cannot possibly be explained by any other way than to assume that they aredue to local glacial scouring.

One of the simplest ways of assessing the rate of erosion due to glaciers is by the measurement ofsediment being carried by melt water issuing from glacier snout. On the basis of observations by Reid,Thorarinson and Corbel from Muir, Hoffellsjokul and St. Sorlin glaciers respectively, Rice (1977)suggests that the mean erosion rate by active glacier lies in the range of 1 to 5 mm/year which is seen tobe much higher than most of the figures for stream erosion. Glacial erosion includes two processes,namely plucking and abrasion. Plucking occurs when moving ice freezes on to the bed rock and pullsout blocks which are then carried away. Abrasion is due to grinding effect. Grooves formed on thebottom can be 2 m deep and 100 m long, even though grooves up to 30 m deep and ten km long have alsobeen observed. Large blocks of un-weathered rock found in both glacial and fluvio-glacial deposits aremainly due to plucking.

Erosional and Depositional LandformsIce streams flowing in high mountainous areas have modified their valleys to such a great extent thattheir forms are distinctly different from the valleys caused by fluvial erosion. Some of the mostimportant erosional landforms produced by glacial erosion are cirques, glacial troughs and hangingvalleys.

CIRQUES: Cirque is a French word-meaning amphitheatre like basin, not completely enclosed. It isthe most distinctive, common landform caused by glacial erosion in mountain high lands. It is a steep

Fig. 4.2 Cirque

sided semi-circular basin found at valley heads; but it may notconnect in its downstream part with a valley. The name is appliedto shallow basins which mark the steps of snow banks whichnever grow into glaciers. A typical cirque consists of a steep headwall on the upstream side, followed by a deep basin and then agradually sloping up surface known as threshold, see Fig. 4.2.

The longitudinal profile of cirques approximately follows theequation of the form y = (1 – x) e–x and is almost independent of rock type. Conditions which favourmaximum cirque development are: (i) rather wide spacing of prelacies valleys so as to permit expansionwithout intersection of adjacent cirques at an early stage; (ii) adequate snowfall which can form largesnow fields and glaciers, but not heavy enough to form ice-caps; and (iii) fairly homogenous rockswhich permit cirque extension equally well in any direction.GLACIAL TROUGHS: Next in importance to cirques is the most distinctive topographic feature inglaciated mountains, namely glacial trough. It is the valley, which is modified, in its cross-sectionalshape and the longitudinal profile due to glaciers. Most glacial troughs were originally stream cut

Headwall

Basin

Threshold

River Morphology82

valleys. Glacial trough heads at the lower edge of the cirque threshold; however, there is a drop fromcirque threshold to the floor of glacial trough. The longitudinal profile of the glacial trough is irregularand ungraded; the profiles are seldom smooth and concave upward type. Instead, they have a series ofglacial steps, which are more pronounced in the upper reaches than in the lower. Glacial steps have beenattributed to differential glacial abrasion in contracting and expanding sections of the valley, effect ofvarying rock hardness and to preglacial irregularities. Presence of jointed rocks can also lead to glacialsteps. The cross-sectional profile of a glacial trough is significantly different from that of an unglaciatedvalley in mountainous area. While many glacial troughs are U-shaped, stream formed valleys inmountains are usually V-shaped. Davis has suggested that the cross profile of a glacial trough follows acatenary curve. The difference in the cross profiles of glacial troughs are often related to the differencein the thickness of glacier, valley lithology, structure of rocks in which the trough is cut, and the numberof times the valley is glaciated. Some portion of the glacial troughs may exhibit flat floors, which areattributed to the deposition subsequent to the trough development. The material deposited may be due toaggradation caused by deposition of outwash material by glacial recession or post-glacial alluvialdeposit.HANGING VALLEYS: The tributaries usually join the river valley accordantly i.e., there is nodifference in bed elevation of the main river valley and that of the tributary. However, glacial troughsoften have tributary troughs or valleys joining the main trough discordantly, producing elevation dropsat the junction. This is known as the hanging valley. Some valleys in Kashmir and in Sikkim exhibithanging valleys of this type (see Wadia 1961, Krishnan 1982). However, it may be emphasised thathanging valleys cannot be interpreted as evidence of past glaciation because they can be formed due toreasons other than glaciation; for example a hanging valley can be formed if the main stream isdegrading rapidly and the tributary is intermittent.

Glacial deposits are usually heterogeneous and lack stratification. These deposits are of three types,namely end moraine, lateral moraine, and ground moraine, depending on whether the deposition tookplace at the end of, at the side of, or beneath an ice stream. Only some glaciers build end moraine; thisdepends on whether the ice front maintains itself in one position for a sufficiently long time. Then if theice-fed stream emerging from the glacier is capable of transporting the end moraine, it wouldn’t deposit.Lateral moraines form along the sides of an ice stream mainly from the materials, which are contributedfrom the valley sides above the glacier by weathering and mass movement. Lateral moraines are usuallypatchy and may or may not be found on both sides. Ground moraine is more closely associated with icecaps than with ice streams.

The streams flowing on, within or beneath the glacier deposit the material eroded and transportedby the glaciers and ice streams. This material is known as glacio-fluviatile. The most common landformsin this material are valley trains, eskars, kame terraces, and outwash fans or deltas. These are describedby Thornbury (1969).

4.8 FLUVIAL MORPHOLOGY

Fluvial morphology deals with streams and stream systems as produced by the action of flowing water.The features produced on the land surface by flowing water can be aptly called fluvial landscapes. Asthe erosion cycle proceeds the morphology of streams also changes and the streams pass through thethree stages of development as the earth’s surface namely youth, maturity and old age. Although the


stage reached by the stream usually corresponds to that of the surrounding topography, this is notnecessarily the case. Usually the stream is less youthful in character near its mouth than in the vicinity ofits head waters (Hack 1960).

If one considers a newly uplifted land mass as the starting point and traces the successive changes,which occur with time, the first stage of the stream will be youth. Here streams have relatively steepslopes and they are engaged in cutting their channels downwards. Lateral erosion and valley widening isextremely small. The cross section of the stream will be V-shaped with no or little flood plain. Ayouthful valley is shown in Fig. 4.3. Streams in youth may not have cut down enough resistant rock massto attain a gradual profile; hence rapids and falls may exist along its course because sufficient time hasnot passed, since they were uplifted, for the stream to cut down and eliminate them. There are frequentchanges in the slope of the stream caused by the differences in hardness of the strata over which theyflow. Johnson (1932) suggests that early youth ends when lakes are eliminated and middle youth endswhen falls and rapids are eliminated.

Fig. 4.3 Youthful valley

Late youth ends and early maturity starts when the rate of down cutting decreases and the rate oflateral erosion increases; establishment of grade also marks the passage from youth to maturity. Earlymaturity ends and late maturity begins when the valley width equals the width of the belt covered by themeanders of the stream. V-shaped valleys and rapids and waterfalls disappear which are characteristicof youthful age of stream. Figure 4.4 shows a mature valley.

In the old stage there is pronounced meandering activity as a result of which width of flood plainexceeds several times the width of the meander belt. Oxbow lakes and swamps are usually present as aresult of cut-offs developed naturally. Natural levees, which form banks confining stream channels, maybe built up until the channel is some metres above the general level of the flood plain. Typical old stageis shown in Fig. 4.5.

River Morphology84

Fig. 4.4 Cross-valley profiles for various stages of stream

It sometimes happens that during the cycle of erosion certain changes occur which cause streams toincise their channels with greater vigour. This renewed down cutting is known as rejuvenation. Threeprinciples causes for rejuvenation are: (i) World wide changes in seal level, (ii)Tectonic changes and(iii) Climatic changes.

Equilibrium in Natural StreamsGeo-morphologists as well as engineers have used the concept of equilibrium in streams. A stream inequilibrium is called a graded stream or a poised stream. Mackin (1948) has given the followingdefinition of a graded stream:

“A graded stream is one in which, over a period of years, slope is delicately adjusted to provide,with available discharge and with prevailing channel characteristics, just the velocity requiredfor the transportation of load supplied from the drainage basin. The graded stream is a system inequilibrium; its diagnostic characteristic is that any change in any of the controlling factors willcause a displacement of the equilibrium in a direction that will tend to absorb the effect of thechange”.

Fig. 4.5 Old-age stream

Youth

Meander belt= Valley – floor width

Mature Old


Thus, the four variables related to the concept of a graded stream are slope, discharge, channelcharacteristics and sediment load. In a natural stream, the discharge is continuously changing due toprecipitation, infiltration, evaporation and withdrawals. Although stream tends to pick up sediment ordeposit it until load equals capacity, because of rapid variations in flow it cannot do so. Hence, in veryshort times the stream cannot be in equilibrium. Similarly, since the tendency of the streams is to lowerthe land surface to the sea level, over very long periods the stream cannot be in equilibrium. Thus,neither in very short not very long periods can a natural stream be considered to be in true equilibrium(Lane 1955). Yet, for all practical engineering purposes, most of the alluvial streams are in equilibriumover periods of the order of a few decades. In such streams, the bed may go down during high flows andfill back during low flows; yet the net amount of change is not sufficiently large to be detected byquantitative measurements. Most of the alluvial streams which are not affected by human interferencescan be said to be graded or in equilibrium. Construction of dams, withdrawal or addition of clear water,addition of sediment load, contraction of stream and cutting off the bends are some the ways in whichthe equilibrium of the stream is disturbed by human activities.

Characteristics of Graded StreamsTo get better appreciation of the stream morphology the characteristics of graded streams are brieflyenumerated here. Firstly the slope of a graded stream, in general, decreases in the downstream directionyielding a concave profile. Secondly, partly as a consequence of decreasing slope in the downstreamdirection, the stream drops the coarser material that it cannot transport, a phenomenon known as sorting;and partly due to abrasion, the bed material of an alluvial stream becomes finer in the downstreamdirection. Thirdly in humid regions as more and more tributaries join the main stream; the dischargeincreases in the downstream direction. However, if the stream passes through arid region, the dischargecan actually decrease in downstream direction as in the case of the Euphrates in Iraq. This is primarilydue to seepage and evaporation.

In addition, the upper part of the drainage basin is the main source of sediment even though therunoff from this part of the catchments may be small. The runoff from the rest of the basin is large but itcarries relatively less sediment. This leads to decrease in the average concentration of sediment in thedownstream direction necessitating a smaller slope. Lastly, because of finer material, streams usuallyhave relatively narrow channels i.e. larger width to depth ratio, in the downstream direction. As a resultthe stream has greater hydraulic efficiency and flows with a smaller slope.

A graded stream may show aggradational tendency, albeit temporary, under the followingconditions (Cotton 1941):

1. If dissection of upland region is in progress and a vast number of smaller new valleys andravines come into existence in the stage of youth. To carry relatively higher load stream mayincrease slope by aggradation.

2. If the river after it is graded flows in a wider channel than it has hitherto had in youth, loss ofdepth in the stream may rebuilt in a reduction of velocity and transporting power that it needssteeper slope to carry the load.

3. As a river develops increasingly large curves by lateral corrasion, its length increases and slopedecreases and hence carrying power decreases resulting in aggradation.

4. Decrease in water volume due to infiltration, evaporation or withdrawal can cause increase inslope due to aggradation.

River Morphology86

Variation of Sediment SizeIt is important for a river morphologist to know how the sediment characteristics change along thestream. The most important characteristic of sediment is its median size. It is found that in most of thestreams there is reduction in size of sediment due to wearing or abrasion, fragmentation, weathering,dissolution and hydraulic sorting. Hydraulic sorting takes place in a stream because the sedimenttransport ability of the stream reduces in the downstream direction. It is difficult to know the relativeimportance of these processes in the reduction of sediment size. Hence, it is easier to model thereduction in size by assuming that, as done by Sternberg in 1875 (Rohan 1967), the reduction in weightof the particle dW is proportional to its weight W and the distance travelled dL. Hence

dW = – CW dL ...(4.4)

where C is the constant of proportionality. Integration of this equation with the initial condition W = Wowhen L = 0 yields

W = Wo e–CL ...(4.5)

Further since for spherical particle W ~ d3 and Wo ~ do3, one gets

d3 = do3 e–CL

or d = do e– a1L ...(4.6)

a1 = c

3 is known as the abrasion coefficient. Here d is the sediment size. This equation known as

Sternberg’s law is found to be valid on the Rhine in Germany. In Japan it is found to be valid forsediments coarser than 4.0 mm in size. Shulits (1941) has stated that a1~ (particle velocity)1/4. Values ofa1 are found to vary between 0.006 km–1 and 0.11 km–1; however, it is not possible to predict its valueat present.

If dW is assumed to be proportional to surface area of the particle and dL, and one uses the initialcondition W = Wo when L = 0, the following equation is obtained from Eq. (4.4).

W = Wc

Lo

13 1

3

3-

F

HG

I

KJ ...(4.7)

Lastly another formula known as Schaffernak’s formula (see Rohan 1967) is also some times usedin describing the reduction in sediment size. This formula is

d

do

= 1 – C2L

do

...(4.8)

where as C and C1 are having dimensions, C2 is dimensionless. Typical values of C2 for some reaches ofthe Rhine, Danube and Mur vary from 4 ´ 10–8 to 45 ́ 10–8. It may be mentioned that the sediment sizevaries very slowly with L and hence with proper choice of C, C1, or C2 any of the three equations can befitted to a given set of data.

As regards the size distribution, it may be mentioned that while sandy materials are unimodal,gravely material is usually bimodal. Analysis of data of sandy and gravel-bed rivers by Garde (1972) has


shown that over the entire range the sample does not follow log-normal distribution; however between

d15.9 and d84.1 sizes it can be assumed to do so. The geometric standard deviation sg = 1

284 1

50

50

15 9

d

d

d

d.

.

+F

HG

I

KJ

is related to the median size d50 by the relation

sg = 2.4 d500 34. ...(4.9)

for 0.20 mm < d50 < 20 mm. Here d50 is in mm.

Classification of StreamsFor systematic discussion about streams, it is advantageous to classify them; classification of streamsenables one to make generalization about a group of streams having similar attributes. As can be seenbelow this classification is done using objective, qualitative or quantitative criteria. According toRosgen (1996) such classification often helps in (i) prediction of river behaviour from its appearance;(ii) development of specific hydraulic and sediment transport relations for a given stream type, (iv)extrapolating site specific data to stream reaches having similar characteristics; and (v) providing aframe of reference for communicating about stream morphology among different disciplines.

As discussed earlier Davis (1899) divided the streams into youthful, mature and old, depending ontheir stage of development in the cycle of erosion. This classification gives only qualitative attributes ofeach type. Davis (1890) also distinguished between consequent streams following the natural slope ofland surface; subsequent streams flowing into consequent streams from the sides at right angles to thedip and parallel to the strike; resequent streams as tributaries to subsequent ones more or less parallel toconsequent main streams; obsequent streams flowing against the dip of the beds; and insequent streams,which show no apparent relation to the dip of the beds. These are shown in Fig. 4.6 and discussed indetail by Worcester (1948). However, the classifications of Davis do not take into account the mainhydraulic variables on which stream size, shape and plan form depend.

Fig. 4.6 Relation of drainage totopography and geological structure

(Davis 1890)

Depending on the variation flow in the stream with time,streams can be classified into three categories. Perennial orpermanent streams are those, which flow throughout the year.These get their water from lakes, snow banks or glaciers, or landfrom direct precipitation, and which maintain regular flow. Thoseperennial streams, which have cut deep into sediment or otherstrata, may receive ground water flow also. Intermittent streamsare those whose sources of water fail intermittently. They occurmainly in regions of seasonal rainfall or snowfall, and particularlycommon to semi-arid regions. Ephemeral streams flow only in

response to precipitation; they are not fed by springs or by slowly melting snow.As discussed in Chapter II, Horton, Strahler and others have developed a system of ordering

channels in a drainage network; channels of the same order show similar characteristics, as shown byRznystin (1960).

Plan-form or channel patterns can be defined as the traces of the channel in plan as obtained fromair-photos or as presented on the map. Plan-forms of alluvial streams are of importance to hydraulic

C - consequent, S - subsequent,R - resequent, O - obsequent,I - insequent streamL - original land surface

SCL

OB

River Morphology88

engineers as well as to geo-morphologists and sedimentologists. For the hydraulic engineer not only theplan-forms but also their spatial and temporal variation is important to decide the location of bridges,barrages, levees and other structures. For the geo-morphologist they are an indication of modern riverbehaviour; plan-forms also throw light on the past morphology of the stream. A sedimentologist studiesplan-forms and the associated sedimentary deposits in order to develop knowledge about old streams.Lane (1957) analysed data from sand-bed rivers and rivers flowing through coarser material from USAand other countries and broadly classified the streams according to plan-forms into straight, meanderingand braiding patterns. He further indicated that plan-forms are essentially a function of slope andbankful discharge. Leopold and Wolman (1957) followed the same classification as that of Lane. Plan-forms can be classified depending on whether the stream flows in a single channel or in multi-channels.Streams flowing in a single channel can be straight or meandering. However, in nature, streams do notflow straight for more than 10 to 20 channel widths and even in straight channels the talweg shows ameandering pattern. Plan-form classification is shown in Fig. 4.7.

Fig. 4.7 Classification of plan-forms

Plan form of streams

Single channel streams

Straight Meandering BraidedDeltaicReticulateAnabranching

Incised meanders Meanders in flood plains

Irregular Regular

Simple Compound

Simple(sine, parabolic, circular, etc.)

Compound

RegularIrregular

Classification accordingto shape

Classification accordingto valley width

Underfit

Overfit

Classification accordingto movement

Free (Lateral migration)

Inactive

Migrating downstream

Multi channel streams


The meanders can be either incised or in plain and can take various shapes in plan. Meanderingstreams can be further classified depending on whether the meanders move downstream, laterally or arestationary. Chitale (1970) classified meanders into regular and flat, irregular and flat, regular and acute,irregular and acute, simple, and compound meanders (see Fig. 4.8 (a) and Fig. 4.8 (c)). He also statedthat a particular stream might have a single channel in one reach and multiple channels in other reach, afact noticed on many streams. The multi-channel streams are classified into braided, deltaic, reticulateand ana branching. These are schematically shown in Fig. 4.8(b).

Fig. 4.8(a) Plan-forms of rivers

It is appropriate to describe two other forms of streams based on the relative width of meander andthe valley. A mis-fit stream (Dury 1969) is defined as one, which occupies a valley formed by a streamof considerably larger or smaller discharge. An under-fit stream occupies the valley the valley formed bya stream of greater discharge. Most of the streams, which are under-fit, now have had their channelforming discharge reduced due to climatic changes. An over-fit stream occupies a valley formed by

Incised meanders (irregular)

MeanderbeltMB

Compound meanders Buyuk meanders river (Turkey)

Definition sketch for meandering stream

Straight reach of valley creek, Pa (U.S.A.)

0 100 m 150 m

150790 m

ML

Meander length

MW

Widthb

Point bar

Talweg

River Morphology90

much smaller discharge; however an over-fit stream will usually remove all signs of small streamchannel and widen its valley to conform to its present flow. Therefore, over-fit stream is a transient stageand is rarely found. Dury (1969) has discussed about another type of under-fit stream, called Osage type,which is named after the Osage river in Missouri (USA). This type of stream lacks meanders; however,it has pool and riffle sequence spaced at an interval of five channel widths. It behaves as if it werestraight; however it does not reflect the curves of the valley. The apparent width to depth ratio of streamsof Osage type is about forty, larger than ten as observed on meandering rivers; but actually in an under-fit stream of Osage type it is the wave length of the former stream and width of the shrunken present daystream. These types of plan-forms are shown in Fig. 4.8 (c).

Fig. 4.8(b) Plan-forms of rivers

S

Under-fit meandering streamOsage-type

LL

R

LL

S

Valley meander lobe

R Stream

Valley meander scar

L

S S

Deltaic patternReticulate pattern

Diamantina river (Australia)

Anabranching pattern ofDarling river (Australia)

High land

Braided stream

Darlingriver

High land

Free meanders oxbow lakes and meander scarsPembina river near Monola (Canada)


Schumm (1968, 1977) has classified stream channels flowing through sandy materials, based on themode of sediment transport (i.e., predominantly suspended load, mixed suspended load, andpredominantly bed-load), percent of silt-clay in the perimeter of the channel, and channel stability(graded, depositing i.e. excess sediment load, and eroding i.e., with sediment load deficiency). This isgiven in Table 4.2.

It may be mentioned that Blench (1955), and Simons and Albertson (1963) have also recognized theimportance of bed and bank material in shaping the geometry of stable channels. Allen (1965) hasdiagrammatically represented Schumm’s ideas in terms of size and sinuosity, which is shown in Fig. 4.9.

Kellerhals et al. (1972, 1976) have given a further refinement in the classification of river channels,which is primarily based on the interpretation of air photos and detailed survey of Canadian rivers. Thedetailed data needed for classification include: (i) whether the stream is aggrading, degrading, partlyentrenched, or entrenched with no flood plains, (ii) channel plan-form description, namely straight,sinuous (MB < 2 W), irregular or regular meanders, or tortuous meanders (q between channel axis andvalley trend greater than 90o), (iii) presence of islands and basis; and (iv) lateral activity namelymeanders moving downstream, downstream progression and cut-offs, entrenched loop development,avulsion etc. Figure 4.10 gives Kellerhal’s classification of lateral activity. This classification is veryexhaustive but rarely used in engineering design. Further, some of the attributes cannot be quantified.

Fig. 4.8(c) Meander classification according to Chitale (1970)

Compound meanders in Rind river (U.P.) India

Irregular and sharp meanders inSai River (U.P.) India

Regular and sharp meanders inMississippi river

Irregular and flat meanders inKen river (U.P.) India

Regular and flat meanders inMahi river (Gujrat) India

Compound meandersSimple meanders

Irregular and acute meandersRegular and acute meanders

Irregular and flat meandersRegular and flat meanders

River Morphology92

Fig. 4.9 Diagram relating stream channel stability to sinuosity and character of stream load (Allen 1965)

Table 4.2 Classification of channels according to Schumm (1968, 1977)

Mode of sedimenttransport

Percent of silt-clay

W/D: width to depth ratio, Si: sinuosity

Stable (graded) Depositing (excessload)

Eroding (Deficiencyof load

Suspended load85-100 percent

100 W/D less than 10 Sigreater than 2 slope

relatively flat

Major deposition onbanks, causing

narrowing of channel

Bed erosion; channelwiden-ing minor

Mixed, suspendedload 65-85% bed-load

35-15%

30 W/D : 10 – 40

Si : 1.3 to 2Slope relative moderate

Initially majordeposition on banks

followed by stream beddeposition

Initial stream bederosion; followed by

channel widening

Bed-load 35-75percent

- W/D greater than 40Si less than 1-3Slope relatively steep

Stream bed depositionand island formation

Bed erosion minimal,Channel widening

predominant

Finally, streams can also be classified depending on the type of material on their bed, character ofthe sediment transported, and the slope. Boulder rivers have large size cobbles and boulders on theirbed; they are found in mountainous regions with very steep slopes and they carry much finer materialeroded from the catchments. Only in catastrophic floods do the boulders on the bed move. These riversare usually entrenched. Gravel- bed rivers have gravel and sand on their bed, have steep slopes and arepaved during normal flows. During the floods the pavement is destroyed. These are found in thefoothills and have large width/depth ratio. Rivers in flood-plains flow through the material deposited bythem, carry material forming the bed and banks of the river, and have relatively much flatter slope ascompared to that of gravel-bed and boulder streams. Their bank material may be slightly cohesive andthey carry varying amount of wash load.

On the basis of a study of a number of streams in USA, Rosgen (1996) has proposed a hierarchicalclassification of streams. His classification provides the physical, hydrologic and geomorphic way oflinking the driving forces and response variables at different levels of inquiry. Thus as one moves fromLevel I to Level IV, one progressively takes into account geomorphic characterization, morphologicalclassification, stream condition and validation level. To facilitate the classification Rosgen used

Suspended loadHigh Low

Calibre of stream loadFine Coarse

Low

Channel

sin

uosity

Hig

h

Sta

bili

sation

ofm

eander

belt

by

channelfills

Good

Poor


Entrenchment ratio ER (= width of flood prone area at an elevation twice the bankfull depth/bankfull width)

Width to depth ratio W/D = (Bankful width/mean bankfull depth)

Sinuosity Si = (Stream length/valley length) and Slope S

Thus at Level I , based on ER, W/D ratio, sinuosity, slope and channel pattern, the streams areclassified into nine types designated as Aat, A, B, C, D, DA, E, F and G as indicated in Table 4.3.

Table 4.3 Rosgen’s stream classification at level – I (Rosgen 1996)

Stream Type Aat A B C D DA E F GER < 1.4 < 1.4 1.4 – 2.2 > 2.2 N.A. > 2.2 > 2.2 < 1.4 < 1.4

W/D < 12 < 12 > 12 > 12 > 40 Highly < 12 > 12 < 12variable

Si 1.0 – 1.1 1.0 – 1.2 > 1.2 > 1.4 N.A. Highly > 1.5 > 1.4 > 1.2variable

Slope S > 0.10 0.04 – 0.02 – < 0.02 < 0.04 < 0.005 < 0.02 < 0.02 0.02 –0.01 0.03 0.039

N.A.-Not applicableThe brief description of these nine types of streams is given below:

Aat: Very deep, entrenched torrent streams, mildly curved in plan, high relief, zone of deposition,step-pool morphology

A: Steep, entrenched step-pool streams, high transport of debris; erosional or depositionalcharacter, mildly curved in plan.

B: Moderately entrenched, moderate slope, very stable plan, longitudinal profile and stable banks,mildly curved in plan

C: Low gradient, meandering, point bar, riffle/pool topography, alluvial channel with moderateentrenchment and W/D ratio, broad valley.

D: Braided channel with longitudinal and transverse bars-eroding banks with very wide channel,abundance of sediment supply, aggradational tendency.

DA: Anatomising channels, well vegetated flood plain, stable stream banks, broad valley, low bed-load and high wash load.

E: Low gradient, highly meandering, low W/D ratio, broad valley flood plain with alluvialmaterial, high meander width ratio.

F: Entrenched meanders on low gradient, and high width/depth ratio, meanders very unstablelaterally with high bank-erosion, pool-rifle morphology

G: Entrenched gullies, step-pool morphology, narrow valleys, unstable high erosion rates.The Level II in the classification subdivides the streams in each class into a maximum of six

categories, namely 1, 2, 3, 4, 5, 6 depending on the channel material i.e. (1) bed rock (2) boulders (3)cobbles (4) gravel (5) sand, and (6) silt and clay. These are written as A1, A2, A3, A4 …A6 etc. Thus A5

River Morphology94

stream will be of A type with sandy material. It also takes into account bankfull discharge andcorresponding hydraulic parameters in determining quantities such as entrenchment ratio, W/D andManning’s n.

Aim of Level III classification is to provide description of stream condition as related to stability ofstream, its potential, and function. This is based on additional inputs about hydrology, biology, ecology,and human activity. It evaluates and quantifies the channel stability, bed-stability (aggrading, degradingor stable), and bank erosion. Level IV classification is based on reach specific observations forverification of process based assessments of stream condition, potential and stability predicted frompreceding analysis. The book by Rosgen contains valuable information for practicing rivermorphologists. Since a large number of sketches are included in the book, the text connects easily withthe field conditions.

4.9 TOPOGRAPHY PRODUCED BY STREAMS

During the cycle of erosion as the streams develop they bring down a large quantity of sediment whicheventually goes into the sea. While streams perform the erosional work in the upper reaches and

Fig. 4.11 Idealized fluvial system

deposition of sediment in the lower reaches various typesof topography are produced. According to Schumm(1971) the fluvial system can be divided into three zones,named Zone 1, Zone 2 and Zone 3 in the downstreamdirection. The upper most part of the drainage basin isprimarily the sediment source area (Zone 1); the waterand sediment are derived here. Zone 2 is the transfer zonewhere for stable channel, the input is equal to output.Zone 3 is the sediment sink or the area of deposition. Since the sediment is stored, transported anderoded in each zone, within each zone one process is predominant as mentioned above. The three zonesare schematically shown in Fig. 4.11 are discussed below.

Topography Resulting from Stream ErosionVALLEYS: Usually gullies grow into ravines and ravines into valleys. Development of valleyinvolves three concomitant processes namely valley deepening, valley widening and valley lengthening.Valley deepening takes place due to hydraulic action, abrasion and weathering. Valley widening takesplace by lateral erosion near the valley base which can lead to under cutting of slope, rain wash on thevalley sides, gulleying on valley sides and mass wasting. The depth of any stream-cut valley is limited tothe level of the body of water into which it flows. Valley lengthening can take place in three ways: (i)extension by the process of head ward erosion, (ii) increase in the size of their meanders, and (iii) upliftof land or lowering of sea level.

The valley profile near the head will be V-shaped and will gradually change to U-shaped towardsthe mouth. The longitudinal profile will generally be concave upwards with longitudinal slopedecreasing in the downstream direction. The stream slope changes as S = So e

– a x, where So is the slopeat x = 0 and S is the slope at a distance L from the upstream end, and a is a constant. This decrease inslope is due to the following reasons as mentioned earlier: (i) size of the material transported by thestream decreases in the downstream direction due to abrasion and sorting; (ii) In humid regions the

Zone 2(Transfer)

Zone 1(Drainage basin)

Zone 3(Deposition)


discharge in the stream increases in the downstream direction. Thus there is decrease in sedimentconcentration in downstream direction thus requiring a smaller slope; (iii) Because of the finer materialstreams usually have relatively narrow channels (i.e., larger depth to width ratio) in the downstreamdirection, such channel is more efficient in transporting sediment at a flatter slope.

If S = – d Z/dL is substituted in the equation S = So eaL where L is measured in downstream direction

and the condition Z = Zo at L = 0 is used, one gets

– dZ

dL= So e

–aL ...(4.10)

\ – Z = – So

a e–aL + const

The value of constant can be obtained from the condition Z = Zo at L = 0. Hence –Zo + So

a = const,

and hence – Z = - So

a e–aL1 +

So

a – Zo

or (Zo – Z) = So

a (1 – e–aL1) ...(4.11)

The low water profiles of the Mississippi river between Fort Jackson and Cairo, of the Ohio riverfrom Cairo to Pittsburgh, both in U.S.A., and San Juan river in Argentina are found to follow Eq. 4.11.The value of a was found to be between 0.0010 and 0.00183. Brush (1961) and Hack (1957) haveemphasised the importance of lithology in determining the longitudinal profile and have proposed anequation of the form

S = a Lb ...(4.12)

For streams in the forded Appalachions in Pensilvania (U.S.A.) they found “a” to vary between0.013 and 0.15 and “b” between – 0.47 and –1.0, for different lithological formations.STREAM TERRACES: Stream terraces are topographic surfaces, which mark former valley floorlevel. They are vestiges of former flood plains although some may have little or no alluvium on them.Thus one can have either bedrock terraces or alluvial terraces, which may consist of gravel, sand andsilt. Terrace formation can be explained in the following way. When the stream is graded, it forms a flatvalley. Later when the stream is rejuvenated it first cuts down through valley flat to a new grade. Indoing so it develops a second valley flat inside and below the first one. Repeated rejuvenation candevelop successive terraces at lower levels. Individual terraces may be narrow or a few kilometres wide.Height between successive terraces may be a few metres to a few hundred meters, see Fig. 4.12.

Topography Resulting from Stream DepositionFLOOD PLAINS: As the stream becomes graded the rate of down cutting decreases as compared tothe lateral erosion; hence there is increased meandering activity. Impingement of flow duringmeandering widens the valley floor thereby producing flood plain. Thus flood plain is a strip of

River Morphology96

relatively smooth land bordering a stream and over flowed at the time of high waters. When the flooddischarge exceeds the bankful discharge it flows across the flood plain. Two processes which areresponsible for formation of most of the flood plains of the great rivers of the world are the deposition onthe inside of river curves and erosion on the outer side of meander curves. When stream is in the maturestage the width of valley floor is approximately equal to the width of the meander belt. In the lowerreaches of mature stream the valley width is much larger because the stream meanders and wanders, seeFig. 4.13.

Fig. 4.12 Development of river terraces

Fig. 4.13 Natural levees and flood plan

MEANDERING: Earlier in this chapter reference is made to meandering as one of the plan- forms ofsingle channel streams. The word meandering comes from the name of the stream in south easternTurkey, which was at one time known as Buyuk Meanderes (Lane 1957). This stream being very

Bed Rock

Flood plain River Alluvium

RiverT T

Scarp

T2

T2

T3

T1

T1


crooked in plan, a stream having a winding course and having either regular sinuous pattern or irregularpattern is known as a meandering stream. There are some streams which follow sinuous or irregularpath, but which have cut into solid rock or hard strata in deep gorges. These are called incised orentrenched meanders, see Fig. 4.14. Entrenched meanders can also form in the flood plain whenwinding pattern is formed in a mature or old stream and rejuvenation takes place where it starts cuttingdown again. The terms used to describe meandering pattern are shown in Fig. 4.8 (a). Meander lengthML is the tangential distance between corresponding points at the extreme limits of fully developedmeanders. Meander belt MB is the width between tangents drawn outside of the meanders of the stream.Investigator such as Inglis and Central Board of Irrigation and Power, India has accepted this definition.However, Davis (1909) and others consider meander belt as the space enclosed between the tangents. Inthe present text the former definition has been used. Meander width Mw = MB – B where B is the widthof the channel. The ratio of stream length to valley length is known as the sinuosity.

Fig. 4.14 Incised meanders of the Dolores river

Because of changing conditions of flow, stream slope, sediment size, sediment load and lithologythe meandering pattern along the length can be regular or can change along its length; the latter are thencalled irregular meanders. The irregularity results from variation in discharge along the length due totributaries, withdrawal of water, presence of lakes, rock outcrops, weirs and barrages, and non-homogeneity of strata through which the stream flows. In most of the cases, from the point of view ofanalysis, it is justified to use average values of ML, MB, Mw and sinuosity to characterise the meanderpattern in a given reach. Leopold and Wolman (1957) have set an upper limit of sinuosity of 1.5 fordifferentiating straight streams from and meandering streams. For some Indian rivers sinuosity valuesup to 2.5 have been reported whereas a value of about 5.5 is considered to be the upper limit. The shapeof meanders is rarely truly sinuous; it is many times arc of a circle, parabola or some other curve. Onemay some times come across a case where the stream has a primary meandering pattern on which issuperposed a meander pattern of smaller meander length and belt. This happens if the stream has morethan one dominant discharge.

The meander pattern in the flood plain of a stream is normally not static but it moves in thedownstream at a small velocity; however it is likely to be influenced by the variables such as discharge

River Morphology98

and slope which give an idea about the erosive power of stream, and the nature of strata. The Klarafvensriver in Sweden has migrated a distance of about one meander length in 2000 years (Lane 1957). Thereare also certain streams in which the migration process consists of gradual lateral enlargement ofmeander loop, with periodic cut-offs. Such meanders are called free meanders. The Tigris river in Iraqhas shown this characteristic (Garde 1976). There are also some streams in which the meander pattern isstationary; these are classified as inactive meanders.NATURAL LEVEES: Natural levees are long embankments formed by the deposition of alluvialmaterial by the rivers when they overflow their banks. When streams overflow their banks the velocityis appreciably reduced and hence the carrying capacity of the flow is decreased. This causes depositionof some of the coarser sediment load resulting in the formation low ridge along the banks of the stream;these are called natural levees; (see Fig. 4.13). Natural levees are highest near the riverbank and slopegradually away from it. Natural levees may be one or two kilometre in width. They cause the presentmeander belt of the river to stand up above the flood plain as a low alluvial ridge. These levees may bebuilt up until the river channel is several meters above the general level of the flood plain. This hasoccurred in the case of the Yellow river in China and the Mississippi river in U.S.A. In many casestributary streams have difficulty in breaching the natural levees and many flow in the same flood plainfor many kilometres before breaking through the levee to join the main stream.DELTAS: As the stream flows into lakes, ponds, sea or in rare case in rivers, the velocity of flow isdecreased and the sediment being carried by the stream is deposited forming what is known as delta, ifthe waves or currents in the body of water into which it empties are not strong enough to carry away thesediment brought in by the stream on which delta is formed. The amount of sediment deposited and itspattern depend on the size of sediment, changes in the water level of the body, and waves and currents.The name delta comes from the Greek word D to which the deposition pattern resembles. However, theshape of delta can vary depending on the local condition; the Nile river delta has a triangular shape inplan, whereas the Mississippi river delta and some others have long extensions of tributary channels,which are some times called bird foot deltas. Almost all the deltas are formed by splitting of the mainchannel into a number of branching distributaries channels. Reduction of flow in each branch due tobranching causes reduction in flow in each branch causing further deposition. This deposition blocksthe distributaries and more distributaries are formed.

As along as the rate of supply of sediment from the stream is greater than the rate of removal bywaves and currents, the shore line of the delta continues to move downstream especially in shallow seas.Advance rates of some of the deltas in the world are given (Pitty 1971) in Table 4.4.

Table 4.4 Rates of advance of some deltas in the world

River Rate in m/yr.

Volga 170

Mississippi 400Orinoco 200Don 10

Po 20Kilia Delta of Danube 27Tigris–Euphrates 25–50

Yellow river (1870–1936) 300–350


While the delta growth is continuous in some case, in other cases it is spasmodic. Half of the totalannual growth may take place during a single week as in the case of Lactature delta in Northern Sweden.

Silvister and de La Cruz (1970) have analysed the data of 53 deltas from all over the world andobtained the following relationships for the characteristics of deltas:

Apex to sea length L in km = 45

100

0 30

10 25

Q

C Cs

FH

IK

.

.b g

...(4.13)

Area of fan A in km2 = 46 3

100 10

0 2 30

0 40

..80 .

.

Q t

C

e

s

FH

IK

FHIK

Number of distributaries N = 268 S1

1000FH

IK

where Q is the average annual discharge in m3/s, Cs is the (slope of continental shelf ´ 104), S1 is theriver slope in percent, and Te is the average annual temperature in oF. They have also a relationship formaximum width of delta.

Conditions favouring the deltaic accumulation are (Sparks 1972):i) large sediment load of the stream;

ii) usually large river; otherwise action of sea might disperse the sediment;iii) reasonably shallow water offshore; very deep water may inhibit delta building. Thus Congo

river which virtually debouches into submarine canyon has no delta;iv) coasts on which wave energy is low; andv) small tidal range.

The Mediterranean, Black Sea, Caspian Sea bear witness to this in the deltas of the Nile, Rhone, Po,Danube and Volga. However, deltas can be built in areas of larger tidal range provided that theconditions (iii) and (iv) above are met. Irrawati and Ganges deltas are in the area of 5.5 m and 4.5 m tidalrange respectively.

In general, large rivers of the world have large deltas with a large number of tributaries. TheOrinoco River in Venezuela has thirty-six tributaries. The size of the deltas of the Yellow river and theOrinoco River is nearly same. Since deltaic regions are most fertile, these are thickly populated. A fewdeltas are shown in Fig. 4.15.

The main structural features of coarse-grained deltas differ considerably from those of fine-graineddeltas. Where bed load is carried into the delta area, this material gives rise to more rapid changes indeltaic pattern and if it reaches the delta front, it may be deposited as forest beds. In fine-grained deltas,where accumulations are essentially deposited from suspended load, distinctive sets do not develop.There are also contrasts in the average inclination of sub aerial parts of the delta, those on small coarse-grained deltas being rather steep up to several meters per km and overlapping with the order of gradients

U

V

|||||||

W

|||||||

River Morphology100

Fig. 4.15 Some large river deltas

Fig. 4.16 Longitudinal section of delta

Tigris-Euphrates Ganges-Brahmaputra

TigrisEuphrates

Persian gulf

Bay of Bengal

Calcutta

Bhagira

thi

GangaDacca

Gulf of Guinea

Bay of Bengal

Puri

Para dip

False pointMahanadiCuttack

MahanadiNaraj

Silt and clay

Sea level

Carbanaceousmatter

Deltaflank bay Barrier islandDelta

flank bayDelta fringe distributory channelsBarrier island

Coastalinterdeltaic sediments

Deltaic sedimentsCoastal

interdeltaic sediments

Longitudinal section

Silt and clay

Gravel Sand

Sea level

Carbanaceousmatter

Deltafringe

Lowerdeltaic plain

Upperdeltaic plain

Prodelta marine

Subaqueousdeltaic plain

Subaerialdeltaic plain

Cross section


on bahadas. On fine-grained deltas, the inclination is much flatter, of the order of 5 cm per hundredmetres. A typical longitudinal section through the delta is shown in Fig. 4.16.ALLUVIAL FANS: When mountain stream flows out on a gently sloping plain adjacent to theranges or flows into another stream of greater slope, its velocity decreases and coarse gravel, sand andfine sediment are deposited in the form of a fan in outline. This accumulation of sediment is known as analluvial fan. Alluvial fans have been studied over the past eighty years or so, and an exhaustive list ofreferences and the present state of knowledge are given by Rachocki (1981). Figure 4.17 shows thesketch of an alluvial fan and its internal structure. Fans can be classified into dry fans and wet fans. Dryfans are formed under dry conditions and their streams are ephemeral. For dry fans, mudflow and debrisflow deposits frequently comprise a large part of deposits. These fans are relatively small and have beenextensively studied. Wet fans are formed by perennial stream flow. Kosi fan discussed by Gole andChitale (1966) is a wet fan and is discussed in Chapter 13. This fan is produced by the huge quantity ofsediment load brought down by Kosi on the Gangetic plain.

Fig. 4.17 Alluvial fan and its internal structure

Alluvial fans are found in the foothills of mountains irrespective of climatic conditions. They wereand are being formed at the fronts of ice-caps and glaciers, as well as in moderate semi-arid and aridregions. However, the largest alluvial fans are formed in the foothills of mountains in drier regions of theworld. Intensive weathering together with periodic rainfall events is conducive for the production andtransportation of large amounts of sediment by the ephemeral streams. Langbein and Schumm (1958)consider an average precipitation of 250 to 350 mm as optimum for the development of fans. Suchconditions simultaneously reduce plant cover and ensure adequate supply of water for the transportationof sediment.

Gravel Sand Silt

Clay

Mud flow layers

Mountain front

Canyon

Bed rock

River Morphology102

Allen, Morisawa, Thornbury and others believe the commonly accepted explanation for theinitiation of fan, to be the drastic reduction in slope between eroding valley and receiving plain.However, according to Bull, change in the confinement of the channel is also an important factor, whichfacilitates fan construction by reducing the rate of sediment transportation. Infiltration of water in theupper portions of fan further reduces the transporting capacity; this water reappears as strings in themiddle and lower portions. Braided stream pattern is characteristic of streams flowing across alluvialfans, and as a result of repeated channel shifting, streams at one time or other flow down in almost everypossible radius of the fan.

Most alluvial fans exhibit a semi-circular shape in plan. Alternating periods of deposition and soilprofile formation are characteristic of most alluvial fans, because the depositional area shifts from onepart of the fan to the other during the construction of cone shaped deposit. According to Bull (1962), ifsufficient time is available for weathering to occur between periods of deposition, a series of soilprofiles will result. Alluvial fan deposits are composed of two main facies, water laid deposits and massflow deposits. These deposits are poorly sorted even though layers can be distinguished. Mass flows thatoccurred recently in the fan’s evolution show two separate deposits. The upper part near the apexconsists of large particles and lower part of mudflow. Mudflow is a type of debris flow, which consistsmainly of sand and finer sediment. The particle size in general decreases in the downstream direction.

Fan dissection is a general term used which includes both entrenchment and incision of the fan. Fanentrenchment is down cutting into the fan surface of a channel that is contributing sediment to the fansurface. Entrenchment usually occurs during fan construction. Fan incision is down cutting into fansurface by channel that crosses the fan margin. Incision is usually associated with fan destruction.According to various investigators, the two possible causes for dissection are tectonic movements andclimatic changes. According to Lobeck, fan dissection is a natural process-taking place due to reductionof sediment load.

A few words about fan dimensions are in order. The radius of the fan may range from severalhundred metres to one hundred kilometres with the slopes averaging between 3° and 6°. Anstey (1965)studied fans in Western U.S.A. and Baluchistan in Pakistan. From a sample of almost 2000 fans, hefound that greatest number of fans have radii between 1.6 km and 8.0 km. The largest fan in his samplehad a radius of 25 km. The upstream slope values may be as high as 10° – 15° while the lower slope canbe less than 3°. With the passage of time thickness of fan deposition increases under most climaticconditions. Borehole data as well as the dating techniques have been used to estimate the rates accretionfrom 0.50 m to 3.0 m per thousand years. Some attempts have been made to relate empirically the fanarea Af and fan slope Sf to the drainage area A. According to Bull (1962)

For basins underlain by 48-86 percentAf = 2.4 A0.88

shale and mud stoneSf = 0.023 A–0.16 ...(4.14)

For basins underlain by 58-68 percentAf = 1.3 A0.88 ...(4.15)sand stone

Sf = 0.022 A–0.32

Here A and Af are in miles2. These results indicate that the fan slope decreases with increasing fanand drainage area of the basin.


POINT BARS: When the bed of the channel bend is deformable, scour occurs on the outer side of thebend and the sediment gets deposited on the inner side of the bend forming the bar commonly known aspoint bar. In order to explain the process involved in the formation of point bar, consider flow in a rigidboundary bend. As the flow enters such a bend, the average velocity in the vertical U varies as 1/r wherer is the radius of curvature. This free vortex flow velocity distribution gradually changes to forcedvortex flow distribution along the bend length; in forced vortex flow U ~ r. To maintain this distributiona transverse slope towards the inside is caused to the water surface. The friction at the boundary causesvelocity variation in the vertical. This variation in velocity in the vertical along with the transverse slopeinduces secondary flow in the bend which is directed towards the inside of the bend near the bottom andtowards the outside of the bend near the water surface, see Fig. 4.18. According to Rozovskii (1961), thelocation from the beginning of bend at which development of secondary flow is complete is affected byroughness coefficient and the ratio of depth to centre-line radius, see Chapter 6.

Fig. 4.18 Flow in a rectangular bend and development of secondary flow

The secondary circulation is dissipated at a distance of 1 77. .C

gD

F

HGI

KJ from the end of the bend.

Interaction between the main flow and secondary flow causes redistribution of shear stress on the bed.There is higher shear stress on the outer side of the bend land smaller shear stress on the inner side. Thisdistribution for a typical bend in trapezoidal channel is shown in Fig. 4.19. The shear stress at the bedhas a small component towards the inside of the bend, which causes sediment to move towards theinside of the bend.

In the case of flow around the bend in a channel with deformable bed scour occurs on the outer sideof the bend and the sediment gets deposited on the inner side of the bend, forming a bar known as pointbar. For a high constant discharge the bed topography is such that the sediment transport rate is the sameat all the sections in the bend. The bed topography and the talweg observed in the South Esk bend are

Lowerlayer

Upper layer

Ou

ter a

B

W SW S

ua

ub

Inn

er

River Morphology104

shown in Fig. 4.20, as given by Bridge (1983). It is found that large-scale bed topography such as pointbar changes very little with discharge. The point bar at the bend apex extends about 0.60 to 0.8 times thedistance across the bend.

4.10 VARIABLES IN RIVER MORPHOLOGY

As discussed earlier, Schumm (1971, 1977) divides the fluvial system in three zones as shown in Fig.4.11. Zone 1 in which the uppermost is the drainage basin, watershed or sediment source area. Water andsediment are predominantly produced in this zone. Zone 2 consists of the main river system and can becalled the transfer zone where for a stable river sediment input and output are equal. Zone 3 is thesediment sink or area of deposition, the sediment is deposited on alluvial fans, flood plains and deltas.Whereas Zone 1 is the primary concern of geo-morphologists, Zone 2 is of major concern to hydraulicand river engineers, and geo-morphologists associated with river channel morphology. Zone 3 is ofmain concern to geologists, coastal engineers as well as river engineers.

In connection with river morphology, three “times” are considered. In Zone 1, one considersgeologic time as an important independent variable. This refers to the time from the beginning oferosion cycle to the present and can be millions of years. During this period, erosion occurs in Zone 1and characteristics of fluvial system progressively change. During graded time span which is a smallpart of geologic time, there may be small progressive change in landforms, but by and large the systemcan be considered to be equilibrium. This is the time span considered by Mackin in defining a gradedstream, which is considered to be in equilibrium; this time span can be a few hundred years. Duringsteady state time a true equilibrium may exist in which landforms are time-independent. This is the timespan considered by hydraulic engineers where variables such as drainage pattern, drainage density can

Fig. 4.19 Shear distribution in a trapezoidal bend

60°

Separation

Outside edge W S

Separation

Inside edge W S

FLOW

0.80.6

1.01.2 1.4

1.5

1.6

1.8

2.01.8

2.0

1.51.4

1.2

1.00.8

0.6

1.0

1.2

1.0


be considered constant. Steady state time can be of the order of a month or less. For geo-morphologists,the geologic time and graded time are of significance.

In geologic time, the time, initial relief, geology (i.e., the lithology and structure) and palaeoclimateare the independent variables where as palaeohydrology, relief (i.e., volume of the system above baselevel), valley dimensions (width, depth and slope) are dependent variables.

In graded time span, time is no longer an independent variable even though the drainage system asa whole may be undergoing progressive change of small magnitude. Initial relief has also nosignificance. However geology, palaeoclimate and palaeohydrology, relief, valley dimensions, climate,vegetation and hydrology (mean water and sediment discharge) are independent variables. The onlydependent variable is channel morphology i.e. channel dimensions and slope.

During steady state time (which is a short duration of a week to a month) true steady stateequilibrium may exist. During this time span, channel morphology assumes an independent statusbecause it is inherited from graded time. Hence in this state geology, palaeoclimate, palaeohydrology,relief, valley dimensions, climate (i.e., mean precipitation, temperature etc.) vegetation, hydrology(mean discharge of water and sediment) are independent variables. On the other hand, observed waterand sediment discharge and hydraulics of flow are dependent variables. The dependent and independentvariables in different times are listed in Table 4.5.

4.11 NEOTECTONICS AND EARTHQUAKES

During the cycle of erosion the land surface is affected not only by the erosional forces but also by theinternal forces, which cause displacement of earth’s surface due to movement of earth’s plates andresulting stress building. This displacement is usually slow and can be gradual uplift, subsidence orlateral displacement. Neotectonics refers to these gradual and presently active aseismic crustaldeformations. If this happens in the vicinity of an alluvial stream, uplift or subsidence can causedegradation or aggradation respectively thereby altering the gradient upstream, at the axis of movementand in the downstream reach.

The minimum rate of uplift estimated by Zeuner (see Schumm 1977) for the Alps and theHimalayas are a millimetre per year. In California the average mountain building rate in modern times is0.80 mm/year. The present rate of isostatic uplift in North America is 0.50 mm/year. The subsidence inthe surrounding area caused by the storage of water and sediment in Lake Mead, U.S.A. was 1.3 mm/year. According to Schumm et al. (1987) many streams such as the Mississippi and Rio Grande inU.S.A. and Amazon, Niger, Tigris, Euphrates, Rhine and Indus are affected by such structural

Fig. 4.20 Observed bed topography of south Esk bend

10 M

5

6

7

4

332

1

River Morphology106

instability. In Northern Iraq (i.e., Ancient Mesopotamia) Diyala River that is the tributary of the Tigrishas incised into its alluvial deposit due to uplift during the past 1000-1200 years. As a result theinundation canal system developed in the earlier times has had to be abandoned. Upwarping of theBrahmaputra basin is found to be partly responsible for flood problems in Bangladesh. Similarly,tectonic uplift is likely to be at least partly responsible for the shifting of the river Kosi through 110 kmto the west in the past 200 years. Such uplift and downwarping may look innocuous during a shortperiod but can cause aggradation, degradation or change in plan form in different stretches of thestream. This aspect has been studied by Ouchi (1985) in the laboratory and his results are summarised inthe Table 4.6.

Reach A: from 2.0 to 3.5 m where no significant uplift or subsidence occurred. Reach B: from 3.5 to4.65 m, the upstream half of the uplifted or subsided zone. Reach C: from 4.65 to 5.75 m downstream ofuplifted or subsided zone.

Reach D: from 5.75 to 7.0 m where no significant uplift or subsidence occurred.The lateral movement along the fault may cause a lateral shift in the stream crossing the fault. Such

a shift has been observed in the case of Narmada River in India. It has also been reported that prior toUttarkashi earthquake of 20th October 1991 of magnitude 7.1, horizontal and vertical movements werenoticed in Garhwal, Himalayas during 1972-1978. Horizontal movements were about 30 to 150 mmwhile vertical movements ranged from 10 to 90 mm.

Earthquakes in Zone 1 can cause large-scale land slides and mass movement and produce enormousamount of sediment which eventually reaches the stream and can cause aggradation, change in planform, shifting of tributaries and flooding in Zones 1 and 2. This is what happened in the Brahmaputraafter 15th August 1950 earthquake of 8.6 magnitude, see Gee (1951). The effects that were observedimmediately after that earthquake and in subsequent years were

Table 4.5 Stream variables during different times (Schumm 1977)

Variable Geologic Time graded Steady

Time I N.R. N.R.

Initial relief I N.R. N.R.

Geology (Lithology and Structure) I I I

Palaeo climate I I I

Palaeo hydrology D I I

Relief or volume of system above base level D I I

Valley dimensions (width depth, slope) D I I

Climate (mean temperature, precipitation, seasonality) X I I

Hydrology (mean discharge of water and sediment) X I I

Channel morphology X D I

Observed Qw, Qs X X D

Hydraulics of flow X X DI = Independent D = Dependent

NR = Not relevant X = Indeterminate


Table 4.6 Effect of uplift and subsidence on channel morphology (Ouchi 1985)

Zone A B Axis C D

m 2.00 3.50 4.50 5.65 7.00

Bria

ded

chan

nel Aggradation

Talweg shiftSubmerged bars

DegradationTerrace formation

Single bars

AggradationBraided

Upl

iftS

ubsi

denc

e

DegradationSingle Talweg

AggradationBraided

Flooding DegradationSingle talweg

Mea

nder

ing

chan

nel Aggradation Flooding

Multiple channelsDegradation Aggradation

Sinuosity increaseBank erosion

Sinuosity increaseBank erosion

Upl

iftS

ubsi

denc

e

Degradation Aggradation Local scour

Flooding, cut-off Multiple channels

Flow Direction

zone of uplift or subsidence

i) Some tributaries got blocked by temporary dams created by the debris falling in them from landslides;

ii) Subsequent bursting of these dams caused large floods;iii) A large quantity of sediment was brought down in the Brahmaputra causing aggradation of the

order of two to three metres over several kilometers; andiv) Some tributaries shifted their course.

According to Walters (1975) channel widening and meander cut-offs in the Mississippi river in theearly 19th century were due to New Madrid earthquakes of 1811 and 1812.

References

Anstey, R.K. (1965) Physical Characteristics of Alluvial Fans. U.S. Army Natick Laboratory, Tech. Rep. ES-20

Bloom, A.L. (1978) Geomorphology: A Systematic Analysis of Late Cenozoic Landforms. Prentice Hall Inc.,Englewood Cliffs (U.S.A.), Chapter 12.

Bridge, J.S. (1983) Flow and Sedimentary Processes in River Bends: Comparison of Field Observations andTheory. In River Meandering: Proc. of Conference Rivers 1983, ASCE, pp. 857-872.

Brush, L.M. Jr. (1961) Drainage Basins, Channels, and Flow Characteristics of Selected Streams in CentralPennsylvania. USGS Prof. Paper 282-F

Bull, W.B. (1962) Relations of Alluvial Fan Size and Slope to Drainage Basin Size and Lithology in WesternFrenso County, California, USGS Prof. Paper 450-B.

River Morphology108

Bull, W.B. (1964) Alluvial Fans and Near Surface Subsidence in Western Fresno County, California, USGS Prof.Paper 237-A.

Chitale, S.V. (1970) River Channel Patterns. JHD, Proc. ASCE., Vol. 96, HY 1, Jan. pp.201-222

Cotton, C.A. (1941) Landscape: As Developed by the Processes of Normal Erosion. Cambridge University Press,U.K.

Craig, R.C. (1982) The Ergodic Principle in Erosion Models. In Space and Time in Geomorphology (Ed. ThorneC.E.). George Allen and Unwin Ltd., London. pp. 81-115.

Davis, W.M. (1909). Geomorphological Essays. Ginn and Co., U.S.A.

Dury, G.H. (1969) Relation of Morphology to Runoff Frequency : In Introduction to Fluvial Processes (Ed.Chorley R.J.) Mathuen and Co. Ltd., Chapter 9.11

Esterbrook, D.J. (1969). Principles of Geomorphology. McGraw Hill Book Co., New York, U.S.A.

Garde, R.J. (1972) Bed Material Characteristics of Alluvial Streams. Sedimentary Geology. Vol.7. pp 127-135

Garde, R.J. (1978) Irrigation in Ancient Mesopotamia. ICID Bulletin, New Delhi, Vol..27, No. 2, July, pp. 11-22.

Garde, R.J. and Kothyari, U.C. (1990). Erosion Prediction Models for Large Catchments. InternationalSymposium on Water Erosion, Sedimentation and Resources Conservation. CSWCRTI, Dehradun, Oct, pp.89 - 102.

Gee, E.P. (1951).The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629-638.

Gole, C.V. and Chitale, S.V. (1966) Inland Delta Building Activity of Kosi River. JHD, Proc. ASCE, Vol. 92, No.HY-2, March, pp. 111-126.

Hack, J.T. (1957). Study of Longitudinal Stream Profiles in Virgina and Maryland. USGS Prof. Paper 294-B.

Hack, J.T. (1960). Interpretation of Erosional Topography in Humid Temperature Regions. Am. Jour. Sci. Vol.285A, pp. 80-97.

Horton, R.E. (1945) Erosional Development of Streams and Their Drainage Basins: Hydrophysical Approach toQuantitative Morphology. Geo. Soc. of Am., Bull. Vol.56.

Johnson, D. (1932). Streams and Their Significance. Jour. of Geol. Vol. 40, Aug. – Sept.

Kellerhals, R., Church M. and Bray D.I. (1976) Classification and Analysis of River Processes JHD, Proc. ASCE,Vol. 102 No. HY 7 July pp. 813-830

King, L.C. (1962). Morphology of Earth. Oliver and Boyd., U.K.

Krishnan, M.S. (1982). Geology of India and Burma. CBS Publishers and Distributors, India. 6th Edition, ChapterIII.

Lane, E.W. (1955). The Importance of Fluvial Morphology in Hydraulic Engineering. Proc. ASCE, Paper 745,July, pp. 1-17.

Lane, E.W. (1957). A Study of Shape of Channels Formed by Natural Streams Flowing in Erodible Material. USArmy Engineers Division, Missouri River, Corps of Engineers, Omaha, U.S.A. No. 9.

Langbein, W.B. and Schumm, S.A. (1958). Yield of Sediment in Relation to Mean Annual Precipitation. Trans.AGU, Vol. 39. pp. 1076-1084.

Leopold, L.B. and Wolman, M.G. (1957). River Channel Patterns: Braided, Meandering and Straight. USGS Prof.Paper 282-B, 85 p.

Leopold, L.B. and Wolman, M.G. (1960). River Meanders. Bull. Geol. Soc. of Am. Vol. 71, pp. 769-794

Mackin, J.H. (1948). Concept of Graded River - Bull. Geol. Soc. of Am. Vol. 59, pp. 463-512.

Neill, C.R. (1970). Discussion of Paper “Formation of Flood Plain Lands” JHD., Proc. ASCE, Vol. 96, HY – 1,Jan., pp. 297- 298.

Ouchi, S. (1985). Response of Alluvial Rivers to Slow Active Tectonic Movement. Geol. Soc. of Am. Vol. 96,April, pp. 504-515.


Penck, W. (1924) Die Morphologische Analyse. Jour. Engelhorns Nachfolger, Stuttgart.

Pitty, A.F. (1971). Introduction to Geomorphology. Mathuen and Co., London. pp. 233-236.

Rachocki, A. (1981). Alluvial Fans: An Attempt at an Empirical Approach. A Wiley – Interscience Publication,John Wiley and Sons, New York, U.S.A., 157 p.

Rice, R.J. (1977). Fundamentals of Geomorphology. Longman Inc., New York, U.S.A. 1st Edition.

Richards, K. (1982) Rivers. Mathuen and Co., London. Chapter 8.

Rohan, K. (1967).On the Problems of Longitudinal Profile Stabilization in Streams Transporting Sediment. Proc.12th Congress of IAHR, Fort Collins, U.S.A., Vol. 3 – C28, pp. 237-248.

Rosgen, D. (1996) Applied River Morphology. Pagoda Spring, Colorado (U.S.A.)

Rozovskii, I.L. (1961) The Flow of Water in Bends of Open Channels. Israel Program for Scientific Translations,Jerusalem.

Schumm, S.A. (1969). Geomorphic Implications of Climatic Changes. In Introduction to Fluvial Processes (Ed.Chorley R.J.) Mathuen and Co., London, Chapter 11.11

Schumm, S.A. (1971). Fluvial Geomorphology: The Historical Perspective. In River Mechanics (Ed. Shen H.W.)Published by H.W. Shen, Fort Collins, U.S.A., Chapter 4.

Schumm, S.A. (1977). The Fluvial System. A Wiley – Interscience Publication. John Wiley and Sons, New York,U.S.A.

Schumm, S.A, Mosley, N.P. and Weaver, W.E. (1987). Experimental Fluvial Geomorphology. A Wiley Inter-Science Publication. John Wiley and Sons, New York, U.S.A., 2nd Edition.

Simons, D.B. and Albertson, M.L. (1963) Uniform Conveyance Channels in Alluvial Material, Trans. ASCE, Vol.128, pp. 1.

Silvester, R. and de La Cruz, C.d. R. (1970) Pattern Forming Forces in Deltas. JWHD, Proc. ASCE, Vol. 96, No.WW-2, May, pp. 201-217.

Shulits, S. (1941) Rational Equation for river Bed Profile. Trans. AGU, Vol. 22., pp. 522-531

Sparks, B.W. (1972). Geomorphology. Longman Group Ltd., London, 2nd Edition, pp. 275-279.

Thornbury, W.D. (1969). Principles of Geomorphology. Wiley International Edition, John Wiley and Sons Inc.,New York, U.S.A., 2nd Edition.

Wadia, D.N. (1961). Geology of India. MacMillan and co. Ltd., London. 3rd Edition (Revised)

Walters, W.H. Jr. (1975). Regime Changes of the Lower Mississippi River. M.S. Thesis, Civil EngineeringDepartment, Colorado State University, Fort Collins, U.S.A.

Worcester, P.G. (1948). A Text Book of Geomorphology. D. Van Nostrand Company Inc., New York, 2nd Edition.

5C H A P T E R

Hydraulics of Alluvial Streams

5.1 INTRODUCTION

Alluvial streams are those, which flow through sandy material, carve their channels through it and carrywater and sediment. In dealing with alluvial streams the material in the bed and banks of the channel isgenerally assumed to be non-cohesive, though some of the fine sediment in transport may settle on thebanks and make the bank material cohesive. In the discussion below unless otherwise stated the flow isassumed to be steady and uniform and the channel is taken as prismatic. Gravel-bed rivers are thoseflowing through very coarse material with rather steep slopes, and their characteristics are discussed inChapter VII. The following aspects of the alluvial streams are relevant to the theme of the book and arediscussed below.

• Beginning of motion of uniform and non-uniform material: critical shear, and critical velocityapproaches

• Modes of sediment transport

• Bed-forms• Resistance to flow• Sediment transport

■ Bed-load

■ Suspended load■ Total load

5.2 INCIPIENT MOTION

Consider a channel with given slope and bed material. As the discharge (and hence the depth flow) isgradually increased and bed condition observed, it will be seen that up to a certain depth there is nomovement of sediment on the bed. However, with further increase in depth a stage is reached whenrandom occasional motion starts on the bed. This is known as the incipient motion condition or the

Hydraulics of Alluvial Streams 111

condition of critical motion. In determining this condition in laboratory experiments, the criterion couldbe a single particle moving, a few particles moving, general movement on the bed, or the limitingcondition when the rate of sediment transport tends to zero. Out of these the last one is considered morerational even though, in the past investigators have used one or the other criteria, which has madecomparison of formulae for critical tractive stress difficult. Knowledge of the condition of incipientmotion is important in sediment transport studies, in the design of channels carrying clear water, anddegradation phenomenon.

In the case of steady uniform flow the average shear stress on the bed is given by to = gf RSo whereR is the hydraulic radius and So is the bed slope, which is equal to the water surface slope Sw and slopeof energy line Sf. In the case of non-uniform flow this shear stress is given as to = gf RSf . The conditionof incipient motion for given sediment can be related to the average shear stress on the bed to to, averagevelocity of flow U or velocity at the level of particle ud.

Empirical Equations: Critical Shear Stress ApproachDuring the latter part of the 19th century and first four decades of the 20th century, a number ofinvestigators carried out experiments in the laboratory to determine the critical shear stress at whichsediment of given characteristics would move. Equations proposed by Kramer, USWES, Chang, Krey,Schoklitsch, Indri, Sakai and Aki and Sato (see Garde and Ranga Raju, 2000) fall under this category.Most of these formulae can be expressed as

toc = Fr r

rs f

f

d

M

-F

HGI

KJ...(5.1)

and can take the form toc = const r r

rs f

f

d

M

-F

HGI

KJ. All these formulae recognise that the toc depends on,

r rr

s f

f

-F

HGI

KJ d and M; here M is Kramer’s uniformity coefficient. However, their actual forms are

different, because (i) each equation is based on a limited amount of laboratory data, and (ii) these arebased on different criteria for defining critical condition viz. isolated, appreciable or general movementon the bed.

Some theoretical and semi-theoretical analyses have also been carried out by investigators such asShields, White, Kurihara, Iwagaki, and Egiazaroff (see Garde and Ranga Raju, 2000) to determine theincipient motion condition for cohesionless sediment particles of size d. However, we will discuss onlyShields’ (1936) analysis since it is based on sound principles and even after seven decades the results areoften quoted and widely used.

Shields� (1936) AnalysisAccording to Shields, at condition of incipient motion of the sediment particle of size d on the bed, thedrag force on the particle caused by fluid flow is equal to the force required to move the particle. UsingKarman-Prandtl’s equation for velocity distribution in turbulent flow, namely

River Morphology112

u

ud

*

= f1 u d

v*F

HIK ...(5.2)

one can determine ud. Here ud is the velocity at the top of the particle level, u* = shear velocity tr

o

f

, d

is the particle size, and v the kinematic viscosity. The fluid force on the particle is given by F1 = CD p d2

4

rf ud

2

2 = CD rf

ud2

2 ́ a2 d

2 where a2 is a constant that depends on the shape of the particle. But the drag

coefficient CD = f2 u d

vdF

HIK = f3

u d

v*F

HIK .

Hence F1 = f3 (R*) rf u*

2

2 f1

2 (R*) a2 d2 ...(5.3)

where R* = u d

v*

The resisting force F is related to the submerged weight of the particle and the coefficient offriction. Hence F can be expressed as

F = a1 (gs – gf) d3 ...(5.4)

where a1 depends on the shape of the particle and the coefficient of friction. Equating F and F1 underincipient motion condition and introducing the subscript c to indicate incipient motion condition, onegets

a1 (gs – gf) d3 = f3 (R*c) rf

u c*2

2 f1

2 (R*c) a2 d2

ort

g goc

s f d-d i=

2 1

2

aa

f (R*c)

where R*c = u d

vc* . The coefficient a1 and a2 can be assumed to be constant for particles of given shape.

Hence under the condition of incipient motion

tgoc

s dD= f

u d

vc*F

HIK or t*c = f (R*c) ...(5.5)

Shields used closely graded sediment viz. sand, barite, granite, amber, and brown coal with relativedensity varying between 1.06 and 4.25. He used the critical condition corresponding to the case where

bed-load transport is zero and produced a graph between tgoc

s dD and

u d

vc*F

HIK . Later the mean curve


through the points was drawn by Rouse (1939) who gave wide publicity to Shields’ work in English-speaking countries. Recently Shields’ work has been critically examined by Buffington (1999) whopointed out certain ambiguities in Shields’ presentation; however the writer feels that this criticism doesnot reduce the importance of Shields’ work. Yalin and Karahan (1979) used large volume of data oncritical shear stress of nearly uniform material and prepared a modified curve between t*c and R*c. Thetwo curves of Shields’ and Yalin and Karahan are shown in Fig. 5.1. It is relevant to mention the

significance of parameters used by Shields. The graph tgoc

s dD vs

u d

vc*F

HIK bears similarity to the

transition function for friction factor for pipes. The straight line portion on the right has d¢ < < d and isapplicable for hydrodynamically rough surface. In the region 2.5 < R*c < 40, the laminar sub-layer and d

are of same order of magnitude and it represents the transition region. For u d

vc*F

HIK < 2.5 the boundary is

hydrodynamically smooth and d¢ >> d.

Fig. 5.1 Critical tractive stress relation for developed turbulent flow according to Shields, and Yalin and Karahan

Two additional comments are warranted about Shields’ diagram. Some investigators have arguedthat according to dimensional analysis the ratio of depth of flow to size of sediment would be anotherrelevant parameter governing critical condition. Even though such argument looks logical, it must berealised that flow conditions including turbulence close to the wall, which are responsible for sedimentmovement, depend on shear velocity and relative distance from the wall measured in terms of multiplesof particle diameter. The thickness of boundary layer that equals the depth of flow in open channels isnot important. Secondly, Gessler (1965) has emphasised that the shear stress on the bed fluctuates andfollows Gaussian law with standard deviation of 0.57. Hence in a sediment mixture there is no cut-offparticle size such that one could say all particles larger than cut-off size will stay in bed and those finerwill be moved. In other words the sediment movement is probabilistic in nature. The statistical variationof shear stress as well as orientation of individual particles is responsible for this. By sampling the bedsurface layer, Gessler determined that size for which the probability of remaining in bed is 0.50; theaverage shear stress was critical for that size. In this way he obtained critical stress values for varioussizes and obtained curve similar to Shields’ curve. In this analysis Gessler made no allowance for theeffect of sediment non-uniformity on toc. He obtained toc values somewhat smaller than those obtained

by Shields for the same u d

vc*F

HIK . According to Gessler (1965) this has happened primarily because

u d/v*c

10�1

10�2

t oc/(

�)d

g sfg

10�1

100

101

102

103

Yalin-Karahan

Shields

Data from different sourcesfor developed turbulent flow

100

River Morphology114

Shields has considered difference between time-averaged bottom shear stress and critical shear stress inobtaining the condition for zero bed-load transport, whereas he should have used the time average ofdifference between instantaneous bottom shear stress and critical shear stress. According to Shields, andYalin and Karahan, limiting value of t*c for coarse material is 0.060 and 0.045 respectively.

It may be noticed that u*c occurs in both the parameters of Shields relationship; hence if one wantsto determine t*c or u*c for given Dgs, rf, d and v, a trial and error procedure has to be used. This can beavoided by using another parameters R0

2* defined as

R02* = (R*c)

2 D g

ts

oc

dFHG

IKJ =

D gr

s

f

d

v

3

2 ...(5.6)

and R02* can be plotted against

tgoc

s dD. Choosing different points on the curve in Fig. 5.1 the following

table is prepared which can give directly values of tgoc

s dD and hence toc for known values of, Dgs, rf v

and d.

Table 5.1 Variation of t

goc

s dD with Ro

2* according to Fig. 5.1

Ro2* 0.01 0.05 0.926 6.40 60.0 2065 3225 11764 40000 108900

and above

tgoc

s dD0.25 0.20 0.14 0.10 0.066 0.031 0.031 0.034 0.04 0.045

Mantz (1979, 1983) has carried out experiments on transport of sediment in the size range of 0.01mm to 0.10 mm. According to him if soft water is used these sediments exhibit the same packingproperties as cohesionless material. His critical shear results support Yalin and Karahan’s curve for fullydeveloped flows.

It needs to be mentioned that in turbulent flow all flow parameters fluctuate and so does theboundary shear stress. Therefore beginning of motion of sediment particles as well as its transport on thebed is a stochastic phenomenon. As mentioned earlier Gessler (1965), Grass (1970), Yalin (1977) andMantz (1979) have used a stochastic approach in the analysis of sediment movement. Another commentthat needs to be made is the role of lift force in Shields’ analysis. When the fluid flows past a sphericalparticle resting on the bed, a lift force is generated due to modification of flow pattern around theparticle (Jeffrey 1929). The magnitude of this force would depend on the same parameters as the drag ordrag coefficient, namely u*d/v. Hence lift force is implicitly taken into account in Shields’ analysis.

Critical Velocity ApproachThe idea of using average velocity of flow for describing the incipient motion condition is logical sincethe average shear stress on the boundary will depend on U and D or R; further U and D or R can be more


directly obtained than to. Earlier attempts were made by Brahms, Airy and Rubey to relate criticalvelocity to size and relative density of the particle (see Garde and Ranga Raju 2000). Thus equating thedynamic force on the sediment particle to its resistance to motion, Brahms obtained

x p d2

4 rf

ud2

2 =

p d3

3 (gs – gf) tanq ...(5.7)

Here x is the fraction indicating the part of frontal area of the particle exposed to the flow, tan q isthe friction coefficient, and ud is the velocity at the level of particle at which particle will move. Thisgives

oru k d

u K W

d

d

2

61

=

=

UV|

W|...(5.8)

when the particle is under the incipient motion condition. Here K and K1 are constants and W is theweight of the particle. Some empirical or semi-theoretical equations have been proposed for ud or Umainly for hydrodynamically rough boundary.

These are based on analysis of experimental data for nearly uniform material and are listed below.

Garde (1970)

uds

fdcr

D gr

= 1.51 ...(5.9)

Neill (1968)

Ud

crs

f

D gr

= 1.414 D

dFHIK

1 6/

...(5.10)

Garde (1970)

Ud

crs

f

D gr

= 0.5 log D

dFHIK + 1.63 ...(5.11)

Levy (see Bogardi 1974)

U

gdcr = 1.4 1

7+

FHG

IKJ

lnD

d ¼ if 1.0 £ D

d £ 60 ...(5.12)

U

gdcr = 1.4 ln

D

d7FHIK ¼ if D

d > 60 ...(5.13)

River Morphology116

With certain manipulation of equation for the mean velocity in open channels and the Shields’

curve, it is possible to obtain expressions for Ud

crs

f

Dgr

as related to D

d and Ro*

2 = Dgr

s

f

d

v

3

2 for

hydrodynamically smooth, transition and rough boundaries. For this, consider the equation

U

u*

= 5.75log10 12 2765

.R

dx

FHG

IKJ

which is valid for plane surface; Here x is related to u d

v* 65 as follows:

u d

v*

.65

1160.2 0.3 0.50 0.70 1.0 2.0 4.0 6.0 10 and more

x 0.7 1.0 1.38 1.56 1.61 1.38 1.10 1.03 1.0The above equation can be written as

U

dcr

s

f

Dgr

= t*c1/2

5 75 6 26 5 75. log . . logD

dx+ +L

NMOQP

for uniform sediment. This needs to be used along with Shields’ relationship (in Tabular form) between

t*c, Ro2 and

u d

vc* . For each value of t*c and Ro

2 different values of D

d are chosen and knowing

u d

vc* , x

is determined and then U

dcr

s

f

Dgr

. Thus a set of values of U

dcr

s

f

Dgr

, D

d and Ro*

2 were obtained along with

u d

vc* . On the basis of these generated values the following equations are obtained

Smooth boundary u d

vc* .<F

HIK2 5

U

dcr

s

f

Dgr

= 1.77 D

dFHIK

0 166.

Ro2 0 05

d i.

Transition 2 5 7 0. .*< <FH

IK

u d

vc

U

dcr

s

f

Dgr

= 1.38 D

dFHIK

0 18.

...(5.14)

Rough u d

vc* .>F

HIK7 0

U

dcr

s

f

Dgr

= 1.656 D

dFHIK

0 18.

U

V

|||||||

W

|||||||


Figure 5.2 shows comparison of equations for U

dcr

s

f

Dg

r

for rough boundaries.

Critical Shear Stress for Non-uniform SedimentsWhen the channel bed consists of a mixture of different sizes of non-cohesive sediment, the criticalshear stress toci of any size di in the mixture can be determined by carrying out a series of experimentsunder steady uniform flow condition with decreasing shear stress and preparing a graph of qB vs to foreach size. By setting the condition that to = toci when the dimensionless bed-load transport of size di isnegligibly small (or less than a predetermined value), toci can be determined for different sizes in themixture. Value of toci for any size di is affected due to sheltering effect caused by the presence ofsediments of size greater than di and relatively greater exposure to flow for larger sizes. Hence if one

takes arithmetic mean size da as the reference size, and further defines t*ci = tgoci

s diD and t*ca = t

g

*ca

s daD

Fig. 5.2 Comparison of equations for Ucr / (∆g rs d / f ) for rough boundary

10(

d/

)D

gf

sr

Ucr

D/d

10000

0

100010010

2

1

3

4

5

6

7

8

9

GardeEq. 5.11

Eq. 5.10

Eq. 5.14c

Eq. 5.12

Levy

Neill

River Morphology118

where toci and toca are critical shear stress for sizes of di and da respectively, it is logical to expect that

t

t

*

*

ci

ca would be a function of

dida

FHGIKJ

.

Analysis of Egiazaroff (1965), Ashida and Michiue (1971), Hayashi et al. (1980) and others

indicates that indeed t

t

*

*

ci

ca is primarily a function of

dida

FHGIKJ

when the material is coarse and hence

viscous effects can be neglected. The equations proposed by these investigators are listed below andplotted in Fig. 5.3.

Egiazaroff (1965)

t*ci = 0 10

192

.

logdida

FHG

IKJ

...(5.15)

Ashida and Michiue (1971)

t*ci = 0 10

192

.

logdida

FHG

IKJ

...(5.16)

When dida

FHGIKJ

is between 0.40 and 1.0, they found that this equation gives a larger value than

observed when dida

FHGIKJ

is less than 0.40. Tentatively they assumed

t

t

*

*

ci

ca= 0.85

dida

FHGIKJ-1

...(5.17)

for dida

less than 0.40.

Hayashi et al. (1980)

t*ci = dida

FHGIKJ-1

for dida

£ 1.0

U

V

|||

W

|||

...(5.18)

t

t

*

*

ci

ca=

loglog /

88

2

di dab gL

NMM

O

QPP

for dida

> 1.0

Earlier it was found that the value of t*ca varied between 0.05 and 0.02 and an average value of 0.03was recommended.


Recently Patel and Ranga Raju (1999) have collected addition data and found that t*ca depends on

the geometric standard deviation sg = d

d84

16

FHG

IKJ

the relationship between the two being

t*ca = 0 045

0 60

..

sg

...(5.19)

Patel and Ranga Raju (1999) have also proposed the following relationship between t

t s

*

*

ci

c and

dids

t

t s

*

*

ci

c =

dids

FHGIKJ-0 96.

...(5.20)

in which t*cs = t

g s

oc

s dD and ds = dg sg there is a relationship between t*cs and sg as listed below.

Hence for known size distribution of bed material one can determine sg, geometric mean size dg andds = (dg

sg). Then knowing t*cs from the table below for known, sg Eq. 5.20 will give t*ci for the size di.

Their studies also indicated that if arithmetic mean size is used, Hayashi’s equation yields more accurateresults than the other equations.

Fig. 5.3 Variation of t*ci /t*ca with di /da for mixtures

Table 5.2 Relationship between sg and t *cs

sg 1.0 1.5 2.0 3.0 6.0t*cs 0.045 0.03 0.21 0.15 0.13

20.0

d

da

i

1.0 10.00.10.05

10.0

1.0

0.2

t

a

*c

*ct

Egiazaroff (1965)Ashida-Michlue (1971)Hayashi et al. (1980)

River Morphology120

5.3 MODES OF SEDIMENT TRANSPORT

Once the shear stress acting on the bed exceeds the critical shear stress for the bed material, the sedimentparticles start moving in the general direction of flow and the manner in which these are transporteddepends on the flow conditions, ratio of densities of sediment and fluid and the size of the particle.These modes of transport can be classified into the following categories.

Contact loadThe sediment particles that roll or slide along the bed for some time, then come to rest and again startrolling or sliding constitute the contact load. Hence contact load is the material rolled or slid along thebed in substantially continuous contact with the bed.

Saltation loadThe sediment particles hopping or bouncing along the bed thereby losing contact with the bed for sometime constitute saltation load. Hence saltation load is the sediment bouncing along the bed, or moveddirectly or indirectly by the impact of bouncing particles.

Bed-loadSince saltation load, especially in streams, is difficult to measure, it is clubbed with contact load andsediment moved on or near the bed is called bed-load.

Suspended loadSuspended load is the material moving in suspension in the fluid, being kept in suspension by theturbulent fluctuations.

According to the theory of suspended sediment distribution; if w

ko

u*

> 5.0 there is no suspended

sediment (see section 5.7). Hence taking Karman constant k = 0.40, the material will be transported as

bed-load if wo

u*

> 2.0; however material of size d will move if tg

o

s dD is greater than that gives by

Shields’ diagram. Hence for purely bed-load transport the conditions to be satisfied are tg

o

s dD is greater

than tgoc

s dD and

wo

u*

is greater than 2.0.

One can also assume that when vertical turbulent fluctuation near the bed is greater than the fall

velocity wo, sediment will go into suspension. At the edge of laminar sub-layer ¢u

u

2

*

= 2.5 to 3.0 and

¢

¢

v

u

2

2 0.4 to 0.50. Hence it can be assumed that near the bed ¢v 2 » u* at incipient suspension. Several

investigators e.g. Van Rijn, Sumer, Celik and others have related wo

su*

to D gr

s

f

d

v

3

2 and it is found that this

variation is fairly well represented by the empirical equation


1

2 3 4

wo

su*

= 0.5 D gr

s

f

d

v

3

2

0 40F

HGI

KJ

.

up to D gr

s

f

d

v

3

2 values of 20. Here u*s is the shear velocity at incipient suspension of sediment of size d

and fall velocity wo.Daniel, Durand and Condolios (1953) have presented an interesting description, albeit qualitative,

of the mechanism of saltation. They have considered four idealised positions in which a particle will befound on the surface of the bed and the possibility of their movement by saltation is discussed. Thesepositions are shown in Fig. 5.4.

Fig. 5.4 Particle position and its susceptibility to saltate

Out of the four possible positions, the particle in position 2 is more likely to travel by saltation underfavourable hydraulic condition. The two forces acting on the particle are the submerged weight of theparticle acting vertically downwards and resultant hydrodynamic force, which consists of drag and lift.Where the lift is equal to the submerged weight of the particle, the particle will be lifted up therebyincreasing the lift. The particle acquires a vertical velocity and eventually in the final stages of takingoff, the movement is accompanied by a quick rotation as shown in the second part of the figure.

The particle in position 1 will either slide or roll over the layer of other particles. Particle in position3 can have the saltation movement only if the particles upstream of it move in such a way that theparticle in position 3 is brought in position 2, or the particle in position 3 occupies some other positionbecause of the impact of the particle in saltation movement. The particle in position 4 will be set inmotion mostly under the condition of direct or indirect effect of particle in saltation.

According to Kalinske (1942) the height of saltation, for the same particle size, is proportional tothe ratio of mass densities of sediment and fluid. Hence it is apparent that the height of saltation in air isabout 800 times that in water for the same particle. For this reason saltation is not very important for

River Morphology122

sand transport in water. The phenomenon of saltation is further analysed by Hayashi and Ozaki (1980).While Einstein assumed that the saltation height hs is twice the diameter of the particle, Hayashi and

Ozaki’s analysis indicates that hs/d i.e. the dimensionless height of saltation depends on t¢* and wo d

vwhere t¢*,

is the dimensionless grain shear stress and the value of hs/d can vary between 0.1 and 6.0

(see Fig. 5.5); similarly the step length ls

d also depends on t¢* and

wo d

v (see Fig. 5.6); however when

wo d

v greater than about 100, as assumed by Einstein (1950)

l s

d » 100 ...(5.21)

Fig. 5.5 Saltation heights (Hayashi and Ozaki 1980)

At this stage it is interesting to know about the motion of individual particles moving as bed-load.With the advent of radio isotopes, some information has been gathered about the average rate at whichsediment particles move on the channel bed. Such measurements by Hubbell and Sayre (1964) in thecase of the Middle Loup river, and laboratory flume indicate the following.

Table 5.3 Rate of movement of individual particles

U m/s D m d mm Bed condition Ug m/hr

Middle Loup river in USA 0.527 0.76 0.29 Dunes 0.9Lab. flume 2.44 m wide 0.610 0.317 0.93 Long low dunes 2.0Lab. flume 2.44 m wide 0.326 0.317 0.19 Ripples 0.02

Thus, it can be seen that the average velocity of particles moving as bed-load is much smaller thanthe flow velocity. The analysis of Engelund and Fredsoe along with Luque and Van Beek indicates that(see Garde and Ranga Raju, 2000) the average velocity of bed particle Ug is given by

t¢*

10�1

108

6

4

2

18

6

4

2

10�1

2 10�14 6 8 8642 21

ls

d

R = d/v

/ = 2.65

C = 0.50

ef

r

w

r

o

s f

L

R = 40eg100400

R 2000ef ³

4R

= 10ef


Fig. 5.6 Step lengths (Hayashi and Ozaki 1980)

U

ug

*

= 9 1 0 7-

FHG

IKJ

. *

*

t

t

c ...(5.22)

where t*c can be obtained from Shields’ diagram. It may be further mentioned that when the particlegoes into suspension it is carried by the flow in the forward direction at the flow velocity at that level.

It is appropriate to mention distinction between bed material load and wash load at this place. Thesediment load carried by an alluvial stream can be divided into bed material load and wash load. Bedmaterial load is that part of the sediment load carried by the stream that has originated from the bed andbanks of the stream; hence it consists of sediment sizes found in appreciable quantity in the bed andbanks of the stream. Bed material load correlates well with the hydraulic conditions in the stream. Theother part of the sediment load is composed of those fine sizes not available in appreciable quantities inthe bed and banks of the stream. This part, known as wash load, is washed into the stream from thecatchment and is usually finer. Hence, the amount of wash load carried by the stream is more related tothe hydrologic conditions of catchments than to the hydraulic conditions in the stream. For this reason itis difficult to estimate the amount of wash load carried by the stream. It is usually not possible tostipulate the size limit for wash load. For sandy streams with flat slopes, the wash load may be in the clayand silt range. On the other hand in the case of mountain streams with steep slopes, wash load may be inthe range of coarse to fine sand. Einstein (1950) recommends that the limiting size for the wash loadmay be arbitrarily taken from the mechanical analysis of the bed material, as that size of which tenpercent of the material is finer. Hence one can write

Total load of stream = (bed material load) + (wash load)

Bed material load = (bed-load + suspended load)

101 2 10

�14 6 8 8642 21

ls

d

R = 40eg

100

R = d/v

/ = 2.65

C = 0.50

ef

r

w

r

o

s f

L

R=

4

ef

200

t¢*

10080

60

40

20

108

6

4

2

1

= 100 t¢*

10

400

³ 2000

ls

d

River Morphology124

5.4 BED-FORMS IN UNIDIRECTIONAL FLOW

Once the critical shear stress on the bed in unidirectional flow is exceeded, the sediment particlesforming the bed are transported at a rate, which increases with increase in shear stress on the bed. Thebed in the process remains plane under some conditions, but under other conditions developstransversely oriented bed features known as ripples, sand waves or dunes, and antidunes as observed byBlasius, Cornish, and Gilbert and recently by Simons et al. These bed-forms travel beneath the flow,take part in the sediment transport, and govern the relationship between flow velocity, flow depth andslope. In other words, they affect the friction and sediment transport. They also leave back acharacteristic imprint in the enclosed deposits. The purpose of this section is to describe thecharacteristics of these bed-forms and study the methods available for their prediction.

Definitions of Bed-formsThe Task Force of ASCE (1966) has given the following descriptions/definitions of various bed-forms:

Ripples are small bed-forms with wavelengths less than about 0.30 m and heights less thanapproximately 30 mm. They occur only rarely in sediments coarser than approximately 0.60 mm. Theseare sometimes called current ripples.Dunes are bed-forms larger than ripples but smaller than bars (see below) and are out of phase withwater surface gravity waves that accompany them. These are some times called sand waves or sand bars.Bars are bed-forms having lengths of the some order as the channel width or greater, and heightscomparable to the mean depth of generating flow. Point bars at the bend and alternating bars fall in thiscategory.

With increased shear stress, dunes tend to get washed out and especially for finer material they can

be completely washed out and a flat or a plane bed can form. At this stage Froude number U/ gD can

be high but less than unity.Further increase in flow leads to the formation of symmetrical sinusoidal sand waves on the bed and

similar water surface waves in phase. These are known as standing waves. Further increase in flowcauses these waves to move upstream, increase in amplitude and then break. These are called antidunes.After breaking of waves the bed becomes plane and undergoes the same sequence. These bed-forms areshown in Fig. 5.7.

Jackson II (1975) classifies bed-forms occurring in shearing flows on the basis of bed-form size,time span of existence, superposition, flow regime and channel process. The larger bed-forms (macro-forms), such as point bars, pools and riffles respond to geo-morphological regime of the environmentand are relatively insensitive to changes in fluid dynamic regime during an individual dynamic eventsuch as a flood in a river. A two-zone structural model of turbulent boundary layer provides a geneticframework for two smaller classes of bed-forms. Meso forms, such as dunes in the rivers, respond toflow conditions in the outer zone of the turbulent boundary layer as the flow varies through the dynamicevent; their life scales correspond with the duration of that event. The smallest bed-forms (micro forms)viz. the ripples are governed by the flow structure in the inner zone i.e. the laminar sub-layer; their livesare much shorter than the periodicity of dynamic events. According to Jackson II, ranges of wavelengths of the different bed-forms are:


Ripples 50 mm to 2.0 mmDunes 0.40 m to 300 mSand waves and alternate bars 10 m to 1000 mSand bars, point bars 500 m to 5000 m

As mentioned earlier, alternate bars and point bars are the largest in each environment and theirdimensions compare to those of the environmental flow system. They are quite insensitive to changes inflow.

Jackson II identifies four different types of super positions of bed-forms. These are as follows:1. Imposition of lower regime bed-form upon the bed-form moulded by higher flow regime e.g.

small ripples migrating over upstream face of dunes.2. Under equilibrium condition such superposition of ripples and dunes can be explained from

stability considerations. According to Kennedy (1969) perturbations of bed-load transport ratesare responsible for ripple formation while perturbations of the longitudinal distribution ofsuspended load cause dunes. Hence when appreciable suspended load is present, ripples anddunes can be superposed e.g., in fine to medium sands.

3. Superposition of fluid dynamic bed-forms on much larger bed-forms that are more permanente.g., large scale ripples on the point bar.

4. Superposition in which neither bed configuration responds to be local fluid dynamic regime;e.g., mid-channel islands and sand bars in braided rivers such as the Brahmaputra river asobserved by Coleman.

Jackson II also discusses about three universal time scales of unsteadiness and discusses the effectof each upon the bed-forms. The shortest time scale is that of the turbulent boundary layer of the flow,

Fig. 5.7 Bed-forms in alluvial channels

(h) Chutes and pools

(g) Antidunes, breaking waves

Breaking antidune wave

(f) Antidunes, standing waves

(e) Plane bed

(d) Washed out dunes or transition

(c) Dunes

(b) Dunes with ripples superposed

(a) Typical ripple pattern

Weak boil

Boil Boil

Pool PodAccelerating flowF < 1r

River Morphology126

for which a wide spectrum of time scales exists. The shortest is the time scale of Kolmogorov and is ofthe order of a second. The largest corresponds to large eddies and their scales are of the order of a minuteor a few minutes. Several investigators attribute large-scale ripples to the eddies of this time scale. Thesecond time scale is related to each dynamic event taking place in the stream. It is the time interval TE inwhich the event occurs e.g., passage of flood. The largest time scale is the geo-morphological scale,which encompasses many dynamic events and is much longer than TE. This time scale reflects theimposition of geological controls on the development of bed-forms.

Bed-forms have been observed and measured on some rivers. Lane and Eden (1940) havesummarised the results of field measurements by Johnson in the Mississippi river at Helena. Sand wavesof height up to 6.7 m and length up to 305 m were observed in a depth ranging from 4 to 9 m. Carey andKeller (1957) have also reported measurements on the Mississippi. Whetten and Fullam (1967) havemeasured dune lengths, dune heights and their migration velocity in the Columbia river downstream ofBonneville dam in USA. Measurements have also been reported by Gallay (1967) on the NorthSaskatchewan river in Alberta (Canada), by Singh and Kumar (1974) in the Ganga, the Yamuna and theSon rivers in India, by Itakura et al. (1986) on the Ishikari river Hokkaido, Japan and by Haque andMahmood (1983) in irrigation canals in Pakistan. Similarly a number of laboratory studies have beenconducted during 1950 to 1985 or so. These data have been utilised to study the bed-form dimensionsand criteria for their occurrence.

Distinction Between Ripples and DunesStudies by Garde and Albertson (1959), Yalin (1971) and Garde and Issac (1993) have indicated thatripples form in the initial stages of sediment movement and are near-bed phenomena. Hence their length

scale is obtained from u* and v as v

u*

. Even though earlier Yalin had indicated that for ripples L

d » 1000,

later he indicated that for u d

v* < 3.5

u L

v* = 2250 or

L

d = 2250/(u* d/v) ...(5.23)

Garde and Albertson (1959) had also proposed that H

L for ripples is governed by

u d

v* and

t

g

o

s dD.

Mantz (1992) related u L

v* and

u H

v* to

u d

v* and

t

g

o

s dD. Garde and Issac (1993) have concluded that

ripples will form if sediment size is less than 0.60 mm, u d

v* is less than 10 – 12 and Froude number

U gD less than 0.80. If Fr is greater than 0.80 ripples are changed to symmetrical sand waves.

According to them ripple length and ripple height are given by


L

d= 4115

u d

v*

.FH

IK-0 316

t

g

o

s dD

FHG

IKJ-0 717.

U

V

|||

W

|||

...(5.24)

andH

d=

u d

v*

.FH

IK-0 660

t

g

o

s dD

FHG

IKJ

0.828

Stability AnalysisThe approach of explaining the formation of ripples, dunes and anti-dunes from the consideration ofstability of a plane alluvial bed transporting sediment has been followed by a number of investigatorssuch as Matsunashi, Engelund and Hansen, Kennedy, Hayashi, Engelund, Fredsoe, Parker, Reynolds,Hayashi and Onishi, and Richards. Most scientists today agree that the problem of sand wave formationis a problem of instability of an original plane bed transporting sediment when it is slightly perturbed bya small sinusoidal disturbance. As a result the flow and sediment transport are perturbed. Then there willbe the following two main possibilities:

1. The change in flow pattern and sediment transport will tend to attenuate the amplitude ofperturbation, so that the bed goes back to the original plane bed state. This means that the planebed is stable.

2. The second possibility is that the flow causes the perturbation on the bed to increase with time,which corresponds to the unstable situation, ultimately leading to formation of ripples, dunesand antidunes.

Basically the analysis starts with the equations of motion and continuity equation on which one-dimensional sinusoidal disturbance is introduced. This causes fluctuation in velocity component andsediment transport. The analysis is essentially linear so that higher order fluctuations are neglected.

The instability caused is primarily dependent on the lag distance d which is the distance by whichlocal sediment transport rate lags the local velocity or shear stress at the bed. The total lag effect is builtof the following possible contributions:

1. fluid friction,2. rate of suspended sediment transport in relation to bed-load transport rate,3. gravity forces on moving bed-load,4. inertia of sediment particles, and

5. percolation in river bed.Such stability analysis has indicated the importance of the following parameters in determining the

flow regime, or stable wave length KD or2pD

LFH

IK : Froude number,

D

d,

U

u¢*,

t

g

o

s dD; here K is called the

wave number.

Dune DimensionsSince the outer region of turbulent boundary layer controls formation of dunes, the length and velocityscales that are most appropriate are the depth D and average velocity of flow U. Hence it is expected thatdune length L = constant ́ D. Yalin, Hino and Van Rijn (see Garde and Issac 1993) found the constant

River Morphology128

of proportionality to be 5.0, 7.0 and 7.3 respectively. Using a large volume of laboratory and field dataGarde and Issac (1993) found that

L = 4.737 D ...(5.25)

which has the correlation coefficient of 0.674 and for which 33.25, 57.19 and 83.38 percent of the datafell within ± 30, ± 50, and ± 100 percent error lines. The stability analysis, on the other hand, indicates

that 2pD

L i.e. KD depends essentially on Fr. Figure 5.8 shows this graph. The empirical equation, which

fits the data reasonably well, is

Fr =1

82

++KD KD

KD KD KD

tanh

tanha f...(5.26)

Fig. 5.8 Variation of KD with Fr for dunes (Garde and Isaac 1993)

It was also found that as u d

v* increases

L

D also increases especially when

u d

v* is between 20 and

30. Earlier Hayashi and Onishi had found that D

d is also an important parameter. Hence assuming that

L

D = f Fr

D

d,F

HIK , Garde and Issac obtained the equation

L

D= 4.58 (Fr)0.397

D

dFHIK

0 0546.

...(5.27)

KD

10

1.6

9876543210

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Fr

Flume, River and canal data

Eq. 5.26 Fr2

=1 + tan h

( ) + 8 tan h KD

KD

KD KD2


Accuracy of prediction of L by this equation is slightly superior to that of the equation L = 4.737 D.A number of equations have been proposed for dune height. Some of these are listed below:

Yalin (1971):H

D=

1

6 1-FHG

IKJ

t

t

*

*

c ...(5.28)

Gill (1971):H

D=

12na

(1 – Fr2) 1-FHG

IKJ

t

t

*

*

c ...(5.29)

where a is shape factor for dunes and lies between 0.50 and 0.637, and n is the exponent of shearparameter in the bed-load equation.

Fredsøe (1975):H

L

f

2=

1

50 1

0 060 40

3

- -

FHG

IKJ

..

**

t

t ...(5.30)

where f is Darcy Weisbach friction factor

Allen (1978):

H

D = 0.079865 + 0.0336

t

t

*

* c

FHGIKJ

– 0.004077 t

t

*

* c

FHGIKJ

2

U

V

|||

W

|||

...(5.31)

+ 0.000239 t

t

*

*c

FHGIKJ

3

– 0.0000045 t

t

*

* c

FHGIKJ

4

where t*c = 0.045

Van Rijn (1984): H

D = 0.11

D

dFHIK-0 30.

(1 – e–0.5T) (25 – T) ...(5.32)

where T =¢F

HGIKJ

t

t

*

* c

Using a large volume of data Garde and Issac (1993) concluded that most of these equations predictdune height with 29 to 35 percent of data falling between ± 30 percent error lines. They also concludedthat by far Allen’s equation is marginally superior to the other equations mentioned above. Figure 5.9shows verification of Yalin’s and Allen’s equations using a wide range of flume, canal and river data. Itmay be mentioned that Garde and Issac used flume and field data covering a wide range as can be seenbelow

Sediment size 0.100 mm to 2.4 mmFlow depth 0.051 m to 51 mHeight of undulation 0.011 m to 5.58 mLength of undulations 0.090 m to 252 m

Channel slope 0.015 ́ 10–3 to 14 ́ 10-3

River Morphology130

On the basis of their analysis they found that the maximum value of H

D designated as

H

D m

FHIK is

primarily a function of d

D and is given by

H

D m

FHIK = 0.22 + 0.4

d

DFHIK

0 60.

...(5.33)

and then they proposed the following equations for H

D.

H D

H Dm

/

/

a fa f

= 341.8 t

t

*

*

.

cFHGIKJ

2 57

if 0.03 £ t

t

*

*

c £ 0.103

...(5.34)H D

H Dm

/

/

a fa f

= 1 if 0.103 £ t

t

*

*

c £ 0.150

U

V

||||

W

||||

H D

H D m

/

/

a fa f

= 012

1 15

.

*

*

.t

t

cFHGIKJ

– 0.06 if 0.150 £ t

t

*

*

c £ 0.80

Ripples and dunes are found to move in the downward direction at a velocity Uw that is given byGarde and Kondap as

U

gDw = 0.021 Fr4.0 ...(5.35)

Fig. 5.9 Variation of H/D with t

t

*

*

c for dunes according to Yalin and Allen (Garde and Isaac 1993)

t*c/t*

H/D

0.10.01 10.01

0.1

1

Yalin and Karahan

Allen

Flume dataRiver data

Canal data


Transverse RibsTransverse ribs are regularly spaced rows of clustered pebbles, cobbles or boulders lying at right anglesto the flow on the bars and the channels of braided streams. Their average longitudinal spacing rangesfrom 0.06 m to as large as 2.5 m, and their height ranges from one to two times the maximum size of bedmaterial. Their wavelength seems to be proportional to the maximum size of the bed material, andinversely related to the stream slope. Laboratory experiments indicate that the transverse ribs areassociated with near critical to supercritical flows.

It must be emphasised that the above relations have been obtained assuming the flow to be steadyand uniform. Even though this may be true in the case of flume studies, the flows in rivers are changingwhich can have effect on bed undulations. To study this effect a population of dunes or any bed-formthat occur in a given reach of the channel can be considered and its statistical properties studied. In otherwords frequency distribution of dune height or length can be studied to determine if the distribution isuni-modal or bimodal. Bimodal distribution would imply two types of undulations. Similarly time seriesanalysis has been carried out on a train of dunes. This type of analysis was initiated after studyingchanging dune characteristics in rivers such as the Fraser in British Columbia (Canada) and in theGironde Estuary in France. Further discussion on this aspect can be seen in Chapter XII of SedimentaryStructures written by Allen.

AntidunesAntidunes are symmetrical sand and water waves that are in phase and which may move upstream,downstream or remain stationary. These were first observed by Cornish and then studied in detail byGilbert, Simons, and Kennedy. These were called antidunes because they moved against the flow evenwhen the sediment is transported downstream. As the waves move upstream their amplitude goes onincreasing. However there is a limit to the maximum steepness of water surface waves, which dependson velocity, depth and sediment size. When this limit is reached the waves break, form a plane bed onwhich sinusoidal waves had formed and then the process is repeated. These waves break when height towavelength ratio reaches approximately 0.14. The wavelength of the surface waves is given by

Ls = 2 2pU

g...(5.36)

Antidunes have been observed on several streams in USA, e.g., the San Juan River in Utah, theMuddy creek in Wyoming, the Mendano Creek in Colorado and on the Assiniboine river in Canada.When the antidunes form Fr number is close to or greater than unity.

Prediction of Regimes of FlowFor several reasons engineers, geomorphologists and sedimentologists are interested in predicting thetype of bed-form that would occur for given flow conditions and fluid, sediment and channelcharacteristics in a stream. This is illustrated by two practically important examples. Figure 5.10 showsthe variations of Manning’s n obtained in laboratory flume for sediment size of 0.45 mm when theaverage shear stress is varied. It can be seen that Manning’s n undergoes a three-fold change as the bed-forms change from plane bed without motion, to ripples, to dunes of lower flow regime to the transitionand then upper flow regime of plane bed and anti-dunes. Thus, the resistance to flow changesappreciably with flow conditions and needs to be predicted correctly.

River Morphology132

As can be seen from the above figure the roughness coefficient undergoes a definite reduction as theflow changes from lower flow regime into transition while dunes are washed out and the bed becomesflat. This is reflected in the discontinuous rating curve between discharge q and depth D for the MiddleLoup and the Pigeon Roost Creek in Mississippi (USA) see Fig. 5.11 (Dawdy 1963).

Fig. 5.10 Variation of n with to

Velocity in feet per second

2 41 10

Velocity in feet per second

2 41 103

5

1

2

4

6

10

Hyd

rau

licra

diu

sin

fee

t

3

5

1

2

4

6

10

Hyd

rau

licra

diu

sin

fee

t

Fig. 5.11 Discontinuous stage discharge curves for the Middle–Loup and Pigeon Roost Creek (USA)

Plane bedRipplesDunesTransitionAntidunes

0.038

0.03

0.02

0.01

0.2 1.0 10to

0.45 mm USGS

0.18 mm Barton-Lin

0.01

0.02

0.03

n

n

0.002


Part of the shear stress to, designated as t¢¢o is used in overcoming the form resistance of bed-formsand only the remaining shear stress t¢o = (to – t¢¢o) is available for bed-load transport. It is found that bed-load transport rate correlates well with t¢o and not with to. Therefore, for the same shear stress andsediment characteristics, the bed-load transport rate will be smaller when dunes than when it is flat coverthe bed. Thus, regime of flow also plays an important role in sediment transport phenomenon.

A number of attempts have been made to develop criteria for the prediction of regimes of flow.These are based on the valuable experimental data collected by Gilbert, U.S.W.E.S., Simons et al. atColorado State University and others, together with data from irrigation canals and natural streams. It isto be cautioned that irregularity in channel cross-section, and unsteadiness and non-uniformly of flow innatural channels can vitiate the prediction of regime in natural rivers made using criteria primarily basedon steady, uniform flows in channels with rectangular shape. In such cases the recipe for successfulprediction is perhaps the combination of laboratory and field evidence. While discussing the variouscriteria proposed by different investigators, the writer feels that as far as possible average flow velocityshould not be used as an independent variable because it is not known a priori. The most commonly

used dimensionless parameters in regime predictors are Froude number U

gD, dimensionless shear

stress t

g

o

s dD

, shear velocity Reynolds number u d

v* ,

u

o

*

w

, D

d, slope S, stream power to U, sediment size

d or Dg

r

s

f

d

v

3

2 , ¢ -F

HGIKJ

t t

t

* *

*

c

c

and U

u¢*. These criteria are listed in Table 5.4 along with some comments.

In the opinion of the writer the most important parameter in the prediction of regime is t

g

o

s dD

or

¢t

g

o

s dD

which is an index of sediment mobility. Greater its value, greater will be the rate of sediment

transport. However ¢t

g

o

s dD

can be computed only if average velocity U is known; for this reason t

g

o

s dD

is to be preferred. Then the Froude number UgD

which is ratio of inertial force to gravity force

should also be important when bed undulations are large and affect the water surface. Hence Garde and

Albertson (1959) proposed t

g

o

s dD

vs Fr criterion shown in Fig. 5.12.

Garde and Anil Kumar (1988) further checked this with additional data. This criterion clubs ripplesand dunes together. Plotting of additional data indicated Fr » 1.0 as a reasonable line of demarcation

between transition and antidunes regimes. Its limitations arise from the use of U along with t

g

o

s dD

.

Engelund and Hansen’s U/u*¢ vs Fr number criterion (1966) is shown in Fig. 5.13. It also works well and

in addition differentiates between negative sinus bed (i.e., anti-dunes) and positive sinus bed. Positive

River Morphology134

Fig. 5.12 t* – UgD

regime criterion of Garde and Albertson (1959)

Fig. 5.13 U/u*¢ - UgD

regime criterion of Engelund and Hansen (1966)

1.0gDU

2 4 60.10.060.06

0.1

1.0

10

t *

Ripple and dunesTransitionsAntidunes

... Blank

... Half solid

... Solid

Ripple anddunes

Modifiedline

Original line

Antidunes

Tra

nsitio

n

1.5gDU/

1.00.50 2.0 2.5

5

10

15

20

25

30

U/U

¢ *

Positivesinus bed

Negative sinus bed(Antidunes)

Plane bed

Ripple and dunesTransition ...Antidunes ...

... Blank

... Half solid

... Solid

Pla

ne

bed

Positive sinusbed (Dunes)


Table 5.4 Parameters used for prediction of regime

Investigator Parameters used Comments

1. Langbein (1942)U

gR vs UR Limited laboratory data of Gilbert of 0.50 mm size;

dimensional parameter

2. Albertson, Simons,u

vsu d

o

* *w n

Flume data with d varying from 0.011 to 4.94 mm. Predictsand Richardson (1958) regimes fairly well for flume data but fails for river data.

3. Bogardi (1974)gd

u*2

vs d Same as above, use of dimensional parameter

4. Garde and AlbertsonU

gDvs

do

s

t

g∆Flume and field data, works fairly well, does not separate

(1959) ripples from dunes, and uses velocity.

5. Garde and RangaS

vsRds f( )∆g g

Flume and field data; does not separate ripples from dues,Raju (1963) works fairly well.

6. Tsubaki and SatoS

vsRds f( )∆g g

Lines of demarcation between dunes and transition, and(1974) transition and anti-dunes differ slightly from Garde and

Ranga Raju (1963).

7. Engelund and HansenUu

vsU

gD′*Has theoretical basis, works well with flume and field data,

(1966) differentiates between positive sinus and negative sinus(anti-dunes), and uses velocity. Needs trial error solution ifvelocity is not known.

8. Simons and Richardson to U vs d Uses both shear and velocity. Uses primarily flume data,(1962) prediction of regimes unsatisfactory.

9. Van Rijn (1984)t

t

g

r n

o

oc

s

f

vsd

−FHG

IKJFHG

IKJ

13

2

1 3∆

Based on flume and some field data, predictive ability mixed.

10. Brownlie (1981)US

dvs

d

s

f

1 3

∆g

r

d, Flow in upper regime if S is greater than 76 ´ 10–3. Needs

trial-error solution if velocity is not known.

sinus bed is one where the disturbance travels in the flow direction; however such a bed is accompaniedby appreciable form drag and is converted into dune pattern. This criterion is based on stability analysis

and finds qualitative support in earlier work by Matsunashi. It suffers from the same drawback as t

g

o

s dD

vs Fr criterion in the use of velocity U as well as shear stress.

River Morphology136

Fig. 5.14 R/d – S/s f∆g gc h regime criterion of Garde and Ranga Raju (1963)

The criterion proposed by Garde and Ranga Raju (1963) which uses S

s fDg / gd i and R/d as two

parameters is shown in Fig. 5.14. Since t

g

o

s dDb g is split into two parameters this criterion recognises the

fact that smaller R/d and S

s fDg g/d i larger, and larger R/d and smaller

S

s fDg g/d i which may have the

same t

g

o

s dDb g can have different regimes. It seems to work well for both flume and field data, and has

the advantage that it does not use velocity. Later analysis by Tsubaki and Sato supported this criterioneven though their lines of demarcation are slightly different. Lastly it may be mentioned that accordingto Van Rijn (1984),

If d* < 10 and T < 3.0 ripples will occur

...(5.37)

If d* < 10 and 3.0 < T < 15.0 dunes will occurIf d* < 10 and T < 15.0 dunes will occurIf T > 15.0 transition will occur

Here T = ¢-

FHG

IKJ

t

t

o

oc

1 and d* = d Dg

r

s

f v2

1 3F

HGI

KJ

/

U

V

|||

W

|||

R/d

Rippleand dunes

Modified line

Original line Tsubaki-Satio

Garde-Raju

Antidunes

Transition

TransitionRipple and dunesAntidunes

Half SolidBlankSolid

No sediment motion

= 0.5t

g

0

(A s)d

103

102

10 104

10510

�5

10�4

10�2

2 10´�2

10�3

S/(

/)

gf

sg


It may be mentioned that only Van Rijn’s and Browntie’s criteria for regime predictions involvekinematic viscosity and hence these take into account the effect of water temperature on flow regimes.With the change in temperature, the fall velocity of sediment particle will change and hence its effectivesize will be different. This is found to have significant effect on bed-forms, resistance and suspendedload discharge. Such studies by Lane, Straub and Taylor have shown increase in suspended load withdecrease in temperature, other conditions remaining same. Colby and Scott (1965) found that on theMiddle Loup river the bed-forms were more pronounced in summer.

5.5 RESISTANCE TO FLOW IN ALLUVIAL STREAMS

As the water flows through a channel, the channel bed, sides and the interface between water and airoffer resistance to flow. The resistance at the interface is usually negligible except when antidunes areformed and even then that part of resistance is included in the overall resistance of bed and banks. Thisresistance to flow is manifested in the slope of energy gradient Sf, which is equal to bed, slope So andwater surface slope Sw in steady uniform flow. The relationship between average velocity U, hydraulicradius R, slope Sf and a coefficient representing roughness of boundary is known as the resistance lawand three commonly resistance equations used in open channel are

Manning’s equation : U = 1

n R2/3 Sf

1/2 ...(5.38)

Chezy’s equation : U = C RSf ...(5.39)

Darcy-Weisbach equation : U = 8g RS

ff ...(5.40)

Writing these equations in non-dimensional form it can be seen that

U

g R Sf

= U

u*

= R

n g

1 6/

= C

g=

8

f

where u* is the shear velocity. Any one of these Eqs. (5.38) - (5.40) can be used to determine the velocityif R and Sf (= So for steady uniform flow) along with the coefficient n, C or f are known. Using sandcoated roughness of uniform size ks along with Karman-Prandtl equation, U/u* can be expressed as

U

u*

= 5.75 log10 12 27. Rx

ks

FHG

IKJ

...(5.41)

One can relate Manning’s n to ks as

R

n g

1 6/

= 5.75 log10 12 27. Rx

ks

FHG

IKJ

River Morphology138

Here x is a function of ks

¢d where d¢ is the thickness of laminar sub-layer d¢ =

116.

*

v

u. The variation of

x with ks

¢d is given in Table 5.5.

Table 5.5 Variation of x with ks′δ

ks′δ

0.2 0.3 0.5 0.7 1.0 2.0 4.0 6.0 10.0 and more

x 0.7 1.0 1.38 1.56 1.61 1.38 1.10 1.03 1.0

When ks

¢d is less than 0.25 the boundary is hydrodynamically smooth; when it is greater than 6.0 it

is rough and when 0.25 < ks

¢d < 6.0 it is in transition. Thus in the case of smooth and boundaries in

transition C, n or f are functions of both u k

vs* and

R

ks

, while in the case of rough boundary they depend

on R

ks

only. If one were to plot R

n g

1 6/

vs R

ks

for hydrodynamically rough surfaces, one gets the

approximation

R

n g

1 6/

= 24.0 R

ks

FHGIKJ

1 6/

or n = ks

1 6

25 6

/

.

which can be compared with the empirical equation obtained by Strickler for a number of Swiss riversflowing through coarse material and having plane bed,

n = d50

1 6

24 0

/

.

Here ks and d50 are in m. For plane bed resistance in alluvial channels, Einstein recommends ks = d65in Eq. (5.41).

Bank Resistance

When the roughness coefficient of bed and banks is different, it is not correct to use R = A

P in the

hydraulic computations; in such situations one can use hydraulic radius with respect to bed Rb inresistance and sediment transport relationships and to can be calculated as gf Rb S. This is computed bysubdividing A into area corresponding to bed Ab, and area corresponding to sides Aw, and assuming U


and S to remain same for main channel as well as Aw. For rectangular channel of width B, depth D,average velocity U and Manning’s coefficient for wall nw, one can write

A = Aw + Ab

or BD = 2DRw + BRb

UVW

and U = 1

nw

Rw2/3 S1/2 ...(5.42)

Hence, Rb = DD

BRw-

FH

IK2 = D 1 2-

FH

IK

R

Bw ...(5.43)

Knowing Rw from Eqn. (5.42), Rb can be calculated.

General Comments on Resistance to Flow with Alluvial BedsIn the case of alluvial streams with shear stress greater than the critical, the analysis of resistancebecomes more complex due to changing bed-forms with the change in flow condition. With theundulations on the bed the resistance of the bed is made up of the resistance due sand particles on planesurface which is called grain resistance, and the form resistance due to the presence of bed undulations.Even though grain resistance may not change significantly with flow, the form resistance will change.Another factor which influences the resistance is presence of sediment in suspension. In the beginningof the 20th century Buckley and Lacey observed reduction in the resistance to flow in the Nile and Indusrivers respectively, in the presence of fine sediment. Similar observations were made by Vanoni andNomicos (1959) in their laboratory studies in which they showed that decrease in resistance is moresignificant when bed is plane than when it has dunes on it. This decrease is due to the damping ofturbulence near the bed. Studies at the University of Roorkee have indicated that in plane bed channels

carrying suspended sediment of fall velocity wo the friction factor decreases when C

USow

is less than

1200 while it is greater than that for clear water flow when C

USow

is greater than 1200. Here C is the

average suspended sediment concentration is ppm by volume.

Resistance of Bed UndulationsIn order to estimate separately the grain resistance and form resistance of bed undulations, Einstein andBarbarossa (1952) divided shear stress on the bed g f Rb S into shear stress corresponding to grainroughness t¢o and that corresponding to form roughness due to bed-forms t²o.

Hence to = t¢o + t²o

...(5.44)or gf Rb S= gf R¢b S + gf R²b S

U

V||

W||or Rb = R¢b + R²b

River Morphology140

where R¢b and R²b are hydraulic radii corresponding to grain roughness and form roughness respectively.Einstein and Barbarossa compute R¢b using Manning’s equation along with Strickler’s equation

ns = d65

1 6

25 6

/

.where ns is for plane bed and d65 is in m. This gives

U

u¢*= 7.66

¢FHG

IKJ

R

db

65

1 6/

...(5.45)

or using Eq.(5.41) with x = 1 and ks = d65 one gets

U

u¢*= 5.75 log10

12 27

65

. ¢FHG

IKJ

R

db ...(5.46)

For river data they determined t¢o using above equations and then determined t²o = (to – t¢o). Further

assuming U

uo¢¢ to depend on bed-load transport rate and hence on Y¢ =

Dg

t

s

o

d35

¢ the relationship between

U

u¢¢* and Y¢ was obtained using data from American rivers with the following ranges

d65 0.220 mm to 7.50 mmR 0.045 m to 4.09 m

U 0.045 m/s to 2.79 m/sS 1.740 ́ 10–4 to 1.72 ́ 10–3

The coordinates of the relationship between U

uo¢¢ and Y¢ as obtained by Einstein and Barbarossa are

given in Table 5.5.

Table 5.5 Relationship between Uu*′′

and Y¢ as given by Einstein and Barbarossa (1952)

Y¢ 0.50 0.70 1.0 1.5 3.0 7.0 9.0 15.0 25.0 40.0

Uu*′′

100.0 62.0 40.0 25.0 15.5 10.0 9.0 7.0 6.0 5.0

It may be mentioned that later studies to verify Einstein-Barabarossa method by Vanoni and Brooks

(1957), and Garde and Ranga Raju (1966) have indicated large errors on U

uo¢¢ and Y¢ plot. One can

compute stage-discharge curve for an alluvial channel using this method in the following manner.


1. Known quantities: channel width B, slope S, d35, d65, rf and rs. Neglect bank friction; hence R¢and R² correspond to R¢b and R²b.

2. Assume R¢ and compute U using Eq. 5.44

3. Calculate Y¢ and find u²* using Table 5.5 and then R²

4. R = R¢ + R² for this R find D and then Q = BDU5. Repeat the procedure with higher value of R¢

Engelund (1966) has proposed the method of estimating t¢o and t²o for known value of to by dividingS into S¢ and S². He proposed the grain resistance to be computed using the equation

U

u¢*= 5.75 log10

¢FHG

IKJ

R

d2 65

+ 6.0 ...(5.47)

It may be noticed that while Einstein and Barbarossa use d65 as roughness length for plane bed,Engelund uses 2d65 implying that plane bed with sediment transport has greater roughness than planebed without motion.

Using some laboratory data by Guy et al. he found that t¢* = ¢F

HGIKJ

t

g

o

s dD 35

is related to t* = t

g

o

s dD 35

and regime of flow. For ripples and dunes, and plane bed he suggested the equations

for ripples and dunes t¢* = 0.06 + 0.4 t2* for t¢* < 0.55

...(5.48)and for plane bed t¢* = t* for 0.55 < t*¢ < 1.0 UVW

Brownlie (1983) extended the second equation in the higher regions of upper flow regime t*¢ > 1.0as

t¢* = (0.702 [t*]–1.8 + 0.298)–1/1.8

To obtain velocity for given depth, slope, d65, d35, and Dgs one must first assume the regime flow,then obtain t¢* and R’ from Eq. (5.47) or (5.48) for known to. Now use Eq. (5.46) to determine U and

check the regime of flow using U

u¢* vs Fr graph in Fig. 5.13. If the assumed regime is correct the solution

is right; otherwise assume a different regime and repeat the procedure.

Lovera and Kennedy (1969) used flume and river data and showed that the friction factor for planebed with motion increases with increase in Re for given R/d whereas the lowest values of f ¢ for givenR/d are those given by Karman-Prandtl’s equation for hydrodynamically smooth boundary; seeFig. 5.15. In their analysis Alam and Kennedy (1969), instead of subdividing R into R¢ and R², split Sinto S¢ and, S² the slopes corresponding to grain roughness and form roughness respectively. Since

f = 8

2

g RS

U =

82

g R

U (S¢ + S²)

f = 8

2

g RS

U

¢ +

82

g RS

U

¢¢ or f = f ¢ + f ²

River Morphology142

Fig. 5.15 Friction factor for flat beds according to Lovera and Kennedy (1969)

where f ¢ are f ² friction factors corresponding to grain roughness and form roughness respectively.Recently Patil (1997) has obtained equation for variation of f ¢ given by Lovera and Kennedy as follows:

f ¢ = m log10 Re + C for Re > Rec

where m = 0.1919 ́ 10–4 R

d + 0.016 if

R

d£ 3000

and = 0.076 ifR

d> 3000

U

V

|||||||||||

W

|||||||||||

C = 0.1396 ́ 10–3 R

d + 0.016 if

R

d£ 3000

= 0.478 ifR

d> 3000

Rec= 0.7256 R

dFHIK

1 7735.

and f = 0.0032 + 0.221/(Re)0.237 if Re < Rec ...(5.49)

He also found that for laboratory and field data having a wide range of variables t¢¢* is given by

t¢¢* = 0.6 t*1.27 ...(5.50)

125100

50

403025201510 12865432= 1

= 10�2R

d

River and flume data

d 0.088 to 0.788 mmD 0.03 to 3.10 mU 0.45 to 2.34 m/s

Re =UR

v

105

2.5 10´4

106 644 66

0.01

0.02

0.03

0.04f¢

Prandtl's smooth boundary relation


Here t¢¢* and t * are with respect to d50. Thus for known to and regime, t²* can be calculated andthen R¢b. Then using Eq. (5.47), U can be calculated.

Using Lovera and Kennedy’s relationship for f ¢, Alam and Kennedy (1969) found that f ² depends

on R/d and Ugd50

or UgR

; when R/d is greater than 3000 approximately, f ² depends only on

Ugd50

(this is true for river data) or UgR

, see Fig. 5.16. As shown by Alam and Kennedy (1969)

determination of depth or velocity when other parameters are known is a trial and error procedurewhereas determination of slope for known velocity, depth and sediment size involves no trial.

Fig. 5.16 Friction factor for bed-forms according to Alam and Kennedy (1969)

Total Resistance ApproachA number of methods have been proposed to determine the velocity of flow in alluvial streams byconsidering the total resistance to flow without splitting it into grain resistance and form resistance. Oneof the earlier attempts in this direction is Lacey’s equation (Lacey 1932)

U = 10.8 R2/3 S1/3 ...(5.51)

which was proposed for stable alluvial channels but is often used for bankful discharge in alluvial rivers.Sugio (JSCE, 1974) has proposed the equation

U = K R0.54 S0.27 ...(5.52)

where K = 6.15 for ripples, 9.64 for dunes and 11.28 for transition regime. Thus one must first determinethe regime of flow by one of the methods involving R, S and d and then use Eq. (5.52).

Garde and Ranga Raju (1966) carried out dimensional analysis and indicated that

U

ds

f

D g

r

= F R

d

S g d

vs f

FHIK

F

HGG

I

KJJ

1 3 3 2/ /

/D g gd iand

1/2

R /db

105

104

103

102

103�

102�

101�

3

2

2

235

302520

1510

25

50

0.7

0.60.50.4

0.3 0.235

30

25

20

15

107.5

0.15

U gRb

U gd = 50

FD = U

gRbF = U

gd

Contours of values of

Contours of values of

Legend

River Morphology144

Fig. 5.17 Relation between U

Rs

f

D g

r

vs Rd

1/ 3FHGIKJ

S/s fD g g

FHG

IKJ

for all regimes and materials with different relative

densities (Garde and Ranga Raju 1966)

First neglecting the effect of viscosity and hence of g1/2 d3/2/v, they obtained the following equation

U

ds

f

D g

r

= K R

dFHIK

2 3/

S

s fD g g/

/FHG

IKJ

1 2

…(5.53)

with K = 7.66 for plane bed without motion,= 3.2 for ripples and dunes, and= 6.0 for transition regime.

Later they plotted U

Rs

f

D g

r

vs R

dFHIK

1 3/

S

s fD g g/

F

HGI

KJ and obtained a continuous relationship for all

the regimes. The mean curve obtained them is shown in Fig. 5.17. Ranga Raju (1970) found that the

scatter on Fig. 5.17 can be reduced if K1 U

Rs

f

D g

r

is plotted against K2 R

dFHIK

1 3/

s

s

f

D g

g

F

H

GGGG

I

K

JJJJ

where K1 and

K2 are functions of d or g1/2 d3/2/v .

Ripples, dunes, transition

No sediment motion

Antidunes R.D. = 2.65

Rd

FHG

1 3/FHG

s

s fDg g/I

KJI

KJ

U

Rs

Dg

fr

10�3

10�4

10�2

10�1

0.05

0.1

1.0

3.0


Patil (1997) found that for a large volume of data in ripple and dune regime covering a wide rangeof related variables the following equation

U

gd= 6.05

R

dFHIK

0 5.

S0.4 ...(5.54)

predicts velocity within ± 30% error for 92 percent of data. For plane bed without motion, and transitionregime Equation (5.53) with K = 7.66 and 6 respectively can be used. These will reduce to

Plane bed without motion U

gd = 7.66

R

dFHIK

2 3/

S0.5 ...(5.55)

and transitionU

gd= 6.0

R

dFHIK

2 3/

S0.5 ...(5.56)

A number of other approaches to prediction of velocity are available e.g., Paris, Brownlie, and thatby Karim-Kennedy. These are discussed by Garde and Ranga Raju (2000). However, for geomorphicanalysis Eqs. (5.54), (5.55) and (5.56) may be adequate for prediction of discharge or stage-dischargerelation. It is further cautioned that in the prediction of velocity in alluvial streams, at present errors ofthe order of ± 30% are likely.

5.6 BED-LOAD TRANSPORT

It was mentioned earlier that when the average shear stress on the bed is greater than the critical shearstress for the material, the material starts moving and there is a range of u* /wo values for which thesediment is transported as bed-load i.e. the material moves on or near the bed. The layer in which the bedmaterial moves can be called the bed layer. The first bed-load equation was proposed by Du Boys(1879). Assuming that the sediment moves in layers, each having a thickness Dh, the layers movebecause of the applied shear stress to = gf DS, and the velocity of layers decreases linearly downwardsfrom (N – 1) DV for top layer to zero at the first layer (see Fig. 5.18), one can write

qB = gs N Dh (N – 1) DV

2...(5.57)

where N is the number of layers and qB is rate of bed-load transport in weight/width/time. The first layerwhere velocity is zero will satisfy the condition that the resisting force is equal to the shear stress. Hence

to = (gs – gf ) N Dh tan fwhere f is angle of repose. When N = 1, to = toc. Therefore to/toc = N and Eq. 5.57 can be written as

qB = g

t

s

oc

h VD D

2 2 to (to – toc)

or qB = Ato (to – toc) ...(5.58)

River Morphology146

The value of A = gs D Dh V

oc2 2t has the dimensions m3/N. Values of A and toc were later determined by

Straub and are given below (See Garde and Ranga Raju, 2000).

Fig. 5.18 Du Boys bed-load transport model

Table 5.7 Values of A/gs and toc in Eq. 5.58 according to Straub (see Rouse 1950)

d mm 0.125 0.250 0.50 1.0 2.0 4.0A/gs x 10–6 m6/N2s 32.32 19.45 11.75 6.89 4.05 2.43

toc N/m2 0.766 0.814 1.054 1.533 2.443 4.310

The empirical equation proposed by Meyer-Peter and Müller (1948) is based on extensive datacollected in Switzerland by Favre, Einstein and Meyer-Peter and Müller. Meyer-Peter and Mûller splitS into S¢ and S² the slopes corresponding to grain and form roughness and found that it is only the shearcorresponding to grain roughness that is responsible for bed-load transport. Since

U = 1

n Rb

2/3 S1/2 and U = 1

ns

Rb2/3 S¢1/2

¢S

S =

n

nsF

HIK

2

. Here ns = d90

1 6

26

/

where d90 is in m. Using data covering the following range of variables

Relative density 1.25 to 4.22Slope 4.00 ́ 10–4 to 2.00 ́ 10–2

Depth 0.01 m to 1.20 mArithmetic mean size of sediment 0.40 mm to 30 mm

Meyer-Peter and Müller obtained the equation

t*¢ = n

nsF

HIK

3 2/

t

g

o

s adD

FHG

IKJ

= 0.047 + 0.25 fB2/3 ...(5.59)

W.S.

Bed to

Dh(N � 1) DV

DV = 0

DV

2 DV


where fB = qB

sg

r

r r

f

s f-

13

1 2

gda

FHG

IKJ

/

where da is the arithmetic mean size. The above equation can be written in the form

fB = 8 (t*¢ – 0.047)3/2 ...(5.60)

Two observations can be made here. The first is that dimensionless bed-load transport is related toexcess shear (t*¢ – 0.047), and that even though Meyer-Peter and Mûller started with the division of S

into S¢ and S¢¢, the term n

nsF

HIK

3 2/

t

g

o

s adD

FHG

IKJ in Eq. (5.59) really represents

g

g

f b

s a

R S

d

¢

Db g. Therefore, to fit

the experimental data, in reality they have subdivided Rb into R¢b and R²b. Ning Chien (1954) has foundthat Eq. (5.59) predicts bed-load transport rate as well as Einstein’s equation (see below) for uniformsediments and also for non-uniform sediments if all sediment particles in the mixture are moving and asingle size da is used. Hansen has used this equation to compare the observed values of bed-loadtransport rate on the Skive-Karup river and found the two agreed fairly well. However, generally correctsize distribution of transported bed-load is not obtained.

A number of theoretical or semi-theoretical approaches have been made to study bed-load transport,namely by Einstein (1942), Kaliske, Bagnold, Engelund and Fredsøe, and Yalin out of which onlyEinstein’s method will be discussed here briefly. Einstein (1942) started with probabilistic approach tobed-load movement. He disagreed with the premise that a definable critical condition for bed-loadmovement exists. Since turbulent shear stress and lift near the bed fluctuate, Einstein assumed that asediment particles moves if the instantaneous hydrodynamic lift on the particle exceeds the submergedweight of the particle. Once the particle is in motion, the probability of the particle being re-deposited isassumed to be equal at all points on the bed. Lastly, the average distance travelled by any particlemoving as bed-load is assumed to be constant. He thus obtained relationship between bed-load

parameter fB = qB

sg

r

r r

f

s f-

13

1 2

gd

FHG

IKJ

/

and flow parameter Y¢ = g g d

g R S

s f

f

-

¢

d id i

. The relationship fB =

F (Y¢) was determined using laboratory and field data. Later Einstein (1950) presented a moresophisticated analysis to study fraction wise transport of non-uniform bed material.

In this later version Einstein modified the bed-load function to take into account fraction wise bed-load transport, by defining

f* i = q i

iB B

b sg

r

r r

f

s f-d i

13

1 2

gdi

FHG

IKJ

/

where qB iB is bed-load transport rate of the fraction i and ib is the fractional availability of this size di inthe bed. The parameter Y* i is defined as

River Morphology148

Y* i = xi Y log .

log.10 6

10 6 65d

D

FH

IK

L

N

MMMM

O

Q

PPPP

g g

g

s f id

R S

-

¢

d i

The parameter Y* i is made up of three parts. Part 1 namely xi is the hiding factor that depends on d

di

x

where dx is the characteristic size. Variation of x i with d

di

x

is given below

Table 5.8 Variation xi with di /dx in Einstein’s method

di /dx 0.10 0.2 0.4 0.6 1.5 and abovexi 150 35 6.8 2.2 1.0

The fraction Y is dependent on d65

¢d and its variation is given below in Table 5.9.

Table 5.9 Variation of Y with d65/d¢ in Einstein’s method

d65/d¢ 5.0 3.0 5.0 1.6 1.10 0.9 0.70 3.5 0.30

Y 0.52 0.53 0.60 0.80 0.82 0.80 0.65 0.44 0.22

The term log .

log.10 6

10 6 65d

D

FH

IK

L

N

MMMM

O

Q

PPPP

arises from the fact that lift on the particle is related to the near bed velocity

which must be measured in sediment mixture at a distance 0.35 dx above the theoretical bed. Thecharacteristic size dx is given by

dx = 0.77 D if D

¢d > 1.8

and dx = 0.39 d¢ if D

¢d < 1.8

where D = d

x65 and x is given in Table 5.5. The third part Y* i is reciprocal of dimensionless shear stress

with respect to grain. The curve between Y* i and f* i obtained by Einstein (1950) is shown in Fig 5.19with data by Gilbert, and Meyer-Peter and Müller plotted on it. A number of questions have been raised


Fig. 5.19 Einstein’s relationship between f* and Y* (Einstein 1950)

on the assumptions made in the deviation of Einstein’s bed-load function. These can be seen inRaudikivi (1976) and Yalin (1971). In spite of these questions, Einstein’s method is considered to be themost logical attempt to rationalize the complex problem of bed-load transport of non-uniform sediment.

The formula of Einstein (1942) was, modified by Brown (see Rouse, 1950) using the parameters fand Y defined as

f = q

FB

sg g ds

f

r

r-

L

NMM

O

QPP

F

HG

I

KJ1 3

1 2/

and Y = g g

t

s f

o

-FHG

IKJ

d = 1

t*

and F = 2

3

36

1

2

3

+

-FHG

IKJ

v

gd s

f

r

r

– 36

1

2

3

v

gd s

f

r

r-

FHG

IKJ

He expressed the variation of f with Y as

f = 40 t3* = 40

3Y where Y £ 5.5

U

V||

W||

...(5.61)

0.465 f = e–0.39 Y where Y > 5.5

The parameters F in Einstein-Brown formula appears in Rubey’s formula for fall velocity ofsediment particle and was introduced to account for the fall velocity of sediment particles. Gill (1968)

f* � y* Curve compared withmeasured points foruniform sediment

• d = 28.65 mm Meyer Peteret al. (1934)

• d = 0.785 mm Gilbert (1914)

A =*

1

0.023B =*

1

7.0

f*

0.0001 0.001 0.01 0.1 1.0 10

100

10

1.0

0.1

y*

River Morphology150

investigated Einstein-Brown relationship using data of Gilbert, and Simons-Richardson and found itnecessary to modify it to

f = 40 t

t

o

oc

-FHG

IKJ

13

...(5.62)

to account for deviation in f values at low shear stresses.It may be mentioned that at Roorkee (India) systematic investigations have been carried out to

include effect of sediment non uniformity on the rate of bed-load and total load transport. According toPatel and Ranga Raju (1996), the fraction wise bed-load transport can be calculated as follows:

1. Divide the bed material into a number of fractions and determine the geometric mean size andavailability in the bed ib of each fraction.

2. Compute toc for size da using Shields’ curve and also t¢o3. Determine Kramer’s uniformity coefficient M for the mixture and CM using the Equation (5.63)

CM = 1 for M ³ 0.38 ...(5.63)CM = 0.7092 log M + 1.293 for 0.05 £ M £ 0.38

UVW

4. Compute Cs for known values of ¢t

t

o

oc

from Equation (5.64)

log Cs = – 0.1957 – 0.9571 log . log¢F

HGIKJ-

¢FHG

IKJ

FHG

IKJ

t

t

t

t

o

oc

o

oc

01949

2

+ 0.0644 log¢L

NM

OQP

t

t

o

oc

3

...(5.64)

5. Compute xB from Eq. (5.65)

CM xB = 0.0713 Cds

o

s i

¢FHG

IKJ

t

gD

–0.7514

...(5.65)

and then compute xB ¢F

HGIKJ

t

g

o

s idD

6. Read fB from Fig. 5.20 and determine

qB iB = ib gs fB (g di3)1/2

D g

g

s

f

FHG

IKJ

1 2/

5.7 SUSPENDED LOAD TRANSPORT

As mentioned earlier at higher shear stresses the sediment particles go into suspension. Owing to theweight of the particle, there is a tendency for the particle to settle which is counterbalanced by theturbulent motion i.e. turbulent velocity components. Also there is a continuous exchange of sediment


Fig. 5.20 Variation of fB with xB τo

s id∆γFHG

IKJ

for field data with non-uniform sediments (Patel and Ranga Raju 1996)

particles from suspension to the bed and bed to the suspension. Various mechanisms have beensuggested by which a sediment particle moving on the bed goes in suspension. According to the liftconcept initially proposed by Jeffreys and used by Einstein, when the instantaneous lift on the particle isgreater than its submerged weight, the particle moves up in the flow and is transported as suspendedload. According to Laursen while the particle is moving along the bed over a dune or small irregularity,it loses contact with the bed momentarily as it is launched over the crest and is carried in suspension.According to Sutherland (1967) the turbulent flow consists of round or oval shaped eddies; these eddiesare distorted and flattened as they approach the channel bed and the velocity within the eddy increases.Their impingement on the laminar sub-layer disrupts it and causes spots of high shear stress at differentplaces on the bed and causes motion of the particles. If the turbulent velocity component at the place ofimpingement is large enough and in vertically upward direction, the particle can be entrained in the flow.In fact, all the three mechanisms discussed above work together in the process of suspension.

When sediment goes into suspension, the concentration of suspended load in the vertical decreaseswith increase in distance from the bed. In general, finer the sediment, more uniform is the distribution ofsuspended sediment in the vertical. The two most common ways of expressing the concentration ofsuspended sediment are:

1. Absolute volume of solids per unit volume of water–sediment mixture. This can also beexpressed in parts per million by volume or in percent.

2. Dry weight of solids per unit weight of mixture. This again can be expressed in parts per millionby weight or in percent.

101

fB

10�6

fB

100

10�1

102

10�5

10�4

10�3

10�2

10�1

xB

Curve based on uniform sediment

Data from different sources

10�2

10�1

100

101

xB =¢t

g

o

s idD

River Morphology152

Suspended Sediment Distribution EquationThe suspended sediment is subjected to two actions: the first is the upward and downward turbulentvelocity fluctuation v¢ and the second is the gravitational action that causes settling of sediment which is

heavier than water. Since there is a concentration gradient ¶

¶

C

y at any distance y from the bed, due to

turbulence, there is a net transfer of sediment in the upward direction equal to Îs ¶

¶

C

y where Îs is the

sediment transfer coefficient. The downward transfer per unit area will be woC where wo is fall velocityof sediment and C is the concentration. Hence for steady, uniform and two dimensional flow, thecontinuity equation demands that

Îs ¶

¶

C

y + woC = 0 ...(5.66)

The same equation can be obtained from general diffusion equation for sediment in open channels.Equation (5.66) was first used by the German meteorologist Schmidt in 1925 to determine thedistribution of dust particles in the atmosphere. If Îs and wo are assumed to be independent of y, Eq. 5.66can be integrated to obtain

ln C

Ca

=

y

az

wo

sÎ d y

U

V

|||

W

|||

...(5.67)

andC

Ca

= e

wy ao

s

-Î

-( )

Here Ca is the concentration at a distance “a” from the bed. Schmidt obtained this equation in 1925.Considering that momentum transfer and sediment diffusion in vertical in turbulent flow are similar, onemay assume Îs = b Îm where em is momentum transfer coefficient and b is a coefficient. If one assumesb = 1, Îs = Îm and Îm can be determined from combining the following equations

Îm = t

r f

¶

¶

u

y

t = to 1-FHIK

y

D

U

V

|||||

W

|||||

...(5.68)

to = gs D S

and¶

¶

u

y=

u

yo

*

k


where D is the depth of flow, ko is Karman constant the value of which for clear water flow in openchannel is 0.40; and the last term of Eq. (5.68) is obtained from Karman-Prandtl equation for velocitydistribution in turbulent flow. This gives

Îs = Îm = u* ko y D y

D

-FH

IK ...(5.69)

Substitution of the value of Îs from Eq. (5.69) in Eq. (5.66) and subsequent integration gives

C

Ca

= D y

y

a

D a

Zo-

-

FHG

IKJ

U

V||

W||

...(5.70)

where Zo = w

k

o

ou*

This equation was first published by Rouse in 1937 but was independently derived by Ippen earlier.For further discussion of Eq. (5.70) it is essential to state the assumptions made in its derivation becauseany deviation from it in its verification can be attributed to one or more of the assumptions made. Theseassumptions are (see Garde and Ranga Raju, 2000):

1. Derivatives with respect to t, x and z are assumed to be zero; this means the flow is steady,uniform and two dimensional in nature.

2. Higher order derivatives of C with respect for x, y, and z are neglected. This assumption isjustified for small values of Zo but can introduce errors when Zo is large and sedimentconcentration distribution near the bed is skew.

3. Intensity and scale of turbulence for upward and downward flows are the same and v’ andmixing length l have unique values for given y.

4. While evaluating Îm it is assumed that r f is constant; yet mass density of fluid will bemaximum near the bed and will decrease upwards.

5. While integrating Eq. (5.66) it is assumed that wo is independent of y; however because ofconcentration gradient and turbulence, the fall velocity of a particle near the bed will be smaller,and increase as y increases.

6. Îs is assumed to be equal to Îm.7. Logarithmic velocity distribution law holds well with Karman constant k = 0.40. Vanoni,

Garde, Barton and Liu and others have ascertained validity of logarithmic law for velocitydistribution law; however some investigators who have determined k from the whole velocitydistribution have found it to vary. However, if it is determined from the velocity variation nearthe bed, k is found to be essentially constant by Coleman.

Two other attempts to integrate Eq. (5.66) may be mentioned. Lane and Kalinske (1941) found thatas a simplification an average value of Îm = Îs = u* D/15 can be used for wide rivers. Hence integrationof Eq. (5.66) gives

C

Ca

= eo

u Dy a- F

HIK -

w

*

( )15

...(5.71)

River Morphology154

Laursen (1980) expressed Îs as

Îs = b Î

-FH

IK

m

yD

1

where b is introduced believing sediment may not follow the turbulent fluctuations exactly and (1 – y/D)representing correlation coefficient, and integrated Eq. (5.66) to get

C

Ca

= a

y

o

o uFHGIKJ

w

bk *

...(5.72)

Here value of b between 1 and 1.5 is recommended.In addition to three sediment distributions laws (Equation 5.70, 71 and 72) a few other equations

have also been obtained by investigators such as Einstein, Hunt, Tanaka and Sugimoto, Navntoff, Willisand others. However, the most often used equation, because of its simplicity, is Eq. (5.70). Hence, it isdesirable to consider this equation further. Equation (5.70) indicates that when y = D, C = 0 and wheny = 0, C = ¥; both these boundary conditions are unrealistic. At the boundary the concentration cannotexceed sediment concentration of stationary bed, and at y = D there will be finite though smallconcentration of suspended load, especially for finer material. However, Eq. (5.70) gives realisticdistribution in the remaining range of y.

Some studies have been carried out about variation of Îs. The sediment transfer coefficient can be

obtained directly from Eq. (5.66) as wo

C y¶ ¶/. Vanoni (1946) and Ismail (1952) found that for the fine

sediment Îs is greater than Îm i.e. b is greater than unity while for coarse material Îs/Îm is less thanunity. Raudkivi (1967) expresses Îs/Îm as

Îs/Îm = Rs ls/Rl

where Rs is correlation coefficient between C¢ and v¢, R is correlation coefficient between u¢ and v¢ andls and l are mixing lengths for sediment and fluid respectively. Hence variation of Rs, R, ls and l with ywill determine variation of b with y. Coleman (1970) analysed the Enoree river data on distribution ofsuspended sediment and studied variation of Îs/u* D with y/D and found that Îs/u*D increases withincrease in y/D from 0 to about 0.25 and after which it remains essentially constant up to y/D = 1.Further for given y/D, Îs/D increases slightly with increase in wo/u*. Thus for Enoree river data Îs/Dvalue for y/D = 0.90 increased from 0.06 to about 0.30 as wo/u* increased from 0.347 to 0.908.

One can also study the effect of Zo or wo/u* on the distribution of C. When Zo is small i.e. when wois small and/or u* is large, the concentration does not very much in the vertical. When Zo is large i.e.when wo is large and/or u* is small, concentration distribution will show considerable variation with y. Infact it can be seen that when Zo is less than 0.03, the concentration will be almost constant in the vertical(this happens for silts and clays). When Zo is greater than 5.0, suspension is insignificant. Figure 5.21shows variation of C/Ca with (y – a)/(D – a) for a/D = 0.05 various value of Zo.


The general validity of Eq. 5.70 has been shown by the experimental data collected by Vanoni,Vanoni and Namicos, Barton and Lin and others in laboratory flumes and data on rivers such as theMissouri and the Enoree. Such verification has also indicated that even though observed and computeddistribution are similar, Z observed by the slope of C/Ca vs (D-y)/y curve is not equal to Zo computed as

wko

ou*

. This has been attributed to various reasons such as change in fall velocity due to turbulence and

concentration, change in turbulence characteristics due to presence of bed-forms and concentrationgradient, secondary circulation and variation in Karman constant.

Integration of Sediment Distribution Equation (Eq. 5.70)It can be seen that the distribution of suspended sediment concentration in the vertical can be obtained if

one knows Zo and reference concentration Ca at “a”. Assuming Zo can be calculated as wko

ou*

, still the

reference concentration must be known. In this connection Karman anticipated that Ca would depend onsize of sediment in suspension and shear stress to on the bed. Lane and Kalinske (1939) showed that forsome American rivers and canals Ns/Nb depends on wo/u* where Ns is the concentration of material offall velocity wo in suspension near the bed and Nb is the fraction of the same material found in the bed inpercent by weight. Kalinske and Hsia (1945) found that Ns/Nb depends also on u* d/n.

Einstein (1950) assumed that the bed-load transport rate qB iB of a given size range occurs in a bedlayer of thickness 2d where d is the representative size of the range. The velocity at the edge of the layer

is 11.6 u¢*. Hence the concentration of bed-load can be taken as C2d = q i

u dB B

116 2. *¢ a f =

q i

uB B

23 2. *¢. This is

Fig. 5.21 Distribution of suspended load in a flow according to Eq. 5.70

Relative concentration C/Ca

aD

= 0.05

y � a

D � a

1.0

0.9

0.8

0.6

0.7

0.5

0.4

0.3

0.2

0.1

0 01 02 03 04 05 06 07 08 09 10Bottom

w

k

o

ou*Zo=

4.02.0

1.0

0.5

0

0.2

5

0.1

25

0.0

625

0.0

313

River Morphology156

considered as suspended load concentration at a = 2d. Garde (1959) using laboratory data of nearly

uniform materials found that C2d in percent by weight depends on u u d

vo

* *

w

FHG

IKJ

or u d

vo

*2

w, see Table 5.10.

Otherwise a single measurement of suspended load concentration at known elevation can be made.

With known Ca and Zo Eq. 5.70 along with the velocity distribution law can be combined andintegrated over the depth of flow to find the total amount of suspended load carried by the stream perunit width. As done by Einstein the logarithmic velocity distribution

u

u¢* = 5.75 log

30 2

65

. y x

d

FHG

IKJ

...(5.73)

can be used, or a simple relationship such as

u

um

= y

D

nFHIK ...(5.74)

can be used with free steam velocity um and n known. The suspended sediment transport rate qs can beobtained by integrating (Cudy) over the depth. The upper limit of integration is y = D. For lower limit ofintegration one can use y = 2d as suggested by Einstein (1950) which seems reasonable for plane bed.Brooks (1963) and, Harrison and Lidicker (1963) made the following suggestion for the lower limit ofintegration. They suggest that the largest of the following three be taken as lower limit.

1. a = 2d as suggested by Einstein;2. Value of “a” at which u = 0 according to logarithmic velocity distribution law, i.e.,

a

D= e–ko um/u*

3. Value of a

D at which extrapolation of suspended sediment distribution will yield a limiting

concentration of 480 kg/m3. If Cmd is the concentration at mid depth.

C

Cmd

b

zoFHG

IKJ

1/

= a

D

For details of calculation of suspended load by Einstein’s method (see Garde and Ranga Raju,2000).

Table 5.10 Variation of C2d with u d

v*2

oω according to Garde (1959)

u dv

*2

oω5.0 8.0 10.0 14.7 20.0 40.0

C2d in % by weight 0.01 0.02 0.06 0.40 2.0 2.0


Relations for Sediment DischargeIn many morphological studies estimates of suspended load carried by the stream may be needed. UsingLane and Kalinske’s method (1941) it can be shown that

qs = q Ca Pe15(wo/u*)A ...(5.75)where A = a/D where suspended load concentration is Ca, q is the water discharge per unit width and Pdepends on wo/u* and weakly on n/d1/6 where n is Manning’s n. The parameter P is given by

P = e– 8.0 wo/u* ...(5.76)

Thus if a single measurement of Ca at ‘a’ is known along with q, D and u*, qs can be determined.Garde and Pande (1976) showed that for laboratory and field data, the following relationship holdsgood:

q

qs

fg= 5.10 ́ 10–5

u

o

*

wFHGIKJ

4

...(5.77)

By combining Kikkawa’s relation qs a D2S for u* >> wo and Chezy’s Equation q2 a D3S one gets qsD a q2 which for small variation in depth of flow can be written as

qs ~ q2 ...(5.78)Data on many rivers and canals indicate that the power of q varies between 1.92 and 2.20 indicating

the validity of the above proportionality.Van Rijn (1984) has proposed that qs be estimated using the equation

qs = gs D U Ca F ...(5.79)

in which qs is in wt/width/time, Ca is the reference concentration at y = a given by

Ca = 015 50

1 5

3

. .

*

d T

ad...(5.80)

Here “a” is taken to be equal to ks or D

100 whichever is greater. The roughness parameter ks is

obtained from the equation

U

u*

= 5.75 log R

kb

s

+ 6.25 ...(5.81)

Lastly the correction factor F in Eq. 5.79 depends on a/D and Z¢.where Z¢ is obtained from

Z¢ = w

b

os

u0 4. *

+ f ...(5.81)

b = 1 + wo

u*

FHGIKJ

2

U

V

|||||

W

|||||

for 0.01 < wos

u*

£ 1.0, j = 2.5 wos

u*

.8FHG

IKJ

0

C

Ca

b

FHGIKJ

0 40.

River Morphology158

Here wos in Eq. 5.81 is for fall effective size ds and is given by

d

ds

50

= 1 + 0.011 (s9 – 1) (T – 25)

and T = ¢ -t t

t

o oc

oc

b g. Variation of F with and a/D is shown in Fig. 5.22.

5.8 TOTAL LOAD TRANSPORT

As mentioned already, the total load carried by the stream is the sum of suspended load and bed-loadtransported per unit time per unit width of channel. It does not include wash load which is not related toflow conditions; hence it is the bed material load. Suspended load and bed-load can be calculated fordifferent fractions of the bed material and added to get the total load. Methods for such calculation arealready discussed earlier in this chapter. For many morphological studies such refined calculations maynot be needed. Therefore in this section only equations for computation of total are discussed which useonly one representative size such as d50 or da. If all size fractions are moving these methods can also beused for fraction wise sediment transport; however the results are approximate because of coarserparticles are not included in these methods.

(1) Laursen�s Method (1958)Based on flume and some field data with sediment size ranging from 0.011 mm to 4.08 mm, Laursenproposed the relationship

Fig. 5.22 Variation of F with Z ¢ and a/D (Van Rijn 1984)

Z¢

0 1.0 2.0 3.0 4.0 5.0

10�3

10�2

10�1

100

F

0.01

0.05

a7D = 0.1


C

d

Do

oc

FHIK

¢-

LNM

OQP

7 6

1/

t

t

= F u

o

*

w

FHGIKJ

...(5.82)

where C is total concentration in percent by weight, toc is critical shear for median size d computedusing Shields’ method and the function F (u* /wo) is obtained experimentally as below:

u

o

*

w10-2 10-1 0.6 2.0 4.0 10 30 40 200 103

F u

o

*

w

FHGIKJ

3.95 6.0 10 27 102 103 104 2 ́ 104 3.8 ́ 104 5.5 ́ 104

(2) Relation between qs/u* gs d and to/Dgs dGarde and Dattatri (1963) used data with size range 0.011 mm to 0.93 mm and obtained the relation

q

u dT

sg *

= 16 t*4.0 ...(5.83)

while Graf and Acaroglu (1968) used flume data of Gilbert, Guy et al. and obtained the relationship

q

u dT

sg *

= 10.39 t*2.52 ...(5.84)

Here qT is total load transport ratio in weight/width/time. It is known that exponent of t* depends onmode of sediment transport. A lower value around 2 corresponds to bed-load transport whereas a highervalve indicates a substantial amount of suspended load in the total load. Hence variation in the exponentof t* in the above equations can be explained.

(3) Bagnold�s (1966) ApproachBagnold equated rate of doing work by transport of bed-load and suspended load to the available streampower toU and the transport efficiencies and obtained the following equation:

qT = t

r r

o

s f

U

1- /d i

ee e

uBs B

s

otana w+ -

LNM

OQP1b g ...(5.85)

Here u s is the average velocity of suspended load which can be taken equal to U, eB = bed-loadtransport efficiency whose value lies between 0.05 and 0.11, es = suspended load transport efficiencywhich is 0.015, tan a = coefficient of intergranular solid friction of bed material whose value variesbetween 0.375 and 0.75; and qT is in weight/width/time.

The above equation is simplified to the form

qT = t

r r

o

f s

U

1- /d i

e UB

otan.

a w+

LNM

OQP0 01 ...(5.85 a)

River Morphology160

(4) Engelund and Hansen�s Equation (1967)Engelund and Hansen postulated that when there are dunes on the bed, the energy required for movinga sediment particle over a dune height H can be equated to the drag forces acting on the particle duringthe same period. On the basis of this hypothesis they obtained the equation for sediment transport as

f fT = 0.40 t*5/2 ...(5.86)

where the friction facto f = 2 g R S/U2 UVW

The equation was obtained using flume data in the size range 0.10 mm to 0.93 mm with dunes,transition, standing waves or anti-dunes on the bed. It needs to be emphasized that even though theequation is derived for duned bed, it gives reasonably good results for other regime also, and subsequentverification has given good results.

(5) Ackers and White (1973, 1980)Using the accepted premise that whereas bed-load transport is related to shear stress with respect tograin, total shear is responsible for sediment transport when suspended load predominates, Acker andWhite have obtained the equation

u

U

c*F

HIK

1

g

g

f

s

C D

d= C2

F

C

c

1

3

14

-FHG

IKJ

...(5.87)

where F1 = u

d

c

s

f

*1

Dg

r

F

H

GGGG

I

K

JJJJ

U

D

d

c

3210

1 1

log

F

H

GGGG

I

K

JJJJ

-

is the sediment mobility parameter, and the constant c1, c2, c3 and c4 are functions of dimensionlesssediment size d* as given below

For 1.0 £ d* £ 60.0

c1 = 1.0 – 0.56 log d*

c2 = 2.86 log d* – (log d*)2 – 3.53

c3 = 0 23

1 2

.

*/d

+ 0.14

c4 = 9 66.

*d + 1.34

For d* > 60.0

c1 = 0, c2 = 0.025, c3 = 0.17, c4 = 1.5

Here C is the total load concentration by weight. Initially this equation was developed using flumedata and limited amount of field data. However, later it was tested with lot more field data and found togive satisfactory results.


(6) Yang�s Equation (1972, 1973)Yang approached the problem of total load transport from the point of view of energy expenditure andrelated rate of sediment transport to dimensionless stream power US/wo

log CT = A + B log US US

o

c

ow w-

FHG

IKJ

...(5.88)

where A and B were related to u d

v* and

u

o

*

w. Here USc is the critical stream power required to move the

sediment. His final equation is

log CT = 5.435 – 0.286 log wo d

v – 0.457 log

u

o

*

w +

...(5.89)

1799 0 409 0 314. . log . log *- -LNM

OQP

w

w

o

o

d

v

u log

US U S

o

cr

ow w-

FHG

IKJ

U

V

|||

W

|||

where Ucr is the critical velocity for incipient motion and is to be calculated using the Eq. (5.90)

Ucr

ow=

2 5

0 06

.

log .*u d

vFH

IK -

+ 0.66 for 0 < u d

v* < 70

U

V

|||

W

|||

...(5.90)

andUcr

ow= 2.05 for

u d

v* > 70

Yang found that the above equation gives satisfactory results for flume data as well data from the field.

(7) Shen and Hung�s Equation (1971)Using regression analysis Shen and Hung started with the equation

log CT = ao + a1 X + a2 X2 + a3 X3

where X = US

o

0 57

0 32

0 0075.

.

.

wLNM

OQP

and is calculated in fps system of units. Their final equation is

log CT = – 10704.5 + 324214.747X – 326309.6X2 + 109503.872X3 ...(5.91)

Here CT is concentration of bed material in ppm by weight. This equation is based on over 500 datapoints out of which 63 correspond to river data of Middle Loup and Niobrara in USA and the rest toflume studies.

River Morphology162

(8) Effective Shear Stress Approach of Ranga Raju et al. (1981)Vittal et al. (1973) defined effective shear stress t t for ripple and duned bed as the shear stress requiredto give the same total load transport rate of the same sized material on plane bed. The effective shearstress is always less than the average shear stress of dune bed channel.

Ranga Raju et al. (1981) after analysis of extensive data for dune bed channels found that the

dimensionless effective shear stress t

g

t

s dD is given by

t* t = t¢* ¢F

HGIKJ

t

t

o

o

m–

...(5.92)

where t¢o is computed using Manning’s equation with Stickler’s ns = d1 6

24

/

. Here m is given as

m = 0 if u

o

*

w £ 0.50 when suspended load is absent

U

V

|||

W

|||

and m = 0.2 u

o

*

w – 0.10 when

u

o

*

w > 0.50

When t* t is used in the sediment transport relationship, a unique relationship is obtained between

fT = qT

sg

r

r r

f

s f-d i

13

1 2

gd

FHG

IKJ

/

and t* t for all bed-forms i.e. ripples, dunes, and plane bed. In the range

of 0.05 £ t* t £ 1.0, this relationship can be expressed as

fT = 60 ¢t*3

¢F

HGIKJ-

t

t

o

o

m3

...(5.93)

This equation is based on 900 data points out of which 235 belonged to river and canal data.

(9) Brownlie�s Equation (1981)On the basis of analysis of laboratory and field data covering a wide range of pertinent variables,

Brownlie has proposed the following equation for concentration of bed material load CT in ppm byweight.

CT = 7115 CF U U

dcr

s

f

-

L

N

MMMMM

O

Q

PPPPP

D g

r

1 978.

S0.6601 R

dFHIK- 0 3301.

...(5.94)


The coefficient CF for field data is 1.268 and for flume data it is unity. The critical velocity Ucr isgiven by

U

g dcr

s

f

D

r

= 4.596 t*.c

0 529 S- 0 1405. sg – 0.1606 ...(5.95)

Here sg is the geometric standard deviation of the bed material.

(10) Karim-Kennedy�s Equation (1983)Unlike many other methods, Karim and Kennedy linked the problems of prediction of resistance andsediment transport in alluvial streams. Based on the analysis of 615 data points out of which about 100points were for the Missouri river and rest from flume data, they obtained the following equation

log q

g gd

T

ss f

f

r r

r

-FHG

IKJ

L

NMM

O

QPP

3

1 2/ = – 2.2786 + 2.9719 V1 + 0.2989 V3 V2 + 1.06 V1 V3 U

V

|||||||

W

|||||||

...(5.96)

where V1 = log U

ds

f

D g

r

F

H

GGGG

I

K

JJJJ

, V2 = log D

dFHIK

V3 = log u u

dc

s f

* *

/

-F

HG

I

KJ

D g r

Here d is taken as d50.

Relative Accuracies of Different Total Load EquationsMany attempts have been made to find the relative accuracy of the above methods of computing totalload transport rates in alluvial streams. However, the difficulty in the interpretation of these results isthat these investigators have used different sets of data and total number of data points are from flumestudies as well as field data. The criteria used for assessing the accuracy of these equations using thesame sets of data are usually the percent of data falling within ± 30 percent error lines, or percent of thedata for which prediction of total load is within 0.750 to 1.5, 0.5 to 2.0, or 0.33 to 3.0 times the observedvalue. On the basis of such assessment the following general observations can be made. First, theequations proposed by Ackers and White, Yang, Ranga Raju et al. and Karim and Kennedy have used alarge data base of laboratory and field data; hence these equations are likely to give more representativeresults than the other equations based on limited data. Further, even though Engelund and Hansen’sequation is based primarily on flume data, subsequent verification by other investigators have shownthat it gives very satisfactory results. Coming to specific observations, ASCE Task Force (1971) applied

River Morphology164

various methods of total load estimation then available to sediment discharge measurements on the riverColorado at Taylor’s Ferry, and the Niobrara river near Cody (Nebraska) and found that Engelund andHansens’s method gives much better accuracy than the other methods. Ackers and White (1980) used1000 data points from flume studies and 260 points from field data and found that Ackers and White’s,and Engelund and Hansen’s equations give more accurate prediction than the other equations. Van Rijn(1983) used 500 data points from field data and found that consistently Engelund and Hansen’s equationgave best results; then came Ackers and White’s equation and then Yang’s. On the other hand Yang andMolinas (1982) reported good prediction by Yang’s equation for flume data. Hence it is felt that Yang’sequation is not very reliable for field conditions involving large depths, fine sediment, or both. Bechtelerand Vetter (1989) used the data of six rivers on sediment transport rates; these were the Rhine, theMississippi, the Rio Grande, and the Rio Puerto in New Mexico, the Five Mile Creek and the Niobrara.On these rivers the suspended load was measured and bed-load was estimated using Meyer Peter andMûller equation. They found that among the 15 total load equations tested, Karim-Kennedy’s equationgave best results; then came Bagnold, Laursen and Yang’s equations. Nakato (1990) used data on theSacramento river at gauging stations near Butte City and Colusa in California, U.S.A. where discharge,suspended sediment load and bed material data were available. He tested the accuracy of equationsproposed by Ackers-White, Einstein-Brown, Engelund-Fredsoe, Engelund-Hansen, Inglis-Lacey,Karim, Meyer-Peter and Mûller, Van Rijn, Schoklitsch, Toffaleti and Yang. According to Nakato, thepredictions are not at all satisfactory by most of these formulae and predictions would have been worstif computed depth and not measured depth were used. Considering all these observations it is prudentfor the river morphologists to use three or four equations for determining the sediment transport rate ina given case and then make his own assessment on the basis of these results and his judgment. With thepresent state of knowledge, predictions within ± 50 percent error can be acceptable.

References

Ackers, P. and White, W.R. (1973) Sediment Transport: New Approach and Analysis. JHD, Proc. ASCE, Vol. 99,No. HY-11, pp. 2041-2060.

Ackers, P and White, W.R. (1980) Bed Material Transport: A Theory for Total Load and its Verification. Proc. 1stIntl. Symposium on River Sedimentation, Beijing (China), March, B10–1-20.

Alam, A.M.Z. and Kennedy, J.F. (1969) Friction Factors for Flow in Sand Bed Channels, JHD, Proc. ASCE, Vol.95, No. 6, Nov. pp. 1973-1992.

Allen, J.R.L. (1978) Computational Methods for Dune Time Lag: Calculations Using Stein’s Rule for DuneHeight. Sedimentary Geology, Vol. 20, No. 1,

ASCE Task Force on Bed-forms in Alluvial Channels: Nomenclature for Bed-forms in Alluvial Channels (1966).JHD, Proc. ASCE, Vol. 92, No. HY-3, May, pp. 51-64,

Ashida, K. and Michiue, M. (1971) An Investigation of River Bed Degradation Downstream of a Dam. Proc. 14thJapanese Congress of IAHR, Paris, Vol. 3, pp. C30-1 to 9.

Bagnold, R.A. (1966) An Approach to the Sediment Transport Problem from General Physics–USGS ProfessionalPaper 422-1.

Bechteler, W. and Vetter, M. (1989) Comparison of Existing Sediment Transport Models. 4th Intl. Symposium onRiver Sedimentation, Beijing (China) Vol. 1, 466-473.

Bogardi, J.L. (1959) Sediment Transport in Alluvial Streams. Academiai Kiado, Budapest. 95p.


Brooks, N.H. (1963) Calculation of Suspended Load Discharge from Velocity and Concentration Parameters.Proc. FIASC, USDA (Washington), Paper 23, pp. 229-237.

Brownlie, W.R. (1981) Prediction of Flow Depth and Sediment Discharge in Open Channels. W.M. KeckLaboratory, Caltec (USA), Rep. No. KH-R-43A.

Brownlie, W.R. (1983) Flow Depth in Sand-Bed Channels. JHE, Proc. ASCE, Vol. 109, No. HY-7, pp.959-990.

Buffington, J.M. (1999) The Legend of A.F. Shields. JHE, Proc. ASCE, vol. 125, No.4, April, pp. 376-387.

Carey, W.C. and Keller, M.D. (1957) Systematic Changes in the Beds of Alluvial Rivers. JHD, Proc. ASCE, Vol.83, No. HY-4, Aug. pp. 1331-1 to 24

Chien, N. (1954) Meyer-Peter Formula for Bed-load Transport and Einstein’s Bed-load Function, IER, MRDSeries No. 7.

Colby, B.R. and Scott, C.H. (1965) Effect of Water Temperature on the Discharge of Bed Material. USGS Prof.Paper 462-G.

Coleman, N.L. (1970) Flume Studies of the Sediment Transfer Coefficient. WRS, Vol. 6, No. 3, pp. 801-809.

Daniel, P., Durand, R. and Condolios, E. (1953) Introduction a l’etude de la Saltation. La Houille Blanche, No. 2,Special B.

David, J.K and Gangadhariah, T. (1983) The Effect of Nonuniformity in Grain Size on the Initiation of GrainMotion. Proc. 2nd Intl. Conference on River Sedimentation, Nanjing (China), B-16, pp. 434-439.

Dawdy, D.R. (1963) Discontinuous Depth – Discharge Relationship for Sand – Channel Streams and Their Effecton Sediment Transport. Proc. FIASC, USDA (Washington), Paper No. 35, pp. 309-324.

Du Boys, P. (1879) Le Rhone et les Rivers a Lit Affouillable Annales Des Ponts et Chaussees, Vol. 18, Series 5, pp.141-195.

Egiazaroff, I.V. (1965) Calculation of Non-uniform Sediment Concentrations. JHD, Proc. ASCE, Vol. 9, No.4, pp.225-247.

Einstein, H.A. and Barbarossa, N.L. (1952) River Channel Roughness. Trans. ASCE, Vol. 117, pp. 1121-1132.

Einstein, H.A. (1942) Formulas for the Transportation of Bed-load. Trans. ASCE, Vol. 107, pp. 561-573.

Einstein, H.A. (1950) Bed-load Function for Sediment Transportation in Open Channel Flows, USDA, Tech. Bull.No.1026.

Engelund, F. (1966) Hydraulic Resistance of Alluvial Streams. JHD, Proc. ASCE, Vol. 92, No. HY-2, March pp.315-326, and Closure of Paper in JHD, Proc. ASCE, Vol. 93, No. HY-4, July 1966.

Engelund, F. and Hansen E. (1967) A Monograph on Sediment Transport in Alluvial Streams. Tensisk Forlag,Denmark.

Fredsøe, J. (1975) The Friction Factor and Height - Length Relations in Flow Over a Dune Covered Bed. Instituteof Hydrodynamics and Hyd. Engineering, Tech. University of Denmakr, Progress Report No. 37.

Gallay, V.J. (1967) Observed Forms of Bed Roughness in an Unstable Gravel River. Proc. Of 12th Congress ofIAHR, Fort Collins, U.S.A., Vol. 1, pp. 85-94.

Garde, R.J. (1959) Total Sediment Transport in Alluvial Channels. Ph.D. Thesis submitted to Colorado StateUniversity, Fort Collins, USA.

Garde, R.J. (1970) Initiation of Motion on a Hydrodynamically Rough Surface; Critical Velocity Approach. Jour.of Irrig. and Power of CBIP (India) Vol. 27, No. 3, July, pp. 271 to 282.

Garde, R.J. and Albertson, M.L. (1959) Sand Waves and Regimes of Flow in Alluvial Channels. Seminar II, Proc.8th Congress of IAHR, Montreal (Canada), vol. 4, 28 SII-1-7.

Garde, R.J. and Anil Kumar (1988) Verification of Regime Criteria for Alluvial Streams. Indo-British Workshopon Sediment Measurement and Control. Chandigarh (India). Paper No. 4.1, Feb. pp. 1-12,

River Morphology166

Garde, R.J. and Dattatri, J. (1963) Investigations of the Total Sediment Discharge of Alluvial Streams, RoorkeeUniversity Research Journal, Vol. 6, No. 2, pp. 65-78.

Garde, R.J. and Isaac, N. (1993) Bed Undulations in Unidirectional Alluvial Streams. Report Submitted to UGC,CWPRS, Pune, Nov.

Garde, R.J. and Pande, P.K. (1976) Use of Sediment Transport Concepts in the Design of Tunnel Type SedimentExcluders. ICID Bull. Vol. 25, No. 2, pp. 101-109.

Garde, R.J. and Ranga Raju, K.G. (1966) Resistance Relationships for Alluvial Channel Flow. JHD, Proc. ASCE,Vol. 92, No. HY-4, July, pp. 77-100.

Garde, R.J. and Ranga Raju, K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems.New Age International (P) Ltd., New Delhi.

Gessler, J. (1965) The Beginning of Bed-load Movement of Mixtures Investigated as Natural Armouring inChannels. Laboratory of Hydraulic Research and Soil Mechanics, Swiss Federal Institute of Technology, Rep.No. 69.

Gill, M.A. (1968) Rationalisation of Lacey’s Regime Flow Equations, JHD, Proc. ASCE, Vol. 94, No. HY-4, July,pp. 983-995.

Gill, M.A. (1971) Height of Sand Dunes in Open Channel Flows. JHD, Proc. ASCE, Vol. 97, No. HY-12, Dec. pp.2067-2074.

Graf, W.H. and Acaroglu, E.R. (1968) Sediment Transport in Conveyance Systems, Pt. 1, Bull. Intl. Assoc.Scientific Hydrology Vol.13, No. 2.

Grass, A.J. (1970) Initial Instability of Fine Sand. JHD, Proc. ASCE, vol. 96, HY-3, March, pp. 619-631.

Haque, M.I. and Mahmood, K. (1983) Analytical Determination of Form Friction Facto. JHE, Proc. ASCE, Vol.109, No. 4. pp. 590-610

Harrison, A.S. and Lidicker, A.C. (1963) Computing Suspended Sand Loads from Field Measurements. Proc.FIASC, USDA (Washington), Paper 56, pp. 484-492.

Hayashi, T. (1970) Formation of Dunes and Anti-dunes in Open Channels. JHD, Proc. ASCE, Vol. 96, No HY-2,Feb. pp. 357-366.

Hayashi, T. and Ozaki, S. (1980) On the saltation Height and Step Lengths of Sediment particles in the Bed-LoadLayer. 1st International Symposium on River Sedimentation. Nanjing (China) B13-1-10.

Hayashi, T. Ozaki, S. and Ichibashi, I. (1980) Study of Bed-load Transport of Sediment Mixture. Proc. 24thJapanese Conference on Hydraulics. pp. 35-43.

Hubbell, D.W. and Sayre, W.W. (1964) Sand Transport with Radioactive Tracers. JHD, Proc. ASCE, Vol. 90, HY3,May, pp. 39-68.

Ismail, H.M. (1952) Turbulent Transfer Mechanism and Suspended Sediment in Closed Channels. Trans. ASCE,Vol. 117, pp. 409-434.

Itakura, T., Yamaguchi, H. Shimuzu, Y., Kishi, T. and Kuroki, M. (1984) Observations on Bed Topography Duringthe 1981 Flood in the Ishikari River. Jour. Of Hydro-Science and Hydraulic Engg., Japan

Jackson II, R.G. (1975) Hierarchical Attributes and a Unifying Model of Bed-forms Composed of CohesionlessMaterial and Produced by Shearing Flow. Bull. Geo. Soc. of America, Vol. 86, Nov. pp 1523-1533,

Jeffrey, H. (1929) On the Transport of Sediment in Stream . Proc. Cambridge Philosophical Society. Vol. 25, pt 3,pp. 272-276.

JSCE (1974) Task Committee Report on Bed Configuration and Hydraulic Resistance of Alluvial Streams, Nov

Kalinske, A.A. (1942) Criteria for Determining Sand Transport by Surface Creep and Saltation. Trans. AGU, Vol.23, pt. 2, pp. 639-643.

Kalinske, A.A. and Hsia, C.S. (1945) Study of Transportation of Fine Sediment by Flowing Water. Studies inEngg. Bull. No. 29, Univ. of Iowa, (USA), 30 p.


Karim, M.F. and Kennedy, J.F. (1983) Computer – Based Predictors for Sediment Discharge and Friction Factorfor Alluvial Streams. Proc. 2nd Intl. Symposium on River Sedimentation, Nanjing (China) A-18, Oct. pp.219-233.

Kennedy, J.F. (1969) The Formation of Sediment Ripples, Dunes and Antidunes. Annual Review of FluidMechanics, Vol. 1, pp. 147-168.

Lane, E.W. and Kalinske, A.A. (1939) The Relation of Suspended to Bed material in Rivers. Trans. AGU, Vol. 20,pp. 637-641.

Lane, E.W. and Kalinske, A.A. (1941) Engineering Calculations of Suspended Sediment. Trans. AGU, Vol. 22, pp.603-607.

Lane, E.W. and Eden, E.W. (1940) Sand Waves in Lower Mississippi River. Jour. Of Western Society of Engineers(USA), Vol. 45, No. 6, pp. 281-291.

Langbein, W.B. (1942 Hydraulic Criteria for Sand Waves. Trans AGU, pp. 615-618.

Laursen, E.M. (1958) The Total Sediment Load of Streams. JHD, Proc. ASCE, Vol. 84, No. HY-1, Feb., pp. 1530-1 to 36.

Laursen, E.M. (1980) A Sediment Concentration Distribution Based on Revised Prandtl Mixing Theory. 1st Intl.Symposium on River Sedimentation, Beijing (China) – B-1 to 9.

Li Zenru, Chen Yuaner and Zao Yun (1983) A Remark on Shields’ Diagram. Proc. 2nd Intl. Symposium on RiverSedimentation, Nanjing (China) B-7, pp. 329-341.

Lovera, F and Kennedy, J.F. (1969) Friction Factors for Flat Bed Flows in Sand Channels. JHD, Proc. ASCE, Vol.95, No. HY-4, July, pp. 1227-1234.

Mantz, P.A. (1992) Cohensionless, Fine Sediment Bed-forms in Shallow Flows. JHE, Proc. ASCE, Vol. 118, No.5, May, pp. 743-764.

Mantz, P.A. (1979) Incipient Transport of Fine Grains and Flakes by fluids–An Extended Shields’ Diagram.Closure of Discussion, JHD, Proc. ASCE, Vol. 106, HY-7, pp. 1173-1190.

Mantz, P.A. (1983) Review of Laboratory Sediment Transport Research Using Fine Sediments. Proc. 2ndInternational Symposium on River Sedimentation, Nanjing (China), p. 532-557.

Meyer-Peter, E. and Müller, R. (1948) Formulas for Bed–Load Transport. Proc. of 2nd Congress of IAHR,Stockholm, Paper No. 2, pp-39-64.

Nakato, T. (1990) Tests of Selected Sediment–Transport Formulas–JHE, Proc. ASCE, Vol. 116, No. 3, March, pp.362-379.

Neill, C.R. (1968) Note on Initial Movement of Coarse Uniform Material. JHR, IAHR, Vol. 6, No. 2, pp-173-176.

Patel, P.L. and Ranga Raju, K.G. (1996) Fraction wise Calculation of Bed-load Transport. JHR, Vol. 34, No. 3, pp.363-379.

Patel, P.L. and Ranga Raju, K.G. (1999) Critical Tractive Stress of Non-uniform Sediments, JHR, IAHR, Vol. 37,No. 1, pp. 39-58.

Patil, B.M. (1997) Some Studies on Resistance to Flow in Alluvial Streams. ISH Jour. of Hyd. Engg., Vol. 3, No.1, pp. 50-60.

Ranga Raju, K.G. (1970) Resistance Relation for Alluvial Streams. La Houille Blanche, No. 1.

Ranga Raju, K.G., Garde, R.J. and Bharadwaj, R.C. (1981) Total Load Transport in Alluvial channels, JHD, Proc.ASCE, Vol. 107, No. HY-2, p. 179-191.

Raudkivi, A.J. (1976) Loose Boundary Hydraulics. Pergamon Press, Oxford, Civil Engg. Div. 2nd Ed. P. 144.

Rouse, H. (1939) An Analysis of Sediment Transportation in the Light of Fluid Turbulence. SCS-TP-25, USDA.

Rouse, H. (Ed.) (1950) Engineering Hydraulics. John Wiley & sons, pp. 794-795.

River Morphology168

Shen, H.W. and Hung, C.S. (1971) An Engineering Approach to Total Bed Material Load Regression Analysis.Proceedings of Sediments Symposium to Honour Prof. Einstein, Chapter 14.

Shields, A. (1936) Anwendung derhAhnlichkeitsmechanik und Turbulenzforschung auf die Geschiebebe wegung.Mitteilungen der Pruesspsichen Versuchsanstalt für Wasserbau und Schiffbau, Berlin, No. 26.

Singh, I.R. and Kumar, S. (1974) Mega and Grant Ripples in the Ganga, Yamuna and Son Rivers, Uttar Pradesh,India. Sedimentary Geology, Vol. 12.

Sutherland, A.J. (1967) Proposed Mechanisms of Sediment Entrainment by turbulent Flows. JGR, Vol. 72, No. 24,Dec. pp. 6183-6194.

TCPSM (1971) Sediment Transportation Mechanics : H – Sedimentation Manual – JHD, Proc. ASCE, Vol. 97,HY-4, pp. 523-567.

Van Rijn L.C. (1983) The Prediction on Bed-forms, Alluvial Roughness and Sediment Transport. DHL Rep 5487-III, The Netherlands.

Van Rijn, L.C. (1984) Sediment Transport, Part III : Bed-forms and Alluvial Roughness. JHE, Proc. ASCE, Vol.110, No. 12, Dec. pp. 1613-1641.

Van Rijn, L.C. (1983) Discussion of “Sediment Transport and Unit Stream Power function” by Yang, C.T. andMolinas, A. (JHD, Proc. ASCE, June 1982), JHD, Proc. ASCE, Vol. 109, No. HY-8, pp. 1785-1787.

Van Rijn, L.C. (1984) Discussion Sediment Transport, Part II : Suspended Load Transport, JHE, Proc. ASCE, Vol.110, No. 11, Nov.

Vanoni, V.A. (1946) Transportation of Suspended Sediment by Water. Trans. ASCE, Vol. III, pp. 67-102.

Vanoni, V.A. and Brooks, N.H. (1957) Laboratory Studies of the Roughness and Suspended Load of AlluvialStreams. Caltec Rep. No. E-68, Dec.

Vanoni, V.A. and Nomicos, G.N. (1959) Resistance Properties of Sediment – Laden Streams. JHD, Proc. ASCE,Vol. 85, No. 5, pp. 77-107.

Vittal, N., Ranga Raju, K.G. and Garde, R.J. (1973) Sediment Transport Relation Using Concept of EffectiveShear Stress. Proc. of Intl. Symposium on River Mechanics, IAHR, Bangkok, pp. 489-499.

Whetten, J.T. and Fullam, T.J. (1967) Columbia River Bed-forms. Proc. Of 12th Congress of IAHR, Fort Collins(U.S.A.), Vol. 1, pp. 107-114.

Yalin, M.S. (1971) Mechanics of Sediment Transport. Pergamon Press, Oxford (U.K.)

Yalin, M.S. and Karahan, E. (1979) Inception of Sediment Transport. JHD, Proc. ASCE, Vol. 105, HY-11, Nov.pp. 1433-1443.

Yang, C.T. (1972) Unit Stream Power and Sediment Transport. JHD, Proc. ASCE, Vol. 98, No. HY-10, pp. 1805-1826.

Yang, C.T. (1973) Incipient Motion and Sediment Transport, JHD, Proc. ASCE, Vol. 99, No. HY-10, p. 1679-1704.

Yang, C.T. and Molinas, A. (1982) Sediment Transport and Unit Stream Power Function. JHD, Proc. ASCE, Vol.108, No. HY-6, June, pp. 776-796.

6C H A P T E R

Hydraulic Geometry and PlanForms of Alluvial Rivers

6.1 INTRODUCTION

Chapter 5 was devoted to the discussion of the hydraulics of alluvial streams in which problems ofincipient motion of uniform and non-uniform sediments, bed-forms, their characteristics and their effecton resistance and sediment transport, prediction of bed-forms, prediction of velocity, modes of transportof sediment and computation of bed-load, suspended load, and total load transport were discussed. In allthese discussions the channels were assumed to be straight, the banks non-erodible, the channel shapenearly rectangular and the discharge constant. These conditions are seldom met in natural alluvialstreams. Hence this chapter is devoted to the discussion of alluvial streams in which discharge, channelwidth and plan-form are varying in time and/or space. The following aspects are discussed in thischapter.

Stable Channels Carrying SedimentChannels flowing through sandy material with non-cohesive bed and banks or banks with somecohesion are used to carry water for irrigation. These channels carry nearly constant discharge and carryknown but small sediment load. Further their plan-form is imposed and does not change. Britishengineers proposed the design method for such channels in the Indian subcontinent in the earlytwentieth century. Further work on this was done in U.S.A. and other countries and design methods havebeen proposed using resistance and transport relationships. Such analysis has made possible design ofchannels carrying known discharge and sediment load.

Hydraulic Geometry of Alluvial StreamsTaking clue from stable channel relationships, attempts were made to determine relationships for width,depth, area and slope of alluvial streams assuming a constant hypothetical flow, called bankful

River Morphology170

discharge or dominant discharge or mean annual discharge, as being responsible for shaping thechannel. Some optimisation techniques have also been used to determine the hydraulic geometry ofchannels and streams; these are discussed in brief. Lastly, relationships for hydraulic geometry obtainedby using the method of dimensional analysis are discussed.

Flow in Rigid-bed and Alluvial Channel BendsTo understand the flow in meandering stream it is desirable to know the characteristics of flow in bendswith rigid bed and sides as well as with alluvial boundaries. The aspects discussed here include velocitydistribution in the longitudinal and radial directions, growth and decay of secondary circulation, super-elevation, head loss in bends, shear distribution near curved stream bed and bed topography.

Braiding and MeanderingThe two most important plan-forms, namely braiding and meandering are discussed in detail. Theaspects regarding braiding that are dealt with include mechanism of braid formation, causes of braiding,types of bars in braided streams, and braiding parameters, which quantify the extent of braiding. Asregards meandering attention is focussed on change from pool and riffle sequence in straight channel tothat of a meandering stream, meander characteristics, processes governing meander-bend migration,and meander theories. The discussion is concluded with a discussion on the criteria for plan-forms.

6.2 STABLE CHANNELS CARRYING SEDIMENT

The efforts of British engineers working in India during late 19th and early 20th centuries were aimed atobtaining dimensions of the channel and the velocity of flow which will yield non-silting and non-depositing sections of alluvial channels carrying a given discharge and sediment load, and flowingthrough non-cohesive sandy material. Traditionally these irrigation canals taking off from the headworks are provided with elaborate arrangements for sediment removal at the head works and/or in thecanals so that they carried a limited amount of bed material load (of the order of 100 to 500 ppm byweight). On the basis of work done by Kennedy, Lindley, Woods and Lacey himself, Lacey (1930) foundthat the area, perimeter, hydraulic radius, velocity and slope of such regime channels are uniquelydetermined by the design discharge Q in m3/s and size of the bed material d in mm. Specifically Laceyobtained the following equations,

P Q

AQ

f

RQ

f

U f Q

Sf

Qf d

=

=

=

FHGIKJ

=

=

=

U

V

|||||

W

|||||

4 75

2 28

0 47

0 4390 0003

1 76

5 6

11 3

1

1 3

11 3 1 6

11 3

1 6

.

.

.

..

.and 1

...(6.1)

Hydraulic Geometry and Plan Forms of Alluvial Rivers 171

where cross sectional area A, perimeter P, hydraulic radius R and velocity U are in metric units. Here f1is known as Lacey’s silt factor and d is the median size of bed material in mm. Out of the first fourequations only three are independent and the fourth can be obtained there from. Since 1930 severalinvestigators have attempted to modify or improve these relations; however Eq. (6.1) are more widelyused. Some attempts have been made to estimate the sediment load carried by Lacey channels. Ahmadand Rahman (1962) using flume data have proposed the relation,

1000 q S

o

2 3

1 2w

= 1 + 5 C 2 3 ...(6.2)

where q is discharge per unit width in ft2/s, wo is the fall velocity of sediment in ft/s and C is bedmaterial concentration in ppm by weight. Similarly, Dixon and Westfall (see Garde and Ranga Raju,2000) have used flume, canal and river data to obtain the bed material transport rate as

qT = 0.0011U

o

4

w

...(6.3)

Blench (1957) argued that the effect of bed and bank materials must be taken into accountseparately in determining the dimensions of stable channel and its slope. Hence, Blench introduced bedfactor Fb and side factor Fs and defined these as

Fb = U

D

2

...(6.4)

Fs = U

W

3

in which A = WD and W is mean width of the channel. The slope equation proposed by him is

U

g DS

2

= 3.63 (UW/n)0.25 ...(6.5)

The inclusion of Reynolds number UW/n was justified saying walls acted as smooth boundary;however this reasoning does not seem to be tenable. Equation (6.4) can be expressed in terms of Q, Fsand Fb as

W = FF Qb

s

1 2 (a)U

V

||||

W

||||

D = FF Qs

b

FHG

IKJ

1 31 3 (b) ...(6.6)

S= F F

g Qb s5 6 1 2 1 4

1 61 91

n

.(c)

River Morphology172

in SI units. The bed and side factors are given by

Fbo = 1.9 dmm

Fb = Fbo (1 + 0.012 CB)

and Fs = 0.10 for loam of very slight cohesion ...(6.7)

= 0.20 for loam of medium cohesion

= 0.30 for loam of high cohesion

Here, Fbo is the bed factor with vanishing bed-load and CB is the bed-load transport rate in ppm byweight. For sides made of rounded gravel embedded in fines, Blench proposed that Fs be found by theequation

Fs = d 4 ...(6.8)

where d is in mm. Finally, he has proposed an equation alternative to Eq. 6.6 (c) which includes bed-loadconcentration; however, this equation is not used much.

Simons (1957), Simons and Albertson (1963) analysed data from Punjab and Sind canals alongwith canals in USA and found that if the perimeter P, area A and hydraulic radius R are expressed as P,A, R = mQn, the values of m and n depend on the nature of bed and bank material, thus supporting thecontention of Blench that nature of bed and bank material plays an important role in determining thehydraulic geometry of stable channels. The values of m and n obtained by Simons and Albertson (1963)are given in Table - 6.1.

Table 6.1 Regime equations of Simons and Albertson, P, A, R = mQn

Category Sand bed and Sand bed and Cohesive bed Coarse non-cohesivebanks cohesive banks and banks material

P m 6.33 4.74 4.63 3.44n 0.512 0.512 0.512 0.512

A m 2.57 2.25 2.25 0.939

n 0.873 0.873 0.873 0.873

R m 0.403 0.475 0.557 0.273 n 0.361 0.361 0.361 0.361

Thus, canals flowing through sandy bed and cohesive banks, and cohesive bed and banks will havesmaller perimeter, smaller area and greater depth (or hydraulic radius) than canals flowing throughsandy bed and banks for the same discharge. For the first three categories, they also suggested Blenchtype slope equations, namely


Sand bed and banksU

gDS

2

= 0.324 (UW/n)0.370U

V

||||

W

||||

Sand bed and cohesive banksU

gDS

2

= 0.525 (UW/n)0.370 ...(6.9)

Cohesive bed and banksU

gDS

2

= 0.885 (UW/n)0.370

Gupta (1967) and Kondap (1977) used dimensional analysis and wrote

W

d

A

ds , 2 and S= f

Q

dd

Cg d

s

f

2

3 2

Dg

r

n

, , and1 2

F

H

GGGG

I

K

JJJJ

where Ws is water surface width and C is total load concentration. It was further found out from analysis

of field data that W

ds and

A

d2 are insensitive to variation of C. Hence, using Sind and Punjab canal data

as also the data of US canals collected by Simons, Kondap (1977) proposed the following equations:

W

ds = 0.212 g d Q

dds

f

1 2 3 2 0 231

2

0 458

n

r

FHG

IKJ

F

H

GGGG

I

K

JJJJ

.

.

Dg

...(6.10)

A

d2 = 2.21Q

dds

f

2

0 855

Dg

r

F

H

GGGG

I

K

JJJJ

.

...(6.11)

As regards the slope he suggests the following equation

S

s fDg g

= 0.0423U

d

d

ys fDg r

F

HG

I

KJFHGIKJ

1 5

1

1 095. .

...(6.12)

where y1 = W

As . Chang (1980) realized that for designing a stable channel to carry a given discharge Q,

and given sediment transport rate QT and flowing through non-cohesive sediment of size d, one has the

River Morphology174

resistance law and the sediment transport law to determine the width, depth and slope, even if oneassumes a trapezoidal channel with given side slope Z:1. Since there are three unknowns and only twoequations, Chang imposed the condition that the channel adjusts the width, depth and slope in such amanner that the stream power per unit length of channel (Qgf S) is minimum. On this basis he hasproposed the algorithm shown in Fig. 6.1 for the computation of W, D, S, for known Q, QT, d andtrapezoidal channel of known side slope Z: 1.

Fig. 6.1 Chang’s algorithm for design of stable channel (Chang 1980)

Is Q = Qc?

Is S minimum ?

Data : Q, QT, d Z:1

Assume B

Assume D

Use sediment transport lawand compute S

Use resistance law and computeU and then Qc

Is Q = Qc ?

Is S minimum ?

Print B, D, S

YesYes

No

No

Yes


White et al. (1981) have shown that optimizing (maximizing) the sediment transport rate QT forgiven Q, S, d and Z yields the same results as those obtained by minimizing S for given Q, QT, d and Z.Thus, it seems possible to use optimization technique for channel design. However, White et al. foundthat for given QT, the ratio of computed slope to observed slope ratio for existing stable channels variedbetween 1 and 3 whereas predicted depths and widths showed better agreement. Hence, according tothem, in general the predicted results are not accurate enough for using this method in those cases whereempirical equations of better accuracy can be used. However, this algorithm is of great value in thedesign of channels which carry large quantity of sediment load and for which Lacey type equationscannot be used. In fact Chang (1980, 1988) used the algorithm given in Fig. 6.1 with side slopes 2:1,resistance law proposed by Lacey, viz.

U = 1 346.

Na

D1/4 R1/2 S1/2 ...(6.13)

where f1 = 1.76 d , Na = 0.0225 f11/4, D is the mean depth of flow, and DuBoys bed-load equation to

prepare Q vs. S/d1/2 curves for different values of Ws and D; this is shown in Fig. 6.2. Here d expressedis in mm and other quantities are in fps units. He also prepared a graph between S/d1/2 and Q with QT/Qas the third variable as shown in Fig. 6.3. Here QT has been calculated using Engelund-Hansen formula.

It can be seen from Fig. 6.3 that in Sind, Punjab and Simon’s canal data Q

QT varies from 50 to about 200

ppm. Chang also found that Engelund-Hansen formula produced better conformity with measuredsediment loads than DuBoys or Einstein-Brown formula. He also compared the computed and theobserved values of Ws and Ws/D for these canal data and found good agreement. Chang has mentionedthe fact, commonly used by design engineers that in sandy material for canal to be stable, Froudenumber should be kept between 0.2 and 0.3 and quoted the flowing relationship between Fr and R/d

Fig. 6.2 Variation of B and D with Q and S/d1/2 for stable channels (Chang 1980)

River Morphology176

proposed by Athauallah and Simons

Fr = 4.388R

dFHIK

- 0 31.

...(6.14)

6.3 HYDRAULIC GEOMETRY OF ALLUVIAL STREAMS

Dominant DischargeUse of a constant hypothetical discharge in the study of hydraulic geometry of streams was more or lesssimultaneously done in India, Europe and USA so that simple relationships could be developed for P, A,R or D and U, which are similar to those for stable canals. In following this approach one must bear inmind some important differences between flow in stable canals and alluvial or gravel-bed rivers,because of which this extension has to be done cautiously. These are:

1. Wide variation in the discharge and sediment load carried by the streams and very largedifference between their maximum and minimum values. On the other hand canals carry afairly constant discharge with limited variation in sediment load.

2. Large variation in the size of bed and bank material is found in streams; as a result armouringcan take place in streams having large standard deviation of bed material.

3. Whereas stable canals have more or less regular shape, river cross sections are invariablyirregular.

4. The plan-form of stable canals is fixed whereas in streams it changes along the length.5. The slope of the river as well as the characteristic size of bed material change along the length,

whereas canal sections are designed for a constant Q, S and d.

In spite of these limitations river channel dimensions seem to be adjusted by erosion and depositionso that the channel can contain all but the highest flows it experiences. Hence, it seems reasonable toexplore if one or more geometrical characteristics of river cross-sections can be related to a hypotheticalconstant discharge.

Fig. 6.3 Variation QT/Q with Q and S/d1/2 for stable channels (Chang 1980)


Bankful and other Characteristic DischargesThis concept of a constant discharge has been used widely to describe the river regime. In order to makestable canal formulae applicable to rivers, Inglis (1947) introduced the concept of dominant discharge;according to him, “there is the dominant discharge and its associated charge and gradient to which theriver channel returns annually. At this discharge the equilibrium is most closely approached andtendency to change is least. This condition may be regarded as an integrated effect of all varyingconditions over a long period of time”. Expressed differently, dominant discharge is a hypotheticalconstant discharge which would produce the same result (average width or meander dimensions) ascaused by the actual varying discharge. Intuitively he assumed this discharge to be bankful discharge forIndian rivers in plains and that it could be used in relations for width, depth, meander width etc. Hefurther found that for Indian rivers in the plains of North India, bankful discharge is ½ to ¾th of the flooddischarge.

While studying the hydraulic geometry of rivers in the Great Plains of USA, Leopold and Maddock(1953) used the mean annual discharge Qma and found that this discharge had a frequency of twenty fivepercent, i.e., for 91 days in a year the discharge was equal to or greater than Qma.

Nixon (1959) studied the bankful discharges of 22 non-tidal rivers in England and Wales to explorethe possibility of obtaining Lacey-type equations for rivers in U.K. Comparison of bankful discharge of22 rivers at 29 sites led Nixon to conclude that bankful discharge is such a discharge, which is equaledor exceeded 0.60 percent of the time. Further this percentage is not dependent on the magnitude of thedischarge. This conclusion was based on the data for two to five year period except for the river Thamesfor which 72-year data were available. It may also be mentioned that percentage of time varied from2.91 to 0.10 in individual cases.

Williams (1978) has discussed the merits and demerits of various methods of determining thebankful stage and corresponding discharge obtained there from. Williams distinguishes between theactive flood plain where water spreads every year during the flood and sediment deposition occurs, andthe inactive flood plain or terrace which is part of the valley flat which is submerged only during the rarefloods and where sediment deposition does not occur. Among eleven methods available in literaturewhich are proposed by geologists and geomorphologists, he prefers the following three methods for thedetermination of bankful stage.

1. Average elevation of active flood plain;2. If elevation vs. W/D ratio is studied, the elevation at which this ratio is minimum;3. If log-log plots of area of cross-section versus width are prepared, the elevation at which the

slope of the curve suddenly changes.

Once the bankful stage is determined, the corresponding discharge can be determined from therating curve at the nearby gauging station. Alternatively, knowing Q vs A, W or D graphs at a station, onecan find the bankful discharge for the known depth. The method would be to use Manning’s equation fora reach after averaging out the hydraulic parameters at the bankful stage at two or more cross-sectionsand choosing an appropriate value of n. He also studied the flow frequency duration curves at thegauging stations and determined the frequency of bankful discharge. On the basis of analysis of data at28 gauging sites in Western USA with 233 data points he found that determining the bankful dischargeQb at a given site gives inaccurate results and hence this method should not be used; instead bankfuldischarge in a given reach is more meaningful. Further, rating curve approach is recommended. He hasproposed the equation

River Morphology178

Qb = 4.0 A Sb1 23 0 31. . ...(6.15)

where Ab is cross-sectional area at bankful stage in m2 and Qb is the bankful discharge in m3/s. Thisequation is based on the following ranges of Ab, S and Qb

Ab = 0.70 m2 to 8510 m2, S= 0.000 041 to 0.081,Qb = 0.50 m3/s to 28 320 m3/s

This equation gives an average standard error of 41 percent in Qb. Similar equation was alsoproposed by Riggs (1976).

Qb = 3.39 A Sb1 295 0 316. . ...(6.16)

which was found to give larger error than Eq. (6.15). As regards frequency or return period for bankfuldischarge for active flood plain stations, Williams found the average return period mode of about 1.5years on the annual maximum series; however because of the wide range (1 to 32) years, the spread andskewness of the distribution, the average value loses its significance. Hence, he did not recommend thismethod for the determination of bankful discharge. For record it may be mentioned that therecommended values of return periods for bankful discharge by some investigators are

Nixon (1959) 2.2 yrs

Leopold et al. (1964)and Carlson (1965) 1.5 yrs

Dury (1973) 1.58 yrs

Hence, the only two characteristic discharges that seem to be preferred for studying bankfulgeometry are the mean annual discharge Qma and the bankful discharge Qb; the relationship between thetwo was graphically represented by Chang (1979) using the data of Schumm and Carlson. Garde et al.(2002) plotted the data of Kellerhals et al. and obtained the relationship (see Fig. 6.4)

Qb = 17.253 Qma0.843 ...(6.17)

Fig. 6.4 Relation between Qb and Qma

107

Qma

106

106

105

104

103

102

10

Qb

105

103

102

10 104

CarlsonSchummKellerhals

Best fit line

Q = 17.253 Qb

0. 843

ma


Here Qb and Qma are in m3/s. In studying river bed variation in transient flows in alluvial streamsone would prefer to use a characteristic discharge related to sediment transport or bed level variationrather than using bankful discharge. This concept has been used by Schaffernak (1950) who introducedthe term bed-generative discharge which he defined as the discharge that transports the largest volumeof coarse material. Figure 6.5 illustrates how this discharge is computed; Fig. 6.5 (a) shows thefrequency-discharge curve while Fig. 6.5 (b) is the sediment discharge vs. water discharge relationshipfor the stream. In Fig. 6.5 (c) the abscissa is obtained by multiplying the frequency DF of a particulardischarge by the corresponding sediment discharge rate Qs while the ordinate is the discharge. Thedischarge that gives the maximum Qs DF is the bed generative discharge.

Komura (1969) defines the dominant discharge as that constant discharge which will transport thesame quantity of sediment load as is transported by the varying discharge during the same period or year.Hence,

Qd = S

S

1

1

NTi i

NTi

Q Q

Q...(6.18)

where N is the total number of mean daily discharges, Qi and QTi are the corresponding total sedimentdischarges. According to Komura in the above equation mean monthly discharges be used if flood has along duration, and mean daily discharge or maximum monthly discharge if flood duration is small.Further, if one utilizes the empirical relation between discharge and sediment load in the form QT = a Qb,the above equation reduces to

Qd = S

S

11

1

Ni

b

Nib

Q

Q

( )+

...(6.19)

NEDCO (1959), defines the dominant depth Dd as

Dd = DQ dt

Q dt

TO

T

TO

T

zz

...(6.20)

where D is the depth at sediment transport rate QT.

Fig. 6.5 Determination of bed generative discharge

Q Fs DQsDF

Q QQ

(a) (b) (c)

River Morphology180

Enough information is not available about the relationship between Qb and Qd or bed generativedischarge. Gandolfo (1955) found that the bed generative discharge is greater than Qd corresponding toaverage sediment transport rate and that the latter is greater than Qma. The relationship between Qb andQma is already given in Fig. 6.4.

6.4 EMPIRICAL RELATIONSHIPS FOR HYDRAULIC GEOMETRY

Leopold and Maddock (1953) explored the applicability of equations of the type

W = a Qb

...(6.21)

U

V

|||

W

|||

D = c Qf

U = k Qm

Qs = p Qj

at a station for variable discharge, and along the stream length for mean annual discharge Qma, by usingdata from American rivers in Great Plains and South-West. Since Q = WDU it follows that for both thesetypes of relationships ack = 1 and b + f + m = 1. For twenty cross-sections representing a variety of riversLeopold and Maddock found that “at a station” the average values of b, f and m were b = 0.26, f = 0.40and m = 0.34. Since the depth increases faster than the width, the (width/depth) ratio decreases withincrease in discharge. The relationship between suspended load discharge Qs and Q at a station showedgreater scatter, with j values ranging between two and three. Since j is greater than unity, it is obviousthat at a station Qs/Q i.e., suspended sediment concentration increases as Q increases. While relatingwidth, depth and velocity to discharge along the stream, they preferred to use mean annual dischargeQma which had an average frequency of 25 percent, i.e., it is equaled or exceeded one day in every fourdays over a long period. With this discharge Qma in Eq. (6.21), average values of b, f and m were b =0.50, f = 0.40 and m = 0.30. It may be noted that values of b and f and m agree fairly well with thoseobtained by Lacey. In as much as the percentage of land not contributing sediment increases in thedownstream direction and percentage of land contributing water discharge increases in downstreamdirection, one would expect Qs/Q to decrease in the downstream direction, as concluded by Rubey(1933). However, individual rivers may differ in this respect.

Experience has shown that “at a station” relationships are significantly affected by the climaticchanges, namely depending on whether the stream is perennial, ephemeral or in arid or semi-arid region.

Nixon (1959) while studying the hydraulic geometry of rivers in England and Wales found that thebankful discharge Qb is equaled or exceeded 0.6 percent of the time i.e., on the average about two daysin a year. He further found that in the equation P = W = aQb the coefficient “a” depends on the frequencyof discharge used, see Table 6.2.

Table 6.2 Dependence of constant of proportionality in W = aQb on the frequency ofdischarge (Nixon 1959)

Percentage frequency 30 20 10 5 3.7 0.6“a” in W = aQb in SI units 8.87 7.61 6.16 5.23 4.84 3.00


Nixon also mentioned that if the mean annual discharge were used, the constant in the aboveequation would be 7.66 which is not much different from that for 20 percent frequency. For rivers inEngland and Wales, Nixon found that

W = 1.65 Qb1 2/

...(6.22)

U

V

|||

W

|||

D = 0.545 Qb1 3/

U = 1.112 Qb1 6/

Qs = 0.9 Qb3 4/

in SI units for Qb ranging from 10 m3/s to 500 m3/s. After Leopold and Maddock as well as Nixon’sworks were published, a number of investigators in U.S.A., U.K., Norway, Malaysia, Brazil and PuertoRico applied the same technique using either bankful discharge or discharge of certain frequency andobtained the exponents b, f, m. Similar studies were also conducted in U.S.A., U.K. and other countrieson gravel-bed rivers (see Chapter VII).

Langbein (1964) considered streams in humid regions in which the discharge increases in thedownstream direction. He stipulated that along with the three equations of Leopold and Maddock for W,D and U two additional equations can be considered as

S a Qz ...(6.23)UV|

W|and Manning’s n n a Qy

so that b + f + m = 1

...(6.24)UV|

W|and m =

2

3 f +

z

2 – y

since in the downstream direction stream would satisfy continuity and Manning equation. In addition,he stipulated that (i) streams have a tendency for uniform distribution of work per unit width along thechannel, and (ii) the rate of work in the whole system is also as small as possible. On these premises heshowed that

S= W

Q2

U

V||

W||or z =

b

2 – 1

Further, to fulfill the conditions mentioned above he argued that |b2 + f 2 + m2 + z2 + (1 + z2)| shouldbe minimum. This condition is satisfied by the following values.

b = 0.53, f = 0.37, m = 0.10, z = – 0.73

These values of b. f and m agree fairly well with those obtained by Leopold and Maddock.Some support to this approach of studying the hydraulic geometry of rivers was provided by Smith

(1974) who represented a straight stream channel as a surface

River Morphology182

y = y (x, z, t) ...(6.25)

subjected to the following three conditions: (i) sediment mass is conserved during the transport; (ii)channel has the form just sufficient to carry the total discharge of water given the law of watermovement; and (iii) the channel has the form just sufficient to carry its total sediment discharge giventhe sediment transport law. Smith also assumed that the channel is carried in non-cohesive material andthat one has the freedom to choose a time scale for which the channel has a steady state form. He furtherassumed that Q and Qs increase linearly with x, and lateral sediment transport rate is equal to

longitudinal transport rate multiplied by ¶

¶

D

z. He used Manning’s equation for flow velocity and

sediment transport equation of the form

qs = const q2 S2 ...(6.26)

Rather than solving the system of equations, Smith tried to find out the values of the exponentswhich will satisfy all the imposed conditions. He thus obtained

W ~ Qb7 11/ , D ~ Qb

3 11/ , U ~ Qb1 11/ and S ~ Qb

- 2 11/ ...(6.27)

in the downstream direction. These values are comparable to those obtained by Leopold and Maddock,and by Langbein.

In order to study the variation of the exponents b, f and m. Park (1977) analysed data from 139 “ata station” sites and data from 72 “in the downstream” direction. The ranges of variation in b, f and mobtained by Park are listed below in Table 6.3. In the analysis of data in downstream direction Q used isthe observed or estimated Qb or Q with a return period of 2.33 years.

Table 6.3 indicates that values of b, f and m vary over a wide range and hence for a given streamthese values can be very different from those given by the theory. To study further the simultaneousvariations of these exponents, Park plotted b, f and m on tri-axial diagram with one side for eachexponent. Typical tri-axial diagrams for at a station and downstream exponents in different climaticconditions are shown in Figs. 6.6 and 6.7. The climatic factors did not seem to affect “at a station”exponents. Hence, Park suggested that local factors such as the composition of bank material,differences between braiding and meandering reaches, between pools and riffle sections, flowmagnitude, suspended load and channel migration might be responsible for such variations.

Table 6.3 Summary of distribution characteristics of hydraulic geometry exponents data (Park 1977)

At a station; N = 139 In downstream direction; N = 72

Exponent B f m b f m

Range 0.20 – 0.59 0.06 – 0.73 0.07 – 0.71 0.03 – 0.89 0.09 – 0.70 0.51 – 0.75

Modal class 0.01 – 0.10 0.30 – 0.40 0.40 – 0.45 0.40 – 0.50 0.30 – 0.40 0.10 – 0.2

Theory (1)* 0.23 0.42 0.35 0.55 0.36 0.09

Theory (2)** 0.68 0.30 0.90

(1)* Leopold and Langbein (2)** Smith


Fig. 6.6 Tri-axial graph of at-a-station hydraulic geometry exponents (Park 1977)

As regards the “downstream” data, Park found that for perennial streams in semi-arid regions theexponents are similar to those found in humid temperate climate, whereas ephemeral streams in semi-arid region tend to have lower b and high f exponents. In addition local factors such as lithology,variation in bank erodibility, channel instability, coarser bed material, and the downstream variation inslope are also responsible for the variation in b, f and m. On the basis of this study of tri-axial diagramsunder various environments, Park casts doubt on the use of mean values of the samples of exponents tocharacterise the hydraulic geometry of streams in particular areas, and suggests that quoting meanvalues gives a misleading impression. While Park concentrated on the effect of environmental factors onb – f – m variation, Rhodes (1977, 1987) concentrated on the effect of hydraulic factors.

Some recent studies do not endorse Leopold and Maddock’s conclusion that this is a rational oreven a good way of describing cross-sectional channel adjustment. Some have also questioned whetherlog-linear model of hydraulic geometry is either appropriate or meaningful. However, the greatest

River Morphology184

drawback seems to be the non-inclusion of sediment size, difference in specific weights of sediment andwater, and channel slope from the downstream relationships. However, in spite of these limitationsinvestigators continue to use this analysis as a basis, since in regional and climatically homogenousregions they may give good approximation of hydraulic geometry.

Studies of Leopold and Maddock, and Langbein indicate that for downstream geometry m = 0.05 to0.10 indicating that velocity at bankful stage or for mean annual discharge varies very slowly in thedownstream direction. Leopold, Wolman and Miller (1964) show constancy of U for 50 year and 5 yearfloods in Yellow Stone basin, see Fig. 6.8. Some studies indicate that constant velocity along the lengthof the stream is attained at a stage between mean annual discharge and modest over-bank stage of 5 yearflood (Chorley 1969). This needs further study in view of the commonly accepted view that streamvelocity decreases as it flows from mountains to the plains.

Some other efforts to include additional variables to describe the hydraulic geometry, include theinvestigations of Schumm (1977) who analyzed the data on channel dimensions, mean annual discharge

Fig. 6.7 Tri-axial graph of down stream hydraulic geometry exponents


Qma and bed and bank sediments at 36 cross-sections from semi-arid to humid regions in the GreatPlains of U.S.A. and Plains in New South Wales in Australia in sand-bed streams. Schumm indicatedthat (width/depth) ratio in these channels was related to the percentage of silt-clay M in the perimeter ofchannel (see Fig. 6.9), and obtained the equations

W/D = 255 M–1.08

...(6.28)

U

V||

W||

W = 0.38 Qma0 38. /M0.39

D = 0.6 Qma0 29. M0.342

Fig. 6.8 Variation of average velocity at Q5 and Q50 in Yellow stone river basin and down stream (Leopold et al. 1984)

Fig. 6.9 Variation of width to depth ratio with M (Schumm 1977)

Wid

th/D

epth

Rat

io (

F)

Q Discharge cfs50

Q Discharge cfs5

1,000,000100,00010,0001,000

Discharge in cfs

5

5

10

10

Mean

velo

city

inft/s

River Morphology186

where Q is expressed in ft3/s and D and W in ft. Gregory and his associates (see Fergusson 1981) studiedbankful dimensions vis-à-vis the catchment area in humid areas and found that for catchment area Abetween 0.1 and 4.0 km2, W ~ A0.32, D ~ A0.16 and channel capacity ~ A0.48. Hey (1982), and Hey andThorne (1986) while analyzing gravel-bed river data from U.K. related width and depth to bankfuldischarge, d50 and the sediment transport rate Qs. These types of relationships developed in differentcountries are listed by Wharton (1995).

Since in the relationships discussed above some have used bankful discharge and some meanannual discharge, it is difficult to compare their results. Further, in studying the transient flows dischargeneeds to be replaced by some hypothetical constant discharge related to sediment transport or riverbedvariation. Lastly, the relationships developed above do not contain other variables such as slope,sediment size, Dgs and are not dimensionally homogenous. These aspects are discussed in the next twosections.

6.5 NON-DIMENSIONAL RELATIONS FOR HYDRAULIC GEOMETRY

Some attempts have been made to obtain non-dimensional form of equations for W, D and U or A. ThusRybkin in 1947 (see Goncharov 1962) used the data from the upper Volga and the Oka basins andproposed the following equations

W = a1 wo

gS

2FHGIKJ

Q g Sb

o ow w

a

2

2 1

FHGIKJ

L

NMM

O

QPP

...(6.29)

U

V

||||||

W

||||||

D = a2 wo

gS

2FHGIKJ

Q gSb

o ow w

a

2

2 2

FHGIKJ

L

NMM

O

QPP

U = a3 wo

gS

2FHGIKJ

Q gSb

o ow w

a

2

2 3

FHGIKJ

L

NMM

O

QPP

where wo is the fall velocity of bed material and a1 , a2 anda3 as well as a1, a2 and a3 are constants. In

1950 Velikanov proposed the following form of the equations

W

d= a1

Q

d gdSb

2

1FHG

IKJ

a

...(6.30)

U

V

|||

W

|||

D

d= a2

Q

d gdSb

2

2FHG

IKJ

a

According to his analysis a1 = 0.50 to 0.53 and a2 = 0.25 to 0.27. Ananian (1961) obtaineda1 = 2.70 and a1 = 0.42. Mukhamedov and Ismaghilov (1969) analysed the data from the middle andlower reaches of the Amu Darya and obtained the following equations for W and D


g

g

s

s

W S

dD

= 3.8 Q

d gdS

Sb

s f2

5 2 0 48

Dg g/

/ .

F

HGI

KJL

NMM

O

QPP

...(6.31)

U

V

|||

W

|||and

g

g

DS

dsD

= 0.095 Q

d gdS

Sb

s f2

5 2 0 28

Dg g/

/ .

F

HGI

KJL

NMM

O

QPP

which can be reduced to a simpler form as

W

d= 3.8

Q

d gd Sb

2

0 48FHG

IKJ

.

S

s fDg g/

.FHG

IKJ

0 20

...(6.32)

U

V

|||

W

|||

D

d= 0.095

Q

d gd Sb

2

0 08FHG

IKJ

.

S

s fDg g/

.FHG

IKJ

- 0 30

These equations have not been tested using data from other countries.Garde et al. (2002) have analyzed a large volume of data on the hydraulic geometry of rivers from

different countries given by Leopold and Wolman (1957), Schumm (1969) Chitale (1970) andKellerhals et al. (1972). The ranges of basic variables used by them are

Qb = 4.24 m3/s – 52 800 m3/s...(6.33)W = 5.80 m – 943 m

UV|

W|S= 4.1 ́ 10–5 – 6.8 ́ 10–3

They studied the possibility of relating W/d, D/d and A/d2 to Q1 = Q

d gdb

2 , Q2 = Q S

d gdb

2 and

Q3 = Q

d gdSb

2 . The second parameter Q2 = Q S

d gdb

2 represents the dimensionless stream power while

the third parameter is that earlier used by Ananian and others. In general the results were more accuratewith Q1 and Q3 than Q2. These equations are listed below along with percent of data giving less than ±50 percent error.

Equation % of data giving error between ± 50%

W/d = 7.5 Q10 425. 78

...(6.34)D/d = 0.14 Q10 430. 74

U

V||

W||A/d2 = 1.80 Q1

0.855 82

River Morphology188

W/d = 2.9 Q30 402. 79

...(6.35)D/d = 0.06 Q30 405. 56

U

V||

W||A/d2 = 0.16 Q3

0.807 74

see Fig. 6.10, 6.11 and 6.12 corresponding to Eq. (6.35).

Fig. 6.10 Variation of W/d with Q3 for River data (Garde et al. 2003)

Fig. 6.11 Variation of D/d with Q3 River data (Garde et al. 2003)

The two equations which give velocity at bankful discharge with reasonable accuracy are Lacey’sequation

U = 10.8 D2/3 S1/3

...(6.36)

U

V||

W||

andU

gd= 2

D

dFHIK

0 60.

S0.40


6.6 FLOW AROUND BENDS WITH RIGID AND ALLUVIAL BEDS

While discussing point bars, some introductory comments were made about secondary circulationdeveloped in channel bends and its effect on shear distribution and formation of point bar. In thissection, flow around bends in rigid-bed and alluvial channel bends is discussed further. The aspectsdiscussed below include velocity distribution in radial and transverse directions, the development anddecay of secondary circulation, super-elevation and transverse bed profiles in alluvial bends.

Velocity Distribution in Rigid Bed BendsThe analysis of flow in rigid-bed bends is carried out using Reynolds’ equations of motion incylindrical-polar coordinate system. To obtain tangible results, the following assumptions are made:

1. The flow is steady so that ¶

¶ t = 0;

2. The depth of flow is much smaller than the channel width or the radius of the bend;

3. Pressure distribution in the vertical is hydrostatic;4. Purely viscous stresses involving m or n are neglected in relation to Reynolds stresses;5. Eddy viscosity is assumed to be constant and scalar;6. Except in the regions close to the walls the velocity component vy is very small compared to v

q

and vr and hence can be neglected; and

7. Secondary flow is fully developed and hence ¶

¶q

= 0 and ¶

¶ r <<

¶

¶ y.

Hence Reynolds’ equations of motion reduce to

– v

rq

2

= – ¶

¶ r (g D) + Î

¶

¶

2 2

2

v

yr (a)

...(6.37)

U

V

|||

W

|||

g Ie + Î ¶

¶

2

2

v

yq = 0 (b)

Fig. 6.12 Variation of A/d2 with Q3 River data (Garde et al. 2003)

River Morphology190

and continuity equation ¶

¶ r (vr r) = 0 ...(6.38)

Velocity Distribution vo ( y): Rozovskii (1957) has studied four types of velocity distributions vo asa function of h = y/D namely Eqs. (6.39), (6.40), (6.41) and (6.42).

Logarithmic Law

v v

vmax

*

-

= 1

k

ln y

DFHIK

which can be reduced to

v

Vcp

= 1 1+ +

FHIK

FHG

IKJ

L

NM

O

QP

g

C

y

Dk

ln ...(6.39)

Here, v* = gDS, vmax = Vcp 1+

FHG

IKJ

F

HG

I

KJ

g

Ck

, k = Karman constant, the value of which recommended

by Rozovskii is 0.50, C is Chezy’s coefficient, and Vcp is average velocity in the vertical. It may bementioned that the subscript q is omitted here for convenience. Power law

v

vmax

= hn, where h = y

D ...(6.40)U

V||

W||or

v

Vcp= (1 + n) hn

v

Vcp= 1

31 2

+ - -

LNM

OQP

m

C

m

Cha f where m = 22 to 24 ...(6.41)

andv

vmax

= 1 12

- -P ha f where P = 0.37 + 3 3.

C...(6.42)

Out of these equations, Rozovskii found that Eq. (6.39) gives reliable results while Zimmerman(1977), and Zimmerman and Kennedy (1978) used Eq. (6.40) in their analysis.

Velocity Distribution vr: The velocity distribution in radial direction for hydrodynamically smoothand rough surfaces has been obtained by Rozovskii by using Eq. (6.39).

Hydro-dynamically smooth bend

v

Vr

cp

= 4 D

r F

g

CF1 2

2h ha f a f-

L

NM

O

QP ...(6.43)

He found that change in Chezy’s C from 60 to 30 made very little difference in distribution of nrexcept near the bed and water surface.


Hydro-dynamically rough bend

v

Vr

cp

= 4 D

r F

g

CF1 4

2h ha f a f-

L

NM

O

QP ...(6.44)

where F4 (h) = F2 (h) + 0.8 (1 + ln h)

The functions F1 (h), F2 (h) and F4 (h) are plotted in Fig. 6.13, while experimental data arecompared with Eq. (6.43) in Fig. 6.14 which shows correctness of Eq. (6.43).

Fig. 6.13 Variation of F1 (h), F2 (h) and F4 (h) with h

Fig. 6.14 Comparison of Eq. (6.43) with experimental data (Rozovskii 1957)

h

v

V

r

D

r

cp

0–10 –8 –6 –4 –2 2 4 6

1.0

0.8

0.6

0.4

0.2

0.0

h

River Morphology192

Growth and Decay of Secondary CirculationIn a long bend, Rozovskii defines the angle qlim as the angle at which the growth of circulation ispractically complete, and qlim is given by

qlim = 2 3. C

g D

rc...(6.45)

Here, D can be taken as average depth and rc is center line radius of the bend.Decay of vr : If vro is surface velocity at the exit of the bend, it will decay with x the distance

measured from the end of the bend according to the law

V

Vrx

ro

= eg

CxD ...(6.46)

Hence the length required to reduce vro to vrx is

x

D=

C

g ln

V

Vro

rx

and if one assumes that when vrx/vro = 0.10, the circulation has died out, the length required is

L

D= 2.303

C

g...(6.47)

Distribution of Longitudinal Velocity Over WidthAccording to Rozovskii’s observations, the maximum velocities move nearer the convex (inner) bankand are stronger, the sharper the bend. However, then the transformation takes place gradually and themaximum velocity gradually moves over to the concave (outer) bank. If the bend is sufficiently gentle,on emerging from it, the maximum velocity is already found near the concave bank. On emerging fromthe bend, the velocities become sharply redistributed with their maximum coming almost in to contactwith the continuation of concave bank.

Super ElevationSuper elevation (SE) is the difference in water levels between the outer and inner banks of the bend, andcan be obtained from the equation of motion in the r direction, namely

gf ¶

¶

D

r= rf

V

rcp2

...(6.48)

where Vcp is the average velocity in the vertical at radial distance r. If it is known how Vcp varies with r,the above equation can be integrated to obtain

SE = (Do – Di) = 1

g

r

r

t

oz V

rcp2

dr


Here, Do and Di are the depths at outer and inner banks respectively.1. If Vcp is constant across the bend, integration of the above equation gives

SE (Do – Di) = V

gcp2

lnr

ro

i

LNM

OQP ...(6.49)

2. If Vcp varies according to free-vortex law, as assumed by Shukry (1950) i.e. Vcp = K/r, one gets

SE = K

g

2

2

1 12 2r ri o

-

LNM

OQP ...(6.50)

Assuming the depth of flow upstream of the bend to be the average depth in the bend, and U tobe the average velocity, Ippen and Drinker (1962) reduced the above equation to

SE = U

g

2

2 2W

rc

1

12

2

-

FHG

IKJ

L

N

MMMMM

O

Q

PPPPP

W

rc

...(6.51)

3. If it is assumed that velocity variation follows forced vortex pattern i.e., higher velocities nearthe outer bank and lower near the inner bank, Vcp ~ r, this assumption together with theassumption of constant average specific energy leads to the equation

SE = U

g

2

2 2W

rc

1

12

2

-

FHGIKJ

L

N

MMMMM

O

Q

PPPPP

W

ri

...(6.52)

Apmann (1973) studied the relationship between super elevation and discharge, to predict the latterif the former is known. On the basis of the analysis of data from rectangular and trapezoidal channels,natural channels and ducts with included bend angle varying from 45° to 360°, Apmann expressed superelevation as

K U

g1

2

2= SE ...(6.53)

He found that the coefficient K1 is primarily a function of ro/ri and r

Wc q

, the relation being

K1 = 5

4 tanh

r

Wc qFH

IK ln

r

ro

i

FHGIKJ

...(6.54)

River Morphology194

As regards separation of flow on the inner side of the bend, Rozovskii has found that the possibilityof separation is greater, the deeper the stream and the gentler the bank slope, or in short the greater thefriction on the bank. With small depths and vertical walls, flow without separation is possible even whenrc /W is equal to unity. Thus, he found that in streams with small (depth/width) ratio, formation of eddyzone at very sharp turns is possible along the convex bank, but along the convex banks which have steepslope, it is less likely to occur.

Head-loss in BendsHead loss in a bend is caused because of the following reasons (Rozovskii 1957):

1. Altered velocity distribution of longitudinal velocity component over the width of the stream;2. energy required to cause secondary circulation;3. increase in boundary friction due to circulation;

4. increase in energy loss of internal friction due to presence of secondary circulation;5. altered velocity in the vertical; and6. energy loss due to separation in sharp bends.

The equation proposed by Rozovskii for head loss in open channel bends is

hb = 24 60

2

g

C

g

C+

L

NM

O

QP

r

D U

g

2

2...(6.55)

No independent check on this equation seems to have been made. By qualitative reasoning Bagnold(1960) has postulated that the resistance in bends in pipes and open channels can be partly attributed toforce required to the creation of secondary flow and partly to overcome the boundary friction andwritten

f = D

rc + const

r

Dc

and shown that at rc/D values between 2 and 3 the resistance is minimum. Leopold and Wolman (1960)have also compiled field evidence to suggest that in meandering streams, bends commonly tend to havea value of rc/W between 2 and 3. Hence, Bagnold argued that some principle of energy minimizationmay be involved in meander formation.

6.7 SHEAR DIRECTION NEAR CURVED STREAM BED AND BEDTOPOGRAPHY

Because of the presence of secondary circulation, radial shear stress is caused on the bed which isdirected from outer towards inner side of the bend in radial direction. As a result, the resultant shearstress has a small radial component, which is responsible for cross-sectional bed deformation in alluvialchannel bends. This aspect of flow in bends is studied by Engelund (1974), Kikkawa et al. (1976),Zimmermann (1977), De Vriend (1977), Zimmermann and Kennedy (1978), Odgaard (1982) and


others. Figure 6.15 shows the directions of bed shear tq in streamwise direction, shear in radial direction

tr and the resultant shear to.

From geometry one can write,

to = t tq

2 2+ r

tan y = t

tq

r = t

t

t

t

r

or

o

12

+

FHGIKJ

...(6.56)

tan y »

t

tq

r

since tr << to. Here y is the angle between stream wise shear stress and resultant shear. To obtain anexpression for tr, the average shear stress around the wetted perimeter in radial direction was calculatedby equating its moment about the center of cross-section to the moment produced by the interaction ofthe vertical velocity gradient and the streamline curvature. Using Eq. (6.40) and expressing the

exponent n as n = 113.

f, Zimmermann obtained the following expressions for to and tr.

to = r f f U2

8 and

tr = 1

3 rf

113

113 2 263

.

. .

f f

f

+

+a f

D

rc2 U2

hence, tan y = b(f ) D

rc

FHGIKJ

...(6.57)

where b(f ) = 9 04

383 6 78

.

. .

+

+

FHG

IKJ

f

f f...(6.58)

Fig. 6.15 Motion of a particle on transverse sloping plane

River Morphology196

Figure 6.16 shows variation of b(f) with f according to Eq. (6.58). It can be seen that b(f ) and hencetan y decrease rapidly as f increases; this decrease is attributed to more uniform vertical distribution ofstreamwise velocities as the channel becomes rougher. For large values of f, b(f ) decreases gradually. Itmay be mentioned that Engelund (1974) obtained value of b(f ) as 7.0 for smooth channels, whileRozovskii (1957) recommends a value between 10 and 12 for rough as well as smooth beds.

The method of estimation of variation of depth along the radial direction as given by Engelund(1974) is given below. Considering the motion of a sediment particle on a channel bed with a smalltransverse bed slope a and with shear stress deviating by an angle d from the local flow direction, thedrag force on the particle in the longitudinal direction will be

FD = g g

p

s f Ld

F- -

LNM

OQPd i

3

6 tan f cos a

where f is the angle of repose, and FL is the lift force on the particle. In the transverse direction theforces on the particle have the component

g g

p

s f Ld

F- -

LNM

OQPd i

3

6 sin a – FD tan y

Hence, tangent of the deviation angle d will correspond to the ratio between transverse andlongitudinal force components; or

tan d = tan

tan

a

f

– tan y ...(6.59)

This result is valid only as long as the angle a is small and sediment is transported predominantly asbed-load.

In the case of steady, uniform flow in a circular alluvial bend, there will be a small sedimenttransport in the radial direction which will be balanced by the radial bed slope developed givingincreased depth at the outer wall. Thus inward sediment transport is balanced by the outward componentdue to transverse bed slope. Equilibrium will be attained when y is equal to d. Engelund obtained

Fig. 6.16 Variation of b(f) with f (Zimermann 1977)


tan y = 7 D

r,

7 D

r=

1

tanj

d D

d r

which on integration gives

D = C1 r7 tan f.

The constant of integration can be determined from the condition that at r = rc, D = Dc. Hence, thedepth D at any radial distance will be given by

D = Dc r

rc

FHGIKJ

7 tanj

...(6.60)

Engelund recommends the value of f = 30°The particle size distribution in a bend is not uniform when the river bed material is graded; the

coarser sediment accumulates near the concave bank and finer near the convex bank. Odgaard (1981,1982 and 1984) has suggested a method for prediction of the particle size distribution in a bend. As afirst approximation, he assumed that the bed profile is a straight line and further assumed that thedimensionless critical shear stress tc is proportional to d-2/3, and obtained the particle size distribution inthe radial direction as

d

dc

= D

Dc

FHGIKJ

5 3/

r

rcFHIK

3 2/

...(6.61)

He has also found that the radial distribution of average velocity in the vertical is given by

V

Vcp

cpc

= d

dcF

HIK

1 6/

D

Dc

FHGIKJ

2 3/

r

rcFHIK

1 2/

...(6.62)

Here Dc and Vcpc are the centre line depth and centre line average velocity in the vertical.River bends can be either entrenched or meandering surface bends. Entrenched bends include those

bends, which follow the bends in the valley. The river on the floor of valley forms meandering surfacebends, which is erodible. In these bends the nature of bank material predominantly determines the radiusof curvature of bends. These bends are also classified into free bends, limited bends and forced bends.The banks in free bends are composed of alluvial material, which is easily erodible. In limited bends, thebanks are composed of consolidated parent material, which limits lateral erosion, as in entrenchedbends. In forced bends, the stream impinges straight on the parent bank at an angle between 60° to 100°

approximately. For these bends r

Wc varies from 4.5 to 5.0 for free bends, 7.0 to 8.0 for limited bends and

2.5 to 3.0 for forced bends. Meandering rivers assume a natural alignment consisting of bends andshallows in the crossings between bends. The profile of the talweg consists of successive deeps andpools in the bends and shallows or shoals in the crossings.

River Morphology198

6.8 BRAIDED RIVERS

The basic mechanism of initiation and development of braiding has been studied through laboratoryexperiments carried out by Leopold and Wolman (1957), Edgar (1973), Zimpfer (1975), Hong andDavies (1974) and Ashmore (1982). Leopold and Wolman (1957) have suggested the followingsequence of events in the development of braided reach. In an originally single or undivided reach ashort submerged bar is deposited during high flows. The head of this gravel bar is composed of coarsefraction of bed-load that is moving along the center of the channel. Most of the finer particles move overit, some are trapped on or behind it leading to its growth in the downstream direction. Simultaneously itgrows laterally. When it becomes sufficiently wide, it starts affecting the channel along its side byincrease in velocity, which initiates widening of the channel. The bar gradually gets stabilized due tovegetation that induces some more deposition on and around it. Later similar process starts in thedivided channels leading to island formation and division of channels. Observation by Hong and Davies(1979), Ashmore (1982), Zimpfer (1975) and Edgar (1973) at Colorado State University indicate thatthe channel division can occur either by separation around middle bar; or incision of a new channelacross the diagonal bar. Ashmore (1991) has shown that braiding can be accomplished in four ways:accumulation of a control bar, chute cutoff of point bars, conversion of transverse unit bars to midchannel braid bars, and dissection of multiple bars. The Brahmaputra river in Assam (India), the Kosi inBihar (India) and parts of the lower Mississippi are excellent examples of braided streams.

A braided river reach is characterized by a number of alluvial channels with bars and islandsbetween meeting and dividing, and present the intertwining effect of a braid when seen from the air.Braided rivers may be considered as a series of channel segments that divide and rejoin in more or lessregular and repeatable manner. However, even in a braided reach a single dominant channel can bedistinguishable. Plan-form of braided rivers can change radically with the change in discharge; hencesome investigators e.g., Bristow and Best (1993) have opined that the fluctuations in discharge are a pre-requisite for braiding especially in sand bed rivers, even though flume experiments in gravel carried outby Ashmore at constant discharge discount this observation. A few rivers act as single channels atbankful stage and have characteristic braided pattern at lower stages; however in many other rivers someof the islands are permanent and at low stage as well as at high stage the rivers show braided pattern.

It seems that presence of wide range of sediment sizes in the bed material is conducive to barformation and hence braiding. Braiding has been observed and studied in laboratory flumes as well as inrivers as large as the Brahmaputra and the Mississippi. Plans of braided rivers often reveal the grosssimilarity in the appearance of braided patterns. Study of braided rivers is not only important from thepoint of view of river morphology; braided alluvial deposits form substantial hydrocarbon reservoirs,sites for deposition and accumulation of heavy minerals, and important sand gravel reserves (Schumm1977).

Leopold and Wolman (1957) on the basis of study of the hydraulic characteristics of divided andundivided channels indicate that for a divided stream (i) the slope is steeper, (ii) width is larger, and (iii)depth is smaller, than that for an undivided stream. The ratio of slope of divided to undivided streamvaries for 1.3 to 2.3, while the ratio of corresponding widths ranges from 1.05 to 2.0.

Causes of BraidingIt has been observed that the important variables that affect the braiding of rivers are discharge and itsvariability, the size distribution of the bed material and the rate and size distribution of sediment load,


width, depth, slope, climate and geologic factors. It is observed on many rivers that a given channel canchange in a short distance from a braided to meandering and vice versa; such changes are thereforeattributed to the variations in locally independent variables. It is also observed that those riversdominated by braided as against the meandering channels have on the average a higher floodpeakedness, higher total discharge range and higher monthly discharge variability. Braiding isdeveloped by sorting as the stream leaves behind those fractions of the load it is incompetent totransport. If the stream is competent to move all sizes that it is transporting but is overloaded aggradationmay take place without braiding.

Lane (1957) studied plan-forms of a number of streams as well as their history, and concluded thatthere are two primary causes of braiding; these are (i) overloading i.e., stream may be supplied withmore sediment than it can carry and hence part may be deposited; and (ii) steep slopes causing a wideshallow stream in which bars and islands may readily form. All steep slope type braided channels havemany characteristics in common in addition to that of multiple channels; these are i) relatively straightcourse of main channel; ii) steep longitudinal slopes; iii) wide channels; iv) shallow depths; v) sand orcoarse bed material; and vi) usually high bed-load. Since braided form can be due to steep slope or dueto aggradation resulting from the overloading of stream with sediment, or due to combination of the two,braided streams can be classified into the following five subdivisions as per Lane (1957):

I Braiding due to steep slope: a) Braiding due to steep slope with degradationb) Braiding due to steep slope with approximate equilibrium

II Braiding due to aggradation: c) Braiding due to steep slope with aggradationd) Braiding due to moderate slope with aggradatione) Braiding due to low slope with aggradation

Types of Bars in Braided RiversAs described by Miall (1977) the bars occurring in a braided river can be classified as under (see Fig.6.17)

Fig. 6.17 Principal types of bars (Miall 1977)

River Morphology200

Longitudinal BarsThese are diamond or lozenge shaped in plan and are elongated parallel to flow direction. They arebounded by active channels on both sides and may have partially eroded margins. Bars formed in gravelare most commonly of this type. Longitudinal bars are the classical braid bars of Leopold and Wolman(1957) and the sequence of events leading to their formation is discussed earlier. The initial bar reliefmay be no greater than the size of the largest fraction of the bed material but as growth continues it mayincrease to as much as metre. Bar length may reach several hundred metres. The internal structure of thebars is massive or crude horizontal bedding.

Linguoid or Transverse BarsLinguoid or transverse bars are most typical of sand braided rivers. They are found to occur in channelsthat are deep and confined within narrow banks. The characteristic shape of linguoid bars is rhombic orlobate, with upper surfaces that dip gently upstream towards the preceding bar and downstream facingavalanche – slope terminations. These bars vary in width from a few metres to 150 m and length up to300 m. Most typical heights of these bars range from 0.50 to 1.0 m. Dunes and ripples commonly coverLinguoid bars that are exposed to view in modern rivers. Transverse bars are geometrically similar tolinguoid bars, except that they tend to have straighter crests.

Point Bars, Side Bars, Lateral BarsGeometrically these bars are similar. They form in the areas of relatively low energy such as inside of themeander. Point bars are usually associated with a meandering river, but they also occur in a braidedenvironment. Side bar is the longitudinal deposition along the side. Other large-scale structures areobserved in fairly large rivers.

Thus sand waves observed by Coleman (1969) in Brahmaputra, and dunes and bars observed inrivers such as the Lower Red River (Alberta) fall in this category. Figure 6.17 shows longitudinal bar,Linguoid bar, point bar and side bar. Large and sudden changes in water discharge mean the bed isseldom if ever in equilibrium with the flow. Such reduction in flow has two effects on the bed – higherrelief structures may be eroded or dissected, and smaller scale structures may be superimposed. Barrelief tends to be smoothened over as a result of reduction in flow and consequent sheet flow or waveaction. In the last stage of decreasing flow the deposition of this sheet of silt or mud takes place and thechannel fills in inactive areas.

After an extensive study of literature and braided stream deposits, Miall (1977) has classified thesedeposits into three gravel facies Gm, Gt and Gp, five sand facies St, Sp, Sr, Sh and Ss, and two fine-grained facies Fi and Fm. Their description, associated sedimentary structures, and interpretation aregiven in Table 6.4.

Braiding ParametersIn recent times some thought has been given to characterise the braiding pattern, see Friend and Sinha(1993). As a result, three parameters have been proposed (see Fig. 6.18).

Brice Index BI = 2 S Li/Lr

where S Li is the length of the islands or bars in a reach and Lr is the reach measured midway betweenthe banks of the channel. The factor two accounts for the total length of the bars.


Table 6.4 Lithofacies and sedimentary structures of modern and ancient braided-stream deposits(Miall 1977)

Facies identifier Lithofacies Sedimentary structures Interpretation

Gm gravel, massive or crudely ripple marks, cross beds in sand longitudinal bars, channel-bedded, minor sand silt units, gravel imbrications lag depositsor clay lenses

Gt gravel, stratified broad, shallow trough cross-beds minor channel fillsimbrications

Gp gravel, stratified planar cross-beds linguoid bars or deltaicgrowths from older barremnants

St sand, medium to very solitary (theta) or grouped (pi) dunes (lower flow regime)coarse, may be pebbly cross beds

Sp sand, medium to very solitary (alpha) or grouped linguoid bars, sand wavescoarse, may be pebbly (omikron) planar cross beds (upper and lower flow

regime)St sand very fine to coarse ripple marks of all types, ripples (lower flow regime)

including climbing ripplesSh sand, very fine to very horizontal lamination, parting or planar bed flow (lower and

coarse, may be pebbly streaming lineation upper flow regime)Ss sand, fine to coarse, may broad, shallow scours (including minor channels or scour

be pebbly eta-cross-stratification) hollowsFl sand (very fine), silt, mud, ripple marks, undulatory deposits of waning floods,

inter-bedded bedding, bioturbation, plant rootlets, overbank depositscaliche

Fm mud, silt rootlets, desiccation cracks drape deposits formed inpools of standing water

Fig. 6.18 Calculation of braiding indices of Brice (1964), Rust (1978) and Sinha (1993)

River Morphology202

Braiding parameter of Rust (1968) RI = S L

Lb

m

where S Lb is the sum, in a reach, of the braid lengths between the channel talweg divergences andconfluences, and Lm is the average of meander wave lengths in the reach. Friend and Sinha (1993) haveproposed braid–channel ratio BR which is defined as

BR = Lctot/Lcmax

where Lctot is the sum of mid-channel lengths of all the segments of primary channels in a reach, andLcmax is the mid-channel length of the widest channel through the reach. The ratio BR is a measure oftendency of the channel belt to develop multiple channels in a reach. If the reach has a single channel,BR will be unity. For the Gandak river in India BR was found to vary from 1 to 5.5.

Modeling of BraidingIn order to explain why and under what conditions alluvial streams braid, Engelund and Skovgaard(1973), Parker (1976), Fredsøe (1978) and Kishi and Kuroki (1985) have treated braiding as a stabilityproblem. A double periodic disturbance with different wave lengths in the flow direction x and lateraldirection z is introduced on the bed of an alluvial channel and the resulting flow is analysed usingshallow water flow model. It is found that the deviation of sediment from the mean flow direction has animportant effect on the amplification of the disturbance leading to braiding. This analysis is usuallylinear in that higher order of the disturbances and their derivatives are neglected. Such analysis has

shown that dimensionless shear stress tg

o

s dD, width to depth ratio W/D, Froude number Fr =

U

gD and

slope are the important parameters that decide whether the stream will braid or meander. The criteria forformation of braiding are discussed later in this chapter.

Another approach to explain braiding phenomenon is that of random walk model proposed byRachocki (1981). In this approach it is assumed that at the mouth of the valley a stream channel maymove downstream in one of three ways: to the right, to the left or it can bifurcate. The minimum distancetraveled in uni-directional flow in the model is termed as the step. Each step is graphically representedby the diagonal of grid square. After the first step, the channel is again able to follow one of these threeoptions. Choosing three dice from a set of thirty, which avoids systematic error, generates the model.The dice are changed after every three model generations. The following procedure was used byRachocki (1981). After the dice have been thrown, their values are added. If the total is even, the streamdeviates to the right, if it is odd it deviates to the left, and if the number is divisible by three it bifurcates.After several steps are followed the pattern obtained is that of a braided stream, (see Fig. 6.19). It may beseen that the approach is purely statistical and does not involve any consideration of fluvial dynamics,bank erodibility etc. as such the approach is unlikely to satisfy river morphologists.

6.9 MEANDERING

In Chapter IV a brief mention has been made about the classification of plan-forms of alluvial streams.In this section additional hydrodynamic information will be presented regarding process of meandering,theories of meandering, meander parameters and criteria for the prediction of major plan-forms.Callander (1978) has given an excellent review about the state of knowledge on meandering.


Meandering appears to begin with the establishment of pools and riffles sequence. Straightlaboratory channels with bed comprising of homogenous material deform into pools and rifflessequence when water flows over the bed and sediment transport takes place. Kinoshita (1957, 1961)observed that the free meanders of a stream start first with the formation alternate bars, or pools andriffles sequence; these change the streamline curvature and velocity variation to induce bank erosionand deposition; this starts meandering process when banks are erodible. The average pool spacing isabout five times the bed width. As the meanders form, the alternate pools migrate to alternate sidesgiving approximate wave lengths of two inter-pool spacing of ten bed widths as observed in nature (seeFig. 6.20). It is interesting to briefly mention about the studies conducted by Agarwal (1983) whoimposed a two-dimensional harmonic disturbance near the bed of sediment transporting channel. With0.27 mm sand and disturbances having frequency of 1.8 to 3.4 Hz, he found that when bed is coveredwith dunes (low Fr) the disturbance did not have any effect on the bed. On the other hand when the bedwas plane and transporting sediment (Fr = 0.8) the disturbance produced alternate bars and pools over27 m long flume. He also carried out some runs in which alternate bars and pools were formed in theinitial length of flume due to disturbance and then the disturbance was removed. In such runs, aftersufficient time the entire flume was covered with bars and pools. His studies thus showed that twodimensional harmonic disturbance can induce formation of alternate bars and pools, and that if suchdisturbance is introduced on the upstream side it can change the bed downstream to alternate pools andbars.

Once the talweg takes a sinusoidal course due to formation of alternate bars and pools it causesredistribution of velocity; it also initiates development of secondary flow. If the banks are erodible theyare eroded on the convex side of the talweg and more sediment is brought into the channel, which istransported to the other side by secondary flow thus developing the point bar. In this way, in an erodiblechannel formation of alternate bars and pools leads to meandering of the channel. Field studies haveshown that riffles tend to be eroded somewhat at lower stages of flow and the eroded material depositsin the pools. As the discharge is increased to approximately the bankful discharge, the pools are scoured

Fig. 6.19 Random walk model of braiding (Rachocki 1981)

River Morphology204

and scoured sediment forms riffles. Hence, hydraulic geometry of meandering streams is related to thechannel-forming discharge. Since the channel width is related to Qb as W ~ Qb

1/2, it seems logical torelate meander parameters to W. Once a meandering pattern is developed it is likely to persist unlesssome really powerful factor comes into play. Experience on the Mississippi, the Ganga and other rivershas shown that the obstacles including the variation in the cohesiveness of alluvium distort or evensuppress the meanders. Hence meander geometry is significantly affected by the nature of strata throughwhich it flows.

In natural streams, alternate bars will form if the stable width for channelforming discharge (e.g.,Lacey width) is less than the confining width, which is fixed by rigid banks or “khadir”, and thedischarge is low. Thus they occur in channelised flows at lower stages. Alternate bar formation has beenexperimentally and analytically studied by Kinoshita, Hayashi (1980), Sukegawa (1972, 1974) andParker (1976).

A typical meandering stream is shown in Fig. 6.21. As mentioned in Chapter-4 meandering loopsare irregular most of the time; further they change their shape and size in the downstream direction.Hence any average values of meander characteristics for a given reach only give us an approximate ideaabout their dimensions. It must also be mentioned that along the reach of the river, it may be braiding inone reach and meandering in another, since local conditions governing the plan form may change.

Rivers cutting into bedrock have also been found to meander. In such rivers the erodibility of thebed rock along its length would govern the meandering pattern. Further such meanders would be moreor less stationary unlike meanders in alluvial strata (see Leopold and Wolman 1960). It is interesting tonote that the relationship between width and ML for such meanders of the Gulf stream of North Atlanticfollow the same trend as that for meanders in rivers in plains. Laboratory experiments of Friedkin(1945), Inglis (1949), Agarwal (1983) and field studies on many rivers have indicated that the meanderpattern as a whole moves downstream in many rivers; this is by far the most common situation. Hickinand Nanson (1975) used dendro-chronological method to measure the rate of migration of bends of theBeatton river. The average rate of migration of ten bends was 0.475 m/yr. The maximum rate occurredwhen Rm/W ratio was approximately 3 implying a rapid approach to limiting value of this ratio to 2.5.Here Rm is mean radius of the bends. However, on some streams such as the Tigris in Iraq and the

Fig. 6.20 Formation of pools, riffles and meandering channel

Meandering channel

10 W

RifflePool

5 W

W

Initial straight channel

Meandering talweg


Pembina river near Manola, Alberta (Canada) the migration consists of gradual lateral enlargementwithout or with small downward movement. Such meanders are called free meanders in Russianliterature. The enlargement of loops can occasionally result in natural cutoffs. According to Neill (1970)downstream migration seems to be usually associated with alluvial fills in narrow valleys whereas freemeandering tends to occur in broad flats. In engineering applications to river training it is essential tostudy historical changes of the river under consideration while planning river improvement works.

Processes Governing Meander Bend Migration (Chang 1988)Meander bends may migrate downstream or laterally as mentioned earlier. This process is governed bychannel curvature, flow curvature and variation of secondary circulation along the bend. As long asthere is an angle between the flow path and the channel path, the primary flow and secondary flow havecomponents in streamwise and cross-stream directions. As mentioned in the section on flow in bends,secondary circulation is responsible for transporting sediment from the concave bank downstream andtowards the convex bank. Essentially the migration of a bend depends on the relative depth of flow andsharpness of the bend, and delayed response of flow curvature to channel curvature. The longitudinalcomponent of shear caused by the main flow causes bank erosion wherever the flow hugs the bank; thisarea is shown hatched in Fig. 6.22; deposition occurs along the banks away from the flow path. Thebank resistance, vegetation on the banks and mode of bank failure also govern the method of migrationof bends. Figure 6.22 shows four cases of different combinations of channel curvature and flowcondition. In Case–A with low flow and mild bend curvature, secondary flow develops and the flowline is more in line with channel configuration; the maximum flow curvature is close to apex and hencelateral migration of bend takes place. Case–B refers to mild channel curvature and high flows. In thiscase flow changes its direction slowly due to inertia and hence maximum flow curvature takes place

Fig. 6.21 Typical meandering river-the White river in Arkansas (U.S.A.)

River Morphology206

further downstream from the apex thereby causing downstream migration. In Case–C with low flowand sharp bend, the flow is unable to follow bend curvature and attacks the outer bank downstream ofapex, thus leading to downstream migration. In Case–D corresponding to high flow and sharp bend,there is sufficient difference in bed and flow curvature. This leads to downstream migration togetherwith reduction in bend curvature.

Meander CharacteristicsThe main characteristics of a meandering river are the shape, size and mobility of meander loops. Thesecharacteristics play an important role in the location, design and maintenance of hydraulic structuressuch as bridges, barrages, flood embankments and guide bunds.

An arc of a circle, a sine curve or a parabolic curve can describe meander shape, even though thecommon practice is to fit an arc of a circle and characterise it by the average radius Rm. The other twolength dimensions that characterise meanders are meander length ML and meander belt MB. Thesecharacteristics depends on whether meanders are incised or are in flood plain, process and stage ofdevelopment of meanders, discharge, slope and sediment size, and terrain through which the river flows.Therefore, these parameters cannot be precisely estimated by any theory and the most commonly usedtechnique for their estimation is statistical correlations using laboratory and field data collected byFriedkin, Ackers and Charlton, Ferguson, Jefferson, Inglis, Bates, Shaw, Leopold et al, Carlson,Schumm, Chitale and others. Most of these relationships are of the form ML, MB = const. Q1/2, where Qis mean annual discharge or bankful discharge. However since channel width W ~ Q1/2 one can expectML, MB and Rm to be related channel width. Those relationships, which are based on use of dimensional

analysis or some form of stability or theoretical analysis, take the form M

dL or

M

dB = f

Q

d gd

2

2

FHG

IKJ

or

M S

DL = f (Fr) where Fr =

U

g D. Some of these relation-ships are listed in Table 6.5 along with the data

used by the investigators.

Fig. 6.22 Common modes of meander bend deformation in relation to flow pattern (Chang 1988)


Table 6.5 Relations for meander geometry

Investigator Relations proposed Data used Remarks

Furguson (1863) ML = 6.0 W Ganga data

Jefferson (1902) MB = 17.6 W American and European rivers

Inglis (1938) ML = 6.06 W = 29.6 Q1/2 Jefferson’s data For rivers in flood

MB = 17.6 W = 84.7 Q1/2 plainsRm = 20.64 Q1/2

ML= 11.45W = 25.4 Q1/2 Jefferson’s data Incised streams

MB = 27.3 W = 56.4 Q1/2

Rm = 14.0 Q1/2

Inglis (1939) ML= 27.4 Q1/2 Shaw’s data for 16 rivers in Orissa Rivers in flood plainsLeopold et al. (1964) ML = 10.9 W1. 01 Fifty rivers ranging from models

MB = 2.7 W1.1 to large rivers

ML = 4.7 Rm 0.98

Dury (1958) ML = 32.9 Q 0.55 American river data. RelationML = (10 to 14) W used in Europe as design criterion

Prus-Chinsky ML = 15 W

Ackers and ML = 38 Q0.467 Laboratory data withCharlton (1970) MB = 18.5 Q0.505 d = 0.15 mm

Schumm ML = 1890 Q0.34/M0.74 Thirty eight sites on Australian M = % of silt and clay

and Western USA rivers in banks

Lewin (1961) ML = 20 W1. 04 English and Scottish river data A1is catchment areaML ~ Ai

0.3 to 0.4 in km2

Chitale (1970) Si = 1.429 (d/D)–0.077 42 river data Si = S ´ 104 Si isS*

0.052 (W/D)–0.065 sinuosity

Ackers andM

dL = 123 Q d

ds

f

/

.

2

0 378D g

r

F

HGG

I

KJJ River and flume data

Charlton (1970)

Anderson (1967)M

AL

c

= 72 Fr1/2 Ac = cross sectional

area

Hansen (1967) ML = 56D

ff Darcy–Weiscbach

coefficient

Altunin (see ML = (12 to 15) W Rivers of Central AsiaKondratev 1950)

Kudryashov (1954- ML = 449 Q0.5 S0.50 Laboratory data58) (see Kondratev MB = 142 Q0.74

1950)

Contd.

River Morphology208

It may be seen from the above table that many of the equations proposed for ML and MB are notdimensionally homogenous. Dimensional homogeneity requires that ML = K1 MB = K2W and Rm = K3W.

According to Hayashi and Ozaki (see Hayashi 1980), in the relation ML = KW, K depends on Froude

number U

gD and decreases with increase in Fr as indicated below

Fr 0.10 0.20 0.40 1.0K 40 20 10 7

Agarwal’s relation (1983) between ML and Q is shown in Fig. 6.23. Any one of the relations givenin Table 6.5 or Fig. 6.23 can be used to estimate ML. On the other hand, for rivers in flood plainsMB = 3 ML, ML/W = 10 to 14 and minimum value of Rm/W = 2 to 3 seem to be good thumb rules.

Hayashi and Ozaki ML = K W Data from Japanese rivers, K is a function of Fr(see Hayashi 1980) Leopold and Wolman,

Schumm & Chitale

Hansen (1967) ML S/D = const Fr2

Agarwal (1983) ML = Nonlinear function of Q1/2 Based on field and flume dataML = 2.1 MB with Q up to 104 m3/s

Si = 0.97 Q dds

f

/

.

2

0 033D g

r

F

HGG

I

KJJ S0.04

Contd.

Fig. 6.23 Variation of ML with Q (Agarwal 1983)


Relations such as those mentioned above overlook the random character of meandering. Wallis(1973) repeated the same experiment 60 times in a small flume using crushed polythene of mediandiameter 2.6 mm and relative density 1.46 and measured meander characteristics at 30 s interval usingphotographic technique. His measurements indicated the stochastic nature of meander properties. Thewave-lengths followed uni-modal distribution with a coefficient of variation of 0.22. Both mean andstandard deviation increased with time but the ratio of the two remained nearly the same. Spectralanalysis approach has been used by Toebes and Chang (1967), Speight (1965) and Fergusson (1975).

Theories of MeanderingEngineers and geomorphologists have given a number of reasons as to why streams meander. These arebriefly discussed below.

Excess energy conceptSchoklitsch (1937) and Inglis (1947, 1949) have argued that meandering is the natural way of reducingexcess energy (and hence excess slope) of the stream by increasing its length. On the basis of Bagnold’sfindings that for a large number of natural bends the ratio of radius of bend to channel width liesbetween 2 and 3 at which the bend loss is minimum, Leopold and Wolman (1960) believe that someprinciple related to minimization of energy is associated with meander formation. A somewhat similarprinciple is used by Ramette (1980). On the other hand, Joglekar argues that the primary cause ofmeandering is excess sediment load. According to Indian engineers, the excess sediment load duringfloods tends to deposit on the bed and increase the slope. This deposition creates shoals on the bedcausing deviation in the flow. If the banks are erodible this deviation in flow direction can initiatemeandering. However, this hypothesis cannot explain the formation meanders in glacial streams,observed by Leopold and Wolman (1960). Yang (1971) also has questioned the validity of thehypothesis that streams meanders in order to dissipate excess energy. Hence, he has introduced a law ofleast time rate of energy expenditure according to which, during the evolution towards its equilibriumcondition, a natural stream chooses its course of flow in such a manner that the time rate of potentialenergy expenditure per unit mass of water along its course is minimum. Or

DDH

t= f (discharge, valley slope, sediment concentration, geological constraints)

However, this concept is not further developed linking flow parameters to meander characteristics.

Earth�s rotation theoryGilbert (1884), Eaking (1910) and Neu (1967) have given earth’s rotation as a cause of meandering.Due to rotation of earth, a body on the earth’s surface experiences a Coriolis force which representsinertia of the body to partake in the rotational motion. Due to this force a body moving in the north-southdirection in the northern hemisphere will experience a force towards the east which can deflect the bodyin that direction. The tendency of the Mississippi river and some other rivers in Alaska to deflect to theright is often quoted in support of this theory. Neu (1967) has shown that the secondary circulationdeveloped due to earth’s rotation is proportional to D/U of the stream and the latitude of the place. Thedeviations caused by this circulation can be of the order of 10° to 20°. However it is argued that if earth’srotation alone were responsible for meandering, all the streams at or near the equator should be straight,

River Morphology210

whereas meandering streams are found on the equator as well as elsewhere on the earth’s surface.Further, it has been shown by Quaraishy (1944) that the tendency of the stream to deflect either to theright or to the left is just a chance, and force due to earth’s rotation is relatively small. Lastly theerodibility of banks plays a major role in meandering, which is not taken into consideration in such atheory. Hence it is felt that even though earth’s rotation may play a small part in the meandering process,it cannot be the sole reason.

Disturbance theoryProponents of disturbance theory argue that any disturbance caused on the bed or in the flow at theupstream end causes changes in the flow pattern in the downstream direction leading to meandering.This disturbance can be differential deposition across the channel width in an overloaded stream, ortransverse oscillations in the flow, or an inclined entry into the channel. Earlier Griggs (1906), Werner(1951) and Hjulstrom (1957) have suggested this mechanism. Friedkin (1945) was able to initiatemeandering in a laboratory channel with mobile boundary by allowing flow at an angle. Agarwal (1983)was able to obtain alternate bars in a laboratory flume by imposing a two-dimensional harmonicdisturbance near the bed. Lewin’s (1976) observation on the Ystwyth river where a straight channelchanged to a meandering one without apparent changes in geological or hydro-geological conditionssupports this theory. The change in Ystwyth river began with the formation of lobate transverse bar.Since the disturbance imposed on the flow can be decomposed into harmonics and for a given flowcondition, one of the harmonics can cause instability to form meanders, disturbance theory can be linkedto instability theory discussed later where the investigators have assumed that meanders occur as a resultof unstable response of the bed to a small perturbation.

Helicoidal motion theorySome investigators argue that helical motion or secondary circulation is somehow responsible foroccurrence of meandering. Since secondary flow is present in all the channels, it is believed thatsecondary circulation has to become unsymmetrical so as to cause meandering. This is probably causedby unsymmetrical cross-section of the channel and/or by the changing resistance characteristics of bankand bed along the channel length, see Leliavsky (1955), Prus-Chacinsky (1954), Onishi et al. (1976),Jain and Kennedy (1976), and Shen (1983). Prus-Chacinsky has shown that by introducing an artificialsecondary flow at the entry of the first bend, it is possible to produce various patterns of secondary flowat the entry of the first bend, and various kinds of secondary flows in the next successive bends. This inturn, affects the circulation in the next bend, and so on. Prus-Chacinski ascribes meandering to anydisturbance which produces the initial circulation. Onishi et al. (1976) have concluded that the mostimportant cause of meandering is secondary flow, which produces point bars, modifies the distributionof velocity across the channels, modifies the shape of ripples and dunes on the bed and affects theentrainment and transport of sand on the bed. This concept is loosely linked to disturbance theory.

Conceptual model of Leopold and LangbeinLeopold and Langbein (1978) have proposed a model according to which the meander form is the sameas the most favourable itinerary of a rod of fixed length and defined by a random walk process betweentwo points. They obtained a curve analogues to the rod buckling in with some real meanders. Theconcept is true provided that the constraints (discharge variation, erodibility, and human interferenceetc.) can be included in the random walk process. However, it is felt that inclusion of such constraintswould result in a different shape.


Ramette�s approachAccording to Ramette (1980) the five characteristics of river geometry, namely width W, depth D, freesurface slope S, meander wave length ML and meander amplitude MB are functions of discharge Q, d50,d90 and valley slope Sv which vary along x direction. His model computes the first five when the last fourare specified. According to Ramette the river characteristics adjust in such a manner that its efficiency ofbed erosion is maximum under two constraints: the discharge Q is the bankful discharge and flow issaturated with sediment i.e., it is carrying the maximum possible sediment load. Hence he uses thefollowing relationships

1. Sediment discharge formula of Meyer-Peter and Müller QB = K W (to – toc)3/2

2. Manning-Stricker equation Q = K1 (WD)5/3 (W + 2D)–2/3 (S)1/2

3. Reduction in sediment size according to Sternberg’s law4. Maximum value of channel slope equal to valley slope: Sv £ S

5. Saturation of flow ¶¶Q

xB = 0

The potential energy of erosion from sand surface to the depth D of liquid mass is QgD/2, while

kinetic energy recovered after erosion is Q U Uo

2 2

2

-d i where U is velocity at depth D and width W, and

Uo is initial velocity. The energic efficiency of erosion of bed is maximum when

Q U Uo2 2

2

-d i

2

QgD i.e.,

U U

gD

o2 2-d i

is maximum, or

d

dx

U U

gD

o2 2-R

S|

T|

UV|

W|

d i = 0

From the above equations, Ramette has shown that the efficiency is maximum and the flow issaturated when b = W/D lies between 15 and 21. According to Ramette, in the upstream reach of theriver where Sv = S, W, D, Q and da are such that the saturation condition is satisfied but not the maximumefficiency condition, W/D is less than 15 and river is straight and tending to equilibrium (b and dadecreasing). Here da is arithmetic mean size of bed sediment. When 15 < b < 21 the river is nearequilibrium. If da is less than da1 then S is less than Sv and river meanders. The limiting diameter da1 is afunction of discharge, valley slope and initial value of da/d90. When b is greater than 21, the river is ofbraided type. Thus if variation of da along the river axis is known, it is possible to find the distance x1upstream of which S is equal to Sv, and downstream of which meanders will appear. As a result of hisanalysis, Ramette has given a criterion for plan form determination in terms of da, Q

0.465 with W/D as thethird variable on which regions of straight, meandering and braided reaches are indicated, see Fig. 6.24.Further assuming that Rm/W = 2.5 for meanders as indicated by Leopold and Wolman, he has shown thatML/MB = 2.5 and ML/W = 7 to 11. Ramette’s criterion has been checked by Agarwal (1983), but theresults are not encouraging.

River Morphology212

6.10 STABILITY ANALYSIS AND CRITERIA FOR PLAN-FORMS

As mentioned earlier bank erosion constitutes the necessary requirement for the occurrence ofmeandering in alluvial rivers. According to the experiments of Kinoshita (1957) meandering is causedfirst by the erosion of bed leading to the formation of alternate bars in channels with non-erodiblevertical walls, which then leads to meandering if the walls are erodible. Hence the theory of alternate barformation in non-erodible walled channel can provide an insight into the formation of meanders andbraids. This theory is based on a stability analysis in which small perturbations that are double harmonicfunctions of x and z coordinates are introduced on the sediment transporting bed in rigid walls channeland the conditions under which these are attenuated or amplified are studied. For such an analysis theequations of continuity for flow and sediment, and sediment transport and resistance laws are used.Depending on whether the analysis is two or three dimensional, the investigators have used two or threeequations of motion. Most of the investigators use linearisation so that higher order terms involvingperturbations are omitted. Reynolds (1965) and Hayashi (1967), Callander (1969), Sukegawa (1971,1972), Hayashi and Ozaki (1978) and Parker (1978) have used shallow water flow models, whileEngleund and Skovgaard (1973) have used turbulent shear flow model. In these theories the factorcausing the instability of the erodible bed is the phase difference existing between shear stress gradientand bed form gradient in the flow direction. However, these theories lead to the unjustifiable conclusionthat larger the mode of the braids m is in Eq. (6.63), larger is the growth of braid unless some additionalcharacteristic of sediment transport is taken into account. Here m is the braiding mode in the equationfor double sinusoidal migrating disturbance on the bed

h = ho cos pmz

W sin

2p x

L...(6.63)

In Eq. (6.63) h is the disturbance imposed on the otherwise flat bed, m is the mode of sinusoidaldisturbance in z direction, W is the channel width, L is the wave length of disturbance in the flow

Fig. 6.24 Ramette’s criterion for plan-forms


direction x, and z is the lateral direction. When m = 1 the pattern is meandering while m = 2 or 3 willrepresent braiding modes as shown in Fig. 6.25.

According to Hayashi and Ozaki (1978) it is the spatial lag distance d between the local bed-loadtransport rate and local shear stress that plays an important role in the formation of braids of mode m = 1i.e. meandering. This lag-distance that was originally estimated by Einstein as 100 d has been modifiedto

d = l1d 1 41

3

+-

RS|

T|

UV|

W|

L

N

MMM

O

Q

PPP

aD S

do

s f*

/r rd i...(6.64)

U

V

||||

W

||||

or d = l1 d 1 51

3

6+-

RS|

T|

UV|

W|

L

N

MMM

O

Q

PPP

af D

dFo

s f

r*/r rd i

where S is average channel slope, f is average friction factor of the bed, Fr = U

g Do

, U and Do are

average velocity and depth of flow in the undisturbed flow, l1 = 100 and a* = 4.35 as proposed byEinstein. Since d is greater than l1d, spatial lag distance is greater than the step length l1d. For non-equilibrium flow Einstein and Brown formula for bed-load transport is modified as

Fig. 6.25 Meandering and braiding

River Morphology214

fx (x, z) = q x z

gd

Bx

s

f

,a f

rr

-FHG

IKJ

1 3

× F = 40 á t* (x – d), z ñ3

...(6.65)

U

V

||||

W

||||

fz (x, z) = q x z

gd

Bz

s

f

,a f

rr

-FHG

IKJ

1 3

× F = fx (x, z) × w x z

u x z

,

,

a fa f

where F = 2

3

36

1

36

1

2

3

2

3+

--

-v

gd

v

gds f s fr r r r/ /d i d i

t* = t

r r*

( )s f gd-

Here qBx and qBz are the x and z components of volumetric bed-load transport rate, d is thecharacteristic size of sediment, u and w are the components of average velocity in x and z directionsrespectively, fx and fz are dimensionless transport rates, and F is dimensionless fall velocity of sedimentparticle. The two dimensional equations of motion, continuity equations for flow and sediment, andresistance law are

Dynamic Equations

uu

xw

u

zg

D

x x DgS

uw

xw

w

zg

D

z z D

x

f

z

f

¶¶

+ ¶¶

+ ¶¶

+ ¶¶

FHG

IKJ

+ - =

¶¶

+ ¶¶

+ ¶¶

+ ¶¶

FHG

IKJ

+ =

R

S||

T||

h tr

h tr

0

0...(6.66)

U

V

||||||||

W

||||||||

Continuity Eq. for flow¶

¶ x (u D) +

¶¶ z

(w D) = 0

Continuity Eq. for Sediment¶¶

ht

+ ¶¶q

xBx +

¶¶q

zBz = 0

Resistance law tx = f r f u2

2 × tz = tx

w

uFHIK and f = 2

u

U*F

HIK

2

= 2 S

Fr2

When the disturbance of the form of Eq. (6.63) is imposed on the bed, small perturbations in variousquantities with respect to steady flow condition will be (see Fig. 6.26)


h = hx = xu = u + u¢, w = w¢

U

V

|||

W

|||

D = Do + x – htx = to + t¢xtz = t¢z

qBx = qBo + q¢BxqBz = q¢Bz

Here uo, Do and qBo are steady state average velocity, depth of flow and sediment transport raterespectively, h and x are displacements imposed on the bed and displacement of free surfacerespectively, to is average bed shear stress in steady flow and primed quantities represent theperturbations. These are then substituted in the equations of motion Eq. (6.66), and linearisation is donewith respect to perturbed quantities. The resulting equations are then non-dimensionalised aftereliminating t¢x, t¢z, q¢Bx and q¢Bz and solution postulated in the form

hr = ho cos lzr exp [i k (xr – Ctr)]

...(6.67)ur = uo cos lzr exp [i k (xr – Ctr)] + i y1

U

V

|||

W

|||

wr = wo cos lzr exp [i k (xr – Ctr)] + i y2

xr = xo cos lzr exp [i k (xr – Ctr)] + i y3

Here ho, uo, wo and xo are the normalized values of h, u, w and x at t = 0, k and l are thedimensionless wave numbers of sinusoidal disturbances in x and z directions respectively, namely

k = 2p D

Lo and

l = m D

Wop

and y1, y2 and y3 are phases of ur, wr and xr with respect to hr respectively. Also complex velocityC = Cr + i Ci where Cr is dimensionless velocity of disturbance and Ci is the amplification factor. Form = 1, the dominant wavelengths are expected to be those for which the initial rate of growth of hr are

Fig. 6.26 Definition sketch

River Morphology216

positive and maximum. Solution of this system of equations constitutes the Eigen value problem andHayashi and Ozaki have done this. They have arrived at the following conclusions

1. When SW

m DopFHG

IKJ

2

<< 1 the rate of growth of hr is largest for waves of mode m = 1 i.e., for sand

waves associated with meandering, and the ratio L/W is given by

L/W = f1 (Fr)

where f1 (Fr) = 2

m

10 19 7

5 8 5 25 110 141 44 4

2 2

2 4 2 4 6 8

1 2

+ +

- + + + + + + +

L

NMM

O

QPP

Fr Fr

Fr Fr Fr Fr Fr Fr

d i

d i

/

» 3.66 1

FrFr+F

HIK ...(6.68)

and the effect of lag distance on formation of meandering is crucial.

2. When SW

m Dp o

FHG

IKJ

2

>> 1, the dominant wave length is given by

L

W=

6

2p

13 2m /

WS

Do

FHG

IKJ

1 2/

...(6.69)

and the rate of growth has a maximum for certain value of mode m. Hence the braid of such amode is theoretically possible.

3. When W S

m DopFHG

IKJ

2

» 1, the dominant wave length is given by

L

W=

1

m f2 (Fr)

...(6.70)

and f2 (Fr) = 2 2 18 10 72 4 1 2

- +RST

UVW

Fr Fr

Fr9 + 2

/

and the rate of growth is largest when m = 1.Analysis of laboratory data indicated that alternate bars are formed when WS/Do < 0.31 which

agrees with the above conclusions. Hence Hayashi and Ozaki have related L with W and Fr as thirdvariable, see Fig. 6 27. It may be noted that L corresponds to meander length ML.

Criteria for Prediction of Plan-formsThe earlier predictors for plan forms were based on the relation between discharge and slope. Thus Lane(1957) analyzed data from models and rivers in USA with average discharge varying from 2.8 ´ 10–3 to25,000 m3/s and slope S varying from 1.59 ́ 10-5 to 5.49 ́ 10–3 and found that


when S ³ 4.1 ́ 10–3 Q–0.25 the channel is braided

and when S £ 7.0 ́ 10–4 Q–0.25 it is straight

When the slope lies between these two limits the channels are meandering. It may be mentioned thatLane did not propose a quantitative criterion to distinguish between straight and meandering channels.Leopold and Wolman (1957) analysed the data from American and some Indian rivers with mean annualdischarge varying from 8.4 to 28 000 m3/s and slope varying from 8.9 ´ 10–5 to 3.6 ́10– 2 and foundthat

if S ³ 0.0125 Q–0.44 streams are braided

and if S £ 0.0125 Q–0.44 streams are meandering

while relatively straight channels with sinuosity less than 1.5 were scattered on both sides at this line.Leopold and Wolman have also observed that the channel patterns braided, meandering or straight, eachoccurs in nature throughout the whole range of possible discharge and slope. Some of the largest riversin the world are braided e.g. the Lower Ganges, the Amazon, the Brahmaputra and parts of theMississippi. Leopold and Wolman’s principal point of discussion is that there is continuum of streamchannels having different characteristics that are reflected in the combination of hydraulic factors—each pattern is associated with certain of these combinations.

Henderson (1963) has included the effect of sediment size in Q–S criterion and modified theequation demarcating braided streams from meandering ones to

S= 0.517 d1.14 Q–0.44

where d is in m and Q in m3/s.

Fig. 6.27 Comparison of predicted and observed meander length (Hayashi and Ozaki 1978)

River Morphology218

Chang (1980) used the condition of minimization of stream power and proposed a criterion between

S

d and Q for identifying the plan-forms, see Fig. 6.28. Region below line 1 represents the condition of

no transport of bed-load. Region between lines 1 and 2, called region I, represents stable channels withflat slopes, low velocity and low bed-load transport rate and width to depth ratio of 4 to 20; naturalchannels in this region have a meandering pattern and occasionally straight channel for which valleyslope is equal to channel slope.

According to Chang, rivers falling in region II have smaller of the two slope minima and are lessstable. The channel geometry is sensitive to slope and slight increase in slope tends to increase thechannel width and decrease the depth of flow. Rivers falling in this region are often braided. For riversin region III width and depth are sensitive to slope and those rivers are braided, the extent of braidingbeing directly related to slope. Rivers in region IV are highly braided and have width to depth ratiogreater than 100. On Fig. 6.28 Chang also gives contours of equal depth and width. The equations ofthree lines in fps units are

Line 1S

d= 0.00238 Qb

-0 51.

...(6.71)

U

V

|||

W

|||

Line 2S

d= 0.05 Qb

- 0 55.

Line 3S

d= 0.047 Qb

- 0 51.

Precise location of line L is not known. Here Q is expressed in cfs and d in mm. When Q isexpressed in m3/s and d in mm, the constants in the above equations are 0.000 386, 0.007 04 and 0.00763 respectively.

Fig. 6.28 Regime channel geometry for sand bed rivers (Chang 1980)


Hayashi and Ozaki (1978) have proposed the criterion for prediction of plan-forms, using the

method of stability analysis. According to them the plan-form depends on WS

Do

and Fr = U

g Do

.

Fr ³ 3.16 W S

Do

FHG

IKJ

1 2/

Straight

3.16 W S

Do

FHG

IKJ

1 2/

³ Fr ³ 2 W S

Do

FHG

IKJ

1 2/

Transition from straight to meandering

2 W S

Do

FHG

IKJ

1 2/

³ Fr ³ W S

Do

FHG

IKJ

1 2/

Coexistence of meandering and braiding

W S

Do

FHG

IKJ

1 2/

³ Fr Braiding

see Fig. 6.29. Using regime type relationships, Hayashi and Ozaki expressed Do, W and U as a function

of Q namely Do ~ Q0.36, W ~ Q0.55 and U ~ Q0.05 and converted Fr – W S

Do

criteria into S – Q criteria,

namely

Fig. 6.29 WS/Do – Fr criterion for channel patterns (Hayashi 1980)

River Morphology220

S ³ 7.0 ́ 10–3 Q–0.37 braiding

S £ 7.0 ́ 10–3 Q–0.37 meandering

Agarwal (1983) has verified S vs. Q criterion using available flume and field data, and concludedthat this criterion does not predict the plan-form correctly. This may partly be due to the fact that somedata especially laboratory data have constant discharge while field data have either bankful discharge ormean annual discharge.

On the basis of the stability theory, Parker (1976) has concluded that in rivers transporting sediment,when Do/W < 1.0 at the formative discharge (both these conditions are almost universally satisfied), thetendency towards either meandering or braiding exists. Further meandering occurs when S/Fr << Do/W,braiding occurs when S/Fr >> Do/W and transition between meandering and braiding occurs when S/Frlies between these two limits see Fig. 6.30. This criterion is based on the laboratory data of SAF,Wolman and Brush, Schuum and Khan, Ashida and Narai, Ackers and Charlton and Qurashy, and fieldobservations of Simons and some rivers.

Fig. 6.30 S/Fr – Do/W criterion of Parker (1976)

Ramette (1980) has proposed d vs Q0.45 S criterion as shown in Fig. 6.24 for prediction of planforms, and verified it with a few experimental data of Henderson. Agarwal has used data from a numberof laboratory studies and field data and found that most of the points for straight channels fall in thecorrect region while the data for meandering and braiding channels are scattered widely and hence hefound the criterion to be unsatisfactory.

Many Japanese investigators have proposed criteria for alternate bars and braids. Sukegawa (1971,

1973) has developed a criterion using u

u c

*

*

vs W S

Do

FHG

IKJ

1 4/

graph, whereas Ikeda (1973) uses u

u c

*

*

vs

W S

Do

FHG

IKJ

1 3/

plot. Kishi and Kuroki (1975) have used u

u c

*

*

vs W S

Do

FHG

IKJ

1 2/

plot and Tamai et al. (1978) have


used u

u c

*

*

vs W S

Do

FHG

IKJ

plot. It may be mentioned that Muramoto and Fujita (1977) have developed plan-

form criterion using W

Do

vs D

doF

HIK graph.

It may be pointed out that stability analysis and other approaches have revealed that the parameters

governing plan forms are W

Do

, Fr, S, f, u

u c

*

*

, tt

o

c

, D

do and lag distance d. These are related by six

equations (see Hayashi 1980, and Hayashi and Ozaki (1978)) and hence one can choose only three as

independent parameters. Three possibilities are (i) W

Do

, S, Fr, (ii) W

Do

, S, tt

o

c

or u

u c

*

*

and (iii) W

Do

, S,

u

u c

*

*

. The analysis indicates that W

Do

and S occur as W S

Do

.

Agarwal (1983) has analysed a large volume of laboratory and field data from various countries toverify the plan form criteria proposed by Lane, Leopold and Wolman, Parker, Ramette and thoseproposed Hayashi and Ozaki, and other Japanese investigators and found that these criteria do notpredict the plan-forms correctly. Therefore he has proposed two criteria, first between t* and Fr, and

other between t* and W S

Do

which seem to demarcate plan forms reasonably well, see Fig. 6.31 and 6.32.

Fig. 6.31 Criterion for river channel patterns (Agarwal 1983)

River Morphology222

Lastly Kuroki and Kishi (1985) have used stability analysis and developed a criterion for prediction

of plan-forms. Their analysis indicated that plan-forms depend on t*, W S

Do

0 2.

and S. On this diagram

(see Fig. 6.33) three regions where no bars occur, bars and braiding occur are indicated. Figure 6.33 also

Fig. 6.32 WS/Do – t* criterion for plan-forms (Agarwal 1983)

Fig. 6.33 Criterion for meso scale bed-forms (Kuroki and Kishi 1985)


shows that for large values of t* , no bars occur if W S

Do

0 2.

is less than 4 to 5, bars occur if 5 < W S

Do

0 2.

< 20

to 30 and braiding occurs for W S

Do

0 2.

values greater than 50.They also found that the dimensionless

length of bars L/W primarily depends on t*, decreasing with increase in t* for small values of t* andgradually increasing with increasing in t* for larger t* values. For t* between 0.1 and 6, L/W variesbetween 2 and 6 with an average value of 4.

References

Agarwal, V.C. (1983) Studies on the Characteristics of Meandering Streams. Ph.D Thesis, I.I.T. (formerlyUniversity of Roorkee), Roorkee.

Ahmad, M. and Rahman, A. (1962) Appraisal and Analysis of New Data from Alluvial Canals of West Pakistan inRelation to Regime Concepts and Formulae. Proc. of West Pakistan Engg. Congress, Lahore, Vol. 46, Paper351.

Allen, J.R.L. (1965) A Review of the Origin and Characteristics of Recent Alluvial Sediments, Sedimentology,Vol. 5, pp. 89-191.

Ananian, A.K. (1961) Determination de la Formation du Lit des Riveres, Cree Par Suite de L’Abaissement de laCote des Leurs Bases d’Erosion. Proc. of 9th Congress of IAHR, Dubrovnik, pp. 1102-1113.

Apmann, R.P. (1973) Estimating Discharge from Super-elevation in Bends. JHD, Proc. ASCE, Vol. 99, No. HY1,Jan, pp. 69-79.

Ashmore, P.E. (1982) Laboratory Modeling of Gravel Bedded Stream Morphology. Earth Science Processes, Vol.7, pp. 201-225.

Ashmore, P.E. (1991) How Do Gravel – Bed Rivers Braid? Canadian Jour. of Earth Sciences, Vol. 28, pp. 326-341.

Bagnold, R.A. (1960) Some Aspects of the Shape of River meanders. USGS Prof. Paper No. 282-E.

Blench, T. (1957) Regime Behaviour of Canals and Rivers. Butterworth Scientific Publications, London.

Bristow, C.S. and Best, J.L.(1993) Braided Rivers : Perspectives and Problems. In Braided Rivers (Eds. Best J.L.and Bristow C.S.), Geo. Soc. Special Publication No.75, pp.1-11.

Callander, R.A. (1969) Instability and River Channels. JFM, Vol. 36, Pt. 3, pp. 465-480.

Callander, R.A. (1978) River Meandering – Annual Review of Fluid Mechanics, Vol. 8, pp. 129-158.

Carlson, C.W. (1965) The Relation of Free Meander Geometry to Stream Discharge and its GeomorphicImplications. Am. J. Sci. Vol. 263, pp. 864-885.

CBIP (1989) River Behaviour, Management and Training. Central Board of Irrigation and Power, New Delhi, Vol.1, pp. 36-37.

Chang, H.H. (1979) Minimum Stream Power and River Channel Patterns. Journal of Hydrology, ElsevierScientific Publishing Co., Amsterdam, Vol. 45, pp. 303-327.

Chang, H.H. (1980) Stable Alluvial Canal Design. JHD, Proc. ASCE, Vol. 106, No. HY5, May, pp. 873-891.

Chang, H.H. (1988) Fluvial Processes in River Engineering. John Wiley and Sons, New York. A WileyInterscience Publication, pp. 271-284.

Chitale, S.V. (1970) River Channel Patterns. JHD, Proc. ASCE, Vol. 96, No. HY1, Jan. pp. 201-221.

Chitale, S.V. (1976) Shape and Size of Alluvial Channels. JHD, Proc. ASCE, Vol. 102, No. HY7, July, pp. 1003-1011.

River Morphology224

Chorley, R.J.(Ed.) (1969) Introduction to Fluvial Processes. Mathuen and Co. Ltd., London, Chapter 7.II by Dury,G.H..

Coleman, J.M. (1969) Brahmaputra River Channel Processes and Sedimentation. Sedimentary Geology, Vol. 3,pp. 129-239.

De Vriend, H.J. (1977) A Mathematical Model for Steady Flow in Curved Shallow Channels. JHR, IAHR, Vol.15, pp. 37-54.

Dury, G.H. (1973) Magnitude – Frequency Analysis and Channel Morphology. In Fluvial Geomorphology (Ed.Morisawa, M.), State University of New York, Binghamton, pp. 91-121.

Eaking, H.M. (1910) The Influence of the Earth’s Rotation upon the Lateral Erosion of Streams. Jour. Geol. Vol.18, pp. 435-447.

Edgar, D.E. (1973) Geomorphic and Hydraulic Properties of Laboratory Rivers. M.S. Thesis, Colorado StateUniversity, USA, 156 p.

Engelund, F. (1974) Flow and Bed Topography in channel Bends. JHD, Proc. ASCE, Vol. 100, No. HY11, No. pp.1631-1648.

Engelund, F. and Skovgaard, O. (1973) On the Origin of Meandering and Braiding in Alluvial Streams. JFM, Vol.57, pp. 289-302.

Fergusson, R.I. (1975) Meandering Irregularity and Wave Length Estimation. Jour. of Hydrology, Vol. 26, pp. 315-333.

Fergusson, R.I. (1981) Channel Form and Channel Changes. In British Rivers (Ed. Lewin, J.). Gorge Allen andUnwin, London, pp. 90-125.

Fredsøe, J. (1978) Meandering and Braiding of Rivers. JFM, Vol. 84, Pt. 4, pp. 609-624.

Friedkin, J.F. (1945) Laboratory Study of the Meandering of Alluvial Rivers. USWES, Vicksburg, Mississippi,USA, 40p.

Friend, P.F. and Sinha, R. (1993) Braiding and Meandering Parameters. In Braided Rivers (Eds. Best, J.L. andBristow, C.S.) Geographical Society Special Publication No. 75, pp. 105-111.

Gandolfo, J.S. (1955) Discussion of Design of Stable Channels by Lane E.W., Trans. ASCE, Vol. 120, pp 1271-1279.

Garde, R.J., Kumar, A. and Singh, A.K. (2002) Hydraulic Geometry of Straight and Meandering Channels. Proc.of HYDRO-2002 Conference of ISH on Hydraulic Structures, Water Resources and Ocean Engineering, IIT,Bombay, pp.15-19.

Garde, R.J. and Ranga Raju, K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems,New Age International (P) Ltd., New Delhi.

Gilbert, G.K. (1884) The Sufficiency of Terrestrial Rotation for the Deflection of Streams. Nat. Ac. of Sci. (USA),Vol. 3.

Gill, M.A. (1968) Discussion of Dominant Discharge of Platte-Missouri Confluence. JWWHD, Proc. ASCE, Vol.94, No. WW4, pp. 527-529.

Goncharov, G.N. (1962) Dynamics of Channel Flow (Translated from Russian), Israel Program for ScientificResearch and Published by USDI and NSF, USA.

Griggs, R.F. (1906) The Buffalo River : An Interesting Meandering Stream. Bull. Geol. Soc. Am. Vol. 38, No. 3.

Gupta R.D. (1967) Total Sediment Load as a Parameter in the Design of Stable Channels. M.E. Thesis, I.I.T.Roorkee.

Hayashi, T. (1980) Plan Forms of Alluvial Rivers. Proc. of 1st intl. Workshop on Alluvial River Problems,Roorkee, pp. 4-1 to 19.


Hayashi, T. and Ozaki, S. (1978) Alluvial Bed Form Analysis I, Formation of Alternating Bars and Braids. Proc. ofUS-Japan Bi-national Seminar on Erosion and Sedimentation, Hawaii, Chap. 7-1 to 39.

Hey, R.D. (1982) Design Equations for Mobile Gravel – Bed Rivers. In Gravel-bed Rivers (Eds. Hey, R.D. andThorne, C.R) John Wiley and Sons, Chichester, pp. 553-574.

Hey, R.D. and Thorne, C.R. (1986) Stable Channels with Mobile Gravel Beds. JHE, Proc. ASCE, Vol. 112, No. 8,Aug. pp. 671-689.

Hjulstorm, F.A. (1957) A Study of the Meander Problem. Institute of Hydraulics, Royal Institute of Technology,Stockholm, Bull. No. 51.

Hong, L.B. and Davies, T.R.H. (1974) A Study of Stream Braiding: A Summary

Inglis, C.C. (1947) Meanders and Their Bearing on River Training. ICE (London), Maritime Paper No. 7, pp. 3-54.

Inglis, C.C. (1949) The Behaviour and Control of Rivers and Canals (With the Aid of Models). Pt. 1, CWINRS,Research Publication No. 13.

Ippen, A.T. and Drinker, P.A. (1962) Boundary Shear Stresses in Curved Trapezoidal Channels. JHD, Proc.ASCE, Vol. 88, No. HY5, pp.143-179.

Kellerhals, R., Church, M. and Bray, D.I. (1976) Classification and Analysis of River Processes. JHD, Proc.ASCE, Vol. 102, No. HY7, July, pp. 813-829.

Kellerhals, R., Neill, C.R. and Bray, D.I. (1972) Hydraulic and Geomorphic Characteristics of Rivers in Canada.River Engineering and Surface Hydrology. Rep. 72-1, Res. Council of Alberta, Edmonton (Canada).

Kikkawa, H., Ikeda, S. and Kitagawa, A. (1976) Flow and Bed Topography in Curved Open Cannels. JHD, Proc.ASCE, Vol. 102, No. HY9, September, pp. 1327-1342.

Kinoshita, R. (1957) Formation of Dunes on River Bed – An Observation on the Condition of River Meandering(In Japanese). Proc. JSCE, No. 42.

Kinoshita, R. (1961) Investigation of Channel Migration of the Ishikari River (In Japanese) Science andTechnology Agency, Bureau of Resources, No. 31, 138 p.

Kishi, T. and Kuroki, M. (1985) Hydraulic Characteristics of Alternating Bars (In Japanese), Hokkaido University,Hydraulic Laboratory Report.

Komura, S. (1969) Computation of Dominant Discharge. Proc. of 13th Congress of IAHR, Kyoto (Japan), Vol. 5.1,pp. 265-268.

Kondratev, N.E. (Ed.) River Flow and River Channel Formation (Translated from Russian), Israel Program ofScientific Translation, Published by USDI and NSF, USA.

Kondap, D.M. (1977) Some Aspects of Flow in Stable Channels. Ph.D. Thesis, University of Roorkee (now I.I.T.Roorkee)

Kuroki, M. and Kishi, T. (1985) Regime Criteria on Bars and Braids. Hydraulics Papers, Civil and EnvironmentalEngineering Research Laboratory, Hokkaido University, Sapporo (Japan).

Lacey, G. (1930) Stable Channels in Alluvium. Paper No. 4736, Min. Proc. ICE. (London), Vol. 229, pp. 259-384.

Lane, E.W. (1957) A Study of the Shape of Channels Formed by Natural Streams Flowing in Erodible Material.US Army Engineer Div., Missouri River, Corps of Engineers, Omaha (Nebraska) USA, MRD Series No. 4,106 p.

Langbein, W.B. (1964) Geometry of River Channels. JHD, Proc. ASCE, Vol. 90, No. HY2, March, pp. 301-347.

Leliavsky, S. (1955) An Introduction to Fluvial Hydraulics. Constable and Co. Ltd., London, pp. 115-120.

Leopold, L.B. and Langbein, W.B. (1978) Les Meanders des Rivieres. La Bibliotheque “Pour La Science” LesPhenomenes Naturrels.

Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Stream Channels and Some PhysiographicImplications. US G.S. Professional Paper 252, 58 p.

River Morphology226

Leopold, L.B. and Wolman, M.G. (1959) River Channel Patterns : Processes in Geomorphology. W.H. Freemanand Co., San Francisco (USA).

Leopold, L.B. and Wolman, M.G. (1960) River Meanders, Bull. of Geo. Soc. of America, Vol. 71, pp. 769-794.

Leopold, L.B., Wolman, M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman andCo., San Francisco, (USA).

Lewin, J. (1976) Initiation of Bed Forms and Meanders in Coarse Grained Sediment. Geo. Soc. of America, Bull.Vol. 87, pp. 281-285.

Miall, A.D. (1977) A Review of the Braided-River Depositional Environment. Earth Science Reviews, Vol. 13,pp. 1-62.

Mukhamedov, A.M. and Ismaghilov, H.A. (1969) Some Morphological Relationships in the Middle and LowerReaches of the Amu Darya. Proc. of 13th Congress of IAHR, Kyoto (Japan), Vol. 5.1, pp. 191-193.

Muramoto, Y. and Fujita, Y. (1977) Study on Meso-Scale River Bed Configuration (In Japanese). Annuals, DPRI,Kyoto (Japan), No. 20, B-2, pp.243-258.

NEDCO (1959) River Studies in Niger and Benue. North Holland Publication, Holland.

Neill, C.R. (1970) Discussion of formation of Flood Plain Lands by Carrey, W.C., JHD, Proc. ASCE, Vol. 96, No.HY1, Jan. pp. 297-298.

Neu, H.A. (1967) Transverse Flow of a River Due to Earth’s Rotation. JHD, Proc. ASCE, Vol. 93, No. HY5, Sept.pp. 149-165.

Nixon, M.A. (1959) A Study of Bankful Discharge of Rivers in England and Wales. Proc. ICE. (London), PaperNo. 6322, Dec., pp. 157-173.

Odgaard, A.J. (1981) Transverse Bed Slope in Alluvial Channel Bends. JHD, Proc. ASCE, Vol. 107, No. HY12,December, pp.1677-1694.

Odgaard, A.J. (1982) Bed Characteristics in Alluvial Channel Bends. JHD, Proc. ASCE, Vol. 108, No. HY11,November, pp.1268-1281.

Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armor Layers. JHE, Proc. ASCE, Vol. 110, No. HY9,September, pp.1267-1272.

Onishi, Y., Jain , S.C. and Kennedy, J.F. (1976) Effects of Meandering in Alluvial Streams. JHD, Proc. ASCE, Vol.112, No. HY7, September, pp.899-917.

Park, C.C. (1977) World-Wide Variations in Hydraulic Geometry Exponents of Stream Channels: An Analysis andSome Observations. Jour. of Hydrology, Vol.33, pp.133-146.

Parker, G. (1976) Cause and Characteristic Scales of Meandering, and Braiding in Rivers. JFM Vol. 76, Pt. 3.

Prus-Chacinski, T.M. (1954) Patterns of Motions in Open Channel Bends. Assoc. Intl. d’Hydrologie, Publ. 38,Vol. 3, pp.311-318.

Quaraishy, M.S. (1944) River Meandering and Earth’s Rotation. Current Science, Vol. 13, October, pp.36-39.

Rachocki, A. (1981) Alluvial Fans: An Attempt at an Empirical Approach. Wiley Interscience Publication, JohnWiley and Sons Inc., (USA).

Ramette, M. (1980) A Theoretical Approach on Fluvial Processes. 1st Intl. Symposium on River Sedimentation,Beijing (China), C16- 1 to 18.

Reynolds, A.J. (1965) Waves on the Erodible Bed of an Open Channel. JFM, Vol. 22, Pt. 1, pp. 113-133.

Rhodes, C.C. (1977) The b-f-m Diagram: Graphical Representation and Interpretation of at a Station HydraulicGeometry. Am. Jour. Sci. Vol. 277, pp. 73-96.

Rhodes, C.C. (1987) The b-f-m Diagram for Downstream Hydraulic Geometry. Geografisca Annaler, Series A,69A (1), pp. 147-161.


Riggs, H.C. (1976) A Simplified Slope-Area Method for Estimating Flood Discharges in Natural Channels.USGS, J. Res., Vol. 4, pp. 285-291.

Rozovskii, J.L. (1957) Flow of Water in Bends of Open Channels. Academy of Sciences of the Ukrainian SSR,Kiev, 233 p. (Translated from Russian by NSF, Washington D.C.), 233 p.

Rundquist, L.A. (1975) A Classification and Analysis of Natural Rivers. Ph.D. Thesis, Colorado State University,Fort Collins, USA, 377 p.

Rubey, W.W. (1933) Equilibrium Conditions in Debris Laden Streams. Trans. AGU, pp. 497-505.

Schaffernak, F. (1950) Flussmorphologie und Flussbau. Springer Verlag, Vienna.

Schoklitsch, A. (1937) Hydraulic Structures, Vol. 1, Am. Soc. Mech. Engineers, 504 p.

Schumm, S.A. (1969) River Metamorphosis. JHD, Proc. ASCE, Vol. 45, No. HY1, January, pp. 255-273.

Schumm, S.A. (1977) The Fluvial System. John Wiley and Sons. A Wiley Interscience Publication, New York,Chapter V, pp. 106-111.

Shen, H.W. (1983) Keynote Examination of Present Knowledge of River Meandering. River Meandering – Proc.of the Conference Rivers-83, ASCE, New York, USA, pp. 1008-1013.

Shukry, A. (1950) Flow Around Bends in an Open Flume. Trans. ASCE, Vol. 115, paper No. 2411, pp. 751-779.

Simons, D.B. (1957) Theory and Design of Stable Channels in Alluvial Material. Ph.D. Thesis. Colorado StateUniversity, Fort Collins, USA.

Simons, D.B. and Albertson, M.L. (1963) Uniform Water Conveyance Channels in Alluvial Material. Trans.ASCE, Vol. 128, Pt. 1, pp. 65-107.

Smith, T.R. (1974) A Derivation of Hydraulic Geometry of Steady State Channels form Conservations Principlesand Sediment Transport Laws. Jour. of Geology, Geological Notes, Univ. of Chicago, Vol. 82, pp. 98-104

Speight, J.G. (1965) Meander Spectra of the Anabunga River. Jour. of Hydrology, Vol. 3, pp. 1-15.

Sukegawa, N. (1970) On the Formation of Alternate Bars in Straight – Alluvial Channels. Trans. JSCE, Vol. 2, pp.259-261.

Sukegawa, N. (1971) Conditions for Occurrence of River Meanders (In Japanese), Proc. JSCE, Vol. 2, Pt. 2.

Sukegawa, N. (1972) Criterion for Alternate Bars Formation. Memoirs of the School of Science and Engineering,No. 36, Waseda University (Japan), pp.77-84.

Tamai, N., Nagao, T. and Mikuni, N. (1978) On Large Scale Bar Patterns in a Straight Channel (In Japanese), Proc.22nd Japanese Conference on Hydraulics. .

Tobes, G.H. and Chang, T.P. (1967) Plan-Form Analysis of Meandering Rivers. Proc. of 12th Congress of IAHR,Vol. 1, pp. 362-369.

Wallis, I.G. (1973) On the Development of River Meanders. Part I: Laboratory Experiments, Monash University,Geophysical Fluid Dynamics Lab. Paper No. 57, 28 p.

Werner, P.W. (1951) On the Origin of River Meanders. Trans. AGU, Vol. 32, pp.898-902.

Wharton, G. (1995) Information from Channel Geometry – Discharge Relations. In Changing Rivers (Eds.Grunnell, A. and Petts G.), John Wiley and Sons, Chicester, pp. 325-346.

White, W.R., Paris, W.E. and Bettess, R. (1981) River Regime Based on Sediment Transport Concept. Rep. No. JJ201, Hydraulic Research Station, Wallingford, U.K.

Williams, G.P. (1978) Bankful Discharge of Rivers. W.R. Research, Vol. 14, No. 6, December, pp. 1141-1154.

Wolamn, M.G. and Leopold, L.B. (1957) River Flood Plains : Some Observations on Their Formation. USGSProfessional Paper, 282-C.

Woodyer, K.D. and Flemming, P.M. (1968) Reconnaissance Estimation of Stream Discharge FrequencyRelationships. In Land Evaluation (Ed. Stewart, G.A.) Macmillan of Australia, pp. 287-298.

River Morphology228

Yang, C.T. (1971) On River Meanders. Jour. of Hydrology, Vol. 13, pp. 231-253.

Yang, C.T. (1976) Minimum Unit Stream Power and Fluvial Hydraulics, JHD, Proc. ASCE, Vol. 102, No. HY7,July, pp. 919-934.

Zimmermann, C. (1977) Roughness Effects on Flow Direction Near Curved Stream Beds. JHR, IAHR, vol. 15,No. 1, pp. 73-85.

Zimmermann, C. and Kennedy, J.F. (1978) Transverse Bed Slope in Curved Alluvial Streams. JHD, Proc. ASCE,Vol. 104, No. HY1, Jan.. pp. 33-48.

Zimpfer, G.L. (1975) Development of Laboratory River Channels. M.S. Thesis, Colorado State University, FortCollins, USA, 111 p.

7C H A P T E R

Gravel-Bed Rivers

7.1 INTRODUCTION

Gravel and boulder-bed rivers are those rivers that flow through predominantly gravelly and boulderymaterials respectively. Bathurst characterizes boulder rivers as those rivers in which the width is anorder of the magnitude greater than the median size of the bed material, the depth is of the order ofmagnitude of the bed material size, and the slope is unlikely to exceed 0.05. Not much is known aboutboulder rivers, even though some studies have been conducted about their resistance characteristics.However, the last three decades have seen significant research activity on gravel-bed rivers.

Gravel-bed rivers differ from the commonly encountered sand bed rivers in many respects. Gravel-bed rivers flow through much coarser material having a much wider spectrum of sediment sizes–fromcobbles to fine sand–than sand bed rivers. Their slopes are much steeper (0.001 to 0.05 or even larger)than those of sand bed rivers. In sand bed rivers all the fractions of bed material move for most of thedischarges except the very small ones; however in gravel-bed rivers all the fractions of bed materialmove only at a few flows in a year. During the rest of the time sediment transport takes place over thepavement (see below). The other difference pertains to the bed forms. Unlike in sand-bed rivers, ripplesand dunes do not form in gravel-bed rivers; instead large bed features known as bars, transverse anddiagonal bars, riffles and pools, and transverse ribs of coarse material are common features in gravel-bed rivers. These bed features not only offer resistance to flow but also act as sediment storage spaces.

Further, since the slope of gravel-bed rivers varies over a wide range, the Froude number U/ gD for the

gravel-bed rivers can be less than unity to greater than unity.As regards the plan form, sand-bed rivers are either meandering, transitional or braiding and they

may change from one plan-form to another dramatically as the discharge changes. Gravel-bed rivershave a much greater tendency to be transitional or braided. For cobble and boulder rivers it is rare to findreaches that meander significantly. In other words, it is rather easy to define talweg for sand bed streams;yet for cobble and boulder rivers it is impossible to define its location.

River Morphology230

Since upland areas supply sediment to the river systems, gravel-bed rivers are closer to the sedimentsource. Because the sediment supply events, such as landslides are discontinuous, the sedimenttransport in gravel-bed rivers shows greater variability than the sediment transport in sand-bed rivers. Infact, sediment transport in gravel-bed rivers can be unsteady and non-uniform even for steady waterdischarge. Depending on the supply of sediment to the channel, there may be two orders of magnitude ofvariation in sediment transport rate for a given discharge. This does not happen in sand-bed rivers.Lastly, it is found that gravel-bed rivers are more stable than sand-bed rivers. Hence rapid and large bedlevel variations that often occur in sand-bed rivers do not occur in gravel-bed rivers.

The study of gravel-bed rivers poses some complexities that should be mentioned. The first relatesto the size distribution of the bed material. Since the bed material size varies from cobbles to fine sand,different methods should be used to analyse different size fractions. Also, with such wide variation inthe bed material size, difficulty is experienced in choosing the characteristic size of the bed material forstudies related to resistance, sediment transport and hydraulic geometry. Further complexities arecaused by the formation of the pavement and its destruction that affect the size distribution of thetransported material which also causes a sudden increase in the transport rate once the pavement isdestroyed.

7.2 DATA FOR GRAVEL-BED RIVERS

Several studies have been conducted on gravel-bed rivers in U.S.A., U.K., New Zealand, Canada, Italyand other European countries and these data are available in literature. These data pertain to thehydraulic geometry and resistance to flow either at bankful discharge or other discharges. In many casesthe size distribution of bed material and information on whether the bed was mobile or paved has beengiven. Data collected by Leopold and Wolman (1957) for many American rivers, Kellerhals (1967) forsome rivers in British Columbia, and Bray (1979) for rivers in Alberta (Canada), are useful for the studyof hydraulic geometry of rivers at bankful discharge. Data useful for resistance analysis of mobile andpaved bed at variable discharge are given by Samide (1971) for the north Saskatchewan and Elbowrivers in Canada, Milhaus (1973) for the Oak Creek in U.S.A., Griffiths (1981) for the rivers in NewZealand, Thorne and Zevenbergen (1985) on the Boulder Creek in Colorado, U.S.A., Michalik (1989)on the Wisloka and the Dunajee rivers in Poland, Colosimo, Copertino and Veltri (1988) for gravelrivers in Italy, and by Gladky (1979), Church and Rook (1983) and Hey and Thorne (1986, 1988). Thesedata have been tabulated by Garde et al. (1998).

Field data on bed-load transport in gravel-bed rivers have been mentioned by Bathurst (1987).These are for the rivers Pitzbach in Austria, Elbow in Alberta (Canada), Clearwater in Idaho, Snake inIdaho, Oak Creek in Oregon, Slate in Idaho and Tanana in Alaska, all in the U.S.A. and Aare inSwitzerland. The median size of the surface material for these rivers varied from 12 mm to 260 mmwhile the water discharge varied from 3.0 m3/s to 1680.0 m3/s.

7.3 BED MATERIAL

The sampling of the surface of gravel-bed rivers is usually carried out by one of the following methods:1. Grid or Transect Sampling: Wolman (1954) has proposed grid sampling. In this method a grid

is established over the surface and particles immediately below the grid points are sampled. Intransect sampling all the particles lying along the predetermined line are collected andanalysed.

Gravel-Bed Rivers 231

2. Areal Sampling: All the particles exposed within a predetermined area are sampled. Thismethod was used by Lane and Carlson (1953).

3. Volumetric Sampling of the Surface Area: In this method the sample is acquired either by thephotographic method proposed by Adams (1979), or by removing particles from this area byusing adhesive or grease.

In order to see if d50 of the gravel-bed rivers can be predicted, it was plotted against slope S. In spiteof the scatter it was found that (see Garde et al. 1998) an equation of the form

d50 = 882.5 S 0.492 ...(7.1)

can be fitted through the data; here d50 is in mm. The large scatter is attributed to the fact that the dataused are from diverse lithological environments and also there is a large variation in the dominantdischarge.

It has been reported that gravel-bed materials exhibit bimodality. There usually is a lack of particlesin the range 1 mm to 8 mm. The reasons advanced to explain these characteristics include catchmentgeology, mixing of sediments transported in two different modes viz. traction and suspension,restriction in sediment sizes supplied by the source area and abrasion and sorting during the transport.Odgaard (1984a) found that the size distribution of surface layer particles follows normal distribution.

Analysis of size distribution data for bed materials of gravel-bed rivers has indicated that the sizedistribution neither follows normal nor long normal distribution over the entire range of sizes in thesample.

Fig. 7.1 Variation of d/d50 with percent finer for gravel-bed river materials

Figure 7.1 shows the size distribution plotted as d/d50 versus percent finer on normal probabilitypaper. It can be seen that the average curve passes through d50/d16 = 2.88 and d84/d50 = 2.121. Further,even though there is considerable scatter in the magnitude of d99.9/d50, (from 6 to over 10), its averagemagnitude can be taken as 8.2. The mean curve passing through these points on the normal probabilitypaper can be represented by the straight line using the transformation:

River Morphology232

dt/d 50 = {(d/d50)l – 1}/l ...(7.2)

where l is the parameter to be determined by trial and error, such that the transformed distribution isgaussian. The value of l was found to be 0.40. This value along with the known median size will givethe size distribution when the above equation is used.

It is also interesting to know how the geometric standard deviation for bed material of gravel-bedrivers varies with d50. Earlier studies of bed materials of sand-bed rivers by Garde (1972) and Kothyari(1994) indicate that the geometric standard deviation sg increases as d50 increases and follows theequation

sg = 1.4 d 50 0.34 ...(7.3)

where d50 is in mm and sg = 1/2 ( d84/d50 + d50/d16 ). This is based on data for d50 varying from 0.14 mmto 17 mm. Kothyari also analysed the data with d50 varying from 0.15 mm to 37 mm. Figure 7.2 showsthe variation of sg with d50 for sandy and gravelly bed materials. It can be seen that for gravelly-bedmaterials, sg decreases with increase in d50. Since in general d50/d16 and d84/d50 have different values,variation of d50/d16 and d84/d50 with d50 was studied by Garde et al. (1998). It was found that for gravel-bed materials d84/d50 is nearly constant; however d50/d16 decreases with increase in d50. As a result

sg = 1

2

d

d

d

d50

16

84

50

+FHG

IKJ

decreases as d50 increases.

Fig. 7.2 Variation of sg with d50 for sandy and gravelly bed materials

As regard the size distribution of river bed sediments it may be mentioned that Moss (1962, 1963)has shown that the river bed sediments are deposited as composites and are made up of threepopulations, each of which is related to a specific sediment process. Vischer (1969) found each of thesethree sub-populations to follow log-normal distribution. Since these three populations would be mixedin different proportions, it is very unlikely that the river bed material samples as a whole would followlog-normal distribution.


7.4 PAVEMENT

River beds composed of heterogeneous mixtures of gravel and smaller particles form a surface layerwith thickness of the size of coarse particles. Bray and Church (1980), and Andrews and Parker (1987)have explained the distinction between armouring and paving. If there is no sediment supply from theupstream as in the case of downstream of large capacity dams, the bed surface will get progressivelycoarser and eventually become immobile for all discharges less than the maximum sustained flow. Ifhigher flow occurs, the bed particles will be entrained, the bed will degrade further and the bed surfacewill become somewhat coarser. Such conditions occur downstream of dam and the immobile bed isconsidered to be armored.

The coarse surface layer in gravel-bed rivers, known as the pavement, is maintained by successiveperiods of bed-load transport during which essentially all sizes move. This sediment is supplied from theupstream side and hence the channel remains in equilibrium. The particles on the bed are transportedfrequently within a span of several years. In this process, even if occasionally a few coarse particles onthe bed move, it does not affect the stability of the pavement and hence there are no general motions.Thus pavement is present in gravel-bed rivers even while most available sizes are transported. Studiesby Harrison (1950) and Andrews and Parker (1987) have indicated equal mobility of all particle sizespresent in the sub-pavement material; that is the ratio of transport rate of a given size fraction to itspercentage abundance in the sub-pavement material is approximately constant for all sizes. This hasbeen confirmed by the data on the East Fork, the Snake and the Clear Water rivers all in USA. If equalmobility is to be achieved with respect to the subsurface material, the surface layer must be considerablycoarser than either the subsurface material or the bed-load. The bed-load and the subsurface sizedistributions are approximately equal because the lesser mobility of coarser size fractions iscounterbalanced by their abundance in surface. Field experience has indicated that for gravel-bed rivers,the ratio of median size of the pavement to that of the sub-pavement material ranges from 2.0 to 6.0 withan average value of 2.71. Neill (1968) has suggested the value of toc/D gs d50 = 0.03 constitutes thecriterion for braking of the pavement; here d50 is the median size of the pavement. If d50 of the sub-pavement is used, the corresponding criterion will be toc/Dgs d50 = 0.081 since d50 of the pavement isequal to 2.71 times d50 of the pavement.

7.5 HYDRAULIC GEOMETRY

The average width or perimeter, depth of flow or the hydraulic radius, flow area at the bankfuldischarge, and the slope, describe the hydraulic geometry of the rivers. The knowledge of hydraulicgeometry is needed for the study of problems related to river training, location of bridges and barragesand for navigation. The hydraulic geometry of alluvial rivers and channels has been studied by Lacey(1930), Inglis (1947), Leopold and Maddock (1953) and others. They have related the perimeter P orwidth W, depth D or hydraulic radius R and the area A to the dominant discharge Q and in some case d50or silt factor f1. It is found that

P or W ~ Q0.50

...(7.4)D or R ~ Q0.33

UV|

W|A ~ Q0.8

River Morphology234

approximately. Langbein (1964) has applied the principle of minimum expenditure of power per unit ofthe bed area, and minimum work rate in the whole river system to obtain the parameters of hydraulicgeometry and found that W ~ Q0.53, D ~ Q0.37, U ~ Q0.10 and S ~ Q–0.73. Considering the channel to be inan unstable state, Knighton (1977) studied whether development of the channel to a new staterepresented an attempt by the system to approach some form of dynamic equilibrium. His analysis led tothe condition that

b2 + f 2 + m2 ® minimum

where W ~ Qb, D ~ Q f and U ~ Qm

The hydraulic geometry of gravel-bed rivers has been studied by Kellerhals (1967), Bhowmik(1968), Charlton (1977), Parker (1979), Bray (1982) and Hey (1982). While Kellerhals, Bhowmik,Charlton and Bray have related W, D and U to the bankful discharge Q and median sediment size, Parkerhas used the functional relationship:

W/d, D/d, S, Uds

f

D gr

= F Q dds

f

/ 2 D gr

F

HG

I

KJ ...(7.5)

thus taking the slope as independent variable. If Q1 = Q/d2 D gr

s

f

d, he obtained the following

equations:

W/d = 4.400 Q10.50

...( 7.6)D/d = 0.253 Q10.415

S= 0.223 Q1 –0.41

U

V

|||

W

|||

U

ds

f

D gr

= 0.898 Q10.616

In general, these studies have shown that the geometric parameters strongly depend on Q whereas doccurs to a very small power. Recently Garde et al. (1998) have analyzed the available gravel-bed riverdata with paved as well as mobile bed conditions and studied the hydraulic geometry at bankfuldischarge. The first question that they wanted to answer was whether the slope can be taken asdependent or independent variable. On any given river the slope decreases in the downstream directionas Q increases and d decreases in the downstream direction. When all the available data were plotted asS vs Q, even though S decreased as Q increased, there was considerable scatter which is believed to bedue to the difference in terrain, length of river, lithology and bankful discharge, see Fig. 7.3.

Interpreting the scatter on Fig. 7.3 as implying that S should be taken as an independent variablealong with Q and d, Garde et al. (1998) used the functional relationship:


W, D, A = F (Q, d, D gs, rf and S) ...(7.7)

The viscosity was not considered since we are dealing with very coarse material. As a firstapproximation the geometric standard deviation sg of bed material was also not considered. Usingdimensional analysis the following alternative functional relations were obtained for the study ofgeometry of gravel-bed rivers.

W, D, A, = f (Q) (a)

...(7.8)

W/d, D/d, A/d2 = F1 Q dd

Ss

f

/ ,2 D gr

F

HG

I

KJ = F1 (Q1, S) (b)

U

V

|||||

W

|||||

W/d, D/d, A/d2 = F2 QS dds

f

/ ,2 D gr

F

HG

I

KJ = F2 (Q2) (c)

W/d, D/d, A/d2 = F3 Q d d Ss

f

/ 2 D gr

F

HG

I

KJ = F3 (Q3) (d)

Hence

Q1 = Q/d2 D gr

s

f

d, Q2 = QS ds

f

D grFHG

IKJ

and Q3 = Q/d2 D gr

s

f

dSF

HGI

KJ

Fig. 7.3 Variation of slope with bankful discharge for gravel-bed rivers

River Morphology236

Using 140 data points for both paved and mobile bed at the bankful discharge, the followingequations were obtained. It may be mentioned that the data for paved and mobile bed intermingled andhence the relationships valid for both the cases were developed using Eq. (7.8). It was found thatrelationships involving Eq. (7.8 (a)) and (7.8 (b)) gave the same accuracy and were more accurate thanEq. (7.8 (c)). Further relationships involving Eq. (7.8 (d)) were most accurate. Below are givenequations corresponding to Eq. (7.8 (b)) and (7.8 (d)) and are recommended for use since they aredimensionally homogeneous.

W/d = 7.675Q10.448

...(7.8 b)D/d = 0.504Q10.373

U

V||

W||A/d2 = 3.872Q1

0.821

W/d = 3.872Q30.396 U

V||

W||

D/d = 0.308Q30.330

A/d2 = 1.108Q30.726

...(7.8 d)

It may be mentioned that Q2 = QS/ D g rs fd/ can be interpreted as the dimensionless stream

power. The parameter Q3 where slope occurs in the denominator has been used in Russia to study thehydraulic geometry. Further, equations involving Q3 viz. Eq. (7.8 (d)) give smaller errors than theequations involving Q alone or Q1, and in addition the former are dimensionless while the latterinvolving Q are in dimensional form. Hence, it is recommended that Eq. (7.8 (d)) be used for predictingW, D and A for gravel-bed rivers. For the data used, these equations predicted W, D and A within ±, 30percent error for 58%, 85% and 71% of the data respectively. Variation of W/d, D/d and A/d2 with Q3 areshown in Figs. 7.4, 7.5 and 7.6 respectively.

Fig. 7.4 Variation of W/d with Q3


7.6 BED FEATURES IN GRAVEL-BED RIVERS

As mentioned in the introduction to this chapter ripples and dunes commonly observed in sand bedrivers, do not form in gravel-bed rivers. Instead large scale sedimentary accumulations called bars arepresent in gravel-bed streams. They represent major storage spaces for bed-load sediment that is movedonce in a while and also offer resistance to flow. Taking clue from Jackson II (1975) bed features can beclassified in the following manner.

Fig. 7.5 Variation of D/d with Q3

Fig. 7.6 Variation of A/d 2 with Q3

River Morphology238

The micro and meso forms in the form of ripples and dunes are rather rare in gravel-bed rivers.Antidunes have been found to occur at steep slopes. Hence as regards the gravel-bed rivers, one isinterested in sedimentary accumulations whose scale is channel width or greater. These are looselycalled bars. Their height is comparable with the depth of flow. Bars persist for a long time and areradically modified only during high floods. Bars fall in the category of macro and mega forms.

Table 7.1 Classification of bed features (Jackson 1975, Church and Jones 1987)

Class System scale Typical wave length Time scale Features Remarks

Microforms d 10–2 to 100 m << tc Ripples, lineation Absent in gravel-bed rivers

Mesoforms D 100 to 102 m ~ tc Dunes Rare in gravel-bedrivers. Probablyabsent if d > 0.1 D

Macroforms W 101 to 103 m > = tc Antidunes, unit Uncommon, ofbars, channel bars gravel-ribs

Megaforms ³ = l > 103 m Regime time Bar assemblages A large variety ofsedimentationzones.

tc = time for the flood wave to pass through the reachl = wavelength of bed-forms

When in a portion of the channel carrying sediment the shear stress is reduced, the bed-load beingtransported deposits and forms a bar. Hence bars occur at the apex of the channel bends along theconvex bank, places where the channel widens, at the junctions and at flow divergence. According toChurch and Jones (1987), if D is less than 3d bars will not occur. Further if t* is to be greater than 0.05

ggf

f

DS

dD 90

= 0.05 and if D gs/gf = 1.65, S @ 0.08 d

D90

Substituting d90/D = 0.30 one gets S = 0.025.Hence the upper limit of the slope for the bar formation is about S = 0.05 after which the sediment

would be washed off. Smith (1978) has identified five unit bar features, these are:1. Longitudinal or spool bars: These are formed in the centre of the channel at a relatively wider

section. These are convex and elongated and they grow by upstream deposition of coarsematerial and downward deposition of finer material. Crescent bar is its early form.

2. Transverse bars: These tend to form at an abrupt channel expansion. They have lobate frontand an upstream ramp.

3. Point bar: Point bars occur near the convex bank of a curved channel. In gravel-bed rivers pointbars often possess a steep outer face and a chute or secondary channel between it and the shore.

4. Diagonal bars: These are oriented obliquely across the channel and are attached to both thebanks. The upstream side is usually anchored at the concave bank. There is an upstream rampand there may be an avalanche face on the downstream front. Bars that are attached to the bankstend to be more stable than those that are detached.


5. Alternate bars: These bars form on alternate sides of the channel and talweg meanders betweenthem. Pools form opposite the bars while riffles form at the cross over point between bars.Alternate bars are a feature of straight channels. Since alternate bars are a three dimensionalphenomenon, their formation is related in part to the channel width.

Twice the pool to pool spacing l = aW where the constant a is found to vary between 4 and 17 withan average of 10. According to Chang et al.

l S

D= 3 Fr2 ...( 7.9)

According to Ikeda (1984)lW = 22.6 f (W/D)0.55

andH

D= 0.189 f (W/D)1.455 ...(7.10)

where H = bar height and f is Darcy-Weisbach friction factor. Different bars are shown in Fig. 7.7.

Fig. 7.7 Different bars

Another bed feature occurring in gravel-bed rivers and which is important from the point of view ofresistance is riffle-pool sequence. Riffle primarily represents a hydraulic resistance element and maystore little or no transient material. Riffles seem to develop by selective scour and deposition along the

Diagonal bar Alternate bar

Longitudinal bar Transverse bar Point bar

Meandering talweg

Point bar

River Morphology240

channel and are formed in gravel-bed rivers when their slope is less than 0.05. These are diagonal riffles.Material eroded from the convergence of flow towards one bank is deposited in the “cross-over zone”,where the flow diverges and the main current moves from one bank to another. Such erosion anddeposition cause riffle and pool sequence shown in Fig. 7.8.

The sediment texture strongly affects the character and relative stability of pool-riffle sequences.When the river bed material is widely graded, the largest sizes are moved more rarely than the remainingmaterial; this is deposited on the riffle. This material on the riffle which induces deposition of morematerial, which increases the stability of riffle for long periods between the floods. When the bedsediments are narrowly graded, all the material is moved relatively frequently and riffles as such do notform. Riffles are then merely leading edge of sediment storage bar. Analysis of data has indicated that:pool to pool distance = (5 to 7) times channel width. Keller and Melhorn (1973) found that

Pool to pool distance l = 5.42 W1.01 in SI units.

The channel width is also found to vary between pools and riffles. Generally riffles are wider thanthe neighbouring pools as a result of flow divergence causing bank erosion. Pool and riffle sequencesare generally very stable and in some cases found to be stationary and moving downstream at a speed ofonly 150–500 m/yr. Parker has given a stability analysis leading to the development of pool-rifflesequences. Theories of pool–riffle sequences are summarized by Richards (1982) and Langbein andLeopold (1968). The latter have proposed a kinematic wave model in which sediment particles move ingroups along the channel. Richards suggests that the generation of turbulent eddies cause alternateacceleration and deceleration of the flow which is responsible for their formation.

Transverse ribs: Transverse ribs are a set of regularly spaced cobble or gravel ridges orientedtransverse to the flow and are found on riffles and steep slopes. Ribs comprise the coarsest sedimentparticles in the channel while finer material is exposed between the ribs. Maximum flow depth in theribbed reaches is about twice the size of largest median axis of the sediment. The bed material size andchannel slope are the two primary factors which determine the rib spacing. Most studies indicated thatribs are upper flow regime bed forms.

According to Koster (1978):

Fig. 7.8 Riffle-pool sequence


W = 0.47 l

...(7.11)Mean rib width U

VWdmax = m l

where l is the mean rib wave length and m = 0.075 to 0.165.

7.7 RESISTANCE TO FLOW IN GRAVEL-BED RIVERS

The resistance relationship is the relationship between average velocity U in the channel, depth D orhydraulic radius R, channel slope S and the coefficient dependent on the resistance offered by thechannel boundary. If the flow is steady and uniform S is the channel slope; however for unsteady, non-uniform flow S should be the slope of the energy line. Three most often used equations for U are thoseof Manning, Chezy, and Darcy-Weisbach.

Equating the relationships for U, the following relationships obtained between n, C and f.

U

gRS=

1 1 6R

n g

/

= C

g =

8

f...(7.12)

where gRS = u* the shear velocity. The objective of this discussion is to obtain predictors for n, f and

C. For gravel-bed rivers n is found to vary from 0.02 to 0.2, and f from 0.01 to 0.5. For boulder riversthese values will be still higher.

When considered in the above form n, f and C will include the frictional resistance of the bed andsides, form roughness due to bed deformation, changes in cross sectional shapes, wave resistance due tosurface waves and form resistance due to changes in channel profile in plan. Since the flow in gravel-bed rivers takes place over very coarse surface material, the boundary would act as hydrodynamicallyrough; as a result Reynolds number in the form of UR/v or u* d/v will not affect resistance. Further, mostof the data available for gravel-bed rivers have width/depth ratio between 10 and 100. Hence, bankresistance can be safely neglected and depth D used in place of R in the resistance relationships. It hasalready been pointed out that conventional ripples and dunes whose character changes with the flow donot form in gravel-bed rivers; various bars or bed features that occur in gravel-bed rivers have beendiscussed earlier. Bars have a close relation with channel shape in plan and these are fairly stable beingradically modified only during high floods. Therefore, it seems more logical not to consider their effecton resistance separately and include it in the overall resistance coefficient. However, it may bementioned that some investigators e.g., Hey (1988) have studied the bar resistance separately.

As regards the characteristic size of bed material Ks to be used, there is considerable discussion inthe literature; various sizes such as d35, d50, d65 and d90 have been used and then the effect of non-uniformity is neglected. The recommendations of some of the investigators are listed below (see VanRijn 1982)

Ackers and White Ks = 1.35 d35

Einstein Ks = 1.00 d65

Engeland and Hansen Ks = 2.00 d65

Hey Ks = 3.50 d84

Mahmood Ks = 5.10 d84

Kamphus Ks = 2.50 d90

River Morphology242

Van Rijn (1982) after analyzing 120 data points from flume and field studies for the plane bedcondition and with width/depth ratio greater than five, found that Ks/d90 varied from a very small valueto almost 12 as (to – tc)/Dgs d50 varied over a wide range, but there was no correlation between the two.The average value of Ks/d90 was three. Since in many data sets the size distribution is not given and onlymedian size is known it is preferable to use d50 in the expression for Ks which is done here.

Lastly some investigators such as Colosimo et al. (1988) have recognized that when Froude number

U/ g D is greater than 1.65 the flow in the open channel becomes unstable and hence resistance

coefficient f should be related Fr, in addition to the relative roughness. Further if t* /t*c is greater thanunity, f should also depend on this parameter. Thus according to them

1

f= a log

bD

ks

FHGIKJ

+ f1 (Fr) + f2 (t* /t*c)

Here t* = to /Dgs d50 and t*c = toc/Dgs d50 Alternatively the expression for velocity can be written inmost general dimensional form as

U

gD= const

U

d

x

50

FHGIKJ

Sy or U/ gd S50 = const (D/d50)x } ...(7.13)

and the constants x and y are determined from the analysis of field data.

Results of The AnalysisAs mentioned earlier Garde et al. (1998) have analyzed a large volume of data in gravel-bed rivers forthe prediction of resistance to flow. Their results are briefly discussed below.

Resistance at bankful dischargeSince the shear stress acting on the bed depends on the stream slope, some investigators e.g. Golubstov(1969) and Bray (1979) have related Manning’s n to S. In general n increases with increase in S. Forpaved as well as mobile bed data at bankful discharge the equation obtained is:

n = 0.168 S0.245 ...(7.14)

However, the mobile bed data scattered more than the paved bed data. The exponent of S obtainedby Bray was 0.177 while Golubstov obtained the value of 0.33. Because of large scatter around the meanline, the above equation is not recommended for use.

Since according to Strickler (n/d)1/6 = constant, one can plot (n/d) 1/6 vs D/d. When this was donethe following relation was obtained.

n/d1/6 = 0.092 D

dFHIK

- 0 135.

...(7.15)

Here d is d50. However the variation of (n/d)1/6 with D/d being weak one can approximate the aboveequation by


(n/d)1/6 = 0.073 for D/d values between 2 and 200. Equation (7.15) shows that

( ) .. .

n dd

D

D

d

D

d

D

nF

D

d1 6

1 6

1 6

0 135 0 166 1 6

0 092FHG

IKJ

= FHIK

FHIK = F

HIK

- -

or

This type of relationship in the form of log-law was suggested by Limerinos (1970). The data gavethe equation (see Fig. 7.9)

D

n

1 6/

= 14.05 log D

d50

FHGIKJ

+ 12 ...(7.16)

whereas using d84 in place of d50 the values of coefficient of logD

dFHIK and constant obtained by

Limerinos were 10.27 and 17.7 while Bray (1979) obtained the values 9.66 and 19.50 respectively. Thisequation gives reasonably good predictions of n at the bankful discharge. Among the equations usingDarcy-Weisbach friction factor f, the following equation:

1

f = 1.229

D

d50

0 302FHGIKJ

.

...(7.17)

was found to be satisfactory. Lastly at bankful discharge the relationship between U gd S50 and D

d50

can be obtained. Alam’s analysis has suggested this type of relationship. This relationship obtained forthe data is (see Fig. 7.10)

U

gd S50

= 3.475 D

d50

0FHG

IKJ

.802

...(7.18)

Fig. 7.9 Variation of D1/6/n with D/d50

River Morphology244

Resistance at varying dischargeHere also preliminary analysis indicated that for any resistance analysis, mobile bed and paved bed dataintermingle and hence all data are treated together including those at bankful discharge. The variation of

n

d50

1 6FHG

IKJ

/

with D

d50

gave the equation:

n

d50

1 6FHG

IKJ

/

= 0.0702 D

d50

0 011FHG

IKJ

- .

...(7.19)

However considering the very small value of the exponent of D

d50

FHGIKJ

and the relatively large scatter,

it is recommended that n

d50

1 6FHGIKJ

/

= 0.08 is a good approximation. Limerinos type equations obtained for

all the data is:

D

n

1 6/

= 9.132 log D

d50

FHGIKJ

+ 15.41 ...(7.20)

Fig. 7.10 Variation of U gd S50 with D

d50 for bankful discharge


Other best fit results for f are:

1

f = 1.557

D

d50

0 183FHGIKJ

.

...(7.21)

and1

f = 1.031 log

D

d50

FHGIKJ

+ 1.74 ...(7.22)

The other two equations for U which are obtained by optimizing the values of exponents of D

d50

FHGIKJ

and S so that the error in the prediction of U is minimum are

U

gd S50

= 4.403 D

d50

0 639FHG

IKJ

.

...(7.23)

andU

gd50

= 2.586 D

d50

0 631FHG

IKJ

.

S0.372 ...(7.24)

see Fig. 7.11. It is recommended that if the conditions at the bankful stage are to be predicted, one shoulduse the equations specifically obtained from bankful discharge data.

Fig. 7.11 Variation of U

g d50 S with

D

d50

FHG

IKJ

for variable discharge

River Morphology246

Universal stage discharge relationWhile discussing about resistance to flow, on which the stage discharge relation depends, it isworthwhile to mention about Grishanin’s (1967) work. Through dimensional reasoning he has shown

that, as an approximation D gW

Q

a f0 25.

remains constant. For 25 sites on 21 rivers in plains, he selected

three discharges on each site namely smallest, largest and close to the mean discharge. It was found thatfor these data:

D gW

Q

a f0 25.

= 0.904 ...(7.25)

with the standard deviation of 0.158. For gravel-bed river data it is found that D gW

Q

a f0 25.

is a function

of D

d50

FHGIKJ

and the relationship between the two is:

D gW

Q

a f0 25.

= 0.459 D

d50

0 117FHG

IKJ

.

...(7.26)

so that one gets the relationship of depth D as

D = 0.459 (g W)0.25 Q D

d50

0 117FHGIKJ

.

...(7.27)

or Q = 14.863 W0.50 D1.766 d500.234 ...(7.28)

It should be noted that the above equation does not involve slope. Hence at best it will be anapproximate relationship.

7.8 SEDIMENT TRANSPORT IN GRAVEL-BED RIVERS

In sand bed rivers relatively large amount of sediment is transported as suspended load. However, ingravel-bed rivers the reverse is usually the case; they carry 10 to 50 percent of total load as bed-load. Theother characteristic of sediment transport in gravel-bed rivers is that the transport of coarser materialdoes not take place on continuous basis as in sand bed rivers but is episodic. In such rivers a largefraction of bed material is immobile even at bankful discharge and moves only during floods. When thetransport takes place it is unsteady and nonuniform because external sediment supply to the stream isfrom overland and gully flows and by landslides and bank collapses. The overland flow supplies finermaterial that is transported as suspended load. However, the material produced by landslides, and cliffcollapse is usually coarser. This material once it enters the channel may be temporarily stored in the


channel in the form of bars and will be released during floods. Short term variations in bed-load can alsooccur due to disruption of pavement layer and scour or fill. All these effects cause unsteadiness and non-uniformity in bed-load transport.

The non-uniformity of the bed sediment plays an important role in sediment transport. A pavementis formed on the bed and at low flows finer material may move over the pavement layer. In such case, thecharacteristic size of transported material may be smaller than that of the parent material as well as thatof pavement. Once the pavement is broken the material is exposed and the size distribution of thetransported material is significantly changed. Under such conditions all sizes of the particle have equalmobility.

Another factor that affects the rate of sediment transport in gravel-bed rivers is the availability ofsediment, which is important in the case of flows over a paved bed. In this case if the transport rate iscalculated for a given case assuming it to be uniform, then the actual rate of transport for that size overpaved bed may be much different because the bed may be unable to satisfy the capacity of flow totransport that sized material. As shown by Misri et al. (1984) and others the bed-load transport of nonuniform sediments can be correctly predicted if exposure and hiding corrections are applied. Once thepavement is broken all sizes can be transported and the effect of non-uniform size distribution isminimum.

Bed-load sampling in gravel-bed riversTo study the applicability of available bed load equations and develop new equations one needs tocarefully collect laboratory and field data on bed-load transport and its size distribution. In the last threedecades bed-load transport in gravel-bed rivers has been measured in New Zealand and U.S.A. onstreams such as the Snake, Clear-Water, Willamete and in the rivers in U.K., Canada, Austria,Switzerland and Poland with the bed material varying from 1 mm to 100 mm or even more. Yet notenough data are available for sediment transport in gravel-bed rivers when the bed is paved and whenthe pavement is destroyed. Further not in all the above cases the size distribution of the transportedmaterial is given. In fact establishments of sediment transport equation for the gravel-bed rivers has metwith limited success because of the difficulties associated with (i) sampling of bed material and bed-loadin streams; (ii) extreme non-uniformity of bed material; and (iii) non-equilibrium bed-load transportassociated with transient runoff events and episodic events associated with storage and release of bed-load.

Three methods have been used to measure the bed-load in gravel-bed rivers. In 1971 Helley andSmith developed a pressure difference type sampler specifically for use in rivers with bed material fromcoarse sand to medium gravel range. This is described by Garde and Ranga Raju (1985); this samplerwas used by Klingeman and Emmett to measure bed-load in East Fork river and had an efficiency of 100percent for particles ranging from 0.5 mm to 16 mm. The conveyor belt system was developed formeasuring bed-load in East Fork river. Material falling into 0.4 m wide and 0.6 m deep tough on the bedof the river through 0.25 m wide and 14.6 m long slot is carried from the trough to the bank and then intothe hopper standing over the weighing machine. Thus the sediment falling per minute was recorded.Vortex bed-load sampler has been used on the Oak Creek and has been discussed by Klingeman andEmmett. The sampler develops a vortex flow to move bed-load through a flume embedded in the floor ofthe weir structure and across the width. The bed-load and portion of the stream flow are removed to anoff-channel where the bed-load sample is collected. The water returns to the creek. The trap efficiencyof vortex tube was found to be 100% for coarse sand and higher fractions. The general design of vortextube is discussed by Garde and Ranga Raju (1985).

River Morphology248

Bed-load equationsWhite and Day (1982) and Bathrust, Graf and Cao (1987) have studied the applicability of some bed-load equations using laboratory data , and laboratory and field data respectively. White and Day, usingflume data found that if Ackers and White’s method is used for the analysis of data, one can use themobility parameter

A = u

d

n

s

f

*

D gr

L

N

MMMMM

O

Q

PPPPP

u

D

d

n

n

*

log3210

1

FH

IK

L

N

MMMM

O

Q

PPPP

-

...(7.29)

where n = 0 for D gr

s

f v2

1 3F

HGI

KJ

/

d > 60 and

n = 1 – 0.56 D gr

s

f v2

1 3F

HGI

KJ

/

d for D gr

s

f v2

1 3F

HGI

KJ

/

d < 60

If for uniform material A is the value of the mobility parameter (to which transport rate is related)and A¢ is its value for the size di in the mixture, it was found that

¢A

A= 0.6

d

di

A

FHGIKJ

-0 5.

+ 0.6 ...(7.30)

and dA is given by d

dA

50

= 1.6 d

d84

16

0 28FHGIKJ

- .

...(7.31)

White and Day proposed use of Ackers and White’s relationship for the computation of fractionwise bed-load transport. Assuming uniform size and using the above relations for computing themobility parameter, the transport rate is calculated and multiplied by the fraction of this size available inthe bed to get the bed-load transport rate of this size. The calculations are repeated for all size fractionsand the quantities added to get the total bed-load transport rate.

The critical condition for the movement of bed-material is normally expressed for gravel-bed rivers

using the dimensionless critical discharge q*c = q

gd

c

503

where qc is the critical discharge at which bed

material moves. Bettess (1984) has obtained the equation:

q*c = 0 134.

S log

1221.

SFH

IK ...(7.32)

for constant toc and rs/rf = 2.65. The plot of q*c versus S for the flume data indicated that the best fit linehas the equation


q*c = 0.15 S–1.2 ...(7.33)

and that Bettess equation gives equally good results. The equation proposed by Schoklitsch namely

qc = 0.26 rr

s

f

-FHG

IKJ

1

5 3/

d

S403 2

7 6

/

/ ...(7.34)

when d40 is replaced by d50 gives about 10% higher value of qc. Bathurst, Graf and Cao (1987) usedlaboratory data with bed material size varying from 2.9 mm to 260 mm and assessed the accuracy ofbed-load equation proposed by Ackers and White (1973), Meyer-Peter and Müller (1948), Smart(1984), Bagnold (1980) and Schoklitsch (1962). These equations are: Ackers and White

qTV = 0.025 qd

D35

Fgr

0171

1 5

.

.

-LNM

OQP

where Fgr = 1

135

0 5

gd s

f

rr

-FHG

IKJ

L

NMM

O

QPP

. U

D

d5 657

10

35

. logFHG

IKJ

L

N

MMMMM

O

Q

PPPPP

...(7.35)

where qTV = volumetric sediment transport rate per unit width. This equation is to be used only for fewflows with Fr less than 0.80.

Meyer and Peter and Müller’s equation:

q*BV = Q

g d

BV

s

fa

rr

-FHG

IKJ

1 3

= 8 n

nsF

HIK -

L

NM

O

QP

3 2

0 047/

* .t ...(7.36)

Here da is the arithmetic mean size of bed material, ns is Strickler’s value of Manning’s roughness

coefficient, while n is the Manning’s coefficient for flow, and t* = g

gf

s a

DS

dDSmart’s Equation: This equation is based on flume experiments using sediment sizes up to 29 mm

and slopes up to 20 percent. The equation is

Q

g d

BV

s

fa

rr

-FHG

IKJ

1 3

= 4.0 d

d90

30

0 2FHGIKJ

L

NMM

O

QPP

.

S0.6 U

u**.t0 5 (t* – t*c) ...(7.37)

River Morphology250

Mizuyama’s (1977) equation

q*BV = 12 24

15 1 11 2

1 2 2

1 2- - -

FHG

IKJ

-FHG

IKJ

L

NMM

O

QPP

L

N

MMM

O

Q

PPP

SS a

t

tmcm

m

cm

m

/

*/ *

*

*

*

/

cos.

qt a

ttd i ...(7.38)

Here, a = f (S) and t*m and t*cm are for d = d50.Bagnold’s equations:

q

qBV

BV¢==

w w

w w

-

- ¢

L

N

MM

O

Q

PP ¢FHIK ¢

FHIK

- -c

c

D

D

d

db g

3 22 3 1 2

// /

...(7.39)

Here, w = stream power q rf S per unit width, wc is the critical value of w and the prime refers tostandard measured values from a reliable experimental plot.

Schoklitsch’s equation:

qBV = 2 5.

/r rs fd i S3/2 (q – qc) ...(7.40)

and qc in SI units is given by:

qc = 0.26

gg

s

f

d

S

-FHG

IKJ

1

5 3

403 2

7 6

/

/

/ ...(7.41)

Verification of the equations using flume data indicated that Schoklitsch’s equation gave betterperformance than the rest of the equations. Further its performance is improved if qc value obtained

from qc* = 0.21 S–1.2 are used. In the case of field data it was found that when (q – qc) is plotted q

SBV3 2/ ,

data for small and large rivers behave differently, see Fig. 7.12. Large rivers with S £ 1.0 percent andrelatively narrow range of sediment sizes (1 to 100 mm) as well as ready supply sediment withinchannel, show relatively closer agreement with Schoklitsch’s Equation than data for small rivers withS ³ 1 percent and relatively wider range of sediment size (1 to 1000 mm). While in the former case thedata fall within one order of magnitude of the line of Schoklitsch’s equation, in the latter case sedimenttransport is over predicted by two orders of magnitude. Hence Bathurst et al. (1987) concluded thatwhile Schoklitsch’s equation can be applied with caution to large rivers, it should be applied to smallrivers for extreme flows when the whole bed is moving.

Parker, Klingeman and Mclean�s equationAfter examining the data of the Oak Creek (U.S.A.) Parker et al. (1982) found that when the shear stressacting on the bed is greater than the critical shear stress for the pavement and thus the pavement is


Fig. 7.12 Variation of qBv/S3/2 with (q – qc), river data compared with Schoklitsch equation

broken, as a first order of approximation the size distribution of the bed-load is nearly the same as that ofthe sub-pavement. Under this condition the rate of bed-load transport is governed by the hydraulicconditions rather than the availability of material. This information is used to develop an empiricalequation for bed-load transport rate as a function of shear stress and d50 of the sub-pavemnent in pavedbed channels. Careful analysis of the Oak Creek data indicated the validity of similarity approach.However small systematic change in size distribution with the shear stress was observed especially nearthe critical condition.

Using the similarity approach proposed by Ashida and Michiue, Parker et al. (1982) used twodimensionless parameters

Wi* =

rr

tr

t tg

s

fBVi i

fi

c

s i

gq fd

-FHG

IKJ

FHGIKJ

RS|

T|

UV|

W|=

UV|

W|1 0

3 2/

*andD

where qBVi is the volumetric bed load transport rate of size di per unit width of the channel and fi is thefraction of size available in the sub-pavement. Plotting Wi

* vs ti* for each size range, the value of ti

*

CachelaPoudre,Colorado

River Morphology252

designated as t*ri at which Wi

* has the pre-chosen value of 0.002. Further denoting t*r50 as the value of

t*i when di = d50 it was found that

tt

ri

r

*

*50

= d

d1

50

1 0FHGIKJ

- .

...(7.42)

and t*r50 = 0.0876. Defining fi = t*

i /t*ri and taking W*

r = 0.002, they found that when W

Wi

r

*

* is plotted

against fi the data tend to plot around a single curve whose coordinates are

Table 7.2 Coordinates of fi Vs W*i

fI 0.90 1.0 1.1 1.2 1.3 1.4

W

Wi*

r*

10– 4.5 2.3 ´ 10–3 1.15 ´ 10–2 3.7 ´ 10–2 8.0 ´ 10–2 1.9 ´ 10–1

This is based on ten size ranges for the Oak Creek in the range of 0.60 to 102 mm. However asystematic deviation was apparent, viz. as fi increase, the value of Wi

* for the finer material tends to fallbelow the mean curve. Parker et al. showed that the above relationship can be integrated to obtain thetotal bed-load transport rate in the form

W

Wr

*

* = G (f50) ...(7.43)

where W* is the dimensionless bed-load transport for poorly sorted gravel-bed when the pavement is

broken, W*r = 0.002 and f50 =

tt

50

50

*

*r

with t*r50 = 0.0876. The above functional relation takes the form:

W* = 0.0025 e[14.2 (f50 – 1) – 9.28 (f50 – 1)2] ...(7.44)

for 0.95 < f50 < 1.165. It is interesting to note that the coordinates of the two curves W*i = 0.002 G (fi )

and W*r = 0.0025 exp. [14.2 (f50 – 1) – 9.28 (f50 – 1)2] match. Parker et al. showed that data for the rivers

Elbow, Snake and Vedder reasonably conform to the above equation for W*. For data with f50 > 1.65 thefollowing equation gives the variation of W* and f50

W*r = 11.2 1

0 822

50

4 50

-FHG

IKJ

..

j...(7.45)

Parker et al. also obtained three empirical equations for three size ranges of the bed material for f50greater than 0.95. However these equations need further verification using data from other streams.


References

Adams, J. (1979) Gravel Size Analysis from Photographs. JHD, Proc. ASCE, Vol. 105, No. HY-10, October, pp.1247-1285.

Ackers, P. And White, W.R. (1973) Sediment Transport: New Approach and Analysis. JHD, Proc. ASCE, Vol. 99,No. HY-11, November, pp. 2041-2060.

Bagnold, R.A. (1980) An Empirical Correlation of Bed-load Transport Rates in Flumes and Natural River, Proc.RSL, A372, pp. 453-473..

Bathurst, J.C. (1978) Flow Resistance of Large Scale Roughness. JHD, Proc. ASCE, Vol. 104, No. HY-12,December, pp. 1587-1603.

Bathurst, J.C. (1985) Flow Resistance Estimation in Mountain Rivers. JHE, Proc. ASCE, Vol. 111, No. 4, April,pp. 625-643.

Bathurst, J.C. 1986. Some Aspects of Gravel-Bed Rivers (Lecture Notes for the British Council Visit), February.

Bathurst, J.C. Graf, W.H. and Cao, H.H. (1987) Bed-load Discharge Equations for Steep Mountain Rivers,Chapter 15 in Gravel-Bed Rivers. (Eds. Thorne, C.R., Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd.,pp. 453-492.

Bettess, R. (1984) Initiation of Sediment Transport in Gravel Stream. Proc. Inst. of Civil Engineers (London), Vol.77, Pt. 2, Technical Note 407, pp. 79-88.

Bhowmik, N.G. (1968) “The Mechanics of Flow and Stability of Alluvial Channels Formed in Coarse Materials”,Ph.D. Thesis, Colorado State University, Fort Collins (U.S.A.).

Bray, D.I. (1979) Estimating Average Velocity in Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 105, No. HY-9,September, pp. 1103-1122.

Bray, D.I. (1982) Regime Equations for Gravel-Bed Rivers, Chapter 19 in Gravel-Bed Rivers. (Eds. Thorne, C.R.,Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd., pp. 517-552.

Charlton, F.G. (1977) An Appraisal of Available Data on Gravel Rivers, HRS Wallingford (U.K.), Rep. No. INT –151, p. 67.

Church, M and Jones, D. (1987) Channel Bars in Gravel-Bed Rivers, Chapter 11 in Gravel-Bed Rivers. (Eds.Thorne, C.R., Bathurst, J.C. and Hey, R.D.) John Wiley and Sons Ltd., pp. 291-338.

Church, M and Rook, R. (1983) Catalogue of Alluvial River Channel Regime Data. University of BritishColumbia, Canada.

Colosimo, C., Copertino, V.A. and Vetri, M. (1988) Friction Factor Evaluation in Gravel-Bed Rivers. JHE, Proc.ASCE, Vol. 114, No. 8, August, pp. 861-876.

Garde, R.J. (1972) Bed Material Characteristics of Alluvial Streams. Jour. of Sedimentary Geology, Vol. 7, No. 2.,pp. 127-135.

Garde, R.J., Prakash, H. and Arora, M. (1985) Hydraulics of Gravel-Bed Rivers. Report Prepared for I.N.S.A.,CWPRS, Pune, 164 p.

Garde, R.J. and Ranga Raju, K.G. (1985). Mechanics of Sediment Transportation and Alluvial Stream Problems.Wiley Eastern Publishers Ltd., New Delhi, p. 618.

Gladky, H. (1979) Resistance to Flow in Alluvial Channels with Coarse Bed Materials. JHR, IAHR, Vol. 17, No.2, pp. 121-128.

Golubstov, V.V. (1969) Hydraulic Resistance and Formula for Computing the Average Flow Velocity of MountainRivers. Soviet Hydrology, No. 5, pp. 500-511.

Griffiths, G.A. (1981) Flow Resistance in Coarse Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 107, No. HY-7,July., pp. 899-980.

River Morphology254

Grishanin, K.V. (1967) The Similarity in Flow at Straight Reaches of Rivers. Proc. 12th Congress of IAHR, FortCollins, U.S.A., Vol. 1, A-28, pp. 226-236.

Harrison, A.S. (1950) Report on Special Investigation of Bed Sediment Seggregation in a Degrading Bed. Rep.Series 33, Issue No. 1, University of California, Berkeley, U.S.A., September.

Hey, R.D. (1982) Design Equations for Mobile Gravel-Bed Rivers, Chapter 20 in Gravel-Bed Rivers. (Eds. Hey,R.D., Bathurst, J.C. and Thorne, C.R.) John Wiley and Sons Ltd., pp. 553-580.

Hey, R.D. and Thorne, C.R. (1986) Stable Channels with Mobile Gravel-beds. JHE, Proc. ASCE, Vol. 112, No. 8,August, pp. 671-689.

Ikeda, S. (1984) Prediction of Alternate Bars Wave Length and Height. JHE, Proc. ASCE, Vol. 110, No. 4, April,pp. 371-386.

Inglis, C.C. (1947) Meanders and Their Bearing on River Training. Proc. Inst. Of Civil Engineers (London),Maritime Paper No. 7, January, pp. 3-54.

Jackson, R.G. II. (1975) Hierachical Attributes and a Unifying Model of Bed Forms Composed of CohesionlessMaterial and Produced by Shearing Flow. Geol. Society Am. Bull., Vol. 86, pp. 1523-1533.

Keller, E.A. and Melhorn, W.N. (1973) Bed Forms and Alluvial Processes in Alluvial Stream Channels : SelectedObservations, In Fluvial Geomorphology (Ed. Morisawa, M.) Intl. Series No. 4, (Bingham Symposium inGeomorphology), Alley and Unwin Ltd., London, pp. 253-284.

Kellerhals, R. (1967) Stable Channels with Gravel Paved Beds. JWHD, Proc. ASCE, Vol. 93, No. WW-1,February, pp. 63-84.

Knighton, A.D. (1977) Short Term Changes in Hydraulic Geometry, Chapter 7 in River Channel Changes. Ed.Gregory, K.G., Wiley Interscience Publications, U.S.A., pp. 101-119.

Koster, E.H. (1978) Transverse Ribs, their Characteristics, Origin and Palaeohydraulic Significance in FluvialGeomorphology. E.D. Miall, Memoir 5 of Canadian Society of Petroleum Geologists.

Kothyari, U.C. (1994) Frequency Distribution of River Bed Materials. Jour. Of Sedimentary, Vol. 42, No. 1, pp.283-291..

Lacey, G. (1930) Stable Channels in Alluvium. Minutes of Proc. Inst. Of Civil Engineers (London), Vol. 229,Paper No. 4736, pp. 258-292.

Lane, E.W. and Carlson, E.J. (1953) Some Aspects Affecting the Stability of Canals Constructed in CoarseGranular Materials. Proc. 5th Congress of IAHR, Minneapolis, U.S.A., September, pp. 37-48.

Langbein, W.B. (1964) Geometry of River Channels. JHD, Proc. ASCE, Vol. 90, No. HY-2, March, pp. 301-347.

Langbein, W.B. and Leopold, L.B. (1968) River Channel Bars and Dunes - Theory of Kinematic Waves. USGSProfessional Paper 422-L, p. 20.

Leopold, L.B. and Maddock, T. (1953) Hydraulic Geometry of Stream Channels and Some PhysiographicImplications. USGS Professional Paper 252, Washington D.C., 57 p.

Leopold, L.B. and Wolman, M.G. (1957) River Channel Patterns: Braided, Meandering and Straight. USGSProfessional Paper 252, Washington D.C., pp. 39-85.

Limerinos, J.T. (1970) Determination of the Manning’s Coefficient from Measured Bed Roughness in NaturalChannels. W.S. Paper USGS, 1898-B, Washington D.C., p. 47.

Meyer-Peter, E. And Müller, R. (1948) Formulas for Bed-Load Transport. Proc. 2nd Congress of IAHR,Stockholm., pp. 39-64.

Michalik, A.S. (1989) Some Aspects of the Bed-Load Transport in Mountain Rivers. Proc. 4th InternationalSymposium on River Sedimentation, Beijing, China, pp. 579-586.

Milhaus, R.T. (1973) Sediment Transport in a Gravel-Bottomed Stream. Ph.D. Thesis, Oregon State University,U.S.A., p. 232.


Misri, R.L., Garde, R.J. and Ranga Raju, K.G. (1984) Bed-Load Transport of Coarse Non-uniform Sediment. JHE,Proc. ASCE, Vol. 110, No. 3, March., pp. 312-328.

Mizuyama, T. (1977) Bed - Load Transport in Steep Channels. Ph.D. Thesis, Kyoto University, Japan, p. 118.

Moss, A.J. (1962) The Physical Nature of Common Sandy and Pebby Deposits I. Jour. Am. Science, Vol. 260.

Moss, A.J. (1963) The Physical Nature of Common Sandy and Pebbly Deposits II. Jour. Am. Science, Vol. 261.

Neill, C.R. (1968) Note on Initial Movement of Coarse Uniform Bed Material. JHR, IAHR, Vol. 6, No. 2, pp. 173-176.

Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armor Layer. JHE, Proc. ASCE, Vol. 110, No. 10,October, pp. 1479-1485.

Parker, G. (1979) Hydraulic Geometry of Active Gravel Rivers. JHD, Proc. ASCE, Vol. 105, No. HY-9,September, pp. 1185-1201.

Parker, G., Klingeman, P.C. and McLean, D.G. (1982) Bed-load and Size Distribution in Paved Gravel-BedStream. JHD, Proc.ASCE, Vol. 108, No. HY-4, April, pp. 544-571.

Richards, K.S. (1982) Forms and Processes in Alluvial Channels. Methuen, London.

Schoklitsch, A. (1962) Handbuch des Wasserbau. 3rd Edition Springer-Verlag, Vienna.

Shulits, S. (1944) Rational Equation for River Bed Profile. Trans AGU, Vol. 22. pp. 522-531

Silvester R. and del a Cruz C.D.R. (1970) Pattern Forming Forces in Delta. JWHD, Proc. ASCE, Vol. 96, No.WW-2, May, pp. 201-217.

Smart, G.M. (1984) Sediment Transport Formula for Steep Channels. JHE, Proc. ASCE, Vol. 110, No. 3, March,pp. 267-276.

Smith, N.D. (1978) Some Comments on Terminology. Ed. Miall, A.D., Memoir 5 of Canadian Society ofPetroleum Geologists, Ottawa, pp. 85-88.

Thompson, S.M. and Campbell, P.L. (1979) Hydraulics of Large Channel Paved with Boulders. JHR, IAHR, Vol.17, No. 4, pp. 341-354.

Thornbury W.D. (1964) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons Inc.,New York, U.S.A., 2nd Edition.

Thorne, C.R. and Zevenbergen, L.W. (1985) Estimating Mean Velocity in Mountain Rivers. JHE, Proc. ASCE,Vol. III, No. 4, April, pp. 612-624.

Van Rijn, U.C. (1982) Equivalent Roughness of Alluvial Bed. JHD, Proc. ASCE, Vol. 108, No. HY-10, October,pp. 1215-1217.

Vischer, G.S. (1969) Grain Size Distribution of Depositional Processes. Jour. Sedimentary Petrology, Vol. 39.

Wadia D.N. (1961).Geology of India. MacMillan and Co. Ltd., London. 3rd Edition (Revised)

Walters W.H. Jr. (1975) Regime Changes of the Lower Mississippi River. M.S. Thesis. Civil EngineeringDepartment, Colorado State University, Fort Collins (U.S.A.)

White, W.R. and Day, T.J. (1982) Transport of Graded Gravel-bed Material, Chapter 8 in Gravel-Bed Rivers. Eds.Hey, R.D., Bathurst, J.C. and Thorne, C.R., John Wiley and sons Ltd., pp. 181-223.

Wolman, M.G. (1954) A Method of Sampling Coarse River Bed Material. Trans. A.G.U., Vol. 35, No. 6, Pt. 1,December, pp. 951-956.

Worcester P.G. (1948). A Text Book of Geomorphology. D.Van Nostrand Company Inc., New York, 2nd Edition.

8C H A P T E R

Fluvial Palaeo Hydrology

8.1 INTRODUCTION

The word palaeo hydrology was probably first used by Leopold and Miller (1954) in the study ofpostglacial chronology of alluvial valleys in Wyoming (USA). In this case they were concerned aboutthe interaction of climate, vegetation, stream regime and runoff, which were obtained under severalclimatic conditions, each different from the present one; this led to the use of the word palaeo hydrology.Since then several investigators such as Schumm (1965, 1977) and Cheetham (1976), have givendifferent definitions of palaeo hydrology. In connection with Quaternary palaeo hydrology Schumm(1965, 1977) stated that palaeo hydrology treats the phenomenon of occurrence of water in theatmosphere, its distribution and composition on the surface of the ground and underground, but hasreference to the past. The term is restricted to that portion of hydrologic cycle that involves themovement of water over the surface of the earth, because runoff and the accompanying sediment loadare of major importance in determining the non-glacial erosional and depositional features of theQuaternary. Since the composition of water on surface would naturally involve sediment, and itsmovement, palaeo hydrology also involves consideration of quality and quantity of the sediment movedthrough the palaeo channels. According to Cheetham (1976) palaeo hydrology is the study of fluvialprocesses operated in the past and their hydraulic implications. Fluvial palaeo hydrology is that branchof palaeo hydrology which deals with erosion, deposition and the characteristics of former channels.

Since the study of palaeo hydrology involves the use of new techniques, conceptual advances andmore interdisciplinary research, International Geological Correlation Programme (IGCP) wasformulated and initiated in 1973 as IUGS/UNESCO activity. In palaeo hydrology progress has beenmade through developments in climatology, hydraulics, geomorphology and sedimentology. The fieldsrelated to palaeo hydrology are:

Palaeo climatology: Study of paleao climates which are climates in periods of geologicpast.

Palaeo geomorphology: The geomorphology of ancient landscapes, especially as representedtoday by features that are buried or newly exhumed.

Fluvial Palaeo Hydrology 257

Palaeo hydraulics: Study of quantitative relationships between hydraulic parameters ofrivers (e.g., depth, width, slope, discharge, sediment type)

Palaeo pedology: Study of palaeo soils i.e., soils that formed by the landscape of thepast.

In palaeo hydrology the interest in hydrologic and fluvial processes goes back to the times whensystematic hydrologic data were not collected, say 10 000 to 15 000 years before present (B.P.), i.e.,during Quaternary period and Holocene and Pleistocene epochs. Evidence available for palaeohydrology of the temperate zone in the past 15 000 years is primarily sedimentological, morphologicaland historical. Sedimentological evidence includes information deduced from the physical properties ofsediments and from organic deposits; this information is useful in the reconstruction of environmentduring the past and assessing the discharges and the changing rates of erosion. Morphologicalinformation can be obtained from the analysis of palaeo channels. Additional historical information isobtained from old maps, records, other historical sources and the dating techniques. As indicated byGregory et al. (1987), in palaeo hydrology as well as historical geomorphology, a retrorespectiveapproach is preferred because it is desirable to reconstruct palaeo hydrology against the basic definitionof hydrology of contemporary environment. An understanding of the present day processes is thereforea must for the interpretation of past hydrological processes. It is also necessary to attempt to extract aconsiderable amount of information of recent human impact before analysing the prehistoric palaeohydrology. In this endeavour a better understanding of the relation of sedimentary deposits and rivermorphology to hydrology is necessary so as to construct palaeo environmental models of terraces,palaeochannels, and other deposits e.g., deltaic deposits. Hence information and discussion in chaptersfive, six and seven and in earlier chapters is useful in palaeo hydrologic studies.

Since climatic changes have occurred during the post-glacial period, it is necessary to know or inferwhat these climatic changes were and how these changes affected the flood and channel formingdischarge which, in turn, would affect the palaeo channels: their dimensions, plan-form and itsvariation, and such other characteristics. It is presumed that the hydraulic data such as flood dischargewere not measured and hence have to be inferred indirectly from whatever measures of palaeo channelsthat are available.

The dating of changes has to be done separately using study of ancient soils, tree rings, pollens andspores, ancient cultural evidence e.g., archaeology, written or oral records, sediments (sedimentologyand stratigraphy), land forms (geomorphology and Quaternary geology), ancient floral and faunaldistribution, and isotope chemistry of ancient waters and elements such as oxygen and carbon.

8.2 OBJECTIVES OF PALAEO HYDROLOGIC STUDIES

The broad objectives of palaeo hydrologic study are to reconstruct components of hydrologic cycle, ofthe water balance and of sediment budgets for the time before continuous hydrologic data werecollected. Continuous hydrologic and hydraulic data including meteorological data, stream gauges,evaporation etc. are available for a little over 100 to 150 years, while some hydrologic records date backto more than 2000 years. Hence, palaeo hydrologic studies can be visualised prior to this period up toglacial age.

The study of fluvial palaeo hydrology would deal with climatic changes in the past and theirinfluence on vegetation, erosion and deposition, palaeo channel geometry, plan-forms, channel formingdischarges, palaeo velocities and probable changes in river courses. Such studies are also useful in

River Morphology258

predicting future changes in fluvial channels and erosion or deposition caused by probable climaticchanges and man-made interferences.

The knowledge of palaeo hydrology and fluvial palaeo hydrology is useful in interpreting thebehaviour of alluvial streams, location of hydraulic structures, choosing sites for storing hazardouswastes, and for exploring valuable deposits in ancient fluvial sediments (Schumm 1977).Hence forstudying fluvial palaeo hydrology one should enquire into how and why climatic changes took place inthe past and what was their effect on vegetation, runoff and erosion rates in arid, semiarid and humidregions. How can one estimate palaeo velocity and palaeo discharge from observed dimensions ofpalaeochannels? How would such climatic changes affect the plan-form characteristics?

The information presented in this chapter is based on the excellent texts and papers written onpalaeo hydrology and related topics by Schumm (1977), Gregory (1983), Berglund (1986), Gregory etal. (1987), Dury (1976) and others.

8.3 BASIS OF ANALYSIS

It is reasonable to assume that climate and climatic changes would affect the erosional and depositionalprocesses and hence the landscape and rivers. Even though climate influences the weathering and soilformation, from the point of view of palaeo studies, the effects of climate on vegetation, runoff andsediment yield from mountainous areas are more relevant. Studies by Langbein et al. (1949), Langbeinand Schumm (1958) and Noble (1965) indicate how mean annual precipitation, average temperatureand vegetal cover affect mean annual runoff and sediment yield. Using data from gauging stations atwhich the discharge was not materially affected by diversions or regulation, Langbein et al. (1949)showed the effect of mean annual temperature on the mean annual runoff, see Fig. 8.1

Fig. 8.1 Variation of mean annual runoff with mean annual precipitation and average temperature (Langbein et al. 1949)

For a given mean annual precipitation, as the temperature increases the mean annual runoffdecreases. Also, Langbein and Schumm (1958) obtained a relation between annual sediment yield andeffective precipitation for drainage basins of approximately 3800 km2 for temperature at 10°C, see Fig.8.2. The definition of 10°C curve is based on known values of runoff for each drainage basin from


which sediment yield data were obtained. These observed values were converted to an effectiveprecipitation, which is the annual precipitation required to produce the known runoff at 10°C using Fig.8.1. On Fig. 8.2 are also shown the range of vegetation as effective precipitation increases. According toLangbein and Schumm the precipitations as well as the temperature influence the sediment yield fromthe catchment. This is so because as the temperature increases, higher precipitation is required toproduce a given amount of runoff. The variation in sediment yield with precipitation is explained by theinteraction of precipitation and vegetation on runoff and erosion. As precipitation increases so does thevegetation that tends to reduce the erosion. On the other hand, as precipitation increases erosion tends toincrease. Langbein and Schumm found that when precipitation exceeds 30 cm, sediment yield decreaseswith increasing precipitation due to more effective grass cover. According to Fournier (1949), inmonsoonal climate the sediment yield may increase again after rainfall exceeds 125 cm under theinfluence of highly seasonal climate.

The role played by vegetation in controlling the rate of erosion is indicated by the studies by Noble(1965) on an experimental watershed in Utah (USA). He found that the erosion rate decreased from2935 kg/ha/storm to a negligible value as the percentage of ground cover changed from 20 to 90. Theeffect of temperature and vegetation on mean annual runoff and erosion rate has also been studied byKothyari and Garde (1991), and Garde and Kothyari (1986). Using such type of information it ispossible to predict what may have been the effect of change in mean temperature, mean annualprecipitation and vegetal cover on the changes in runoff and sediment yield during inter-glaciation andpost-glaciation periods.

While studying palaeo hydrology it is generally assumed that in relatively recent geologic times,during the later part of the Tertiary and the entire Quaternary period, there has been no significantchange in vegetation. Hence the relations between mean annual temperature and precipitation can beused to show how both sediment yield and runoff changed with climatic changes in the geologic past.

The second tool available to study fluvial palaeo hydrology is Lane’s balance analogy according towhich

Qsd ~ QS ...(8.1)

where Qs and Q are sediment and water discharge in the stream, d is the sediment size and S is the streamslope. This analogy would qualitatively predict what would happen to stream slope if Qs or Q are

Fig. 8.2 Variation of sediment yield with climate (Langbein and Schumm 1958)

River Morphology260

changed or there is change in the base level due to sea level changes. Here one can use either meanannual discharge or mean flood discharge. The above proportionality is helpful in interpreting channelchanges due to climatic changes resulting in change in Q and Qs in palaeo conditions. However, thisrelationship does not throw light on the changes in the plan-form of the stream.

Another important relationship is the qualitative relationship for sediment discharge Qs

Qs ~ W M S

DSL

i

...(8.2)

Here W is the average channel width, Si is the sinuosity, and ML meander length. Hence fromrelationships 8.1 and 8.2 one can express what happens to W, D, ML, S, Si if either the water discharge Qor sediment discharge Qs is increased (+) or decreased (–).

Thus one can write

Q W D M S S

Q W D M S S

Q W M S D S

Q W M S D S

L i

L i

S L i

S L i

+ + + + - -

- - - - - +

+ + + + - +

- - - - + +

»

»

»

»

U

V||

W||

, , , , ,

, , , ,

, , , ,

, , , ,

…(8.3)

Another important tool that can be used in palaeo hydrology is the resistance relationship relatingflow velocity U to the depth D or hydraulic radius, slope S, and roughness coefficient e.g., Manning’s nor Chezy’s C, or friction factor f defined in Chapters five and seven. This can be used if palaeo stage isknown along with slope S. The slope that has to be used is the terrain slope or palaeochannel slopeassuming the flow to be uniform. The roughness coefficient can be estimated knowing the size of thebed material and Strickler type equation discussed in Chapters five and seven. Alternatively, one can useother equations such as Eqs. (8.21) or (8.22). Another method would be to estimate Q knowing thecontemporary relation between Q and meander length ML.

Analysis of transverse sections of the valley floor enables one to explain the changes caused bylateral erosion, aggradation and avulsion of channels. Examination of longitudinal profile of flood plainallows one to evaluate the influence of eustatic and tectonic factors in fluvial history. For this reason oneneeds to consider carefully the history of tectonic and neo-tectonic activity in the region and its effect onchannel change.

Sedimentological methods are used to distinguish various facies of fluvial deposits. The facialsetting is different in braiding and meandering systems and hence facial study of fluvial deposit assumesimportance. Stratigraphic analysis of undisturbed deposits of palaeo channels is also important. Sizedistribution of facial units, presence of fills of different ages and recognition of rates of deposition canassist in the reconstruction of many parameters of the past environment.

8.4 CLIMATIC CHANGES: PAST AND FUTURE(SCHNEIDER AND ROOT 2000)

Earth’s climate is very different now from what it was 100 million years ago. It is different from what itwas 20 000 years ago when ice sheets covered much of the Northern Hemisphere. These climatic


changes in the past were driven by natural causes such as variations in the earth’s orbit or CO2 content ofthe atmosphere. However, climatic changes in future will probably have another source namely humanactivity because human actions can indirectly alter the natural flow of energy enough to createsignificant climatic changes. One example is enhancing the natural capacity of the atmosphere to trapradiant energy near earth’s surface – known as green house effect. Burning of fossil fuel that releasesCO2 and using land for agriculture or urbanisation leading to large-scale deforestation will cause globalwarming of 1° to 5°C in the next century. Computer simulation models based on basic laws ofthermodynamics and Newton’s laws of motion can be used to predict future changes in climate.

The last major glacial ice age occurred about 20 000 years ago and the current 10 000 years longinterglacial period (Holocene) began. This has been determined from the ratio two oxygen moleculesO16 and O18 isotopes having different molecular weights entrapped in the ice. Ice cores taken from holesdrilled into some 2000 m of ice in Greenland and Antarctica also provide information on the presence ofCO2, important in studying greenhouse effect. Carbon dioxide concentrations during cold periods weremuch less than in interglacial periods. The temperature during the past 10 000 years (before 1700 A.D.)was remarkably constant. During the transition of Ice Age to Holocene, which took 5000 to 10 000years, the average global temperature increased by 5°C and sea level rose by 100 m. Thus, average rateof natural temperature rise was 0.5° to 1.0°C per thousand years. Thus, climate change was responsiblefor the well known extinctions of woolly mammoths, sabertooth cats, etc. The climatic change was alsoresponsible for change in vegetation. During the last Ice Age most of Canada was under ice; study ofpollen cores indicate that as the ice receded, boreal trees moved northward chasing the ice cap. Itsuggests that the biological communities move intact with a changing climate. It was further noticed thateven though during the transition from last Ice Age to the present inter-glaciation nearly all the speciesmoved northward, they moved individually and not as a group. Since due to increased human activity onthe globe the temperature changes on the earth will be more severe than during inter-glaciation period,such changes are bound to affect vegetation patterns.

Causes for Climatic ChangesThe causes for climatic changes can be external or internal. Stating which components are external orinternal to climatic system depends on the time period and spatial scale being examined, as well as onthe phenomena being considered. External causes can be:

a. Fluctuations in heat radiated by the sun – perhaps related to sun spots – are external to climaticsystem.

b. Influences of gravitational tugs of other planets on the earth’s orbit are also external to climatesystem. According to some scientists such tugs gave rise to 40 000 year ice cycle in the past 2.5million years, 100 000 year ice age and inter-glacial cycles.

c. Changes in volcanic dust or CO2 in the atmosphere. On short time scale these factors areexternal.

d. Effects of green house gases on temperature, on 20 year scale are also external.e. Effect of changes in character of land surface caused by human activity is an external cause.

Some of the internal causes for climate changes are:

a. Dust generation caused by change in plant cover due to changes in climate;b. CO2 and methane levels may rise or fall with ice age cycles; these are internal on a 10 000 years

time scale.

River Morphology262

c. If vegetation cover changes because of climatic change, the land surface change becomesinternal; change in plant cover can influence the climate by changing albedo (i.e., reflectivity tosun light), evapo transpiration, surface roughness and humidity.

d. Unusual patterns of ocean surface temperature – such as the El Nino - are an internal cause.

Climate Change ForecastsTo predict the significant ways the climate might change, one must specify what people do that modifieshow energy is exchanged among the atmosphere, land surface, and space because such energy flows arethe driving forces behind climate. Estimating societal impetus involves forecasting the plausible set ofhuman (or societal) activities affecting pollution over the next century. The next step is to estimate theresponse of the various components of the earth system to such societal forcings. The earth system itselfconsists of the following interacting sub-components, atmosphere, oceans, cryosphere (snow, seasonalice and glaciers) and land surface systems. Since knowledge about societal impetus that will actuallyoccur and the scientific knowledge of each sub-system are still incomplete, such models are not yet fulldeveloped.

Global Warming ForecastsGlobal warming forecasts for 21st century will depend on the projections of population, consumption,land use and technology. The forecast of amount of CO2 emitted per unit energy will depend on theprojections of population and affluence that are increasing and the amount of energy used to produce aunit of economic product. Hence, it is estimated that CO2 emissions will rise several fold over the next100 years (of course this will depend on what kind of energy system is used). Roughly 50 percent of CO2emitted will remain in the atmosphere every year i.e., about 3 billion tons of carbon as CO2. This is halfof fossil fuel injected CO2. Then one needs to estimate CO2 concentration in the atmosphere usingcarbon cycle model and this should be fed in computerised climatic models to estimate its effect onclimate. The simplest model will give the global average temperature while complex atmosphericmodels predict time evolution of temperature plus humidity, wind, soil moisture, sea ice and othervariables in the three dimensions in space. Such a model is known as general circulation model.Ecologists use these inputs to produce forecasts of regional climatic changes in the future. Further,global heating or warming is not uniform but different for centres of continents, oceans and oceanscloser to poles. These temperature differences can cause droughts, high rainfalls, hurricanes and similarother effects. According to Inter-governmental Panel on Climate Change there is likely to be 1.5° to 4.5°C average global rise in temperature in the 21st century.

8.5 PALAEO HYDROLOGIC ESTIMATES OF DISCHARGE AND VELOCITY

In palaeo hydrology considerable attention has been given to prediction of palaeo flood velocity orpalaeo flood discharge from observed channel dimensions or meander characteristics. Prediction offormer river discharges is the primary purpose of palaeo hydrology. Ability to calculate former riverdischarge makes it possible to determine the quantitative water balance of the drainage basin, thehydrologic regime of the river, and some elements of climate, as well as to detect and specifyquantitative changes of some hydrologic and climatic parameters in a given period of the Quaternaryand, possibly for older geologic periods too.


Theoretically there are two ways in which one can determine the past river discharge on the basis ofits effects, firstly through the analysis of preserved morphological effects caused by a given discharge.Unfortunately, the connections between the deposit, its structure, and statistical parameters of grain sizedistribution and the discharge are so complicated and obscure that they cannot be expressed in anyquantitative models. Grain size distribution and its parameters enable one to specify at most the localvelocity at which the deposition of given sediment took place. The top level of deposition gives anindication of lowest palaeo flood level. The other method used is known as slack water deposit (SWD)method which gives an idea of the stage of palaeo flood and is described later.

The second method is to use relation between characteristic discharge, such as mean annualdischarge, Qma bankful discharge Qb or mean annual flood Qmaf and the morphological parameterswhich can be cross-sectional parameters at bankful discharge such as maximum depth Dmax, hydraulicradius R, channel slope S, width to depth ratio and cross-sectional area A, and channel patternparameters such as meander length ML, meander belt MB and meander curvature radius Rm. It must beemphasised that these relations are valid only for some types of rivers. The relations between dischargeand channel cross-section parameters apply to meandering and straight rivers, while the relationsbetween discharge and channel pattern parameters concern only meandering rivers. No suchrelationships are available at present for braided rivers. Such analysis assumes that these geometric(cross-sectional and channel pattern) parameters are only a function of characteristic discharge, eventhough it is known that other parameters such as slope, sediment size and sediment discharge caninfluence the relationship.

Several investigators have worked on developing such empirical relationships between geometricparameters and discharge; a few among them are Jefferson, Carlson, Inglis, Leopold and Maddock,Dury and Williams. They have shown and confirmed that simple power type relationships can beobtained between geometric parameters and discharge viz. D, R, ML, MB ~ Qm. All these relationshipshave been developed to predict the geometrical parameters for known discharge. On the other hand, inpalaeo hydrology, these relations are used to predict characteristic discharge for observed characteristicsof palaeo channel. Hence, the accuracy of these equations can be much different than that given byauthors when discharge predictions are made from these equations. The palaeo channels commonlyappear in the form of (1) exposed cross-sections, (2) abandoned channels on the earth’s surface and (3)rarely as exhumed (or buried) channels. Based on such exposures palaeo fluvial estimates i.e. streamflow of the former channels and channel characteristics can be made from (a) palaeo channel bedsediments (particle size, dune height, etc.), (b) palaeo channel plan-form properties (ML, sinuosity etc.)(c) palaeo channel cross-sectional features e.g., bankful width and (d) palaeo drainage features e.g.stream length, basin area etc. A large number of investigators (see Williams 1986) have dealt with use of(b) and (c) for palaeo fluvial estimates.

One question that needs to be discussed is out of the mean annual discharge Qma, bankful dischargeQb and mean annual flood Qmaf , which one should be used in finding the relationship between dischargeand channel characteristics ? The use of bankful discharge Qb seems to be justified because manyauthors believe it to be the channel-forming discharge, and further it value lies between mean annualdischarge Qma and mean annual flood Qmaf i.e. Qma < Qb < Qmaf. Also, the bankful stage is the onlycharacteristic stage that can be determined on the basis of well-preserved channel or meanderingchannel. It must further be emphasised that these equations being empirical and based on limited data,the accuracy of prediction would depend on the size of the sample and the climatic zone from which thesample is taken.

River Morphology264

Palaeo Velocity DeterminationOne of the simplest method of determination of mean flow velocity U for specified depth D or hydraulicradius R is Lacey’s equation

U = 11 D0.67 S0.33 ...(8.4)

where S is the water surface or channel slope. This is based on 188 observations on canals and riverswith sandy beds. Bray (1979) applied it to 67 gravel and cobble bed rivers for a discharge of 2 yearreturn period and found it to give velocity estimates with a standard deviation of 30 percent. Thisequation has the advantage that it does not require estimation of resistance coefficient as in the case ofequations of Manning, Chezy or Darcy-Weisbach, namely

Manning U = 1 2 3 1 2

nR S/ / ...(8.5)

Chezy U = C RS ...(8.6)

Darcy-Weisbach U = (8 / ) /g RS f 1 2 ...(8.7)

The main difficulty in using the above three equations is regarding correct estimation of Manning’sn, Chezy’s C or Darcy-Weisbach friction factor f. Chow (1959) and Benson and Dalrymple (1967) havediscussed about estimation of Manning’s n based on a base value of n and further increments in it toaccount for vegetation, channel alignment etc. However, such refinement in case of palaeo studies maynot be warranted and estimation of n, C or f by simples equation would suffice.

On the basis of analysis of 1352 measurements for the Odra river basin in Poland, Rotnicki (1983)proposed the equation

U = 0 791 2 3 1 2. / /

nR SF

HIK +0.141 ...(8.8)

with a standard error of 12 percent. Here slope was obtained from topographic maps.

Palaeo Discharge DeterminationRotnicki (1983) has proposed a modified version of the above equation to predict discharge at aparticular instant of time as

Q = 0 921 2 3 1 2. / /

nAR SF

HIK + 2.362 ...(8.9)

with a standard error varying from 7 to 26 percent depending on the discharge.

Williams (1988) used 233 river cross sections from a variety of environments and developed theempirical equation for bankful discharge Qb.

Qb = 4.0A Sb1 21 0 28. . ...(8.10)


where Ab is flow area at bankful stage and S is the slope. This is applicable for 0.5 £ Q £ 28 320 m3/s, 0.7£ Ab £ 8510 m2 and 0.000 041 £ S £ 0.081. For braided channels Cheetham (1980) has analysed Leopoldand Wolman’s data and proposed the equation

Qb = 0.000 585 S–2.01 ...(8.11)

for 0.0000 66 £ S £ 0.003In the case of palaeo fluvial studies Williams (1988) prefers to use average daily flow for a number

of years Q in m3/s. He quotes the equation of Osterkamp and Hedman for 252 sites of variousenvironments in West Central USA,

Q = 0.027Wb1 71. ...(8.12)

where Wb is the bankful width in m. This is applicable in the range 0.8 £ Wb £ 430 m. It may bementioned that Osterkamp and Hedman realised that the size of bed and bank material would affect thecoefficient in the above equation and have given their values in a tabular form (see Williams 1988).Schumm (1972) analysed data of 33 sites in the Great Plains of USA and three sites on theMurrumbidgee River in Australia. His data yields the equation

Q = 0.029W Db1 28 1 10.

max. ...(8.13)

Cariston (1965) used data for 31 rivers in Central United States and related meander wavelength ML

to Q as

Q = 0.000017ML2 15. ...(8.14)

which is applicable to meandering rivers with 145 £ ML £ 15,500 m.

Some investigators have used flood data at a gauging station and related flood discharge of a givenreturn period to the bed width B, meander wave length ML, cross sectional area, A and river sinuosity Si.Thus according to Dury (1976, 1977) analysis of 135 data points of un-braided under-fit streams gavethe following equation

QB

QM

Q A S

L

i

1 58

1 81

1 58

1 81

1 581 09

2 99

32 857

0 83

.

.

.

.

..

.

.

.

=FHG

IKJ

=FHG

IKJ

=

U

V

||||

W

||||

...(8.15)

When the values of B. ML, A and Si are known, Q1.58 can be determined from

Q =

B MA SL

i2 99 32 8570 83

3

1 81 1 811 09

. .( . )

. ..F

HGIKJ

+FHG

IKJ

+L

NMM

O

QPP

...(8.16)

River Morphology266

Palaeo Velocity and Palaeo Discharge in Gravel-bed RiversMaizels (1983) has stated that in the case of gravel-bed rivers it is preferable to assume that criticalconditions prevail at bankful stage. If d is the characteristic size of bed material, for coarse sedimentcritical shear stress will be given by Shields’ function

t0c

s d( )Dg= 0.056

or for Dgs = (1.65 ́9787), toc = 0.092d ...(8.17)

while for streams with 10 percent suspended sediment concentration

toc = 0.078d ...(8.18)

Knowing the palaeo channel slope S, critical depth Dc is obtained as

Dc = 0.092d S–1 or 0.078dS–1 ...(8.19)

The flow depth can also be determined from geomorphic evidence of high water levels, bankfuldepth from the thickness of sedimentary deposits or from field measurements of exposed palaeochannels. Maizels found that for a series of 69 palaeo channels on the abandoned West Greenlandcomputed critical depth Dc was greater than the observed depth D and the ratio D/Dc was highlyvariable, its mean value and standard deviation for clear water, and sediment laden flows being (0.5 and0.44) and (0.83 and 0.49).

Once Dc and S are known, Manning’s n can be found using either Strickler’s equation

n = 0.039d501 6/ ...(8.20)

or Limerinos equation

n = 0 113

116 2

501 6

84

.

. log

/d

D

d+

FHG

IKJ

...(8.21)

or Darcy-Weisbach friction factor f using

f = 0.113D

dc

50

1 3FH

IK

/

..(8.22)

and velocity Uc determined. Some other equations discussed in Chapter VII can also be used.Maizels has discussed the following four methods of palaeo discharge determination.(1) Empirical discharge equations relating mean annual flood discharge, mean annual discharge or

bankful discharge to the channel dimensions or channel form parameters(2) Empirical drainage area-discharge relations such

Q = aAb ...(8.23)


(3) Relations of the type Q as a function of S as proposed by Cheetham (1976) for Leopold andWolman’s braided river data

Qb = 0.000 585 S–2.01 ...(8.24)

(4) Regime type relations in which bankful discharge is related to width or depthMaizels has opined that none of these methods is very useful for coarse-bed palaeo channels; hence

he recommends those methods based on palaeo velocity determination. Further, he made palaeodischarge computations from palaeo velocity determined by five methods namely

(1) using Chezy’s equation with C = (8g/f )1/2

(2) using Manning’s equation with n = 0.039 d501 6/

(3) Manning’s equation with n obtained from Limerinos equation

(4) Darcy-Weisbach equation with f = 0.113D

dcF

HIK

1 3/

(5) Darcy-Weisbach equation with f obtained from White-Colebrook equation and then dischargeobtained as Qc = UcDW.

The discharges Qc obtained by these methods for 69 palaeochannels were compared. On the basis ofthis comparison Maizels recommended that for palaeo channels with coarse gravel-bed, Manning-Limerinos approach is better if channel widths are uncertain, whereas Darcy-Weisbach approach isbetter for well defined channels.

8.6 PALAEO HYDROLOGIC STUDIES IN INDIA

The palaeo hydrologic studies in India are primarily related to establishing palaeo flood records of somerivers in Central and Western India. The method used for these studies is the analysis of slack waterdeposits. Slack water deposits (SWD) are fine-grained sand and silt deposit that falls rapidly out ofsuspension during large floods in protected areas, where the fall velocity is markedly reduced. Suchdeposits take place in stable bed rock canyons expansion and contractions, back flooded tributaries,meander bends, caves, and abrupt channel. The upper layers of SWD closely approximate the actualstage of flood peak. These depths provide a lot of information on palaeo floods. The age of the depositsare determined by radiometric dating of associated organic or archaeological material. It is shown thatthe thickness and grain size of SWD is directly proportional to the flood magnitude. The tops of SWDgenerally provide a minimum estimate of flood peak stage and hence it is possible to estimate minimumpeak discharge with each deposit. In the last two decades some studies have been conducted on fiverivers in Central and Western India with the following objectives in mind : (i) to identify temporalpatterns of large floods during late Holocene; (ii) to identify periods of high and low floods; and (iii) toexamine the relationship between flood regime and palaeo climate.

The rivers studied (see Kale 1999) have been the Narmada at Punasa, the Godavari at Papikonda,the Krishna at Srisailam, the Tapi at Ghuttigarh Khapa and the Luni river at Bhuka. The maximumthickness of SWD ranged from 2.5 m to 10.5 m and 11 to 37 floods are documented in these deposits.Tributary mouths are the most common geomorphic sites for SWD. The slack water deposits at threeplaces on the Luni river near Bhuka in the Tahr desert in North Western India as reported by Kale et al.(2000) are shown in Fig. 8.3. These deposits were dated using luminescence technology. The textural

River Morphology268

and stratigraphical analysis of SWD indicated that near the tributary channel there is higher variabilityin sediment size and predominance of finer sediment units. With increasing distance and elevation thepercentage of sand increases and the sorting improves. Change in sedimentological and stratigraphicalcharacteristics distinguish the individual units. These characteristics imply sediment deposition by floodwaters and also suggest that the sediments deposited at higher level were emplaced by higher magnitudefloods and some of the sediments closer to tributary channel were also deposited by moderate magnitudefloods. The deposits and their dating suggest that the river has experienced at least 17 extreme floods inthe last millennium. Evidence at this site also suggests that no floods comparable in magnitude to July1979 mega flood have occurred during this period. This observation is in conformity with palaeo floodrecord of central India. Comparison of long-term monsoon rainfall series for the Luni basin and theregion reveals a clear link between the two and indicates that the clustering of large floods in the last fewdecades and during the medieval warming period is a regional phenomenon associated with wetterconditions. Long-term fluctuations in Indian monsoon rainfall in the past have been explained in termsof large climatic changes in the Asian monsoon region. For completeness of information it may bementioned that the river Luni at Gandhar has a catchment area of 35 000 km2, width 120-150 m anddepth 4 to 10 m. Maximum one-day rainfall of 100 years return period is 200 to 257 mm. The 1979 megaflood had a discharge of about 4300 m3/s. The flood of 1990 was of similar magnitude.

Kale et al. (1993) have examined the SWD on the Choral river near Barjar in Central NarmadaBasin, India. At several locations, sequences of fine-grained sandy flood deposits have been preserved

Fig. 8.3 Slack water deposits on the Luni river (Kale et al. 2000)


on the channel margins. The stratigraphic studies of the deposits using radio carbon dating revealed that510 + 135 B.P. record of floods is preserved in SWD. It was found that during this period dischargesgreater than 4500 m3/s must have occurred. At least 7 flood units separated by scree deposits, slopewash and charcoal were obtained; see Fig. 8.4. Geomorphic investigations revealed the presence ofboulders with intermediate axis between 23 and 42 cm. Such studies have been carried out on theNarmada near Punasa, the Godavari at Papikonda, the Krishna at Srisailam, and the Tapi at GhuttigarhKhapa and the Luni at Bhuka (see above). The maximum thickness of SWD ranged from 2.5 m to 10.5m and 11 to 37 floods are documented in these deposits.

Fig. 8.4 Slack water deposits on the Choral river near Barjar (Kale et al. 1993)

Figure 8.5 given by Kale et al. (2000) summarises the palaeo flood chronology for Central andWestern India during the late Holocene climatic changes. The top scale indicates C-14 years beforepresent (B.P.). The second scale shows the global temperature changes (RW – Roman Warm, DAC –Dark Ages Cold, EMC – Early Medieval Cool, MW–Medieval Warm, LIA – Little Ice Age, MOW –Modern Warm). Below these are given the chronology of palaeo floods in the Narmada, the Luni and theGodavari. This study shows distinct century scale variations in flood frequency and a noteworthyclustering of large floods during the late Holocene period. The study further indicates a period ofsignificantly reduced frequency of large floods during late Medieval and Little Ice Age periods (i.e.1500 A.D. to 1800 A.D.), and an enhancement in the magnitude and frequency of large floods in thepost 1950 period. The last one thousand years of relatively better resolutions of palaeo flood recordsdemonstrates a good association between palaeo floods and late Holocene climatic changes recognisedin wide spread area of the world. Hence the authors concluded that the century scale variations in floodfrequency and magnitude are linked to long term variations in the monsoon precipitation which are in

C0

C1

C2

C3

C4

C6

Rubble

RubbleShells

Rubble

Rubble

Slope wash

Rubble

Rubble

5170 ± 135 Yrs BP

Sand

Charcoat

150

100

50

0

cmFloodUnits

1

2

3

4

6

Lithosection

SWD- ChoralLocation map

0 4 8 kms

KAMARKAMAR

BARJAR

CHO

RALBARJAR

22°

15

N

¢

74°0 N¢

River Morphology270

turn connected with large scale shift in global circulation patterns and ENSO (El Nino SouthernOscillations) activity.

Similar studies about obtaining monsoonal activity have been carried out by analysing the depositsin the lakes, studying ice cores in glaciers, and deposits in Arabian Sea. Kumar Sagar (1995) studied thelake deposits in Jammu and Kumaon regions. The rates of deposition of sediment were assumed to beproportional to yearly rainfall. This deposition rate varied from 0.55 mm to 1.05 mm/year in the threelakes in Kumaon region while in Naukuchital it was between 0.16 mm to 3.08 mm/year. Kashmir lakesshowed the deposition rate of 5.5 mm for the top 30 cm. A multidisciplinary proxy palaeo climaticinvestigation in Mansar Lake, Jammu indicated periods of enhanced rainfall between 580 B.C. and 300A.D. This period is indicative of wet humid phase. From 300 A.D. to 1400 A.D. the area experienced arelatively dry and arid phase with Medieval warming.

Thompson et al. (2000) recovered three ice-cores from the Desuopu glacier, Tibet using anelectromechanical drill. Their lengths varied from 149.2 m to 167.7 m at about 7000 m above mean sealevel. These cores were analysed over the entire length for their oxygen isotope ratio, chemicalcomposition, and dust concentration. In addition they were analysed for hydrogen isotope, chloride(Cl–), sulphate (SO4

–) and nitrate (NO3–). The bulk of annual precipitation in the Himalayas arrives

during the summer monsoon season and at Desuopu it is net 1000 mm water. The high annualaccumulation allows preservation of distinct seasonal cycles. These studies revealed that the site issensitive to the fluctuations in the intensity of South Asian monsoon, reduction in monsoonal intensityare recorded by dust and chloride concentration. Deeper and older sections of Desuopu cores suggestsmany periods of drought in the region, but none have been of greater intensity than the greatest recordeddrought during 1790-1796 A.D. of last millennium. 20th Century increase in anthropogenic activity inIndia and Nepal, upwind from this site, is recorded by doubling of chloride concentrations and four foldincrease in dust. Like other ice cores from Tibetian Plateau, Desuopu suggests large scale plateau-wide20th century warming trend that appears to be amplified at higher elevations.

Fig. 8.5 Palaeo floods chronology for Central and Western India (Kale et al. 2000)


Sarkar et al. (2000) collected sediment cores from Arabian sea in water depths ranging from 280 mto 1680 m and analysed O18 and C13 composition of foraminifera. It appears that excess of evaporationover precipitation steadily appears to have decreased during the last 10,000 to 2,000 years, mostprobably due to increasing trend in summer monsoon rainfall, contrary to land-based palaeo climaticdata from the region, which indicates onset of aridity around 4000 years ago. This result is consistentwith the hypothesis that significant spatial variability in the monsoon rainfall observed today waspersistent during most of Holocene. The analysis of data also indicated significant periodicities of 700and 1450 years. Similar periodicities have also been reported from North Atlantic and Arabian seasediment cores.

8.7 FLUVIAL PALAEO HYDROLOGIC STUDIES IN INDIA

As regards fluvial palaeo hydrologic studies in India, mention may be made of the efforts to trace thecourse of the river Saraswati about which reference is found in ancient Indian literature. About onehundred years back the British engineer C.F. Oldham sparked the modern quest for the river Saraswatiby questioning why the seasonal river Ghaggar should have a width of about three kilometres in placesunless it earlier occupied the bed of a wider river. Since then wind blown sand dune area of Gantiyaljinear Longewal has been studied extensively by the specialists in remote sensing, hydro geologists,archaeologists and the historians by taking undisturbed cores of sediment plus water from a depth of 70m below the ground surface to trace the course of lost river Saraswati, along which prehistoric cultureflourished in the historic past. The river course has been studied not only from the historic point of viewbut also with the hope that it may ultimately lead to providing sweet water for drinking and irrigationpurposes in otherwise saline area. The records indicate that the river disappeared around 1500 B.C.while the decline started about 3700 years ago. Two logical questions that need to be answered in thisregard are: What courses did the river follow? and Why did it dry up ?

In order to trace the river course water samples collected from underneath were tested using carbondating technique and it was estimated to be 3000-4000 B.P. (Before present) old, i.e., of the Rig Vedicera. Rough course of some buried channels has been traced and sediment samples collected to determinetheir age; the river course has also been confirmed from satellite imageries. Along the river the drillinghas been done to provide sweet drinking water, which is obtained at a depth of 30 m below the surface.

The river course can be clearly seen from marks of palaeo channels as wide as 12 km. One hundredand seventy five archaeological sites have been found along the alluvial plain of the Ghaggar river.Since ancient times the civilisations flourished along the river providing water for drinking andirrigation, it is argued that the Ghaggar must have been the mighty Saraswati of the Vedic period. TheSaraswati was originally fed by two show-fed sources namely Bunderpunch massif in the Garhwal andKapalshikar near Manasarovar in Shivaliks. At Pipli in Haryana the Saraswati probably crossed theGrand Trunk Road of the present and the Saraswati statue is erected there. There is reference inMahabharat that Kurukshetra was to the south of the Saraswati and to the north of the Drashadvati. Theriver is traced from West Garhwal in the Himalayas to the Gulf of Khambat in Gujarat.

Various shifting courses of the Saraswati, as constructed by Ghosh et al. (1983) from all theavailable evidence, are shown in Fig. 8.6. The oldest course obtained by joining abandoned, buriedchannels passed through the present cities of Nohar, Surjansar, Samrau and Panchpadra (course 1). Withthe onset of aridity during Pleistocene and advancement of sand from south-west, the river started

River Morphology272

shifting and eventually followed the course 2 towards west. At that time the present cities of Sirsa,Lunkaransar, Bikaner, Samrau and Panchpadra were on its right bank. Probably during the earlyHolocene period, there was another shifting of the Saraswati towards west between 10,000 and 3800B.C. The two courses followed are shown as course 3. It turned towards west near Nohar and flowedthough Rangamahal, Suratgarh, Anupgarh and Sakhi; hence it severed its confluence with Luni atPanchpadra and discharged into Rann of Kutchh through a river course called Hakra or Nara (Pakistan).Due to increased Aeolian sand that the river had to carry during this period the river aggraded andultimately took another course through Jakhal, Sirsa, Hanumangarh, Pilibangan, Suratgarh, Anupgarhand Sakhi (course 4). Further around 3800 B.C. the Saraswati further made a westward shift atAnupgarh and joined Indus drainage system in Pakistan (see course 5).

What caused the disappearance of the Saraswati? Because of tectonic effects the old Arawali hillscut off the head waters of the Saraswati. The branch of river the Chambal cut deep into the strata

Fig. 8.6 Old and new courses of the Sarswati river


northwards and gradually diverted water of the Saraswati first by the Yamuna and then by the Sutlej.The new channel migrated eastward became the Yamuna; similarly the Sutlej migrated westward andjoined Indus. This diversion caused a drastic reduction in the flow of Saraswati. When the Saraswatiflowed in south-westerly direction, it was flowing against north easterly moving sand advance in Thardesert. Therefore, the Saraswati river could not overcome such sand advance and hence started driftingtowards the north with rotational migration in clockwise direction until it became buried in theAnupgarh plains.

References

Baker V.R. (1983) Large Scale Palaeo Hydrology. In Background to Palaeo hydrology (Ed. Gregory, K.J.). AWiley Interscience Publication, John Wiley and Sons, New York, Chapter 20, pp. 453-478.

Benson M.A. and Dalrymple T. (1967) General Field and Office Procedures for Indirect DischargeMeasurements. Technical W.R. Investigation (USGS) Book 3, Chapter A1, pp. 1-30.

Berglund B.E. (Ed.) (1986) The Handbook of Holocene Palaeo ecology and Palaeo hydrology. John Wiley andSons, Chicester.

Bray, D.I. (1979) Estimating Average Velocity in Gravel-Bed Rivers. JHD, Proc. ASCE, Vol. 105, HY-9, Sept. pp.1109-1122.

Cheetham G.H. (1976) Palaeo Hydrological Investigations of River Terrace Gravels. In Geo-archaeology (Eds.Davidson, D.A. and Shakley, M.L.), Duckworth, London, pp. 335-344.

Chow V.T. (1959) Open Channel Hydraulics. McGraw Hill Book Co., New York.

Dury G.H. (1976) Discharge Prediction, Present and Former, From Channel Dimensions. Jour. of Hydrology, Vol.30, pp. 219-245.

Dury G.H. (1977) Underfit Streams: Retrospect, Perspect and Prospect. In River channel Changes (Ed. Gregory,K.J.). A Wiley Interscience Publication, John Wiley and Sons Ltd., Chicester, Chapter 18, pp. 281-289.

Garde R.J. and Kothyari U.C. (1986) Erosion in Indian Catchments. Proc. 3rd International Symposium on RiverSedimentation. The University of Mississippi (USA), pp. 1249-1258.

Ghosh B., Kar A. and Husain Z. (1983) Comparative Role of the Aravalli and Himalayan River Systems in theFluvial Sedimentation of the Rajasthan Desert. In Geomorphology (Ed. Dixit K.R.) Heritage Publishers, NewDelhi, pp. 209-213.

Gregory K.J. (Ed) (1983) Background to Palaeo hydrology. A Wiley Interscience Publication, John Wiley andSons, Chicester.

Gregory K.J., Lewin J. and Thornes J.B. (Eds) (1987) Palaeo hydrology in Practice: River Basin Analysis. AWiley Interscience Publication, John Wiley and Sons, Chapter 1.

Kale V.S. (1999) Late Holocene Temporal Patterns of Palaeo floods in Central and Western India. Man andEnvironment, Vol. 24, No. 1, pp. 109-115.

Kale V.S., Mishra S., Baker V.R., Rajguru S.N. Enzel Y and Ely L. (1993) Prehistoric Flood Deposits on the CoralRiver, Central Narmada Basin, India. Current Science, Vol. 65, No. 11, pp. 877-878, Dec. 10.

Kale V.S., Singhvi A.K., Mishra P.K. and Banerjee D. (2000) Sedimentary Records and Luminescene Chronologyof Late Holocene Palaeo floods in the Luni River. Catena, Elsevier Publishers, Vol. 40, pp. 337-358.

Kothyari U.C. and Garde R.J. (1991) Annual Runoff Estimation for Catchment in India. JWRPM, Proc. ASCE,vol. 117, No. 1, Jan/Feb., pp. 1-10.

River Morphology274

Kumar Sagar M.G. (1995) A Comparative Study of Monsoonal and Non-Monsoonal Himalayan Lakes, India.Proc. 15th International C14 Conference (Eds. Cook G.T., Harkness D.D., Miller B.F., and Scott E.M.) Vol.37, No. 2, pp. 191-195.

Lacey G. (1934). Uniform Flow in Alluvial Rivers and Canals. Min. of the Proc. Inst. C.E. (London), Vol. 237, Pt.1, pp. 421-453.

Langbein W.B. et al. (1949) Annual Runoff in the United States. USGS, Circular-54. 14 p.

Langbein W.B. and Schumm S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans.A.G.U., Vol. 39, pp. 1076-1084.

Leeder M.R. (1973) Fluviatile Fining – Upward Cycles and the Magnitude of Palaeochannels. Geol. Magazine,Vol. 110, No. 3, pp. 265-276.

Leopold L.B. and Miller J.P. (1954) Post Glacial Chronology for Alluvial Valleys in Wyoming. USGS WaterSupply Paper 1261, pp. 61-85.

Maizels J.K. (1983) Palaeo velocity and Palaeo discharge Determination of Coarse Gravel Deposits. InBackground to Palaeo hydrology (Ed. Gregory K.J.) A Wiley Interscience Publication, John Wiley and SonsInc., New York, Chapter 5, pp. 101-139.

Noble E.L. (1965) Sediment Reduction Through Watershed Rehabilitation, USDA, Misc. Publ. 970, pp. 114-123.

Rotnicki K. (1983) Modelling Past Discharges of Meandering Rivers. In Background to Palaeo hydrology (Ed.Gregory K.J.) John Wiley and Sons Inc., New York, Chapter 14, pp. 321-346.

Sarkar A., Ramesh R., Somayajulu B.L., Agnihotri R., Jull A.J.T. and Burr G.S. (2000) High Resolution HoloceneMonsoon Record from Eastern Arabian Sea.. Earth and Planetary Science, Letters, Vol.117, pp 209-218.

Schneider S.H. and Root T.L. (2000) Climate Change. Available on Internet.

Schumm S.A. (1965) Quaternary Palaeo hydrology. In the Quaternary of the United States (Eds. Wright H.E. andFrey D.G.) Princeton University Press, Princeton. pp. 783-794.

Schumm S.A. (1977) The Fluvial System. A Wiley Interscience Publication, John Wiley and Sons , Chicester.

Thompson L.G., Yao T., Mosley-Thompson E., Davis M.E., Henderson K.A. and Lin P.N. (2000) A HighResolution Millennium Record of the South Asian Monsoon from Himalayan Ice Cores. Science Magazine,Vol. 289, No. 5486, pp. 8.

Williams G.P. (1978) Bankful Discharge of Rivers. W.R. Res. Vol. 14, No. 6, pp. 1141-1154.

Williams G.P. (1988) Bankful Palaeo fluvial Estimates from Dimensions of Former Channels and Meanders. InFlood Geomorphology (Eds. Baker V.R. Kochel R.C. and Patton P.C.) A Wiley Interscience Publication, JohnWiley and Sons, New York, Chapter 19, pp. 321-334.

9C H A P T E R

Bed Level Variation in Streams

9.1 INTRODUCTION

The concept of a graded stream or stream in equilibrium has been introduced in Chapter 4. The balancebetween yearly water discharge Q, yearly bed material discharge Qs, channel slope S, and the bedmaterial size d for such streams is expressed qualitatively by Lane’s balance analogy (Lane 1955)

QS~ Qs d ...(9.1)

This qualitative statement is illustrated in Fig. 9.1 and is valid when channel plan-form and channelwidth remain the same. This equilibrium can be disturbed by natural causes or man-made changes, andthen the channel adjusts to the new conditions by either increasing the slope over a reach (known asaggradation), or by decreasing the slope over a reach (known as degradation). Thus, if Qs increasedkeeping Q and d the same, the slope will increase by sediment deposition so that with the increasedslope and unaltered Q and d, the stream can carry the increased sediment load. In a similar manner, if Qis increased keeping Qs and d the same, a smaller slope will be required to carry this sediment load; thisis achieved by lowering of the bed levels resulting in reduction in slope and thus degradation results.

Since a stream in equilibrium must satisfy continuity equations for flow and sediment, andresistance and sediment transport relationships, one can get the exact form of Eq. (9.1) if choice is madeof resistance and sediment transport relationships. Assuming Q and d to remain unchanged along thelength of the stream and using Manning’s and Du Boys equations, one can write

Q

Q nD S

Q BqS

ds s

=

= =

U

V

|||

W

|||

BDU

=1

BD

constant BD3/4

( ) / /2 3 1 2

2 2

...(9.2)

River Morphology276

Eliminating D from these equations, one gets (Garde and Ranga Raju 2000)

Q S Q d B n

Q S Q ds

s

6 7 7 5 3 4 1 5 6 7

6 7 7 5 3 4

/ / / / /

/ / /

~

~

- UVWor

...(9.3)

if channel width B and Manning’s n are assumed to be constant. Similar analysis has been presented byJensen et al. (1979) and Klaassen (1995). If some other equations were used for resistance and rate ofsediment transport, the exponents of Q, S and d would have been slightly different; however Lane’sbalance analogy would still be valid qualitatively.

If the rate at which sediment entering a given reach of the stream is less than that at which it is goingout, the excess sediment will be picked up from the bed and banks, and there will be lowering of bedlevel unless the bed is non-erodible; this is known as degradation or retrogression. Thus for degradation

to occur ¶

¶

Q

xs must be positive. On the other hand, if the rate at which sediment enters a given reach of

a stream is greater than the rate at which it goes out, the channel bed experiences deposition of sediment;

this is known as aggradation. For aggradation to occur ¶

¶

Q

xs must be negative. Aggradation or

degradation occurs over large lengths and both are slow processes. Degradation particularly mayproceed for years before it becomes evident. Aggradation and degradation taking place upstream anddownstream of large dams respectively are well studied and documented.

When alluvial streams are partially obstructed by hydraulic structures such as bridge piers, guidebunds, spurs or abutments, the local flow pattern around the structure is drastically changed causinghigh velocities and shear stresses in the vicinity of the structure causing local lowering of the bed level.This is known as local scour. Local scour occurring around structures such as bridge piers can endanger

Fig. 9.1 Lane’s balance analogy

Aggradation DegradationSQ Qs d

Bed Level Variation in Streams 277

their foundations causing bridge collapse. This chapter is devoted to the discussion of degradation, localscour around bridge piers, aggradation, and aggradation upstream of dams.

DEGRADATION

9.2 TYPES OF DEGRADATION

Mention of the phenomenon of degradation is found in Irrigation Manual by Mullins published in 1889,in his book on Irrigation works in India by Buckley in 1905, and in U.S.A. by Gilbert (1917) when heclearly differentiated between scouring and degradation. Degradation occurring in a stream can proceedeither in the downstream or in the upstream direction depending on the basic cause of degradation(Galay 1980, 1983).

If the reduction in the slope is caused by reduction in Qs, reduction of d or increase in Q at theupstream end, downstream-progressing degradation will occur. On the other hand, if an increase inslope is imposed at the downstream end, upstream Q, Qs and d remaining the same, upstream-progressing degradation will result. Upstream-progressing degradation occurs if the level of the lake inwhich the river discharges drops suddenly. It is found that, in general, upstream-progressing degradationtakes place at a much faster rate than the downstream-progressing degradation, because in the formercase, increase in slope results in substantial increase in the bed material discharge. In the case ofdownstream-progressing degradation, the slope is progressively reduced and the bed material dischargeis asymptotically reduced to zero; hence, it takes much longer time. Occurrences of downstream andupstream-progressing degradation are shown in Fig. 9.2.

Fig. 9.2 Upstream and downstream progressing degradation (Galay 1980)

Note: D/s = downstream progressing degradationU/s = upstream progressing degradation

U/s

U/s

D/s

D/sD/s D/s D/s

D/s

D/s

D/sD/sD/s

U/s

U/s U/s

U/sU/s

U/s

U/s

U/sU/s

U/s

U/sU/s

DegradationProgress

River SituationTributaryNo Tributaries Tributary with D/s

River Morphology278

The composition of bed material of the degrading stream plays an important role in the process ofdegradation. Consider degradation taking place downstream of a large capacity reservoir which trapsmost of the sediment load carried by the stream. If the bed material is uniform and the stream slope isrelatively large, the flow deficient of sediment load picks up more sediment from upstream reaches andrelatively less from the downstream reach. As a result, stream slope reduces by rotation of stream bedabout some downstream control where the water level is held constant. When the slope has reduced tothe extent that shear stress on the bed is critical for that size, degradation will stop; see Fig. 9.3. This isknown as rotational degradation.

Fig. 9.3 Definition sketch for rotational degradation

However, if the bed material of the degrading stream is non-uniform and the shear stress exerted bythe flow is such that all the particles on the bed are moving, initially rotational degradation will takeplace thereby reducing the shear stress acting on the bed. When the reduced shear stress to2 is equal tothe critical shear stress for the d80 or d90 of the bed material, the coarsest fractions of the bed materialwhich could not move start accumulating on the surface. Fifty to sixty percent areal coverage by suchmaterial on the surface forms an effective protective armour coat which stops further reduction in slopeand hence rotation of the bed. Now degradation takes place by the removal of finer particles atessentially a constant slope. This is known as parallel degradation. For given parent material, any shearstress smaller than to2 will give one size distribution of armour coat and increasing shear stress willcoarsen the armour coat. The armour coat is coarsest at to2 for a given non uniform bed material.

Harrison (1950) has studied the armour coat formation. He found thati) Progressive coarsening of surface layer in armour coat development causes an increase in the

effective roughnessii) A layer of non-moving particles of one particle size thickness is effective in preventing erosion.iii) The non-moving particles in the pavement arrange themselves in a characteristic shingling

formation.

iv) As per Einstein’s bed-load theory Dg s id

t0

= 27 gives the limiting size beyond which there is no

movement.


The concept of parallel degradation was first introduced by Gessler (1965). Gessler conductedexperiments on degradation using non-uniform sediment at a constant slope and the experiments werestopped when the bed was armoured resulting in practically no movement. The surface layer wassampled and the ratio of fraction of sediment of a given size range di in the top layer of armour coat to itsfraction in the parent material was determined. This ratio pi was taken as the probability of the sizeremaining stationary for the applied shear stress t0. This value was also interpreted as the probabilitythat instantaneous shear stress on the bed was smaller than the critical shear stress for that size. Theaverage shear stress was considered critical for that size fraction for which pi was 0.50. In this way thecritical shear stress curve similar to Shields’ curve was prepared. This curve is shown in Fig. 9.4. When

t

t0

0c

obtained in this manner was plotted against pi on normal – probability scale, it yielded a straight

line as shown in Fig. 9.5 with a standard deviation of 0.57, thereby indirectly indicting that shearfluctuations on the bed follow normal distribution. Later studies by Little and Mayer (1972) and Davies(1974) have given slightly smaller values of the standard deviation viz. 0.43 and lower value of criticalshear stress for coarser material. Use of Figs. 9.4 and 9.5 enables one to compute size distribution ofarmour coat for parallel degradation for known parent bed material. Gessler found that for grain size

having Dg s id

t0

greater than 50, pi can be taken as 100 percent.

Figure 9.6 shows qualitatively the regions of no motion, parallel degradation and rotationdegradation in relation to size distribution of bed material and initial shear stress. Here da is the averagesize of the bed material size. According to Egiazaroff (1965) if applied shear stress is less than thecritical shear stress for di = 0.4 da, there will be no movement; if the shear stress is greater than thecritical shear stress for di = 0.4 da and less than the critical shear for di = 3.0 da parallel degradation

Fig. 9.4 Gessler’s criterion for incipient motion

River Morphology280

Fig. 9.5 Relation between probability of movement Pi and dimensionless bed shear stress t

t0

0c

(Gessler 1995)

Fig. 9.6 Regions of no motion, and parallel and rotational degradation

would result. If applied shear is greater than critical shear for di = 3.0 da, rotational degradation results.The demarcating value of shear stress between parallel and rotational degradation has been obtained byMittal (1985) by using Gessler’s method for some hypothetical mixtures. The mean curve between


t

g

0

501

i

s dD and Kramer’s uniformly coefficient M defined as M =

d p

d p

i i

i i

D

D

0

50

50

100

åå

along with available data

plotted on it is shown in Fig. 9.7. The coordinates of the mean curve in Fig. 9.7 are given in Table 9.1.

Table 9.1 Variation of t

goi

s 50idD with M (Mittal 1985)

M 0.20 0.30 0.40 0.80

t

goi

s 50idD0.19 0.10 0.06 0.04

Fig. 9.7 Variation of t

goi

s 50idD with M (Mittal 1985)

Little and Mayer (1972) have proposed the equations

d

da

i gi

50

50 s= 0.908

u

gs f

*

.

/

3

0 353

1r r -

F

HGG

I

KJJd i

...(9.2)

s

s

ga

gi

= 1.317 – 0.2458 sgi

River Morphology282

Here u* = t

roi

f

and sgi and sga are geometric standard deviations of parent material and armour

coat respectively.Using limited data Shen and Lu (1983) proposed the following equation for d50a

d

da

i

50

50

= 0.853. ¢F

HGIKJ

t

to

oc

sgi0.885 ...(9.3)

in which t¢o is the shear stress with respect to grain roughness and sgi is geometric standard deviation ofparent material of median size d50i.

Using Little and Mayer’s data and the data from San Luis Valley canals, Odgaard (1984) found thatthe size distribution of armour coat follows normal distribution. Recently Garde et al. (2004) have

plotted size distribution data for armour coat from a number of studies in the form of d

di

a50

vs percent

finer and found Odgaard’s conclusion to be true except for very small and very large values of d

di

a50

.

Here d50a is median size of the armour coat. The distribution has a standard deviation of 0.57. Hence, ifd50a can be determined for known size distribution of the parent material and known to, armour coat sizedistribution is known. Garde et al. (2004) have proposed the following equation for d50a

d

da

i

50

50

M = 0.3 + 1.361 exp. -

FHG

IKJ

R

S||

T||

U

V||

W||

1648

50

1 241

.

*

.

tD

dii

...(9.4)

Here M is Kramer’s uniformity coefficient of initial mixture, t* i = t

g0

50

i

s idD and D is depth of flow.

This equation is based on a large volume of data and is found to be more accurate than Eqs. (9.2) or(9.3).

9.3 DOWNSTREAM-PROGRESSING DEGRADATION

As mentioned earlier, downstream-progressing degradation is related to the changes in Q, Qs or d at theupstream end. The situations under which downstream-progressing degradation takes place arediscussed below.

Degradation Downstream of High Dams and BarragesWhen a high dam is constructed on a movable bed river, it traps a very large percent of the incoming bedmaterial load; this percentage can be as high as 95 percent. As a result, water released from the dam is


deficient in sediment load as compared to its sediment transport capacity. Hence the flow picks upsediment from the bed (and from the banks if bed is non-erodible) and the bed level goes down therebydecreasing the slope. The rate and extent of degradation depends on many factors such as flow releasesfrom the dam, downstream slope, size distribution of the bed material and its variation with depth,downstream control. Extensive observations have been made in U.S.A. and other western countries ondegradation occurring downstream of dams on several streams. In this connection papers by Stevens(1938), Hathaway (1948), Bondurant (1950), Vetter (1953) and Galay (1983) may be seen. Table 9.2gives the information on the extent and length of degradation, duration and bed material description forfew dams, Galay (1988) has observed that degradation across the stream may not always be uniform. Hementions the case of degradation below the Gardiner dam on the South Saskatchewan river in Canada,where at a section 1.6 km downstream of the dam about 200 m of the 1000 m width had experienced 2–3m lowering while it was much less in the rest of the channel width. This is likely to be due to non-uniform releases of flow from the dam as well as the non-uniformities in bed material across the width.

A brief discussion is necessary about the changes in bed level downstream of barrages in Indo-Gangetic plain of the Indian subcontinent, where thick alluvial strata exist. Barrage is a low–heightgated weir used to raise the water level so that canals can take off from the upstream of the barrage. TheIslam Weir on the Sutlej River failed due to excessive degradation. Two metres of degradation causedthe failure of part of the weir. It has been found that downstream of such weirs the bed degrades for a fewyears which is followed by aggradation. This occurs probably because of the manner in which the gatesare operated. The data on barrages in India, Pakistan and Egypt indicate that degradation of the order of0.8 m to 2.0 m has occurred in the past.

Table 9.2 Data on degradation downstream of high dams (Adapted from Garde 1955 and Galay 1983)

River Dam Degradationm Strata Length of Period ofdegradation km observation years

Saalach (Germany) Reichenhall 3.0 - 9.0 km up to confluence 21 with Saalach River

Missouri (U.S.A.) Fort Peck 1.5 Alluvial About 80 km 11.5

Wisconsin (U.S.A.) Praire Du Sac 2.3 Sandy - 18

South Canadian Conchas 3.1 Sand and 32 km 10(U.S.A.) gravel

Rio Grande (U.S.A.) Elephant Butte 2.1 to 2.4 -do- About 150 km 2

Wolf Creek (U.S.A.) Fort Supply 2.4 Sand - 4.5

Colorado (U.S.A.) Hoover 7.1 Sand and 111 km 14gravel

Colorado (U.S.A.) Imperial 3.1 -do- - 18

Yuba (U.S.A.) - 4 to 5.5 Gravel - 2

Yellow (China) Sanmexia 4 Fine sand 68 4

Mainstee (Canada) Junction 3.7 Sand and clay - 12

River Morphology284

Data on four weirs Khanki, Rupar, Rasul and Marala on the rivers the Chenab, the Sutlej, theJhelum and the Chenab respectively during the period 1891-1927 indicated (see Garde 1955) that therate of degradation varied from 3 cm/year to 24 cm/year while the rate of recovery ranged from 6 cm/year to 13 cm/year.

It may be mentioned that the degradation that has occurred on the Ratmau torrent in North Indiaover a period of 100 years has been well documented and discussed briefly in Chapter 11.

Increase in Water DischargeAn alluvial river will experience degradation if water discharge in the stream is increased by flowdiversion. Since increased flow with the same slope and sediment size has higher sediment transportcapacity, the flow picks up sediment from the bed and banks of the river, and degradation occurs; seeFig. 9.13(b). Such degradation has been observed by Kellerhals et al. (1977) on the Mattagami riverflood way (Adam Creek) in Ontario, Canada, and also on the Five Mile Creek in Wyoming (U.S.A.)where clear water flow was added to the creek from waste water of the irrigation project (Lane 1955).Change of land use, such as deforestation, can also increase flood discharge and cause degradation,however the extent of degradation would depend on the supply of sediment from the upper part of thecatchment. In a similar manner, an exceptionally high flood can cause lowering of stream bed in thedownstream direction. However, degradation occurring during high flood seems to depend on the natureof flood and sediment concentration hydrographs. Degradation will occur during the rising limb ofhydrograph if river is carrying relatively less sediment load compared to its capacity. Such lowering ofthe order of five metres occurred during 1933 on the Yellow river reach of about 50 km around Lungmen(Todd and Eliassen 1940).

Gravel MiningWhen sediment is removed from the channel bed for construction activity, the sediment transported bythe stream will get deposited in the depression created by removal of material, and hence the flowdownstream will have less sediment load compared to its capacity. As a result, degradation occurs in thedownstream reach. Such degradation of a few metres was observed on the Cherry Creek near Denver(U.S.A.) (Lane 1947). Similarly, extensive degradation along with local scour has been observed at amajor bridge in Canada by Cullen and Humes (see Galay 1983).

Storage of Bed MaterialDownstream-progressing degradation has also been found to occur below alluvial fans. As the riveremerges from a single steep channel from the mountainto the plain, it deposits most of its coarse bedmaterial on the alluvial fan and the river flows in multiple channels. When such channels join into asingle channel at the base of the fan, it is deficient in bed material load; hence, degradation can takeplace. Such degradation has been observed by Galay (1983) in Iran.

Degradation at Channel BifurcationsDownstream-progressing degradation also occurs at channel bifurcations. Consider a channel taking offfrom the main stream and further assume fifty percent of the flow is diverted. If the stream is carryingappreciable quantity of bed load, the diversion channel will carry a very large percent of bed load due toformation of secondary circulation at the bend. As a result the main branch will carry less bed load andwill experience degradation, while the branch may experience aggradation.


9.4 UPSTREAM-PROGRESSING DEGRADATION

If the water level of the lake or the sea into which the river discharges falls, an increased water surfaceslope is imposed on the river. Hence, the river picks up material from the bed to fulfill its increasedtransport capacity and degradation occurs. Such degradation has been observed in rivers in Iran andRussia due to lowering of Caspian sea level (Ananian 1961). Such degradation progresses upstream andif upstream flow and sediment load conditions remain the same, final degradation profile would beparallel to the original bed. If a tributary is joining such a degrading stream, the tributary alsoexperiences upstream-progressing degradation. Such degradation has occurred on the Big Sioux river inU.S.A. and on the Peace river in Canada (Galay 1983).

Execution of cut-off in a meandering river causes increase in the bed slope in the cut-off leading todegradation upstream of the cut-off and aggradation downstream as shown in Fig. 9.13(d). Yearke(1971) has reported 4.5 m of lowering of bed level following the development of cut-off on the Peabodyriver. Similarly, removal or shift in the control section along the river channel can also cause degradationor aggradation. If the main river, to which a tributary joins, shifts towards the tributary due to channelshifting, the tributary will experience upstream-progressing degradation. The tributary will experienceaggradation if the main river shifts away from the tributary; see Fig. 9.13(c). This is due to lowering orrises in temporary base level of the tributary.

Under special conditions, a combination of downstream-progressing and upstream-progressingdegradation can occur simultaneously in a given stream. Such occurrence on the Brenta River in Italy isreported by Galay (1980). Upstream and downstream-progressing degradation is shown in Fig. 9.2.

9.5 EFFECTS OF DEGRADATION

Lowering of riverbed due to degradation has beneficial as well as harmful effects. Some of the importanteffects are discussed below (Garde and Ranga Raju 2000).

i) Lowering of bed level downstream of a dam can affect the functioning of the hydraulic jumpbased energy dissipator. Lowering of tail water can move the hydraulic jump downstream andin the extreme case the jump may form outside the stilling basin.

ii) Degradation downstream of dams and weirs on permeable foundation will increase theeffective head and hence the uplift.

iii) Lowering of bed level downstream of the dam lowers the water level at irrigation outlets andmay make them ineffective. Similarly in the case of navigable rivers, considerable lowering ofwater level may make the navigation locks ineffective.

iv) Lowering of bed levels in the main river can initiate degradation in the tributaries and sub-tributaries, and cause additional scour at bridges and abutments.

v) Degradation in a stream causes lowering of ground water levels in adjacent areas.

vi) Increase in effective head (i.e. difference between head and tail water levels) at the dam meansthat additional power can be generated. This can be anticipated and provision can be made inthe design. Such provision for increased power generation was made at Uppenbornpowerhouse on the Saalach River in Germany and Praire Du Sac dam on the Wisconsin Riverin U.S.A.

vii) Degradation causes increase in the capacity of the channel and hence helps in lowering highflood levels.

River Morphology286

9.6 PREDICTION OF DEPTH OF DEGRADATION

Prediction of the depth of degradation needs to be discussed separately for in rotational degradation andfor parallel degradation. Let us assume that Q, S, Qs and d are known as well as the location of thecontrol section, and that the sediment supply is completely cut-off. Hence first rotational degradationwill occur and shear stress to on the bed will reduce to to2. Hence one has two equations

t02 = gf D2 S2 ...(9.5)UV|

W|and Q =

1

nf

B D25 3/ S2

1 2/

If nf is known, these equations can be solved to determine D2 and S2.Using Stricker type equation for known d50a, d, nf can be calculated; thus depth D2 and S2 can be

known. Then depth of degradation at the dam will be L (S – S2) where L is distance of control sectionfrom the dam. Subsequently parallel degradation will take place at constant slope. Gessler (1965) hasfound that the lowering of bed level in parallel degradation is about 2 d90 of the original mixture.

Transient degradation profiles can be obtained using any one of the mathematical models available,see Chapter 12. However, in using these models one has to use some conceptual model for coarsening ofthe bed material with time. These are summarized by Murthy et al. (1998).

9.7 CONTROL OF DEGRADATION

In recent times, three methods have been tried to control degradation. These are artificial feeding ofsediment, artificial armouring of the bed and construction of weirs (Scheuerlein 1989).

Artificial Sediment FeedingWhen the stream is degrading due to deficiency in sediment load, the degradation can be reduced orarrested if properly estimated sediment load of known sizes is fed every year on regular basis. Thismethod was first applied at the Upper Rhine River downstream of Iffezheim barrage. The sedimentfeeding began in 1978 and has been continued without interruption. Since the original river bed is in thegravel range, sand mixed with gravel and having an average size of 20 mm is being fed at 10,000 m3/year to 21 000 m3/yr. The conditions favourable for using this method are that there is no barrage on theRhine downstream of the Iffezheim barrage, and that the feeding material is available close at site. Thefeeding material is transported and dropped by means of barges over a length of 760 m. The annual costin 1986 was seven million D.M.

Artificial ArmouringArtificial armouring means formation of a complete cover on the bed with a layer of coarse materialwhich is capable of resisting the shear exerted by the flow. To stop washing away of fine materialunderneath, a filter of graded material or geotextile can be used. The armour thickness should be 0.8 to1.0 m. The size distribution of the armour coat can be obtained using Gessler’s analysis combined withestimation of design flood of 100-year return period. Scheuerlein (1989) quotes one case where thismethod is applied, namely in one of the two Danube branches in Vienna, called Neue Donau. The areacovered is 3 Mm2. The armour coat can be constructed on dry bed, or at low velocity.


Construction of Weirs or DamsIf a weir or dam is constructed in a reach which is degrading because of an upstream dam, it createsbackwater and reduces velocity, thereby reducing degradation. It can also cause aggradation which canoffset the degradation due to the dam upstream. Construction of a series of dams also moderates theflood, thereby reducing the transport capacity. This has been actually observed on the Colorado River inU.S.A. where a series of dams – Hoover, Parker and Imperial – is constructed. In the case of NagaHemadi barrage on the Nile River, degradation of the order of 0.8 m occurred after eight years ofoperation. A subsidiary weir had to be constructed to control the degradation.

It must however be mentioned that all these methods usually protect a certain reach of the river fromfurther degradation. Degradation would occur downstream of that reach if the flow is still capable oftransporting sediment and there is no supply from the upstream.

Progress of degradation is also sometimes arrested by the presence of non-erodible material such asrock reef or lenses of heavy gravel.

LOCAL SCOUR AROUND BRIDGE PIERS

Scour is the local lowering of the stream bed around a hydraulic structure. Scour takes place aroundbridge piers, abutments, spurs and breakwaters due to modification of flow pattern causing increase inlocal shear stress which, in turn, leads to removal of material and hence scour. Huber (1991) hasreported that since 1950 over 500 bridges have failed in U.S.A. and majority of failures were due toscour of foundation material. Such failure is primarily due to three causes:

i) Inadequate knowledge about scour phenomenon when the bridge was constructedii) Inadequate data and knowledge about design flood; andiii) Increase in the loading on bridges due to increase in the size of trucks and wagons and

frequency of loading.The total lowering of stream bed at any site can take place due to four reasons (see Garde and

Kothyari 1995).

1. Degradation taking place at bridge site due to dam upstream. In extreme cases, the bed can godown by as much as 4 to 6 m.

2. In the case of bridges on rivers in Indo-Gangetic plain, the river width in the vicinity of thebridge is reduced by providing embankments and guide bunds. If the approach flow width anddepth are B1 and D1, and B2 and D2 represent width at bridge site and depth of flow, these arerelated as

D

D2

1

= B

B1

2

0 60 0 79FHGIKJ

. .to

...(9.6)

Hence, reduction in width can lead to lowering of bed level.

3. Lowering of bed level that takes place due to modification of flow pattern; this is known aslocal scour.

4. Additional lowering of bed level can take place due to concentration or non-uniform flowdistribution across the river width at the bridge.

River Morphology288

In this section, attention is focused on local scour that takes place due to modification of flowpattern. Earlier studies have indicated that depending on the type of pier and free stream conditions, aneddy structure comprising all or anyone or none of the vortex systems can form. These includehorseshoe vortex system, the wake vortex system, and/or the trailing-vortex system. Figure 9.8 showsthe formation of a horseshoe vortex at the pier. This increases the local shear and causes scour.Measurement of shear stress around bridge pier has shown that the average shear stress around the piercan be about four times the shear stress in main channel, while the instantaneous shear stress is about 10to 12 times the average shear stress in the main channel.

9.8 FACTORS AFFECTING SCOUR

A number of experimental investigations on scour around bridge piers have been carried out since 1940.Two excellent reviews published in 1975 and 1977 summarise the state of art on scour at that time. Thefirst was prepared by U.P. Irrigation Research Institute and published by CBIP (1975), and the second isby Breusers, Nicollet and Shen (1977) published in the Journal of Hydraulic Research of IAHR. On thebasis of these reviews and work published since then, factors affecting scour depth can be summarizedas follows.

1. Whether the incoming flow is clear water flow or sediment transporting flow: when u

uc

*

*

is less

than unity, clear water flow occurs; when it is greater than unity sediment transporting flow

Fig. 9.8 Vortex system and definition for scour


occurs. Here u* = g DSd i is average shear velocity in the channel and u*c is its value when the

bed material just starts moving. Other conditions remaining the same clear water scour is aboutten percent more than scour in sediment transporting flow; further clear water scour depth dscincreases asymptotically while equilibrium scour depth dsc in sediment transporting flow isattained in finite time.

2. Depth of flow: Melville and Sutherland (1988) have shown that when depth of flow to pierwidth ratio D/b is greater than 2.6, the scour depth does not depend on the depth of flow;however for smaller depth, depth of flow affects the scour depth.

3. Effect of Shape of Pier Nose: The shape of the pier nose affects the strength of horse-shoevortex as well as the separation around the bridge pier; hence it affects the scour depth. Thiseffect is quantified by the coefficient Ks, which is defined as the ratio of the scour around thepier of given shape to that around a cylindrical pier under identical conditions. The values of Kshave been determined on the basis of works of Tison, Laursen and Toch, Chabert andEngeldinger, Larras, Garde and Paintal, and Garde (Garde and Kothyari 1995), and aretabulated below.

Table 9.3 Average values of shape coefficient Ks

Shape Ks

Cylindrical 1.0

Rectangular (d/b = 2 to 6) 1.1 to 1.25Lenticular (2 : 1, 3 : 1, 4 : 1) 0.93, 0.79, 0.70

Elliptical (2 : 1, 3 : 1) 1.0, 0.86

Triangular with apex angle 15o , 30o , 60o, 90o, 0.45, 0.61, 0.75, 0.88, 0.94, 1.00120o , 150o

4. Angle of Inclination of Pier with Flow: When the pier axis makes an angle with the generaldirection of flow, two major changes take place in the flow field. First is that the separationpattern is drastically changed except in the case of cylindrical pier. Secondly the open widthbetween piers, perpendicular to the flow direction is reduced as the angle of inclination isincreased. This effect is incorporated by introducing a coefficient Kq for non-circular piers,which is defined as the ratio of scour around the bridge pier at a given angle of inclination tothat at 0° angle of inclination under identical conditions. On the basis of works by Laursen, andVarzeliotis, the following values are recommended (Garde and Kothyari 1995).

Table 9.4 Effect of angle of inclination q on scour for rectangular pier (–/b = 60)

q° 0 7.5° 15° 30° 45°Kq 1.0 1.17 1.37 2.37 3.77

5. Opening Ratio: The opening ratio a is defined as a = B b

B

-a f where B is centre to centre

spacing of piers and b is pier diameter, or width. Analysis of extensive data by Garde et al.

River Morphology290

(1987) has shown that D D

Dsc seorb g

~ a–0.3. Here Dsc or Dse are scour depths measured below

water surface for clear water and sediment transporting conditions respectively.6. Bed Material Characteristics: Scour depth is affected by relative density of sediment, its median

size and geometric standard deviation. For all field problems, relative density of sediment canbe taken as 2.65. According to Lacey’s approach Dse ~ d–1/6 where d is the sediment size.Kothyari (1989) has experimentally found that in clear water scour dsc ~ d–0.31 while insediment transporting flow dse ~ d– 0.07. Here dsc and dse are scour depths below average bedlevel in clear water and sediment transporting flows. The effect of sediment non-uniformly isstudied by Ettema (1980) and Kothyari (1989). If Ks is defined as

Ks = Equilibrium scour depth for non - uniform sediment of given

Equilibrium scour depth for uniform sediment of size 50

50

d

d

then the variation of Ks with geometric standard deviation sg of the bed material is as follows.

Table 9.5 Variation of Ks with s

sg £ 1.5 2.0 2.5 3.0 2.5 4.0 4.5Ks 1.0 0.75 0.40 0.30 0.24 0.19 0.13

Kothyari (1989) has further suggested that to take into account the effect of sediment non-uniformity, one can alternatively use effective sediment size deu defined as follows:

deu = d50 if sg £ 1.124...(9.7)

UVWdeu = 0.925 d50 sg

0.67 if sg £ 1.124

7. Effect of Stratification and Unsteadiness of Flow: Effect of the stratification on scour has beenstudied by Ettema and Kothyari in the case of clear water scour. It is concluded thatstratification in which a relatively thin coarse top layer covers a thick fine bottom layer is thecritical condition which should be considered for design.Similarly, unsteadiness of the flow also affects the scour depth. This aspect has been studied byKothyari (1989) and a method has been developed to estimate scour under unsteadiness of theflow.

8. Flow Parameters: Most of the equations developed using experimental or field data can beclassified into the following groups:

Group – I

Here d

Dse is related to

b

DFHIK in the form

d

Dse = f

b

DFHIK ...(9.8)


Thus, Breusers and Ettema have proposed the equation

d

Dse = K

b

DFHIK ...(9.9)

Where K = 1.4 according to Breusers and 3.0 according to Ettema. According to Laursen andToch

d

Dse = 1.35

b

DFHIK

0 70.

...(9.10)

Group – II

Here D

Dse or

D

bse is related to Fr =

U

g D and

b

D. Thus according to U.S. Corps of Engineers

D

bse = 2.1

b

DFHIK

0 65.

Fr0.20 ...(9.11)

While according to Coleman

D

Dse = 1.39

b

DFHIK

0 90.

Fr0.20 ...(9.12)

Group – III

Here D

bse or

D

Dse is related to or Fr, Ns =

U

ds

f

Dg

r

or Re = Ub

v. Two typical equations in this

category are those of Shen et al. (1969) and Carsten (1975).Shen et al. (1969)

dsc = 0.000223 Re0.619 ...(9.13)

Here dsc is in ft and Re = Ub

v.

Carsten (1975)

d

Bsc = 0.546

N

Ns

s

2

2

0164

5 02

-

-

LNM

OQP

.

.

.83

...(9.14)

9.9 EQUATIONS FOR PREDICTING SCOUR DEPTH

Even though a number of equations have been proposed for estimation of depth of scour around bridgepiers, only four methods are discussed here and verified with field data.

River Morphology292

Lacey-Inglis EquationAccording to Lacey the depth of flow DLQ at the dominant discharge Q is given by

DLQ = 0.47 Q

fl

FHGIKJ

1 3/

...(9.15)

in which f1 is Lacey’s silt factor given by fl = 1.76 dmm . Inglis found that on the basis of data on 14

bridges in North India, equilibrium scour depth below W.S. Dse is given by

Dse = K DLQ ...(9.16)

where K varied from 1.76 to 2.59 with an average value of 2.09. When this equation is used for designpurposes, discharge that is to be used is the one with return period of 50 or 100 years. In the light ofdiscussion above regarding factors affecting scour, it stands to reason that K in Eq.(9.16) should dependon factors such as sediment size, pier shape and obliquity of flow. Further, since Lacey’s equation isvalid for sandy non-cohesive material and data on scour by Inglis are also from bridges in alluvial rivers,Lacey-Inglis method should not be used for clayey or gravelly beds.

Another method developed on the basis of extensive data using uniform and non-uniform sedimentsis the one proposed by Kothyari et al. (1989). According to this method, the scour in clear water flow isgiven by

d

dsc = 0.66

b

dFHIK

0 75.

D

dFHIK

0 16.

U U

dc

s f

2 20 40

-L

NMM

O

QPPD g r/

.

a–0.30 ...(9.17)

where the average critical velocity is given by

U

dc

s f

2

D g r/= 1.2

b

dFHIK

– .0 11

D

dFHIK

0 16.

...(9.18)

Similarly, scour under sediment transporting flow is given by

d

dsc = 0.88

b

dFHIK

0 67.

D

dFHIK

0 40.

a–0.30 ...(9.19)

These equations are for uniform sediment. When sediment is non-uniform, effective size deu isused in place of d in the above equations. Alternatively, one can compute dsc or dse for uniform sedimentand multiply it by Ks which depends on sg.

It may be mentioned that Melville and Sutherland have proposed an equation for maximum possiblescour depth as

dsem= 2.5b ...(9.20)

This scour depth below the general bed level is reduced by multiplying factors which depend onwhether the scour is clear water scour, depth is shallow and sediment is non-uniform. These coefficientsare determined using experimental data.


9.10 VERIFICATION OF EQUATIONS FOR SCOUR DEPTH

The equation proposed by Lacey-Inglis, Laursen-Toch, Melville-Sutherland, and Kothyari et al. wereverified (see Garde and Kothyari 1995) using scour data for 17 bridges in India, 55 bridges in U.S.A., 6bridges in New Zealand, and 5 bridges in Canada. The result of this verification is summarized in Table9.6. and comparison of observed versus computed depth of scour by Lacey-Inglis and Kothyari et al.methods are shown in Fig. 9.9 and 9.10 respectively.

Fig. 9.9 Comparison of (Ds)c vs (Ds)o using Lacey-Inglis method (Garde and Kothyari 1995)

Fig. 9.10 Comparison of (ds)c vs (ds)o using Kothyari et al. method (Garde and Kothyari 1995)

(d ) in mos

101

102

100

10–1

10–1

100

101

102

(d)

sc

inm

Line of perfect agreement

U.S. data

Newzealand data

U.G. canal dataganga at Mokameh

Other data of RDSO

Ravi river data

Inglis data

Canadian data

Legend :

U.S. data

Newzealand data

U.G. canal data

ganga at Mokameh

Other data of RDSO

Ravi river data

Inglis data

Canadian data

(d ) in mcs

101

102

100

10–1

10–1

100

101

102

(d)

sc

inm

Line of perfect agreement

Legend :

River Morphology294

From this study it was concluded that among the four methods studied, methods given by Kothyariet al. and Melville-Sutherland yield nearly the same accuracy and are better than Lacey-Inglis orLaursen-Toch method. Their added superiority lies in the fact that they take into account all factorswhich affect the scour depth.

The time variation of scour has been studied by Islam et al. (1986) who found that scour depth ds atany time t is given by

d

ds

se

= sinmax

/p t

t

m

2

1LNM

OQP ...(9.21)

where m and tmax are given by

m = 0.135

D

dD

b

FHIK

FHIK

0 087

0 25

.

. ...(9.22)

Equations (9.21) and (9.22) are based on the following ranges of related variables:Sediment size d 0.20 mm–7.8 mm

Fall velocity w 0.026 m/s–0.41 m/sFlow depth D 0.02 m–0.70 mPier diameter b 28.5 mm–240 mmVelocity U 0.10 m/s–1.30 m/s

It must be mentioned that to use Eq. (9.21), one must estimate dse by one of the method discussedearlier.

The time variation of scour as well as scour depth for clear water scour can be determined using thealgorithm proposed by Kothyari (1989); this algorithm is shown in Fig. 9.11. First the diameter of thehorse-shoe vortex is computed. Then it is assumed that the average shear stress at the pier nose is fourtimes the average shear stress in the channel, and when the former reaches the critical value, scour stops.

As the scour develops, the horse-shoe vortex sinks into the bed and its area increases by ds

2

2 tanj where

Table 9.6 Relative accuracy of prediction of scour depth by different equations

Percent of data falling within given error band

Method ± 30% ± 50% ± 90%

Lacey-Inglis 59 85 100

Laursen-Toch 38 65 98

Melville-Sutherland 79 95 100

Kothyari et al. 86 96 100


ds is the scour depth and f is the angle of repose of bedmaterial. Due to increase in the area, the shear stress inthe vortex decreases, and its is assumed that shear atany time t, tpt it is given by

tpt = 4 t0 A

At

cl

0FHGIKJ

...(9.23)

where Ao and At are the original and new areas of

vortex and c1 is a constant. The time required to move a

single particle is assumed to be t* = d c

p ut t

2

0 *

and the

probability pot is given by

p0t = 0.45 t

g

pt

s dD

FHG

IKJ

3 45.

= 0.45 t*.pt

3 45 ...(9.24)

where t*pt = t

g

opt

D s d.

When a single particle is removed, the timeelapsed is t*. By repeating the process one cancalculate S t* i.e. the time required to cause scour depthof a, 2d, 3d … etc. When the shear stress in the scourhole reaches critical value for size d, no further scourwill take place. By calibrating the model with knowndata of scour depth variation with time, the constants c1and c2 in the above equations were found to be 0.57and 0.05. This model can also be used to study scourdepth variation with time when discharge is varyingwith time.

Fig. 9.11 Algorithm for computing time varyingscour (Kothyari 1989)

9.11 SCOUR IN GRAVELLY MATERIAL

As discussed in detail in Chapter – 7 gravel-bed rivers are basically different from alluvial rivers. Thebed material in gravel-bed rivers is very coarse and has a large standard deviation. Further, these riverstransport sediments on the surface and ultimately form the pavement or armour layer. As mentionedearlier the standard deviation of the pavement is around two.

Not enough is known about scour in gravel-bed rivers and the data are very few. In the absence ofadequate data, the IRC-78-2000 code recommends that scour depth in gravel-bed rivers be estimatedusing Lacey-Inglis approach and estimating depth of flow by the formula

Calculate horse-shoe vortex diameter

/ = 0.28 ( / )0.85

D

D d b Dv

v

Start

Red andb,d,D,S,B,U, , dsg rfs

A Do = / 4P2

v

R BD B D= /( + 2 )

t go = RSf

A = +0t Ad

2 tan

2

f

s

t = 4( / )A0.57

opt tA t

t*

.pt

3.45P = 0.45ot

t d p U t= 0.05 / *oto

t = *1 –1t tl

d Id=s

t and dsII

Print

End

Yes

I = I + 1

Is

*

£ t*c

pt

t

No

River Morphology296

DLq = 1.13 q

fl

2 1 3FHGIKJ

/

...(9.25)

where q is discharge in m3/s, and sill factor of fl = 24 is recommended. However, this method has notbeen supported by field data. Further, since relationship between depth and discharge for gravel-bedrivers is different than Lacey’s (see Chapter 7) it is not logical to base estimation of scour depth ingravel-bed rivers on Lacey’s equations. On the other hand, since the methods of Kothyari et al. andMelville and Sutherland take into account the size of bed material its gradation and stratification, theseare likely to give more reliable results as shown by Garde and Kothyari (1995).

9.12 SCOUR IN COHESIVE SOILS

The process of scour in non cohesive materials is discussed above. However when the river bed consistsof gravel, sand, silt and clay the scour phenomenon becomes more complex, and very little is knownabout variation of scour depth with time, maximum depth of scour and extent of scour. A fewmeasurements of scour in clayey soils are available (Kand 1993, Namjoshi 1992). Laboratoryexperiments have been carried out by Ansari (1999) and Ansari et al. (2002). These references alongwith that of Briaud et al. (1999) may be seen in this regard.

9.13 PROTECTION OF SCOUR AROUND BRIDGE PIERS

A number of devices have been tried to reduce scour depth around bridge piers. These devices eithermodify the flow pattern created by horseshoe vortex or provide a hard surface which prevents horse-shoe vortex from sinking or protects the surface from erosion. These include piles, collar plates, delta-wing-like passive device and slot in the pier or vanes. Their relative effectiveness has been studiedamong others by Gangadharaiah et al. (2003). Except piles and vanes, the other devices have not beentested on prototype bridges. In the laboratory these devices are found to reduce scour by 40 to 70percent. Another method which has greater potential of using in the field, is the use of rip-rap of propersize around the pier which will resist scour. This has been studied by Wõrman (1989), and Bhalerao andGarde (2003) and used in the field by Wörman. As mentioned earlier the instantaneous shear stressaround the pier can be 10 to 12 times the average shear stress in the channel. If the median size of thearmour layer is so chosen that it is stable at this shear stress, and if riprap has a standard deviation ofabout two, one or two layers of rip-rap adequately protect the bed from scouring.

AGGRADATION

In general, aggradation in a stream takes place when the stream is carrying more sediment than itstransport capacity. If the sediment load coming into a reach in a given time is greater than the sediment

load going out in the same time, i.e. when ¶

¶

Q

Ss is negative, the excess sediment gets deposited on the

bed and the bed level rises i.e. ¶

¶

Z

t is positive. Aggradation occurs under a variety of conditions; these

are discussed below.


9.14 OCCURRENCE OF AGGRADATION

Increase in Sediment LoadThe increase in sediment load can take place for different reasons. Thus, during the gold rush period(1850-1905), large quantities of mining waste were dumped in the Yuba river in California as a result ofwhich the general bed levels increased gradually. This was reflected in the rise in low water level atMarysville, see Table 9.7. When the mining was stopped because it became uneconomical, the bedlevels were lowered gradually. Similarly, large quantities of gravel have come down in gravel-bed riversin the Doon Valley (Uttaranchal, India) partly due to mining activity and partly due to erosion due todeforestation; as a result in some rivers bed levels have risen by as much as 3 to 4 m; see Fig. 9.12 andFig. 9.13(a).

Fig. 9.12 Aggradation in the Doon valley stream

Excess sediment can be brought into the stream as a result of landslides and heavy rainfall. Thus, inthe Mu-Kwa river in Taiwan (see Lane 1955) the bed level rose by as much as 12 metres in three yearsand the powerhouse was completely buried in sediment. Sometimes the landslides and destruction ofhills result from high intensity earthquake followed by floods, as occurred in the Brahmaputra after1950 earthquake. As a result, the bed levels rose by 2-3 m in long stretches of the river (see Chapter 14).

Table 9.7 Rise in low water level at Marysville on the Yuba (Bolt et al. 1975)

Year Water level elevation (m) Year Water level elevation (m)

1850 12.10 1905 17.90

1860 13.40 1910 17.00

1870 14.70 1920 16.10

1880 16.90 1930 14.60

1890 16.80 1940 14.40

River Morphology298

The increase in the sediment load in the tributaries and the main stream can also occur due toreduction in vegetal cover as a result of overgrazing, deforestation, climatic changes or man’s activitiessuch as road building etc. As a result, the tributaries and main stream can experience aggradation.

Lastly, irrigation channels may aggrade if excess sediment enters into it when sediment excludersand ejectors are either not provided or are not functioning properly. This has happened in the case ofEastern Kosi main canal in which bed levels have risen by 2 to 3 m in a reach of 4 km during nine years.The canal was designed according to Lacey’s method and had a bed material size of 0.20 mm (Sahayet al. 1980).

Aggradation of 11.5 km reach of the Ganga Canal from its head works at Mayapur up to Patharipowerhouse in Uttaranchal (India) needs special mention (Mohan and Agarwal, 1980). This canal takesoff from the river Ganga at Mayapur near Haridwar (India). The canal is about 150 years old and carriesa maximum discharge of 311.5 m3/s. It has a slope of 0.000725 in the first 1.6 km and 0.000230 up toPathari powerhouse 11.6 km downstream. Because of landslides and heavy rainfall in the Alakananda,a major tributary of the Ganga, sediment concentration in the Ganga ranged from 36 000 to 13 500 ppmduring 21st July to 27th July 1970. In the feeder channel at Bhadrabad near Pathri the suspendedsediment concentration ranged from 16 286 to 15 584 ppm. During this period the canal dischargegradually reduced to 71 m3/s while the water level at Pathri was held constant. It was found that thecanal had silted to the extent of 2 to 3 m in this reach. This resulted in the closure of the canal for a fewmonths leading to disruption of supply of water to irrigation and considerable expenditure on removal ofsediment. Later for proper functioning, of the canal a limit on maximum permissible concentration to beallowed in the canal was fixed.

Withdrawal of Clear WaterIf relatively sediment free water is diverted from a stream, otherwise in equilibrium, downstream of thepoint of withdrawal the river cannot carry the sediment load with reduced discharge; hence it willexperience aggradation. This withdrawal can be for irrigation or water supply purposes. Suchaggradation has occurred on the Rio Grande, and the Arkansas rivers in U.S.A. (see Lane 1955). Whenaggradation occurs either due to increase in sediment load or reduction in water discharge, the transientand equilibrium bed profiles obtained are shown in Fig. 9.13(a). Such a reduction in peak flows anddischarge can also be caused by stream piracy in which part of the water is diverted to the pirated stream.Profiles obtained due to withdrawal of sediment load or increases in discharge are shown in Fig.9.13 (b).

Aggradation Due to Reduction in Water Slope (or Increase in WaterLevel)The aggradation occurring upstream of the section of increase in sediment load or decrease in dischargeis due to rise in water level at section 0-0. Aggradation occurring upstream of dam falls in this category.When a dam is constructed on a stream to store water for irrigation, water supply, power generation orfor flood control, a backwater is caused as a result of which velocity of flow reduces as one approachesthe dam. Hence, reduction in sediment transport capacity leads to deposition of coarser sedimentupstream where backwater starts while finer sediment gets deposited closer to the dam; see Fig. 9.13 (b).Sedimentation of reservoirs reduces their capacity to store water, raise water levels in the upstreamreaches of the river, and increase evaporation due to increase in water surface area. In literature one


Change of hydrograph can also lead to aggradation. In many rivers, most of the bed changingactions take place during peak flows. If by building one or more dams in series, the flood peak ismoderated, the total annual sediment transport capacity of the stream is significantly reduced. And yetthe sediment supply from the tributaries on the downstream side of dam will be unaltered and so thestream will not be able to carry this load; hence bed level can rise or part of the degradation can be offset.

Fig. 9.13 Bed profiles in aggrading and degrading stream

finds several cases of reservoirs getting filled ina few years. The 14 m high dam on the Nan-Shik-Chi river in Taiwan was filled completelyin 8 years. Whereas the river slope was 1 in 120,the final slope of bed was 1 in 250. Similarly, 53m high Ichari diversion dam on the YamunaRiver has silted up to the crest in five years from1972 to 1979. Reservoir sedimentation isdiscussed in detail later in this Chapter.

Aggradation at ChannelBifurcationIf a channel takes off from the main stream, theoff taking channel will carry relatively more bedload compared to the main stream because ofthe development of secondary flow. Hence, ifthe main stream is carrying appreciable bedload, the off taking channel is likely to aggrade.

Other Cases of AggradationA stream which discharges into a lake or the seabuilds its delta. With the passage of time, thedelta grows into the lake or sea thereby causingincrease in the length of the river and reductionin slope inducing aggradation. This aggradationfills the river channel and the river spills overthe banks forming new channels. Similarincrease in length leads to aggradation of thetributary if the main stream to which it joinsshifts away from it due to migration. This isshown in Fig. 9.13 (c).

Similar situation also occurs on alluvialfans. In many cases fan can start as deltaformation in a lake and after enough time haselapsed, the lake will be completely filled. Thenthe river just keeps building the fan higher andhigher (Gessler 1971).

(d) Aggradation and degradation at cut-off

Original bed

New bed

cut-off

B

b

A

a C

c

D

d

(c) Aggradation of tributary due to shifting of main stream

Old position New position

Tributary

Aggraded profile

(b) Degradation due to increase in or decrease in QsQ

Final bed

Original bed

DQ DQs

O

Transient bed levels

O

(a) Aggradation due to increase in or decrease in QQs

DQDQs

O

O

Final bed

Transient bed levelsOriginal bed

River Morphology300

Degradation, Aggradation and Planned Removal of DamsIt is reported that 85 percent of dams in U.S.A. will be at the end of their operational design lives by2020 (Evans et al. 2000). Hence, planned removal of dams as a viable river management alternative isbeing considered seriously in U.S.A., and some case studies in this regard have been conducted in orderto gain information on physical, chemical and biological impacts of removing dams. In the context ofthe theme of this chapter, important issues that need to be addressed include rates and mechanics ofsediment removal from reservoirs; how watershed geomorphology and hydrology affect these rates andmechanisms; how far and quickly the sediment will be transported downstream, and how downstreamsedimentation will affect channel morphology and biotic communities.

Doyle et al. (2003) have reported the channel adjustments that have taken place following two damremovals in Wisconsin (U.S.A.). When the dam is removed upstream reach will experience degradationwhile downstream reach will experiences aggradation. The details of two small dams removed are asfollows:

River Koshkonong BarabooDam Rockdale Lavalle

Catchment 360 km2 575 km2

River slope u/s of dam 0.0007 0.0005River slope d/s of dam 0.004 0.0002Sediment Silt to coarse gravel Mixture of fine sand and silt

Dam height 3.3 m 2.0 m

The changes that took place after removal of dam can be the summarized as follows: Immediatelyfollowing the dam removal water surface elevation decreased dramatically but the reservoir sedimentsurface remained undisturbed. Channel flow during this period was wide and shallow with low velocity.Next, the channel bed incised and the flow concentrated into a narrow, deep channel with steep bank andhigh flow velocity. Head cut formed at the upstream boundary. Large amount of fine and then coarsesediment was mobilized and transported downstream. As the incision continued beyond critical bankheight, the channel started widening and large quantities of the material were transported downstream.With this, the downstream channel started aggrading initially coarser sediment was deposited and thenthe finer one as water surface slope decreased adequately.

Effects of FloodsAccording to Bull (1985), the following factors tend to promote net aggradation during floods:

i) Abundance of stored sediment on hill slopes as a result of either abundant soft rock types and/or rates of rock weathering that exceed denudation rates.

ii) Climatic changes that greatly decrease vegetative cover on hill slopes, or increase rainfallintensity.

iii) Fires that remove the vegetative cover or expose the hill slopes to accelerated erosion.

iv) Unstable slopes subject to landslides that introduce large volumes of sediment directly intostream channels.

v) Lack of relative vertical uplift.


Streams that aggrade during floods include watersheds with abundant landslides. Climaticallyinduced decreases in vegetal cover and concurrent increases of hill slope sediment yield have favouredaggradation of valley floors in extremely arid to extremely humid climatic settings. Aggradation can beestimated by determining the new equilibrium slope for changed conditions. The transient bed profilescan be computed using methods described in Chapters 11 and 12.

RESERVOIR SEDIMENTATION

Dams are constructed on rivers so that they form reservoirs which impound water that is later used forirrigation, water supply and industrial purposes, power generation, recreational purposes and floodcontrol. They also help in controlling the variations in flow in the downstream channel. Most reservoirsserve multiple purposes. When water is impounded in the reservoir, the flow velocity is smallest near thedam and it gradually reaches the velocity in the stream at the end of the backwater. As a result, thesediment transport capacity of flow progressively reduces towards the dam and coarse material getsdeposited in the upstream reach while medium and finer material gets deposited near the dam. Very finematerial which remains in suspension at the dam will travel downstream over the spillway and throughoutlets. This deposition progressively reduces the storage capacity of the reservoir. Even though apredetermined dead storage is provided assuming that sediment would deposit there, yet significantamount of sediment may start depositing in the upstream reaches right from the beginning and causedepletion of the reservoir capacity.

Depletion of reservoir capacity with the passage of time is a serious problem because ultimately theusable capacity of reservoir will be completely lost and a new reservoir may have to be built. Dams arevery expensive and alternate reservoir sites are not easily available. Some idea can be given about ratesof reservoir sedimentation. Yasuoka reservoir on the river Tenrya in Japan which had a capacity of 51Mm3 lost 80 percent of the capacity in 13 years. The Ichari reservoir on the river Yamuna in India lostalmost 100 percent capacities in five years of operation. Zuni reservoir on the river Zuni in New Mexico,U.S.A. lost 58 percent capacity in the first two years. On the basis of survey of 132 reservoirs all overU.S.A., spanning over a period of 20-30 years, the average annual loss of capacity is found to be 0.70percent. Sedimentation rates in China are much higher. Twenty large reservoirs in China were losingtheir capacity at an average rate of 2.3 percent per year during 1960-1978; the maximum rate was 7.1percent for Quintgonxia reservoir on the Yellow river, see IRTCES (1985). For eleven large reservoirs inIndia, the sedimentation rate varied between 0.08 and 1.78 percent per year, while average loss was 0.65percent.

There are many direct and indirect effects of sedimentation in reservoirs. These are discussed indetail in the UNESCO (1985) publication and are briefly enumerated below.

Upstream Effects1. Raising of bed level and water level in the upstream reach; rise in the water table which results

in the appearance of marshes.

2. Increase in water surface area causes increased evaporation loss and weed growth.3. Accumulated sediment upstream of dam may choke the bottom outlets.4. Since a very large percent of sediment is trapped in the reservoir, the flow in the downstream

channel is deficient in sediment load; this causes degradation in the channel and/or channelwidening. Effects of the degradation have been discussed earlier in this chapter.

River Morphology302

5. Construction of dam and impoundment of water reduces low and medium floods in thedownstream channel. This may stop the erosion of cones of sediment deposits at the confluenceof steep gradient tributaries joining the main stream.

6. The water released from the dam is free of sediment and contains mainly dissolved solids. Thisleads to impoverishment of biomass in downstream channel, which leads to decrease ofproductivity of fish and breeding.

7. There are a number of economic consequences of reduction in the storage capacity of reservoir,which include reduction in energy production, agricultural production, and non-availability ofwater for domestic and industrial use.

Discussion of Reservoir Sedimentation needs consideration of the following aspects:

• Sediment inflow and trap efficiency• Movement of sediment in reservoirs and sediment deposition• Modelling of sediment deposition• Methods of preserving or restoring reservoir capacity

9.15 SEDIMENT INFLOW AND TRAP EFFICIENCY

Annual sediment inflow can be assessed in different ways. If any reservoirs are in operation in the regionand their surveys are available, the same rate in tons/km2/yr can be used for the reservoir underconsideration. For a better accuracy erosion rate can be calculated using the equations proposed inChapter 3 where it is related to annual rainfall, catchment slope, drainage density, catchment area andvegetal cover factor. If suspended sediment measurements are available for few years and dischargeinflows for longer duration, a certain percent of suspended load can be taken as bed load and, flow andsediment duration curves can be prepared to determine average annual sediment inflow rate (seeChapter 3). If no sediment load (suspended or bed load) measurements are available, one has to use oneof the total sediment transport equations described in Chapter 5 to prepare Q vs QT curve and then assessaverage sediment transport rate. For future predictions flows can be generated using availabletechniques in hydrology and then determine QT determined from QT vs Q curve. Ideally, sedimenttransport data are required for a period, at least equal to half the life of the project (Mahmood 1987).Since this is seldom available, engineers and planners have to work with inadequate data, and effort ismade to extend it using statistical techniques. It may also be emphasized that hydrologic series showgreater variability in arid or semi arid climates than in humid climates.

In assessing the sediment inflow, the impact of natural events such as high magnitude earthquakes,eruption of volcanoes, landslides, and catastrophic flood play an important role, even thoughquantification of their contribution may be difficult or impossible. A few examples can be cited here insupport of this statement. New Madrid earthquakes between December 1811 and February 1812, thegreatest earthquakes in U.S.A. in Southern Missouri, were felt over 100 000 km2 area. These brought inlarge quantities of sediment in the Mississippi river and changed its channel morphology (Mahmood1987). The 1950 earthquake in the Brahmaputra Valley brought into the stream very large quantity ofsediment, which affected the morphology of the Brahmaputra. Had there been a reservoir on the river inthe downstream, it would have shown very rapid sedimentation. Similarly, the 1971 heavy monsoon andlandslides in the Alakananda valley brought down huge quantities of sediment in the Ganga River and


caused sedimentation problem in the Ganga canal. Lastly, volcano eruption of Mt. St. Helens (U.S.A.)in May 1980 brought in 50 million tons of debris and mud flows in the Cowlitz river channel. It isestimated that in the four months after eruption, about 140 million tons of suspended sediment weredeposited by the Cowlitz river into Columbia River in U.S.A. As a result, of Mt. St. Helen’s eruption,sediment yield of the Columbia River had increased to 40 million tons/yr from the pre-eruption value of10 million tons/yr (Mahmood 1987).

Trap efficiency has been defined in Chapter 3 as the percentage of incoming sediment load that isretained in the reservoir. It depends on a number of factors such as the size of sediment, variation in theflow coming into the reservoir, characteristics of the reservoir, method of reservoir operation and time.A method, which takes into account all these factors on the determination of trap efficiency, is notavailable at present. However, Brune’s (1953) curve which is based on data obtained from 44 normallyponded reservoirs covering drainage areas of 4-480 000 km2, and which relates trap efficiency Te to theratio of reservoir capacity to annual inflow is often used to determine Te. This has been later verifiedusing data from reservoirs in India, China and South Africa; this is given in Fig. 3.9. The mean curve canbe represented by the equation

Te= 100 11

1 50-

+FHIK

L

N

MMMM

O

Q

PPPP

C

I

...(9.26)

where C is the reservoir capacity upto mean operating level and I is the average annual inflow bothexpressed in the same units. The period of computation for Brune’s method should not be less than tenyears. Heinemann’s (1981) data show that Brune’s curve overestimates trap efficiency for smallreservoirs.

Swamee and Garde (1977) have analysed laboratory and field data on sedimentation of reservoirsand found that the reservoir capacity Ct after sediment deposition, at any time t is given by

C

Ct =

t

t

t

t

e

m

e

m

FHGIKJ

+FHGIKJ

L

NMM

O

QPP

14 0 25. ...(9.27)

Here C is the original capacity of reservoir and te is the period required to fill the reservoir up toheight of dam. This can be estimated by dividing C by average annual rate of sediment inflow. The

exponent m varies between 0.75 and 1.0, and m and te can be determined by plotting C

Ct vs t on log-log

scale for few years and fitting a straight line in the initial period of silting. The exponent m is the slopeof the straight line and t = te when Ct = C.

River Morphology304

9.16 MOVEMENT AND SEDIMENT DEPOSITION IN RESERVOIRS

Three agencies which control the movement and deposition of sediment in reservoirs are river flows,wind effects and solar inputs. When wind blows over the water surface in the lake formed by a dam, itexerts a shear stress on the water surface and causes water surface to move in the direction of wind. Thisleads to formation of waves, water surface currents and the associated counter currents underneath.These counter currents carry the near-bed settling suspension. The solar heating is also responsible fordeveloping currents and transporting sediment in the reservoir. The difference in temperature betweendeep layers and surface layers causes thermal currents. Lastly, when river flows into the reservoir, itcarries with it bed material which moves as bed load or in suspension, wash load and dissolved solids.As a result of interaction between river flows, and wind and solar effects there can be three types offlows of sediment-laden water, which are shown in Fig. 9.14. Inflows which are of high density becauseof heavy suspended load or which are colder than water in the reservoir will cause underflow. If theinflowing water is warmer than the surface water in the reservoir, it may flow over the surface asoverflow. When the inflowing water is slightly colder than the surface water, it flows as interflow. Thecoarsest sediment may get deposited as deltaic deposits.

Fig. 9.14 Overflow, interflow and underflow in reservoir

Lane (1953) has classified the deposits in the reservoir into bottom-set beds, fore-set beds, top-setbeds and density currents, see Fig. 9.15. Bottom-set beds are formed of fine sediments brought into thereservoir and which move farther near the dam before they settle. The fore-set bed is formed of thecoarser sediment carried by the stream on or near the bed, and is deposited where the current is retardedas it flows into the lake. This happens when horizontal water surface in the reservoir intersects thecurrent. These beds are more inclined downwards in the direction of flow. Top-set beds are mainlycomposed of coarser sediment (sand and gravel) and are usually sloped upstream at a low gradient fromthe edge of fore-set beds. They extend as far back as the backwater curve extends upstream of reservoir.The top-set bed deposits do not reduce the reservoir capacity, but they cause flooding problems inupstream reach due to rise in bed and water levels. Zhou Zhide (1991) has analyzed the slopes of top-setbeds of a number of reservoirs in China and found that, on the average their slope is about 0.5 So whereSo is river slope.


When the water entering the reservoir carries large concentration of fine material, because of lowvelocities in the reservoir the sediment settles near the bed and forms a thick layer of high density whichmoves slowly towards the dam. These are known as the density currents. By provision of very low leveloutlets the density currents can be vented out of the reservoir. Conditions favourable for the formation ofdensity current are (i) high sediment concentrations (ii) fine sediment (iii) steep stream slope, and (iv)large depth of flow. Density currents have been found to occur in both Lake Mead and Elephant Buttereservoirs on the Colorado River in U.S.A., and Naodehai reservoir on the Liuhe River in China.Experience has shown that under most favourable conditions only 5 to 20 percent of sediment in thereservoir can be vented out in the form of density currents. Basic mathematical description of theappearance, propagation, modification and outflow of density currents is briefly described in UNESCO(1985) Report.

Shape and Deposition ProfilesThe shape of deposition profile in the reservoir depends on a number of factors such as river slope,normal pond level and its variation, size distribution of sediment, shape of the reservoir, and ratio ofincoming sediment load to the reservoir capacity. These profiles are classified into three categoriesnamely deltaic deposits, wedge-type deposits and narrow band type deposits, and are shown in Fig.9.16. Deltaic deposits are by far the most common where the material is not very fine and water level iskept relatively high for a considerable length at time. Such deposition has occurred in the Gobindsagarreservoir on the Sutlej River in India, and in Guanting reservoir on the Yongting River in China.

Wedge type deposition occurs in gorge-type reservoirs in which the storage capacity is smallcompared to the incoming load. Hence the sediment soon reaches upto the dam resulting in a wedgeshaped profile. Such deposition has occurred in Bajiazui reservoir on the Pu river in China, the Matatilareservoir in India and in Heisonglin reservoir on the Yeyu River in China.

In some gorge-type reservoirs where the incoming load is small and fine in size, the sedimentdeposits more or less uniformly in the form of a thin band if water level in the reservoir fluctuates to agreat extent. Such narrow-thin band type of deposition has occurred in Mayurakshi reservoir in Indiaand in Fengman on the Mudan River in China. Based on the experience on the Chinese reservoirs,IRTCES (1985) has given the following criteria for formation of deltaic and wedge-type deposits.

Fig. 9.15 Longitudinal section through a reservoir showing various types of the deposits

River Morphology306

Fig. 9.16 Deltaic, wedge-type and narrow band deposits inreservoirs

Average reservoir capacity in

Average annual sediment inflow in tons

3m >

2.0 and D H

H < 0.15 : Deltaic deposits

Average reservoir capacity in

Average annual sediment inflow in tons

3m <

2.0 and D H

H < 0.15 : Wedge type

Here DH and H are average yearlyfluctuation and head at dam respectively.

9.17 MODELING OF SEDIMENTDEPOSITION

Modeling of sediment deposition can be doneeither by using empirical methods or by usingmathematical modeling. Here two empiricalmethods are described while the mathematicalmodeling is discussed in Chapter 12.

Empirical Area ReductionMethodThe empirical area reduction method proposedby Borland and Miller (1958) is developed onthe basis of the analysis of data from 30reservoirs in U.S.A. having capacities rangingfrom 4.9 ́ 106 to 7.6 ́ 108 m3 and is based onthe premise that the sediment load in narrowreservoir will travel farther, because theaverage velocity of flow will be higher innarrower reservoirs than in wide reservoirs.Further, a steep narrow reservoir has a betterchance of developing density currents than the one that is wide and flat. On the basic of this, reasoningBorland and Miller have classified the reservoirs in four categories depending on the exponent q in theequation

C (h) = a hq ...(9.28)

where h is the height depth measured above the river bed at dam axis C (h) is the storage capacity atdepth h; see Table 9.8.

10.6

7

15.5

4

21.6

4

26.5

1

32.4

1

37.4

9

44.8

0

50.9

0

55.8

2

63.0

9

10.4

1

75.2

8

80.1

6

350

380

410

440

470

500

Ele

vation

inm

Ele

vation

inm

Ele

vation

inm

F.R.L. 515.11

Distance in km u/s of dam

Gobindsagar reservoir

Original bed - 1958

1962

19661975

1970

Years

5 10 15 20

Original bed (1957)

19641971

Wedge-type

Full reservoir level 308.46 m

Spillway crest 301.45 m

Min. drawdown level 295.66 m

311

305

299

293

Top of dam 310.9 m

287

281

2750

Matatila reservoir


Mayurakshi reservoir

0 4 8 12 14 16 18 20


122

116

110

104

98

92

86

Original bed (1955)

Sx =0.0

0115

(1963-63)

Narrow-band

Live storage

Dead storage

Deltaic deposit

Wedge-type deposit

Narrow band deposit


Table 9.8 Reservoir classification and distribution parameters (Borland and Miller 1958)

Type Description Q in Eq. 9.28 Position of deposition C1 m n

I Lake 3.5 – 4.5 Top 3.42 1.50 0.20

II Flood Plain–Foot hill 2.5 – 3.5 Upper middle 2.32 0.50 0.40

III Hill 1.5 – 2.5 Lower middle 15.88 1.10 2.30

IV Gorge 1.0 – 1.5 Bottom 4.23 0.10 2.50

Analysis of sediment volume deposited versus fraction of reservoir depth curves obtained for thesereservoirs were converted into relative depth p versus dimensionless relative areas Ap see Eq. (9.29).

Ap = C1 pm (1 – p)n ...(9.29)

Here and As = A

Ks

1

where K1 = 0

1

z As dp and As is area of sediment deposit at relative elevation p. the

values of m and n were computed by trial and error procedure using least square technique, and thenwith m and n known, C1 is fixed by the consideration that the total areas under the curve must be unity.The computations can be carried out in Tabular form given below.

Table 9.9 Computations using empirical area reduction method

Elevation m Original Original Relative depth p Ap 1st Trial

area m2 capacity m3 Sediment Sedimentarea m2 volume m3

Procedure1. Determine q from reservoir capacity vs. depth curve

2. Determine the type of reservoir3. Fill in columns 1, 2, 3 from known data at regular intervals of h

4. Find in m3 the apparent volume of sediment to be deposited at the end of T years5. Determine the value of p for elevations in Col. 1 and enter Col. 4

6. Determine Ap values for p values in Col. 4 using Eq. (9.29) and enter in col. 57. Assume zero elevation at the dam up to which sedimentation has reached and carry trial No. 1.

Areas at and below approximated zero elevation at each increment will be those in col. 2.New areas for each contour elevation above assumed zero elevation are obtained by dividingthe original areas at zero elevation in Col. 2 by corresponding Ap values in Col. 5 andmultiplying this by the ratio K1 values at each succeeding increment.Thus, if assumed elevation is 4190 where surface area is 3000 and Ap at elevation 4190 is 1.125,K1 = 3000/1.125 = 2667.

River Morphology308

The new area at each succeeding elevation is the Ap at that elevation times 2667. This is enteredin Col. 6.

8. Increment sediment volume between two elevations h1 and h2 is

DV = A A1 2

2+

´ (h2 – h1)

and is entered in Col. 7.9. If the assumed elevation is correct, summation of terms in Col. 7 will be equal to sediment

volume to be distributed.10. If they are not equal, assume a different elevation and repeat the procedure.

A solved example is given by Borland and Miller (1958) which can be seen.Some comments on this method are necessary. This method does not account for temporary or

prolonged reservoir draw down brought about as an operational necessity or as deliberate sedimentsluicing operation. It also does not consider the sediment size distribution as a factor in the problem. Inpractice these conditions can be accounted for by shifting the computed reservoir type in Table. 9.8upwards or downwards. Thus, if fine material forms a large part of the sediment load, or if the reservoirexperiences considerable draw down, its type can be shifted downward (Mahmood 1987). Further, itneeds to be emphasized that the empirical area reduction method is to be applied for sedimentaccumulated over long periods, such as few decades and not for year-to-year accumulation. Also, manytimes a reservoir may not have a unique value of q for its entire depth. In such cases, the reservoir typeis selected on the basis of q value in the segment where most of sedimentation will occur.

Figure 9.17 shows percent of depth plotted against percent of deposition for the four types ofreservoirs along with data for Panchet Hill, Nizamsagar, Gobindsagar, Maithon, Mayurakshi, Matatila,

Fig. 9.17 Depth-wise sediment distribution in Indian reservoirs (Murthy 1971)


and Margomahally reservoirs as given by Murthy (1971). It may be noted that except for very deepGobindsagar reservoir formed by Bhakra dam and Margomahally, deposition occurs mostly in the upperpart of reservoir i.e. almost half of the sediment is deposited where the depth ranges from 20 to 30percent of the maximum depth.

Miraki�s MethodOn the basis of analysis of deposition profiles in nine reservoirs in India where delta type triangulardeposition profiles were obtained, Miraki (1983) has suggested the following method for computingdeposition profile at any time t. The annual sediment volume entering the reservoir can be computedusing Garde and Kothyari’s Eq. (3.39) and using Brune’s trap efficiency curve, the volume of sedimentdepositing in the reservoir can be calculated and converted into apparent volume depositing in thereservoir at the end of T years. The triangular profile is characterized by upstream slope Su, downstreamslope Sd and maximum depth of deposition Zp (see Fig. 9.18). These are given by

Fig. 9.18 Definition sketch for deposition in reservoir

Z

Hp = 0.717

T

et

FHGIKJ

0 285.

...(9.30)

U

V

|||

W

|||

S

Su

o

= 0.34 0 T

et

FHGIKJ

- 0 08.

S

Sd

o

= 3.850 T

te

FHGIKJ

0 20.

Here H is average depth at the reservoir and So is average channel slope. The term te is the numberof years required to fill the reservoir completely. Hence

te = Volume of reservoir at FRL

Annual vol. of sediment trap efficiency in flow 2650

average unit wt. of sediment´ ´

RST

UVW

River Morphology310

The volume of sediment deposited under a given profile requires average width of deposition overthe reach of deposition. Once this is determined from the reservoir characteristics, the two volumes canbe compared and made equal by changing Su or Sd slightly. The first peak occurs a distance of 0.42 Lrfrom the reservoir where Lr is length of the reservoir defined as shown in Fig. 9.18; at this place, flowdepth is 0.51 H. The peak was found to move in the downstream direction at a speed of 300 m/yrapproximately. This method was used for the Almatti reservoir on the river Krishna in India and theresults were compared with those obtained by HEC-6 model. The two results were comparable.

9.18 METHODS FOR PRESERVING AND RESTORING RESERVOIRCAPACITY (UNESCO 1985, IRTCES 1985)

Various methods are adopted by engineers and planners to decrease the quantity of sediment enteringinto reservoir, to reduce the quantity of sediment depositing in the reservoir, and to recover part or wholeof the capacity lost for storage. These are briefly discussed below.

Methods to Reduce Sediment Deposition in Reservoirs1. Soil Conservation: Sediment entering the reservoir can be reduced by following soil

conservation methods such as watershed land-treatment measures which reduce sheet erosion;these methods are soil improvement, proper tillage methods, strip-cropping, terracing and croprotation. Reforestation of barren areas also reduces erosion. These methods are very effective insmall areas, but in large areas, it is a slow process and the effects cannot be seen in short time.The success of this method has been demonstrated in the Tungabhadra reservoir project inIndia, the Gunating reservoir on the Yongding River in North China and Eel river basin inCalifornia (U.S.A.) (UNESCO 1985). Construction of various structures such as check damson tributaries and gullies, stream bank revetments to reduce bank erosion and sills for bedstabilization also help in reducing sediment entry into the reservoir.

2. Vegetative Screens: Vegetative screens, either natural or artificial at the head of the reservoirreduce the velocity of flow and cause sediment deposition, thereby reducing sediment enteringin the reservoir. However, such screens have adverse effects in that they cause flooding of thearea and rise in water table. Such screens were used on the Pecos River above Lake McMillan,and the Elephant Butte dam on the Rio Grande in U.S.A. and the Hongshan reservoir on theLoaha River in North East China. The effects of vegetative screens have been discussed by Lara(1960) and Maddock (1948).

3. Flow Regulation: Flow regulation is effected during floods by lowering the reservoir level byopening bottom outlets under controlled or uncontrolled condition, so that flood waterscontaining high sediment concentration are allowed to flow out and only water with lesssediment concentration is stored. This has been practised on the Heisonglin and Sanmenxiareservoirs in China.

4. Venting of Density Currents: When conditions in the reservoir are favourable and densitycurrent is formed, allowing it to pass through outlets is a good method of reducing sedimentdeposition. This has been done in the case of the Elephant Butte and Lake Mead reservoirs onthe Colorado river, U.S.A., Iril Emda reservoir in Algeria, and Nebeur reservoir in Tunisiaamong others. It is estimated that in most favourable conditions 5 to 20 percent of totalsediment entering the reservoir can be vented out in this manner.


5. Drawdown Flushing: In this method the water level in the reservoir is lowered so that velocityis increased and sediment deposition is reduced. Lowering of water level can also induceerosion of deposited sediment. This has been done on many reservoirs such as the Ouchi–Kurgan reservoir in USSR.

Recovery of StorageThis can be achieved by flushing, dredging or siphoning of deposited material

1. Flushing: Periodic emptying and flushing operations can be used in large reservoirs to recoverlarge percent of storage. This has been done on Hengshan reservoir in China and Sefidrudreservoir in Iran.

2. Dredging: Generally dredging is undertaken when other methods are not effective, thereservoir is relatively small and it is economical in terms of use of water e.g. when reservoir isused for drinking water purposes or irrigation. This has been used in the case of few reservoirssuch as Akiba and Miusa reservoirs in Japan, Rand Mines reservoir in South Africa and LakeRoslyn in Oregon in U.S.A.

3. Siphoning: Siphon dredging uses the hydraulic head difference between upstream anddownstream water levels of the dam to induce suction which removes sediment. This has beendone at Rioumajou dam in France.

References

Ananian, A.K. (1961) Determination de la Formation de Lit de Riviers Cree’ par Suite de l’abaissement de la Cotede Leurs Bases d’Erosion. Proc. 9th Congress of IAHR, Dubrovnik (Yugoslavia), pp. 1102-1113.

Ansari, S.A. (1999) Influence of Cohesion on Local Scour. Ph.D. thesis, University of Roorkee, Roorkee (India).

Ansari, S.A., Kothyari U.C. and Ranga Raju, K.G. (2002) Influence of Cohesion on Scour Around Bridge Piers.JHR, IAHR, Vol. 40, No. 6, pp 717- 729.

Bhalerao, A.R. and Garde, R.J. (2003) Design of Rip-rap for Protection Against Scour Around Bridge Piers.Workshop on Bridge Scour, River Training and Protection Works, New Delhi (India), Oct. pp. 1-9.

Bolt, B.A., Horn, W.L., Macdonald, G.A. and Scott, R.F. (1975) Natural Hazards, Springer Verlag, Germany.

Bondurant, D.C. (1950) Sediment Studies at the Conchas Reservoir in New Mexico, ASCE, Proc. Separate, No.29,

Borland, W.M. and Miller, C.R. (1958) Distribution of Sediment in Large Reservoirs. JHD, Proc. ASCE, Vol. 84,No. HY2, Pt. 1, pp. 1587- 1 to 9.

Breusers, H.N.C., Nicollet, G. and Shen, H.W. (1977) Local Scour Around Cylindrical Piers. JHR, IAHR, Vol. 15,No. 3, pp. 211-252.

Briaud, J.L., Ting, F.C.K., Gudavali, R., Perugu, S. and Wei, G. (1999) SRICOS: Prediction of Scour Rate inCohesive Soils at Bridge Piers. JGGE, ASCE, Vol. 125, No.4, pp 237- 246.

Brune, G.M. (1953) Trap Efficiency of Reservoirs. Trans. A.G.U., Vol. 34, No. 3, pp. 409-418.

Bull, W.B. (1985) Floods, Degradation and Aggradation. Chapter 10 in Flood Geomorphology (Eds. Baker, V.R.Kochel, R.C. and Patton, P.C.), A Wiley Interscience Publication, John Wiley and Sons, N.Y. pp. 157-165.

CBIP (1975) Local Scour: A Review. Literature Review 34 Compiled by UPIRI, Roorkee (India).

Davies, B.E. (1974) Armouring of Alluvial Channel Beds. M.E. Thesis, University of Canterbury, Christchurch,New Zealand.

River Morphology312

Doyle, W.M., Stanley E.H. and Harbor, J.M. (2003) Channel Adjustments Following Two Dam Removals inWisconsin. W.R. Research. Vol.39, No.1, ESG 2, 1-15.

Egiazaroff, I.V. (1965) Calculation of Non-uniform Sediment Concentration. JHD, Proc. ASCE, Vol. 91, No. HY-4, July, pp. 225-247.

Ettema, R. (1980) Scour at Bridge Sites. University of Auckland, Auckland, New Zealand, Rep. No. 117.

Evans, J.E., Mackey, S.D., Gottgen, J.F. and Gill, W.M. (2000) Lessons from a Dam Failure. Ohio Jour. of Science,Vol. 5, pp. 121-131.

Galay, V.J. (1980) Engineering Aspects of River Bed Degradation. Annual Conference of Canadian Soc. of CivilEngg, Winnipeg, H/7:1 -16.

Galay, V.J. (1983) Causes of River Bed Degradation. W.R. Research, Vol.19, No. 5, Oct., pp. 1057-1090.

Gangadharaiah, T., Sethia, B. and Sheshagiri Rao, R. (2003) Scour Protection Around Bridge Piers andAbutments. Workshop on Bridge Scour, River Training and Protection Works, New Delhi (India), Oct. pp. 27-41.

Garde, R.J. (1955) A Report on Degradation Below Dams. Report submitted to Civil Engg. Dept., Colorado A. andM College, Fort Collins (USA).

Garde, R.J. and Kothyari, U.C. (1995) State of Art Report on Scour Around Bridge Piers. Report Submitted toIIBE, Pune. 109 p.

Garde, R.J. and Ranga Raju K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems.New Age International Publishers, New Delhi.

Garde, R.J. and Ranga Raju K.G. and Kothyari, U.C. (1987) Effect of Unsteadiness and Stratification on LocalScour. Research Report, Civil Engg. Dept., University of Roorkee (India).

Garde, R.J. Sahay, A. and Bhatnagar, S. (2004) Grain Size Distribution of Armour Coat. Proc. of Intl. Conferenceon Hyd. Engg. Research and Practice, I.I.T. Roorkee (India), Oct.

Gessler, J. (1965) The Beginning of Bed Load Movement of Mixtures Investigated as Natural Armouring inChannels. Laboratory of Hyd. Research and Soil Mechanics, Swiss Federal Institute of Technology, Zurich,Rep. No. 69.

Gessler, J. (1970) Self Stabilizing Tendencies of Alluvial Channels. JWWHD, Proc. ASCE, Vol. 96, No. WW2,pp. 235-249.

Gessler, J. (1971) Aggradation and Degradation. In River Mechanics (Ed. Shen, H.W.), Published by H.W. Shen,Fort Collins, U.S.A. Vol. 1, pp. 8-1-24.

Gilbert, G.K. (1917) Hydraulic Debris in the Sierra Nevada. USGS Professional Paper No. 105, 154 p.

Harrison, A.S. (1950) Report on Special Investigation of Bed Material in a Degrading Bed. IER, Univ. ofCalifornia, Berkley, U.S.A., Series No. 33, Issue No. 1.

Hathaway, G.A. (1948) Observations on Channel Changes, Degradation and Scour Below Dams. Paper Presentedat 2nd Conference of IAHR, Stockholm, pp. 287-307.

Heinemann, H.G. (1981) A New Trap Efficiency Curve of Small Reservoirs. W.R. Bulletin, Vol. 17, No. 5, Oct.

Huber, E. (1991) Update : Bridge Scour. Civil Engineering ASCE (U.S.A.), Sept.

IRTCES (1985) Lecture Notes of the Training Course on Reservoir Sedimentation. Beijing (China).

Islam, M.N., Garde, R.J. and Ranga Raju, K.G. (1986) Temporal Variation of Local Scour. Proc. of IAHRSymposium on Scale Effects in Modelling Sediment Transport Phenomenon, Toronto, Canada.

Jensen, P.Ph., Bendegom, L. Van, Berg, J. Van den, deVries, M. and Zanen, N. (1979) Principles of RiverEngineering: The Non-Tidal Alluvial river. Pitman and Co., London, Chapter 4.

Kand, C.V. (1993) Scour-Sand, Clay and Boulders. Bridge Engineering (India), Vol. 9 and 10


Kellerhals, R. Church, M. and Devies, L.B. (1977) Morphological Effects of Interbasin River Diversions. PaperPresented at Hydro-technical Conference, Canadian Soc. Civil Engg. Quebec City.

Klaassen, G.J. (1995) Lane’s Balance Analogy. Proc. of 6th International Symposium on River Sedimentation,New Delhi (India), pp. 671-686.

Kochel, R.C. (1985) Geomorphic Impact of Large Floods : Review and New Perspectives on Magnitude andFrequency, Chapter II in Flood Geomorphology (Eds. Baker V.R.., Kochel, R.C. and Patton, P.C.) A WileyInterscience Publication, John wiley & Sons, N.Y., pp. 169-187.

Kothyari, U.C. (1989) Effect of Unsteadiness and Stratification on Local Scour. Ph.D. Thesis, Civil EngineeringDepartment, University of Roorkee (India).

Lane, E.W. (1953) Some Aspects of Reservoir Sedimentation. JIP, CBIP (India), Vol. 10, No. 2 and 5, April andJuly, pp. 3-14.

Lane, E.W. (1955) The Importance of Fluvial Morphology in Hydraulic Engineering. Proc. ASCE, Paper 745, pp.1-17.

Lara, J.M. (1960) 1957 Sedimentation Survey of Elephant Butte Reservoir. Bureau of Reclamation, USDI, U.S.A.

Little, W.C. and Mayer, P.G. (1972) The Role of Sediment Gradation on Channel Armouring, School of CivilEngineering, Georgia Institute of Technology, Atlanta, Georgia (U.S.A.), ERC-0672.

Maddock, T. (1948) Reservoir Problems with Respect to Sedimentation. Proc. Federal Interagency SedimentationConference, USDI, pp. 9-14.

Mahamood, K.C. (1987) Reservoir Sedimentation : Impact, Extent and Mitigation. World Bank Technical PaperNo. 71, 118 p.

Melville, B.W. and Sutherland, A.J. (1988) Design Method for Local Scour at Bridge Piers. JHE, Proc. ASCE, Vol.14, No. 10, Oct., pp. 1210-1226.

Miraki, G.D. (1983) Sediment Yield and Deposition Profiles in Reservoirs. Ph.D. Thesis, University of Roorkee(India).

Mittal, M.K. (1985) Parallel and Rotational Degradation. Proc. of 2nd International Workshop on Alluvial RiverProblems. University of Roorkee, pp. 17-22.

Mohan, J. and Agarwal, A.K. (1980) Aggradation of Upper Ganga Canal. Proc. of 1st International Workshop onAlluvial River Problems. Roorkee (India), pp.2-61-72.

Murthy, B.S., Surya Rao, S., Rajagopal, H., Tiwari, S.K. and Rajesh Kumar (1998) Flood and Sediment Routing inRiver Systems Mathematical Models. Report Submitted to INCH by Civil Engineering Department, I.I.T.,Kanpur, 159 p.

Namjoshi, A.G. (1992) Anticipated Scour Depth in Non-Alluvial/ Clayey Beds. Proc. Intl. Seminar on BridgeStructure and Foundations. Conference Documentation 3, Vol. 2

NIH (1986) Sedimentation in Reservoirs. Report R.N. 26, National Institute of Hydrology, Roorkee, 98 p.

Odgaard, A.J. (1984) Grain Size Distribution of River-bed Armour Layer. Proc. ASCE, JHE, Vol. 110, No. 10, pp.1479-1485.

Sahay, R.N., Pande, P.K. and Garde, R.J. (1980) Aggradation in Eastern Kosi Main Canal. Proc. 1st InternationalWorkshop on Alluvial River Problems. Roorkee (India), pp. 2-73-78.

Scheuernlein, H. (1989) Critical Review of Various Methods to Prevent or Control Degradation in Rivers. Proc. of4th International Symposium on River Sedimentation. Beijing (China), Vol. 2, pp. 1095-1102.

Shen, H.W. and Lu, J.Y. (1983) Development and Prediction of Bed Armouring. JHE Proc. ASCE, Vol. 109, No. 4,pp. 611-629.

Stevans, J.C. (1938) Effect of Silt Removal and Flow Regulation on the Regime of Rio Grande and ColoradoRivers, AGU, Pt. 2, pp. 653-661.

River Morphology314

Swamee, P.K. and Garde, R.J. (1977) Progressive Reduction of Reservoirs Capacity Due to Sedimentation. CivilEngg. Department, University of Roorkee, Research Report.

Todd, O.J. and Eliassen, S. (1940) The Yellow River Problem. Trans. ASCE, Vol. 105, pp. 346-416.

UNESCO (1985) Methods of Computing Sedimentation in Lakes and Reservoir : A Contribution to IHP-II Project,A-2.6.1 Panel, Feb., 224 p.

Vetter, C.P. (1953) Sediment Problems in Lake Mead and Downstream on the Colorado River. Trans. AGU, Vol.30, No. 2, April, pp. 291-295.

Wörman, A. (1989) Rip-rap Protection without Filters. JHE, Proc. ASCE, Vol. 115, No. 12, Dec. pp. 1615-1630.

Yearke, L.W.C. (1971) River Erosion Due to Channel Relocation. Civil Engineering (Canada), Vol. 4, No. 8, pp.39-40.

Zhide, Z. (1991) Empirical Methods of Estimation of Loss of Reservoir Capacity. Lecture Notes of RegionalTraining Course on Reservoir Sedimentation, New Delhi, pp. 3.6.1-3.6.34.

10C H A P T E R

River Channel Changes

10.1 INTRODUCTION

It is seen in Chapter 9 that human interference in terms of change in Q, Qs or water surface slope in anequilibrium stream can induce aggradation or degradation. Such changes in bed level also take placebecause of change in land use, catastrophic floods, and tectonic or neo-tectonic activity. In thisdiscussion it was assumed that the channel width or plan-form remains unchanged. The changes in bedlevel resulting from human interference were widely studied by engineers in the first six decades of 20th

century. Since then considerable interest has been evinced in changes in drainage pattern and channelchanges as can be seen from the works of Allen (1965), Leopold et al. (1964), Schumm (1969, 1971,1977), Gregory (1977), and Gurnell and Petts (1995). These changes are briefly discussed herein.

Lewin (1977) classifies channel changes into two categories namely autogenic changes andallogenic changes. Autogenic changes are the ones which are inherent in the river regime and involveavulsion, channel migration, cut-offs and crevassing. Allogenic changes are the ones which occur inresponse to system changes involving climatic fluctuations and altered sediment load or discharges, as aresult of human activity. If a channel is migrating in the valley created by it, some geomorphologistsconsider such a stream, in regimen. Newson (1995) has given a sketch indicating the type of changesthat take place in the stream as it debouches from mountains and joins the sea. This is shown in Fig.10.1; this figure indicates that avulsion is more likely to occur when stream is about to enter from steepslope region into the plain with flatter slope. Bank erosion, bar formation and meander shifting occur inthe middle reaches, slumping of banks, building of flood plain and channel migration take place in thelower reaches.

10.2 AVULSION

Horizontal instability of a single channel alluvial stream can take two forms, either avulsion or patternchange. Avulsion is a sudden abandonment of part or whole of the stream for a new course at a lowerlevel of floodplain. This has occurred in the recent history of such streams as the Mississippi and the Rio

River Morphology316

Grande in U.S.A., the Meandros in Turkey, the Rufiji in Tanganyika, the Kosi in India (Allen 1965), andthe Yellow river in China. In an aggrading stream or a stream shifting its position in meander belt, theriver bed rises and forms an alluvial ridge. Greater the height of the ridge above the floodplain, the morelikely it is that local crevassing will result in some permanent change in the stream course and it willflow through one of the palaeo channels or carve a new course. As mentioned by Frisk (1944) theMississippi recently built in its floodplain at least five alluvial ridges along meander belts up to 80 kmapart.

Richards et al. (1993) consider the avulsive channel system, in which the key depositional processinvolves the relationship between channels within the system, rather than the behaviour and propertieswithin a channel. In such a system there is areal sedimentation so that the basin fills relatively uniformlyover time scales of a few thousand years. Such a system exists in the Gangetic plain at the foothills of the

Fig. 10.1 Alluvial stream problem problems involving erosion, deposition etc. (Newson 1995)

Channel aggradesand bank erodes

Conveyance loss offines to floodplain

Erosion of banks asbars acrete

Build up on bankfollowed by collapse

Erosion of banksdue to slumping

Conveyance loss offines to floodplain

Fines washed outto sea

Channel blockage

Slope failure

Knock-on effect of thesediment system

Lowland

Transfer

Upland

River Channel Changes 317

Himalayas. The mechanism of evolution of the present day avulsive systems includes (i) aggradation ofchannel and floodplain by the accumulation of bed-load and suspended load, (ii) increasing but neverthe less subtle topographic differences and flood overspills; and (iii) avulsion due to over spilling andstream capture.

The Gangetic plain consists of 400-600 m thick alluvial deposit in the tectonically controlledHimalayan foredeep basin. This area has experienced two earthquakes in 1934 and 1988 of magnitudes8.4 and 6.5 respectively on the Richter scale. Avulsion has taken place at varying rates across the basin.The higher rate of sediment supply in the northern margin of the Gangetic plain has caused rapidaggradation and more frequent channel shifts on the Kosi mega-fan. Mega-fans are large size fans of100-200 km in width and 100-150 km length in the humid environments. They are triangular in shapewith their apex at the gorge mouth, convex in form and are characterized by steep gradients (20 cm/km).The Ganga plain consists of several fan and inter-fan areas viz. Yamuna-Ganga mega-fan, Sarda fan,Gandak mega-fan and Kosi mega-fan. Inter-fan areas (intercones) are reverse in plan, tapering fromHimalayas, slightly concave at edges and with gradients 10 cm/km or less (Jain and Sinha 2003).

East-west trending Gangetic plain is characterized by geomorphological diversity in terms ofmorphology, hydrology and sediment transport rates of the rivers. Most of the rivers such as the Ganga,the Kosi and the Yamuna display braided as well as meandering plan-forms, and some such as the Kosi,the Bagmati and the Rapti show change from braided to meandering pattern.

Further, most of the streams draining the area are known for their rapid and frequent avulsions albeitwith varying frequencies. As discussed in Chapter 13, the Kosi has migrated 110 km in 200 years beforeit was embanked in 1963. (see Fig. 13.7). The primary reasons for this migration are high sediment load,tectonic activity, frequent floods and general westward slope. The Sarda river has undergone shiftingand river capturing during the last 80 years (Tangri 2000) and the Gandak has migrated eastward by 80km during the past 5000 years.

Data on lateral migration of alluvial steams were collected by Wolman and Leopold (1957). It wasfound by them that while since streams showed continuing tendency for lateral migration over a periodof years, in some instances the stream channel maintained a reasonably stable position and had littlelateral movement over a long period of time. However, the same site experienced very rapid movementduring a succeeding period. In other words, the lateral movement can be continuous or discontinuous.Further, it was found that in general larger streams seem have larger rates of migration. The migrationrate of the Kosi during 1936-1950 periods varied 0.18 km/yr to a maximum of 2.63 km/yr during 1922-1933. The Ramganga river in north India moved westward at 80.5 m/yr during 1795-1806 while itmoved eastward at 4.3 m/yr during 1806-1883 and westward at the rate of 4.0 m/yr during 1883-1945.Table 10.1 gives data on lateral migration rates of some rivers across valleys.

In the case of the Yellow river in China, Chien (1961) has shown that the channel shifting (lateralmigration) varies with the fluctuations in discharge quantified as ratio of maximum flood discharge tothe bankful discharge. In the case of the Yellow river the migration rate varied from 20 m/day to 200 m/day. Such large variation is due to heavy sediment carried by the river. He also found that the amount ofshifting is controlled by the spacing of constrictions or control points along the river.

Jain and Sinha (2003) have studied in detail the avulsive tendency of the river Bagmati using surveyof India topographic maps and satellite imageries. The Bagmati river draining north Bihar plains is ananabranching stream with repetitive avulsive history. Figure 10.2 shows the avulsions in the Bagmati for

River Morphology318

Table 10.1 Data on lateral migration rates of some rivers across valleys (Adapted fromWolman and Leopold 1957)

River Drainage Period of Rate of move- Commentsarea km2 measurement ment m/yr

Watts Branch near 10 1953-1956 0.60 From topographic mapRockville Md.

North River, Va 128 1834-1884 2.44 Local observation

Ramganga river, India 256 000 1795-1806 80.50 (W)1806-1883 4.30 (E)

Kosi river, India … 1883-1945 4.00 (W)

Colorado river near 437 000 150 years 1858- 750.00needles, California 1883 243.00 For one bend

1903-1942 30.00

Yukon river, at Holy Cross, 819 200 1896-1916 36.60 Local ObserverAlaska

Missouri river, near Peru, 896 000 1883-1903 76.20 Rate varied from 15 m/Nebraska yr to 150 m/yr

Mississippi river near 2816 000 1930-1945 45.20Rosedale, Mississippi

the past 230 years in which it may be noted that the river has shifted first towards east, then northeast,south and southwest. The primary causes for the instability of the Bagmati are believed to be variabilityin the peak discharge, frequent over-spilling and relatively high sediment load. Effect of channelavulsion resulting in the abandonment of bridge on the Bagmati is shown in Fig. 10.3.

Avulsion of the TigrisIt is also interesting to discuss the avulsions of the Tigris and the Euphrates rivers in ancientMesopotamia (now known as Iraq). Mesopotamia is in fact one huge delta formed by joining of theTigris and the Euphrates to the Persian Gulf. The ancient city of Ur which was founded about 4000years B.C. on the still marshy limits of the gulf and which served as a seaport during historical times,now lies about 150 km inside (Garde 1978). The Tigris has undergone three shifts, see Fig. 10.4; the firstshift was between slightly south of Samara and slightly north of Baghdad. The old course shifted to thenew one in the 13th century. The second shift south of Ctesiphon is also shown. Both these shifts areinferred by McAdams from the archaeological sites of the Parthian period (311 B.C.–226 A.D.). Thethird shift is shown in the bottom figure. Presently the Tigris follows a winding course in the south-eastdirection downstream of Baghdad for about 400 km. The combined river is then called Shat-al-Arab (theArab stream). However, in the Muslim period up to the 16th century, the Tigris came about 160 kmbelow Baghdad, then came straight south by a channel known as Shat-at-Hai to Wasit. Then 700 kmbelow Wasit the river lost most of its water by irrigation channels and finally became lost in the swamp.


Fig. 10.2 Avulsion of the Baghmati (Jain and Sinha 2003)

Fig. 10.3 Effect of avulsion in the Baghmati river

River Morphology320

Avulsion of the Yellow River (Xu Fuling 1982, Lin and Li 1986)Another example of avulsion is the Yellow river in Peoples Republic of China. This river is known allover the world for the heavy sediment load it carries with relatively small volume of runoff, and is oftenknown as “river of sorrow”. The Huanghe (or the Yellow river) which originates at Togo has an upperreach of 3461 km with a drop of 3480 m; the major tributaries in this reach are the Datonghi, the Taohe,the Huangshui, the Julihe and the Shanshuihe. This reach of the river carries relatively less sediment, thetotal annual sediment load being only 11 percent of the whole river, while the annual runoff from thisreach is 56 percent of the entire river. The middle reach from Togto to Taohuayu is 1235 km long inwhich the major tributaries the Wudinghe, the Yianshui, the Fenhe and others, flowing through Loessregion, discharge into the Yellow river. Hence this reach carries a heavy sediment load. From Taouayu tothe estuary is the lower reach after which the river joins the Bohai sea. This lower reach is 768 km longand flows through a region in which more than 100 million people live. This reach has a flat slope of

Fig. 10.4 Changes in the courses of the Tigris


0.000 125 and the flood discharge in this reach is 4000 m3/s to 5000 m3/s but can reach 10 000 m3/s.Long-term average sediment concentration in the lower reach is 34 kg/m3 while the maximum observedis 594 kg/m3. The sediment concentration in the tributaries can reach as high as 1000 to 1500 kg/m3. Thesediment transported has a size range of 0.002 mm to 0.05 mm. Because of the high concentration andflat slope, almost 50 percent of the sediment carried by the lower Yellow river at Zhenzhou (see Fig.10.5) is deposited in the river. As a result of this aggradation, the river bed between the floodembankments is higher than the ground level outside by 3 to 5 m and is rising at an average rate of 0.1 m/yr. At some places this difference is as large as 10 m.

Fig. 10.5 The Yellow river

Levees or flood embankments in the lower reach of the Yellow river are about 1370 km long whichare attacked during the flood and breaches occur causing flooding of low lying areas and change in theriver course. This avulsive tendency in the lower reach of the Yellow river is present since historic times.Changes in the course of the river since 2000 BC to the present time are shown in Fig. 10.6. As can beseen, the river has swept over a big fan-shaped area between the Huaihe river in the south and the Haiheriver in the north. In the past 1000 years 1593 breaches of the levees have been recorded out of which 26breaches resulted in extensive flooding and the river changing its course to a new channel.

To control floods, the levees have been raised by 2 to 6 m to a height of 10 m; they have also beenwidened so that the top width is now 7 to 15 m and berms have been provided on the landside. Also toprovide additional protection, more than 300 km length of the levees has been provided with stonepitching and more than 5000 short spurs have been constructed.

10.3 STREAM CAPTURE (WORCESTER 1948, LOBECK 1939)

Stream Capture results when one stream flowing in the lower region works head-ward and interceptshead waters of the stream draining in higher area. The stream flowing at the lower level always has theadvantage. An example of stream capture is shown in Fig. 10.7. Figure 10.7 (a) shows the conditionsjust before the capture. The river heading in the escarpment can, because of its steep gradient cut backrapidly into the drainage area of the stream flowing on the plateau above, even if the rocks of the regionare all homogeneous and of equal resistance to erosion. Figure 10.7 (b) shows the condition shortly after

Xining

Lanzhou

Welhe RXi'an Zengzhou

JinheR

Yan'an

Qinshui R L

uohe

R

Feobe

RTa

iyuan

HuangheR

Jinan

BeijingHuhehaote

Tuoke

tuo

Wudin

gR

Yin

chuan

Bohai sea

Yellow sea

River Morphology322

the capture. The captured stream has been diverted by the captor stream and now turns sharply at thepoint of capture, known as the elbow of capture. The difference in level of the two streams results in awaterfall. The captor stream has its discharge increased by the addition of captured stream and begins toshow signs of rejuvenation. Its gorge in deepened, and its tributaries on either side below the point ofcapture cut back rapidly to form other gorges. The beheaded stream, having lost much of its discharge,acquires mature characteristics. It develops small meanders, not suited to the size of its valley. Itbecomes a misfit or underfit stream. Its tributaries build alluvial fans on the valley floor because thebeheaded stream in its shrunken condition can no longer transport its sediment load. Figure 10.7 (c)shows the conditions long after the capture. The headwaters of the captor stream have all developedgorges. The falls at the point of capture have retreated upstream to head of the diverted stream. Withfurther development all the falls and rapids disappear and the only evidence of capture remaining will bethe angular bend.

Stream capture also takes place in the case of stream migrating on the cone or the fan developed byit due to sediment deposition. During its avulsion in a new course, the stream can capture smallerstream. Similarly when the streams meander widely over flood plains, stream capture is common due tolateral cutting and intersection of meanders.

Fig. 10.6 Historical migration of the Yellow river (Lin and Li 1986)

0 About 2000 BC

0 602 BC

0 11 AD

0 1048 AD

0 1149 AD

0 1494 AD

0 1855 AD

0 1938 AD

Beijing

Tianjin

Bohai seaHutu

oR

Fuyang

R

Jinghai

Canoxi

an

Wuyi

Liji

n

Xiao qing RJulu

Jinan

Dongping Lake

Weishan Lake

HuaiyanXuzhou

DangshanShangqui

LankaoZhengzhou

YanjinPuy

aing

Zhanghe RG

aotang

Heze

Wohe RYinhe R

HongheR

Huaihe R

7

5

4

6

1

2

3

03

Nanjing

Yangzhon

Changian


10.4 EROSION AT BENDS

Some studies have been carried out in the past to find out the variables which govern the rate of erosionor migration of bends in alluvial rivers. Wolman (1959) has reported rates of erosion in cohesive riverbanks and recognized the important of seasonality in the rates of erosion. Daniel (1971) has monitoredthe effect of erosion in the form of changes in outer bank of meander bends along streams in Indiana.According to Dury (1961) annual flood magnitude is of importance in this erosion, while Harvey (1975)has commented on the effectiveness of intermediate discharge. Hughes (1977) made measurements onthree meander arcs on the river Cound in U.K. during 1972-74. This river has width to depth ratio of 15.The rates of erosion were measured using 92 pegs and monitoring the distance of the bank line fromthese pegs. The discharge during the study duration varied from 1.0 m3/s to 10.0 m3/s. It was found that

Fig. 10.7 River capture (Lobeck 1939)

River Morphology324

the two meander arcs having large bend radius had average erosion rates of 1.61 m/peg and 1.51 m/pegwhile the third arc which had a smaller radius showed erosion rate of 1.9 m/peg.

It was also found that for discharge less than 2.0 m3/s the erosion rate of banks was minimum. Fordischarges between 2.0 and 8.0 m3/s the erosion rate was moderate, and for discharge greater than 8.0m3/s major erosion changes occurred. The corresponding return periods for 2 m3/s and 8.0 m3/s wereestimated as 10-12 times/yr and 1.5 yrs respectively. Similarly Hooke (1995) studied the migration ofbends on five streams in East Devon (U.K.) having catchment areas between 110 km2 and 620 km2. Hefound the average rate of migration to be 0.37 m/yr while the maximum was 1.32 m/yr.

Studies of Nanson and Hickin (1983) and Hickin and Nanson (1984) throw light on the parameterson which dimensionless migration rate M1/W, where M1 is migration rate in m/s and W is the channelwidth, depends. According to them

M

W1 = f

Stream power, erosional resistance of concave bank material, height of

concave bank, sediment supply rate, r

Wc

F

HGG

I

KJJ

Further, it stands to reason that average bed material size d should come in the picture and it canassumed that sediment supply rate should be related to stream power QS. The above relation can then bewritten as

M

W1 = f

QS

dd

h

D

r

Ws

f

c

2 D gr

, ,erosional resistance of concave bank material,

F

H

GGGG

I

K

JJJJ

where rc is the centerline radius of curvature of the bend, h is the height of concave bank above waterlevel and D is depth of flow. Further, Hickin and Nanson (1984) found that when rc/W = 2.5 the

migration rate of the bend is maximum. This maximum value of M

W1 denoted by K is intuitively assumed

to be a function of stream power, h

D and erosional resistance. Hence he has plotted

M

K W1 vs

r

Wc for

r

Wc

ranging from 1.18 to 13.0 for bends and for which K = M

W1b gmax was 0.02. The graph between

M

K W1 and

r

Wc is shown in Fig. 10.8 and it is anticipated that data for other bends would follow the same trend.

Nanson and Hickin (1983) have further stated that channel migration is discontinuous as a result ofseasonal fluctuations in flow; hence short-term migration rates are not indicative of the averagemigration rate of the bend.


The seriousness of bank erosion can be illustrated by discussing erosion upstream of the Farakkabarrage on the river Ganga (Majumder 2004), see Fig. 10.9. Farakka barrage was constructed across theriver Ganga in 1971 to divert 1135 m3/s (40 000 cfs) of water to its tributary, the Hooghly river, in orderto keep Kolkata port navigable throughout the year. This diversion has been effected by constructing a3.8 km long feeder channel from Farakka barrage. Upstream of the barrage, the river slope is 0.000 06and the bed is made of fine to medium sand. The flood discharge over the past 32 years has variedbetween 36 290 m3/s and 77 778 m3/s. Further, while the distance between the permanent banks is about16 km, the river width is about 2 km in the river reach upstream of the barrage.

Prior to the construction of barrage, the river was flowing straight from Rajmahal to the barrage site.However in 1963 the course of the river started gradually shifting towards the left and attacking thevillage on the left bank e.g. Panchanandpur about 20 km upstream of the barrage, see Fig. 10.9. The rateof bank migration has varied from year to year, but over the past 30 years the apex of the bend hasmigrated through approximately 8000 m giving an average rate of migration of 36.7 m/yr. Configurationof the bend is such that the bend radius is about 14 km giving radius to width ratio of about seven. As aresult of migration of the bend to the east for the past six years, the area eroded has varied from 100 to415 ha per year. The area being fertile it is thickly populated, and hence during a flood, loss of the orderof 500 to 1000 crores of rupees takes place. Further, to the northeast of Farakka barrage flow smallerstreams the Kalindri, the Pagla, the Old Bhagirathi, and the Mahananda. It is possible that if themigration towards the east continues, the Ganga may capture the above mentioned streams one afteranother and then flow along the Mahananda thus changing its course drastically. Hence some steps havebeen taken to arrest this migration; these include building of retired embankments as erosion proceeds,and construction of spurs. However, these measures seem to have only a marginal effect. It seems thateffective management of this problem should involve firstly the stabilization of the eroding bank bygiving proper slope to the bank and then providing bank protection. The next step that needs to be takenis to reactivate the existing small channel on the right side so that it starts carrying increasing amount of

Fig. 10.8 Variation of M

KW1 with

rW

c

r /Wc

141210864200.0

0.2

0.4

0.6

0.8

1.0

M

KW

1

Beatton river data

River Morphology326

Fig. 10.9 Bank-line changes upstream of Farakka barrage on the Ganga

flow there by decreasing the flow along the left bank. This can be assisted, if necessary, by dredgingdownstream of Rajmahal.

Hooke (1995) has summarized information about mechanisms of bank erosion. These are broadlyclassified into three broad categories namely bank weakening, fluvial erosion or entrenchment, andmass failure. Bank weakening can be due to pre-wetting downwards by precipitation front, inwardsfrom the river or upwards by the water table. Similarly bank weakening can occur by desiccationcondition of high temperature and low moisture which can lead to cracking and spalling. Similarlyfreezing and thawing action can also make the bank more susceptible to erosion. Fluvial erosion can bedirect removal of non-cohesive material when flow and shear stress near the bank exceed a certain limitduring flood. Resistance to such type of erosion is affected by vegetation, composition and state of thematerial and its cohesivity. Mass failure can be of two types. Shear, beam and tensile cantilever failuresoccur mainly on composite banks. Initial fluvial failure takes place of basal coarse materials and thenfailure of the upper fine blocks takes place. The second type of mass failure is shear failure. This occursin cohesive materials associated with increased bank angle and/or bank height, high moisture contentand pore pressures. Failure takes places after occurrence of peak flow.

10.5 NATURAL AND ARTIFICIAL CUT-OFFS

In most of the cases the meanders in alluvial streams are not stationary but move slowly in the directionof flow. During the development and movement of meanders there is a gradual lengthening of meanderswhich imparts a lateral movement to meanders. Hence in few cases movement of meanders is in lateraldirection thereby increasing the amplitude of meanders. Increased frictional and bank resistance tendsto halt the lateral movement. When the bend and bank resistance become too large for continued

19971998

1999200020012002

19221939

1967

Bhuti DiaraManikchakManikchak

Rajmahal

Kalindri

Mahananda Bhagirati RailwayPagla

NH34

FarakkabarrageFarakkabarrageFarakkabarrage

1939

1922

Panchanandpur


stretching of the loop, it is easier for the flow to cut across the neck of the loop than to flow along thebend, resulting in a natural cut off. The two ends of the loop that is cut get gradually silted up and giverise to an oxbow lake. Usually small and narrow side channels are available within a neck of themeander loop. These channels are either part of the main channel when the stream was flowing alongthat course or are formed by spilling of floods over the banks. Cut-off may develop along these smallchannels. The development of a small channel in the neck into a major natural cut-off primarily dependson the assistance this channel receives from the major floods in increasing its cross-section. If a largeflood lasts for a relatively long period, the channel gets sufficient time to develop into a full waterway.Development of such a natural cut-off requires two to three years, or probably even more time.

Natural cut-offs have occurred on the Mississippi river in U.S.A. and other rivers in the world. Onthe Mississippi, natural cut-offs have taken place when the cut-off ratio i.e. arc distance along the bendto the neck distance ratio, was between 8 and 10. Analysis of historical data on 145 natural cut-offs onrelatively smaller streams in England and Wales has shown (Lewis and Lewin 1983) that cut-offs haveoccurred for rc/W ratio ranging from 1.0 to 12.0. However, a large number of these cut-offs haveoccurred at rc/W values between 1 and 4. Assuming that the meander pattern is made up of arcs of acircle, Chatley (1940) has shown that, from purely geometric point of view, cut-off occurs when MB =

(2 + 3 ) rc because at this value the neck distance will be zero.

According to Frisk (1944) natural cut-offs are of two types:

Neck Cut-offThis cut-off forms in response to river flow across the narrow neck of the over extended meander loop.For neck cut-off to occur, the neck has to be narrow enough so that the flood water breaks through andforms a cut-off. This type of cut-off rapidly abandons the old bend, forms an oxbow lake and is rapidlysilted up at its end since the sediment can then enter the oxbow lake only from local inflow or from overbank flood flows; further deposited sediment consists of finer sediment, normally decreasing in sizewith distance from the new channel.

Chute Cut-offThis type of cut-off forms in response to the development of a chute across a low lying swale within theenclosed point bar area of an over extended meander bend. The old channel is abandoned slowly andwith the gradual reduction in flow, is filled with silt and sand material and finally with clay. These twotypes of cut-offs are shown in Fig. 10.10. Friedkin (1945) noted in his flume tests that there was alimiting size for each meander pattern and that, when for any reasons this size was exceeded, chute cut-offs invariably occurred. In natural streams they have been observed to occur during flood flows thattended to follow a straight path and during lesser flows when either the loop in question or the adjacentloop became excessively enlarged.

Artificial cut-offs are executed on the streams to reduce the stream length and thereby reduce theflood heights and flood periods, and to shorten the travel distance and increase the manoeuvering abilityof water vessels during navigation along the bends. Pickles (1941) has estimated that if all the bends ina typical alluvial river are cut-off, the average velocity in the stream will increase by about forty percent.In the past artificial cut-offs have been executed on many rivers in the world such as the Mississippi, theArkansas and the Missouri rivers in U.S.A., the Tisza river in Hungary, the Hai river in China and some

River Morphology328

streams in New Zealand. By execution of such cut-offs the length of the Mississippi has been reducedfrom 720 km to 480 km and that of the Tisza from 1299 km to 745 km.

The execution of artificial cut-offs is done slightly differently in Europe and in U.S.A. In Europe,the cut-off is made in the dry and to its full dimensions, and the river is allowed into it. American andNew Zealand practices are similar, in which a pilot channel of small cross-section is made which caninitially carry about 8 to 10 percent of flood discharge and it is allowed to develop by itself. This channeldevelops fully in about 3 to 4 years. Pickles (1941) has given the following suggestions in the design andexecution of cut-offs.

i. The pilot channel should be tangential to the incoming flow as well as while leaving the cut.

ii. The pilot channel should be made on a slight curve, the curvature being less than the dominantcurvature of the river.

iii. Entrance to the pilot channel should be made bell-mouthed.iv. Cut-off should be excavated to the mean river cross-section.v. When a series of cut-offs is to be made, the work should progress from downstream to the

upstream.When a cut-off is executed, there are some short term and some long-term changes in the rivers;

these need to be properly understood. As soon as the cut-off is executed the water surface slope withinthe cut-off reach is increased. This causes M2 profile upstream of cut-offs and M1 profile downstream.Further this change in water surface slope in the upstream reach will reduce the storage and the peakdischarge downstream of cut-off is likely to be increased. The long period change will be in the bedprofile. Reach upstream of the cut-off will experience degradation while that downstream willexperience aggradation.

The effectiveness of cut-offs as means of flood control is discussed by Pickles (1941). Asmentioned earlier, if all the bends are removed, the flow velocity is likely to be increased by about fortypercent. Whether the expenditure involved in straightening is justified as a flood control measuredepends on the width of the flood plain. If the flood plain is approximately 0.8 km wide of less, thechannel improvement using cut-off is justifiable because cost of levee construction will be prohibitive.

Fig. 10.10 Chute and neck cut-offs

Chute cut-off

Neck cut-off

Point bar


If the flood plain is 1.5 to 6.5 km wide, cut-offs together with levee construction are the accepted methodof flood protection. For every wide flood plain, flood protection is seldom attempted using cut-offs.However, cut-offs can still be executed if the stream is used for navigation.

Lastly, it needs to be emphasized that when cut-off is executed the banks in that reach needprotection, otherwise stream will have a tendency to develop a meander loop again.

10.6 CHANNEL PATTERN CHANGES

Sinuosity is earlier defined as length of stream divided the length of the valley. The sinuosity valuesrange from 1 to slightly greater than 3.5. Analysis of American rivers by Leopold and Wolman (1960)indicated that the sinuosity varied from 1.0 to 3.0. The average sinuosity of the Mississippi is 2.3 whileits maximum value at the Greenville Bends at Greenville was 3.3.

In single channel stream it is interesting to study variation in the sinuosity of the stream. Studies bySchumm (1977) have indicated that the sinuosity is significantly affected by the differences in the flowvariation. To support this argument he has given example of two streams the Tanoro and the Guanipa.The characteristics of these two streams are given below.

River d mm Mean annual Qmax m3/s Qmax/Qma Si

discharge Qma m3/s

Tonoro 0.35 11.34 535.6 47.23 1.1

Guanipa 0.35 17.00 104.9 6.17 2.3

From this it seems that Qmax/Qma ratio is morphologically important in determining the sinuosity;higher sinuosity is associated with lower value of Qmax/Qa.

Experiments in a laboratory flume by Khan (1971) have indicated that the sinuosity was function ofslope. For small slopes the channel was straight; when the slope exceeded a certain limit the channelmeandered and sinuosity increased with increase in slope and reached a maximum value. Furtherincrease in slope decreased the channel sinuosity and then the channel became straight and braided.Similar variation between valley slope and sinuosity has been reported for the Mississippi betweenCairo (Illinois) and Head of Passes (Louisiana) by Schumm (1977). Schumm argues that the valleyslope reflects the past discharges and sediment loads while the channel slope corresponds to the presentdischarge and sediment load variations. By plotting valley slope versus channel slope for some streamsand palaeo channels, he found that channels with low percentage of silt and clay in channels, hadsinuosity of unity and the two slopes were almost the same, while for channels with higher values ofpercentage of silt and clay, channel gradient was smaller than valley gradient and streams were sinuouswith different sinuosity.

In a river system, it is many times found that for essentially constant discharge and sediment load,change in river pattern or plan form occurs along the length. The fact that in many cases the channelslope varies slightly but the slope of the valley changes explains this significantly. Within the valley;there are reaches of valley floor that are steeper or gentler than the average stream gradient. Thishappens wither due to tectonic movements or by the large difference between sediment load of thetributary and the mainstream. Hence to maintain relatively constant gradient, the stream lengthens itscourse on steeper reaches.

River Morphology330

Agarwal (1983) analysed the field data and some laboratory data and found that sinuosity dependson slope and discharge. Khan found that sinuosity is related to slope. Schumm (1977) has plottedsinuosity against stream power toU and found that for low values of toU the channels are straight, thenfor a certain range of toU channels meanders, the sinuosity increases and reaches a maximum value andthen decreases. Beyond another threshold value of toU, the stream braids. It is quite possible thatsinuosity would correlate well with dimensionless stream power QS/d2Ö(Dgsd/rf).

It many times happens that with time a river may undergo a complete change of morphology ifchanges take place in discharge and sediment load. Schumm (1969) calls such change the rivermetamorphosis. The changes taking place in bed elevations leading to aggradation or degradation havebeen discussed in Chapter 9. Here change in plan form such as in meander length, sinuosity, and widthto depth ratio of the stream are briefly discussed. The geomorphic approach to such changes is based onthe work done by Schumm (1969, 1971 and 1977) and is briefly discussed below. Schumm’s work hasindicated that at characteristic discharge such as mean annual discharge,

W ~ Q

M

0 38

0 39

.

.

U

V

|||||

W

|||||

S~ M

Q

-

-

0 38

0 32

.

.

ML ~ Q

M

0 34

0 74

.

.

D ~ Q

M

0 38

0 39

.

.

Si ~ M0.24

...(10.1)

and assuming total bed material load ~ 1

M for constant discharge, one can write

Qs » W M S

D SL

i

, ,

,...(10.2)

Here M is the percent of silt and clays in the bank material. By using plus or minus exponent toindicate how various aspects of channel morphology will change if Q or Qs is increased or decreased,the following relationships can be written

Q+ » W+, D+, ML+, S–

...(10.3)Q– » W–, D–, ML–, S+

U

V

|||

W

|||

Q+S » W+, D–, ML

+, S+, S–i

Q–S » W–, D+, M–

L, S– S+

i


Above equations indicate how W, D, ML and S change with change in mean annual discharge, andhow increase or decrease in Qs at constant discharge affect these variables along with sinuosity Si andwidth to depth ratio F. Width to depth ratio of the channel is found to be mainly influenced by the typeof sediment load; as the load increases, F decreases and vice versa. Since in nature change in dischargeor sediment load will rarely occur alone, Schumm considers four possibilities and represents changes inmorphology that will result by the relationships

Q+ Q+S » W+, D±, ML

+, S±, S–i, F

+

...(10.4)Q+ Q–S » W±, D+, ML

±, S–, S+i, F

–

U

V

|||

W

|||

Q– Q+S » W±, D–, ML

±, S+, S–i , F

+

Q– Q–S » W–, D±, M–

L, S± S+

i , F–

Schumm (1971) has further indicated that when channel width, depth, sinuosity and meander lengthare required to be modified because of a hydrologic change, then a long period of instability could beenvisaged with considerable bank erosion and lateral migration occurring before stability is restored. Acouple of examples given by Schumm (1971) are briefly discussed here to emphasize the changes thattake place and time required to effect the change.

The length of the Mississippi river from the mouth of the Big Sioux river to the mouth of the Platteriver was approximately 400 km in 1804 while this length reduced to 240 km in 1935. This reduction isattributed by Towl (see Schumm 1971) to the cutting of timber on the flood plain, and the great flood of1881 and subsequent floods. These floods by reducing the length of river, steepened the slope andwidened the river cross-section.

It may be found that in a given reach of a stream the sinuosity has changed over a period of time.This can happen when the river length changes over a period of time due to natural or artificial cut-offs,or due to growth of the delta. Such changes in length will affect the slope and hence the sinuosity orplan-form of the stream. Such fluctuations in the length of the Mississippi river have been found byWinkley (1970) who showed the river length has changed from about 1680 km to 2056 km and thenreduced to about 1472 km over the past 2000 years. Schumm (1969, 1971) has given a few moreexamples of changes in river morphology due to changes in hydrologic regime over a long period.

The other approaches is make judicious use of relationships and criterion discussed in the earlierchapters to predict change in S, W, W/D ratio and plan-form when changes are effected in Q or QT or S.Thus for a given discharge when S is changed, plan-form changes can be assessed using Lane’s Q vs Scriterion (see Eq. 9.1). Alternately Chang’s diagram (Fig.6.28) between Q and S/d1/2 can be used topredict width, depth and plan-form. When aggradation or degradation takes place equilibrium depth,width and width/depth ratio can be assessed using Eqs.(6.34) or (6.35) proposed by Garde et al.However, it is difficult to predict the time required to effect such changes because the width adjustmentis rather slow and depends on the cohesivity of banks.

10.7 LONGITUDINAL GRAIN SORTING

As mentioned in Chapter 4, the size of bed material of alluvial streams reduces in the downstreamdirection. This has been verified on a number of streams such as the upper Rhine, the Danube, the Niger,

River Morphology332

the Mississippi, the Rio Grande and the Ganga. Sternberg attributed this to abrasion and developedSternberg’s law as given by Eq. (4.6) Similar reduction in size of bed material is also found on beacheswhere littoral drift occurs. The phenomenon of abrasion has been discussed by Pettijohn (1957) inrelation to rates obtained on size reduction in laboratory experiments and reduction of bed material sizein the downstream direction in the streams. He has concluded that

1. Abrasion depends very much on the resistance of minerals to wear and on the diameter ofparticles; the abrasion rate of gravel is much greater than that of sand.

2. Abrasion is also a function of the composition of the material tested.

3. Abrasion rates obtained in experiments by Lane, Daubree, Thiel and others show that abrasioncannot generally be accepted as the sole cause of decrease of particle size in rivers.

Hence, it is believed that some sort of hydraulic sorting process can explain this reduction in size ofbed material of the streams in the downstream direction. Hydraulic sorting can be local over distances ofthe order length of the bed-form or general over much larger lengths. Thus local sorting takes place overdunes and in the bends. The general or longitudinal grain sorting primarily takes place because of spatialvariation of transport of different sediment sizes forming the bed material, and has been studied by Ranaet al. (1973), Diegaard and Fredsøe (1978) and Diegaard (1980).

Rana et al. (1973) considered a stream in which the longitudinal bed profile is in equilibrium i.e.mean bed level of the stream does not change with time, and developed the model for longitudinal grainsorting after making the following assumptions:

1. The flow is steady and constant along channel length.2. The channel is wide and prismatic.3. The channel profile is an independent variable and the channel slope decreases according to the

relationship

S= So e–a1 ...(10.5)

in which S is the slope at distance L, So is slope at L = 0, and a1 is a constant.4. The channel is in equilibrium but the channel bed has been initially formed by aggradation of

material transported from the upstream.5. The bed material at any section in the reach has the same size and gradation as the bed material

discharge in the upstream section.6. The bed material size at the most upstream section is known and is log-normally distributed.

The analysis is carried out in the following manner.

1. The bed material is divided into ten fractions and using Einstein’s bed-load fuction the total bedmaterial discharge and the ratio of total bed load to suspended load fractions is determined.

2. The median diameter and gradation of the computed bed material discharge at the upstreamsection 1 is determined.

3. Knowing the bed material discharge, water discharge and bed material load gradation at section1, the energy slope required at section 2 to maintain the some q and bed material dischargebetween sections 1 and 2 is obtained.


4. For the slope obtained in step 3, L is determined using the slope, Eq. (10.5) And at this distancesection 2 is located.

5. The process is repeated taking section 2 as section1 and following steps 1 through 3 and the bedmaterial size at each section is obtained.

This size was found to decrease in the downstream direction and followed the law

d = do e–a1

and the value of a1 was found to vary with q and total bed material discharge. Further, for a givencombination of these values there was a reduction in the value of a within the bed material size range of0.45 mm to 0.65 mm. It was also inferred by Rana et al. that if the major reduction in size of bed materialis assumed to be due to hydraulic sorting, then under the assumptions made in the analysis, the size ofbed material at any section would change with time.

A slightly different approach has been used by Diegaard and Fredsoe (1978) and Diegaard (1980).The assumptions made by them are:

1. The channel is assumed to be prismatic and of constant width. Further, the discharge per unitwidth is constant at all sections.

2. The longitudinal profile of the river bed is described by the exponential function

Z = Zo e–aL

where Z is bed elevation at L, Zo is bed elevation at L = 0 and a is constant.3. The rate of sediment discharge at L = 0 is constant.4. The median size d and its standard deviation s at the upstream section is known and follows

normal distribution law.5. At the end of the river, the water surface level is assumed to be constant and there is no

backwater effect in the stream.

Using Engelund and Fredsoe’s equation for bed-load and using it for different size fractions,fraction wise bed-load transport is calculated. Similarly fraction wise suspended load transport rate iscalculated using their method for determining reference concentration and Einstein’s method. Themodel works as follows. The river divided into a number of reaches of length DL, and sediment transportinto a section qT (x) and sediment transport out of the section qT (x + DL) is calculated. The resultingchange in bed elevation is computed using the continuity equation for sediment. By using sedimentcontinuity equation for each size fraction, mixing it with the active layer of the bed (assumed to be 0.15times the depth of flow) and resistance law of Engelund-Hansen, the size distribution of the bed materialas well as changes in bed elevation due to aggradation are computed at time Dt. However, the time scalesfor grain sorting and changes in bed profile are much different and the bed profile changes very slowly.Hence, grain sorting can be treated as a quasi-steady process.

Diegaard has used this model to predict the reduction in bed material size of the river Niger, theMississippi and the Rio Grande. His results for the Niger and the Mississippi rivers along with themeasured data points are shown in Fig. 10.11. It is found that the data scatter around mean predictedcurves, but in some cases the scatter is large. The scatter can be attributed partly to various simplifyingassumptions made in the analysis, sampling errors, and to the fact that joining of tributaries can vitiatethe results.

River Morphology334

ReferencesAgarwal, V.C. (1983) Studies on the Characteristics of Meandering Streams. Ph.D Thesis, University of Roorkee,

Roorkee (India).

Allen J.R.L. (1965) A Review of the Origin and Characteristics of Recent Alluvial Sediments. Sedimentary, Vol. 5,pp. 89-191.

Chatley, H. (1940) Theory of Meandering. Engineering (London), Vol. 149.

Chien, N. (1961) The Braided Stream of the Yellow River – Scientia Sinica – Vol. 10, No. 6, pp. 734-754.

Daniel, J.F. (1971) Channel Movement of Meandering Indiana Streams, USGS Professional, Paper 732-A.

Diegaard, R. (1980) Longitudinal and Transverse Sorting of Grain Sizes in Alluvial Rivers. Institute ofHydrodynamics and Hyd. Engg., Technical University of Denmark, Series Paper 26, 106 p.

Diegaard, R. and Fredsoe J. (1978) Longitudinal Grain Sorting by Currents in Alluvial Streams. NordicHydrology, Vol. 9, pp. 7-16.

Dury, G.H. (1961) Bankfull Discharge: An Example of its Statistical Relationships. Bull Intl. Association ofHydrology, Vol. 5, pp. 48-55.

Ferguson, R.I. (1977) Meander Migration: Equilibrium and Change, In River Channel Changes (Ed. Gregory,K.J.) John Wiley and Sons, Chichester, A Wiley Interscience Publication, Chapter 15, pp. 235-248.

Fig. 10.11 Variation of observed and computed diameter of bed material with length (Diegaard 1988)

(a) Niger river

q = 10.6 m /s, S = 1.07 10´–42

L km

0 100 200 300 400 500 600

Measured

Computed

0.2

0.6

0.5

0.4

0.3

0.4

0.6

0.8

1.0

dm

md

mm

L km

100 200 300

Measured

Computed

(b) Mississippi river (Vicksburg)

0


Ferguson, R.I. (1981) Channel Form and Channel Changes. In British Rivers (Ed. Lewin J.). George Allen andUnwin Ltd., London, Chapter 4, pp. 90-125.

Friedkin, J.F. (1945) Laboratory Study of the Meandering of Alluvial Rivers – USWES, Vicksburg, Mississippi(U.S.A.), p. 40.

Frisk, H.N. (1944) Geological Investigations of the Alluvial Valley of the Lower Mississippi River. MississippiRiver Commission, Vicksburg, (Mississippi), U.S.A.

Garde, R.J. (1978) Irrigation in Ancient Mesopotamia. ICID Bulletin, Vol. 27, No. 2, pp. 11-22.

Gregory, K.J. (Ed.) (1977) River Channel Changes. A Wiley Interscience Pulication, John Wiley and Sons,Chichester, (U.K.), 448 p.

Gurnell, A. and Petts, G. (Eds.) (1995) Changing River Channels. John Wiley and Sons, Chichester (U.K.), 440 p.

Harvey, A.M. (1975) Some Aspects of the Relations Between Channel Characteristics and Riffle spacing inMeandering Streams. American Journal of Science Vol. 275, pp. 470-478.

Hickin, E.J. and Nanson, G.C. (1984) Lateral Migration Rates of River Bend. JHE, Proc. ASCE, Vol. 110, No. 11,Nov., pp. 1957-1967.

Hooke, J.M. (1995) Processes of Channel Plan-Form Change on Meandering Channels in the U.K. In ChangingRiver Channels (Eds. Grunell, A. and Petts, G.). John Wiley and Sons, Chichester, pp. 87-115.

Hughes, H.J. (1977) Rates of Erosion on Meander Arcs. In River Channel Changes (Ed. Gregory K.J.) John Wileyand Sons, Inc., A Wiley Interscience Publication, Chapter 12, pp. 193-206.

Jain, V. and Sinha R. (2003) River Systems in the Gangetic Plains and their Comparison with Siwaliks : A Review.Current Science, Vol. 84, No. 8, 25 April, pp. 1025-1033.

Jain, V. and Sinha R. (2003) Hyperavulsive – Anabranching Bagmati River System, North Bihar Plains, EasternIndia, Z. Geomorphologie, N.F. Berlin, Vol. 47, No. 1., pp. 101-116.

Khan, H.R. (1971) Laboratory Study of River Morphology. Ph.D. Thesis, Colorado State University, Fort Collins,(U.S.A.), 189 p.

Leopold, L.B. and Wolman M.G. (1964) River Meanders – Geol. Soc. of Am., Bull., No. 71, pp. 769-794.

Leopold, L.B., Wolman M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman andCompany, San Fransisco.

Lewin, J. (1977) Channel Pattern Changes. In River Channel Changes (Ed. Gregory, K.J.) John Wiley and Sons.Chapter 8, pp. 167-184.

Lewis, G.W. and Lewin, J. (1983) Alluvial Cut-offs in Water and Borderlands, Special Pub., Intl. Assoc. ofSedimentologists, Vol. 6.

Lin, P.N. and Li Guifen (1986) The Chanjiang and Huanghe. Circular No. 1, IAICES, Beijing. 17 p.

Lobeck, A.K. (1939) Geomorphology: An Introduction to the Study of Landscapes. McGraw Hill Book Co. Inc.,New York, pp. 198-201.

Lu Jianyi (1982) Mouth of the Yellow River, Its Evolution and Improvement. The Yellow River Vol. 3, In SelectedPapers of Researchers on the Yellow River and the Present Practice (Ed. YACC) Oct. 1987, pp. 95-105.

Mazumder, S.K. (2004) Aggradation/Degradation of Ganga Near Farakka Barrage. National Symposium onSilting of Rivers Held in New Delhi, C.W.C., 10 p.

Nanson, G.C. and Hickin, E.J. (1983) Channel Migration and Incision on the Beatton River. JHD, Proc. ASCE,Vol. 103, No. 3, March, pp. 327-337.

Newson, M.D. (1995) Fluvial Geomorphology and Environmental Design. In Changing River Channels (Eds.Gurnell, A. Petts, G.) John Wiley and Sons. Chapter 19, pp. 413-432.

Pettijohn, F.J. (1957) Sedimentary Rocks. Harper and Brothers, New York, 2nd Edition.

River Morphology336

Pickles, G.W. (1941) Drainage and Flood Control Engineering. McGraw Hill Book Co., New York, Chapter 11.

Rana, S.A., Simons, D.B. and Mahmood, K. (1973) Analysis of Sediment Sorting in Alluvial Channels. JHD,Proc. ASCE, Vol. 99, No. 11, No. pp. 1967-1980.

Richard, K., Chandra, S. and Friend, P. (1993) Avulsive Channel Systems: Characteristics and Examples. InBraided Rivers (Eds. Best, J.L. and Bristo C.S.) Geological Society Publication No. 75, pp. 195-203.

Schumm, S.A. (1969) River Metamorphosis. JHD, Proc. ASCE, Vol. 95, No. HY1, Jan. pp. 255-273.

Schumm, S.A. (1971) Fluvial Geomorphology. In River Mechanics (Ed. Shen H.W.) Published by Editor, FortCollins (U.S.A.), Chapter 5, pp. 5.1 to 5.22.

Schumm, S.A. and Khan H.R. (1972) Experimental Study of Channel Patterns. Geol. Soc. of Am. Bull. Vol. 83, pp.1755-1770.

Schumm, S.A. (1977) The Fluvial System. John Wiley and Sons, A Wiley Interscience Publication, New York,Chapter 5.

Sinha, R. (1996) Channel Avulsion and Flood Plain Structure in Gandak-Kosi Interfan, North Bihar Plains, India.Zeitscrift fûr Geomorphologie N.F. Supp. Bd. 103, pp. 249-268.

Tangri, A.K. (2000) Proceedings of the Workshop on Fluvial Geomorphology with Special Reference to FloodPlains. IIT Kanpur, pp. 3.1 to 3.12.

Winkely, B.R. (1970) Influence of Geology on the Regimen of A River. ASCE, Natl. Water Resources Meeting(Memphis) Preprint 1078, 35 p.

Wolman, M.G. and Leopold, L.B. (1957) River Flood Plains: Some Observations on Their Formation. Geo. SurveyProfessional Paper 282-C, pp. 87-107.

Wolman, M.G. (1959) Factors Influencing Erosion of a Cohesive River Bank. Am. Jour. of Sciences, Vol. 257, No.1, pp. 204-216.

Worcester, P.G. (1948) A Text Book of Geomoprhology. D Van Nostrand Co., New York, 2nd Edition, p. 150.

Xu Fuling (1982) A Brief Account of Changes of Course of the Lower Yellow River in Past History. The YellowRiver No. 3, In Selected Papers of Researchers on the Yellow River and the Present Practice (Ed. YRCC) Oct.1987, pp. 47-52.Hug

11C H A P T E R

Analytical Morphological Models

11.1 INTRODUCTION

Various changes that take place in the longitudinal profile of an alluvial river as a result of man-made ornatural disturbances introduced in the river are discussed in chapters nine and ten. Those can be studiedeither by using a physical model or an analytical or a numerical model. If the changes taking place arelocal, very often a physical model is used; however when the changes take place over large lengths andare slow, thus requiring a very long time for attaining equilibrium or near equilibrium condition, it isadvantageous to use analytical or numerical models. Problems solved by using physical models withmovable bed include location of bridges, design of guide bunds, location and dimensions of spurs,optimum design of sediment excluders and ejectors, execution of cut-offs, control of sediment entry intocanals and rejuvenation of dying channels. Design of physical movable bed model is based on thedetermination of the dimensionless parameters that govern the process under consideration. Theseparameters include ratios of lengths, velocities, mass densities, and forces. These need to be kept thesame in the model and the prototype so that the model satisfies the conditions of geometric, kinematicand dynamic similarities. If all the corresponding length ratios have the same value in the model and theprototype, the model is geometrically similar; otherwise it is geometrically distorted. Similarly, themodel can have material distortion or force distortion. Alluvial river models are usually distorted andhence the designer of the model has to see what will be the effects of distortion on the behaviour of themodel and the interpretation of results from model to the prototype. Hence, designing a movable bedmodel and interpretation of results from model to the prototype is still an art and each laboratory has itsown method of model design and interpretation of results. Further, each physical model may serve thepurpose of that specific problem only and cannot be used for other rivers.

Analytical and numerical models used to study the morphological changes are based on usinggoverning equations of motion namely, momentum equation, and continuity equations for flow andsediment, and resistance and sediment transport relations. These equations are then combined andsolved for known initial and boundary conditions. To get analytical solutions, one has to make somedrastic simplifications. Such simplifications include one-dimensional flow, linearisation in respect of

River Morphology338

friction, convective acceleration term, and sediment transport rate derivative, and assumption ofuniform sediment. In spite of these restrictions, under certain conditions analytical models providerough and useful results.

When one does not wish to make such simplifications, numerical models can be used where thesystem of equations are solved using numerical techniques with known initial and boundary conditions.Numerical models need calibration and proving with the past data; once the model is proved, it can beused to make predictions. A number of such models are available and these differ from one another inthe degrees of sophistications used in its formulation (see Chapter 12).

This chapter includes a brief description of the governing equations for one-dimensional flows inalluvial streams, their simplifications to get different analytical models and some of their applications.De Vries (1993) initiated this approach and since then some investigators have used these models to getresults for a few practical problems.

11.2 BASIC ONE-DIMENSIONAL EQUATIONS

For solving problems concerning transient bed profiles in alluvial rivers, the basic equations that areused are continuity equations for flow and sediment, dynamic (or momentum) equation, and resistanceand sediment transport relationships. These are derived or discussed below for one-dimensional flowsin which average velocity U, average depth D and sediment transport rate QT or qT

are functions of x andt; here QT = B qT where B is channel width and qT is volumetric sediment transport ratio per unit width.

(a) Continuity Equation for FlowThe continuity equation for flow, which is also called the equation for conservation of mass, whenwritten for open channels, states that the net rate of mass inflow into the control volume would result inthe rate of increase of mass within the control volume (see Fig. 11.1);

or¶

¶ t (rf A dx) +

¶

¶ x (rf AU) dx + rf q¢ dx = 0 ...(11.1)

Here rf is mass density of fluid which is taken as constant assuming sediment concentration to bevery small, A is the cross sectional area, U is the average velocity at a section and q¢ is the lateral in flowrate per unit length from both sides. Taking rf as constant, Eq. (11.1) gives

¶

¶

A

t +

¶

¶

Q

x + q¢ = 0 ...(11.2)

where Q = AU is the discharge in the channel. If lateral inflow is zero, the above equation takes theform

¶

¶

A

t + U

¶

¶

A

x + A

¶

¶

U

x= 0 ...(11.3)

and for rectangular channel of constant width B, Eq. (11.3) reduces to

Analytical Morphological Models 339

¶

¶

D

t + U

¶

¶

D

x + D

¶

¶

U

x= 0 ...(11.4)

since A = BD and D is the average depth of flow. This equation can be used for sediment-laden flows if

the sediment concentration q

qT is much smaller than unity; here qT and q are sediment and water

discharge per unit width.

(b) Continuity Equation for SedimentThe continuity equation for sediment can be derived in the same manner as the continuity equation forflow. Here, the difference between the rates of sediment inflow and outflow from a control volume willcause deposition on the bed or erosion from the bed, thereby changing the bed level, see Fig. 11.1.Therefore,

¶

¶t (B Z d x) +

¶

¶x (QT) d x = 0

and since QT = BqT

U

V||

W||

...(11.5)

¶

¶

Z

t +

1

1- la f ¶

¶

q

xT = 0

Here B is assumed to be constant; qT is volumetric sediment transport rate and l is the porosity. Thisequation is exact if qT represents bed-load only. When some material goes into suspension, an additionalterm needs to be included in Eq. (11.5) to take into account change with respect to time of the suspended

sediment load in the control volume, viz., ¶

¶ t (DCs) where Cs is average concentration of suspended

load. If this term is not included when appreciable amount of suspended load is present, Eq. (11.5) is

Fig. 11.1 Definition sketch for sediment continuity

Datum

Channel bed

Dx

Dz

Z

D

h

U

1 2

W.S

QT +¶

x

QT

¶dx

QT

River Morphology340

approximate. Equation (11.5) indicates that ¶

¶

Z

t is positive i.e., aggradation will occur if

¶

¶

q

xT is

negative i.e., qT decreases as x increases; in other words qT at section 1 is greater than qT at section 2.

(c) One-dimensional Dynamic EquationThe dynamic equation for non-uniform and unsteady flow in an open channel is obtained from theprinciple of conservation of momentum. With reference to Fig. 11.2, for the control volume ABCD,

Fig. 11.2 Definition sketch for momentum equation

(Rate of momentum outflow) – (Rate of momentum inflow) + (Change of momentum within thecontrol volume) = (Summation of components in the direction of flow of all the external forces acting onthe control volume)

These force components are (see Fig. 11.2)Frictional force = – to P d xComponent of gravity force = r g A d x sin q

Component of pressure force in the direction of flow = – r g cos q ¶

¶

D

x d x

Therefore the momentum equation takes the form

¶

¶ x r f U A2d i dx +

¶

¶ t (rf A U) dt = – to P d x + rf g A d x sin q – rf g cos q

¶

¶

D

x d x ...(11.6)

Here U is the average velocity of flow over cross sectional area A, P is the perimeter, to is theaverage shear stress on the perimeter, and q is the angle of inclination of channel bed. Assuming rf to beconstant and dividing all terms by (rf A dx), one gets

¶

¶

U

t +

U

A ¶

¶

U

x + 2 U

¶

¶

U

x +

U

A

2

¶

¶

A

x= –

t

ro

f R + g sin q – g

¶

¶

D

x cos q ...(11.7)


However, according to Eq. (11.3)

¶

¶

A

x= –

1

U ¶

¶

A

t –

A

U ¶

¶

U

x...(11.8)

Further, for small values of q, sin q »� tan q = So » – ¶

¶

Z

x and cos q » 1.0. Also B = constant for

rectangular channel for constant width. With these substitutions Eq. (11.7) becomes

¶

¶

U

t + U

¶

¶

U

x + g

¶

¶

D

x + g

¶

¶

Z

x= –

t

ro

f R...(11.9)

This is momentum equation and the assumptions made in its derivation arei) constant width of rectangular channel;ii) no lateral inflow;

iii) rf is constant which is true if q

qT is very small;

iv) flow being one dimensional, at a section we have average values of U and D, and hencemomentum correction factor b = 1.0, further pressure distribution is hydrostatic; and

v) q is very small.

(d) Resistance RelationsOne can use either Chezy’s equation or Manning’s equation with constant value of C or n. Using

Chezy’s equation the term t

ro

f R can be written as

gU

C R

2

2 and hence Eq. (11.9) takes the form

¶

¶

U

t + U

¶

¶

U

x + g

¶

¶

Z

x= –

gU

C R

2

2 ...(11.10)

It may be mentioned that in alluvial streams a different resistance equation is applicable since bedconditions change with the flow conditions. In unsteady, non-uniform flow C or n will be functions ofstage, x and t. However, for obtaining analytical solutions n or C is assumed to be constant.

(e) Sediment Transport Relation

To evaluate the term ¶

¶

q

xT in the continuity equation one must use a sediment transport formula. de Vries

recommends use of a relation of the type

qT = a Ub ...(11.11a)

Here, a and b are assumed to be constant for the range of depth under consideration. Alternately,some have used equation of the type

River Morphology342

qT = a u*b ...(11.11b)

where a can be function of other parameters such as sediment size etc. but constant; here u* is the shearvelocity. It is further assumed that sediment size is uniform.

11.3 ANALYSIS OF WATER SURFACE AND BED WAVES

Combining Eqs. (11.11) and (11.5) one can write

¶

¶

Z

t +

¶

¶

f

U ¶

¶

U

x= 0 ...(11.12)

where qT = f (U). Further from Eqs. (11.4), (11.10) and (11.12) the following equation is obtained

–U3w + 2 U U2

w + g D Ug q

UT- +

-

¶

¶

L

NM

O

QP2

1 la f Uw –

Ug

1- la f ¶

¶

q

Ut = 0 ...(11.13)

Here Uw = dx

dt is the celerity of the wave. Writing Eq. (11.13) in dimensionless form by introducing

the dimensionless parameters

M = U

Uw , Fr =

U

gD, and y1 =

b

D1-

L

NM

O

QP

la f ¶

¶

q

UT

one obtains

M3 – 2M2 + (1 – Fr–2 – y1 Fr–2) M + y1 Fr–2 = 0 ...(11.14)

It may be mentioned that y1 is proportional to the sediment concentration. Equation (11.14) is acubic equation and hence has three roots namely M1, M2 and M3 and these are functions of Fr and y1.These are given by

M1 = (1 + Fr–1) and it is dimensionless velocity of a small surface disturbance in the direction offlow;

M2 = (1 + Fr–1) and it is dimensionless velocity of a small surface disturbance traveling in directionopposite to the flow;

M3 = y1

21- Frd i when Fr is less than unity and it is the dimensionless velocity of bed form. It is

significantly affected by the sediment transport rate.It is worth noting that when Fr is less than unity, M3 will be positive and the bed disturbance travels

in the direction of flow; however when Fr is greater than unity, M3 will be negative and the disturbancemoves in upstream direction. Figure 11.3 shows variation of |M| with Fr and y1. It can be seen from thisfigure that M1 and M2 are much greater than M3 when Fr number is less than approximately 0.8.Therefore, if the main interest is in the computation of flood or water levels, it is safe to assume M3 » 0i.e., the bed is stationary. On the other hand, if one is interested in predicting the bed level variations, it


can be assumed that |M1, M2| ® ¥ i.e., water depth and velocity variations occur very rapidly. In other

words, flow can be considered quasi-steady and, ¶

¶

U

t and

¶

¶

D

t can be neglected with respect to other

terms in Eqs. (11.4) and (11.9). This is known as quasi-steady formulation. Another implication ofdifferences in relative values of M1, M2 and M3 is that the numerical analysis can be carried out in de-coupled mode; it means that bed can be first assumed stationary and water levels computed usingmomentum equation and then assuming water levels to be stationary, bed levels are computed usingcontinuity equation for sediment and sediment transport law.

11.3 ANALYTICAL MODELS

The analytical models can be obtained from the quasi-steady formulation of the equations discussedearlier i.e.,

U ¶

¶

U

x + g

¶

¶

D

x + g

¶

¶

Z

x= –

gU

C D

2

2 ...(11.16)

U ¶

¶

D

x + D

¶

¶

U

x= 0 ...(11.15)

U

V

|||

W

|||

¶

¶

Z

t=

1

1- la f ¶

¶

q

UT

¶

¶

U

x = 0 ...(11.12)

qT = f (U) ...(11.11)

Fig. 11.3 Relative velocities in alluvial channel

101

Fr

0.80.4 1.2 1.60

100

10–1

10–2

10–3

10–4

10–5

|M|

10–5

10–5

10–4

10–4

10–3

10–3

10–2y2 = 10

–2

M2 M3

M1

River Morphology344

These equations can be combined into one differential equation

¶

¶

Z

t –

¶

¶

q

UT

g

UqgU

-

F

H

GGG

I

K

JJJ2

¶

¶

Z

x

1

1- la f=

gS

Uq g

U

f

-FH

IK2

¶

¶

q

UT

1

1- la f...(11.17)

The analytical models are obtained after linearisation of the above equations and therefore theirsolutions give only the rough estimates of the correct solutions. The non-linearity arises from the terms

U ¶

¶

U

x the friction term g

U

C D

2

2 i.e., g U

C q

3

2 and the term ¶

¶

q

UT . Even though linearisation of these terms

introduces some error, it gives an advantage that resulting equations are amenable to analyticalsolutions.

Taking original bed as the x axis and assuming small changes in the bed level i.e., Z << Do the initialuniform flow depth, and various degrees of linearisation the following models have been obtained andstudied.

Parabolic Model

Here the terms ¶

¶

U

x and

¶

¶

D

x are neglected during the transient condition i.e., there is no draw down or

backwater profile and flow is uniform. Thus,

¶

¶

U

x= 0,

¶

¶

D

x = 0 and

¶

¶

D

t = 0

Hence, Eq. (11.16) reduces to

¶

¶

Z

x= –

U

C q

3

2 ...(11.18)

Differentiating Eq. (11.18) with reference to x one gets

¶

¶

2

2

Z

x= –

3 2

2

U

C q ¶

¶

U

x...(11.19)

Further, according to continuity equation for sediment

¶

¶

Z

t +

1

1- la f ¶

¶

q

xT = 0 or

¶

¶

Z

t +

1

1- la f ¶

¶

q

UT

¶

¶

U

x = 0

Hence, substituting the value of ¶

¶

U

x from Eq. (11.19), one gets


¶

¶

Z

t –

C q2

3 1- la f ¶ ¶q U

UT /

2 ¶

¶

FHG

IKJ

2

2

Z

x= 0

or¶

¶

Z

t= Ko

¶

¶

2

2

Z

x where Ko =

C q

U

2

23 ¶ ¶

-

q UT /

1 la f...(11.20)

Equation (11.20) is the diffusion equation – of the type used in heat conduction – and Ko is knownas the diffusion coefficient, which can be expressed as

Ko = 1

3 U q U

ST

o

¶ ¶

-

/

1 la f

U

UoF

HIK

3

where Uo is the average velocity under uniform flow condition. If one uses the approximation U » Uo,the above expression simplifies to

Ko = bq

STe

o3 1- la f...(11.21)

where qTe is the equilibrium transport rate. Equation (11.19) being parabolic in nature represents theparabolic model for solving transient problems in alluvial streams. Vreugenhill and de Vries (1973)stated that parabolic model is applicable when x is greater than 3 D/So when Froude number is small. Itmay be mentioned that earlier Culling (1960) had used parabolic model probably for the first time by

assuming that bed load transport rate was directly proportional to local bed slope i.e., qTe ~ ¶

¶

Z

x. He

developed solutions for simple hypothetical problems of channel erosion and development oflongitudinal river profiles using time invariant boundary conditions. In spite of the crude assumptionsmade in the derivation of the parabolic model it gives useful results when applied with care, as shownlater.

It can be seen that Eq. (11.17) is of the form

¶

¶

Z

t + (M3 U)

¶

¶

Z

x= a (U)

in which (M3 U) represents celerity of bed wave and a (U) is a measure of damping of disturbance. If a(U) is taken as zero, one gets an equation for the propagation of a simple wave the solution of which isknown. Thus, the so called wave model is represented by

¶

¶

Z

t + (M3 U)

¶

¶

Z

x= 0 ...(11.22)

Analytical solution of the wave equation given above is possible if the equation is linearised i.e.,(M3 U) and a (U) are taken as constants.

If the assumption of uniform flow during the transient stage is not made but still the linearisation isdone, one gets the hyperbolic model for river bed variation, namely

River Morphology346

¶

¶

Z

t –

K

M Uo

3

¶

¶ ¶

2 Z

x t – Ko

¶

¶

2

2

Z

x= 0 ...(11.23)

Here Ko is the same as given by Eq. (11.21). It needs to be mentioned that in the derivation of Eq.(11.23), a constant discharge is assumed whereas for parabolic model such assumption has not beenmade. Vreugdenhill and de Vries recommend that hyperbolic model can be used for x less than 3 D/So.Equation (11.23) can be written as

U M

Ko

3 ¶

¶

Z

t –

¶

¶ x

¶

¶+

¶

¶

FHG

IKJ

Z

tUM

Z

x3 = 0 ...(11.24)

here Ko, M3 and U are constants, U being taken as Uo. If UM

Ko

3 is very small, the above equation can

be approximated to

¶

¶ x

¶

¶+

¶

¶

FHG

IKJ

Z

tUM

Z

Z3 = 0

by neglecting the first term in Eq. (11.24). The above equation can be integrated to yield the wave model

¶

¶+

¶

¶

Z

tUM

Z

x3 = constant

On the other hand, if UM

Ko

3 is large, the second term in Eq. (11.24), ¶

¶ x

¶

¶

FHGIKJ

Z

t can be neglected;

then Eq. (11.24) reduces to parabolic model

¶

¶

Z

t= Ko

¶

¶

2

2

Z

x

Thus the ratio UM

Ko

3 seems to play an important role.

11.4 SOME APPLICATIONS OF LINEAR MODELS

Parabolic ModelLet us first consider the parabolic model. Probably this method was first proposed by Culling (1960)who assumed that sediment transport is proportional to terrain slope and combining it with thecontinuity equation obtained the diffusion equation which is in fact heat conduction equation. He hasalso proposed solution of diffusion equation for different boundary conditions. It may be mentioned thata number of solutions of diffusion equation for different boundary and initial conditions are given byCarslaw and Jaeger (1947).


De Vries (1975, 1993) has applied parabolic model to determine transient bed profiles in a streamwhen the lake level to which it joins at the downstream end is suddenly dropped over a vertical heightZo, see Fig. 11.4.

By neglecting the effects of drawdown one can assume that at t > 0 the flow is uniform. Measuringx in up stream direction the boundary conditions are

Initial condition Z (x, 0) = 0

Boundary condition Z (x, t) = 0 as x ® ¥

and Z (0, t) = – Zo

Equation (11.20) which is a partial differential equation can be reduced to ordinary differential

equation by substituting h = x

K to2

f ¢¢ + 2 h f ¢ = 0

where Z

Zo

= f (h). The solution of this equation for the above boundary condition is

Z

Zo

= – e r f c x

K to2

FHG

IKJ

...(11.25)

Transient bed profiles are shown by dotted lines in Fig. (11.4). Vittal and Mittal (1980) have usedparabolic model for the prediction of degraded profile of the Ratmau torrent caused by trapping ofsediment in the upstream.

Soni (1975), Soni et al. (1980), Mehta (1980), Garde et al. (1981), Jain (1981), Gill (1983) andothers have used parabolic model to study aggradation of river bed due to overloading. Experimentsconducted by Soni and Mehta at Roorkee University in a 30 m long and 200 mm wide flume using

nearly uniform sediments of size of 0.32 mm, 0.50 mm and 0.71 mm and overloading ratio D q

qT

Te

from

Fig. 11.4 Degradation due to lowering of lake level

Transient bed profile

Final bed

Original bed level

¥

¥Changed lake level

Original lake level

t

t = O, Z = 0

W.S

W.St = O

t

River Morphology348

0.50 to 16.0 form the basis of most verifications of parabolic and hyperbolic models. In these testsequilibrium conditions were established for a given discharge and slope and equilibrium transport rateqTe was determined. Then, for given increase in sediment load at upstream end, transient bed and watersurface profiles were obtained. In fact studies by Soni and Mehta have revived the interest in analyticalmodels since then and parabolic and hyperbolic models have been studied in greater detail.

With reference to Fig. 11.5 wide rectangular channel has uniform depth Do and velocity Uo andequilibrium transport rate QTe for channel slope of So; the sediment supply rate at the upstream section isincreased by a constant rate DQT. Using the parabolic model, the initial and boundary conditions are (seeJain 1981):

Z (x, 0) = 0 for t ³ 0

The second boundary condition can be obtained from the fact that sediment volume under transient

bed profile at time t is given by DqT t = o

¥

z (1 – l) Z d x which on differentiation with t yields

DqT = (1 – l) o

¥

z ¶

¶

Z

t d x

Substituting the value of ¶

¶

Z

t from

¶

¶

Z

t = Ko

¶

¶

2

2

Z

x, one gets

DqT = (1 – l) Ko ¶

¶

FHGIKJ

z

x o

But, since ¶

¶

FHGIKJ

z

x at (¥, t) = 0, the second boundary conditions reduces to – Ko

¶

¶

FHGIKJ

z

x at (0, t)

= D qT

1- la f

Fig. 11.5 Aggradation due to overloading

Section of sediment injection

Transient bed profile at t > 0Original bed

UsDo

W.S.

Zo

Qte

DQT


The solution of diffusion equation with these boundary conditions is

Z = 2

1

D q

KT

o - la f

K t x

K t

x

K to

op

FH

IK

-FHG

IKJ

-FHG

IKJ

L

NMM

O

QPP

1 2 2

4 2

/

exp erfcx

2 o

...(11.26)

in which erfc h = 2

p

h

¥

z e- h2

dh

From Eq. (11.26), Zo is given as that value of Z at x = 0, or

Zo = 2

1

D q

KT

o - la f

K to

p

FH

IK

1 2/

or Z

K to

o

= 2

1

D q

KT

op l-a f...(11.27)

Equation (11.26) can be written in dimensionless form as

Z

Zo

= e- -h h p h2

erfca f ...(11.28)

Further, if length of aggradation is that length l where Z

Zo

= 0.01, one gets from Eq. (11.28)

l = 3.2 K to ...(11.29)

Gill (1983) has solved the diffusion equation for aggradation due to overloading by the methoddiscussed above as well as obtaining the solution of diffusion equation by Fourier series. If So is theinitial slope, S¥ is the final slope of bed commensurate with increased sediment load, and L is the lengthof the channel, the boundary conditions are

Z (x, 0) = S0 (L – x)

...(11.30)

Z (x, ¥) = S¥ (L – x)

Z (L, t) = 0 which stipulates that bed at

down stream end remains unaffected

U

V

|||||

W

|||||and –

¶

¶

FHGIKJ

=

Z

xx o

= q

KT

o

¥

-1 la f where qT¥ is the equilibrium

transport rate

Assuming solution to be of the type

Z (x, t) = F (x) + f (x, t) ...(11.31)

he found that F (x) = S¥ (L – x) ...(11.32)

Using the boundary conditions listed above, it is shown that f (x, t) is given as

River Morphology350

f (x, t) = 8

2

L S So - ¥b gp

n=

¥

å 1 3 5, , ...

12n

exp -FHG

IKJ

n K t

Lo

2 2

22

p cos

n x

L

p

2...(11.33)

so that Eq. (11.31) becomes

Z (x, t) = S¥ (L – x) + 8

2

L S So - ¥b gp

n=

¥

å 1 3 5, , ,...

12n

exp -FHG

IKJ

n K t

Lo

2 2

22

p cos

n

L

p p

2...(11.34)

It is also shown that sediment transport rate satisfies diffusion equation, viz.

¶

¶

q

tT = Ko

¶

¶

2

2

q

xT ...(11.35)

and for the boundary conditions qT (o, t) = qT¥ and qT (x, o) = qTe

qT (x, ¥) = qT¥ and ¶

¶

q L t

xT ,a f

= 0,

The solution of Eq. (11.35) is

q q

q qT Te

T Te

-

-¥

= 1 – erf x

K to2

FHG

IKJ

...(11.36)

Adachi and Nakatoh (1969) have applied the diffusion equation for studying silting of reservoirsand have obtained Fourier series solution. They have also determined the value of Ko at dominantdischarge for the river Tenryu in Japan.

Tsuchiya and Ishizaki (1969) have used a sediment transport formula of Sato, Kikkawa and Ashida,namely

qB ~ u3*

and Manning-Strickler type resistance law and obtained the diffusion equation. Further, they haveapplied this equation to predict river bed profiles upstream of Hongu dam on the Joganji river in Japan.This dam on the torrential river was constructed in 1935 and was completely filled in 1939.

As mentioned earlier, Mehta and Soni have studied the application of parabolic model foraggradation due to overloading. As shown by Jain (1981), for 0.32 mm data of Soni, transient bedprofiles obtained by theory using Ko values agreed reasonably well with observed data, even though for

large x

K to2 values there was relatively more scatter. However, Mehta (1980) found that 0.50 mm and

0.71 mm data gave considerable scatter on Z

Zo

vs h = x

K to2 plot when theoretical values of Ko were

used. Hence, he modified the values of Ko for each run so that the transient bed profile matched with Eq.


(11.28). His modified values of Ko called K were found to be function of D q

qT

Te

and K S

qo

Te

1- la f =

f Dq

qT

Te

FHG

IKJ

. Figures 11.6 and 11.7 show variation of Z

Zo

vs x

Kt2 and

K S

qo

Te

1- la f = f

D q

qT

Te

FHG

IKJ

as

obtained by Mehta. The need for modification of Ko to K has been attributed to the assumptions made inthe derivation of parabolic model.

Jaramillo and Jain (1983) applied linear parabolic model to channels of finite length. Park and Jain(1984) have used computer based numerical experiments to determine the rate and extent of aggradationof the bed resulting from overloading. For this they have used Karim and Kennedy’s sediment discharge

and friction factor relations. It was found that, if Z

Zo

= exp (– h2) – h p erfc (h) is fitted for variation

of Z

Zo

with h, the diffusion coefficient K and Zo were found to be functions of Co, So, DC and t as

K = 100.364 Co0.968 So

–0.982 DC0.102

Zo = 100.11 DC0.960 Co0.517 So

0.489 t0.50

Here, Co is the initial sediment concentration by volume, DC is increase in concentration, So is theinitial slope and t is time.

Application of parabolic model has been studied by Vittal and Mittal (1980) and Gill (1983a), fordegradation. Vittal and Mittal have applied parabolic model to predict transient bed profiles of theRatmau torrent in U.P., India. This torrent crosses the Upper Ganga Canal at Dhanauri where a levelcrossing has been constructed in 1850 in which 192 m wide escape for the torrent and 72 m wideregulator is provided for the canal (see Fig. 11.8). Initial bed slope of the torrent was 0.001558 and hasa maximum discharge of 2250.98 m3/s, while minimum flood discharge has been about 200 m3/s. Over

Fig. 11.6 Variation of Z

Zo with h for aggradation due to overloading using modified values of K

h0.70 1.0 0.2 0.3 0.4 0.5 0.6 0.8 0.9 1.0 1.1 1.2

0

0.2

0.4

0.6

0.8

1.0

1.2

Z/Z

o

Different runs (d = 0.32 mm)

River Morphology352

the past 150 years the bed slope of the torrent downstream of the escape is decreasing as shown in Fig.11.9 while the bed slope upstream of the escape has increased due to aggradation. Hence, it is concludedthat the cause of degradation in the lower reach of the torrent is due to reduction in sediment supply. Inthe absence of detailed data they estimated the average transport rate using Engelund-Hansen’s relation

Fig. 11.7 Variation of K So (1 – l) qTe with DqT/qTe

Fig. 11.8 Level crossing of Ganga canal and Ratmau torrent

Dq /qTeT

8

4.0

0 2 4 6 10 12 14 16

3.2

2.4

1.6

0.8

0

KS

(1–

)q

lTe

o Symbol d mm Investigator

0.32 Soni0.50 Mehta0.71 Mehta


and for various trap efficiencies 30, 40 and 50 percent, the bed profiles were computed for years 1924,1947, 1954 and 1976, using parabolic model. The computed profiles for trap efficiency of 40 percentagreed reasonably well with the observed ones, as can be seen in Fig. 11.10. It may be mentioned thatVittal and Mittal used modified values of K as given by Soni and Mehta.

Gill (1983 a) has considered the case of degradation downstream of a dam where due to trapping ofsediment on the upstream of the dam, the sediment supply to the stream is suddenly reduced from qTe toqT¥. Hence, the boundary conditions are

Z (x, o) = So (L – x)

Z (x, ¥) = S¥ (L – x)

and¶

¶

FHGIKJ

=

Z

xx 0

= – S¥ for t > 0

Here, S¥ is the equilibrium slope for reduced sediment supply rate qT¥. These boundary conditionsbeing exactly the same as those used for aggrading channels, earlier solutions also hold well in case ofdegradation. These are

Z (x, t) = S¥ (L – x) + 8

2

L S So - ¥b gp

n =

¥

å 1 3 5, , ..

12n

exp -FHG

IKJ

n K t

Lo

2 2

24

p cos

n x

L

p

2...(11.37)

Error function solution for infinitely long channels or relatively small times

Fig. 11.9 Reduction of bed elevation of the Ratmau torrent with time (Vittal and Mittal 1980)

1845

187719241939

1947

1954196619761977

Notation

Legend

Year

River Morphology354

Z (x, t) = So (L – x) – (S¥ – So) x er f cx

K t

K t x

K to

o

o22

4

2FHG

IKJ

- -FHG

IKJ

L

NMM

O

QPPp

exp ...(11.38)

Studies by Hou and Kawahita (1987) have demonstrated that solutions to linear parabolic modeldisplay unrealistically high values of sediment diffusion. They have numerically indicated that non-linear parabolic model predicts even larger diffusion than the linear one. Consequently, the non-linearmodel is applicable only when the exponent of empirical constant in the sediment transport formuladetermined under equilibrium conditions is modified to include the non-equilibrium processes.

Hyperbolic ModelFor sudden drop in the downstream bed level, Vreugdenhill and de Vries (1973) have obtained thesolution of linearised hyperbolic model (Ko and M3U constant) as well as parabolic model using thetechnique of Laplace transforms and expanded the resulting solutions for large values of time. If

q = x

K to

2

2 and to =

M U x

Ko

o

3 , the expansions are:

Hyperbolic model

Z

Zo

» 1 – 2q

p 1

1

8

1

2

1

62- - +FHG

IKJ

+L

NMM

O

QPP

qt to o

... ...(11.39)

and parabolic model

Z

Zo

» 1 – 2q

p 1

6- +LNM

OQP

q... ...(11.40)

Fig. 11.10 Verification of bed level variation of the Ratmau torrent (Vittal and Mittal 1980)

Distance in km

8

264

0 2 4 6 10 12 14

262

260

258

256

254

252

250

248

246

244

242

Bed

ele

vation

inm

Observed profileafter flood of 1976

Predicted profile for q /q = 0.40D TT

Original bed line


It may be noted that the two expressions will be almost identical if q is smaller than 0.25 and/or, ifto is large (say greater than 10). The latter condition can be transformed into a workable criterion by

substituting the values of Ko and M3. Hence to greater than ten correspondents to l greater than 3D

So

o

.

Thus, parabolic model is a good approximation for large distances; the approximation may also be good

at small distances for small q i.e., large times. The variations of Z

Zo

with to and q for parabolic and

hyperbolic models and for asymptotic expansions are shown for degradation case in Fig. 11.11.

Fig. 11.11 Variation of ZZo

with to and q according to parabolic and hyperbolic models (Vreugdenhil and de Vries 1973)

Linear hyperbolic model has been studied by Zang and Kawahita (1990) which is applicable toalluvial channels of finite length and include a general case of an arbitrary function, of either sedimenttransport or channel bed specified as an upstream boundary condition. They have shown that non-uniformity in both sediment transport rate and river bed is important for short time intervals. For largetimes, the diffusion process becomes dominant and similarity solutions are acceptable. The linear

Parabolic model

id; asymptotic expansion

Hyperbolic model

id; asymptotic expansion

0.7

q3210

0.6

0.5

0.4

0.3

0.2

0.1

0

Z/Z

o

to = 1 2 4 6

4

6

2

to = 1

River Morphology356

solutions provide fair predictions of river bed if the upstream loading DqT/qTe is less than 4.0. Lineartheory also indicates that the sediment celerity is constant, directly proportional to the sedimenttransport rate and inversely proportional to the sediment transport rate and inversely proportional towater depth. Non-linear hyperbolic model has been studied by Zang and Kawahita (1988).

Wave ModelThe wave model was first used by Exner (1925) to explain the mechanism of formation of ripples inalluvial channels. Assuming that acceleration in the flow causes erosion while deceleration would causedeposition, Exner wrote the following equation

¶

¶

Z

t + E

¶

¶

U

x = 0 ...(11.41)

Here Z is the bed elevation, U is the average velocity at a section and E is the erosion coefficient. Ifh represents the elevation of water surface above the datum, (h – z) represents the flow depth and forconstant Q and channel width B, the continuity equation for flow takes the form

(h – Z) BU = Q ...(11.42)

Assuming water surface to be horizontal and taking B as constant, the above two equations can becombined to yield

¶

¶

Z

t +

EQ

B Zh -a f2 ¶

¶

Z

x = 0 ...(11.43)

which is the wave equation. Exner assumed that at t = 0 the bed elevation is given by

Z = ao + a1 cos 2p

l x

EQ

B Zt-

-

F

HG

I

KJ

ha f2...(11.44)

The resulting bed undulations at various times are characterized by constant a1 and velocity of bed

forms equal toEQ

B Zh -a f2. Since the crest of the wave moves faster than the trough, initial symmetrical

bed form becomes unsymmetrical with time, taking the approximate shape of ripple. The resulting bedform has a flat upstream face and steep downstream face. Exner has further improved this analysistaking into account water surface slope, friction and changes in channel width. However, the majorcriticism against Exner’s analysis is that it does not explain as to how a plane bed would developsymmetrical waves in the beginning.

Silva and Kennedy (1989) have used kinematic wave model to analyse river bed degradationdownstream of a section of an alluvial river where sediment discharge is cutoff. They have also includedthe effects of bed coarsening and armoring by using validated mathematical expressions for thesephenomena. They assumed that sediment transport rate in a degrading stream is primarily a function ofdepth of flow, say qT » f (D). This relation is modified to take into account bed coarsening and velocitychanges. Finally, Silva and Kennedy have obtained an implicit expression for D(x, t). This solution was


compared with the solution obtained by IALLUVIAL software for specific problem and the agreementwas reasonably good. It may be mentioned that de Vries has used kinematic wave model for filling oftrench (see de Vries 1993).

References

Adachi, S and Nakatoh, T. (1969) Changes of Top-Set Bed in a Silted Reservoir. Proc. of 13th congress of IAHR,Tokyo (Japan), Vol. 5.1, 3.16 – pp. 269-272.

Carslaw, H.S. and Jaeger, J.C. (1947) Conduction of Heat in Solids. Oxford University Press, New York, U.S.A.

Culling, W.E.H. (1960) Analytical Theory of Erosion. Jour. of Geology, Vol. 68, No. 3, pp. 336-344.

de Vries, M. (1965) Consideration About Non-steady Bed Load Transport in Open Channels. Proc. of 11thCongress of IAHR, Leningrad, Vol. 3, 3.8 – pp. 1-11.

de Vries, M. (1975) A Morphological Time Scale for Rivers. Proc. of 16th Congress of IAHR, Sao Paulo, Brazil,Vol. 2, B3 – pp. 17-23.

de Vries, M. (1993) Lecture Notes on River Engineering. Delft, 139 p.

Exner, F.M. (1925) Ûber die Wechuwirkung Zwischen Wasser und Geschiebe in Flûssen-Sitzber-Akad-Wiss.Wien pt 1a, Bd 134

Garde, R.J., Ranga Raju, K.G. and Mehta, P.J. (1981) Bed Level Variations in Aggrading Alluvial Streams. Proc.of 19th Congress of IAHR, New Delhi, Vol. 2, pp. 247-253.

Gill, M.A.(1983) Diffusion Model for Aggrading Channels. JHR, IAHR, Vol. 21, No. 5, pp. 355-268.

Gill, M.A. (1983a) Diffusion Model for Degrading Channels. JHR, IAHR, Vol. 21, No. 5, pp. 369-378.

Hou, Z. and Kawahita, R. (1987) A Nonlinear Mathematical Model for Aggradation in Alluvial Channel Beds.JHD, Proc. ASCE, Vol. 113, No. HY3, pp. 353-369.

Jain, S.C. (1981) River Bed Aggradation Due to Overloading. JHD, Proc. ASCE, Vol. 107, No. HY-1, Jan. pp.120-124.

Jaramillo, W.F. and Jain, S.C. (1983) Characteristic Parameters of Non-equilibrium Processes in AlluvialChannels of Finite Length. Water Resources Research, Vol. 19, p. 952-958.

Mehta, P.J. (1980) Study of Aggradation in Alluvial Streams. Ph.D Thesis, University of Roorkee (Now I.I.T.Roorkee).

Park, L. and Jain, S.C. (1984) River-Bed Profiles With Imposed Sediment Load, JHE, Proc. ASCE, Vol. 112, No.4, April, pp. 267-279.

Silva, J.M. and Kennedy, J.F. (1989) Proc. of 4th International Symposium on River Sedimentation, Beijing(China), Vol. 2, pp. 1072-1079.

Soni, J.P. (1975) Aggradation in Stream Due to Increase in Sediment Load. Ph.D. Thesis, University of Roorkee(Now IIT Roorkee).

Soni, J.P., Garde, R.J. and Ranga Raju, K.G. (1980) Aggradation in Stream Due to Overloading. JHD, Proc.ASCE, Vol. 106, No. HY1, Jan. pp. 117-132.

Tsuchiya, B. and Ishizaki, T. (1969) Estimation of River Bed Aggradation Due to Dam. Proc. of 13th Congress ofIAHR, Tokyo (Japan). Vol. 1, A-33, 297-304.

Vittal, N. and Mittal, M.K. (1980) Degradation of Ratmau Torrent Downstream of Dhanauri. Proc. of 1stInternational Workshop on Alluvial River Problems, Roorkee (India), pp. 5-43-54.

Vreugenhill, C.B. and de Vries, M. (1973) Analytical Approaches to Non-steady bed Load Transport, DelftHydraulic Laboratory, Research Report S-78-III, 17 p.

River Morphology358

Zang, H. and Kawahita, R. (1988) Non-linear Hyperbolic System and Its Solutions for Aggradaing Channels. JHR,IAHR, Vol. 26, No. 3, pp. 323-342.

Zang, H. and Kawahita, R. (1990) Linear Hyperbolic Model for Alluvial channels. JHE, Proc. ASCE, Vol. 116,No. 4, Apr., pp. 478-493.

12C H A P T E R

Numerical Models forMorphological Studies

12.1 INTRODUCTION

In the previous chapter analytical models for studying transient morphological processes have beendiscussed. It may be recalled that a number of assumptions had to be made to obtain analytical solutions.

For example, flow was assumed to be quasi-steady so that ¶

¶

U

t and

¶

¶

D

t be omitted. Assumption of

steady state water flow is not valid while computing bed level changes during unsteady flow conditions.It is also not strictly valid even if the discharge is constant, since water surface profile computationsdepend on bed slope which varies with time. Further, the channel was assumed to be sufficiently wideand of constant width. In addition, a constant value of Manning’s n or Chezy’s was assumed implyingthat change in C or n due to changes in bed-forms during transient stage is neglected. Still further, thebed material was assumed to be uniform or of small standard deviation so that it could be characterizedby d50 alone. As a consequence, effects of armouring and grain sorting were not included in thosemodels. Also, the sediment transport law used was in the simplest form namely qT ~ Un or qT ~ to

n.However, it must be accepted that in spite of these assumptions one gets solutions which are simple andcan be used as the first approximate solution to transients in alluvial streams. Hence, analytical solutionshave been obtained for degradation and aggradation at a dam, aggradation due to increase in sedimentload, withdrawal of water, and filling of trench.

However, when the above restrictions are violated the analytical solutions do not give acceptableand accurate results. As such since about 1970 a number of numerical models have been developed tosolve problems of morphological changes in alluvial streams. This chapter is devoted to furtherdiscussion of the governing equations, boundary conditions and the basic techniques of numericalcomputation along with related aspects; a discussion of some available software packages and the

River Morphology360

results obtained from them are also presented. In writing this chapter the author has heavily depended onthe excellent works of Cunge et al. (1980), de Vries (1993), and Murthy et al. (1998).

12.2 ONE-DIMENSIONAL EQUATIONS

One-dimensional form of the dynamic equation (St. Vennant equation) for unsteady flow in openchannels was derived in Chapter 11. As indicated by Cunge et al. (1980) this equation can be written indifferent forms, depending on the choice of dependant variables.

(i) Q(x, t), D(x, t)

¶

¶+

¶

¶

FHGIKJ+

¶

¶

Q

t x

Q

AgA

D

x

2

+ gA(Sf – So) = 0 ...(12.1)

Here B = B (D) and A = A (D).

(ii) U (x, t), D(x, t)

¶

¶+

¶

¶+

¶

¶

U

tU

U

xg

D

x + g(Sf – So) = 0 ...(12.2)

It may be mentioned that the channel cross section can be of arbitrary shape and may vary along thelength.

The continuity equation for flow is

¶

¶+¶

¶

A

t

Q

x= 0 ...(12.3)

when there is no inflow from the sides. This can be written as

¶¶

+¶¶

+¶¶

A

tU

A

xA

U

x= 0 ...(12.4)

The continuity equation for sediment is

(1 – l)¶

¶+¶

¶

A

t

Q

tS = 0 ...(12.5)

which for wide channels reduces to

(1 – l)¶¶

+¶¶

Z

t

q

xS = 0 ...(12.6)

for wide channels. Here l is the porosity. If the bed of the channel is composed of non-uniformsediment, this equation has to be applied for each size fraction; this is necessary for simulatingdegradation and armouring. For i th reach and kth fraction of the sediment, one can write

D

D

D

D

Z

t

q

tik sk+

-

1

1( )l= 0 ...(12.7)

Numerical Models for Morphological Studies 361

where DZik = change in bed level in the i th reach due to imbalance in sediment transport capacity for thekth fraction. Total change in kth reach is

DZi = D Zikk

m

=

å1

...(12.8)

Resistance Law and Sediment Transport LawAs discussed in Chapter 5 a number of predictors are available for the resistance coefficient andsediment transport rate, and some studies have been carried out to study their relative accuracy. With thepresent state of knowledge prediction of average velocity U within ±20 to 30 percent error andprediction of transport rate within ±40 to 50 percent error are considered acceptable. The effect of errorsin prediction of U or transport rate on the prediction of bed levels over long periods needs to be studied.

One can use either Chezy’s or Manning’s equation with constant C or n, or C or n changing withchanges in stage or discharge. One can also use any other resistance law which may involve predictionof regime or a trial solution for U, or may be function of sediment transport rate.

Sediment TransportIn analytical models the transport equation of the form qT = mUn or qT = a t*

b have been used. Engelund-Hansen formula corresponds to n = 5 while in Meyer-Peter and Müllers’ formula

n = 3 10 047

-FHG

IKJ

.

*t

Some softwares such as HEC-6 has an option of choosing any one of the five or six formulae for thecomputation of transport capability. Most of the sediment transport formulae in vogue are based onsome basic assumptions which include (i) the flow is steady and uniform, (ii) river-bed is in equilibrium,(iii) there is negligible wash load transport, (iv) the sediment is uniform or with small standarddeviation, and (v) all size fractions are moving. In numerical modeling these formulae are used forunsteady, non-uniform flow by replacing So by Sf . The validity of this extension of use is yet to beverified.

Further, in most of these formulae it is assumed that sediment transport rate at any section isgoverned by the local hydraulic conditions. When such an equation is used for computing transport ratesfor different size fractions it is usually assumed that the transport rate of kth fraction of sediment size isequal to transport rate for that size using a given formula multiplied by the fraction of that size rangeavailable in the bed. This assumption may be acceptable if standard deviation of the bed material issmall and all the sizes are moving. However, for large standard deviations and partial transport ofsediment (during armouring process), the results will be affected due to sheltering effect for smallersizes and greater exposure for sizes larger than the average size.

Realising the complexities in sediment transport formulae and their accuracies, it is prudent to use asimpler formula. Using some available data the engineer should try different formulae and choose theone that gives acceptable results.

River Morphology362

12.3 NUMERICAL SCHEMES OF SOLUTION

The differential equations governing morphological processes in alluvial streams can be solved eitherby finite element method (FEM) or by finite difference method (FDM). Comparing these two methodsZienkieweiz et al. (1975) have observed that for slow flow, where convective terms are insignificant,FEM was superior. They also found that with high velocities, when the convective terms becomeimportant, and in transient problems, FDMs retain some superiority. Similarly in the preliminary stages,studies by Palaniappan (1991) indicated that FEM did not have any superiority over FDM in onedimensional alluvial stream transients. Cunge et al. (1980) also expressed similar view that in modelingof river dynamics FEM has not found wide spread applications and it is found that the method has noadvantage over finite difference one-dimensional models. The real strength of FEM is in solving 2-Dand 3-D problems.

One of the FDMs viz. the method of characteristics is discussed in detail by Abbott (1966) andCunge et al. (1980). This method requires very small time steps, whereas in alluvial stream transientscomputations involve very large times such as 10 to 30 years. Hence while the method of characteristicscan be used for flood propagation involving a few days, it is uneconomical and hence not suited forcomputation of bed level variations in alluvial stream involving large times.

Two methods of computation are available in the other finite difference scheme: these are theexplicit method and the implicit method. In the explicit method a variable at (n + 1) the time level isexpressed fully in terms of known quantities at nth time.

Two schemes of explicit finite difference method that are often used are the Lax scheme and theLeap-frog scheme. With reference to Fig. 12.1 in the Lax scheme the time derivative and spacederivative are expressed as

¶

¶

f

t=

f f f f

tjn

jn

jn

jn+

+ -- + - +1

1 11[ ( )( )]a a

D...(12.9)

¶

¶

G

x=

( )G G

xjn

jn

+ --1 1

2D...(12.10)

where a is the weighting coefficient. Substituting these in the continuity type equation for sediment, onegets

fjn+ 1 = a fj

n + (1 – a) f f t

xG G

jn

jn

jn

jn+ -

+ -

+L

NMM

O

QPP- +

1 11 12 2

D

D( ) ...(12.11)

Thus f can be calculated for (n + 1) time level for known values of f and G at nth level.In the Leap-frog scheme the time and space derivatives are expressed as

¶

¶

f

t=

( )f fjn

jn+ -

-1 1

2 and

¶

¶

G

x =

( )G G

xjn

jn

+ --1 1

2D...(12.12)


and substitution in sediment continuity equation gives

fjn+ 1 = fj

n – 1 – D

D

t

x2 (Gn

j + 1 – Gnj – 1) ...(12.13)

When Dt/Dx = g Do and a = 0 both the schemes give exact solution of fully linearised flow

equations.

The finite difference implicit scheme can be written in general form as

¶

¶

f

t=

y y y yf f f f

t

jn

jn

jn

jn

++ +

++ - - + -11 1

11 1( ) ( )

D...(12.14)

and¶

¶

G

x=

q qG G G G

x

jn

jn

jn

jn

++ +

+- + - -11 1

11( )

D...(12.15)

When the weighting coefficient y = 0.50 and the coefficient q is given a value between 0.5 and 1.0(and preferably slightly greater than 0.50) it represents Preissmann 4-point scheme. There are a fewvariations in this scheme also. The implicit method involves solution of a matrix resulting in escalationof cost of computation.

12.4 CLASSICIATION OF ONE-DIMENSIONAL MODELS

One-dimensional mathematical models are quite useful in prediction of bed and water surface profiles,average depth, velocity and transport rate as a function of x and t. These have been used for solvingproblems such as

i) bed level variation during flood in lower reaches of the river;ii) sedimentation upstream of a dam;

Fig. 12.1 Computational grid

j � 1 j + 1j

(n + 1)

n

(n � 1)

t

River Morphology364

iii) degradation downstream of a dam;iv) modification of a river profile due to construction of embankments and execution of cutoffs;

v) changes in river morphology due to addition or withdrawal of sediment or water;vi) long-term evolution of river bed.One-dimensional numerical models can be classified depending on whether quasi-steady or full

unsteady flow equations are used, and on whether uncoupled or coupled scheme of computation is used.

In quasi-steady models the terms ¶

¶

D

t and

¶

¶

U

t are neglected. As pointed out earlier, this excludes the

case where ¶

¶

U

t is very small but

¶

¶

D

t has to be considered. This situation arises for a river with a

reservoir where, Q being a function of t, there is storage which is a function of ¶

¶

D

t. In unsteady flow

case these terms are retained.In uncoupled scheme of solution the continuity equation and the dynamic equation for flow are

solved along the river course for time D t assuming that the bottom elevations Z(x) do not change duringD t; the solution consists of water stages, water discharges and average velocity at the end of timeinterval D t. Then using the water depth, velocity and slopes that are computed at the nodal points, thetransport capacities are computed at the nodal points, and using sediment continuity equation, changesin bed elevation DZ and new bed profile are computed over the whole reach at the end of D t. The processis then repeated for the next D t. Since in this scheme the water flow equations and sediment continuityequation are uncouples during Dt, it is called uncoupled scheme. When the Froude number is less than0.60 or so (which is usually the case in alluvial rivers), the velocities of propagation of water wave aremuch greater than that of bed wave propagation and hence this scheme of computation is justified inmany cases.

In quasi-steady coupled models, the quasi-steady equations for full momentum equation and thecontinuity for flow and the sediment continuity equation are solved using implicit finite differencescheme. The resulting non-linear algebraic equations are solved simultaneously to achieve couplingbetween water flow and sediment movement. In a similar manner unsteady uncoupled, and unsteadycoupled one-dimensional models can be described.

In all the four types of one dimensional models discussed above, one can use either the explicit orthe implicit scheme of computations. However, it may be noted that most of unsteady coupled modelsuse implicit scheme to solve the governing equations. Although large computational time steps can beused with these schemes, they involve solution of a system of equations using matrix inversion duringeach computational step. Lyn (1987) has suggested that complete coupling between full unsteady flowequations and sediment continuity equation is desirable in the cases where the conditions are changingrapidly at the boundaries. Lyn’s results along with those of Yen et al. (1995) support the view thatuncoupled models with quasi-steady flow have considerable utility in solving alluvial stream transients.Their accuracy can be improved by using more reliable methods of computing sediment transportingcapacity, armouring processes, and friction factor predictors.

The investigations by Cui et al. (1996) and de Vries (1993) indicate cost effectiveness of explicitschemes. Cui et al. (1996) compared the numerical results obtained using coupled and quasi-steady


Table 12.1 Summary of some one-dimensional models for mobile bed simulation

Name Developer Details

1. Delft Hydraulics de Vries et al. Quasi-steady, one-dimensional, qT = aUb, n or CLaboratory assumed constant

2. SOGREAH CHAR-2, Cunge et al. Quasi-steady, 4-point implicit scheme to solveCHAR-3 coupled system.

3. HEC-2 with sediment Simons et al. Quasi-steady, uncoupled, uses M.P. and Müller’s orrouting Einstein’s equation for sediment transport; armouring

effect included

4. KUWASER Simons et al. Quasi-steady, qT = aUb Dc, uncoupled.

5. UUWSR Tucci et al. Unsteady, uncoupled, uses 4-point implicit scheme forflow and explicit scheme for sediment qT = aUbDc

6. HEC-6 Thomas Quasi-steady, variable Manning’s n, choice of sedimenttransport formula, armouring included, uses explicitscheme.

7. FLUVIAL – II Chang and Hill Unsteady, uncoupled, width changes allowed, Graf orEngelund-Hansen formula for sediment transport, usesexplicit scheme for sediment and implicit scheme for flow.

8. HRS Wallingford Bettess and While Quasi-steady, uncoupled, uses Ackers-White orEngelund-Hansen transport formula, implicit scheme,armouring included.

9. IALLUVAL Karim, Kennedy et al. Quasi-steady, partially decoupled, single load mechanism,saturated capacity, armouring included, multi-size predictor.

10. RESSED Chen Quasi-steady, fully decoupled, single load mechanism,multi-size predictor.

11. CHARIMA Holly et al. Unsteady flow, partially coupled, single load mechanism,saturated capacity, single size predictor.

12. MOBED Krishnappan Unsteady, flow, fully coupled, single load mechanism,single size predicator.

13. FLUVIAL – II Chang Unsteady flow, fully decoupled single load mechanismnon-saturated capacity, multi-size predictor.

14. SEDICOUP Holly and Rahuel Unsteady flow, fully coupled, separate bed-loadmechanism, non-saturated capacity, multi-size predictor

uncoupled models for the cases where Froude number is close to unity and also for cases in whichupstream water discharge, sediment inflow rate and the downstream water level varied strongly. Therewas a very good agreement between numerical results obtained using the two models, althoughuncoupled models are inherently unstable than the coupled ones. Hence, uncoupled explicit schemes aremany times preferred and due consideration is given to the convergence and stability.

Some One-Dimensional ModelsA number of one-dimensional numerical models have been developed and used since 1970’s for solvingtransients in alluvial streams. Some of the models are listed below giving name of the model, developerof the model, and its description, see Table 12.1.

River Morphology366

Out of all these models, HEC-6 is discussed here in detail followed by a brief account ofCHARIMA. This is followed by two applications of HEC-6 to study effect of levee spacing on bedelevations in the Kosi and sedimentation studies upstream of a dam in India.

12.5 CONVERGENCE AND STABILITY (CUNGE ET AL. 1980)

The basic idea of convergence is that the discrete solutions to the governing flow equations shouldapproach the exact solutions to those equations when Dx and Dt approach zero. However, since the fullnon-linear partial differential equations do not have analytical solutions, it is impossible to directlycompare analytical and numerical solutions for convergence. Hence, the numerical method is tested onthe corresponding linear form of equations to obtain information about the convergence of the scheme.For linear equations the convergence is ensured if the conditions of Lax theorem are satisfied. Thetheorem states:

“Given a properly posed initial-value problem and a finite difference approximation to it thatsatisfies the consistency condition, stability is the necessary and sufficient condition forconvergence”.Consistency means that the finite difference operators approach differential equations when Dx and

Dt lend to zero. Numerical stability means that the solutions obtained using the numerical scheme arebounded, that a small rounding-off error remains small during computational steps however long andnever become as large as the prescribed significant number. Thus stability means the errors introducedby small perturbations remain smaller than a prescribed value.

In studying the numerical stability, two partial differential equations

¶

¶+

¶

¶=

¶

¶+

¶

¶=

U

V||

W||

U

tg

D

xD

tD

U

xO

0

0and...(12.16)

are used. When the numerical scheme is utilized, the numerical computations can have different

harmonics resulting from the truncation errors, and if during the computations | |C Ut

xC

t

x+

D

D

D

Dor is

always kept less than one, the damping factor for all the harmonics will be less than one and hence thesolution will be stable. This condition is known as Courant condition or Courant-Friedrichs-Levy (CFL)condition. CFL condition of stability is directly linked to the theory of method of characteristics.Courant number Cr is less than one expresses the fact that the computational point (n + 1, j) lies withinthe domain of determinacy of the point of intersection of two characteristics from the neighbouringpoint at nD t level.

In general explicit methods are conditionally stable, Courant condition limiting the permissible timestep Dt. Implicit methods, on the other head, can generally be made unconditionally stable. Preissmannand Delft Hydraulics Laboratory methods are unconditionally stable if q ³ 0.50. Because of conditionalstability of implicit schemes, they have been used often.


12.6 BOUNDARY CONDITIONS (CUNGE ET AL. 1980, DE VRIES 1993)

The boundary conditions required for solving alluvial stream transients are in four forms, namely initialconditions, upstream conditions, downstream conditions and internal conditions. These are brieflydiscussed below.

Initial ConditionsAt time t = 0 the bed elevation Z at all places 0 < x < L must be known i.e., Z (x, 0) is known. In the caseof a meandering channel, since the bed level varies across the width, it is reasonable to take average bedelevation there. In flood problems initial water level along the river length should be known.

Upstream ConditionsTwo conditions are imposed at the upstream; the first is variation of Q with t should be known, i.e.,Q (0, t); this is inflow hydrograph and is needed for solving the momentum equation. Inflow hydrographis usually obtained from historic data for as many years as possible. The other upstream conditionneeded is regarding variation of incoming sediment load with time, i.e., Qs(0, t). This is prepared fromsuspended load measurements. Since it is difficult to measure the bed load, it can either be calculatedusing one of the bed-load equations or estimated and added to Qs(0, t) so that it represents bed materialdischarge. This is needed for solving the sediment continuity equation. Alternatively one can preparerelationship between measured bed material discharge and Q and use it.

Downstream ConditionsFor sub-critical flow, downstream water level must be known in order to determine the water surfaceprofile for known bed elevation and discharge. This usually follows from discharge rating curveh = h (Q). However if the bed level at x = L changes with time due to erosion or deposition, then thedownstream condition can be placed far downstream so that the bed level does not change during thetime of interest.

Internal BoundariesIf within 0 < x < L one or more of the parameters are discontinuous, then the internal boundaryconditions are required. Such situations arise in cases such as withdrawal of discharge DQ (t),withdrawal of sediment load DQs(t), change in river width, confluences and bifurcation. Thesediscontinuities can create discontinuity in bed elevation.

Thus, if two streams 1 and 2 join and form the stream 3 the conditions to be satisfied are

Q Q Q

Q Q QT T T

1 2 3

1 2 3

+ =

+ =

UVW

...(12.17)

For a bifurcation of river 1 into two streams 1 and 3

Q Q Q

Q Q QT T T

1 2 3

1 2 3

= +

= +

UVW

...(12.18)

Further, the distribution of Q1 into Q2 and Q3 should be such that the stage discharge relations forthe two branches 2 and 3 lead to the same water level at the point of bifurcation. The local geometry ofthe branches determines the ratio QT2/QT3.

River Morphology368

Consider the problem of aggradation upstream of a dam. If x is measured from the dam in theupstream direction,Initial condition: Z(x, 0) should be known for 0 = x and L

Downstream boundary condition: D (0, t) should be specified for all t

Upstream boundary condition: Q (¥, t) should be specified and Qs = f (¥, t) should also be given0 £ x £ L and t = 0.

In the similar manner boundary condition for degradation downstream of dam can be given. If x ismeasured from the dam in the downstream direction,Initial condition: Bed level and water level should be known for 0 = x and L at t = 0

Upstream boundary condition: at x = 0 QT (0, t) = QT for t < 0

QT (0, t) = QT1 for t > 0 where QT1 < QT

QT(L, t) = QTe for L large value of L

12.7 CHANNEL CROSS-SECTIONS AND METHOD OF EROSION ORDEPOSITION

Even with the assumption of one-dimensional flow, the channel cross section can be irregular and canhave floodplain on one or both the sides of the main channel as shown in Fig. 12.2.

Fig. 12.2 Channel with floodplain

In such a case the channel is usually divided into a number of sub-sections each having a differentvalue of n or C. Defining the conveyance K as

Q = 1

n AR2/3 Sf

1/2 = K Sf

one can write Q = Q1 + Q2 + Q3 …….where Q1, Q2, Q3 … are discharges in each subsection and Q is the total discharge. Hence

K Sf = SKi Sf or K = S Ki

Further, it is recognized that the floodplain areas often act as storage zones. They store water whosevelocity in the general direction of flow is nil. Hence, models such as HEC-6 define a movable bedwidth at each section and erosion or deposition occurs in that width only.

n4

n5n3n2

n1


In a one-dimensional model even though the flow is one-dimensional sediment movement is threedimensional in nature because of secondary circulation and presence of beds. However, to simplify theanalysis the sediment transport is assumed to be one-dimensional. Also when erosion or depositionoccurs within a section, it can be assumed to occur in one of the following three ways as shown inFig. 12.3.

1. the cross section rises or falls through DZ without change in shape;2. only those parts of the cross section which are below water level move up or down;3. attempt is made to distribute sediment laterally in relation to tractive force (Chang and Hill

1976) or based on other information.As discussed later in HEC-6, movable bed width is identified at each section and effective width

between two sections is also determined. Then knowing the volume of sediment to be deposited oreroded in time Dt, bed level change DZ is computed.

12.8 MODELING OF ARMOURING

Starting with Harrison (1950) a number of laboratory investigations have been carried out byinvestigators such as Hasan (1965), Jaswant Singh (1974), Gessler (1967), Little and Mayer (1972),Garde et al. (1977) Shen and Lu (1983), Odgaard (1984) and Garde et al. (2004). Most of these studieswere aimed at the prediction size distribution of the armour coat for known size distribution of theparent material and the initial flow conditions. The results of some of these investigations have beendescribed in Chapter 10.

Garde et al. (1977) conducted laboratory studies to determine time variation of surface layer of adegrading stream. It was found that the major part of coarsening takes place in a relatively short time;thereafter the process is very slow. If do and df are the median sizes of the parent material and the finalsurface layer, and dt is the median size of the surface layer at any time t, they found that

( ) . ( / ) / .

( ) . ( / ) / ..

..

..

.

1 0 32 0 40

1 5 5 4 00 75

0 170 75

0 753 40

0 75

- = <

- = <

UV|

W|

-

-

F t t t t

F t t t t

for

and for...(12.19)

Here F = (dt – do)/(df – do). The final value df varied along the length according to Sternberg’s law.Here t0.75 is the time at which F = 0.75. To use the above equation one must know df and t0.75. Borah(1989) has also proposed a method for predicting the depth of degradation.

Fig. 12.3 Methods of deposition

River Morphology370

Some attempts have been made to study the time evolution of the armour coat, which is required inany mathematical model used for predicting time variation of erosion and deposition.

In HEC-6 model (1993) developed by Thomas and Prashun (1977) the armouring process isanalysed assuming the bed to consist of two layers: (1) the active layer which predicts the bed surfacedegradation and armouring, and (ii) the inactive layer beneath the armour layer. Using Manning’sequation for U, Strickler’s equation for Manning’s n, and the condition for insignificant sedimenttransport as proposed by Einstein viz. y = Dgsd/to = 30, an equilibrium depth De is defined as theminimum water depth required for a given particle size d to be immobile on the bed, and is given by

De = (q/10.21d1/3)6/7 ...(12.20)

in which q is expressed in ft2/s, De in ft, and d in mm.

When the bed is composed of a mixture of different sized particles, the erosion depth Dse required toaccumulate one particle size thick layer of coarse non-moving material is calculated using the equation,

Dse = 2 SAE.d/3Pc ...(12.21)

Here SAE is the ratio of surface area of potential erosion to the total surface area (which is also takenas equal to the ratio of erodible material remaining in the active zone to the total volume in inactivezone) and Pc is the fraction of the bed material coarser than size d, which can be determined from theknown size distribution curve of the bed material, which is divided into different segments starting fromthe coarsest fraction as shown in Fig. 12.4.

Fig. 12.4 Segmented size distribution curve of bed material

Consider the segment 1-2 and determine the equilibrium depths Deq1 and Deq2 for sizes 1 and 2respectively using Eq. (12.20). If the actual depth of flow Dw is less than Deq2.1, the straight line segmentfrom 1 to 2 in Fig. 12.4 determines the value of Pc and then the final equilibrium depth is calculated asDeq = Dw + Dse. If Dw is greater than Deq2, computations move to segment 2-3 and so on, until either theproper segment is located or the smallest particle size in the bed material is sufficient for armouring thebed, in which case scour or erosion does not occur. The depth between bed surface and equilibriumdepth is the active layer (see Fig. 12.5), and below the equilibrium depth and the erodible limit is theinactive layer. The thickness of the active layer changes with change in U, Dw and slope.

d mm

1

2

3

4

5

6

79 8

100

Pe

rce

nt

fin

er


Ashida and Michiue (1971), Bayazit (1975) and Palaniappan (1991) use the concept of mixingvolume on the bed surface to simulate the armour coat. In these models when sediment flows out of amixing volume, an equal quantity by weight is added to the mixing volume in each computational step.The added sediment has the same grain size distribution as that of the current surface.

Armouring procedures used in CHARIMA (Holly et al. 1990) are identical to those used inIALLUVIAL. It is assumed that as the armouring develops with increasing degradation, the bed surfaceis segregated into two parts: armour coat and part of the bed containing movable size fractions. Hencefraction of the bed covered by non-moving particles Af (t) at any time t can be used as a measure of thedegrading bed. This process depends on the size distribution of the bed material and its variation withdepth, intensity of water discharge and sediment transport, formation and height of bed undulations, andthe stochastic character of the sediment movement. According to the analysis of Karim et al. (1983),Af (t, k) is given by

Af (t, k) = Af (t – 1, k) + CA(t, K )×(1 – l) DZ(t)×P

dk

k

...(12.22)

= 0 when k £ l (t)

and Af (t) = A t kfk t

m( , )

( )=å

l

Here Af (t, k) = fraction of the bed area covered by particle size interval k at any time t; DZ(t) =incremental depth of degradation during current time interval; l(t) = index for lowest grain size intervalwhich is immobile according to Shields’ criterion, and forms the armour coat at time t; CA(t, k) = apositive coefficient; Pk = fraction of bed material in the kth fraction, and m = total number of fractions.The constant CA(t, k) = 1.9 for plane bed while the following empirical equation is used for CA(t, k)

CA(t, k) = 1.902 ad qk

to take into account the effect of bed forms on armouring. Here ad is a function of dune height to waterdepth ratio and hence of t* /t*c; ad = 1.0 when t* /t*C = 1.0 and when t* /t*c = 1.5. Its variation betweenthese two limits is given by a function. Also qk is the probability of kth sediment size fraction to remainon the bed.


W.S

Inactive layer

Active layer

Deq

DwDeq1

Deq2

D = D + Deq w se

River Morphology372

Armouring of the bed surface tends to reduce the sediment transport capacity of the flow andreduces the average height of dune and mixed layer. This reduction is assumed to be linear inCHARIMA.

qsa = qs(1 – Af [t])

qsa = H

2(1 – Af [t])

Here qsa and qs are the transport rates with and without armouring; Tm is the mixed layer thicknessand H is the dune height.

12.9 HEC-6

HEC-6 is a one-dimensional quasi-steady uncoupled model designed to simulate and predict long termchanges in river bed profile over moderate times. It was developed by W.A. Thomas of the Corps ofEngineers of U.S.A. in 1976 and since then the model has been improved upon a few times; the latestversion 4.1 was presented in 1993. It handles a river system consisting of the main, tributaries, and localinflow or outflow points. Hence the model can analyse network of streams, channel dredging andvarious levee and encroachment alternatives. It faithfully deals with sub-critical flows and approximatesthe super critical flow by normal depth.

Input DataThe input data include the geometric data, the sediment data and the hydrologic data. The geometricdata include cross-sections along the length of the reach, Manning’s n values, movable bed width ineach section and depth of sediment material in the bed. Each cross section is defined by a maximum of100 points with station and elevation data. Typical cross-section is shown in Fig. 12.6 indicating mainchannel, left and right over banks, movable bed limit and erodible-bed.

Fig. 12.6 Channel details

Leftover bank

Rightover bank

Main channel

Movable bed limit

Bed materialavailable for scour


The conveyance limits are also specified so that section beyond those limits does not contribute towater conveyance. The channel is divided into a number of sub-sections for each one of whichManning’s n can be specified which can vary with stage of the discharge. For given water level, theeffective depth and effective width are defined. Hence for given Q, velocity can be computed.

The sediment data include fluid and sediment properties, inflowing fraction wise sediment loaddata, the size distribution of the stream bed material, sediment transport capacity’s relationships, andunit weight of sediment. The sediments are classified into silt, clays, sands and boulders usingclassification of the American Geographical Union. These are divided into different size ranges and arerepresented by the geometric mean size. Sediment transport rates for sizes up to 2048 mm are computedand material coarser than 2048 mm only participates in armour coat formation. The sediment inflowdata at the upstream section is given as QT vs. Q curve according to size class. Other properties ofsediment that are needed such as relative density, shape factor, unit weight and fall velocity are alsospecified. The sediment transport capacity at each section is calculated by using one of the alternativesprovided in HEC-6 programme; these include methods of Toffaleti, modifications of Laursen’s methodby Madden, and Copeland, Yang, DuBoy’s transport function, Ackers-White, Colby, Meyer-Peter andMüller.

The hydrologic data include water discharges, temperature, downstream water surface elevationsand flow duration. To reduce the number of time steps used to simulate a given time period, thecontinuous flow hydrograph is treated as a sequence of discrete steady flows; this is sometimes knownas computational hydrograph.

Boundary ConditionsHEC-6 needs specification of upstream as well as downstream boundary conditions and internalboundary conditions. The upstream boundary conditions that are needed are discharge vs. time discretehydrograph, corresponding water temperature and sediment discharge data. HEC-6 provides threeoptions for downstream boundary conditions. These are: (i) rating curve giving Q versus water surfaceelevation data, (ii) water surface elevation as a function of time, or (iii) a combination of the first twooptions. The second option is used with reservoirs where water surface elevations are a function of time.The internal boundary conditions are specified at the internal points within the reach at which watersurface elevations may be specified. This is usually done either by specifying a constant head loss for alldischarges, or by specifying a rating curve at the internal boundary.

Method of CalculationSince HEC-6 is a quasi-steady, uncoupled model, it first uses one-dimensional energy equation forcomputing the water surface profile, starting from downstream section and moving upstream, usingstandard step method. Knowing the initial bed levels at all the sections, and water surface elevation atdownstream section 1, the following equation is solved for water surface elevation at section 2.

WS2 + a2U

g22

2= WS1 + a1

U

g12

2 + he ...(12.23)

Here WS1 and WS2 are water surface elevations, a is the energy correction coefficient based on thedistribution of average velocities in the subsections and he is the head loss due to friction and expansion

River Morphology374

or contraction; the latter is computed as CU U

ge( )a a2 2

21 1

2

2

- where Ce is specified. Equation (12.22) is

solved by assuming WS2 and comparing the terms on the left and right hand side of the equation; amaximum of twenty iterations are carried out. The computations are performed at all sections andhydraulic parameters U, D and W are computed. For computing the sediment capacity, effective depthand effective width are used which are defined as follows:

Effective depth (EFD) = D a Dav i av

N2 3

1

/å

Effective width (EFW) =

a D

EDF

i av

N2 3

15 3

/

/( )

å

where ai = flow area of each trapezoidal element, Dav = average depth of each trapezoidal element, andN = total number of trapezoidal elements in a sub-section.

Knowing velocity, depth and movable bed width at each section these are converted intorepresentative values in each reach for their use in calculating transport capacity. This is done asfollows:Interior points:

U U I U I U I

D D I D I D I

W W I W I W I

S S I S I

U U I D D I W W I S S I

S U I U I

D D I D I

W W I

= - + + +

= - + + +

= - + + +

= + +

= = = =

= + +

= + +

=

0 25 1 0 5 0 25 1

0 25 1 0 5 0 25 1

0 25 1 0 5 0 25 1

0 5 1

0 5 1

0 5 1

0 5

. ( ) . ( ) . ( )

. ( ) . ( ) . ( )

. ( ) . ( ) . ( )

. [ ( ) ( )]

( ), ( ), ( ), ( )

. [ ( ) ( )]

. [ ( ) ( )]

. [ ( )

For upstream boundary:

Downstream boundary:

+ +

=

U

V

|||||||

W

|||||||

W I

S S I

( )]

( )

1 ...(12.24)

Now the sediment transport capacities at any section at a given time are calculated using one of theequations listed earlier and the computations proceed from the upstream towards the downstreamdirection. Sediment continuity equation is then used in finite difference form. With respect to Fig. 12.7,one can write


G G

L L

B Y Y

tu d

u d

sp sp sp-

++

¢ -

0 5. ( )

( )

D = 0

where Gu and Gd are upstream and downstream transports of sediment in time Dt, in (vol./time), and

Bsp is width of movable bed at P,

Ysp and Y¢sp are depths at sediment before and after the time step at P

Gu is size wise sediment load entering the section and

Gd is calculated considering the transport capacity at P, sediment in flow, availability of material inthe bed and armouring.

The time step can be variable, a fraction of a day for high flows to several days or month for lowflows. It should be such that during the time step the bed level change is less than 0.3 m or 10% of depthof flow whichever is smaller. The gradation of the bed material is recalculated after each time interval bycomputing the fraction of bed material size available in the active bed. When scour or deposition occursduring a time step Dt, HEC-6 adjusts the cross-section elevations within the movable bed portion of thecross-sections. For deposition, the stream bed portion is moved vertically only if it is within the movablebed specified and is below water surface. Scour occurs only if it is within movable bed, within theconveyance limits, within the effective flow limits and below water surface. Once scour or deposition

limits are known, ( )

( )

volume of sediment eroded or deposited

effective width length of control volume ´ +L Lu d

gives change in bed elevation

in time Dt. When bed scours, armouring process may start which has been discussed earlier. For otherdetails one may see HEC-6 user’s manual (1993).

Model OutputHEC-6 gives a variety of outputs which include hydraulic data for each trial elevation in each backwatercomputations at all the sections, volume of sediment entering and going out of each reach, trap


(Upstream) (Downstream)

x

p

p

Dt

LdL4

24 3 1t

Time

Section

River Morphology376

efficiency, bed level changes, water surface elevations, sediment transported at each section along withits gradation, and bed material surface composition at each time step. It also gives some additionalinformation.

Model CalibrationNumerical models such as HEC-6 usually need calibration with the known conditions. During thecalibration of the model, the constants in the equations, time step, sediment transport and resistanceformulae used are changed so that the historical conditions are simulated. The known conditions usedfor calibrating the model can be water levels and or bed levels at certain times. Such a calibration alsoaccounts for any inaccuracies in hydraulic and sediment load data as long as consistently the sametechniques of measurements are used. Once the model is calibrated it is assumed that it will predict theresults for the future with reasonable accuracy. However, it may some time happen that such data forcalibration of the model are not available; in such a situation the modeler has to use his past experiencein choosing the coefficient and the equations.

Limitations of HEC-6HEC-6 programme has the following limitations:

i) The model being one-dimensional, development of meanders and lateral bank erosion cannotbe accounted for.

ii) Further, bifurcation of flows and closed loops (i.e., flow around islands) cannot be modelled.iii) Only one junction or local inflow is permitted between consecutive sections; andiv) The model analyses long term erosion or deposition; hence analysis of the single flood events

must be done with great caution.

12.10 CHARIMA

This one-dimensional model was developed at Iowa Institute of Hydraulic Research (U.S.A.) in 1988 tostudy braided river channel network of the Sestina river in Alaska. The model can simulate processessuch as sediment sorting, bed armouring, flow dependent friction factor, and alternative flooding anddrying of perched channels. In addition to the assumptions made in St. Vannant equation, channelnetwork (i.e., total number of channels and their inter connections) is assumed to remain same andcross-sections rise and fall during deposition of degradation. The effect of bends cannot be accountedfor in the model and lateral inflow be accounted for by channels joining at regular intervals. The modelhas been used for flow analysis by CWPRS (1999).

Governing EquationsIn addition to continuity equations for flow and sediment, and momentum equation for unsteady flow,CHARIMA requires

Sediment discharge predictor:F1(Q, A, d50, Sf, D, Qs, ASF) = 0

Friction factor predictor: F2(Q, A, d50, Sf, D, Qs, ASF) = 0

Channel geometry predictor: A = A(D, x)

B = B(D, x)


Hydraulic sorting: Dn50 ® d50

n+ 1

Armouring of bed surface: ACFN = ACFN + 1

Here Sf is the energy slope and ACF is a coefficient.

Solution ProcedureThe solution of these equations is obtained in decoupled mode. CHARIMA follows Preissmann implicitscheme to discretise the water flow and sediment continuity equations. In the first stage sedimentdischarge equations, friction factor equation, channel geometry equations and discretised equation forwater flow are solved in hydraulic sweep. During this sweep the bed elevation Z, d50, armouringcoefficient ACF are held constant assuming the bed to be temporarily stationary. During this stage atgrid point C, water flow, water level, and the sediment transport capacity for each size fraction of the bedmaterial are computed.

In the stage 2, discretised sediment continuity equation is solved in downstream sweep to get newbed levels at each grid point i. The sediment discharge Qs

n+1 computed in stage 1 is treated as constantassuming that it is unaffected by bed evolution process, armouring, and grain sorting. In this stageaccounting procedure is executed using aggradation or degradation computed in stage 2 (i.e. sorting ofbed material to compute new d50 and new armouring factor ACFn+ 1). This procedure is uncoupledbecause it assumes that these processes occur sequentially and not concurrently in given Dt. CHARIMAessentially follows the following flow chart.

Fig. 12.8 Flow chart for CHARIMA

Execute sorting andarmouring procedure

Compute bed level changes

using sediment continuity eq .n

Compute friction factorand sediment discharge

Compute W.L., discharge etc.solve continuity and momentum

equations

Load boundary conditionsTime loop

Iteration loop

River Morphology378

During execution of CHARIMA the sediment load capacities can be determined from anyone of thesediment transport formulae of Karim and Kennedy, Engelund and Hansen, modified Peter Ackers andWhite formula, or the power law predictor. Dune height can be obtained either from Yalin’s relation orAllen’s relation. It also takes into account and model

i) hydraulic sorting of bed material;ii) changes in the composition of bed material;

iii) armouring of the bed surface or armouring factor ACF which is defined as the fraction of bedsurface area covered by non-moving particles;

iv) effect of bed forms on armouring;v) effect of armouring on sediment discharge and the mixed layer thickness.

Armouring process used in CHARIMA is briefly discussed earlier. Many of the procedures andrelations used in CHARIMA are those used in IALLUVIAL model developed at Iowa Institute ofHydraulic Research (U.S.A.) CHARIMA has been used to study long-term evolution of the Missouririver reach between Gavins point dam and Rulo (Nebr), a reach of about 313 km, short term predictionof bed evolution of the Cho-Shui river system in Taiwan and the Sestina river in Alaska. For details ofthe model one can refer Holly et al. (1990).

12.11 APPLICATIONS OF HEC-6

To illustrate the applications of the above-mentioned numerical models, two applications of HEC-6 willbe briefly discussed here. The first relates to the aggradation of the Kosi river in the leveed reach, whilethe second is concerned with aggradation upstream of a dam in India.

Aggradation of the KosiThe river Kosi which is a major tributary of the Ganga originates in Nepal and flows through the state ofBihar before it joins the Ganga at Kursela. The morphology of the Kosi is discussed in detail in Chapter13 and the index map of the Kosi can be seen there; the Kosi has been known for its lateral migrationwhich has been attributed to excess sediment load it carries, eastward slope of the region and tectonicand neo-tectonic activity in the region. To control frequent flooding and lateral migration the barragewas constructed at Bhimnagar and embankments on both sides were built between the barrage and theplace called Mansi. Downstream of Mansi, the river is embanked only on the eastern side upto Koparia.Between 1964 and 1974 it was found that approximately 50 percent of the sediment load of the Kosi wasdeposited upstream of the barrage and the major part of the remaining load was deposited in betweenlevees thereby raising the bed levels.

The spacing between eastern and western embankments varies significantly along 100 km reachthat seems to be responsible for bed level variations. Table 12.2 lists the cross-section number, distancefrom the barrage in km and levee spacing in meters.

At the request of Ganga Flood Control Commission the Kosi problem was investigated at theUniversity of Roorkee (Now IIT Roorkee) by Garde et al. (1990) to study:

1. causes of frequent breaches in the embankments;2. bed level changes that are likely to occur in the embanked reach up to 2005;


Table 12.2 Levee spacing at selected reaches on the Kosi

Cross-section number Distance from the barrage, km Levee spacing m

33 1.27 745841 11.25 7323

48 23.25 550553 31.25 1133563 48.00 12722

65 53.75 1560067 55.50 1854069 60.00 17434

75 68.75 1115681 78.50 927987 84.25 7972

91 94.25 8853

3. bed level changes that are likely to occur if spacing between the embankments is reducedselectively; and

4. calculate sediment load brought into the Ganga by the river Kosi during 1985-2005 with andwithout forward embankments.

Figure 12.9 shows the leveed portion and the locations of different sections. The slope of the riverbetween the barrage and 40 km downstream is about 5.5 ´ 10–4 and it reduces to 2.70 ´ 10–4 upto Mansi.The median size of bed material is 0.25 and has a standard deviation of 1.45. For very low flows the riveris braided but at medium and high flows it flows in a single channel within embankments; hence it wastreated as unbraided in the model.

Fig. 12.9 Leveed portion of the Kosi

River Morphology380

Analysis of the past records gave average monthly discharges which varied 13 170 cfs (373 m3/s) inJanuary to 167 365 cfs (47 544 m3/s) in the month of July. From the discharges available, ten dailycomputational hydrograph was prepared. On the basis of measurements of average suspended sedimentconcentration data at the dam site, the relationship between sediment discharge G in tons/day and Q incfs was obtained in the form

G = aQb ...(12.25)

in which a and b varied as follows:

Table 12.3 Values of a and b in Eq. (12.25)

Range of d in mm

Range of Q in cfs D less than 0.075 mm 0.075 < d < 0.15 mm D > 0.15 mm

a b a B a b

5000 = Q = 30 000 4.33 ´ 10–13 3.86 1.08 ´ 10–9 2.86 2.89 ´ 10–9 2.76

30 000 = Q = 40 000 0.012 1.53 2.043 ´ 10–5 1.89 1.84 ´ 10–6 2.13

After a few trial runs it was decided to use Laursen-Madden’s equation for determining sedimenttransport capabilities. The model was calibrated using bed level data in the leveed portion for the period1975-1984. Values of Dx and Dt were determined from the following considerations. A typical floodwave would take about 7 hours to cover 200 km reach. The time step Dt chosen was much greater thanthis, namely 10 days during the monsoon period and 30 days during non-monsoon period, while Dxequal to 10 km was used. For downstream control the water levels at Kursela were estimated fromanalysis of the Ganga river data and used in HEC-6.

Bed level profiles during 1975-1984 were used with the above mentioned Dx and Dt values and thebest value of Manning’s n which could satisfactorily estimate those bed levels was found to be 0.20; thisvalue was used in further studies.

For the bed level predictions between 1985-2005, monthly discharges were generated usingThomas-Fiering model and using characteristics of monthly flow data from the historic data available.

Analysis of DataDetailed analysis of cross sections at various times and the occurrence of breach at any section,indicated that prior to the actual breach, the deep channel gradually shifted towards the embankmentnear that section. The average lateral rate of deep channel shifting was about 200 m/yr. It was thereforerecommended that the cross-sectional data in the leveed reach be monitored every year after floodseason and the places where the deep channel is close to the embankment be determined. The sectionsdownstream of that would be prone to breaching.

Bed Level VariationsObservations of the longitudinal profiles in the leveed reach for different years indicated thataggradation or bed lowering occurring from section to section was primarily due to the variation inwidth between levees along the river length. It was found that if a narrow section was followed by a


wider section, the material scoured from the narrow reach was deposited in the wider reach causingaggradation. Taking 1984 bed profile as the basis, bed profiles were obtained by using HEC-6 for theyears 1990, 1995, 2000 and 2005. The rise and fall in bed levels along the river reach with respect to1984 levels (both leveed and not leveed) are shown for the years 1995, 2000 and 2005 in Fig. 12.10. Itcan be seen that maximum rise in the bed level at about 2.6 m is likely to occur at about 48 km from thebarrage (section 63) in the year 2005. The computation of water levels indicated that the water levelbetween sections 63 and 91 will be about 1.37 m to 2.13 m below the top of the levee.

A number of proposals for reducing the spacing between the levees thereby reducing aggradationwere considered and tested using HEC-6. These were:

i) uniform reduction in width to 90 percent of the present;

ii) uniform reduction in width to 80 percent of the present;iii) uniform reduction in width to 70 percent of the present;iv) reduction in width to 70 percent of the present width in 12 km reach between sections 63 and

69;v) reduction in width between sections 53 and 75 to 75 percent to 0 percent width;

vi) reduce width between sections 67 and 75 gradually from 70 percent at section 69 to 0 percent atsection 75.

The first three proposals were rejected because these caused increased deposition and rise in waterlevel at most of the sections. Schemes (v) and (vi) are shown in Fig. 12.11. Effect of scheme (vi) on thebed levels within the leveed reach and the downstream of it can be seen in this Fig. 12.10. It may benoted that the proposed scheme (vi) does not significantly alter bed levels downstream of leveed reach,and significantly brings down rise in bed levels between sections 63 and 75. At critical section 63aggradation reduces from 2.59 m to 1.71 m in 2005.

Fig. 12.10 Rise and fall in bed levels in the Kosi with 1984 as the basis

3

km from barrage

200 40 60 80 100 120 140 160 180 200

2

1

0

�1

�2

Bed

ele

vation

m

Scheme 6

BarrageLeveed portion

200520001995

River Morphology382

The study also indicated that if the jacketing proposal (vi) is adopted, the sediment load entering theGanga may increase from (9.8 ´ 107) tons/yr to (.1 ́108) tons/yr, which seems to be only a marginalincrease in view of the high discharges in the Ganga at Kursela.

Sedimentation Studies Upstream of a DamAs a second example of application of HEC-6, computation of sediment deposition profiles upstream ofa dam is discussed. The dam under discussion is located on a river in Southern India and has a height of35.3 m and length of 1560 m. Average riverbed slope in 275 km reach is 0.000091 and bed material ofsize 0.90 mm and sg of 5.5. At about 240-250 km upstream of dam the irrigation scheme and diversionweirs are in operation. Hence it was required to be found out if sedimentation in the upstream of the damwould affect the function of these diversion structures and would raise the flood levels beyondacceptable limits. Since further details about operation of the dam were not available, it was assumedthat full reservoir level of 519.6 m will be maimed and flood discharges will be released accordingly.

Ten daily discharge hydrograph flows varied from 125 m3/s in June to 3150 m3/s in July and about100 m3/s in October. The inflow sediment discharge obtained from suspended load measurements wasrepresented by the equation

Qs = 1.5Q1.65

in which Qs is expressed in tones/day and Q in m3/s. A tributary joining just upstream of the dam, havingten-daily discharge variation from 40 m3/s to 200 m3/s was also modeled. The Manning’s for the mainchannel and the flood plain were estimated to be 0.025 and 0.05 from the meager data available. The bedprofiles obtained for 10, 20 and 30 years of operation, for a constant water level of the dam, obtained byusing HEC-6 are shown in Fig. 12.12. It was found that the bed levels at 245 km upstream of the damwhere lift irrigation scheme is in operation would rise by about 2.20 m in 30 years. When the maximum

Fig. 12.11 Recommended spacing of levees in the Kosi

Bag

mat

i river

Western flood embankment

(existing)

Forwardembankmentas per scheme-V

Forwardembankmentas per scheme-VI

Forwardembankmentas per scheme-V and VI

6359

53

50

67

69

71

75

Eastern flood embankment (existing)

N


observed flood of 13 320 m3/s was passed over 30 year bed profile with 519.6 water level at the dam, theflood levels rose by nearly 2.0 m within 60 to 260 km upstream of the dam.

References

Abbott, M.B. (1966) An Introduction to the Method of Characteristics. Thames and Hudson, London.

Ashida, K. and Michiue, M. (1971) An Investigation of River Degradation Downstream of a Dam. Proc. of 14thCongress of IAHR, Paris, Vol. 3.

Bayazit, M. (1975) Simulation of Armour Coat Formation and Destruction. Proc. of 16th Congress of IAHR, SaoPaulo (Brazil), B 10, pp. 73-78.

Borah, D.K. (1989) Scour Depth Prediction Under Armouring Conditions. JHE, Proc. ASCE, Vol. 115, No. 10, pp.1421-1425.

Chang, H.H. (1982) Mathematical Model for Erodible Channels. JHD, Proc. ASCE, Col. 108, No. HY5, pp. 678-688.

Chang , H.H. and Hill, J.C. (1976) Computer Modelling of Erodible Flood Channels and Deltas. JHD, Proc.ASCE, Vol. 102, No. HY9, pp. 1464-1477.

Chen, Y.H. and Simons, D.B. (1975) Mathematical Modelling of Alluvial Channels. Proc. of Symposium onModelling Techniques, ASCE, San Francisco, pp. 466-483.

Chen, Y.H. and Simons, D.B. (1980) Water and Sediment Routing for the Chippewa River Network System. Proc.of International Conference on Water Resources Development, Taipei (Taiwan), Vol. 2.

Fig. 12.12 Transient bed profiles upstream of the dam

River Morphology384

Correia, L.R.P., Krishnappan, B.G. and Graf, W.H. (1992) Fully Coupled Unsteady Mobile Boundary Flow Model.JHE, Proc. ASCE, Vol. 118, No. 3, pp. 476-494.

Cui, Y., Parker, G. and Parola, C. (1996) Numerical Simulation of Aggradation and Downstream Fining. JHR,IAHR, Vol. 34, No. 2, pp. 185-204.

Cunge, J.A. Holly, F.M. and Verwey, A. (1980) Practical Aspects of Computational Hydraulics. PitmanPublishing Ltd., London, 420 p.

CWPRS (1999) Mathematical Model Studies for Proposed Storm Water Drainage System of Central and NorthRegion of Vasai-Vihar. Central Water and Power Research Station, Khadakwasla, Pune. Tech. Report 3655,65 p.

De Vries, M. (1993) Lecture Notes on River Engineering, Delft International Course, Delft, 139 p.

Garde, R.J., Ali, K.A.S. and Diette, S. (1977) Armouring Process in Degrading Streams. JHD, Proc. ASCE, Vol.103, No. HY9, pp. 1091-1095.

Garde, R.J., Ranga Raju, K.G., Pande, P.K., Asawa, G.L., Kothyari, U.C. and Srivastava. R. (1990) MathematicalModelling of the Morphological Changes in River Kosi. Hyd. Engg. Section, Civil Engg. Dept., University ofRoorkee, Roorkee, 92 p.

Garde, R.J. Sahay, A. and Bhatnagar, S. (2004) Armour Coat Formation in Parallel Degradation. Report Preparedfor Indian National Science Academy, CWPRS, Pune., 45 p.

Gessler, J. (1967) The Beginning of Bed Load Movement of Mixtures Investigated as Natural Armouring inChannel. Translation T-5, W.M. Keck Laboratory of Hydraulics and W.R., Caltec (U.S.A.).

Harrison, A.S. (1950) Report on Special Investigation of Bed Sediment Segregation in a Degrading Stream.University of California, Inst. of Engineering Research, Berkeley (U.S.A.), Series 33, No. 1.

Hasan, S.M. (1965) Experimental Study of Degradation. M.E. Thesis, Civil Engg. Dept., University of Roorkee,Roorkee.

Holly, F.M., Yang, J.C., Schwarz, P., Hsu, S.H. and Einhellig, R. (1990) CHARIMA – Numerical Simulation ofUnsteady Water and Sediment Movement in Multiply Connected Network of Mobile Bed Channels. IowaInstitute of Hydraulic Research, Iowa, Rep. No. 343.

Karim, M.F., Holly, F.M. and Kennedy, J.F. (1983) Bed Armouring Procedure in IALLUVIAL and Application tothe Missouri River. Iowa Institute of Hydraulic Research, Iowa, Rep. No. 269.

Krishnappan, B.G. (1985) Modelling of Unsteady Flow in Alluvial Streams. JHE, Proc. ASCE, Vol. 112, No. 2,pp. 257-265.

Little, W.C. and Mayer, P.G. (1972) The Role of Sediment Gradation in Channel Armouring. School of CivilEngineering, Georgia Institute of Technology, Atlanta (U.S.A.).

Lyn, D.A. (1987) Unsteady Sediment Transport Modelling. JHE, Proc. ASCE, Vol. 113, No. 9, pp. 1-15.

Murthy, B.S., Surya Rao, S., Rajagopal, H., Tiwari, S.K. and Kumar, R. (1998) Flood Estimation Routing in RiverSystem : Mathematical Models. Report Submitted to INCH, IIT Kanpur, Kanpur, 151 p.

Odgaard, A.J. (1984) Grain Size Distribution of River Bed Armour Layers. JHE, Proc. ASCE, Vol. 110, No. 10,pp. 1479-1485.

Palaniappan, A.B. (1991) Numerical Modelling of Aggradation and Degradation in Alluvial Streams. Ph.D.Thesis submitted to University of Roorkee, Roorkee.

Rahuel, J.L., Holly, F.M., Chollet, J.P., Belleudy, P.J. and Yang, G. (1989) Modelling of River Bed Evolution forBed Load Sediment Mixtures. JHE, Proc. ASCE, Vol. 115, No. 11, pp. 1521-1542.

Shen, H.W. and Lu, J.Y. (1983) Development and Prediction of Bed Armouring. JHE, Proc. ASCE, Vol. 109, No.4, pp. 611-629.


Singh, J. (1974) Variation of Bed Material Size in Degrading Channel. M.E. Thesis, University of Roorkee,Roorkee.

Thomas, W.A. and Prashun, A.L. (1977) Mathematical Modelling at Scour and Deposition. JHD, Proc. ASCE,Vol. 103, No. 8, pp. 851-863.

U.S. Army Corps of Engineers (1993) HEC-6 : Scour and Deposition in Rivers and Reservoirs. User’s Manual,Hydraulic Engineering Centrer, Davis, (U.S.A.) 164 p. with Appendix.

Yen, K.C., Li, S.J. and Chen, W.L. (1995) Modelling Non-uniform Sediment Fluvial Process by CharacteristicMethod. JHE, Proc. ASCE, Vol. 121, No. 2, pp. 159-170.

Zienkieveiz, J.C. Gallagher, R.H. and Hood, P. (1975) Newtonian and Non-Newtonian Viscous IncompressibleFlow-Temperature Induced Flow-Finite Element Solution. MAFELAP.

13C H A P T E R

Morphology of Some Indian Rivers

13.1 RIVER SYSTEMS IN NORTH INDIA

From the point of view of morphology of rivers in alluvial material, the Indian rivers originating fromthe Himalayas and flowing through thick alluvial stratum need special mention. These rivers broadlybelong to three basins, namely the Indus basin, the Ganga basin and the Brahmaputra Basin (Rao 1979).

The Indus system of rivers comprises the main river Indus and its tributaries the Kabul, the Swat,and the Kurram joining from the west, and the Jhelum, the Chenab, the Ravi, the Beas and the Sutlejjoining from the east. The five tributaries from the east join the Indus which flows 960 km before joiningArabian Sea. The Indus river originates in Tibet near Manasarovar Lake, passes through the mountainranges of Kashmir and Gilgit, enters Pakistan and emerges out of the hills near Attock. From Attock toits mouth in the Arabian Sea, south of Karachi, it traverses a distance of about 1610 km out of its totallength of 2880 km. The eastern tributaries pass through northwest part of India namely throughKashmir, Punjab and Himachal Pradesh and then flow out to join the Indus in Pakistan.

The Himalayas in the north, and the Vindhyas in the south bound the Ganga basin. The Ganga is notknown by this name either in the beginning or at the end of its length. Downstream of the confluence ofthe Alaknanda and the Bhagirathi at Dev Prayag, the river is known as the Ganga. After traversing adistance of 250 km the river descends on to the plains at Rishikesh, and passing through Hardwar andNarora it meets the river the Yamuna at Allahabad. It further passes through Varanasi, Patna andBhagalpur and then turns towards south. Upstream of Varanasi the Ganga is joined from the north bymajor tributaries the Ramganga, the Gomti and the Tons, and from the south by the Chambal, the Betwa,the Sinda and the Ken. Downstream of Varanasi, when the river enters Bihar, other important tributarieslike the Ghagra, the Gandak, Son, the Bagmati and the Kosi join from the north. In the lower Gangabasin only the Mahananda joins the Ganga. Of all these tributaries the Kosi is known for its instabilitydue to high sediment load and braided plan-forms; hence its morphology is discussed later. Abouthundred kilometers downstream of Rajmahal the river ceases to be called Ganga. It bifurcates intoBhagirathi the lower portion of which below Kalna is called the Hooghly which continues in India andthe Padma, which flows in Bangladesh and forms the southern boundary between India and Bangladesh

Morphology of S

ome Indian R

ivers387

Fig. 13.1 Basins in Indo-Gangetic plain in Indian subconinent

Brahmaputra

Tsangpo

Kosi

Kosi

Kurusela

KolkataHirakud

MahanadiNarmada

Narmada

BetwaSon

GandhiSagar

Chambal

Yamuna

GangaDelhi

Indus

Chenab

Sutlej

Ravi

Chenab

Jhelum

Kabul

Beas

BhakraNangal

Sarda

Ghaghara

AllahabadGandak

Delhi

Lucknow

Kanpur

Ahmedabad

Nagpur Kolkata

Lakshadwip

Sri Lanka

Andaman andNicobarIslands

nI d i a

Mumbai

Chennai

River Morphology388

for some distance. After traversing 220 km further down in Bangladesh the Padma is joined by theBrahmaputra at Goalundo and after meeting the Meghana 100 km downstream, the Ganga joins the Bayof Bengal. Figure 13.1 shows a sketch of these basins in the Indian subcontinent.

The Brahmaputra river rises in the Kailash range of the Himalayas at an elevation of about 5000 m.It is about 2880 km long. After flowing about 1600 km parallel to the main Himalayan range, it entersIndia and after traversing 720 km joins the Padma at Goalundo. The combined stream is then known asthe Padma. In Tibet and India a number of tributaries join Brahmaputra. The Brahmaputra is known forits instability, floods, and bank erosion causing innumerable miseries to the people living in north-eastIndia. Hence, the morphology of the Brahmaputra is also discussed later.

There are certain common characteristics of rivers in these basins namely the Kosi and theBrahamputra which are responsible for their morphological behaviour. These rivers are fed by rainfallas well as snowmelt; hence, their hydrographs have in general two peaks. Further, major parts of theircatchment lie outside India; as a result, India can do very little in terms of soil conservation measures aswell as construction of dam etc., without active cooperation from neighbouring countries. Further, thesestreams originate or pass through fragile Himalayas which erode fast, and hence they carry relativelyheavy sediment load. Also, the entire Himalayan belt from Kashmir to Assam being tectonically activewith frequent earthquakes and neotectonic movements, the morphology of rivers in these regions isaffected by tectonic activity. It may be mentioned that there are a number of subsurface transverse faultsin the region, which influence the morphology of the streams. Further, hilly areas are prone tolandslides, which occur because of unstable hill slopes, earthquakes and intense rainfall. As a result,heavy sediment load enters these streams.

The streams in these regions are classified by Jain and Sinha (2003) into three categories namelymountain-fed, foothills-fed and plain-fed streams. These differ significantly in morphological,hydrological and sediment transport characteristics. Mountain-fed rivers are generally multi-channel,and braided systems, characterized by many times higher discharges and sediment load in comparison tosingle channel sinuous foothill-fed and plains-fed river systems. Mountain-fed rivers such as the Ganga,the Gandak and the Kosi transfer large quantities of sediment from their source areas of high relief andconsequently form large depositional areas (e.g., fans) in plains. The foothill-fed rivers (the Bagmatiand the Rapti) and plain-fed rivers (the Gomati and the Burhi Gandak) derive their sediments fromfoothills and plains and a large proportion of this material is re-deposited in the plains after reworking.It may also be pointed out that many rivers in Ganga basin show tendency towards avulsion.

KOSI

13.2 INTRODUCTION

The river Kosi, which is a major tributary of the Ganga and which is the life line of the state of Bihar inNorth India, originates at an elevation of about 6000 m in the Himalayas and finally discharges into theGanga at Kursela, see Fig. 13.2. Plate 1 shows the aerial view of the Kosi. The river is also sometimescalled the Saptakosi with seven tributaries namely the Sun Kosi, the Arums, the Tamur, in the upperreaches and the Trijuga, the Balan, the Kamla and the Bagmati in the plains. In Sanskrit literature thisriver is referred to as the Kaushiki. It may be mentioned that Kaushiki was the legendary ascetic low-

Morphology of Some Indian Rivers 389

Fig. 13.2 Kosi river basin

caste woman who, after being left by her Brahmin lover, became frivolous and went to various places inquest of pleasure. Hence, there is considerable similarity between the ever-wandering Kosi river andKaushiki. The river Kosi traverses a total distance of 468 km passing through Tibet, Nepal and India.The Kosi is known for shifting its course laterally and thus creating problems of flooding and causingconsiderable loss to human lives, cattle, property, public utilities and agriculture. Hence the river isknown as the “Sorrow of Bihar”. The Kosi is also one of the largest braided rivers in the world.

The Kosi catchment consists of the Himalayas in the eastern part of Nepal and Tibet. The trans-Himalayan portion is a high plateau while the Himalayan portion comprises mountain ranges runningeastward separated by cross-ribs. Portions of the catchment above the elevation of 4900 m are coveredby perennial snow, the snowline being at 3000 m in winter and 4500 m in summer. It may be mentionedthat ten percent of the Kosi catchment is perpetual snow zone of Himalayas and this has a major effecton the nature of annual flood hydrograph. The catchment area within India is flat and lies in theGangetic plains. Out of the remaining, seventy percent is under cultivation and a very small percentunder forest cover in India.

The Kosi forms an inland delta or fan in the Gangetic plain (Gole and Chitale, 1966). The apex ofthe fan is a few kilometers downstream of Chatra, the base extending over a distance of 120 km andheight being about 100 m. It has a slope from north to south and west to east. Kosi fan covers an area of16 000 km2 lying partly in Nepal and partly in north Bihar. It lies between altitudes of 152 m and 34 m

Eas

tern

emba

nkm

ent

32 miles

Scale

Rajmahal

Monghyr

riverGanga

Patna

Sonriv

er

Ghaghara river

Gandak

river

Bagmati river

Kam

larive

rBadiaghat

KurselaKatihar

Pumea

Mahananda

riverJogbani

North Bihar

IndiaNirmali Wes

tern

emba

nkm

ent

Kamrail

TribeniNepal

Ba

lan

rive

r

ChatraBarrage

Barahakshetra

Darjeeling

Sikkim

Tam

urriv

er

Aru

nriv

er

MT Everest

Sun Kosi river

Tibet

Khatmandu

Gan

dak

river

N

River M

orphology390

Plate 1 Aerial view of the Kosi


above the sea level. This fan is covered by old courses of the Kosi now occupied by smaller streams(known locally as dhars), old channel lakes (known locally as chaurs), oxbow lakes and dune-likemounds along the abandoned courses of the Kosi. Their existence is due to the westward shifting ofKosi through 112 km in 223 years (Gole and Chitale 1966).

13.3 CATCHMENT CHARACTERISTICS AND GEOLOGY

The Kosi basin falls within longitude 85° to 89° (E) and latitude 25° 20’ to 29° (N). On its north is theTsangpo (Brahmaputra) and on the south is the Ganga river. On eastern side is the ridge separating itfrom the Mahananda catchment and on the west is the ridgeline separating it from the Gandak/BurhiGandak catchment. There is an 87 m drop in elevation in the 160 km reach between the Chatra gorgeand Kursela near the confluence with the Ganga. The total catchment area of Kosi is 95 156 km2 out ofwhich 20 376 km2 lies in India. Thus, nearly eighty percent of total catchment of the Kosi lies in Tibetand Nepal. The rivers the Trijuga, the Kamla Balan, the Bhutahi Balan and the Bagmati are thetributaries, which join the Kosi from the right in the plains in Bihar. The distribution of the catchmentarea in the Kosi river system is given in Table 13.1.

The three hilly tributaries are the Arun, the Sun Kosi and the Tamur. The Arun Kosi is the longest ofthe hilly tributaries, which drains the Mount Everest. Its catchment area is 34 650 km2 and it contributes37 percent of flow and 36 percent of sediment load of the Kosi at Tribeni. The Sun Kosi is the secondlongest tributary. Its catchment area is 19 000 km2 and it contributes 44 percent of flow and 42 percentof sediment load of Kosi at Tribeni. Tamur Kosi drains Mount Kanchanjunga; its catchment area is 5900km2 and it contributes 19 percent of flow and 22 percent of sediment load of Kosi at Tribeni.

The Bagmati originates in Sheapore range hills at an elevation of 1500 m and has a catchment areaof 13 400 km2 and length of 589 km. The Kamla Balan originates in Nepal and has a catchment area of5445 km2 almost half of which is in the plains. Its length is 320 km. The Trijuga and the Bhutai Balanhave catchment areas of 706 km2 and 1105 km2 respectively.

The geology of the Kosi basin can be divided into three parts, namely the geology of the MountEverest and the Kanchanjunga, which lie in the upper northern most part and form the upper catchment,the Siwalik deposits which lie towards south of Mount Everest and up to Chatra, and the terraces belowChatra. The upper-most part is made up of folded Jurassic strata composed of black shales andargillaceous sand stones. This stratum is 100 to 150 m thick, and contains calcarius, pyrites and ferrouspartings. Underlying the Jurassic shales are dark limestones and below it thick series of metamorphosed

Table 13.1 Distribution of catchment area in Kosi river system

In India (km2) Out side India (km2) Total (km2)

Kosi including hilly tributaries 11 070 63 430 74 500Kamla Balan 2980 2465 5445

Bagmati 6320 7080 13 400Trijuga - 706 706Bhutai Balan - 1105 1105

Total 20 370 74 786 95 156

River Morphology392

limestone, quartzites etc. The Siwalik deposits are alluvial detritus derived from wastes from mountainswhich are swept down by streams and deposited at their foot. These former alluvial deposits have beeninvolved in the upheavals of the Himalayas because of which they may have been folded and elevatedinto their outermost foothills. Weathering of Siwalik rocks has been proceeding at an extraordinarilyrapid rate since their deposition. Because of this, the topography produced is made up of very largeescarpments and dip-slopes separated by broad longitudinal valleys intersected by deep meanderingravines. The terraces below Chatra are made up of conglomerates and thick beds of sand, boulders andshales. The Kosi flood plain is made up of alluvial deposits in the form of a trough, which is tectonic innature and is formed in front of Himalayan chains. Hence, during the past and present times it issubjected to slow neo tectonic movements and earthquakes (NIH 1994). Figure 13.3 shows thegeological map of the Kosi basin.

13.4 GEOTECTONICS

The entire Kosi basin area has been the subject of study by Bordet, Gansser, Hagen and Akiba et al. (seeGohain and Parkash, 1990). The major north dipping thrusts – the Main Central Thrust and MainBoundary Thrust – are present in the area and are active even at present. One can see from Fig. 13.3 amajor fault FF’ at the edge of the Kosi fan which causes an offset of the Siwaliks by about 20 m. Thisarea has also experienced over 45 earthquakes of magnitudes ranging from 4.0 to 8.3 on Richter scale,the most severe earthquake being the one that occurred on 15th Jan. 1934 and was of magnitude 8.3; this

Fig. 13.3 Geological map of the Kosi alluvial fan and adjacent area (Gohain and Parkash 1990)

BurhiGandak R

Ganga

Kosi R

Scale

0 20 km

Kosi alluvium

Alluvium of the Ganga River

Alluvium of the other south,southeast and east flowing streams

Younger alluvial piedmont

Older alluvial piedmont

Upper Siwalik sediments

Middle siwalik sediments

Archaean

Lesser Himalayan Rocks

Faults lineaments

Faults after raiverman et. al., 1983

Fan boundary

F¢


earthquake had its epicenter within 100 km of Barakshetra where a high dam was earlier proposed onthe Kosi. This earthquake was felt all over north Bihar and Nepal and the cities of Munger and Bhatgaon(in Nepal) were completely destroyed while the cities of Patna, Kathmandu and Darjeeling felt theshocks of the earthquake. Kosi basin is also subjected to slow neotectonic upheaval, which may bepartly responsible for the westward migration of Kosi.

13.5 HYDROLOGY

The Kosi catchment is fed by monsoon rainfall as well as snowmelt. As mentioned earlier ten percent ofthe catchment up to Chatra is above perpetual snow zone of the Himalayas. Kosi catchment gets rainfalldue to monsoon, which begins around June, and retreats in the middle of October. This accounts foreighty percent of the annual rainfall. During April and May, thunderstorms occur in the catchment. Theannual rainfall decreases from 1200 mm at the foothills to 350 mm on the southern slopes of theHimalayas. In the Tibetian catchment it is about 250 mm while in the lower parts of the Kosi catchmentit varies from 1380 mm to 1500 mm. July and August provide the maximum rainfall. Mookerjee andAich (1963) have estimated that 74 percent of the discharge of Kosi can be accounted for by theprecipitation in the form of rainfall. Analysis of peak flow in Kosi indicates that the peak flow can be tentimes as large as the mean discharge in a single year. Flow duration curve for the Kosi at Barakshetra isgiven by Gohain and Parkash (1990). Its approximate coordinates are given in Table 13.2

Table 13.2 Flow duration curve for Kosi at Barakshetra

Monthly average discharge in m3/s 300 400 600 700 1400 3600 4300 4800 5800

Percent of time equaled or exceeded 100 80 60 50 40 20 10 5 1

The average annual runoff at Barakshetra is estimated to be 53 040 Mm3 out of which 80 percent iscontributed from June to October. The minimum annual runoff at the same place is approximately 38.83Mm3.

Discharge and Sediment MeasurementsIt was only after 1947 that the government agencies realised the necessity of having adequate andaccurate flow and sediment data for the management of Kosi and established gauging sites. At presentthe Kosi has eight sediment and gauge-discharge observation sites. These are at Barakshetra, BhimNagar barrage, Baltara and Basua on the Kosi, on the Sun Kosi, the Arun and the Tamur at Tribeni, andat Machhuaghat on the Arun. The annual peak flows observed at Barakshetra between 1948 and 1978are listed by NIH (1994). These are given in Table 13.3.

It can be seen that the maximum observed flow at Barakshetra was 25 880 m3/s in 1968 and watersurface elevation for this discharge was observed to be 132.18 m.

Analysis of sediment load carried on the Kosi at Barakshetra for the period 1948-1981 has revealedthat on the average it carries 95 Mm3 of sediment annually, of which coarse, medium and fine sizedmaterials are 18.95, 25.11 and 55.94 percent respectively. Similar measurement made at Baltarabetween 1973-1981 have given average sediment load as 57.35 Mm3 of which coarse, medium and fine

River Morphology394

are 8.2, 19.8 and 72.0 percent respectively. Garde et al. (1990) analysed the sediment load data at thebarrage and found that the sediment load in Tons/day is related to Q in m3/s as

QT ~ Q3.86 for sediment finer than 0.075 mm

QT ~ Q2.86 for 0.075 < d < 0.15

QT ~ Q2.76 for d > 0.15 mm

These are shown in Fig. 13.4. It is observed that sediment concentration of the Kosi increases in thehead reach up to Hanuman Nagar. This increase is primarily due to increase in fine fraction due to

Table 13.3 Peak flows in m3/s at Barakshetra during 1948–1998

13587 12283 9647 11226 9646 5424

24236 7085 5441 7538 10570 59797198 8309 10514 7651 10769 6660

10825 8842 25880 8142 13880 12186

10718 9456 11428 9209 9489 77839829 13343 7792 7990 6912 8818

14322 9170 8171 14831 11332 13391

11346 10223 9257 6987 7136 69498379 7190

Fig. 13.4 Relation between sediment load and Q at the barrage on the Kosi

Q cfs

105

104

105

5 10´3

104

5 10´3

5 10´3

104

106

100

101

102

103

104

105

Datum

Se

dim

en

tlo

ad

into

ns/d

ay

Fine sediment(d < 0.075 mm)

Medium sediment(0.075 < d < 0.15 mm)

Coarse sediment

(d 0.15 mm)³

Scatterof data

Scatterof data

Scatterof data

105


erosion of Belka hill region. Beyond Hanuman Nagar however, the sediment concentrationprogressively reduces due to deposition of coarse and medium fractions. At Kursela where the Kosijoins the Ganga, the average sediment concentration is only 24 percent of that at the gorge. Thisprogressive deposition causes great instability in the river (Godbole 1986).

13.6 SEDIMENT SIZE AND SLOPE

Garde et al. (1990) have analysed the data collected from three boreholes at different cross sections ofthe now embanked Kosi. These bore holes were at the left, right and the center of leveed portion. Thissize distribution is shown in Fig. 13.5. It can be seen that d50, d84.1 and d15.9 sizes are 0.25 mm, 0.37 mm

and 0.175 mm respectively giving geometric standard deviation sg = 1

284 1

50

50

15 9

= +F

HG

I

KJ

d

d

d

d.

.

as 1.455. On

the same figure are plotted data given by CWPRS, Pune. The Central Water Commission has divided theentire reach of Kosi in four segments and the slope in each reach has been given as follows during 1982.

Fig. 13.5 Size distribution of bed material of the Kosi at section 63

d in mm

0.20.06 0.08 0.10 0.4 0.6 0.8 1.0 2.00

20

40

60

80

100

Pe

rce

nt

fin

er

Left bank

Centre

Right bank

CWPRS data

River Morphology396

The longitudinal section of the Kosi river as obtained in 1975 is shown in Fig. 13.6. It can be seenthat between Chatra and the barrage at Bhim Nagar the average bed slope is 9.38 ´ 10– 4, between thebarrage and up to next 32 km downstream the average slope is 5.5 ´ 10– 4, while downstream for the next64 km the average bed slope is 2.70 ´ 10–4. The differences in the slopes between 1975 and 1982 areevidently due to aggradation/degradation.

Extent of reach (in km) below Chatra Bed slope

0 – 42 km 0.001 40042 – 68 km 0.000 71668 – 134 km 0.000 450

134 – 160 km 0.000 110

Fig. 13.6 Longitudinal profile of the Kosi

13.7 MORPHOLOGY OF THE KOSI

Investigators have opined that quite possibly, in the earlier times the Kosi joined the river Mahanandathrough the present course of the river Parman near Araria in Purnea district. This view is supported bythe presence of long stretch of depression varying in width from 30 m to 60 m passing from Forbesganj

106

Distance in km from Chatra

4832160 64 80 96 112 128 144Datum 34

42

50

58

66

74

82

90

98

Bed

Levels

m

2.70 10´–4

5.50 10´–4

Barrage

9.38 10´–4

Chatra


side towards Araria. However, since 1736 the river has shifted towards the west through 112 km in 223years. In this process, it has deposited sand over 7680 km2 land in Bihar and 1280 km2 in Nepal makingthe land almost infertile. Positions of the Kosi during different years are shown in Fig. 13.7. The shiftinghas always been towards the west and the average shifting rate has varied from 0.19 km/year to 1.8 km/year with an average rate of 0.478 km/year at Purnea to Belhi. It can be seen in Fig. 13.7 that the riverhas shifted westward by abandoning its old channels. Since the Kosi carries high sediment load, much ofthe sediment gets deposited during the recession of the flood thereby choking mouths of some of thechannels. As a result, during the next flood the river activates a new channel which gets developed withthe passage of time. Observations indicate that when the Kosi was in flood, the water spread over 16 to

Fig. 13.7 Lateral migration of the Kosi river

River Morphology398

32 km laterally. In the dry season, the river flowed in a number of channels; some of these were deep andothers shallow, indicating that the river was braided in nature. The flow velocity during flood used to beso high in deep channels that a large animal such as an elephant could be washed down. The countryarea looked like a series of islands. In 1883 there was apprehension that Kosi may suddenly change itscourse and flow in the abandoned channels on the east. Shillingford in 1885 published a paper in theAsiatic Society of Bengal and opined that the eastward movement of the Kosi would probably beaccomplished in one great swing and cause great loss to property and life.

Some probable reasons for the westward movement of the Kosi have been proposed. The one earliermentioned is the differential deposition of sediment during the recession of flood causing closure ofsome channels and opening newer ones in the next flood. The second reason that is often quoted is thegeneral westward slope on the Kosi flood plain. Lastly, it is already mentioned that the Kosi plain andadjoining areas are subjected to earthquakes and neotectonics that can cause this shift.

13.8 MANAGEMENT OF THE KOSI

To reduce the flood and sediment problems of the Kosi a number of expert committees have given theirrecommendations a few among them being those of Inglis, K.L. Rao, Leopold and Maddock, KanwarSain and Mitra. Along with these reports there were some review committees of Central WaterCommission of the Govt. of India. They generally agreed that for the proper management of Kosi, thefollowing recommendations be implemented.

1. Catchment area treatment for the Sun, the Arun and the Tamur tributaries; it is estimated (seeCarlson 1985) that the average rates of denudation of Tamur, Sun Kosi and Arun catchmentsare 2.56, 1.43 and 0.51 mm/year, which are quite high and are the source of large sediment loadof the Kosi.

2. Construction of a high dam in Nepal which would arrest a large percentage of coarse sedimentand reduce aggradation downstream. It will also provide for flood control, power generationand irrigation in Nepal.

3. Construction of a barrage at Hanuman Nagar near Bhim Nagar at a distance of 48 kmdownstream of Chatra. This would reduce water surface slope between Chatra and the barrageand thus reduce excessive bank erosion between Chatra and the Barrage.

4. Construction of afflux bunds upstream of the barrage and flood embankments downstream ofthe barrage.

5. Construction of canals on both sides of the barrage for the development of Irrigation of 1.05Mha. and power generation of about 20 000 kW.

The first two recommendations have not been implemented because these areas of catchment and wherea large dam was to be constructed lie in Nepal. The construction of the barrage was started in 1959 andcompleted in 1963. Afflux bunds have been provided on the upstream of the barrage on the east andwest. Afflux bund on the east is 40 km long while that on the west is 14 km long which preventinundation due to ponding in non-monsoon season and afflux caused by the barrage obstruction duringthe flood time. These are shown in Fig. 13.8. Some of the details of barrage are as follows.

Total length = 1150 m

No. of bays at barrage = 46 each of 18.3 m width,


No. of under sluice bays = 6 on the left and 4 on the right each18.3 m widths

Spillway gates = 16 Numbers of 18.3 m ´ 6.4 m

The maximum discharge at barrage is about 14 000m3/s and minimum of 1000 m3/s. To providewater for irrigation and generate waterpower, irrigation canals have been taken from the barrage. Theone on the east is known as Eastern Kosi main canal while that on the west is known as Western Kosimain canal. Right from the beginning both these canals are facing severe problems of sedimentation.This is illustrated by discussing about Eastern Kosi Main Canal whose head works has 32 tunnelscovering four bays of the barrage. The canal was designed to carry 424.5 m3/s; however subsequently asediment ejector was provided at 646 m downstream of the head regulator; hence the discharge at headregulator was increased to 485 m3/s to provide for flushing water requirement for sediment ejector as

Fig. 13.8 Kosi flood embankments

River Morphology400

discussed by Sahai et al. (1980). The canal discharge decreases from 424.5 m3/s to 40.5 m3/s over alength of 41.3 km. In the same distance the bed width changes from 189.7 m to 19.8 m, the full supplydepth changes from 3.5 m to 2.13 m and slope from 0.99 ´ 10– 4 to 1.333 ́ 10– 4. Also at 3600 mdownstream of the head regulator there is 4 m drop, which is used for generation of power. This canalruns in heavy cutting from the head regulator to about 9.15 km downstream.

While the power house was under construction, the canal discharge was gradually increased from44 m3/s in 1964 to 251 m3/s in 1969. Extensive sediment deposition took place in the 41.15 km reach;the yearly sediment volume deposited being 0.14 to 0.25 Mm3. It has been found that both the sedimentexcluder and ejector have failed to function properly. The Western Kosi Main Canal is also plagued withsimilar problems (Sinha 1986).

Flood-EmbankmentsConstruction of flood embankments was taken up in 1955 and was completed in 1959. These are 144km long on the left bank and 123 km long on the right bank, and are designed for flood discharge of 24000 m3/s which is a flood of about 150 year return period. The right bank embankment will be extendedup to Kursela except where the Bagmati and the Kamla join Kosi. The left bank embankment has beenextended up to Koparia, see Fig. 13.8. These embankments provide flood protection to 0.214 Mha inIndia and 51,400 ha in Nepal.

Sedimentation studies have shown that upstream of barrage the bed slope changed from 0.00 061 to0.00 042 between 1963 and 1968. It was also estimated (Chitale 2000) that between 1963 and 1970,35.05 Mm3 of sediment was deposited in 10 km reach upstream of the barrage giving an average depthof deposition of 0.40 m in eight years.

It has also been found that during 1963-1970 there was a general lowering of bed level downstreamof barrage for a length of 23 km. Further downstream there was tendency towards aggradation.

Earlier studies by Sanyal (1980) and others indicated significant aggradation in the lower reaches ofthe Kosi. Concerned about the continuous aggradation in lower reaches of the embanked reach of theKosi, Ganga Flood Control Commission, Govt. of India referred the problem to University of Roorkeewhich used HEC-6 1-D model to study aggradation by using Laursen-Madden relation for sedimenttransport and Dx = 10 km, D t = 10 days for non-monsoon and 30 days for monsoon periods. Table 12.2gives the levee spacing at various sections downstream. The model was calibrated using 7 year’s data ofdischarges and river cross sections for the period 1975-82 and then the model was run for the period1984 to 2005, using discharge data generated using Thomas-Fiering model. The model indicated a risein the bed level by about 2.44 m with reference to 1984 bed levels bringing the water level within 1.37m to 2.13 m of the top of the embankment near Nirmali. Hence, it was concluded that the primary reasonfor aggradation was large spacing between the levees. Aggradation can be offset by either reducing thespacing between levees, or by providing spurs. Some have suggested giving proper slope to the streamin different reaches so that aggradation can be avoided; however the latter solution does not seem to bepracticable.

The morphology of the river-bed in the leveed reach from Gopalpur to Koparia has been studied byGohain and Parkash (1990) by field investigation and also by interpretation of black-white air photoswith a scale of 1:25 000. They have identified the following topographic levels and larger bed features.


Level 1 : Active channel course with low bars;Level 2 : 0.5 to 0.9 m higher than water surface on level 1 during low flows; no vegetation,submerges with a small increases in flow.

Level 3 : About 1 m higher than level 2, sparsely vegetated, submerged during high flows of flood.Level 4 : Between 0.5 and 0.8 m higher than level 3, it comprises the surface the islands and banks.These levels are best developed in the braided reach of the river. The Kosi with the artificial

embankments is a confined braided stream. Figure 13.9 shows braided reach downstream of the barrage.Levels 2 and 3 are relatively unstable and are dissected intensively every year during the flood. Grassand shrubs along the reach cover level 4. Extensive agricultural activities and settlements are seen onthis level and these are flooded when discharge at Barakshetra exceeds 8400 m3/s. Considering adistinct change in the slope of flow duration curve at about 1000 m3/s. (see Table 13.2), it is interpretedthat levels 1 and 2 correspond to low flows in November–February period while levels 3 and 4correspond to monsoon discharges. Gohain and Parkash found that there are a number of channels atany section that can be divided into primary channels which are deep and carry water even at low stages.Usually there are one or two primary channels. The sub-channels are defined as part of the river-bedwhich has only bars with level 2, hence at high flow these get submerged.

Fig. 13.9 Braided reach in leveed portion of the Kosi river downstream of barrage

Channel PatternsIn the Zone 1 between Chatra and Karaya, a distance of about 20 km, the slope is 0.000 45 and oneprimary braided channel is present. Zone 2 is from Karaya to Dumra, a distance of about 96 km. Here theslope is 0.000 48. This is the main braided zone of the river, having two primary channels and a fewmeandering channels on level 4. Zone 3 is a 40 km reach from Dumra to a few km upstream of Kopariain which average slope is 0.0001. One straight channel of sinuosity 1.01 to 1.16 is present. Zone 4extends for a distance of 160 km downstream of Zone 3 up to Kursela. Here the mean slope is 0.000 05

Western flood embankment

Bagm

ati

rive

r

69

75

81

87

91

63

53

4133

Ba

rra

ge

axis Eastern

mfloao

md e b nk ent

River Morphology402

and the stream meanders all along its course. Point bars and sidebars are a common occurrence.Abandoned channels with chute cutoffs and neck cutoffs are common in flood plain.

13.9 PRESENT DAY PROBLEMS OF THE KOSI

One of the major problems faced on the Kosi is breaching of sections of embankment almost every yearleading to huge maintenance cost. It is found that the deep channel takes a different course every yearand affects new reach of levees. Since it is very difficult to predict the behaviour using a mathematicalmodel, every year after the flood has receded, bed levels are taken at different sections and the bed in themovable bed physical model is laid for the new condition. The model is then run for flood discharge toidentify the sections of the embankment that are likely to be attacked during the next flood season.Protection works are undertaken on the basis of the above study as well as on the basis of advice of high-level committee, which visits the site before the monsoon. The protection methods include directstrengthening of embankment or construction of spurs. The physical model studies are carried out atCentral Water and Power Research Station, Pune (India).

The second aspect of concern is the continuing aggradation taking place in the major length ofleveed reach. Even though reduction of spacing between levees can reduce or stop aggradation, noaction has been taken. Aggradation can reduce if sediment is stored upstream behind a large dam;however no serious effort is made in this direction also.

The third concern is about the malfunctioning of both the canals taking off from barrage, as a resultof which there is under utilization of the irrigation potential that has been created.

Also, water-logging problems have occurred in the Eastern Kosi command area and there are alsoproblems related to proper drainage behind leveed reach.

BRAHMAPUTRA

13.10 INTRODUCTION

The Brahmaputra is one of the largest rivers in the world and is known for its high floods and sedimentload, flood damages and instability. The river originates near Manasarovar at an elevation of about 5000m. Within 160 km of this lake are also the sources of two other largest rivers in the Indian subcontinent,namely the Indus and the Ganges. The Sutlej, a large tributary of the Indus also originates in this area.Figure 13.10 shows the course of the river Brahmaputra, while Plate 2 shows the aerial view of theBrahmaputra. The Tibetan portion of the Brahmaputra is known as the Tsangpo, it is called Siang andthen Dihang when it enters Arunachal Pradesh in India. The words Siang and Dihang mean the “big orgreat river”. Brahmaputra means son of the God Brahma. It is interesting to know that Brahmaputra isprobably the only river having masculine name. Near the upstream border of Assam, just upstream ofSadiya it is joined by two tributaries the Dihang and the Lohit. Here the river turns in the westerlydirection and flows through India passing along the cities of Kobo, Dibrugarh, Jorhat, Tezpur,Guwahati, Dubri and Goalpara, and then turns towards south. After flowing for about 337 km theBrahmaputra joins the Padma at Goalundo in Bangladesh.

The total length of the Brahmaputra up to the confluence with the Padma is 2 880 km out of which1625 km is in Tibet, 918 km in India and 337 km in Bangladesh. Similarly the river has a catchment area

Morphology of S

ome Indian R

ivers403

Fig. 13.10 Brahmaputra river system along with the embankments

N1 Manas S1 KapilN2 Pagladiya S2 DhanairiN3 Pachnoi S3 DessngN4 Jia bhargil S4 LohitN5 RanganadlN6 JladholN7 DihangN8 Dibang

Embankment

Nomenclature of the riversNorth bank Soutth bank

Scale 1 cm = 20 km

Jorhat

Nag

apat

kai h

ills

SibsagarS3

DibrugarhS4

N8

N7

Tsangpo

From manasarowar

N5

N6

North lakhimpur

Gamirighat

Silighat

S1 S2

Teepar

N4N3

Mangaldoi

Guwahati

Embankments

India

Meghalaya plateau

Goalpara

Barpeta

N1N2

Dhuri

Himalaya

Bhutan N

River M

orphology404

Plate 2 Aerial view of the Brahmaputra basin


of 29 300 km2 in Tibet, 19 500 km2 in India, 4500 km2 in Bhutan and 4700 km2 in Bangladesh, thusmaking a total of 58 000 km2 drainage area up to the confluence with the Padma.

As the Brahmaputra flows through India, large and small tributaries join the river both from thenorth and from the south. In the entire course of its journey, the Brahmaputra receives as many as 22major tributaries in Tibet, 33 in India and 3 in Bangladesh. The northern tributaries come from higherrainfall region, pass through fragile Himalayas and have steeper slopes. In general, they carry highsediment concentration comprising cobbles, coarse gravel and sand. These tributaries are braided andhave migrating channels over major portion of their lengths. Some of the important tributaries of thenorth are the Subansiri, the Ranganadi the Jia Bhareli, the Sankosh, the Pagladiya and the Manas. Thetributaries on the south bank emerge from comparatively lower levels from Naga-Patki, Khasi and Garohill ranges and flow towards north or north-west at flatter slopes. These tributaries have deepmeandering channels and they carry relatively finer sediment at smaller concentrations. Some of thesouth bank tributaries are the Lohit, the Buri Dihing, the Desang, the Kopili and the Dikhu. These areshown in Fig. 13.10. It may be mentioned that the Brahmaputra is closer to the hills on the southprobably because the river has been pushed southwards during the past because of sediment depositionon the northern side. Another characteristic that is worth noting is that in general, the north bank, atmany places is at a higher elevation than the south bank by three to ten meters as noted by Baruah(1969). The Brahmaputra valley width has a minimum value of 60 km and an average value of 86 km,while the river width varies from 15 to 19 km. Within India the Brahmaputra is braided for most of itslength except where its width is restricted and the river is stable with well-defined nodal points. Suchrestrictions in width occur at a number of places; these locations and average width in km are listed inTable 13.4. These constrictions in the channel would create backwater and changing water surfaceprofile along the river, thereby causing tendency towards aggradation especially for medium flows. Atother places the river width varies from 5 000 m to about 19 000 m. Typical cross sections at Pandu andPancharatna where the river is constricted and at Jogighopa where it is much wider are shown inFig. 13.11.

Table 13.4 Constrictions in the Brahmaputra (Baruah 1969)

Location Total width (km) Width of perennial channel (km)

Murkong - Selek 1.92 0.16

Near Dibrugarh 2.08 0.80Near Dikhumukh 1.60 0-.48Near Helem 2.0 0.72

Silghat 2.56 0.32Near Tezpur 2.40 1.76North of Dihang 1.36 1.04

Downstream of Laterisuti 2.56 1.36Mirkhameri 2.56 0.72Guwahati 1.44 0.72

Near Pandu 0.90 1.151.15 0.90

Hathimura 1.36 1.12

Jogighopa 2.00 1.12Chandor Dinga 3.00 0.56

River Morphology406

Fig. 13.11 Typical cross sections of the Brahmaputra

25002000150010005000

Chalnage (m)

Cross Section of Brahmaputra at Pancharatna

0

Chalnage (m)

Cross Section of Brahmaputra at Pandu

0

Chalnage (m)

Cross Section of Brahmaputra at Johlghopa

1000 2000 3000 4000 5000 6000 7000 8000

500 1000 1500 2000 2500 3000 3500

41

38

35

32

29

26

23

20

60

55

50

45

40

35

30

25

38

36

34

32

30

28

26

24

22

Ele

vation

(m)

Ele

vation

(m)

Ele

vation

(m)

HFL = 36.12 m

HFL = 47.40 m


Range Slope

Kobo to Dibrugarh 0.000 300Dibrugarh to Neamati 0.000 182Neamati to Silghat 0.000 135

Silghat to Guwahati 0.000 115Guwahati to Goalpara 0.000 1136Goalpara to Dubri 0.000 105

Reach between Kobo to Dubri 0.000 147Reach within Bangladesh Reduces from 0.000 09 to 0.000 03

13.11 RIVER CHARACTERISTICS

River SlopeThe longitudinal profile of the Brahmaputra as given by Goswami (1985) is shown in Fig. 13.12. Theslopes of the river prior to 1950 and in recent times are given by Baruah (1969), and by WAPCOS(1993) respectively. These are listed below.

Fig. 13.12 Longitudinal profile of the Brahmaputra bed

Recent alluvial deposits comprising clay, silt, sand and shingle cover the major part of theBrahmaputra valley. The average thickness is about 300 m. Drilling at Pasighat bridge and for oil wellsin Ningru plains of Arunachal Pradesh have provided useful data about the thickness and nature ofalluvial deposits. These borings show repeated sequences of clay, fine sand, coarse sand, coarse sandwith cobbles, pebbles and boulders. Figure 13.13 shows the borehole data on the Dihang near Pasighat,

5000

Distance in 100 km

28 24 20 16 12 8 4 0

4000

3000

2000

1000

0

Ele

vation

m

Manasarowar

China

Shigatse

Tesla dihong

Pe

Enters India

Pasighat Pandu

EntersBangladesh

River Morphology408

Fig. 13.13 Bore log data for bed material on the Dihang near Pasighat

Pictorialrepresentation R.L. in meters Strata description

Filled up sand

Sandy soil mixed with gravel and boulders

60 to 70% of boulders in compacted red soil

70 to 80% Boulders (1500 mm to 3000 mm)

Boulders medium and large size (300 mm 3000 mm)

Boulders of size upto 1200 mm

Boulders of size upto 800 mm

Silt and sand mixed gravel

Silt sand and shingles (size about 63 mm)

Silt sand and gravel (size 50 mm to 5000 mm)

Silt sand and boulders(size between 800 mm to 1000 mm)

Boulders (size between 600 to 1000 mm)

155.190

153.190

150.190

148.190

144.190

140.190

139.190

138.190

137.190

129.800

128.300

127.900


which illustrates the stratified nature of sediment deposits. Presence of coarse fractions would be helpfulin controlling the scour around hydraulic structures such as bridge piers, as well as excessivedegradation due to formation of an armor coat. Bed material in the Brahmaputra river mostly comprisessilt and fine sand. Goswami (1985a) has reported the size distribution of bed and bar material in theBrahmaputra river at Dibrugarh, Salmara, Hatimura, Guma, Goalpara and Pandu. The median size ofthe samples varied from 0.03 mm to 0.30 mm; such a large variation is probably due to the fact that somesamples were collected on the bars while others in the depressed portions. Recently several moresamples were collected by WAPCOS (1993) over a long stretch. It was found that median size of the bedmaterial varied from 0.223 to 0.085 mm with an average of 0.16 mm and the standard deviation variedfrom 1.294 to 2.043 with an average of 1.476. The average size at Pancharatna was 0.138 mm with thestandard deviation of 1.52. Pancharatna is between the outfalls of Manas and Dubri. At Pancharatna10% of the material is finer than 0.06 mm and only 2% of material is coarser than 0.40 mm.

Normally the median size of the sediment decreases in the downstream direction due to abrasionand sorting; however, such tendency is not noticed in the case of the Brahmaputra. There is nosystematic reduction of median size of bed material along the river length. This is attributed to thenumber of tributaries joining Brahmaputra on its way and mixing of their bed material with that of theBrahmaputra. Also abrasion is unlikely to be unimportant in the Brahamputra since most of thesediment moves as suspended load.

The bed material of the Brahmaputra river is composed mainly of varying proportions of fine sandand silt, with only occasional presence of small amount of clay, less than 5% (Goswami, 1985). Particlesize distribution of bank material at Dibrugarh, Hatimura and Dubri, given by Goswami shows that sizesrange from 0.001 mm to 0.20 mm with d50 between 0.05 to 0.15 mm. The vertical profiles generallyinclude two distinct parts – a relatively fine-grained top stratum and a coarser substratum. The coarsesediments probably represent channel bars and islands accreted laterally through wandering channel,and the finer sediments represent vertical accretion from over bank flow.

Bank InstabilityThe bank line of the Brahmaputra is extremely unstable for most of its length. Bank failures are rampantand seem to be function of the hydraulic character of the flow and the engineering properties of the bankmaterial. According to Coleman (1969) several factors are responsible for short-term changes in thebank line. These are

i) rate of rise and fall of water level;ii) number and position of channels active during the flood stage;iii) angle at which the talweg approaches the bank line;

iv) amount of scour and deposition that occurs during flood;v) formation and movement of large bed forms;vi) cohesion and variability in the composition of bank material;vii) intensity of bank sloughing; and

viii) relationship of abandoned river courses to present-day channel.Shear failures in the upper bank material seem to be by far the most widespread model of bank

failures. This is caused either by undercutting of the upper bank material by the current during highflows, producing an over-hanging cantilevered block which eventually fails, or by over steepening of

River Morphology410

the bank materials due to migration of talweg closer to the bank during falling stages. High moisturecontent, low percentage of clay and good sorting of the bank materials in the Brahmaputra make themhighly susceptible to erosion by the river.

13.12 SEISMICITY AND LANDSLIDES

Brahmaputra basin is located in a geodynamically unstable region characterized by active faults andcontinuing crustal movements. According to plate tectonics the Indian plate moving in the north –northeasterly direction is under thrusting the Eurasian plate and is causing deformation and instability inthe Brahmaputra basin. It is believed that many E-W and transverse faults that dissect the Meghalaya –Mikir blocks are active and are responsible for high seismicity. In the 60 years prior to 1980, over 450small and large earthquakes have taken place in this area. Their distribution is as follows

Richter magnitude No. of earthquakes

8 or greater 37 – 8 156 – 7 167

5 – 6 270

Major earthquakes in this region appear to be separated by quiescent periods of about 30 years(Goswami, 1985). Among the earthquakes that have taken place in the region, the two most severeearthquakes were those of 1897 and 1950. The 1897 earthquake of Richter magnitude of 8.7 had itsepicenter in Shillong plateau. It was felt over 450 000 km2 and its effects were noticed even after tenyears. The entire lower portion of the basin up to Goalpara district was affected. The 1950 earthquake ofintensity 8.7 occurred on 15th August and its epicenter was at 50 km north east of India’s border. Itseffects are very well recorded by Gee (1951). The following description is taken from his paper

“Many hills, a few hundred meters in height were shattered from top to bottom, their sidescrushing down into the valley below. Rivers, both small and large became blocked by hugedams of rock, earth and vegetation, and in cases ceased the flow. Even the Subansiri, which hadswollen with monsoon rains practically dried for few days. Then came the bursting of dams,one by one in some cases, in other cases simultaneously. Vast flood waves surged down thevalley carrying everything below them.In some cases lakes thus formed in the hills by these temporary dams endured for longer period.Thus at the head waters of the Tidding river, a tributary of the Lohit, a lake nearly 6.5 km inlength and 0.40 km wide was formed and lasted throughout the winter of 1950 and spring. Itdisappeared in 1951 monsoon. Seventy five of the hills in 27 000 km2 area were mutilated byland slides. About half of the landslides appeared to have occurred on the day of the earthquakeand remaining subsequently when heavy rain occurred.The Dihang became so silted up that its tributaries, the Jigiapani, Deopani and Ghurmura couldnot enter it. These were diverted by the newly formed silt banks of the Dihang up to the town ofSadiya. Lohit was silted up to the extent of one to two meters while Brahmaputra was silted upto two to three meters at Murkong Selek and at Dibrugarh. This earthquake had radically


altered the slope of Brahmaputra, stopping the flow temporarily and bringing about floodingand rapid accumulation of enormous volume of sediment in the channel. The low water levelrose by as much as 3 m at Dibrugarh as a result of this earthquake”.

The sediment deposited in the river as the result of the earthquake moved downstream at a lowvelocity as sediment wave, and its effects were noticed even in 1971.

In addition to the tectonic activity, neotectonic effects have also been noticed as reported by Valdiya(1999). Leveling observations made three times during 1910-1976 have indicated that blocks ofGuwahati-Dergaon section have been consistently rising up at the rate of 0.30 mm to 4.5 to 31 mm peryear at Dergaon (30 km west of Jorhat). Similar uplifting activity is noticed in Guwahati-Goalparasector. Such movements gradually change the slope of the stream and can cause aggradation ordegradation.

Along with the earthquake, landslides also influence significantly the morphology of alluvialstreams. Landslides in the Himalayan region of India occur during the monsoon season. Further, it hasbeen observed that reactivation of old Himalayan landslides, invariably occurs during the monsoonseason after heavy and/or prolonged rains. It has been observed that in all those cases of large landslidesin Himalayan region, the rainfall ratio defined as

ER = Average 24 hour, 2 year rain fall

Average annual rainfall

is greater than 0.08. In fact ER greater than 0.08 and earthquake magnitude greater than 7.0 haveproduced all the large landslides in this region, see Garde and Kothyari (1989). Figure 13.14 showsmap-showing landslide – prone regions of India, while Fig. 13.15 shows locations of epicenters of highmagnitude earthquakes. Foothill region of Arunachal Pradesh is characterized by tightly folded megastructures of alternate stratified layers in which building up of pore pressure is responsible for slopefailures. As mentioned earlier, such land slides brought down heavy debris during 1950 earthquakeresulting in stream blockages, stream diversion and aggradation.

13.13 CLIMATE AND HYDROLOGY

The annual rainfall in the Brahmaputra catchment varies from 100 cm to 400 cm; the map showingisohyets is shown in Fig. 13.16. Most of the rainfall occurs during June to September. The eastern part ofthe catchment experiences pre-monsoon thunder-showers during March-May period. Of the total annualrainfall, about 60 to 70 percent falls during the monsoon period, while 40 to 30 percent occurs duringpre-monsoon season. Only a small percentage of rainfall occurs during the winter. Analysis of stormshas indicated that majority of storms are of 2, 3 or 4 days duration.

Natural vegetation in the Brahmaputra basin varies with altitude from tropical evergreen and mixeddeciduous forests within the valley and foothills to alpine meadows and steppes in the higher ranges,and in Tibet about 20 percent of the Brahmaputra valley is forested.

Discharge data are collected at 33 stations on the north bank tributaries, 58 on the south banktributaries and about 60 stations on the main river where gauge discharge or gauge-discharge-sedimentmeasurements are made.

River Morphology412

Fig. 13.14 Land slides-prone areas in India (Garde and Kothyari 1989)

Fig. 13.15 Locations of epicenters of high magnitude of earthquakes in India

68° 72° 76° 80° 84° 88° 92° 96°

24°

28°

32°

36°

Delhi

Lucknow

E = 0.085R

E = 0.105R

SrinagarShimla

Dehradun

E = 0.115R

Gangtok

E = 0.09R

E = 0.08R

Imphal

Devastating landslideLandslide – pone areas

Earthquake of magnitude between 7.0 to 8.0

Main central thrust

Main boundary thrust

Earthquake of magnitude more than 8.0

68° 72° 76° 80° 84° 88° 92° 96°

24°

28°

32°

36°

Earthquake of magnitude 5.0 to 6.9 on Richter scaleEarthquake of magnitude 7.0 to 8.0 on Richter scale

Earthquake of magnitude more than 8.0on Richter scale

Fault

Ridge


Fig. 13.16 Isohyetal map of Brahmaputra valley and adjoining highlands

Rao (1979) has prepared a diagram showing contribution of mean annual runoff by differenttributaries to the Brahmaputra and variation of mean annual runoff along the Brahmaputra. This isshown in Fig. 13.17, which shows that contribution of the Subansiri, the Jia Bhareli, the Manas and theSankosh from the north, and the Buri Dihang, the Dikshu, the Dhangiri, and the Kopili from south aresignificant.

Regional flood frequency approach has been used by Jakhade et al. (1984) who found that theBrahmaputra basin rivers can be grouped in two hydro meteorologically homogenous zones A and B.Broadly zone A covers Manas to Dihang in the north and Burhi Dihing in the south. Zone B covers allthe southern tributaries in the valley below Burhi Dihing, Sankosh in the north and the main river belowPasighat. Goswami (1985) has analysed annual flood discharge data at Pandu for the years 1971-1974using log-Pearson type III distribution. His analysis gives the mean annual flood at Pandu as 51 156 m3/s with a recurrence interval of 2.1 years while bankful discharge which just overtops the banks has themagnitude of 34 940 m3/s with a recurrence interval of 1.02 years. It may be mentioned that themaximum observed flood occurred in 1962 and was 72 784 m3/s while minimum observed discharge is1757 m3/s. Flood frequency analysis carried by WAPCOS (1993) has given floods of 25, 50 and 100years return period at Pandu as 65 692, 68 964 and 72 028 m3/s respectively. It needs to be mentionedthat difference in water levels between 25 and 100-year floods is less than 1.0 m and hence a large areagets flooded even with floods occurring once in 2 or 3 years.

Analysis of flood data on the Brahmaputra has also shown that the magnitude and time ofoccurrence of maximum flood in the tributaries play an important role in maximum discharge and itsoccurrence at various places along the Brahmaputra. The depth of river, measured from the top of the

180

160140

150200

250

300350

400

350250

300350400

500

350300

250200

250

180

300250

500400300

250200

300

350

300

BurmaNaga land

Arunachal

N

Brahmaputra

Bhutan

Bangladesh

20 0 20 40 60 80 100km

A ss

am

WestBengal

River Morphology414

River Q max/A m3/s km2

Ganga at Harding Bridge (India) 0.067Godavari at Dhauleshwaram (India) 0.280Brahmaputra at Pandu (India) 0.297

Padma at Chandpur (Bangladesh) 0.114Amazon at Obidos (Brazil) 0.048Mississippi at Columbia (U.S.A.) 0.03

bank varies from 4.6 m in a crossing near Dibrugarh to approximately 30 m near the mouth of the Manasriver. At the latter location, the river is confined to a single channel. Low water depths in bends where asingle channel exists vary from 12 to 21 m. In passing it may be mentioned that the ratio of maximumobserved discharge per unit catchment area is quite large in the Brahmaputra river as compared to otherrivers in the world as can be seen from the above table.

13.14 RESISTANCE TO FLOW AND SEDIMENT TRANSPORT

Resistance analysis has been carried out in a given reach at Pancharatna gauging station. Manning’s nvalue is found to vary from 0.05 to 0.03 for low flows and it reduces 0.04 – 0.02 for high discharge of theorder of 30 000 m3/s. The depth at the deepest section at Pancharatna is about 15 m for a discharge ofaround 35 000 m3/s. WAPCOS (1993) had used different methods of predicting resistance and foundthat Garde–Ranga Raju and Engelund’s methods give better results than the methods of Sugio andParis. Since Manning’s n values are much greater than 0.011 obtained by using Strickler’s equation, it

Fig. 13.17 Average annual runoff of the Brahmaputra (Rao 1979)

Notes: Figures represent average annual runoff in Mm

Figurehs in bracket indicate chainage from India–Bangladesh border upstream

BhurbandkaBessamara

Disang(515)5010

Dhansiri(420)6084

Dikshu(505)3511

Kopilikalang(220)8640

GuwahatiPandu

Jogighopa

IndiaBangladesh

Buri Dihang(540)10996

Dibrugarh

Lohit46564

Dibang39085

Kobo

Dihang186290Subansiri (430)

57296

Jia Bhareli (338)28890

Dhansiri (270)2295

Sankosh (O)16556

Manas (85)32258

Goalundo

589000 510450359241

268936

DhubriTezpur


can be inferred that the bed is covered with dunes for low and medium flows. Some measurements weremade in 144 km reach upstream of Dubri during the month of May 1989. The data indicated bedundulations of height about 8 m occurring at a wavelength of 8 to 10 km. Superimposed on these weresmaller undulations or bed forms. Coleman (1969) has reported some echo-sounding measurements onthe Brahmaputra in Bangladesh at Sirajang, Nagabari and Aricha throughout one flood season.Coleman observed ripples (height a few cm to 30 cm), mega-ripples (height ranging from 0.30 m to 1.5m and length ranging from 3 m to over 150 m), and dunes (height ranging from 1.5 m to 7.5 m and wavelength ranging from 40 m to 480 m). He also found sand waves with heights ranging from 7.5 m to 15 mand wave length ranging from 180 m to 900 m; their maximum speed was about 30 m per hour.Relatively high values of n at medium and large flows in the Indian portion of the Brahmaputra indicatethe presence of fairly large bed-forms. The larger n values at very low flows are due to formation ofislands in braided regime.

Most of the suspended sediment measurements are carried out at 0.6 depth and concentration thereis taken as the average suspended sediment concentration. This is divided into three size fractions: fine,medium and coarse. The assumption of taking concentration at 0.6 depths as the average concentrationmay be satisfactory for fine sediment, but it can underestimate sediment load in medium and coarsefractions. Usually suspended sediment discharge Qs is related to the corresponding water discharge anda relation of the form Qs = a Qb established for each river. Using mean monthly values of Qs and Q,Goswami (1988) found b to be 1.78 and 2.53 at Pandu for 1971-76 and 1977-79 data respectively. Theanalysis of suspended load indicate that the river carries relatively more fine material compared tomedium and coarse size fractions. The percentage of fine sediment varies from 70 to 90. Using sedimentmeasurements at Pandu for 1955 to 1980, Goswami (1985) found the sediment yield at Pandu to be 804tons/km2/year while at Bahadurgarh in Bangladesh it is 1128 tons/km2/year. The major tributariescontributing high rates of sediment yield are given in Table 13.5 along with their catchment areas.

Table 13.5 Erosion rates at the tributaries of the Brahmaputra (Goswami, 1985)

Tributary Catchment area A km2 Sediment yield in Tons/km2/year

Dibhing 12 120 3765Subansiri 27 400 959Ranganadi 3077 1569

Jia Bhareli 11 300 4721Dhansiri (N) 1657 463Puthimari 1787 2887

Pagladiya 38 300 1883Beki (Manas) 36 300 1581Lohit 22 077 1960

Buri Dihing 4923 1129

It can be seen that the tributaries from the north bank have almost three times the sediment yield ofsouth bank tributaries. This is due to different geologic conditions, rainfall and the character ofsediment. Similarly, for the catchment of the size of the Brahmaputra, its sediment yield is three to fourtimes that of many rivers of the world.

River Morphology416

No bed-load measurements have been made on the Brahmaputra. However, some efforts have beento estimate it by Goswami (1988) using well-known bed-load equations of Schoklitsch, Kalinske,Meyer-Peter and Müller, Einstein, and Bagnold. It may however be mentioned that these equations havebeen developed using very coarse material whereas the bed material of the Brahmaputra is very fine.Hence the results are questionable. WAPCOS (1993) has used total-load equations of Samaga, RangaRaju et al. and Laursen and computed total load; knowing measured suspended load, ratio of QB/QS wasobtained for various discharges at Pandu. The average of these results indicate the following:

Q m3/s 3600 9600 18 800 36 000

QB/Qs 0.053 0.501 0.189 0.087

Even though the results are erratic, above analyses of Goswami and WAPCOS indicates that, theassumption that the river carries 10-15 percent of suspended load as bed-load may be a goodapproximation.

On the basis of yearly sediment transport rate, estimates have been made of the annual depth oferosion in different catchments. These are tabulated below.

River Average erosion rate in mm/year

Amazon 0.09Mississippi 0.07Yangtze 0.33

Ganga 0.57Brahmaputra 0.41 to 0.81Kosi 1.88

It can be seen that average rates of erosion are quite high in the Kosi and Brahmaputra catchments.Goswami (1988) studied the discharges which carry significant amount total suspended load and foundthat flow events which occur one day or more in a year carry on the average 65.5 percent of the totalsuspended load, while flow events which occur 7.0 days in year carry on the average 31.25 percent oftotal suspended load. Thus he showed that maximum flows do not necessarily carry the maximumpercent of yearly sediment load.

Information about flow duration curve and sediment transport rates can be utilized to determine thecharacteristic discharges for the stream. It has been mentioned that bankful discharges at Pancharatnaand Pandu are approximately 30 000 m3/s and 27 000 m3/s respectively while the mean annualdischarges at these stations are 16 154 and 15 756 m3/s. The bed generative discharge at Pancharatna isestimated to be 56 000 m3/s.

13.15 PLAN-FORMS

As mentioned earlier, for the major part in India the Brahmaputra is braided. The configuration of thechannel undergoes major changes in response to variations in the flow and sediment load. During


November to March when the river discharge is low, the channel is highly braided with a number of barsand islands. After April-May when discharge starts increasing these islands and bars get submerged andriver looks straight. It is interesting to note that when low flow data are plotted on t* vs. WS/D criterionof Agarwal, these data indicate braided plan form, while t * vs. WS0.2/D criterion of Kishi indicatespresence of multiple bars. In general, in the case of braided rivers, the number of channels formed byislands depends on width to depth. Figure 13.18 shows the braided pattern at Dibrugarh in 1928, 1976and 1987. The changes in the channel patterns and their numbers as well as changes in islands in theirshape and number may be noted. The braiding index defined by Brice as the ratio of twice the sum oflengths of bars and islands in a reach to the length of the reach measured mid-way between the banks hasbeen calculated at Dibrugarh and upstream of Palasbari by Goswami (1988) and found to be between 5and 7 indicating the highly braided nature of the river.

Some of the islands formed are small and they get submerged and changed as flood level rises; newor modified islands are formed during the recession of floods. However, some islands becomepermanent and can grow due to vegetation grown on them. Majule is one such and is the largest islandin the Brahmaputra, north of Jorhat at the confluence of the Subansiri with the Brahmaputra. The islandis about 80 km in length along east-west direction 10 to15 km in north-south direction, and is habitatedby 140 000 people. Originally it was 1245 km2 in area prior to 1950 earthquake and due to continuouserosion its area was reduced to 924 km2 in 1971 and to 880 km2 in 1993. This is a matter of greatconcern to engineers (see NIH, 1998) and efforts are being made to control erosion.

Another aspect of changing islands is the change of talweg of main branch of the braided river withchange in flow. This change is large during medium flows, relatively little during high flows, and veryerratic during the falling stages i.e. during November to March. This is very important when the river isused for navigation. This aspect of wandering of the talweg and its relation to bank erosion has beendiscussed by Coleman (1969). With the Brahmaputra carrying heavy load of sediment, bed conditionchanges rapidly and drastically with change in flow. Deposition of sediment at one place causes erosionat other place and triggers changes in talweg from one position to another within the bank-line. Study ofstage and position of talweg at Sirajgang (Bangladesh) indicated that during the rising stage theamplitude of movement of the talweg is large, as much as 3000 m and the movement is gradual; duringthe peak-flows it is relatively small and the talweg remains more or less stable. However, during thefalling stage the talweg movement is irregular and sudden in fashion.

During low water stage the main channel in a braided river, which carries large portion of thedischarge, is commonly situated near one of the river-banks and is slightly curved moving from onebank to other. During the rising stage when the flow increases rapidly, while the flow tends to follow thedeep channel, it is not able to develop rapidly to accommodate increasing flow and hence there istendency for bank-cutting and sloughing. This action helps migration of the talweg in lateral direction.Bank sloughing depends on the nature of the bank material. In as much as the nature of bank materialvaries along the length, sloughing is not uniform; hence the erosion of the banks is different at differentlocations thereby changing the river path. The shifting of the talweg is also influenced by the movementof sand bars and mid-channel islands. This occurs most frequently during the falling stage and the shiftis erratic and sudden. Shifting of the talweg close to the bank causes bank erosion.

River Morphology418

Fig. 13.18 Plan form of the Brahmaputra near Dibrugarh in years 1928, 1976 and 1987

1928

1976

1987

Sonarighat

Dibrugarh

Sonarighat

Dibrugarh

Sonarighat

Dibrugarh

Buri dihang river

Buri dihang river

Buri dihang river

Maijan river

Dibru river

Maijan river

Dibru

river

Maijan

river

Dibru river

N

N

N

20 km0 5 10

20 km0 5 10

20 km0 5 10(a)

(b)

(c)

Scale

Scale

Scale


13.16 FLOODING AND FLOOD PROTECTION

Floods in Assam valley seem to have increased in frequency and intensity since 1950 earthquake whenthe hills were mutilated to a great extent. Floods are caused due to heavy rainfall in the mountains andvalley, and melting of snow in the mountains. Eighty to ninety percent of rainfall occurs during May toSeptember during which time snow also melts. Considerable construction activity and deforestationbrings down large quantities of sediment along with the flow which is responsible for aggradation insome reaches. The valley being wide and flat, an increase of 1 m water level during normal annual floodinundates large areas of flood plain. Encroachment on flood plain and islands accentuates the floodproblem. Based on the analysis of satellite imageries it is found that during 1988 flood, flood plain 10 to50 km in width on northern side and 5 to 30 km wide on southern side was inundated. When theBrahmaputra level is high the tributaries are not able to drain into the main river and cause inundation intheir valleys due to backwater effect. Handique and Borgohain (1991) have given the statistics of flooddamage in Assam valley as indicated below.

Table 13.6 Flood damages during 1953-1989 in Assam valley (Handique and Borgohain, 1991)

Total area affected in M ha Maximum (1988 figures) Average

Crop area affected in M ha 3.823 0.97Damage to crops in crores Rs 334.10 26.67Total damage to crops, houses and public utilities in crores Rs 663.84 54.67

Lives lost 232 38

Another effect of floods is erosion of banks which causes embayment. This sometimes continues tillit joins the neighboring tributary. This results in shifting of outfall of the tributary. This is particularlytrue for south bank tributaries, since slope of tributaries on the south is flatter than that of tributaries onthe northern side of the Brahmaputra river.

To protect certain areas from flooding embankments (or levees) have been built on the northern andsouthern side of the river. Between 1954 and 1989 embankments over a total length of about 940 km ofembankments have been constructed at critical reaches on both sides, these are shown in Fig. 13.10.These levees have top width ranging from 2.5 to 4.6 m, river side slope 3:1 and country side slope 2:1and 8:1 with berm. Usually the free board is about 1.5 m. These levees are subjected to erosion andbreaches at many places during high floods necessitating frequent costly repairs, and provision of spurs.Over 300 breaches have occurred since the levee system was established. Since earlier embankmentswere constructed with inadequate data, these had to be raised and strengthened as the data on higherfloods were obtained. Some towns also had to be protected by dykes. The present day system ofembankments provides protection to about 14 000 km2 of about 30 000 km2 of the total flood prone area.

Many times the embankments have been cut by lateral erosion, not at the highest flood but atsomewhat lower stages and hence the low lying areas have been flooded even though the level of waterin the river is below that of the embankment. As mentioned earlier, floods in the tributaries are alsocaused when the Brahmaputra river flows at a higher level than the tributaries thereby causingbackwater in them.

River Morphology420

To overcome the problems of flood control, bank protection, maintaining navigation channel forriver commerce and to protect cities, towns and other man-made structures, various types of works havebeen constructed. These are (see Weller, 1970).

1. Bandals: These are made from bamboo poles driven 1 to 2 m into river bottom and spaced at 0.5to 1.0 m center to center. Mats of woven bamboo 0.8 m ´ 0.5 m are placed on bamboo polesnear the water surface. Bandals are inclined 30° – 40° with current. These slow down thecurrent and induce deposition, direct the flow into proposed channel and provide adequatedepth for navigation.

2. Bottom Panels: Bottom panels are structures arranged on the bottom at such angles to flow soas to divert bottom current out of existing channel and induce accretion in that area. Each panelis composed of corrugated metal sheets 1.0 m high and 4 to 5 m long. They are placed againstbamboo poles driven 0.6 to 1.0 m apart.

3. Bamboo Palisading: this is composed of a row of bamboo poles 7.5 to 10 cm in diameter placedclosely together and driven 1.2 to 1.5 m into the river bed and 1.8 to 2.4 m of bamboo extendedabove the bed. This structure is strengthened by split bamboo placed horizontally at 0.3 m apartand tied to the vertical bamboo poles with wire. The structure is also adequately braced. This isplaced immediately offshore and approximately parallel to the bank to be protected.

4. Bamboo spurs.5. Tree spurs.

6. Anchored trees.7. Tree Branch Revetment: This is a method of bank protection in which a mattress of tree

branches is placed against the bank to arrest erosion. Three or four branches of trees each 3.0 to3.6 m long are tied together by wire and weighted with stones placed in sacks. This assembly isanchored to the bank with wire ropes and sunk to the river bottom. Other bundles are placed,each over lapping the last until the line of branches is extended from deep water to the bank.

8. Floating rafts and cages made from bamboo.9. Permeable screens made from bamboo.

10. Timber and stone spurs.

11. Stone revetment in which 15 to 25 cm diameter crushed stones are placed with a thickness of0.5 to 0.6 m on 1 V: 1.5 H slope.

Figure 13.19 shows bamboo porcupine spur, permeable pipe spur and RCC porcupine screen usedon the Brahmaputra.

13.17 DRAINAGE OF HINTER LANDS

Because of inadequate hydrologic data in the earlier times, adequate numbers of sluices have not beenprovided in the embankments as a result of which there occurs drainage congestion in some areas,because the natural drainage from protected areas is cut off. It may also be mentioned that physiographicfeatures of the region as a whole are responsible in causing, at least partly, widespread floods. The valleyis surrounded on all sides by hills and mountains with only one inadequate outlet near Dubri thoughwhich the entire discharge of the Brahmaputra must pass. The rivers in the region are also marked by theabsence of lakes that exercise moderating influence on floods.


Fig. 13.19 Some river training structures on the Brahmaputra

River Morphology422

13.18 RIVER BED CHANGES IN BRAHMAPUTRA

Bed level changes in the Brahmaputra have been studied by different methods. Panchang (1964) plottedthe yearly-observed low water level and observed flood level at Dibrugarh for the period 1912 to 1963,see Fig. 13.19, on which he also indicated the occurrence of earthquakes of moderate and severeintensity. WAPCOS (1993) report extended the range of data up to 1966. This figure clearly shows thegradual rise of high flood level; however since these levels are for different flood discharges, one has toexamine the trend of yearly lowest water levels. Since daily low water stages for the season are believedto be comparable from year to year the same can be taken as a reflection of river bed from year to year.This curve in Fig. 13.20 shows lowering of bed during 1914-1918 at the rate of 143 mm/year, 1918-1922period shows gradual aggradation of bed at the rate of 210 mm/year. Similarly during 1947-51 there israpid aggradation at 832 mm/year. These changes are partly due to occurrence of earthquakes in theregion and passage of bed-wave in the downstream direction.

The other approach is based on sediment balance using continuity equation for sediment, accordingto which during a given time

Inflow of sediment

from upstream

Inflow of sediment from

in between tributaries

Outflow from

the reach

Net storage or

loss of sedimetnRST

UVW

+ RST

UVW

- RST

UVW

= RST

UVW

This method was used by Goswami (1985); his studies have indicated that during the period study1971-1979, the Bessamara–Burabandha, and the Pandu–Jogighopa reaches have undergone excessiveaggradation, while the Ranaghat–Bessamara and the Bhurabandha–Pandu reaches have experiencedsome degradation. WAPCOS (1993) had also collected the cross-sectional data at 65 stations along thelength of the Brahmaputra for the period 1957-1989. On the basis of the analysis of these data WAPCOSconcluded that there was no significant deposition or erosion in different reaches; however the erosion

Fig. 13.20 Brahmaputra water levels at Dibrugarh (1913 – 66)

Years

1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 196596

98

100

102

104

106

Wate

rle

velm

Yearly observed lowest W.L.

Yearly observed highest W.L.

Earthquake with strong intensity felt in Assam

Earthquake with mild intensity felt in Assam

(1931 - 66)y = – 0.44 + 0.0536x

(1951 - 66)y = 112.37 + 0.058x


or deposition was not uniform in different reaches. Aggradation of 5 cm/year to erosion of 7 cm/yearwas observed at different locations during 1957-1971. During 1971-1977 about 11.3 cm/year erosionhas taken place. During 1981-1989, aggradation of 2.7 cm/year on the average is noticed; thisaggradation has taken place upstream of Dibrugarh at the rate of 16.8 cm/year during this period. During1959-1989, on the average aggradation has occurred at most of the places at the rate of 1.8 cm/year. Onthe whole it was concluded that large quantities of sediment, which entered the Brahmaputra in 1950,moved downstream till 1971 and hence deposition is indicated at various places. After 1971 up to 1981,the sediment is eroded at decreasing rate and started aggradation after 1981 up to 1989. It is felt thatadditional data are needed to study aggradation/degradation problem in the Brahmaputra and relating itto flow conditions as well as channel contractions and expansions.

13.19 DEVELOPMENT PLANS

The development plans and activities in the Brahmaputra basin are designed to find the solution toproblems discussed earlier and to make the maximum use of the water resources for the betterment ofpeople in the region. Specifically the plan focuses on

1. control of floods;2. aggradation of river channel;

3. drainage problem of hinter land;4. extending embankments and controlling breaches as well as bank cutting and thereby

protecting towns on the banks of the stream; and5. development leading to extension of irrigation, water power and navigation.

To achieve these objectives Brahmaputra Board has been established in 1981 and has been giventhe responsibility of preparing the master plan for development. In the first phase of developmentadditional hydrologic, hydro meteorological and micro-earthquake recording stations are beingestablished. Modernization of flood forecasting network is also being done. Construction of additionallength of embankments and improvement of the existing ones are being undertaken. Further, newschemes for the removal of drainage congestion are identified and will be undertaken.

In the second phase, multipurpose dam projects on the tributaries Pagladiya, Dihang and Subansiriand watershed management and soil conservation programmes will be undertaken. The recent studies(see Goswami, 2004) indicate that even though Brahmaputra basin as a whole has a forest cover of 59percent, in some parts such as Assam it is only 20 percent and is reducing due to deforestation. Shiftingcultivation involving slash and burn technique of agriculture, being widely practised in the hills of North–East and Bhutan, is also a major cause of land degradation and excess sediment. Hence, watershedmanagement programme would control sediment load and reduce aggradation problem.

The Brahmaputra has been serving, for a long time, as an important means of communication inAssam (India), and this water route was linked to Kolkata, Bihar and U.P. Assam used to transport oil,tea, jute, timber, coal, paddy and rice by inland waterways. Prior to 1950 earthquake, 93 percent of teaand 90 percent of jute crop used to be transported to Kolkata by river. However, after 1950, due toextensive deterioration of the Brahmaputra channel due to earthquake, and the establishment ofeffective rail and road transport, these percentages gradually dropped to 65 for tea and 25 for jute in1965. By 1990 the total inland waterways transport was only 2 to 3 percent of total traffic by road, railand inland waterways transport.

River Morphology424

Even though the first steam boat service on the Brahmaputra started only thirty years after the firststeam boat service started on the Mississippi in 1801, the inland navigation developed much faster onthe Mississippi because of massive and sustained investments on the water course and development ofnavigation over 150 years. On the other hand, the Brahmaputra remained essentially in its natural,unregulated and undisciplined state, with the only major concern for flood control. Hence, in the recenttimes Inland Waterways Authority of India and the Directorate of Inland Water Transport of Assam havetaken some initial steps to carry preliminary studies (see IWAI 1990) to develop water transport on theBrahmaputra and its tributaries. There are a number of inland ports on the Brahmaputra such asDibrugarh, Neamati, Tezpur, Guwahati, Pandu, Jogighopa, and Dubri. However, modern facilities ofpermanent nature for cargo handling do not exist in any of these ports; hence these are being planned.Plans are being formulated for fully utilizing the potential of the Brahmaputra for inland water transport.In the first stage design vessel of 100 m length, 12 m width and 2.5 to 3.0 m draft are suggested. To makethe river fully navigable, a number of actions need to be taken such as stabilization of river course,checking formation of shoals, providing minimum depths and widths at low flows, adequate bend radiiand moderate velocity.

13.20 ROLE OF DREDGING

There is some discussion as to the role of dredging in the management of the Brahmaputra river. In thepast (see Baruah and Gogoi, 2004) experimental dredging has been used in the Chimna area nearPalasbari, 30 km downstream of Guwahati in 1974-75. The objective was to control erosion of theembankment system, which was in danger. It was proposed to dredge cut a channel of 30 m width, and7 km length to channelise the flow and reduce the flow through channel near northern bank. However,before the work of dredging was completed, flash flood came. It was later found that the proposedchannel did not develop. However, dredging at Alikash area 40 km from Guwahati on the south side ofBrahmaputra, to control erosion by dredging a pre-aligned channel of length 2.24 km, width 50 m andside slope 1V:2H was successful. Similarly dredging has been used on come tributaries to change thelocal flow, remove blockages or opening mouths of the tributaries. However, it is the considered opinionthat dredging on the main river over long stretches to reduce aggradation is not feasible and economical.

However, when the river is used for navigation and generates adequate resources, dredging can beused to maintain minimum depths at critical sections and for other local adjustments of the section.

References

Baruah, B.B. (1969) Flood and Erosion Control in the Brahmaputra Valley by Making Use of Natural Features,Central Fuels Research Institute, 59 p.

Baruah, B. and Gogoi, P.K. (2004) Experiences of Dredging in Brahmaputra and Tributary, Seminar on Silting ofRivers, Problems and Solutions, CWC, New Delhi, 6 p.

Bristow, C.S. (1993) Sedimentary Structures Exposed in Bar Tops in the Brahmaputra River, Bangladesh. InBraided Rivers (Eds. Best, J.L. and Bristow C.S.) Geol. Society, Special Publication No. 75m, pp. 277-289.

Carlson B. (1985) Erosion and Sedimentation Processes in Nepalese Himalays. International Centre for IntegratedMountain Development (ICIMOD), Occasional Paper No. 1, Khatmandu, Nepal.


CBIP (1986) Seminar on Morphology of Ganga River. Central Board of Irrigation and Power, New Delhi,November, 146 p.

Chitale, S. V. (1984) Kosi -The Problem River of North Bihar. Journal of Irrigation and Power of CBIP, Vol.41,no.2, April, pp.197-202.

Chitale, S. V. (2000) Future of the Kosi River and the Kosi Project. Journal of Institution of Engineers (India), Vol.81, December, pp.109-114.

Coleman, J.M. (1969) Brahmaputra River: Channel Processes and Sedimentation. Sedimentary Geology, Vol. 3,pp. 129-239.

CWPRS (2002) Mathematical Model Studies for Proposed Bridge on Kosi River at NH-57 Crossing (Bihar).Central Water and Power Research Station, Technical Report No. 3926, Sept.

Dhanju, M.S. (1976) Study of Kosi River Flood Plains by Remote Sensing. Hydrology Review, vol.2, No.4,October, pp. 43-48.

Garde, R.J. and Kothyari, U.C. (1989) Land Slides and Their Effects on River Regime, Proc. 4th Intl. Symposiumon River Sedimentation, Beijing (China), Vol. 2, pp. 819-831.

Garde, R. J., Ranga Raju, K. G., Pande, P.K., Asawa, G. L., Kothyari, U. C. and Srivastava R. (1990) MathematicalModelling of the Morphological Changes in the River Kosi. Civil Engg. Department, University of Roorkee(Now IIT Roorkee), 58p.

Gee, E.P. (1951) The Assam Earthquake of 1950. Jour. Of Bombay Natural History Society, Vol. 50, No. 3, pp.629-635.

Godbole, M.L. (1986) Morphology of the Gandak and the Kosi Rivers – A Comparison. Seminar on Morphologyof Ganga. CBIP, New Delhi, November, pp. 29-51

Gohain, K. and Parkash B. (1990) Morphology of the Kosi Megafan. Chapter 8 in Alluvial Fans: A Field Approach(Ed. Rachocki, A. H. and Church, M.) John Wiley and Sons Ltd., pp.151-177.

Gole, C.V. and Chitale, S.V. (1966) Inland Delta Building Activity of Kosi River. JHD, Proc. ASCE, Vol. 92, No.HY-2, March, pp. 111-126.

Goswami, D.C. (1985) The Pattern of Sediment Yield from River Basins of the Brahmaputra System, N.E. India.The North Eastern Geographer, Vol. 71, Nos. 1 and 2, pp. 1-11.

Goswami, D.C. (1985a) Brahmaputra River, Assam, India: Physiography, Basin Denudation and ChannelAggradation. W.R. Research, Vol. 21, No. 7, July, pp. 959-978.

Goswami, D.C. (1988) Estimation of Bed-Load Transport in the Brahmaputra River, Assam. Indian Journal ofEarth Sciences, Vol. 15, No. 1, pp. 14-26.

Goswami, D.C. (1988) Magnitude and Frequency of Fluvial Processes in the Brahmaputra Basin, Assam: SomeObservations. Geomorphology and Enviironment, The Allahabad Geographical Soc., Allahabad (India), pp.203-211.

Goswami, D.C.(1990) Morphology of Brahmaputra (Cyclostyled Unpublished Lecture Notes).

Goswami, D.C. (2004) Alluvial Regime and Channel Morphology of the Brahmaputra River : Some Observations.Seminar on Silting of Rivers, Problems and Solutions, CWC, New Delhi, 8p.

Handique, G.R. and Borgohain, J.K. (1991) The Brahmaputra River System, The Senteniel, April 13.

Handique, G.R. and Borgohain, J.K. (1991) Long Term Projects. The Senteniel, April 20.

IWAI (1990) Detailed Report for Development of Inland Water Transport on national Waterway No. 2, InlandWaterways Authority of India Report.

Jain, V. and Sinha, R. (2003) River Systems in the Gangetic Plains and Their Comparison with Siwaliks: AReview. Current Science, Vol. 84, No. 8, April, pp. 1025-1033.

River Morphology426

Jakhade, G.S., Murthy, A.S. and Sethurathinam (1984) Frequency Floods in Brahmaputra Valley. Journal ofIrrigation and Power, CBIP (India), Jan., pp. 41-47.

Mookerjea D, and Aich, B.N. (1963) Sedimentation in Kosi -A Unique Problem. Journal of Institution ofEngineers (India) vol.43. b) Godbole, M.L. Morphology of the Gandak and the Kosi Rivers -A Comparison.pp39-S2.

NIH (1998) Majuli River Island: Problems and Remedies – North Regional Research Centre, National Institute ofHydrology, Guwahati, 27p.

NIH (1994) Erosion, Sedimentation and Flooding in River Kosi. National Institute of Hydrology, Roorkee, SR -26,229p.

Panchang, G.M. (1964) High Floods in Brahmaputra – A Retrospect. Journal of Irrigation and Power, CBIP(India), Jan., Vol. , pp. 67-71.

Rao, K.L. (1979) India’s Water Wealth: Its Assessment, Uses and Projections. Orient Longman Limited. 267p.

Sahai, R.N., Pande, P.K. and Garde, R.J. (1980) Aggradation in Eastern Kosi Main Canal. Proc. of 1st Intl.Workshop on Alluvial River Problems, University of Roorkee (Now I.I.T., Roorkee), 2-73 to 78.

Sanyal, N. (1980) Effect of Embankment of River Kosi. Proceedings of 1st International Workshop on AlluvialRiver Problems, Roorkee.

Sinha, R.K. (1986) Morphology of the River Kosi, M. E. thesis, Water Resources Development Training Centre,University of Roorkee (Now IIT Roorkee), 51 p.

Sinha, R. (1995) Sedimentology of Quaternary Alluvial Deposits of Gandak-Kosi Interfan, North Bihar Plains.Journal of Geol. Society of India, vol.46, November. pp. 521-532.

Sinha, R., Friend P.F. and Switsur, V. R. (1996) Radiocarbon Dating and Sedimentation Rates in the HoloceneAlluvial Sediments of the North Bihar Plains, India. Geol. Magazine, Vol.133, No.1, pp.85-90.

Valdiya, K.S. (1999) Why Does the River Brahmaputra Remain Untamed? Current Science, Vol. 76, No. 10, 25May, pp. 1301-1305.

WAPCOS (1993) Morphological Studies of Brahmaputra River. Unpublished Report Prepared by Water andPower Consultancy Services (India) Ltd., New Delhi.

Weller, H.E. (1970) Brahmaputra River Bank Protection in India. Journal of Irrigation and Power, CBIP (India),April, Vol. No., pp. 177-189.

14C H A P T E R

Rivers and Environment

14.1 INTRODUCTION

Streams in natural condition generally exist in a state of dynamic equilibrium, in which the amount ofsediment delivered to the channel from the drainage basin is in long-term balance with the capacity ofthe stream to transport sediment; in such a case, channel dimensions and slope remain fairly invariantand over a period of time there is neither aggradation or degradation. In such streams, a balance alsoexists between communities of aquatic organisms inhabiting in the stream and the biochemicalprocesses that recycle nutrients from natural pollution sources to the water. The physical processes suchas aeration, dispersion, currents and sedimentation, chemical processes such as photosynthesis,metabolism, and biological processes such as biological flocculation and precipitation act together andnaturally purify water. Aerobic purification processes require free oxygen, and are dominant in naturalstreams, although anaerobic processes occur as well where free oxygen is absent.

Organic matter and nutrients in the streams are decomposed and resynthesised through chemicalreactions in association with aquatic organisms. The material is transformed by cycles of nitrogen,carbon, phosphorus and sulphur in aerobic decomposition. These processes create Biological OxygenDemand (BOD) that depletes the dissolved oxygen in water. Re-oxygenation is effected throughaeration, absorption and photosynthesis. Riffles and other turbulence creating units such as dunes, bars,and bends in the stream enhance aeration and oxygen absorption.

Fish and other aquatic organisms that utilize dissolved oxygen in water for respiration maysuffocate if oxygen concentration is severely depleted. Excessive loading of streams with organic matterand nutrients can create significant biochemical oxygen demand and reduce dissolved oxygen to criticallevels.

Pollution sources can be grouped into point sources and non-point sources. Domestic sewage andindustrial wastes are called point sources because they are generally collected by a network of pipes andchannels and carried to a single point of discharge. Pollution by point sources can be prevented bypassing the pollutant through a properly designed waste treatment plant prior to discharging it into thestream. On the other hand, urban and agricultural runoffs are characterized by multiple discharge points.

River Morphology428

Treatment of non-point source wastes is generally difficult. Nutrient enrichment causes rapidmultiplication of algae, blooming, death and decomposition during the low flow periods resulting insevere depletion in oxygen and fish kills. The aquatic organisms inhabiting natural streams can beclassified into:

Aquatic plants: These include seed bearing plants, mosses and liverworts, ferns, horse tails andalgae.

Aquatic organisms: Moulds, bacteria and viruses.Aquatic animals: These include vertebrates and invertebratesVertebrates: Fish and amphibiansInvertebrates: Mollusks (Mussels, snails, slugs) and anthropoids (insects spiders, mites), worms

and protozoa

Streams in their natural state tend to maintain equilibrium between populations of aquaticorganisms and available food. The population dynamics of aquatic organisms in a stream ecosysteminvolves substrate utilization, food web, nutrient spiraling and the growth curve. The waste organicsubstances in the stream form the substrate on which micro organisms grow and become part of the foodweb. Growth of micro organisms follows sequent portions of the growth curve including nutritionallyunrestricted exponential growth, nutritionally restricted growth, and stationary or declining growth dueto environmental conditions.

The circulation, capture, release and recapture of nutrients is known as nutrient spiraling. Theability of the stream to a assimilate nutrients and store them in the living tissue of plants and animals istermed as the assimilative capacity of the stream. The streams, which have a relatively high assimilativecapacity, are known as healthy streams and this is needed for maintaining good water quality. Thepresence of larvae of stoneflies, caddisflies and dragonflies generally indicates good quality of water,whereas large populations of rat-tail, maggot, blood worm and sewage fungus indicates polluted water.Conditions or health of a stream ecosystem is reflected by its biological activity. Biological integrity isdefined as the ability of an aquatic ecosystem to support and maintain a balanced, integrated, adaptivecommunity of organisms having a species composition, diversity and functional organizationcompatible to that of the natural habitats of the region. The main factors and some of their importantchemical, physical and biological components that influence and determine the integrity of surfacewater resources are:

i) Flow Regime: Precipitation, run-off, high and low flows, stream velocity, base flow, land use,etc.

ii) Habitat Structure: Channel morphology, pool-riffle sequence, bed material, slope, in streamcover, canopy, substrate, width/depth ratio, sinuosity, bank stability, etc.

iii) Energy Source: Sunlight, organic matter inputs, nutrients, seasonal cycles, primary andsecondary production.

iv) Chemical Variables: Dissolved oxygen, pH, temperature, alkalinity, solubility, adsorption,hardness, turbidity and nutrients.

v) Biotic Factors: Reproduction, disease, parasitism, feeding, predation and competition.Any natural disturbance or human activity that affects one or more of the above factors will affect

the biological integrity and hence water quality.

Rivers and Environment 429

14.2 ACTIONS CAUSING DISTURBANCE IN STREAM SYSTEM ANDTHEIR IMPACTS (OSMG 2004)

Stream system can be affected by human actions or natural disturbances in the catchment, in the streamcorridors or in the stream. These actions include:

i) Deforestation, construction activity and agricultural activity in the basin.

ii) Construction of dams and reservoirs and other hydraulic structures such as energy dissipators,spillways, hydro-power plants, bridges, irrigation outlets, locks, bank protection works andembankments.

iii) Development of water resources projects, water-power projects and thermal projects alongstream banks.

iv) Development of irrigation, flood plains and uplands.v) Stream canalization for navigation and flood control using methods such as cut-offs, stream

straightening and flow diversion.vi) Dredging of channels and disposal of dredged material.

vii) Use of streams for discharging urban sewage, industrial wastes and heated discharges.As a result of the above mentioned actions causing disturbance in the stream system, the following

changes may take place in the stream ecosystem:i) Changes in physical and chemical aspects of water quality and in-flow regime.ii) Modification of channel and ecosystem morphology.iii) Excessive non-point source pollution including sedimentation and nutrient enrichment.

iv) Deterioration of stream substrate quality and stability.v) Destabilization of stream banks and bed.vi) Modification of water temperature regime by removal of tree canopy, induction of thermal

discharge, and alteration of base flow regime.vii) Introduction of exotic species that disrupt dynamic balance.

viii) Problems arising out of displacement and resettlement of population such as transfer ofdiseases.

It is not possible to discuss the impacts of all these activities on river channels and water quality inthe context of the theme of the text. Hence, only effect of construction of dams and reservoirs and powerplants, and some aspects of pollution of river waters will be discussed here.

14.3 ENVIORNMENTAL EFFECTS OF HYDRAULIC STRUCTURES

When one wants to study the effects of hydraulic structures on the environment, one should study theprobable effects on water quality, land, atmosphere and society. Parameters to be studied for waterquality have already been mentioned in general earlier and details are given in sections 14.4 and 14.8.As regards the land one should consider salts, sedimentation, erosion, aggradation or degradation,vegetation, landslides and reservoir induced seismicity, terrestrial animals, ground water levels andrecreation. The aspects related to atmosphere are air pollution, humidity, temperature and evaporation.Social aspects will be many which may include displacement, development and prosperity.

River Morphology430

It is necessary to ensure that the identified effects are truly significant and that some significanteffects have not been overlooked. TCEEHS (1978) recommends the effects be described by one of thefour numbers 1, 2, 3, 4 to indicate the dependence; thus

1. Variable may be increased by causal factor,

2. Variable may be decreased by causal factor,3. Variable may be increased or decreased by causal factor, and4. Variable is unaffected by causal factor.

The hydraulic structures that can be considered include reservoirs, dams, outlets, energydissipators, power plants, bridges, sediment excluders and ejectors, embankments, spurs and channelrectification works such as cut-offs, channel contractions and dredging.

14.4 DAMS AND RESERVOIRS

Since ancient times dams have been constructed on streams and reservoirs have been formed. Generallydams and reservoirs serve many purposes such as flood control, power generation, supplying water forirrigation, drinking and industrial use, navigation and recreation. Since independence, India haswitnessed rapid growth in the construction of large dams and elaborate canal networks. Over 4000projects have been constructed in last five decades and 700 projects have been proposed to meetincreased demand for power and achieve larger irrigation potential (Raghuvanshi et al. 2000). Thisactivity has caused several social, ecological and economic problems.

As a result of completion of such water resources projects, the society is greatly benefited in termsof dependable and clean drinking water, greater availability of food, better health, sanitation andincreased per capita income; availability of increased power has also resulted in greater industrialactivity and better living standards. Tourism and recreational facilities created by water resourcesprojects have led to social and cultural improvements e.g., Brindavan gardens, Ramganga garden,Kalinadi Kunj, Jaikwadi garden and Gobindsagar reservoir. (Goel and Agarwal, 2000). Flocking of rarespecies of birds and increase in wild life have also been reported near Ramganga, Rihand and Matatilareservoirs.

As against these beneficial effects, a number of adverse effects have also been reported. Formationof reservoirs due to construction of dams submerges large areas including those of forests and a numberof people are ousted from submerged areas. Table 14.1 gives some data on submergence, ousted numberof people and installed power capacity.

Thus, it can be seen that as a result of construction of these dams, large areas including forests havebeen submerged and ousted a large number of people from their homes. Resettlement and compensationto inhabitants of the submerged areas include determination of areas that will be submerged, evaluatingcompensation for their properties, selection of alternative sites for settlement and distribution of land.Such considerations were not made in the case of the Volga lake in Ghana which submerged about 8200km2 area. The submergence area was greatly underestimated. Similarly, in the case of the Roseiresreservoir on the Blue Nile river in Sudan, only a few months before submergence people were asked tomove and submergence was underestimated by two metres (Murthy 1976). Submergence of forest areasaffects the habitat of many wild life species as can be seen from Table–14.2.


Two other environmental effects of construction of large dams for water storage and its utilizationare water logging and salinization, and water-borne diseases. About 2 to 3 million ha of land every yearis going out of production due to salinity problems. Water logging results primarily from inadequatedrainage and over irrigation, and to a lesser extent, from seepage from canals and ditches. Water loggingconcentrates salts, drawn up from lower portions of the soil in the plant’s rooting zone. The build up ofsodium in the soil is particularly detrimental form of salinization which is difficult to rectify. Theirrigation-induced salinity can arise as a result of use of any irrigation water, irrigation of saline soils,and rising levels of saline ground water combined with inadequate leaching.

Water-borne or water related diseases are commonly associated with the introduction of irrigation.The diseases most directly linked with irrigation are malaria, bilharzias, filaria, cholera, gastroenteritis,viral encephalitis and goitre. Other irrigation related health risks include those associated with increased

Table 14.1 Submergence areas and number of oustees under some existing and proposedhydroelectric projects (Raghuvanshi et al. 2000)

Project Total area of Forest area Number of oustees Installed capacitysubmergence submerged (ha) (MW)

Narmadasagar 91 348 40 332 150 000 1000

Ukai – Kakrapur 60 000 22 260 50 000 300

Bargi 36 729 18 000 114 000 90

Sardar Sarovar 34 996 11 640 45 515 690

Omkareshwar 9393 2471 12 295 390

Idukki 6475 6475 4500 230

Tehri 5200 1600 85 600 2400

Table 14.2 Submergence of forests and wild life habitats under hydroelectric projects(Raghuvanshi et al. 2000)

Sr. Project name Forest area under Characteristic wild life species inNo. submergence (ha) submergence zone

1. Narmadasagar multipurpose project 40 332 Tigers, sambar, chital, fishing cat andotter

2. Sardar Sarovar multi-purpose project 11 600 Four horned antelope, crocodile andotter

3. Idukki hydroelectric project 6475 Elephants

4. Parmbikulam Aliyar project 2800 Tiger, elephant, gaur

5. Kariakutty Karapara multi-purpose project 1690 Lion tailed macaque, nilgiri langur,tiger, elephant, sloth bear, gaur

6. Tehri hydroelectric project 1600 Himalayan mountain sheep

7. Rajghat irrigation project 990 Tiger, black buck, crocodile, greatIndian bustard

8. Ramganga hydroelectric project 280 Tiger, elephant, hog bear, gharial

River Morphology432

use of fertilizers, herbicides and pesticides. The occurrence of these diseases in the population havebeen noticed in Ghana, Nigeria, Egypt, Ethiopia and other countries.

Large versus Small DamsConstruction of large dams and reservoirs usually entails enormous costs and displacement of a largenumber of people as can be seen from Table 14.1. Resettlement of these oustees is many times neglectedand hence leads often to protests, hunger strikes, stoppage of work and costly litigations that furtherdelay the work. Unfortunately, people who are likely to be affected are not consulted or taken intoconfidence. Further, we do not have a National Rehabilitation Policy and credible implementing andmonitoring procedures for rehabilitation. There is always a complaint that these people do not get faircompensation and a guaranteed share in the prosperity that the project brings. These conditions needimmediate improvement.

Considering these effects, many environmentalists argue that instead of building one large dam, afew small dams should be built. However, this idea is not feasible for the following reasons (Indiresan2000).

i) A number of small dams cannot control floods or generate electricity as a high dam can.ii) Per 1000 m3 of storage, the capital cost for large, medium and small dams varies in the ratio of

approximately 1:3:6; hence it will be costlier to build smaller dams than a single large dam forachieving the same storage.

iii) Other things being equal, doubling height of dam increases the storage by about eight times andpower potential sixteen times; hence it is better to build large dams when feasible.

iv) Since rainfall in India is erratic and occurs in 3 or 4 months, water needs to be stored to meetirrigation, water supply and power needs especially when drought occurs. This is unlike inEurope where precipitation occurs all through. Hence large dams are needed.

v) Evaporation loss in India is about 1.2 to 1.4 m annually; hence, storage required has to be large.

Further, it has to be realized that providing food, drinking water and power to millions of people ismore important than preventing displacement of a few thousand people. This is not to say that thelegitimate needs and aspirations of the oustees should be overlooked. Similarly, legitimate actions haveto be taken to protect the environment. In the three gorges project about one third of the investment hasbeen set aside for rehabilitation and environmental protection. Considering all these aspects it mayprudent to have good mix of large and small dams for the development of water resources in the country.

Reservoir Induced SeismicityIt has been found all over the world that in some cases, after the reservoir is filled, the adjacent areas aresubjected to reservoir-induced earthquakes (Kolhi and Bhandari 1991, Gupta 1992). Such reservoir–induced earthquakes have occurred after impoundment of the Shivajisagar lake formed by Koyna damand at Bhatsa dam in Maharashtra, and at Sriramsagar dam on the Godavari in India. Such earthquakeshave also occurred at Hsinfengkian reservoir in China, at lake Mead formed by Hoover dam on theColorado river in U.S.A., Nurek and Tokgotul reservoirs in Russia, Aswan dam in Egypt and at manyother places.

A few details about reservoir-induced earthquakes at Koyna dam can be given. The Koyna dam ofheight 103 m and the Shivajisagar reservoir are located in peninsular India about 200 km from Pune.


Soon after impoundment of the reservoir in 1962, the nearby area started experiencing earth tremors andthe frequency of these tremors increased from the middle of 1963 onwards. These tremors wereaccompanied by sounds similar to those of blasting. Between 1963 and 1967, five earthquakes occurredwhich were strong enough to be recorded by many seismological observatories in India. The majorearthquake at Koyna occurred on December 10, 1967, which had a focal depth of 10 km ± 2 km and hada magnitude of 6.0. This earthquake claimed about 200 lives, injured over 1500 people and renderedthousands homeless. It also caused damage to hoist tower of the dam and developed horizontal crackson both the upstream and downstream faces of a number of monoliths, and damaged a large number ofhouses, bridges and culverts.

Realising the socio-economic importance of reservoir induced seismicity, UNESCO formed aworking group on these phenomena and since then a number of symposia on reservoir-inducedseismicity have been organized. A number of theories/explanations have been suggested to explain whyand under what conditions the seismicity is caused. Investigation of fluid injection-induced earthquakesat the Rocky Mountain Arsenal near Denver, Colorado, (U.S.A.) during 1960’s and Evan’s work on themechanism of triggering earthquakes by increase of fluid pressure have helped in understanding thephenomenon of reservoir-induced seismicity. Gough and Gough have explained triggering ofearthquakes due to incremental stress caused by water load in the reservoir. Gupta et al. (see Gupta1992) identified the rate of increase of water level, duration of loading, maximum levels reached and theduration of retention of high water levels among the important factors affecting the frequency andmagnitude of reservoir-induced earthquakes. Other studies by Nyland, and Bell and Nur have alsoindicated that the three main effects of reservoir loading relevant to inducing earthquakes are (i) theelastic stress increase that follows the filling of the reservoir; (ii) the increase in pore fluid pressure insaturated rocks due to decrease in pore volume caused by compaction in response to elastic stressincrease; (iii) and pore pressure changes related to fluid migration. It is also found that reservoir-inducedearthquakes are associated with shear fracturing of rocks. The shear strength of rocks is related to theratio of the shear stress along the fault to the normal effective stress across the fault, the latter beingequal to normal stress minus the pore pressure. Hence, increase in pore pressure can trigger earthquakeif rocks are under initial shear stress. During the past four decades, scientists have gained someknowledge about RIS but a lot more needs to be learned. It may be mentioned that the largest reservoir-impoundment triggered earthquakes have exceeded magnitude of six. On the basis of RIS observationson a number of dams, it has been well established that major RIS events are produced by enhancedforeshock activity. Such analysis has indicated that, if two earthquakes of magnitude greater than 4occur at RIS site within a short interval of say 2-3 weeks, there is an enhanced probability for occurrenceof earthquake of magnitude greater than 5. Studies have suggested that in the case of a large reservoir(volume in excess of 1000 Mm3 usually impounded behind a dam height greater than 100 m) it isdesirable to carry out geological mapping for the entire reservoir area to determine faults andcompetence of rocks (Gupta 1992).

14.5 WATER QUALITY IN RESERVOIRS

Construction of a dam forms a reservoir the capacity of which is progressively reduced due tosedimentation. Since depending on the capacity to inflow ratio for the reservoir, the water is stored in thereservoir for different time periods before it is released; the quality of water in the reservoir is differentfrom that flowing in the stream. The following factors need to be considered in the study of water qualityin reservoirs (TCEEHS 1978).

River Morphology434

TemperatureTemperature plays an important role in controlling many hydraulic, chemical and biologicalphenomena. In this regard, the temperature range as well as rate of temperature change are important.The temperature affects the behaviour of biological organisms, and the rates of chemical andbiochemical reactions. A 10°C rise in temperature approximately doubles the reaction rate. Similarly,thermal stratification takes place in deep reservoirs. Near the water surface is the layer known asepilimnion in which temperature is fairly constant and it is in aerobic condition. Near the bottom is acold-water layer known as hypolimnion in which there is depletion of dissolved oxygen. Rise intemperature upto a certain limit may increase the growth rate of fish and beyond that limit a rapid die-offtakes place. Warm water fish may survive in temperature higher than 34°C. At higher temperature, fishmay starve due to increased rate of respiration and higher food requirement. Temperature is also foundto affect reproduction ability, digestion and longevity of fish.

TurbidityThe turbidity of water due to suspended material reduces the light transmission characteristics of water.Hence, increase in turbidity decreases the algae growth. Suspended solids can also clog gills of fish andcover benthic organisms.

pHpH is the logarithm of the reciprocal of hydrogen ion concentration in water and it normally varies from6 to 9. A value of pH less than seven indicates acidic liquid while value greater than seven indicatesalkaline liquid. pH plays an important role in many chemical and biological reactions. Extremes in pHas well as fluctuations in its value can have adverse effect on aquatic life. Anaerobic activities in thehypolimnion of some reservoirs can reduce pH resulting in slightly acidic waters.

SalinityDissolved solids can enter the reservoir through the inflowing water or through ground waterinfiltration. Salinity of the reservoir water can also increase as a combined result of high evaporationrates and long detention times. High salinity water entering a reservoir can establish densitystratification patterns similar to thermal stratification. In such cases mixing of oxygen-rich surfacewaters into oxygen-depleted bottom water is inhibited at the interface named chemocline. Water ofincreased salinity may result in discharges that are less suited as a source of water for industrial andirrigation uses. In addition, higher the salinity, the lower is the oxygen saturation concentration forwater.

Dissolved Oxygen (DO)Dissolved oxygen concentration in water plays an important role in determining the quality ofdischarged water. Adequate DO is necessary for the life of aquatic organisms and fish. Equilibriumconcentration of DO resulting when water is in contact with air is known as saturation concentration andthis is directly proportional to pressure and inversely proportional to salinity and temperature.Ultimately DO concentration is equal to net oxygen sources and sinks affecting the aquatic system.Oxygen is obtained by water by photosynthetic activity by aquatic plant and re-aeration from theatmosphere. Dissolved oxygen is consumed by the following processes: (i) biochemical oxygen demand


resulting from oxidation of nitrogenous and carbonaceous matter; (ii) respiration by benthic organisms,fish, zooplankton and other species; (iii) chemical oxygen demand resulting from oxidation of methane,hydrogen sulphide and certain other compounds of iron and manganese; and (iv) inflow of water withlow dissolved oxygen. When dissolved oxygen concentration becomes very low, toxic and noxioussubstances can be generated and in extreme case fish kills can result.

Iron and ManganeseThe source of these metals in impounded water can be from geological out croppings in reservoirbottom, from inflow of tributary streams, ground water infiltration, and decomposition of organicmaterial by biological action. For drinking water, their concentrations should be limited to 0.30 mg/l

and 0.05 mg/l respectively.

PhosphorusPhosphorus is an essential nutrient for the growth of aquatic plants; but only a small amount is requiredfor this growth. Orthophosphate form of phosphorus is readily taken up and assimilated byphytoplankton and periphyton. Reservoirs tend to reduce phosphorus content of water dischargedthrough mechanisms of biological uptake and assimilation, chemical precipitation and physicaladsorption. Most soluble phosphorus released to the water results from decomposition of sediments.Under anaerobic conditions, high concentrations of phosphorus occur in the hypolimnion of reservoir. Ifthis water is released downstream, it can result in algae blooms which reduces the dissolved oxygen.

NitrogenIf dissolved nitrogen concentration in water is very large it can cause gas bubble disease in fish in whichgas bubbles develop under skin, in the fins, tail and mouth, and behind eye-balls. This can lead to gasembolism and death.

Nitrogen is available in water in five forms: Nitrogen gas, organic, nitrite, nitrate and ammonianitrogen. The nitrogen cycle can operate either in aerobic or anaerobic conditions. Under aerobicconditions, nitrates are reduced to ammonia form and then assimilated in cellular form. Under anaerobicconditions, different reactions take place in nitrogen cycle and nitrates are reduced to ammonia and thenunder certain conditions to nitrogen gas, a process known as nitrification. In aquatic nitrogen cycle,other process that may take place is nitrogen fixation in which molecular nitrogen, in the presence ofenergy source, is incorporated into biological material.

Vaidya et al. (2004) have analysed the water quality data from two reservoirs–Panchet and Ujjani–in the Bhima basin in Maharashtra (India). Panchet is located in the hilly regions and is less affected byhuman activity; Ujjani on the other hand is a much larger reservoir and is affected by quality andquantity of water received from upstream industrial areas. Over a year phosphorus as orthophosphate,phytoplankton and secchi disk depths indicating clarity of water were measured. High concentration ofsoluble reactive phosphate or orthophosphate helps in growth of algae and depletion of dissolvedoxygen. In both reservoirs orthophosphates over the entire depth varied between 0.10 to 0.25 mg/l,while secchi depth in monsoon and in winter ranged 0.8 to 2.0, and 2.0 to 4.0 m respectively.

River Morphology436

14.6 THERMAL AND HYDRO-POWER PLANTS

Often thermal and nuclear power plants are built near reservoirs or rivers. These plants release a largeamount of heat as waste heat. Part of it is released in air through chimneys and the remaining heat isextracted by cooling water circulated in condensers. This heated water passes through an open channeland then is discharged into a cooling pond such as reservoir or a stream. The temperature of coolingwater rises through 8°–10°C during the passage through condensers. Discharge of this water back intothe reservoir or stream poses a major engineering and environmental problem. As discussed earliertemperature change causes physical, chemical and biological effects on aquatic organisms, as well asthe thermal structure of water body. Hence, Environmental Protection Act 1986 stipulates that thetemperature rise of cooling water discharge from thermal power stations to the receiving body shouldnot be more than 5°C higher than the intake water temperature.

The water body receiving heated discharge is usually divided into two zones: (i) small near field ofhigh temperature where dissipation of heat takes place primarily due to entrainment of cold water fromthe surrounding, and (ii) large far field with relatively lower temperature where head loss is due toevaporation and radiation. Since temperature continuously decreases as one goes away from dischargepoint, Maharashtra Pollution Control Board states that the temperature in the receiving water at 15 mfrom the discharge point shall not be more than 5°C above the ambient temperature.

Vaidhankar and Deshmukh (1992) who carried out survey of reservoir temperatures at Obra,Jatpura and Korba thermal power stations found temperature rise of 5°C or more over relatively shortdistance. The length of initial mixing zone for deep pond of Obra was about 100 m while for shallowreservoir of Korba it was 500 m. Further depending on the depth of reservoir, vertical stratification wasfound to exist with temperature difference of 3° to 10°C between bottom and the surface.

As regards the hydropower plants, a few environmental problems can be briefly mentioned. Waterpassing through the turbines entraps nitrogen and water released downstream in some cases is found tobe super saturated with nitrogen (El-Shami 1977). This causes gas-bubble disease and increase in fishmortality rate in the tail race channel. In some cases, the turbine water releases have low dissolvedoxygen concentration partly due to inflow water having low dissolved oxygen and additional depletionof oxygen in the hypolimnion of the reservoir. Since a depletion of DO concentration below a certainlimit is harmful to aquatic organisms, in extreme cases artificial re-aeration can be resorted to. This wasstudied in laboratory and pilot field tests on Fort Patrick Henry dam in U.S.A. (Ruane et al. 1977). In thiscase, laboratory and small-scale field studies were conducted to select the most promising diffuser onthe basis of oxygen transfer efficiency, operation and maintenance problems and economics. Theselected diffuser from small-scale experiments was tested in a pilot scale tests and then modificationswere made in it.

Change in discharge releases in the downstream channel because of construction of hydropowerplant on a stream can cause some positive and some adverse effects. Drastic reduction in flow in thedownstream channel will reduce plant and animal populations associated with the area. Further,regulated flow in the downstream channel could prevent the adverse effects on the aquatic habitat, giventhat a certain minimum flow is always maintained.


14.7 RECREATION

With rapid growth in population, the demand for outdoor recreation is continually increasing. Sincewater-oriented activities play an important role in outdoor recreation, rivers and reservoirs areincreasingly used for fishing, hunting, boating and other water sports. Sedimentation and erosion canseriously hamper these activities, increase the maintenance cost and reduce the life of such facilities. Afew of the problems associated with recreation that are caused by erosion and sedimentation are brieflydiscussed below (Bondurant and Livesey (1965):

1. Deposition of inert silt and sand is sterile as far as propagation of either fish or fish food isconcerned. Similarly, thin deposits of fine sediment and sludge seal the surface againstcirculation of water and oxygen and can wipe out hatches of various food species. Formation ofnormal reservoir delta also tends to inhibit reproduction of fish that travel to open riverupstream of reservoir to spawn.

2. Small inlets to reservoirs, known as coves, are ideal sheltered places for boat docks andlaunching ramps. If these are blocked by sedimentation, recreation can be hampered. Suchdeposition can also occur due to littoral drift caused by wave action. Adequate provision of adyke can control the situation.

3. Erosion of bank line by wave action is also undesirable from the point of view of recreation.Hence, if bank line is eroding, proper bank protection needs to be given.

4. Fishing and boating are also practised in the clear water releases below a dam. Many times sandbars in such area are used for docking and launching of boats. If such bars are not protected,they are likely to be washed away in a degrading stream.

14.8 STREAM POLLUTION

Rivers while they flow from mountains to plains and then to the sea experience withdrawals of wateralong their courses for agricultural, industrial or municipal use. Similarly, on their way pollution in theform human and animal waste, agricultural drainage water and industrial effluents are discharged inthem. If the existing pollution in flow is greater than the natural assimilative capacity of the stream, thequality of water deteriorates in the downstream direction, as is the case in many Indian rivers. Pollutionresults in loss of aquatic flora and fauna leading to loss of livelihood for river fisher folk, impact onhuman health from polluted water, loss of habitat for many bird species, and loss to inland navigationpotential. Further, many Indian rivers are linked with history and religions beliefs of the people and areused for bathing and religious rites. Hence, people expect the rivers to be clean and unpolluted.However, since many cities and villages on the stream banks do not have sewage and wastewatertreatment facilities, untreated sewage and industrial wastewater are dumped in the rivers. Floods tend towash down this polluted water but in lean season, the problem is aggravated. Table 14.3 lists the majorpollutant categories and principal sources of pollutants.

The major pollutant categories are briefly discussed below. Anything that can be oxidized inreceiving water uses molecular oxygen in water and consumes dissolved oxygen (DO). Human wastes,food residue, waste from food processing and paper industries, crop residues, leaves etc. fall in thiscategory. Nitrogen and phosphorus are the major nutrients required for growth. Problem arises whenthey become excessive and the food web is grossly disturbed. Excessive nutrients lead to growth of

River Morphology438

Table 14.3 Major pollutant categories and principal sources of pollutants (Davis and Cornwell 1998)

Point sources Non-point sources

Pollutant category Domestic wastes Industrial wastes Agricultural Urban runoffrunoff

Oxygen demanding material Yes Yes Yes Yes

Nutrients Yes Yes Yes Yes

Pathogens Yes Yes Yes Yes

Suspended Solids/Sediment Yes Yes Yes Yes

Salts No Yes Yes Yes

Toxic Metals No Yes No Yes

Toxic Organic Chemicals No Yes Yes No

Heat No Yes No No

algae, which in turn becomes oxygen-demanding material when they die. Major sources of nutrients aredetergents, fertilizers and food processing wastes. Pathogenic organisms are micro organisms found inwastewaters and include bacteria, viruses and protozoa excreted by diseased persons and animals.

Excess of pathogenic organisms in water make it unfit for drinking and swimming. Organicsuspended solids may exert demand on oxygen. Inorganic suspended solids create problems for fishspawning. Colloidal suspended material reduces penetration of light in water. High concentration ofdissolved solids make the water unfit for drinking if its concentration increases beyond a certain level,even crops can be damaged and soils may become unfit for agriculture. Toxic metals and toxic organiccompounds enter rivers through agriculture runoff, urban runoff and industrial wastes. These includepesticides, herbicides and zinc. These are concentrated in food chain and are very harmful to aquaticspecies and human beings. As discussed earlier heat is discharged in reservoirs and rivers by thermalpower plants and also by some industrial processes. It can be beneficial to some aquatic fish whileharmful to others.

The general parameters determined from laboratory analysis, to evaluate water quality and degreeof pollution are pH, conductivity, BOD, Nitrate-N, Nitrite-N, and fecal coliform. The generalparameters estimated once a year or so include phenophelne alkalinity, total alkalinity, dissolved solids,total suspended solids, nitrogen, hardness, fluoride, phosphate, chlorides etc. Similarly, micro-pollutants in water and sediment that are determined when needed include heavy metals, cyanide, totaliron and pesticides.

14.9 RIVER ACTION PLANS

For maintaining the quality of river water, the pollution levels in the Indian rivers have been obtained bymonitoring a limited number of physical, chemical and biological parameters, which could determinethe changes in the characteristics of water. In view of the deterioration in water quality over the past fewyears, the Government of India has taken initiative to improve the water quality of the Ganga and otherrivers, and given water quality criteria for designated best uses (DBU) as listed in Table 14.4. A briefmention may be made of Ganga Action Plan, which was launched in 1985 to prevent pollution of the


Table 14.4 Water quality criteria for designated best uses

Class Parameters

pH DOMg/l BODl Total coliform Freemg/l MPN/100 ml ammonia

mg/l

A Drinking water source without 6.5 – 8.5 6.5 or more 2.0 or less 50 -treatment but with disinfection

B Outdoor organized bathing 6.5 – 8.5 5.0 or more 5.0 or less 500 -

C Drinking water source after 6.5 – 8.5 4.0 or more 3.0 or less 5000 -treatment and disinfection

D Wildlife and fisheries 6.5 – 8.5 4.0 or more - - 12

E Irrigation, Industrial cooling and 6.5 – 8.5 Electrical conductivity 22-60µ mho/cm Sodiumcontrolled waste disposed absorption ratio 26 Boron: 2.6 mg/l

Ganga river and improve its waste quality. The plan was initiated after the initial survey by CentralPollution control Board which indicated that out of the total pollution load on account of the municipalsewage, 80 percent came from class 1 towns having population over 100 000. The plan was cast torestore river water quality to the following standards.

BOD not greater than 3 mg/lDO not less than 5 mg/lTotal coliform not greater than 10 000 MPN per 1000 l

Fecal not greater than 2500 MPN

To accomplish this task, 281 schemes have been sanctioned under Ganga Action Plan, whichinclude interception and diversion schemes, sewage treatment plants, low-cost toilets and electriccrematories. With the completion of these schemes, improvement has been notices in levels of BOD andDO. Hence, second phase of GAP and NRCP (National River Conservation Plan) has been startedalong 18 interstate rivers.

14.10 STREAM RESTORATION

Stream restoration and mitigation is a process that involves recognizing natural and human induceddisturbances that degrade the form and function of the stream and riparian ecosystems or prevent itsrecovery to a sustainable condition. Restoration includes a number of activities designed to enablestream corridors to recovers dynamic equilibrium and function to maintain channel dimensions, patternand profile so that over a period of time the stream channel does not degrade or aggrade. FISRWG(1998) identifies three levels of stream improvement: (a) restoration (b) rehabilitation and (c)reclamation.

Restoration is defined as the establishment of the structure and function of ecosystems. Ecologicalrestoration involves returning an ecosystem as closely as possible to the pre-disturbance conditions andfunction. Restoration also implies that it will provide the highest level of aquatic and biological diversitypossible. The basic principles of stream restoration include:

River Morphology440

1. analysis of channel history and evolution;2. analysis of cause and effect of change;

3. analysis of current condition;4. development of specific restoration goals and objectives prior to design;5. holistic approach to account for channel process, riparian and aquatic function;6. consideration of passive practices such as fencing against livestock;

7. natural channel design to restore function.Rehabilitation is defined as a procedure for making the land useful again after a disturbance. It

involves the recovery of ecosystem functions and processes in a degrading habitat. Rehabilitationestablishes geological and hydrologically stable landscapes that support biological diversity.Reclamation is defined as a series of activities intended to change the function of an ecosystem, such aschanging wetland to farmland.

Restoration principles, practices and methods of monitoring are being evolved on the basis ofstudies on small and medium sized streams in some western countries such as U.S.A. and U.K. Thestructures used in stream restoration include vegetation, wood, and constructed rock and woodstructures. In U.K. (see Brookes 1995) river restoration project (RRP) was formed to promoterestoration of rivers for conservation, recreation and amenity. The project utilizes the expertise of riverecologists, engineers, planners, fisheries biologists and geomorphologists to establish demonstrationprojects to show how restoration techniques can be utilized to recreate natural ecosystem in damagedriver corridors (Brookes 1995). Research needs to be carried out to study their effectiveness indegrading and aggrading streams, and to extend the methods to larger streams.

References

Bondurant D.C. and Livesey, R.H. (1965) Sedimentation Aspects in Recreational Planning. JHD, Proc. ASCE,Vol. 91, No. HY5, Pt. 1, Sept. pp. 51-64.

Brookes, A. (1995) River Channel Restoration: Theory and Practice. In Changing River Channels (Eds. Gurnell,A. and Petts, G.) John Wiley and Sons, Chichester, pp. 369-388.

Davis, M.L. and Cornwell, D.A. (1998) Introduction to Environmental Engineering. WCB McGraw HillCompany, 3rd Edition.

El-Shami, F.M. (1977) Environmental Impacts of Hydro Electric Power Plants. JHD, Proc. ASCE, Vol. 103, No.HY9, Sept., pp. 1007-1020.

FISRWG (1998) Stream Corridor Restoration: Principles, Processes and Practices. Federal Inter Agency StreamRestoration Working Group. National Technical Information Service, Springfield, Va (U.S.A.).

Gupta, H.K. (1992) Reservoir Induced Earthquakes. Development in Geotechnical Engineering, No. 64, ElsevierBook Co., Amsterdam, 364 p.

Goel, R.S. and Agarwal, K.K. (2000) River Valley Projects and Environment: Concerns and Management in Indiacontext. In Environmental Impacts Assessment in Water Resources Projects (Ed. Goel, R.S.), Oxford and IBHPublishing Co., New Delhi, pp. 71-87.

Indiresan, P.V. (2000) Dams or Damn: Perceptions and Facts. In Environmental Impacts Assessment in WaterResources Projects (Ed. Goel, R.S.), Oxford and IBH Publishing Co., New Delhi, pp. 89-103.


Kolhi, S. and Bhandari, R.K. (1991) Reservoir Induced Seismicity in Peninsular India. Proc. Institution ofEngineers (I) Civil, Vol. 72, pp. 47-55.

Murthy, B.N. (1976) Men-made Lakes and its Effects on Ecosystem. CBIP (India), Miscellaneous Publication No.6, 26 p.

OSMG (2004) Natural Stream Processes. Ohio Stream Management Guide No. 3, 8 p.

Raghuvanshi, A., Mathur, V.B. and Mukherjee, S.K. (2000) Hydropower Projects and Challenges to WildlifeConservation in India – An Overview. In Environmental Impacts Assessment of Water Resources Projects(Ed. Goel, R.S.) Oxford and IBH Publishing Co., New Delhi, pp. 389-401.

Ruane, R.J., Vijander, S. and Nicholas, W.R. (1977) Aeration of Hydro Releases at Fort Patric Henry Dam. JHD,Proc. ASCE, Vol. 103, No. HY10, Oct. pp. 1135-1145.

TCEEHS (1978) Environmental Effects of Hydraulic Structures. Task Committee on Environmental Effects ofHydraulic Structures. JHD, Proc. ASCE, Vol. 104, No. HY2, Feb. pp. 203-221.

Vaidhankar, D.V., and Deshmukh, D.N. (1992) Environmental Effects of Hot Water Releases From Power Plantsand Some Practical Aspects of Regulation Acts in India. Proc. of 1st National Symposium on EnvironmentalHydraulics, CWPRS, Pune (India), June 1992, pp. 274-293.

Vaidya, S., Swain, K.K., Kamble, K.J. and Basu, A.K. (2004) Tropic State of Panchet and Ujjani Reservoirs inRelation to Phosphorus Concentration and Other Factors. International Conference on HydraulicEngineering: Research and Practices. IIT Roorkee (India), Vol. 2, Oct. pp. 407-416.

15C H A P T E R

Data Requirements forMorphological Studies

15.1 INTRODUCTION

When one plans to develop the water resources of the basin and utilise them fully, it is necessary to havethe master plan for the development which will take into account the needs of the population at presentand in near future, and the potential for development of the water resources. Such a plan may includeconservation of water for irrigation, domestic and industrial use, power generation, flood control toprotect certain areas from flooding, and channel improvement for stabilizing the river channel to makethe whole or part of the stream navigable. It may also include use of water bodies for recreationalpurposes and environmental management of the basin. Further these developments may have to becarried out on the main river and the tributaries. In all probability these developments would be executedover a long period spanning a few decades, even though the general overall plan may be developed inthe initial stages, and based on the experience gained and the performance of the project during earlierstages, the plan may be modified later.

Irrespective of the details about the development, the engineer concerned with planning must carryout the morphological study of the river which would indicate the present health of the river and wouldalso indicate how the river regime would change after the developmental works are executed. Such amorphological study is essential for every river. Even though some data required for such a study will bepurpose specific, it is possible to discuss, in general, about the data required for the morphologicalstudies and their significance. Geologists, hydrologists, hydraulic engineers, cartographers,archaeologists and other scientists collect these data.

15.2 MAPS, AIR-PHOTOS, SATELLITE IMAGERIES

An index map showing the river reach under consideration and on which are shown the majortributaries, locations of various structures (weirs, dams, bridges) on the river, gauging-sites and

Data Requirements for Morphological Studies 443

important cities is the starting point. Further information can be obtained from topo-sheets; topo-sheetswould give information about valley or river slope, rough idea about plan-form of the river, and changesin it along the stream length. If such older topo-sheets are available it is possible to examine them to findout if the river has tendency for shifting its course or changing its plan-form; also range of shifting andcontrol points can be identified. Such control points are of great use in locating bridges and barrages.Aerial photographs for general purpose (1:50000 scale) and for special purpose (1:10000 to 1:5000scale) that can cover 10-15 km length of the river can be used for the same purpose. Such photographsare also utilised to study changes in the channel induced by human activities such as regulation,reservoir construction, gravel dredging, deforestation, afforestation, changes in agricultural practice,urbanisation, mining activity, bank stabilisation, and channel straightening. Also considerableinformation about the terrain surrounding the valley, valley features, terraces, floodplain, presence ofbars and channel patterns, ox-bow lakes and abandoned channels can be obtained from suchphotographs. In this connection one is referred to an excellent publication by Kellerhals et al. (1972)that gives a set of aerial photographs of some rivers in Alberta (Canada) along with relevant hydraulicdata. Historical changes in the river can many times be discerned from archaeological excavation as wasdone in the case of the Tigris river in Mesopotamia (Modern Iraq) and the river Saraswati in India. Sincein the earlier times the villages or the settlements used to be located on the banks of the river, it waspossible to find out the changes in the courses of the Tigris, Euphrates and Diyala from archaeologicalexcavations, see Garde (1978). Figure 10.4 shows the present and ancient course of the Tigris.

Historical data on channel changes can be studied in relation to the climatic, hydrological andenvironmental changes that have taken place in earlier times. Hence such information is very valuable.

Remote Sensing (Lillesand and Kiefer 1994)The technique of remote sensing derives information about the objects on the earth’s surface withoutphysically coming in contact with it. The process involves (i) making observations using sensorsmounted on platforms; (ii) recording the observations on a suitable medium; (iii) transmission of data tothe ground station; (iv) corrections to data to remove geometric and radiometric distortions, which iscalled pre-processing; and (v) generation of output in the form of photographic enlargements withappropriate rectification. These are called satellite imageries.

The sensors used are either active sensors or passive sensors. Sensors, which illuminate the targetwith energy and measure the reflected/scattered radiation from the target are called active sensors e.g.,active radiometers and radars. Sensors which sense reflection/radiation from the earth illuminated by anatural source such as the sun are called passive sensors. While discussing about the sensors the spatialresolution and spectral resolution need special mention. Spatial resolution is the length of the side of thearea on the ground represented by a picture element (commonly called as pixel) on the image. Spectralresolution is the width of the spectral band and the number of spectral bands in which the image is taken.Narrow band widths in certain regions of electro-magnetic spectrum allow one to discriminate variousfeatures more easily. Hence one needs to have more number of spectral bands each having narrow bandwidth and these bands together should cover the entire spectral range.

The sensors are mounted on a platform such as a balloon, an aircraft or a satellite, which are at aconsiderable height from the earth’s surface. The size of the object that can be discriminated by thesensor depends on the resolving power of the sensor and the height of the platform. As one goes higherand higher, larger areas can be seen and covered by the sensor; however the size of the object appears

River Morphology444

smaller as one goes higher and in fact certain objects may not be seen at all beyond a certain height. Thesatellites used for remote sensing are of two types, namely geostationary and near earth, polar orbiting.Geostationary satellites are stationary with respect to the earth and are at an altitude of about 36000 km.These are used for meteorological applications. Near earth, polar orbiting satellites are at a much loweraltitude, a few hundred to few thousand kilometres.

In India, the National Remote Sensing Agency (NRSA) at Hyderabad has been carrying out airborne remote sensing surveys on behalf of various users. With the flight facility, air surveys from about150 m to 10,000 m altitude can be carried out. The sensors available with NRSA are aerial surveycameras, air borne multi spectral scanner, air borne magnetometer systems, ocean colour radiometer andside looking air borne radar. NRSA also acquires data from Indian and various other satellite missions.Some of these are IRSA-1A, 1-B, 1-C, 1-D, IRS-P2. Satellite radar data are also available from ERS-1,ERS-2 and Japanese Earth Resources Satellite Fuyo-1, in addition to Landsat and SPOT archival data.Similarly very high resolution data are available from Russian DD-1, KVR-100 and KFA-3000 systems.Their ground resolution varies from 70 m to about 2 m.

The data are recorded in high density digital tapes (HDT) or digital linear tapes (DLT), CD-ROMS,or 8 mm exabyte digital tapes on a variety of media and formats such as photographic products [blackand white, false colour composite (FCC)] and digital products (CD-ROMS and DATS). These dataproducts can be effectively used in morphological, water resources and other studies. To obtain satellitedata one needs to specify

i) area of interest i.e., latitude and longitude;ii) survey of India topo-sheet number;iii) satellite mission;iv) path and row;

v) date of pass; andvi) sensor.Knowing these details one can browse through the imageries at NRSA site for different dates of

pass and for different satellites and sensors and choose the desired ones

Digital Image ProcessingVisual interpretation of an imagery or photograph requires extensive training and intensive labour, andthe special characteristics are not always fully evaluated because of limited ability of the eye todistinguish tonal values of an image. Hence, in the applications where spectral patterns are highlyinformative, it is preferable to analyse digital, rather than pictorial image data.

The digital image data are composed of a two-dimensional array of discrete picture elements orpixels. The intensity of each pixel corresponds to the average brightness or radiance measuredelectronically over the ground area for that pixel. In digital image data, each pixel in a grid stores adigital number (DN) which is a positive integer quantifying original electrical signal from the sensor,using analogue to digital conversion. Typically the DN values of the digital image range from 0 to 255,the range representing the set of integers that can be recorded using 8-bit binary computer coding scale.

The digital image processing (DIP) involves manipulation and interpretation of digital images withthe aid of computer. The digital image is fed into the computer one pixel at a time. The computer isprogrammed to insert these data into an equation or series of equations, and store the results of the


computation for each pixel. These results form a new digital image that may be displayed or recorded inpictorial format or it may be further manipulated by additional programme. The digital imageprocessing further involves three operations namely, (a) pre-processing (b) image enhancement, and(c) image classification. Pre-processing operation involves the initial processing of data to correctgeometric distortions, to calibrate the data radiometrically, and to eliminate noise present in the data.Image enhancement operation involves use of techniques for increasing the visual distinctions betweenfeatures in the scene in order to increase the amount of information that can be visually interpreted fromthe data. The enhanced image can be displayed on the monitor or can be recorded in a hard copy formatin black and white or in colour. Image classification is done to automatically categorise all pixels in animage into land cover classes or themes. Normally multi-spectral data are used to perform the imageclassification. Such classification can distinguish land mass, water bodies, vegetal cover etc.

Remote sensing can be used to study the following aspects of river morphology:1. flood inundation mapping,2. variability and changes in channel plan-form,3. flood plain geomorphology–identification of flood plain features such as ox-bow lakes, levees,

scroll bars,

4. identification of bank erosion zones,5. vegetal cover in the catchment and its variation, and6. types of land use in catchments including agricultural, urban and industrial developments and

their spatial and temporal variation.The special advantage of remote sensing lies in the fact that data can be obtained at regular intervals

of time and hence time varying phenomena in river morphology can be monitored and studied. Further,some areas may be inaccessible and hence visiting such places and collecting data may be otherwiseimpossible; in such situations remote sensing methods are useful.

15.3 LITHOLOGY AND TECTONICS

Information about lithology is important to the river engineer in many ways. Some information on thetype of rocks underlying the surface material is provided on the geomorphic map. Additionalinformation can be collected from bore hole data at bridge and dam sites, from bore wells and othersources. Such data can be used to prepare lithological map.

The infiltration, soil erosion from the catchment and overland flow are affected significantly bylithology, in addition to climate, vegetation, the rock type and structure, the drainage structure, drainagedensity and drainage frequency. River channel shape and longitudinal slope also depend on rock type;the plan-form of the river is also controlled by the material through which the river passes. Further,lithology governs the initial particle size of the bed material, its resistance to abrasion and therefore thereduction of sediment size along the river length. The reduction in slope along the length is related toreduction in sediment size and hence to lithology.

The occurrence of large and medium earth quakes in the basin brings about important changes inthe river regime because large quantity of sediment can be brought into the tributaries and main riverdue to land slides triggered by the earthquakes. A map showing major faults, and locations of suchearthquakes along with their magnitude should be prepared. There are instances where rivers have been

River Morphology446

completely blocked due to such land slides and subsequently causing flash flood wave due to bursting ofearth embankments, and ultimately affecting the river channel dimensions and plan-form.

Slow uplift and subsidence of land is commonly known as neo-tectonics. Neo-tectonic activity canalso include significant rates of movement along faults. Such slow uplift or subsidence of a fewcentimetres per decade can cause perceptible change in the river slope which in turn causes large scalecutting or deposition in the channel, widening of the channel, meander cut-offs and such other changes.Such changes have occurred in the Mississippi river during 19th century and in the case of the Diyalariver, a major tributary of the Tigris river in Iraq. A progressive uplift over 6000 years caused the Diyalato incise about 15 m, see Schumm (1977). Hence, such tendencies need to be noted in the region underconsideration and its probable effect assessed. Various fluvial anomalies such as local development ofmeanders or braided pattern, local narrowing or widening of channel, anomalous ponds, alluvialmarshes or alluvial fills, variation of levee width, discontinuous levees, or variation in sinuosity arepossible indications of neo-tectonics.

15.4 VEGETAL COVER

The information on land use and vegetal cover is required for hydrologic studies as well as for theestimation of erosion rates. This information can be obtained from State Departments of Irrigation,satellite imageries and also from Irrigation Atlas maps prepared by the Government of India. Vegetalcover can be classified as arable area, scrub and grass lands, forest area and waste lands, their percentarea found out and vegetal cover map for the area can also be prepared. Changes in land use will changethe vegetal cover and affect discharge and erosion rate. Hence historical data on vegetal cover can beextremely useful in explaining change in erosion rate with time.

15.5 GEOMORPHIC MAP

Geomorphic map is a map which includes relevant landforms, materials, and processes. Such a map isprepared using a set of efficient symbols, which are recommended by technical committees, and use ofcolour systems. Such a geomorphological map which may contain a lot of unwanted information can beconverted into a purpose oriented map carrying only that information which is necessary for a specificuse. Geomorphic maps are extensively used in planning and economic development related to regionaland territorial planning, agriculture and forestry, civil engineering, and prospecting and exploitation ofthe natural resources. Geomorphological mapping as it is known today was first used in Poland in1950’s and has been extensively used in Europe, USA and other countries. Information that can beincluded on a geomorphic map for river development can be changes in land slope and sharp junctions;if necessary contours can be shown by different colour. Depending on the requirement the mappingscale can be 1:10000 to 1:75000. Bedrock as well as geologic structure and superficial material can beshown. The symbols used for slopes, rocks, geologic structure, and superficial unconsolidated materialsare shown in Fig. 15.1. Forms of fluvial origin such as streams, channels, point bars and oxbow lakescan also be shown. Slope instability features are also shown in the map using brown colour. In addition,symbols are also recommended for showing geologic structure etc. These symbols are shown in Fig.15.2. Such a map can be of immense use in the initial stages of planning of the project. Cook andDoornkamp (1978) have shown a typical geomorphic map for an area in South Africa, see Fig. 15.3.

River Morphology447

Fig. 15.1 Symbols for superficial unconsolidated material

Gravel

Sand

Silt

Duricrust

Boulders angular

Boulders rounded

Clay

Shells

Peat

Symbols for bed-rock lithology

SnaleC

Mudstone

Siltstone

Gabbro

Rhyolite

Schist

Gneiss

Sandstone

Breccia

Conglomerate

Andesite

Basalt

Migmatite

Marble

Chalk

Limestone

Dotomite

Igneous Granite

Diorite

Metamorphicquartzite

State phyllite

Sedimentary

Angular convexbreak of slope

Angular concavebreak of slope

Smoothly convexchange of slope

Smoothly concavechange of slope

Angle of slopedegrees

Cliffs (bedrock 40° or more)

Break of slope concave & convextoo close together

Change of slope to allow use ofseparate symbols

Convex slope unit

Convex slope unit

Morphological mapping symbols

River Morphology448

Fig. 15.2 Geomorphic symbols

Symbols for geological structure (usually shown in purple)

Slope instability features (usually shown in brown)

Symbols of fluvial origin (usually shown in blue)

Lovees

Point bars

Erosion terrace

Accumulationterrace

Alluvial fan

Delta

Swamp

Permanent lake

Temparary lake

Area susceptibleto flooding

FLUVIAL EROSION OF SLOPES

Rill

Gully

Sheet

Badlands

Stream

River channel

Dry river channel

Later fall (rapids)

Spring

Sand bar

Cut-off meander

Oxbow lake

Landslide (type undetermined)

Rotational slide (with back tilt)

Non circular rotational slide with graben

Flow slide

Mud slide

Sand run

Rock fall

Solifluction lobe

Soil creep

Horizontal strata

Dip and strike(dip in degrees)

Vertical strata(long axis is strike)

Overturned strata

Anticlinal axis(plunge in degrees)

Synclinal axis(plunge in degrees)

Joints (lines showtrue or ientation)

Tick on downthrownside, made in degreesthrow (T) in metres

Showing relativemovement of thetwo sides

3

3

1 1

1 1

T 150

20

Faults


15.6 BASIN CHARACTERISTICS AND MORPHOMETRY

River processes are largely controlled by the topography of the drainage basin. A river tends to shifttowards the position of topographic minimum, as observed in the case of the river Kosi in North India.Such topographic minimum occurs commonly due to subsidence. Topography also affects the manner inwhich the deposition takes place on the flood plain. Overbank deposits preferentially occur in low areaswhere the velocity is small, increasing the rate of aggradation at these sites and producing variation inthe thickness and facies.

The catchment characteristics that should be studied are catchment area, its shape, averagecatchment slope, vegetal cover characteristics, average drainage density and such other characteristicswhich affect the erosion rate in the catchment and determine the nature and magnitude of floodhydrograph.

The morphometric parameters of a river basin assume great importance since they influence anumber of hydrologic processes operating in the basin. Horton initiated the work of characterisation of

Fig. 15.3 Typical geomorphic map (Cook and Doornkamp 1978)

Narrow out crop of quartzite

Accumulation terrance

Major river incision

Ridge

Rock wall-graniteRock wall-quartzile

Planation surface

Residual hill

Crest of residual hill

Angular crest of residual hill

MorphologyLithology Slope movement

Granite

Quartz vein

Igneous complex(mainly schist)

WIthwater sand system(quartzite and shale)

Strike of dipping beds

Fault

Fault (inferred)

Talus slope-grass covered

Slump

Group of small slumps

Superfical creep

Drainage

Permanent water course

Impermanent water

Rill erosionGullery erosion

Spring

Gr GrSc

ScGr

Sc

Sc

ScSc

Sc

Ws

Ws

Gr+

+Sc

Ws

Q

Structure

River Morphology450

river networks and then significant contributions were made Strahler, Shreve and Schumm. Amongthese parameters the area of the catchment A plays an important role since flood discharge is related toA by many investigators e.g. Dicken, Ryve, Inglis, Emmett and others by equations of the form

Q = const An ...(15.1)

Other morphometric parameter is drainage density Dd km-1, which depends on lithology, geologicstructure and soil characteristics of the basin. Drainage density will be higher in hard rock terrain whichhas low permeability. Greater amount of vegetation reduces the drainage density. Since drainagechannels convey water and sediment from catchment area to the stream, importance of drainage densityin the river processes can be appreciated. Along with other parameters erosion rate from the catchmentdepends on the drainage density and average catchment slope.

Slope as a relief parameter not only affects velocity and sediment transport, but also affects the plan-form. Hypsometric curve that shows percentage of total elevation plotted against percent of total area,provides a representation of the erosional development of the drainage basin and should be prepared.

The morphometric parameters are also useful in constructing the geomorphic instantaneous unithydrograph (GIUH) in which the peak discharge and time to peak are related to Horton’s numbers RA,RB, RL and internal scale parameter L

W and mean velocity of stream flow U-, see Rodriguez-Iturbe and

Valdes (1979).

15.7 SEA-LEVEL FLUCTUATIONS, CLIMATIC AND OTHER CHANGES

The relative sea level changes over a period of time can occur either on global scale or on regional scale.Global changes occur because of the mechanisms affecting the sea level worldwide; on the other handthe regional changes are caused because of uplift or subsidence of the land. On global scale the sealevels rose rapidly during 5000 B.C. and 3000 B.C. when the former ice sheets of the ice age melted.According to Gribben and Lamb (1978) between 2000 B.C. and the present the sea levels may havedropped by about three meters, while at present times the sea level is rising at the rate of 1 mm per year.Similarly significant changes in sea levels were observed on the east and west coast, and the Cauveri, theMahanadi and the Godavari deltas in India during 5000–10000 years B.C. Even though these changesover a span of few decades may not be important, they would play an important role in river geometry,plan-form and aggradation/degradation over a period of centuries.

The climatic changes have been discussed in the chapter on Palaeo hydrology. The changes inprecipitation and temperature affect the vegetation, and runoffs as well as the sediment yield from thecatchment. As these parameters control the river behaviour, they directly influence the channel plan-form and geometry. Therefore a river morphologists needs to collect the data on palaeo climatic andpalaeo hydrologic changes, along with long term changes in the sea level and carefully assess theireffect on the historical changes in the river.

In addition detailed information be obtained on human activity in the catchment such as mining,road and other construction activity and deforestation or reforestation, which can directly influence theriver flows and sediment load.


15.8 CROSS-SECTIONS, LONGITUDINAL SECTION AND PLAN-FORM

The cross-sections and the longitudinal section for the river reach and its tributaries under investigationconstitute the basic information required for hydraulic calculations. The cross-sections shouldpreferably be taken at regular intervals along the reach and in addition at important places such asgauging stations, bridges, sharp contractions and at hydraulic structures. The cross-section should coverthe entire width of the channel and flood plains on both sides up to permanent banks (khadirs). Oneshould mark on each section the lowest, mean and maximum water levels along with point of minimumelevation, and also record information about the nature its occupancy of flood plain. An average cross-section in a given reach is often required for hydraulic and sediment local calculations. Sliding thecross-sections so that the average bed levels of the sections coincide and then tracing the average sectioncan obtain this.

The longitudinal section should be prepared from the average bed levels of the main channel at eachsection and on it one should show where the tributaries join as well as the locations of important placesand gauging stations. Mean annual discharges of tributaries and main river can also be shown at criticalsections. Similarly the bed slope in different reaches can be shown on the longitudinal section. Thelocations of important structures such as dams should also be depicted. The cross-sectional andlongitudinal section data are useful in the calculation of water surface profiles as well as in assessingaggradation or degradation in subsequent periods. The knowledge of low water levels at a few sectionsover a period of time can be utilised to determine the changes in bed levels.

A map or maps showing the plan-form of the river in the river-reach under consideration is alsoessential. Such a map shows plan-form of the river in different reaches, acute bends and meander loops,ox-bow lakes, unstable reaches of river, location of bridges, barrages and proposed locations ofstructures, and the talweg. Such information about cross-sections, longitudinal section and mapshowing plan-form is needed not only for main river but for the tributaries also. A preliminary studyshould also be made as average bend radius to channel width ratio as well as its minimum values. Thisinformation is useful in design of guide bunds and cut offs.

The river plan-form is classified into straight, meandering and braided. One parameter often used inriver plan-form analysis is sinuosity. Normally sinuosity is defined as the ratio talweg length to thelength along the valley. However, Friend and Sinha (1993) have proposed that instead of talweg length,one should use mid-channel length in defining sinuosity. According to them the revised definition canbe used for a single or multiple channels; in the case of multiple channels mid-channel length of thewidest channel in each reach of the channel belt can be taken.

For braided rivers, normally some form of a braiding index is used; however its definition variesfrom one investigator to other. Brice (1964) defined it as

Braiding Index = Sum of length of all islands or bars in a reach

Length of reach measured midway between banks of channel belt

According to Rust (1978)

Braiding Index = Sum of length from / divergence to / convergence of surrounding talwegs

Mean of meander wave length for each channel belt

u s d s

River Morphology452

Another parameters used for describing channel is its width/depth ratio. This ratio is related tocharacteristic discharge by Leopold and Maddock (1953), while it is related to Q and bank silt/claypercentage by Schumm (1977). The entrenchment of river can be quantified by the ratio

Entrenchment Ratio = width of flood plain

width of main channel

While collecting data on river reaches of a dynamic river system for the purpose of its management,it is necessary to classify the reach on the basis of ordering of river network as done first by Horton (seeChapter 2), on the basis of plan-form and river sinuosity into straight, meandering or braided, accordingto channel size, or for management purposes based on lateral erosion or deposition, aggradation,degradation or armouring, susceptibility to disturbance, etc. If repeated river channel cross sections andplan-form surveys are not available, it is difficult to ascertain river channel adjustment that may takeplace over a period of 10 to 100 years especially if changes in channel depth are needed which cannot beobtained from aerial surveys. For this purpose the National River Authority of U.K. (NRA 1990) hasdeveloped a system to classify river channel susceptibility to disturbance. The site visit utilises thefollowing scheme to classify the susceptibility of reach to disturbance and entered in GIS.

Table 15.1 NRA (1990) Classification of river channel susceptibility to disturbance

Susceptibility Score Descriptionto change

High 8-10 Channel conforms to natural state, exhibits signs of free meandering and has fullydeveloped point bars, pools–riffles

Moderate 5-7 Shows signs of previous alterations but has many natural features and showstendency towards recovering to higher state

Low 2-4 Substantially modified by previous works, likely to possess artificial cross-section,no bank-side vegetation.

Channelised 1 Channels where bed and banks are provided with hard protection

Navigable 0 High level of flow regulation, bank protection and needing strategic dredging

Based on the experience of river channel adjustments in the Thames basin, U.K., the followingclassification for lateral and vertical adjustments is evolved (Downs 1992, 1995).

Stable SDepositiond DLateral migration m R M

Enlargement e C U EStable Deposition Lateral

migration Enlargement


Channel Adjustment CategoriesS - Stable m - Less severe lateral migration

D - Deposition e - Less severe enlargementM - Lateral migration R - Recovery reachE - Enlargement U - Undercutting reachd - Less severe deposition C - Compound reach

Here category C represents channel-indicating aggradation with erosion of channel banks; categoryU represents continuous erosion and migration of full width channel with coarse inner bank deposits.Similarly, Rosgen (1996) has provided a scheme for management of rivers. This is based on thedevelopments since 1973 and makes use of extensive data dominant bed material, river slope, width todepth ratio, sinuosity and entrenchment ratio. This is briefly discussed in Chapter VII.

15.9 BED AND BANK MATERIAL

Information about the size distribution of bed and bank material is required in determining the resistanceto flow, estimation of sediment load, channel adjustment processes and in the analysis of problemsrelated bank stability and lateral erosion.

If adequate time and resources are available the bed material should be sampled at all the sectionsalong the channel in order to find out how the characteristics of bed material change along the riverlength; otherwise a few representative sections be chosen. Due to non-uniform flow across the channelwidth and change in lithology along the channel length, a large variation in size distribution can befound across the channel at a given section and along the river length. Hence, it is necessary to takeenough number of samples in a cross section and along the length. A core sample is preferred especiallyif dunes are present, the core depth should be approximately equal to the dune height. Such samples ina cross section can be mixed to form a composite sample, whose size analysis is carried out. For reliablesize distribution, the sample mass M used for the size analysis is related to d84 in mm as

M = 0.02 d843 0. ...(15.2)

where M is in Kg. For high accuracy the coefficient can be changed to 0.20 (see Jansen et al. (1979).Drag bucket or grab bucket sampler can be used for collecting the sample. These samplers have beendiscussed in detail by Garde and Ranga Raju (2000), Jansen et al. (1979) and Van Rijn (1986). In a fewcases especially at bends and point bars, the coarse surface material should also be sampled.

Size distribution of the sediment samples should be determined and it should be seen whether itfollows normal or log-normal distribution. From the size distribution curves d90, d84.1, d65, d50, d35 andd15.9 should be listed at all the cross sections since these sizes appear in resistance and sedimenttransport calculations. Also geometric standard deviation sg and Kramer’s uniformity coefficient bedetermined. The median size of bed material decreases in the downstream direction due to abrasion andsorting. In the absence of other perturbations such as joining of the tributaries, d50 decreases withincreasing in L as

d50 ~ const e–a L ...(15.3)

where the constant = size of d50 when L = 0 and a is a coefficient.

River Morphology454

As regards the bank material, it may be mentioned that in addition to the size distribution, other soilproperties may be also important since bank material is usually cohesive. The presence of clay mineralsplays an important role in the process of bank erosion. Water content, salt content and ion exchangeaffect the strength of clays. Leaching of salts from clay is found to reduce its strength to 1/100 to1/1000th of its original value. In general cohesive soils offer greater resistance to erosion and hence therewill be less sediment load in the case of cohesive banks.

Assessment of the bank material can be done with the help of Table 15.2.The shear strength of the soil, its effective cohesion, and plasticity index are some other soil

properties of interest when bank stability is considered. Table 15.2 gives the Field EngineeringEstimates of Plasticity Index.

Table 15.2 Field assessment of material (Cook and Doornkamp 1978)

S1 Very soft Easily moulded in fingers; shows distinct heel marks

S2 Soft Moulds in fingers with strong pressure; faint heel marks

S3 Firm Very difficult to mould in fingers; difficult to cut with hand spade

S4 Stiff Cannot be moulded in fingers; requires hand-picking for excavation

S5 Very stiff Very tough and difficult to move with hand-pick requires great effort for excavation

R1 Very soft rock Material crumbled under firm blows with sharp pick

R2 Soft rock Can be scraped and peeled with knife

R3 Hard rock Can be broken if hand specimen is hammered

R4 Very hard rock

R5 Very very hard rock

Table 15.3 Field engineering estimates of plasticity index (Cook and Doornkamp 1978)

Term Plasticity index Dry strength Field test

Non plastic 0-3 Very low Falls apart easily

Slightly plastic 4-15 Slight Easily crushed with fingers

Medium plastic 15-30 Medium Difficult to crush

Highly plastic 31 + High Impossible to crush with fingers

15.10 HYDROLOGIC DATA

A map showing the distribution of average annual rainfall over the catchment as well as averagemonthly rainfall distribution in the wettest month are always useful. In addition the rainfall distributionin the most severe storm that has occurred on the catchment is useful to the hydrologist. For meaningfulestimation of flood hydrographs, data of spatial and temporal distribution of rain in the catchment isessential. Hourly rainfall data for all stations in catchment is generally preferred. But for large


catchments daily or ten-day average rainfall data for period of 25 to 30 years is generally preferred. Inabsence of such data Isopluvial maps of IMD giving rainfall distribution over catchment for average andsevere conditions can be used. From these data the maximum, minimum, and average annualprecipitation over the catchment as well as its standard deviation can be obtained.

At the selected gauging stations along the river and at its tributaries, stage discharge relationsshould be available. In the absence of such a curve, the same can be prepared by using one of theresistance relationships discussed in Chapters 5 and 7. In addition, at a few selected gauging stations oneshould have yearly hydrographs from which water availability can be assessed. Flow duration curve atthe gauging site is required in assessing yearly sediment transport and hence it should be prepared fromall available data. From these data maximum, minimum and mean discharge can be obtained along withthe corresponding stages or depths of flow.

Annual flood discharge series at critical gauging stations should be analysed, appropriateprobability distribution function fitted to the data and design flood discharges of known return periodshould be determined. The flood marks or flood levels during highest observed floods be obtained fromlocal enquires; these are very useful for extrapolation of water levels for design or higher discharges.

In the analysis of hydraulic geometry and related aspects of river morphology, various dischargesare used. The Indian practice is to use the bankful discharge and relate channel width, depth, meanderlength and meander width to it. Since in many situations the bankful discharge is not well defined, meanannual discharge which has a return period of 2.33 years has been used by Schumm (1977) and Leopoldand Maddock (1953). Some investigators also use average daily discharge for the whole year. Anotherdischarge which is often used in Europe is the bed generative discharge. This is a constant dischargeflowing through out the year that would carry the same amount of sediment load as carried by thevarying discharge. These discharges should be evaluated.

Knowledge of low discharge of a known dependability is useful in problems related to navigation,water supply, degradation of water quality, changes in water temperature, recreational use, andrecreation of water. The information usually required is 7-day low flow of 10 year return period. Givena stream flow record of 15 or 20 years, or more, the annual minimum flow for 1, 3, 7, 14, 30, 60, 90, 120,150 and 273 days can be obtained and a frequency curve prepared for each n – day flow. The frequencycurve can be defined graphically or mathematically.

For navigation studies along with the low discharge of known dependability, the width and thedepth of flow in the reach are also needed to assess use of the river for navigation, and to plan rivertraining works at low flows. The variation of low water level along the river length with time givestendency of the river to aggrade or degrade.

15.11 SEDIMENT LOAD DATA

Usually suspended load concentrations are measured at the gauging station along with the dischargemeasurement. If these measurements are not adequate, arrangements should be made to collect datawith increased frequency especially during the high flows. Before the suspended sediment data aresubjected to further analysis it is necessary to remove wash load from it since the rate of wash loadtransport is related to supply of sediment from the drainage basin whereas the rate of bed materialtransport is related to flow condition. Arbitrarily it is assumed that sediment load, finer than 10% size of

River Morphology456

bed material constitutes wash load. Thus knowing size distribution of suspended sedimentconcentration, the wash load can be estimated and removed. Knowing the average suspended loadconcentration and water discharge, the rate of suspended load transport can be obtained. Except in smallrivers it is not possible to measure the rate of bed-load transport even though some bed-load samplersare available. For preliminary study it is prudent to assume that the bed-load is a certain percent ofsuspended load, its actual value depending on the sediment size etc. Otherwise one of the bed-loadequations e.g., Meyer-Peter and Müller can be used. Some procedures are available for computingfraction wise bed-load transport. However, for preliminary analysis, such refinement may not bewarranted. The suspended or total sediment transport rate thus obtained can be related to waterdischarge Q, by a relation of the type

Qs or QT = const Qm ...(15.4)

where m may vary from 1.2 to 3.0. The sediment rating curve for Qs or QT can be prepared for differentsizes or different seasons. Such analysis is required to know the amount of sediment transported by theriver every year. It is also useful in aggradation/degradation studies. One can also obtain the bedgenerative discharge by combining the flow duration curve and QT vs Q relationship.

If any reservoirs have been built either on the main river or on its tributaries, their survey reportsshould be studied to obtain their rates of sedimentation. These give an idea about yearly sediment loadscarried by the tributary or main stream. In the same manner catchment erosion rates under the presentland use and urbanisation, as well as in the earlier times when human activity did not affect thecatchment characteristics. On the basis of these estimates, along with changes in the river channel andflood plain levels, the sediment balance in the river system should be studied. This may involverelatively large time span of few decades to hundred years. This type of analysis involving sedimentbudget, and channel and flood plain accretion or erosion has been modelled by Trimble (1995) who hasidentified five conceptual models of valley storage fluxes depending on the time variation of the process(quasi steady or unsteady), climatic region (arid or humid) and perturbations in it, human activity, andamount of energy available. Such analysis enhances our understanding of the fluvial processes andthrows light on the magnitude and time-scales of sediment storage fluxes under different environmentalconditions.

15.12 STRATIGRAPHIC STUDIES

The relationship between geomorphic processes and sediment is also important in understanding thehistory of rivers. Sediment on the surface is easily visible and can be easily studied as discussed earlier.The subsurface deposits in reservoirs, lakes, fans and deltas can be studied using techniques such assinking deep bore holes and examining the cores, using seismic reflection data from different layers orelectric log records. One can also see sediment exposed in sections in stream banks. Much informationcan be obtained from their studies. The basic rules followed by the geologists and geomorphologists instudying sediment in sections are (Kale and Gupta 2001):

1. Law of superposition: An underlying layer or strata is older than the overlying layer unless thestrata have been disturbed.

2. Any disturbance to a layer of sediment is post-deposition in time, for example faults.3. A vertical sequence of strata usually indicates a lateral continuing for the same strata.


These layered strata tell us about the operating process and the depositing environment. If thesurface of contact between the two neighbouring strata is smooth, it implies that the higher or upper onewas deposited over the lower one in an environment of small velocity without disturbing the lowerstrata. If the interface is wavy or uneven, it indicates erosion between two events of deposition. Thissequence can occur in two ways. A high velocity event such as rising flood may cause erosion while therecession of flood may cause deposition. The other way would be one event of high velocity wouldcause erosion of sediment and then another event may cause deposition. However, it is usually difficultto tell the extent of scouring of the lower layer. If a soil (palaeosol) occurs between two layers, it can beconcluded that considerable time has elapsed when neither erosion nor deposition occurred.

Geologists normally study the following properties of each stratum:Size classColour

ThicknessInternal structureBounding surfaceSpecial characteristics

Size class in general would be related to size of deposited material e.g., clay, silt, sand, gravel,pebbles or boulder. Larger size of sediment will indicate higher velocity while finer size would indicatea smaller velocity. Colour is an indication of the source of material from which the sediment is derived.It is also related to the environment in which the sediment is deposited or environment after itsdeposition. Presence of oxidised iron gives reddish tint while presence of organic material gives greyishtint. Thickness of the stratum is proportional to the amount of sediment carried by the flow. Further, ifthe sediment deposited is coarser, it suggests a high discharge event. The internal structure refers to thepattern in which the particles are deposited in the stratum. This is related to the flow velocity and particlesize. In the lower regime i.e. ripples and dunes in finer material, different types of cross bedding areobserved. When the flow is near critical and material is coarse sand, horizontal lamination is obtained.Thus by examining the change in structure inside a single stratum one can get information about theflow regime. The bounding surfaces of the stratum can also be interpreted in terms of erosion anddeposition as related to the flow velocity.

As mentioned earlier an erosional bottom surface indicates a relatively higher velocity which coulderode the previously deposited sediment. If mud cracks are present in the upper bounding surface alongwith rootlets, this is indicative of shallow flow condition of low velocity.

Special features to be noted in deposited material are the presence of animal and plant remains andcarbonate concretions (Kankars). Similarly sorting of coarse deposited material and their roundness canalso be noted. Exposed vertical section should be logged and graphical presentation be made. Also thesize distribution of deposited material in each stratum can be prepared and whether it is coarseningupwards or fining upwards be noted. Such analysis provides valuable information about the processescausing deposition. Some diagnostic characteristics of fluvial deposition are: erosion, sorting,stratification, shallow water features e.g. mud cracks and repetition of units in the vertical.

A facies is a body of sediment with a specific characteristic of its own. The characteristic can bebased on composition, structure, texture, fossil content, etc. The depositional facies have been classifiedby Miall (1977, 1996) and are shown in Table 15.3. In the same manner sediment deposits in braided

River Morphology458

and meandering streams have been studied and models built for variation in the texture and structure ofdeposits.

15.13 WATER QUALITY RELATED DATA

Since river water is used for domestic, industrial, recreational purposes as well as for irrigation, coolingwater and water power generation, it becomes necessary to collect relevant data on water quality toassess its suitability for specific uses. The water quality standards depend on type of water use as well ason the degree of development of the nation, and hence water quality standards vary from one country toother. The type of data deeded and its frequency of collection have to be, therefore, decided depending

Table 15.4 Description of deposition facies (Adapted from Miall 1977, 1996)

Facies Sediment texture Major sediment structure Morphological identificationnotation

Gmm Matrix– supported gravel Massive Pebris flow (plastic)

Gmg Matrix–supported gravel Vertical change in clast size Debris flow

Gm Predominantly massive Imbricated or horizontal gravel Channel bed deposits, longitudinalgravel with weak bedding, barssome sand or fines or fences

Gt Stratified gravel Trough cross bedding Small channel fill

Gp Stratified gravel Planar cross bedding Bars

St Very coarse to fine sand, Trough cross bedding Dunespebbles may be present

Sp Very coarse to fine sand, Planar cross bedding Bars and sand wavespebbles may be present

Sr Coarse to very fine sand Ripple marks, cross lamination Ripples

Sh Coarse to fine sand, pebbles Horizontal laminations and Plane bedsmay be present lineations of different types

Ss Very coarse to fine sand, Shallow, broad scours Small channel or scoureddepression

pebbles may be present fills

Ft Fine sand, silt and clay silt Very small ripples, rootlets Shallow deposition: in waning floodsand clay bioturbation, calcrete etc. abandoned channels, or overbank

Fsm Silt, clay Massive Backswamp, abandoned channelfills

Fra Carbonate deposits Massive, dessication cracks, Deposits draped around pools ofrootlets water in abandoned channels or over

bank

P Nodules, linear forms in Palaeosolspalaeosols


on water usage. These aspects will be decided by an expert on water quality and the engineers. However,certain general comments can be made.

For drinking water purposes the chlorides content, concentration of heavy metals such aschromium, copper, zinc, cadmium, mercury and lead need to be measured. Varying percentages ofheavy metal bond with sediment particles and can be transferred to agricultural land, and can eventuallybe absorbed by crops, grass, cattle and sheep. Non-biodegradable organic substances such aschlorinated hydrocarbons from pesticides and herbicides, and industrial processes such as paper millsalso need to be measured.

When water has to be used for thermal power plants for cooling purposes, temperature variation andlimits on it become important. For water used for irrigation purposes, the salt content is the mainparameter for determining suitability of water. It is known that large human settlements such as those inMesopotamia have disappeared in the past because of salinization of irrigation fields. Plants varyconsiderably in their sensitivity to a number of substances that are toxic (e.g., beryllium) or they have arange within which they are beneficial to plant growth and beyond which they have detrimental effect.

The important sources of pollution of stream water are municipal sewage, urban runoff, industrialwastes, agricultural runoff and natural pollution due to minerals and detritus from watershed enteringthe stream. Hence, some of the parameters commonly measured to assess water quality include BOD(biological oxygen demand), COD (chemical oxygen demand), TOC (total organic carbon), fixed andvolatile dissolved and suspended solids, chlorides, alkalinity, organic and inorganic phosphorus andnitrogen.

For water used for water power generation, the most important parameters are size, concentrationand composition of sediment entering turbines.

15.14 CATALOGUE OF INFORMATION ON MORPHOLOGICAL STUDIES

When one is entrusted with morphological studies of a given reach of the river with some specificobjectives, it is always beneficial to collect data on the river under consideration and adjoining similarrivers and prepare a catalogue or information listing the problem, how was it solved, how did the riverrespond to the changes made, what were the consequences of the river response? Such analysis of a fewsituations done with an objective approach, always gives valuable clues, albeit qualitative, about thepossible alternatives for managing the river under consideration. This can also suggest if certain aspectsneed to be studied on physical or mathematical model and the additional data that need to be collected.

References

ASCE (1980) Characteristics of Low Flows – Task Committee Report. JHD, Proc. ASCE, Vol. 106, No. HY5,May, pp. 717-731.

Brice J.E. (1994) Channel Patterns and Terraces of the Loup River in Nebraska. U.S. Geological Survey Prof.Paper 422-D, D1-D41.

Colby B.R., (1957). Relationship of Unmeasured Sediment Discharge to Mean Velocity. Trans. AGU, Vol. 38, No.5, Oct.

Cook R.V. and Doornkamp J.C. (1978) Geomorphology in Environmental Management. Clarendons Press,Oxford (U.K.), Chapter 14.

River Morphology460

Downs P.W. (1992) Spatial Variations in River Channel Adjustments : Implications for management in South- EastEngland. Ph.D Thesis, University of Southampton, 340 p.

Downs P.W. (1995) River Channel Classifications for Channel Management Purpose. In Changing RiverChannels (Eds. Gurnell A. and Petts G.) John Willey & Sons, Chichester, 16 – 347-365.

Friend P.F. and Sinha R. (1993) Braiding and Meandering Parameters. In Braided River (Ed. Best, J.L. andBaristow C.S.) Geological Society Special Publication, No. 75, London, pp. 105-111.

Garde R.J. and Dattatri J. (1963) Investigations of Total Sediment discharge of Alluvial Streams. RoorkeeUniversity Res. Journal, vol. 6, No. 2, pp. 65-78.

Garde R.J. and Ranga Raju K.G. (2000) Mechanics of Sediment Transportation and Alluvial Stream Problems.New Age International Ltd. Publishers, New Delhi.

Gregory K.J.(Ed) (1977) River Channel Changes. A Wiley Interscience Publication. John Wiley and Sons, NewYork, 450 p.

Gribben J. and Lamb H.H. (1978) Climatic change in Historic times : In climatic Changes (Ed. J. Gribben)Cambridge University Press, Cambridge, London, pp. 68-82

Jansen P. ph., Bendigo L. Van, de Vries M., and Zanen A. (1979) Principles of River Engineering – The Non-tidalAlluvial River. Pitman, London.

Kale V.S. and Gupta A. (2001). Introduction to Geomorphology. Oriental Longmans Ltd., Calcutta. 264 p.

Kellerhals R. Neill C.R. and Bray D.I. (1972). Hydraulic and Geomorphic Characteristics of Rivers in Alberta.Research Council of Alberta, River Engineering and surface Hydrology Report 72-1, 54 p.

Lane E.W. and Borland W.M. (1951). Estimating Bed-Load. Trans AGU, Vol. 32, No. 1, April.

Leopold L.B. and Maddock T. (1953). The Hydraulic Geometry of River Channels and Some PhysiographicImplications – USGS Professional Paper 252, 57 p.

Lillesand T.M. and Kiefer R.W. (1994) Remote Sensing and Image Interpretation. John Wiley and Sons, Inc., NewYor. Chapters 1 and 7.

Miall A.D. (1977). A Review of the Braided River Depositional Environment. Earth Science Reviews, Vol. 13, pp.1-62.

Miall A.D. (1996). The Geology of fluvial Deposits: Sedimentary Facies, Basin analysis and Petroleum Geology.Springer Verlag, Berlin.

Münault A.V. (1986). Dendrochronology Applied to Mire Environments. In Handbook of HolocenePalaeoecology and Palaeohydrology. (Ed. Berglund B.E.) John Wiley and Sons Inc., New York. Chapter 18,pp. 371-385.

NRA (1990) River Stort Morphological Survey: Appraisal and Watercourse Summaries. Compiled by Brookes A.and Long H., National River Authority, U.K.

Olsson I.U. (1986). Radiometric Dating. In Handbook of Holocene Palaeoecology and Palaeohydrology (Ed.Berglund B.E.). John Wiley and Sons Inc., New York. Chapter 14, pp. 273-312.

Rodriguez–Iturbe and Valdes J.B. (1979) The Geomorphic Structure of Hydrologic Response. W.R. Research, Vol.15, No. 6, pp. 1409-1420.

Rosgen D. (1996) Applied River Morphology, U.S.A.

Rust B.R. (1978). A Classification of Alluvial Channel Systems. Canadian Society of Petroleum Geologists,Memoir 5, 187-198.

Schumm, S.A. (1977). The Fluvial System. A Wiley Interscience Publication. John Wiley and Sons Inc., NewYork.

Trimble S.W. (1995) Catchment Sediment Budget and Change. In Changing River Channels (Ed. Grunnel A. andPetts G.) John Willey & Sons Ltd., Chichester, U.K.


Van Rijn L.C. (1982). Sediment Transport – Part II : Suspended Load Transport. JHE, Proc. ASCE, Vol. 110, No.11, pp. 1613-1641

Van Rijn L.C. (1986). Manual : Sediment Transport Measurement. Delft Hydraulics Laboratory, Delft(Netherlands), March.

AA p p e n d i x

Outline of Report on RiverMorphology

1. OBJECTIVE

Discuss general and specific objectives in undertaking the specific morphological study. Detail out anyspecific information sought. Mention about the agency sponsoring the study and the terms of reference.

2. GENERAL DESCRIPTION OF THE CATCHMENT

Give general description of the location of the catchment, climatic conditions, description of the terrain,catchment area and shape, relief, average slope, surface geology, land-use, drainage density, tectonicand neotectonic activities, land slides.

Annual rainfall and its variation, storm distribution of rainfall and other rainfall characteristics,temperature ranges.

3. VALLEYS AND STREAM

Approximate width of the valley at the bottom and the top, depth, vegetation on valley walls, presence ofrapids, falls, oxbow lakes and rock-outcrops; valley slope and its variation along length, terraces—arethey present? How many? Their approximate widths, wide mountainous valley or stream cut valley,underfit or overfit stream and probable reasons for it.

Present condition of the stream-incised or flood-plain, flood marks, water level marks on hydraulicstructures and their use in discharge and water level estimates, approximate depth during floods,channel slope and its variation, qualitative description of bed and bank material and their sizedistribution, study of other engineering properties of bank material, analysis of bore hole data, variationof median size of bed-material and its standard deviation along length, presence of boulders and large

Outline of Report on River Morphology 463

material on the bed, tendency toward armouring, general description of bed features, their averageheight and length and three dimensionality.

Analysis and interpretation of data from archaeological studies, historical and travel records, aerialphotographs, old and new cartographic maps and satellite imageries about changes in river plan forms,river course, avulsion, channel slope and its variation; palaeo studies on palaeo channels, palaeo floodsetc.

4. HYDRAULICS OF THE STREAMS

Collection of hydraulic data from other agencies; analysis of discharge and sediment load data of thepast-ascertaining their reliability and consistency; study of Qs vs Q curve, estimation of 10-daily floodand sediment load graph; estimation of bankful discharge and bed-generative discharge; bed-load andwash load estimation; stage-discharge relationship, estimation of Manning’s n and its variation.Analysis of width, depth, area of stream, and meander characteristics and plan forms and comparisonwith results from established methods to identify any anomalies.

Analysis of floods and low flows: flood records, maximum, minimum and mean annual flood;analysis of flood series to estimate floods of different return periods used by engineers in the design,map of area of flooded, analysis of low flows.

Estimation of average erosion rate of catchment and its discussion, variation of plan-forms as afunction of distance and time; such information is useful in the location of bridges, barrages etc.

Study of longitudinal profile of the stream as a function of time to see in which regions bed levelsare changing and find reasons for the same; estimate approximate rates of aggradation and degradation;similarly study reaches in which excessive erosion of bank line and bends is taking place.

Study of bed-level variation at existing bridges, spurs, barrages, guide banks and embankments andmethods used to control it.

Water-quality studies taking into account the general and specific requirement of morphologicalstudies.

5. MAN-MADE INTERFERENCES

Identify man-made interferences along the stream in the past and their effect on the river profile andplan-form; anticipate interferences of human beings that are likely to occur in future in order to fulfillthe objectives; comments on the analysis that can be carried out to study these effects.

6. MORPHOLOGY OF STREAMS IN THE REGION

Compare study of morphological problems in the stream under consideration and other streams in theregion. Find if such study can throw light on some of the problems.

7. RECOMMENDATIONS OF GENERAL AND SPECIFIC NATURE:

8. REFERENCES


blank

Author Index

Abbott, M.B. 362

Acaroglu, E.R. 159

Ackers, P. 160, 164, 249

Adachi, S. 350

Adams, J. 231

Agarwal, A.K. 298

Agarwal, K.K. 430

Agarwal, V.C. 203, 211, 220, 230

Agnihotri, R. 274

Ahmad, M. 171

Aich, B.N. 393

Alam, A.M.Z. 141, 143

Albertson, M.L. 91, 126, 133, 172

Allen, J.R.L. 92, 129, 315, 316

Ali, K.A.S. 384

Ananian, A.K. 285

Anil Kumar 133

Ansari, S.A. 296

Anstey, R.K. 102

Apmann, R.P. 193

Armstrong, C.L., 67

Arora, M. 230

Asawa, G.L. 425

ASCE 163

Ashida, K. 118, 371

Ashmore, P.E. 198

Bagnold, R.A. 159, 194, 249

Bajpai, I.P. 32

Baker, V.R. 273

Banerjee, D. 273

Barbarossa, N.L. 139

Baruah, B. 424

Baruah, B.B. 405, 407

Basu, A.K. 441

Bathija, T.S. 67

Bathurst, J.C. 230, 248, 249

Bayazit, M. 371

Bechteler, W. 164

Belleudy, P.A. 384

Bendegom, L.Van 312

Benson, M.A. 264

Berg, J. Van den 312

Berglund, B.E. 258

Best, J.L. 198

Bettess, R. 227, 248

Bhalerao, A.R. 296

Bhandari, R.K. 432

Bharadwaj, R.C. 167

Bhatnagar, S. 312, 384

Bhowmik, N.G. 234

Blakely, B.D. 49

Blench, T. 91, 171

Bloom, A.L. 75

Bogardi, J.L. 115

Bolt, B.A. 297

Bondurant, D.C. 283, 437

Borah, D.K. 383

Borgohain, J.K. 419

Borland, W.M. 52, 306

Bradford, J.M. 69

Bray, D.I. 108, 225, 230, 233, 234, 242, 243, 264, 460

Breusers, H.N.C. 288

Briaud, J.L. 296

Brice, J.E. 200, 451

Bridge, J.S. 104

Bristow, C.S. 198

Brookes, A. 440

Author Index466

Brooks, N.H. 140, 156

Brown, L.R. 35

Brownlie, W.R. 141, 162

Bruijnzeel, L.A. 22

Bruk, S. 52

Brune, G.M. 303

Brush, L.M. Jr. 95

Buffington, J.M. 113

Bull, W.B. 102, 300

Burr, G.S. 274

Callander, R.A. 202, 212

Campbell, P.L. 255

Cao, H.H. 248, 249

Carey, W.C. 126

Carlson, C.W. 25, 231

Carlson, E.J. 231

Carslaw, H.S. 346

CBIP 288

Chandra, S. 366

Chang, H.H. 173, 175, 178, 205, 209, 218

Charlton, F.G. 233

Chatley, H. 327

Chatterjee, P.K 54

Cheetham, G.H. 256, 265

Chen, W.L. 385

Chen Yuaner 167

Chen,Y. H. 365

Chien, N. 147, 317

Chitale, S.V. 89, 101, 389, 391, 400

Chollet, J.P. 384

Chorely, R.J. 184

Chow, V.T. 264

Church, M. 108, 225, 230, 233, 238, 313

Coleman, N.L. 154, 200, 409, 415

Colosimo, C. 230, 242

Condolios, E. 121

Cook, R.V. 446

Copertino, V.A 230

Cornwell, D.A. 438

Correia, L.R.P. 384

Cotton, C.A. 85

Coyle, J.J. 67

Craig, R.C. 76

Cross, B.V. 70

Cui,Y. 364

Culling, W.E.H. 345, 346

Cunge, J.A. 360, 362, 366

Dalrymple, T. 264

Dangler, E.W. 67

Daniel, J.F. 323

Daniel, P. 121

Dattatri, J. 67, 159

David, J.K. 165

Davies, B.E. 72, 279

Davies, L.B. 313

Davies, T.R.H. 198

Davis, M.E. 274

Davis, M.L. 87, 438

Davis, W.M. 9

Dawdy, D.R. 132

Day, T.J. 248

de La Cruz, C.d. R. 99

de Vriend, H.J. 194

de Vries M. 312, 345, 347, 354, 357, 364

Dekov, A.P. 52

Dendy, F.E. 34

Deshmukh, D.N. 436

Dhanju, M.S. 425

Dhruva Narayana 64

Diegaard, R. 332

Dietrich, W.B. 58

Diette, S. 369

Doornkamp, J.C. 446

Downs, P.W. 452

Doyle, W.M. 300

Drinker, P.A. 193

Du Boys, P. 5, 145

Dunne, T. 58

Durand, R. 121

Dury, G.H. 89, 90, 258, 265, 323

Dutton, C.E. 8

Eaking, H.M. 209

Eden, E.W. 126

Edgar, D.E. 198

Egiazaroff, I.V. 118, 279

Einhellig, R. 384

Einstein, H.A. 6, 122, 139, 147, 149, 155

Author Index 467

Eliassen, S. 284

Ellison, W.D. 48

El-Shami, F.M. 436

El-Swaify, S.A. 34

Elwell, H.A. 44

Ely, L. 273

Engelund, F. 133, 141, 160, 194, 196, 202, 212

Enzel, Y. 373

Esterbrook, D.J. 72

Ettema, R. 290

Evans, J.E. 300

Exner, F.M. 6, 356

F. A.O. 47, 57

Fargue, O. 5

Fergusson, R.I. 209, 335

FISRWG 439

Flemming, P.M. 227

Foster, G.R. 39

Fournier, F. 41, 47, 259

Fredsoe, J. 129, 202, 332

Friedkin, J.F. 203, 209, 327

Friend, P.F. 200, 202, 336, 451

Frisk, H.N. 316, 327

Fujita, Y. 221

Fullam, T.J. 126

Galay, V.J. 126, 283, 284

Gallagher, R.H. 385

Gandolfo, J.S. 180

Gangadharaiah, T. 165, 296

Garde, R.J. 4, 24, 64, 66, 86, 98, 115, 126, 133, 136, 140,143, 153, 155, 157, 159, 178, 187, 233, 234, 242, 254,282, 287, 296, 312, 303, 313, 318, 369, 394, 395, 411,453

GARMIN 54

Garrel, R.M. 68

Gee, E.P. 4, 106, 410

Gessler, J. 113, 114, 279, 286, 299, 369

Ghosh, B. 271

Gilbert, G.K. 5, 9, 209

Gill, M.A. 129, 149, 347, 349, 351, 353

Gill, G.M. 312

Gladky, H. 230

Glock, W.S. 12

Godbole, M.L. 395

Goel, R.S. 430

Gogoi, P.K. 424

Gohain, K. 392, 393, 400

Gole, C.V. 101, 389, 391

Golubstov, V.V. 242

Goncharov, G.N. 186

Goswami, D.C. 23, 407, 410, 413, 415, 416, 417, 423

Gottgen, J.F. 312

Graf, W.H. 159, 248, 249

Grass, A.J. 114

Gregory, K.J. 24, 257, 258, 315

Gribben, J. 450

Griffiths, G.A. 230

Griggs, R.F. 210

Grishanin, K.V. 246

Gudavali, R. 311

Gupta, A. 456

Gupta, R.D. 173

Gupta, H.K. 432, 433

Gurnell, A. 315

Hack, J.T. 76, 95

Handique, G.R. 419

Hansen, E. 133, 160

Haque, M.I. 126

Harbor, J.M. 312

Harrison, A.S. 156, 233, 369

Harvey, A.M. 323

Hasan, S.M. 369

Hathaway, G.A. 283

Hayashi, T. 118, 122, 203, 208, 212, 213, 219

Heede, B.H. 40

Heinemann, H.G. 303

Henderson, F.M. 217

Henderson, K.A. 274

Hey, R.D. 186, 230, 234, 241

Hickin, E.J. 204, 324

Hill, J.C. 365

Hines, W.G.S. 69

Hjulstorm, F.A. 210

Holeman, J.N. 35

Holly, F.M. 371, 384

Hong, L.B. 198

Author Index468

Hood, P. 385

Hooke, J.M. 324, 326

Horn, W.L. 311

Horton, R.E. 14, 17, 19, 26, 76

Hou, Z. 354, 356

Howard, A.D. 13

Hsia, C.S. 155

Hsu, S.H. 384

Hubbell, D.W. 122

Huber, E. 287

Hudson, N.W. 46

Hughes, H.J. 323

Hung, C.S. 161

Husain, Z. 273

Hutton, J. 8

Ichibashi, I. 166

Ikeda, S. 194, 220, 225, 239

Indiresan, P.V. 432

Inglis, C.C. 177, 204, 209, 233

Ippen, A.T. 193

IRTCES 301, 305, 310

Isaac, N. 126, 127

Ishizaki, T. 350

Islam, M.N. 294

Ismaghilov, H.A. 186

Ismail, H.M. 154

Itakura, T. 126

IWAI 424

Jackson II, R.G. 124, 237

Jaeger, J.C. 346

Jain, S.C. 210, 347, 351

Jain, V. 317, 388

Jakhade, G.S., 413

Janda, T. Dunne 68

Jansen, P. 276, 453

Jaramillo, W.F. 351

Jeffrey, H. 114

Jhonson, C.B. 70

Johnson, D. 83

Jones, D. 238

JSCE 143

Julien, P. 63

Jull, A.J.T. 274

Kale, V.S. 267, 268, 269, 456

Kalinske, A.A. 121, 153, 155, 157

Kamble, K.J. 441

Kand, C.V. 296

Kar, A. 273

Karahan, E. 113

Karim, M.F. 163, 371

Kawahita, R. 354, 356

Keefer, D.K. 10

Keller, E.A. 240

Keller, M.D. 126

Kellerhals, R. 91, 230, 233, 284, 443

Kennedy, J.F. 141, 143, 163, 194, 210, 356, 384

Khan, H.R. 329

Khanal, N.R. 31

Khosla, A.N. 38, 64

Kiefer, R.W. 443

Kikkawa, H. 194

King, L.C. 75

Kinnell, P.I.A. 45

Kinoshita, R. 203

Kishi, T. 202, 220, 222

Kitagawa, A. 194, 225

Klaassen, G.J. 276

Klingeman, P.C. 247

Knighton, A.D. 233

Kochel, R.C. 313

Kolhi, S. 432

Komura, S. 179

Kondap, D.M. 173

Kondratev, N.E. 207

Koster, E.H. 240

Kothyari, U.C. 24, 63, 64, 66, 231, 259, 287, 290, 411, 425,

Krishnan, M.S. 79, 80

Krishnappen, B.G. 365

Kuenen, P.H. 68

Kumar, A. 224

Kumar, R. 313

Kumar, S. 126, 270

Kuroki, M. 202, 220, 222

Kusumagar, M.G. 273

Lacey, G. 6, 143, 170, 233

Lamb, H.H. 450

Lane, E.W. 52, 72, 85, 88, 96, 126, 153, 155, 157, 199, 216,231, 240, 284, 297, 304

Author Index 469

Langbein, W.B. 25, 30, 44, 181, 210, 233, 258

Lara, J.M. 310

Laursen, E.M. 154, 158

Laws, J.O. 45

Leeder, M.R. 273

Lehre, A.K. 58

Leliavsky, S. 210

Leopold, L.B. 30, 41, 52, 88, 97, 177, 180, 184, 198, 209,210, 217, 230, 233, 240, 256, 315, 317, 329, 452, 455

Lewin, J. 209, 257, 315, 327

Lewis, G.W. 327

Li Guifen 320

Li, R.M. 69

Li, S.J. 385

Lidicker, A.C. 156

Lillesand, T.M. 443

Limerinos, J.T. 243

Lin, P.N. 274, 320

Little, W.C. 279, 281, 369

Livesey, R.H. 437

Lobeck, A.K. 321

Lovera, F. 141

Lu Jianyi 335

Lu, J.Y. 282, 369, 384

Lyell, C. 8

Lyn, D.A. 364

Macdonald, G.A. 311

Mackenzie, F.T. 68

Mackey, S.D. 312

Mackin, J.H. 2,84

Maddock, T. 52, 177, 180, 233, 310, 452, 455

Mahmood, K. 126, 303, 336

Maizels, J.K. 266

Malm, D.E.G. 31

Manandhar, I.N. 24

Mannering, J.V. 49

Mantz, P.A. 114, 126

Mathur, V.B. 441

Mayer, P.G. 279, 281, 369

Mazumder, S.K 325

McCool, D.K. 50

McLean, D.G. 255

Meade, R.H. 35

Mehta, P.J. 347, 350

Melhorn, W.N. 240

Melton, M.A. 26

Melville, B.W. 289

Meyer, L.D. 49

Meyer-Peter, E. 6, 146, 249

Miall, A.D. 199, 200, 457

Michalik, A.S. 230

Michiue, M. 118, 164, 371

Mikuni, N. 228

Milhaus, R.T. 230

Miller, C.R. 54, 306

Miller, J.P. 41, 68, 184, 226, 256, 335

Miller, V.C. 32

Milliman, J.D. 35

Mirkari, G.D. 309

Mishra, P.K. 273

Mishra, S. 273

Misri, R.L. 247

Mittal, M.K. 280, 347, 351

Mittal, R.S., 17

Mizuyama, T. 250

Mohan, J. 290

Molinas, A. 164

Mookerjea, D. 393

Morgan, R.P.C. 39, 43, 50, 63

Morisawa, M.E. 18, 21, 24

Mosley, N.P. 109

Mosley-Thompson, E 274

Moss, A.J 232

Mozzherin, V.I. 52

Mukhamedov, A.M. 186

Mukherjee, S.K. 441

Muller, R. 6, 146, 249

Münault, A.V. 460

Muramoto, Y. 221

Murthy, A.S. 426

Murthy, B.N. 430

Murthy, B.S. 286

Mutchler, C.K. 47

N.I.H. 313, 393

Nagao, T. 228

Nakatoh, T. 350

Namjoshi, A.G. 296

Nanson, G.C. 204, 324

Author Index470

NEDCO 179

Negev, M. 62

Neill, C.R. 115, 204, 233, 460

Neu, H.A. 209

Newson, M.D. 315

Nicholas, W.R. 441

Nicollet, G. 288

Nixon, M.A. 177, 180

Noble, E.L. 258, 259

Nomicos, G.N. 139

NRA 452

Odgaard, A.J. 194, 197, 231, 282, 369

Olsson, I.U. 460

Onishi, Y. 210

Osaki, S. 122

Osborn, J.F. 29

OSMG 429

Ouchi, S. 10, 106

Ozaki, S. 208, 212, 213, 219

Palaniappan, A.B. 362, 371

Panchang, G.M. 422

Pande, P.K. 157, 313, 425

Paris, W.E. 227

Park, C.C. 182

Park, L. 351

Parkash, B. 32, 392, 393, 400

Parker, G. 202, 203, 212, 220, 233, 234, 250, 384

Parola, C. 384

Parsons, D.A. 45

Patel, P.L. 118, 119, 150

Patil, B.M. 142, 145

Patton, P.C. 274

Pechinov, D. 69

Peltier, L.C. 26

Penck, W. 75

Perugu, S. 311

Pettijohn, F.J. 332

Petts, G. 315

Pickles, G.W. 327, 328

Piest, R.F. 40

Pitty, A.F. 98

Playfair, J. 8

Pogorzelski, H.A. 31

Powell, J.W. 8

Prakash, H. 230

Prasad, R.C. 24

Prashun, A.L. 370

Prus-Chacinski, T.M. 210

Quaraishy, M.S. 210

Quinton, J.N. 68

Rachocki, A. 101, 202

Raghuvanshi, A. 430

Rahman, A. 171

Rahuel, J.L. 365, 384

Rajagopal, H. 313

Rajesh Kumar 313

Rajguru, S.N. 273

Ram Babu 67

Ramesh, R. 274

Ramette, M. 209, 211, 220

Rana, S.A. 332

Ranga Raju, K.G. 118, 119, 136, 140, 143, 150, 153, 312,425, 453

Rao, K.L. 413

Raudkivi, A.J. 149, 154

Rendard, K.G. 50

Reynolds, A.J. 212

Rhodes, C.C. 183

Rice, R.J. 74, 78, 81

Richards, K. 240, 316

Riggs, H.C. 178

Rikson, R.J. 68

Robinson, A.R. 40, 43

Rodriguez-Iturbe, I. 29

Roehl, J.E. 40, 57

Rohan, K. 86

Rojas, R. 63

Rook, R. 230

Root, T.L. 260

Rose, C.W. 45, 60

Rosgen, D. 87, 92

Rotnicki, K. 269

Rouse, H. 113, 153

Rozovskii, I.L. 190, 196

Ruane, R.J. 436

Rubey, W.W. 180

Author Index 471

Ruhe, R.V. 10

Rundquist, L.A. 227

Rust, B.R. 202

Rzhanitsyn, N.A. 15, 87

Sahay, A. 312, 384

Sahay, R.N. 298, 400

Sangeet, S. 67

Sanyal, N. 400

Sarkar, A. 271

Sato 350

Sayre, W.W. 122

Schaffernak, F. 179

Scheideggar, A.E. 15

Scheuernlein, H. 286

Schick, A.P. 10

Schneider, S.H. 260

Schoklitsch, A. 209, 249

Schumm, S.A. 11, 17, 19, 25, 27, 38, 44, 74, 91, 104, 105,184, 198, 256, 258, 265, 315, 329, 330, 331, 452, 455

Schwarz, P. 384

Scott, C.H. 137

Scott, R.F. 311

Sethia, B. 312

Sethurathinam 426

Sharma, T.C. 64

Shen, H.W. 161, 210, 282, 288, 369

Sheshagiri Rao, R. 312

Shields, A. 111

Shimuzu, Y. 166

Shreve, R.L. 15, 30

Shukry, A. 193

Shulits, S. 86

Silva, J.M. 356

Silvester, R. 99

Simons, D.B. 62, 91, 172, 336

Singh, A.K. 224

Singh, I.R. 126

Singh, J. 369

Singh, R. 68

Singhvi, A.K. 273

Sinha, R. 200, 202, 317, 388, 451

Sinha, R.K. 400

Skovgaard, O. 202, 212

Smart, G.M. 249

Smart, J.S. 17

Smith, D.D. 46, 47

Smith, K.G. 14

Smith, N.D. 238

Smith, T.R. 181

Somayajulu, B.L. 274

Soni, J.P. 347

Sparks, B.W. 99

Speight, J.G. 209

Spomer, R.G. 69

Srivastava, R. 425

Stanley, E.H. 312

Steele, J.G. 67

Sternberg 86

Stevans, J.C. 283

Stevens, M.A. 69

Stocking, M.A. 44

Strahler, A.N. 14, 17, 25

Sukegawa, N. 203, 212, 220

Surya Rao, S. 312

Sutherland, A.J. 289

Swain, K.K. 441

Swamee, P.K. 303

Swanson, D.N. 68

Switsur, V. R. 426

Tamai, N. 227

Tangri, A.K. 317

TCEEHS 430, 433

TCPSM 52

Thomas, W.A. 370

Thompson, L.G. 270

Thompson, S.M. 255

Thornbury, W.D. 13, 82

Thorne, C.R. 186, 230, 257

Thornes, J.B. 273

Ting, F.C.K. 311

Tinkler, K.J. 7

Tiwari, A.K. 44, 68

Tiwari, S.K. 313

Tobes, G.H. 209

Todd, O.J. 284

Tricart, J. 53

Trimble, S.W. 59, 456

Tsuchiya, B. 350

Author Index472

U.N.E.P. 69

U.S. Govt. and IIHR 69

U.S.S.R. National

Committee for I.H.D. 69

UNESCO 301, 305, 310

Vaidhankar, D.V. 436

Vaidya, S. 435

Valdiya, K.S. 411

Van Rijn, L.C. 69, 129, 157, 164, 241, 242, 453

Vanoni, V.A. 139, 140, 154

Verwey, A. 384

Vetri, M. 230

Vetter, C.P. 283

Vetter, M. 164

Vijander, S. 441

Vischer, G.S. 232

Vittal, N. 162, 347, 351

Vreugenhill, C.B. 345, 354

Wadia, D.N. 79, 80

Walling, D.E. 24, 35, 57, 58

Wallis, I.G. 209

Walters, W.H. Jr. 107

WAPCOS 407, 413, 422

Weaver, W.E. 109

Wei, G. 311

Weller, H.E. 420

Werner, P.W. 210

Wharton, G. 186

Whetten, J.T. 126

White, W.R. 160, 164, 175, 248, 249

Williams, G.P. 177, 264, 265

Williams, M.A. 45, 48

Winkely, B.R. 331

Wischmeier, W.H. 46, 47, 48

Wolman, M.G. 41, 88, 97, 184, 198, 209, 217, 230, 317, 323,335

Woodyer, K.D. 227

Worcester, P.G. 1, 74, 321

Wõrman, A. 296, 329

Xu Fuling 320

Yalin, M.S. 113, 114, 126, 129, 149

Yamaguchi, H 166

Yang, C.T. 161, 164, 209

Yang, G. 384

Yang, J.C. 384

Yao, T. 274

Yearke, L.W.C. 285

Yen, K.C. 364

Young, A. 38

Zanen, N. 312

Zang, H. 354, 356

Zao Yun 167

Zernitz, E.R. 13

Zevenbergen, L.W. 230

Zhide, Z. 304

Zienkieveiz, J.C. 362

Zimmermann, C. 194

Zimpfer, G.L. 198

Subject Index

ablation 81

actions causing disturbance in stream system 429

aggradation 276, 296

due to floods 300

due to increase in sediment load 297

due to change in water surface slope 298

due to withdrawal of clear water 298

at channel bifurcation 299

other occurrences 299

planned removal of dam 300

occurrence 297

allogenic changes 315

alluvium 58

alluvial fans 101

alluvial rivers

hydraulic geometry and plan forms 169

hydraulic geometry 176

analytical models 337, 343

applications 346

one-dimensional equations 338

one-dimensional dynamic equation 340

analysis of w.s. and bed waves 342

hyoperbolic model 345, 354

parabolic model 344

wave model 345, 356

aquatic organisms 428

area of drainage basins 19

armouring models 369

assimilative capacity 428

autogenic changes 315

avulsion 315

of the Tigris 318

of the Yellow river 320

bars 199, 237

alternate 239

diagonal 238

longitudinal 200

point 200

transverse 200

base level 72

basin shape 21

bed-forms 124

antidunes 124, 131

bars 124

in unidirectional flow 124

distinction between ripples and dunes 126

dunes 124

ripples 124

stability analysis 127

transverse ribs 131

bed-load transport 145

DyBoy’s equation 145

Meyer-Peter and Mûller’s equation 146

Patel and Ranga Raju equation 150

bed-load equations for gravel-bed rivers 248

Ackers and White 248

Bagnold 250

Meyer Peter and Mûller 249

Mizuyama 250

Parker et al. 250

Schoklitsch 250

Smart 249

bed material load 123

bends 189

distribution of longitudinal velocity over width 192

entrenched 197

Subject Index474

flow in rigid and alluvial bends 189

free bends 197

growth and decay of secondary

circulation 192

head loss 194

shear distribution and topography 194

super elevation 192

velocity distribution in rigid

bed bends 189

bifurcation ratio 16

biological integrity 428

biological oxygen demand (bod) 427

Brahmaputra 402

bank stability 409

climate and hydrology 411

development plans 423

drainage of hinterlands 420

flooding and flood protection 419

plan forms 416

resistance to flow and

sediment transport 414

river bed changes 422

river characteristics 407

role of dredging 424

seismicity and landslides 410

braided rivers 198

types of bars 199

longitudinal 200

lingioid 200

lateral 200

point 200

side 200

causes of 198

parameters 200

modeling of 202

braiding indices 200

Brice index 200, 451

Rust index 202, 451

Braid channel ratio 202

channel pattern changes 329

channel slopes 28

characteristics of graded streams 85

characteristic discharges

bankful discharge

bed generative discharge 179

dominant discharge 177

mean annual discharge 177

CHARIMA 376

chars 391

chemoclinie 434

cirques 81

classification of models 364

coupled 364

fully unsteady 364

quasi-steady 364

uncoupled 364

climatic changes 260

causes 261

forecasts 262

colluvium 58

conceptual model of valley storage 59

consistency 366

continuity equation

for flow 338

for sediment 339

convergence (of numerical scheme) 366

Courant condition 366

Courant–Friedrich–Levy condition 366

critical shear stress 111

for uniform materials 111

for non-uniform sediment 117

critical velocity approach 114

cut-off 326

artificial cutoff 327

chute cutoff 327

natural and artificial 326

neck cutoff 327

dams–large vs small 432

dams and reservoirs 430

Darcy–Weisbach equation 5

data requirements for morphological studies 442

basin characteristics and

morphometry 449

bed and bank material 453

catalogue of information 459

cross-sectional, longitudinal section, plan-form 451digital image processing 444

geomorphic map 446

hydrologic data 454

Subject Index 475

lithology and tectonics 445

maps, air photos, satellite imageries 442

remote sensing 443

sediment load data 455

stratigraphic studies 456

vegetative cover 446

water quality data 458

degradation 276, 277

at dams and barrages 282

at bifurcations 284

control of 286

downstream progressing 282, 285

effects of 285

gravel mining 284

increase in discharge 284

parallel 284

planned removal of dam 300

prediction of depth 286

rotational 278

storage of bed material 284

types 277

downstream progressing 282

upstream progressing 277

deltas 98

dhars 391

diastrophism 71

diffusion model 244

disturbances in stream system and

their impacts 429

dissolved oxygen 434

dominant discharge 176

bankful discharge 177

drainage basin 11

drainage basin characteristics and hydrology 29

drainage density 24

drainage patterns 12

centripetal 13

dendritic 12

deranged 12

highly violent 13

parallel 12

radial 12

rectangular 12

trellised or lattice like 12

drainage texture 13

dune dimensions 127

dunes 127

dynamic equation 340

dynamic simulation model 62

entrenchment ratio 93, 452

environmental effects 429

of hydraulic structures 429

dams and reservoirs 430

epilimnion 434

equilibrium in natural streams 84

erosion 34

equations 48

factor 65

factors affecting 41

gully erosion 24, 39, 40

modeling of 60 rates (global) 35

rates in Indian catchments 64

rill 29

sheet 44

types 39

erosion and depositional landforms 61

erosion at bends 323

erosivity indices 47

erosion models

dynamic simulation 62

EUROCEM 63

process based 60

stochastic 64

erosional and depositional land-forms of glaciers 81

cirques 81

deltas 98

fans 101

glacial troughs 81

hanging valleys 82

fluvial hydraulics 1

fluvial morphology 82

fluvial palaeo hydrology 256

fluvial palaeo hydrologic studies in India 271

geomorphological instantaneous unit hydrograph (GIUH) 29,450

geomorphology 7, 71

Subject Index476

geologic time scale 77

geomorphic cycle (erosion cycle) 72

criticism 74

rejuvenation of cycle 74

geomorphic processes 71

endogenous 71

exogenous 71

glaciation 80

in India 80

glacial movements and erosion 81

glaciers 80

ice cap 80

ice streams 80

glacial troughs 81

valley glaciers 80

global warming 262

forecast 262

graded stream 2, 84

characteristics 85

gravel-bed rivers 229

bed material 230

bed-load equations 248

bed-features 237

bed-load sampling 247

data 230

hydraulic geometry 233

pavement 233

resistance to flow 241

resistance at bankful discharge 242

resistance at varying discharge 244

sediment transport 246

universal stage discharge curve 246

hanging valleys 82

healthy streams 428

HEC-6 372

applications to Kosi 378

reservoir sedimentation 382

Helly smith sampler 247

historical developments 4

in fluvial hydraulics 4

in geomorphology 7

Horton’s area ratio 20

length ratio 18

laws 16, 17

number 25

hydraulic geometry of alluvial streams 176

empirical relations 180

non-dimensional relations 186

hydropower plants 436

hypolimnion 434

hypsometric curves 27

ice-caps 80

ice-streams 80

incipient motion 110

critical velocity approach 114

empirical equations CTF 111

Shields’ analysis 111

for non-uniform sediments 117

Kosi 388

catchment characteristics

and geology 391

channel patterns 401

discharge and sediment measurements 393

flood embankments 400

geotectonics 392

hydrology 393

management of Kosi 398

morphology of Kosi 396

present day problems 402

sediment size and slope 345

landscape evolution

non-cyclic concept 76

Lane’s balance analogy 259, 275

Lax theorem 366

Lithology 21

longitudinal grain sorting 331

Maddock’s classification (unmeasured load) 52

mass wasting 24

Manning’s equation 5

meander belt 97

length 97

free 98

meandering 202

meander bend migration 205

meander characteristics 206

relations for geometry 207

theories 209

Subject Index 477

measurement of sediment yield 50

mechanics of sheet erosion 44

modeling of armouring 369

HEC-6 372

CHARIMA 376

modes of sediment transport 119

bed load 120

bed material load 123

contact load 120

saltation load 120

suspended load 120

wash load 123

natural levees 98

neotectonics and earthquakes 105

non-cycle concept of land scaped evoluation 76

numerical model 360

numerical schemes 362

explicit method 362

finite difference 362

implicit method 363

one dimensional models

boundary conditions 367

classification 363

equations 360

list of models 365

osage type stream 90

overland flow 60

oxbow lake 327

palaeo climatology 256

palaeo geomorphology 256

palaeo hydraulics 257

palaeo hydrology 256

palaeo hydrologic studies 257

palaeo peology 257

basis of analysis 258

estimation of Q and U 262, 264

in India 267

objectives 257

palaeo velocity determination 264

in gravel-bed rivers 266

pavement 233

peneplain 72

physiography 2

plan-form 87

plan-form criteria 212, 216

problems in river morphology 2

randon walk model 29, 30

recreation 437

regimes of flow

prediction 131

rehabilitation of stream 440

relief 26

relief aspects 26

relief ratio 26

remote sensing 443

restoration of stream 439

reservoir sedimentation 301

density current 305

empirical area redution method 306

method of preserving and

Miraki’s method 309

modeling of sediment deposition 304

movement and sediment deposition 304

restoring capacity 310

shape and deposition profile 305

sediment inflow and trap efficiency 302, 303

upstream effects 301

reservoir induced seismicity 432

reservoir surveys 53

resistance equations 241

bank resistance 138

Darcy Waisbach equation 5, 137

Engelund’s method 141

general comments 139

in alluvial streams 137

Manning’s equation 5, 137

of undulations 139

Strickler’s equation 138

river action plans 438

rivers and environment 427

river morphology 2

river systems in India 386

ruggedness number 25, 26

Saraswati river 271

sea level fluctuations 450

Subject Index478

scour 276

around bridge piers 287

factors affecting 288

in cohesive soils 296

in gravelly materials 295

Kothyari’s equation 292

Lacey–Inglis method 292

Melville–Sutherland method 292

prediction of scour depth 296

protection of scour 291

verification of equations 293

secondary circulation 103

sediment budget concept 58

sediment delivery ratio 23, 56

sediment discharge 157

relations 157

sediment production and yield 23

sediment yield 23, 34, 35

computation 56

measurement 50

sheet erosion mechanics 44

sinusity 97

slack water deposits 267

soil erosion 34

gullies 39

rills 39

sheet 39

types of 39

soil loss equations 48

slope ratio 28

stable channels 170

carrying sediment 170

stable channel design

Lacey’s method 170

Blench’s method 171

Chang’s method 174

Simon’s method 172

Kondap’s method 173

stability (numerical) 366

stability analysis 127

for bed-forms 127

for plan forms 202

Sternberg’s equation 86

stream

action causing disturbances in 429

assimilative capacity 428

biological integrity 428

capture 321

flow regime 23

habilitation 440

equilibrium 427

frequency 24

order 14

pollution 437

reclamation 440

restoration 439

sinuosity 97

terraces 95

stream classification

boulder 92, 229

consequent 87

ephemeral 40, 87

flood plains 92

gravel bed 92, 229

insequent 87

intermittent 87

misfit 89

obsequent 87

osage 90

over fit 89

perennial 48, 87

resequent 87

subsequent 87

under fit 89

submergence of land and forests 431

suspended load transport 150

integration of sediment distribution equation 155

measurements 150

Rouse equation 153

sediment distribution 152

theories of meandering 209

conceptual model 210

disturbance 210

earth’s rotation 289

excess energy 209

helicoidal motion 210

Ramette’s theory 211

thermal and hydro power plants 436

topography 73

mature 73

old 73

Subject Index 479

old stage 83

youthful 73

topography produced by streams 94

alluvial fans 101

delta 98

flood plains 95

meanders 96

natural levees 98

point bars 103

stream terraces 95

valleys 94

total load transport 158

total load equations

Ackers and White 160

Bagnold 159

Brownlie 162

Effective shear stress approach 162

Engelund and Hansen 160

Garde–Dattari 159

Graf–Acaroglu 159

Karim–Kennedy 163

Laursen 158

Shen and Hung 161

Yang 161

trap efficiency 303

equations 303

universal soil loss equation 42, 48

unit weight of sediment 55

valley glaciers 80

variables in river morphology 104

variation in sediment size 86

vegetation 22

vortex bed-load sampler 247

water quality

in reservoirs 433

dissolved oxygen 434

iron and manganese 435

nitrogen 435

pH 434

phosphorus 435

salinity 434

temperature 434

turbidity 434

wash load 123

wave model 356

river morphology - garde - india

Documents