stable channel analysis and design - pdhonline.com · stable channel analysis and design 2012...

PDHonline Course H145 (4 PDH)

Stable Channel Analysis and Design

2012

Instructor: Joseph V. Bellini, PE, PH, DWRE, CFM

PDH Online | PDH Center5272 Meadow Estates Drive

Fairfax, VA 22030-6658Phone & Fax: 703-988-0088

www.PDHonline.orgwww.PDHcenter.com

An Approved Continuing Education Provider

http://www.PDHonline.org

http://www.PDHcenter.com

© Joseph V. Bellini

Overview

Estimating Channel Velocity Method of Maximum Permissible Velocity (soil, riprap, & veg) Method of Maximum Tractive force (soil, riprap, & veg) Geometric Design of Channels Slope Revetment (riprap, gabion, and articulated concrete block) HEC-RAS Stable Channel Design Tool

2


References

Sediment Transport Technology, Water and Sediment Dynamics, Simon & Senturk, Open Channel Hydraulics, V.T. Chow, McGraw-Hill Sediment Transport, Theory and Practice, Yang, McGraw-Hill USGS Water-Supply Paper 2339, "Guide for Selecting Manning's Roughness

Coefficients for Natural Channels and Flood Plains," by George J. Arcement, Jr.,and Verne R. Schneider Design of Riprap Revetment, Hydraulic Engineering Circular No. 11 (HEC-11),

Federal Highway Administration (FHWA) Design of Roadside Channels with Flexible Linings, Hydraulic Engineering Circular

No. 15 (HEC-15), Federal Highway Administration (FHWA) Articulated Concrete Block, Revetment Design, Factor of Safety Method, National

Concrete Masonry Association, TEK 11-12 Hydraulic Stability of Articulated Concrete Block Revetment Systems During

Overtopping Flow, 1989, FHWA-RD-89-199 Standard Guide For Analysis And Interpretation Of Test Data For Articulating

Concrete Block (ACB) Revetment Systems In Open Channel Flow, 2008, ASTM7276-08

3


ESTIMATING CHANNEL VELOCITY

4


Channel Velocity Estimates

Average Channel Velocity (Manning’s Equation)

– v = Average channel velocity (fps)–R = Hydraulic radius = Area/wetted perimeter (feet)–Sf = Friction slope (feet/foot)–Sf = So = Channel bottom slope (feet/foot) for uniform flow–n = Manning’s ‘n’ (roughness) value (see subsequent pages)

2/13/249.1fSR

nv

5


Manning’s ‘n’ Values

The Manning roughness coefficient is oftenassumed constant regardless of flow depth.At very shallow depths, the effects of theroughness in the channel bottom are morepronounced producing higher n-values.However, assuming the channel bottom andbanks have similar cover, the n-valuequickly decreases with increased depth tonearly constant until reaching bank full. Inoverbank floodplain areas, n-valuestypically vary significantly with depth.

Manning’s equation is commonly used tocompute the friction slope (Sf) at eachcross-section when developing watersurface profiles under gradually varied flowconditions using the direct-step or standard-step methods.

6



7



8


Relationship for Manning's roughness coefficient, n, that is a function of the flowdepth and the relative flow depth (da/D50) for gravel/stone lined channels. Thisrelationship is used to compute Manning’s n in FHWA’s HEC-15.

This equation applies where 1.5 ≤ da/D50 ≤ 185.

Where,n= Manning's roughness coefficientda= average flow depth in the channel, ftD50 = median riprap/gravel size, ftα= unit conversion constant, 0.262 (0.319 (SI))

Manning’s ‘n’ Values for Gravel/Stone Lined Channels

50

6/1

log23.525.2 Dd

dna

a

9


Manning’s ‘n’ Values for Grass Lined Channels

4.04.00

RSCCn nn 528.010.0 hCC sn

where,

Cn= Grass roughness coefficient

Cs= Density-stiffness coefficient

h= Stem height (ft)

α= Unit conversion constant, 0.262 (0.319 (SI))

t0 = Average bottom shear (psf)

γ = Unit Weight of Water, typically 62.4 #/cf

10


Depth-Averaged Velocity in Conveyance Tubesfrom HEC-RAS (1D, Steady-Flow)

11

1. Select Steady Flow Run

2. Select Flow Dist’n Locations

3. Select # of flow/velocity sub-sections;either globally or by cross-section. Select‘OK’, then select ‘Compute’ from step 2.


Depth-Averaged Velocity in Conveyance Tubesfrom HEC-RAS (1D, Steady-Flow)

120 140 160 180 200 220 240

342

343

344

345

346

Whitford CC Proposed Plan: Current model 7/21/2010

Station (ft)

Ele

vatio

n (ft

)

Legend

EG 100-yr

WS 100-yr

4 ft/s

5 ft/s

6 ft/s

7 ft/s

8 ft/s

Ground

Ineff

Bank Sta

.039 .042 .036

12

After selecting ‘Compute’, plot a cross-section of interest and you will seeconveyance tubes; each showing theaverage velocity per tube.


Vertically-Averaged Velocity from 2D Flow Model

13


EVALUATING EROSIVENESS BASED ONMAXIMUM VELOCITY METHOD

14


Method of Maximum Velocity – Non-Cohesive Soil

15


Method of Maximum Velocity – Cohesive Soil

16


Method of Maximum Velocity – Vegetation

17


EVALUATING EROSIVENESS BASED ONMAXIMUM TRACTIVE FORCE/SHEAR METHOD

18


Method of Maximum Tractive ForceShear Stress in Fluids

Fluids (liquid and gases) moving along solid boundary will incur a shear stress onthat boundary. The ‘no-slip condition’ requires that the velocity of the fluid at theboundary (relative to the boundary) is zero, but at some height from the boundarythe velocity must equal that of the fluid.

For all Newtonian fluids in laminar flow, shear stress is proportional to the strainrate in the fluid where the viscosity is the constant of proportionality. However, fornon-Newtonian, this is no longer the case; for these fluids, the viscosity is notconstant. The shear stress, for a Newtonian fluid, at a surface element parallel to aflat plate, at the point y, is given by:

Where μ = Dynamic viscosity v = Velocity y = Height above the boundary

Shear stress at the boundary is:

yvy

)(

0)0(

yyvy

0

yyv

19


Method of Maximum Tractive ForceEstimating Average Bottom Shear

From the Momentum Equation for non-uniform flow:

Solving for the friction force (Ff) andconsidering that the applied shear (tractive)force equals the friction force:

Assuming negligible change in depth andcross sectional area between sections:

Therefore:

Assuming a relatively small friction slope,the average tractive force on wetted area inpsf is:

Assuming a wide channel (B/y > 10), whereR ~ y, the average tractive force on wettedarea in psf is:

fFWPPvvgQw

sin211122

sin21112200 WPPvvgQAFf

21 PP 2211 vv

sinsin00 LAWA sinsin0 R

LWLAp

00 RS

00 yS

20


Method of Maximum Tractive Force – Applied Ave. Bottom Shear

21


Applied Shear on Curved Channels (from USACE)

5.0max 65.2)(

Brc

o

o

22


Applied Shear on Curved Channels (from FHWA’s HEC-15)

dbb K

where,

tb= Side shear stress on the channel(psf)

Kb= Ratio of channel bend to bottomshear stress

td= Shear stress in the approach channel(psf)

Rc= Radius of curvature of the bend tothe channel centerline (ft)

T= Channel top (water surface) width (ft)

05.1

0073.0206.038.2

00.22

b

ccb

b

KTR

TRK

K Rc/T≤2

2<Rc/T<10

Rc/T≥10

23


Method of Maximum Tractive Force – Critical (Permissible)Shear for Non-Cohesive Soil (from USGS)

24


Method of Maximum Tractive Force – Critical (Permissible)Shear for Cohesive Soil (from USGS)

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Method of Maximum Tractive Force – Vegetation & Riprap (from FHWA’sHEC-15)

500.4 Dp

For riprap:

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Design of Stable ChannelsNorth American Green Software Demo (from HEC-15)

http://www.nagreen.com/27


Design of Stable ChannelsNorth American Green Software Demo

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STABLE CHANNEL GEOMETRY

29


Stable Channel Geometry (from USBR)

Side slopes (USBR)

Dimensions oftrapezoidal sections(USBR)

Ad 5.0 zdb

4z

1 d

b

A=Area

30


Stable Channel Geometry – Freeboard (from PADEP)

Freeboard (Critical Slope Method – PADEP)Uniform flow at or near critical depth is unstable due to

waves present at the water’s surface.Sufficient freeboard must be provided to prevent waves

from overtopping the channel.Flow is considered “unstable” when So is between 0.7Sc

and 1.3Sc. If unstable flow exists, compute minimumfreeboard as

For a stable channel, the minimum freeboard should be25% of the flow depth.Generally, freeboard should not be less than 0.5 feet

3/4

256.14RDnS m

c

TADm

VDDVF 075.0

3025.0

31


Stable Channel Geometry – Ideal Stable Cross Section

From the USBR, ideal section geometry to evenly distribute shear:

x

ddy

maxmax

tancos Tan

dA2max2

213

2

max

sincos1 S

Ed

nv

f

c

Sd

97.0max

Tan

dT 22

max

Equation for bank curves Equations for geometry Equations for velocity

2sin

411

2sinE

32


Stable Channel Geometry – Ideal Stable Cross Section

Example:

Given:g=9.81 m/s2; Sf=0.0006; n=0.022; γ=1000 kg/m3; D50=12 mm;Q=10 m3/sec

For a given lining type, it was determined that:

τc = 0.9 kg/m2

Solution:

VQBdA max

213

21fSRn

V

21

35

max49.1 Sd

nQB cent

21

35

max Sd

nQB cent

English Metric

f

c

Sd

97.0max

33


Stable Channel Geometry – Stable Channel Slope

2/1

3964

SAD gg

BV

A gg

Where there is insufficient amount of coarse material to develop an armorlayer, degradation will continue until the channel reaches a stable slope.Refer to example on next page.

whereAg = volume of material to be degraded per unit channel width (sf)ΔS = So – SL

SL = Limiting slope (Meyer-Peter-Muller Method)d = Mean flow depth (feet)d50 & d90 = Particle diameter at 50% and 90% passing (mm)

SD

L gg 813

34

ddndSL

2/36/19050 )/)()(19.0(



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36


SLOPE REVETMENT DESIGN

37


Design of Stable ChannelsSlope RevetmentTypes of slope revetment: Riprap Gabion Grouted rock Pre-cast articulated concrete block

38

Slope Revetment – Riprap (Safety Factor (SF) Method)

by γ

dSiv

e Fo

rce

Div

ided

M

axim

um T

ract

cossintan

tancos'

SF

2

sin1' τo = Shear along the side

slope (from Lane chart b )

2

sintan

sin2costan

501

21DS ws

o

above) Φ = Angle of repose λ = Angle between

horizontal & velocity vector


tan

50ws horizontal & velocity vector along the slope plane.

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Slope Revetment – Riprap (USBR)

For relatively stable flow (uniform, straight, or mildly curved (curve radius/channelwidth > 30)), impact from wave action and floating debris minimal, and little or nouncertainty in design parameters); stability factor of 1.2.Based on Sg = 2.65; use specific gravity correction factor if other than 2.65.Stability factor is used to reflect the uncertainty in the hydraulic conditions and isdefined as the ratio of the average tractive force/critical shear of riprap. If otherthan 1.2, apply the stability factor correction factor in Table 1 below.

5.0

2

2

1 sinsin1

K

Where,

D50 = Mean riprap particle size

C = Correction factor

Va = Average velocity in channel (fps)

Da = Average flow depth in channel (ft)

θ = Angle of channel bank

φ = Riprap material angle of repose

C = Correction factors

5.11

5.0

3

50001.0KdVCCD

a

asfsg

5.1112.2

g

sg SC

5.1

2.1

SFCsf

40


Slope Revetment – Riprap

Design considerations

• Rock gradation

• Filter (granular or fabric)

• Bank slope (maximum recommended is 2:1)

• Bank preparation; cleared and grubbed.

• Thickness

• D100 or 1.5D50, whichever is greater

• > 12”

• Increase thickness by 50% for under-water placement

• Increase thickness by 6” to 12” where riprap may be subject to attackfrom floating debris, ice, or large waves.

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Slope Revetment – Gabions

42


Slope Revetment – Gabions

43


Slope Revetment – Grouted Rock

44


Slope Revetment – Articulated Concrete Block

45


Slope RevetmentArticulated Concrete Block (ACB) Safety Factor (SF) Calculation

tdes = to = Ave BottomShear (see Page 18)tc = Critical Shear fromtesting (see note 1)

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Notes:1. Critical shear obtained from tests

conducted per protocol in FHWA-RD-89-199 or ASTM 7276-08.

2. SF is heavily influenced byprotrusion, Δz (assumed to be ‘0’for tapered block).


Articulated Concrete Block (ACB) DesignStability in a Hydraulic Jump

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30 40 50

Ener

gy R

atio

Froude Ratio

Test Data Test Data Envelope Curve from Test report

Envelope Curve for 50TBlock

Acceptable

Unacceptable

47


STABLE CHANNEL DESIGN TOOL IN HEC-RAS

48


Stable Channel Design Tool in HEC-RAS

The Copeland Method (Copeland, 1994) was developed at the USACEWaterways Experiment Station through physical model testing and field studiesof trapezoidal-shaped channels. – Applicable to alluvial channels.

The Regime Method is an empirically based technique originally using actualdata gathered by British engineers for irrigation canals in India. A stream isstable at the design discharge when there is no net annual gain or loss ofsediment through the reach under study. – Applicable for long-term (annual)simulations.

The Tractive Force Method is analytically based. Channel stability is achievedas long as the actual shear stress on a selected particle size of the bedmaterial is less than the critical shear stress (that which just initiates motion ofthe selected bed particle size). – Applicable for use channels lined with gravelor rock.

49


Stable Channel Design Tool in HEC-RASCopeland Method Defines stability as sediment inflow = sediment outflow Inflowing sediment must be established; which can be done by providing a

sediment concentration or by allowing RAS to compute the sedimentconcentration by the geometric and sediment properties of an upstreamreach. (Capacity calculation using Brownlies Equation.)

50


Stable Channel Design Tool in HEC-RASCopeland Method

MinimumStreamPower –Optimal fordesign

51


Stable Channel Design Tool in HEC-RASCopeland Method

MinimumStream Power– Optimal fordesign

52


Stable Channel Design Tool in HEC-RASTractive Force Method

Can solve forD75 and any ofthe followingparameters;slope, depth, orwidth.

Input – Discharge, temperature, specific gravity, angle of repose, side slope, andManning’s n.

Pick 2 of D75, depth, width, and slope to solve; RAS solves the other 2.

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