reward reference manual 2.5

8/12/2019 ReWaRD Reference Manual 2.5

1/110


2/110

2 ReWaRD 2.5 Reference Manual

Information in this document is subject to change w ithout no ticeand do es not represent a co mmitment on the part of G eocentrixLtd. The software described in this document is furnished under alicence agreement o r non-disclosure a greement and ma y be usedor copied only in accordance with the terms of that agreement. Itis against the law to copy the software except as specificallyallow ed in the licence o r non-disclosure agreement. No pa rt of thismanual may be reproduced or transmitted in any form or by anymeans, electronic or mechanical, including photocopying andrecording, for any purpose, w ithout the express written permissionof G eocentrix Ltd.

1992-2001 G eocentrix Ltd. All rights reserved.

G eocentrix and ReWaRD are registered tradema rks of G eocentrixLtd.

Frodingham and Larssen are registered trademarks of Corus plc inthe United Kingdom.

Microsoft and Windows are registered trademarks of MicrosoftCorporation. IBM is a registered trademark of Internationa l BusinessMachines Corp. O ther brand or product names are trademarks orregistered trademarks of their respective holders

Set in Optimum using Corel WordPerfect 8.0.

Service Release 2.55 (4/01).

Printed in the UK.


3/110

Acknow ledgements 3

AcknowledgmentsReWaRD 2.5 was designed and written by Dr Andrew Bond andIan Spencer of G eocentrix Ltd. The prog ram w as o riginallycommissioned by British Steel Ltd.

The ReWaRD Reference Manual w as w ritten by D r Andrew Bond.

Pa rts of ReWaRD w ere developed w ith the assistance o f ProfessorDavid Po tts o f Imperial Co llege of Science, Techno logy, andMedicine and D r Hugh St John of the G eotechnica l Co nsultingGroup.

The follow ing people assisted w ith the testing of this and previousversions of the program: Vassilis Po ulopoulos (Geocentrix); Roma inArnould (Geotechnical Co nsulting G roup); Andy Fenlon (NonsuchVideographics); Joe Emmerson (British Steel); and Kieran Dineen(Imperial College).


4/110



5/110

Table of contents 5

Table of contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Chapter 1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

About this book 9Conventions 10Where to go for help 11User manual 11Reference manual 11O n-line help 11Tooltips 11

Technical support 12Sales and marketing information 12

Chapter 2Earth pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Earth pressure conditions 13Earth pressures as built 14Earth pressures at minimum safe embedment 14Earth pressures w ith maximum safety factors 14Earth pressures at failure 14Stresses in the ground 15Total or effective stresses? 15Vertical total stress 15Pore water pressure 16Vertical effective stress 17Horizontal effective stress 17Horizontal total stress 18Pressures from surcharges 19Available calculation methods 19Uniform surcharges 20Parallel strip surcharges 20Perpendicular strip surcharges 24Parallel line surcharges 25

Perpendicular line surcharges 29


6/110


Area surcharges 30Point surcharges 32Design pressures 34Soil pressures 34Surcharge pressures 35Combined earth pressures 35G roundw ater pressures 36Tension cracks 36Combined w ater pressures 38Total pressures 38Minimum active pressures 38Low -propped walls 38Earth pressure coefficients 41Coulomb 41Rankine 42Packshaw 43Caquot &Kerisel 43

Kerisel &Absi 44

Chapter 3Required embedment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

O ut-of-balance moment 45Cantilever walls 45Fixed-earth conditions 45Single-propped w alls 46Free-earth conditions 46Multi-propped walls 47

Chapter 4Structural forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Cantilever and single-propped walls 49At minimum safe embedment 49With maximum safety factors 49At failure 50Multi-propped walls 51Design structural forces 52Bending moments 52Shear forces 52Prop forces 52

Chapter 5


7/110

Table of contents 7

Pecks envelopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Distributed prop loads 53Pecks envelopes 53Envelope for sand 54Envelope for stiff clay 54Envelope for soft to medium clays 55Obtaining prop loads from Pecks envelopes 56

Chapter 6Base stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Factor-of-safety against basal heave 57Stability number 57Rigid layer correction 58

Chapter 7Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Database of w all movements 59

Surcharge loading factor 60Database for sands 60Cantilever and propped walls 60Database for stiff clays 62Cantilever walls 62Propped w alls 63Database for soft clays 65Cantilever and propped walls 65System stiffness 67

Chapter 8Durability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C orro sio n o f steel piling in va rio us enviro nments 69

Chapter 9Safety factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Design approaches 71Safety factors in earth pressure calculations 72G ross pressure method 72Nett pressure method 73Revised (or Burland-Potts) method 75Strength factor method 76Limit state methods 77Safety factors for structural forces 80At minimum safe embedment 80


8/110


With maximum safety factors 81At failure 81

Chapter 10Engineering objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Construction stages 83G round profiles 83Sloping ground 83Stepped ground 83Excavations 85Sloping excavations 85Berms 85Plan dimensions 88Soils 88Soil classification system 88Database of soil properties 90Critical state parameters 99

Fissured soils 99Layers 100Dip 100Rigid layers 100Water tables 101Retaining walls 101Section properties 101Rowes parameter 103King-post (or soldier-pile) walls 103Surcharges 104Elastic reflection parameter 104Duration/effect 105Imposed loads 105Duration/effect 105

Chapter 11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107


9/110

Chapter 1: Introduction 9

Chapter 1Introduction

ReWaRD is an advanced program for designing embeddedretaining walls under a variety of ground and loading conditions.The program implements a number of techniques for designingretaining walls, including those given in the latest UK andinternational standards, such as BS 8002 and Eurocode 7.

This chapte r of the ReWaRD Reference Manual outlines thecontents of this book, explains the conventions that are usedherein, and tells you what to do if you need help using theprogram.

About this bookThis Reference Manual is divided into the following chapters:

Chapter 1 Introduction Chapter 2 Earth p ressures Chapter 3 Required embedment Chapter 4 Structural forces Chapter 5 Pecks envelopes Chapter 6 Base stability Chapter 7 Displacements Chapter 8 Durability Chapter 9 Safety factors Chapter 10 Engineering objects

Chapter 11 References


10/110


ConventionsTo he lp you loca te and interpret information easily, the ReWaRD User Manual uses the follow ing typo graphica l conventions.

This Represents

Bold Items on a menu or in a list-bo x; the text on a button ornext to an edit control; or the label of a group box

Item1


11/110

Chapter 1: Introduction 11

Where to go for helpYour first source of help and information should be the ReWaRDmanuals and the o n-line help system.

User manualThe ReWaRD User Manual explains how to install and useReWaRD. It includes a n overview of the program, a tutorial, andseparate chapters giving detailed information about ReWaRDsStockyard and Workbooks.

Reference manualThe ReWaRD Reference Manual (this book) gives detailedinformation abo ut the calculat ions ReWaRD pe rforms. The manualassumes you have a working know ledge of the geo technical designof embedded retaining walls.

O n-line helpThe on-line help system co ntains deta iled informa tion abo utReWaRD. Help appears in a separate window with its owncontrols. Help topics that explain how to a ccomplish a task appea rin windows that you can leave displayed while you follow theprocedure.

To open the on-line help system:

Press F1Click the Help button in a d ialogue b ox

Choose a command from the Help menu

If you need assistance w ith using on-line help, choose the How ToUse Help command from the Help menu.

TooltipsIf you pause w hile pa ssing the mouse po inter over an ob ject, suchas a too lba r button, ReWaRD displays the name o f that ob ject . Thisfeature, called Too ltips, makes it ea sier for you to identify wha t yousee and to find w hat you need.


12/110


Technical suppo rtTechnical support for ReWaRD is availab le d irect from G eocentrixor through your local distributor. If you require technical support,please co ntact G eocentrix by any o f these means:

Voice: + 44 (0)1737 373963Fax: + 44 (0)1737 373980E-mail: [email protected]: www.geocentrix.co.uk

Please be at your computer and have your licence number readywhen you call.

Alternatively, you can write to the following address:

ReWaRD Technica l Suppo rtG eocentrix LtdScenic House54 Wilmot WayBansteadSurreySM7 2PYUnited Kingdom

Please quote your licence number on all correspondence.

Sales and marketing informationFor sales and marketing information about ReWaRD, please contact

ReWaRD Sales on the same numbers as above.


13/110

Chapter 2: Earth pressures 13

Chapter 2Earth pressures

This cha pter gives deta iled information about the theory andassumptions behind ReWaRDs earth pressure calculations.

In order to calculate earth pressures, ReWaRD divides the groundinto a number of discrete horizons . Each horizon contains:

A soil layer (if below ground level on the retained side of thewall or below formation level on the excavated side)A maximum of one w ater tab leA maximum of one prop or anchorAn unlimited number of surchargesAn unlimited number of imposed loads

The results of ReWaRDs ea rth pressure ca lculat ions a re availab leat the top and bottom o f each horizon and (w hen present) at anyinternal sub-horizons within the horizon. ReWaRD inserts sub-horizons into an horizon when:

Earth pressures increase w ith depth in a non-linear ma nner (suchas w hen a non-uniform surcharge is applied to the w all)Earth pressures are needed for structural force calculations (toensure sufficient accuracy in the bending mo ments)

Earth pressure co nditionsReWaRD allows you to calculate earth pressures for a number ofconditions:

As builtAt the minimum safe embedmentWith maximum safety factorsAt failure

The follow ing paragraphs explains the assumptions tha t are mad efor each of these conditions and the tab le be low summarizes these.


14/110


Condition Wall length* Safetyfactors**

Inequilibrium?

As built L ( No***

At minimumsafe embedment

< L ( Yes

With maximumsafety factors

L > ( Yes

At failure


15/110


Stresses in the groundThis sec tion de scribes the w ay ReWaRD ca lculates the stressesacting in the ground, owing to the weight of soil and water:

Vertical total stress ( Fv)

Pore water pressure (u)Vertical effective stress ( FNv)Horizontal effective stress ( FNh)Horizontal total stress ( Fh)

Tota l or effec tive stresses?The follow ing table indicates when ReWaRD calculates ea rthpressures using total stress or effective stress theory.

Constructionstage designatedas...

Type of layer...

Drained Undrained

Short-term Effective stress Total stress

Long-term Effective stress Effective stress

Vertical total stressThe vertica l tota l stress in an horizon ( Fv) is ca lculated from the unitweight and thickness of any soil layers and standing water abovethe po int being considered:

Fv mz

0

( dz ( w h sw

where z is the depth below the ground surface; ( is the layer's bulkunit weight; ( w is the unit w eight of wa ter; and h sw is the height ofany standing w ater.

When there is no water table acting in the horizon or the watertable is Dry, ( is equal to the soil's unsaturated unit weight;

otherwise it is equal to the soil's saturated unit weight.


16/110


Pore w ater pressureDrained horizonsThe po re water pressure (u) at a d epth (z) in a drained horizon isca lculated as follow s.

If no w ater tab le is present o r the water tab le is dry:

u 0

If a w ate r table is present and it is hydraulica lly connected to theoverlying water regime:

u u T (Mu

Mz )(z z T )

where u T and zT are the pore water pressure and depth(respectively) at the top of the horizon; and Mu/ Mz is the porepressure gradient.

If a water table is present but it is not hydraulica lly connected tothe overlying water regime:

u u A (Mu

Mz )(z z W )

w here u A is the ambient pore wate r pressure specified b y the w atertable; zW is the depth of the water table; and Mu/ Mz is the porepressure gradient.

The value of Mu/ Mz is determined by the type of wa ter table presentin the horizon (see on-line Help).

Undrained horizonsThe pore water pressure in undrained horizons is calculated as fordrained ho rizo ns, but it is irrelevant to the calculation of tota l ea rthpressures and is therefore not displayed.


17/110


Vertical effective stressDrained horizonsThe vertical effective stress in the ho rizon ( FNv) is given b y Terz aghi'sequation:

F

v Fv u

where Fv is the vertical tota l stress and u the pore w ate r pressure atthe co rresponding depth.

Undrained horizonsThe vertica l effective stress in undrained horizons is irrelevant to thecalculation of total earth pressures and is therefore not displayed.

Horizontal effective stressDrained horizonsThe ho rizo ntal effective stress in a drained horizo n ( FNh) is ob tainedfrom the vertica l effective stress ( FNv) via the eq uation:

F

h K F

v K c c

w here K and Kc a re drained ea rth pressure coefficients and c N is thesoil's effect ive cohesion.

The va lue o f K depends on the so ils angle of friction ( N), the angleof wall friction (*), the dip of the horizon ( $) and the mode offailure (active or passive):

K f (N, *, $, mode of failure )

See the section Earth pressure coefficients in this chapter for de tailson the precise fo rm of the function f .

Kc depends on the value of K and also the soils effective cohesion

(cN), wall adhesion (a), and the mode of failure:


18/110


K c 2 K (1 a

c )

w here the + sign is used for active co nditions and the ! sign forpassive (Potts &Burland, 1983).

If the retaining w all is a king-post w all, then the earth pressurecoefficients below formation level on the excavated side o f the wallare calculated as described in Chapter 10 in the section entitledRetaining Walls .

Undrained horizonsThe horizontal effective stress in undrained horizons is irrelevant tothe ca lculation o f tota l earth pressures and is not d isplayed .

Horizo ntal total stressDrained horizonsIn drained horizons, the horizontal total stress ( Fh) is given byTerza ghis equation:

Fh F

h u

where FNh is the horizontal effective stress and u the pore waterpressure a t the corresponding depth.

Undrained horizonsIn undrained horizons, the horizontal total stress ( Fh) is given by:

Fh K u Fv K uc C u

w here Ku and Kuc a re undrained earth pressure c oefficients and C uthe soils undrained shear strength.

The value of K u is 1 in all cases, whereas the value of K uc depends

on the soils undrained strength (C u), the undrained wall adhesion


19/110


1Recommended for cohesionless, but not necessarily fo r cohesive,soils

(au), and the mode of failure (active or passive):

K uc 2 1 a u

C u

w here the + sign is used for active co nditions and the ! sign forpassive.

If the retaining w all is a king-post w all, then the earth pressurecoefficients below formation level on the excavated side o f the wa llare calculated as described Chapter 10 in the section entitledRetaining Walls .

Pressures from surchargesThis section describes the w ay ReWaRD ca lculates ea rth pressuresarising from the presence of surcharges.

Available calculation methodsReWaRD supports a number of methods for assessing the effectsof surcharges, as listed below:

Boussinesqs theory (see Clayto n &Militiski, 1986) [B]Hybrid e lastic method ( ibid.) [HE]Wedge analysis (see Pappin et al. , 1985) [W]Krey's method 1 (British Steel Piling Handbook, 1988) [K]

Terzaghis method (see CIRIA 104, 1984) [T]

Not every method can be used with every surcharge, as thefollowing table indicates (in this table, the headings correspond tothe letters given above in square brackets).

Surcharge type B HE W K T

Uniform Special method not needed


20/110


21/110


22/110


otherwise it is narrow . In this equation, x is the perpendiculardistance between the wall and the nearest edge of the surcharge;y is the w idth of the surcharge; and N is the soil's angle of friction.

The horizo ntal stress varies with dep th below the surcharge (z) asshow n below .

a

c

b

x y

z a

b + c

x y

z

Wide Narrow

For wide strip surcharges, the maximum horizontal stress is givenby:

(Fhq )ma x q tan2 (45 E

N

2)

and for narrow strip surcharges, it is given by:

(Fhq )ma x

4 q ta n2 (45 E N

2)

2 x

y [1 tan2 (45 E

N

2)]

The vertical stress for both wide and narrow strip surcharges isassumed to b e:


23/110


Fvq Fhq

tan2(45 E N

2)

The dimensions a, b, and c on these diagrams are given by:

a x tan N 1

2b (1 tan2(45

N

2))

b x

tan (45 E N

2)

c y

tan (45 E N

2)

Krey's methodThe ho rizo ntal stress is calculated from plasticity theory, assumingzero w all friction and adhesion.

The horizo ntal stress varies w ith depth below the surcharge (z) asshow n below .


24/110


a

b + c

x y

z

The maximum horizontal stress is given by:

(Fhq )ma x

4 q ta n2 (45 E N

2)

2 x

y

[1 tan2 (45 E N

2

)]

The dimensions a, b, and c on this diagram are the same as for theWedge analysis.

The vertica l stress is assumed to be:

Fvq Fhq

tan2(45 E N

2)

Perpendicular strip surcha rgesReWaRD provides two methods of calculating the effects ofperpend icular strip surcharges.

Boussinesqs theoryThe vertica l and horizontal stresses resulting from a perpendicularstrip surcharge o f magnitude q are ca lculated from the eq uations:


25/110


Fvq q

B[" sin" cos (" 22)]

Fhq 2q < "B

w here tan (" + 2) = (x + y)/z; tan 2 = x/z; z is the depth below thesurcharge; x is the distance along the wall to the nearest edge ofthe surcharge; y is the width of the surcharge; and < is Poisson'sratio.

Hybrid elastic methodThe vertical stress is ca lculated from Boussinesq s theo ry, and thehorizontal stress is given by:

Fhq K a Fvq

w here Ka is the active earth pressure coefficient for the horizon.

Parallel line surchargesReWaRD provides five method s of ca lculating the effects of parallelline surcharges.

Boussinesqs theoryThe vertica l and horizontal stresses resulting from a perpend icularline surcharge o f magnitude Q are ca lculated from the equations:

Fvq 2Q z 3

BR 4e R


26/110


Fhq 2Q x 2z

BR 4e R

where R2 = x2 + z2; eR is the elastic reflection parameter (see the

section entitled Surcharges in Chapter 10); z is the depth b elow thesurcharge; and x is the perpendicular distance between the walland the surcharge.

Hybrid elastic methodThe vertical stress is calculated from Boussinesqs theo ry, and thehorizontal stress is given by:

Fhq K a Fvq

w here Ka is the active earth pressure coefficient for the horizon.

Wedge analysisThe ho rizo ntal stress is calculated from plasticity theory, assumingzero w all friction and adhesion.

The horizo ntal stress varies with dep th below the surcharge (z) asshow n below .

a

b

x

z



27/110


(Fhq )ma x

4 Q tan2 (45 E N

2)

x [1 tan2 (45 E N

2

)]

The dimensions a and b are as defined for parallel strip surcharges.


Fvq Fhq

tan2(45 E N

2)

Krey's methodIn this metho d, the horizo ntal tota l stress increase is ca lculated fromplasticity theory, assuming zero wall friction and adhesion.

The horizo ntal stress varies with depth below the surcharge (z) asshow n below .

a

b

x

z



28/110


(Fhq )ma x

4 Q tan2 (45 E N

2)

x [1 tan2 (45 E N

2

)]

The d imensions a and b are the same as for parallel stripsurcharges.


Fvq Fhq

tan2(45 E N

2

)

Terzaghi's methodTerzaghi's method is ba sed on elasticity theory, modified to matchfield and model experiments.

The vertica l stress is ca lculated from Bo ussinesq s theo ry.

The horizo ntal stress depends on the proximity of the surcharge tothe retaining wall. A line surcharge is considered near to the w all if:

x

H 0.4

otherwise it is far from the wall. In this equation, x is theperpendicular distance be tween the w all and the surcharge; a nd His the height of excavation below the surcharge.

For near line surcharges, the horizontal stress varies with depthbelow the surcharge (z) according to the formula:


29/110


Fhq 0.20Q

H

( z

H )

(0.16 [ z

H

]2)2

For far line surcha rges, the horizontal stress varies with depth below the surcharge a cco rding to the formula:

Fhq 1.28Q

H

( x

H )2 ( z

H )

([ x

H ]2 [ z

H ]2)2

Perpendicular line surcha rgesReWaRD provides two methods of calculating the effects ofperpend icular line surcharges.

Boussinesqs theoryThe vertica l and horizontal tota l stresses resulting from aperpendicular line surcharge of magnitude Q are calculated fromthe equations:

)F vq 2Q z 3

BR 4

)F hq 2Q z

BR 2 x:

(Fhq )AREA 0



32/110


Fvq Fhq

tan2(45 E N

2)

Point surchargesReWaRD provides three methods of calculating the effects of areasurcharges.

Boussinesqs theoryThe vertical and horizontal stresses resulting from a po int surchargeof magnitude P are calculated from the equations:

Fvq 3

2P

z 3

BR 5e R

Fhq P

2BR 2[

3z (v 2 x 2)

R 3(1 2


33/110


Terzaghi's methodTerzaghi's method is ba sed on elasticity theo ry, modified to matchfield and model experiments.

The vertica l stress is ca lculated from Bo ussinesq s theo ry.

The horizo ntal stress depends on the proximity of the surcharge tothe reta ining w all. A point surcharge is considered near to the wa llif:

x

H 0.4

otherwise it is far from the wall. In this equation, x is theperpendicular distance be tw een the w all and the surcharge; and H

is the height of the excavation below the surcharge.

For near point surcharges, the horizontal stress varies with depthbelow the surcharge (z) according to the formula:

Fhq 0.28P

H 2

( z

H )2

(0.16 [ z

H ]2)3

co s2(1.1 1 )

For far point surcharges, the horizontal stress varies with depthaccording to the formula:

Fhq 1.77P

H 2

( x

H )2 ( z

H )2

([ x

H ]2 [ z

H ]2)3

co s2(1.1 1 )

In these eq uations, 1 = tan! 1 (v/x), w here v is the distance a long the


34/110


35/110


horizons.

Surcharge pressuresEarth pressures resulting from the presence of surcharges alone aretermed surcharge p ressures in ReWaRD and given the symbol E q .

Unfac tored surcharge pressures a re given by:

E q Fhq

where Fhq is the horizonta l pressure resulting from any surcharges.

Design surcharge pressures are given by:

E qd E

q

f Eq

where fEq is the appropriate safety factor for the selected designstanda rd (see Chapter 9).

Co mbined earth pressuresThe combined earth pressures (E) from the w eight o f soil (E s) andthe presence of surcharges (E q ) are given by:

E E s E q

If the combined earth pressures are negative and the horizoncannot sustain tension (see the section on Layers in Chapter 10),then:

E 0

If the design total pressure acting in the horizon on the retainedside of the wall is less than the minimum active pressure (P minret, see


36/110


below), the design earth pressure E d is increased so that:

E d P min W d

w here W d is the design w ate r pressure acting in the horizo n on theretained side of the w all (see below).

G roundw ater pressuresWater pressures resulting from pore w ater pressures in the so il aretermed groundw ater pressures in ReWaRD and given the symbolW s.

Drained horizonsG roundwater pressures in drained horizo ns are given by:

W sd W s u

where u is the pore pressure in the soil.

Undrained horizonsG roundwater pressures in undrained horizo ns are given by:

W sd W s 0

Tension cracksTension cracks may form on the reta ined side of the w all w hen thecombined earth pressure E is negative and the horizon cannotsustain tension. Whether an horizon can sustain tension or notdepends on the properties of the layer contained in that horizon(see the section o n Layers in Chapter 10).

Tension c racks may be dry, wet, or floo ded (see the sec tion o nLayers in Chapter 9) and are limited in extent to w hatever depth isspecified in the selected design standard (see Chapter 9).

Water pressures resulting from tension cracks are termed tension


37/110


crack pressures in ReWaRD and given the symbol W tc.

Dry tension cracksIn dry tension cracks:

W tc 0

Dry tension cracks should only be specified if there is noopportunity for water to collect in any tension crack that formsbetw een the w all and the ground.

Wet tension cracksIn w et tension cracks:

W tc ( w (z z wps )

where ( w is the unit w eight of wa ter, z is the depth below groundsurface, and z wps is the depth o f the phreatic surface (i.e. the depthof the uppermost water table).

Flooded tension cracksIn floo ded tension cracks:

W tc ( w z

where ( w and z are as given abo ve. If the uppermost w ate r table isabove ground level (in the ca se of standing wa ter), then:

W tc ( w (z z wps )

where z wps is negative in value. Flooded tension cracks give themost pessimistic estimate of tension crack pressures.


38/110


Combined water pressuresThe combined w ater pressures (W) from the soil (W s) and anytension crack (W tc) are given by:

W d

W m axim um of W s

and W tc

Tota l pressuresDesign total pressures are given by:

P d E d W d

If, at any depth on the retained side of the wall, the design totalpressure is less than the minimum active pressure (see be low ), thenthe design earth pressure is increased so that P

d equals P

min.

Minimum active pressuresThe minimum active pressure (Pmin) sets a lower limit to the designtotal pressure (P d) acting on the retained side of the w all:

P d P min

(CIRIA Report 104 uses the term minim um equivalent fluid pressure MEFP instead of minimum a ctive pressure.)

The minimum active pressure increases w ith depth (z) according tothe formula:

P min M z

where M is a co nstant specified b y the selected design standard.

Low -propped w allsResearch at Imperial College (Nyaoro, 1988) has shown that theearth pressures acting on single-propped retaining walls that are


39/110


propped at or nea r excavation level are different to those a ssumedin conventiona l limit equilibrium calculations.

A single-propped w all is considered to be low-propped if theoverturning moment o f the tota l pressures acting on the w all ab ovethe prop (M above) exceeds the restoring moment due to the totalpressures ac ting on the w all below the prop and above excavation level (M below ).

Ma b o v e

Mb e l o w

When a w all is low-propped, the wall moves:

Aw ay from the soil above the propInto the so il below the prop on the retained side of the w allAway from the soil below the prop on the excavate d side

The co rrespo nding horizontal stresses are ca lculated using thefollowing earth pressure coefficients:

Abo ve the prop: a ctiveBelow the prop on the retained side: intermediate betweenactive and passiveBelow the prop on the excavated side: active

Drained horizonsThe ea rth pressure coefficients in drained ho rizo ns are given by:

K = Ka and Kc = Kac ab ove the level of the prop


40/110


K = Ki and Kc = Kic below the level of the prop on the retained sideK = Ka and Kc = Kac be low the level of the prop o n the excavated side

where the subscripts a and i denote active and intermediate conditions, respectively. K i and Kic are given by:

K i K a (K p K a )z p

d p

and

K ic

K ac

( K pc

K ac )

z p

d p

where z p is the depth below the level of the prop and d p is thedepth of the wall toe below the level of the prop.

When z p = 0, Ki = Ka and Kic = Kac . When z p = dp, Ki = Kp and Kic =Kpc . The nega tive sign in front of K pc ensures that the horizontaleffective stress at the to e of the wall eq uals the full passive pressure,i.e. Fhi = KpFv (Kpc)c'.

Values o f Ka and Kp are given in the sect ion in this chapter entitledEarth pressure coefficients . Formulae fo r Kac and Kpc are given in thesection entitled Stresses in the ground , under the head ing Horizontal effective stress .

Undrained horizonsThe earth pressure coefficients in undrained horizons are given by:

Ku = 1 and Kuc = Kauc ab ove the level of the propKu = 1 and Ku = 1 and Kuc = Kiuc below the level of the prop onthe retained sideK

u = 1 and K

uc = K

auc below the level of the prop on the

excavated side


41/110


where the subscripts a and i denote active and intermediate conditions, respectively. K iuc is given by:

K iuc 2 (1 2 z p d p

) (1 a u C u

)

w here z p is the de pth below the level of the prop, d p is the depth ofthe wall toe below the level of the prop, C u is the soil's undrainedshear strength, and a u the undrained w all adhesion.

The fo rmula fo r K auc is given in the section in this chapter entitledStresses in the ground , under the head ing Horizontal total stress .

Earth pressure co efficientsReWaRD calculates earth pressure coefficients according tow hichever theory is spec ified in the selected design standa rd. Theearth pressure theories that have been implemented in ReWaRDare those due to:

CoulombRankinePackshaw Caquot &KeriselKerisel &Absi

CoulombCoulomb (1776) developed an earth pressure theory for rigid (i.e.incompressible) soil which fails on a critical, discrete , planar shea rsurface. Coulomb's w ork was later extended by Mayniel (1808) andMller-Breslau (1906).

ReWaRD ca lculates C oulomb 's ea rth pressure coefficients using theformulae given by Mller-Breslau (1906) for a frictiona lcohesionless soil with sloping surface and a frictional wall:


42/110


K a sin2 (90 E N) cos *

sin (90 E *) [1 sin (N *) sin (N $)

sin (90 E *) sin (90 E $)]2

K p sin2 (90 E N) cos *

sin (90 E *) [1 sin (N *) sin (N $)

sin (90 E *) sin (90 E $)]2

where N = the soil's angle of friction; * = the angle o f wall friction;and $ = the slope of the soil surfac e (mea sured positive upw ards).

Rankine Rankine (1857) extended earth pressure theory by deriving asolution for a complete soil mass in a state of failure.

ReWaRD calculates Rankine's ea rth pressure coefficients using thefollowing formulae:

K a co s2 $

co s $ (cos2 $ co s2 N)


K p co s2 $



where the symbols are as given above for Coulombs theory.

Rankine's theo ry assumes that the resultant force o n a vertica l planeac ts parallel to the ground surface, and can o nly be used w hen theangle of wall friction (*) eq uals the ground slope ( $).


43/110


The cos * term in these formulae is replaced by cos $.

Packshaw ReWaRD obtains Packshaws (1946) earth pressure coefficientsfrom a database o f values taken from C ode of Practice CP 2 (1951).

Account is taken of sloping soil surfaces by increasing the value ofKa by 1% for every 1 E of inclination above the horizontal (asrecommended in the British Steel Piling Handboo k, 1997). Since K acis proportional to the square root of K a (see the section entitledHorizontal effective stress abo ve), it therefore increases by 0.5% forevery 1 E of inclination.

Ca quot &KeriselCaquot and Kerisel (1948) derived active and passive earthpressure coefficients using log spiral fa ilure surfaces.

ReWaRD calculates Caquot and Kerisel's active earth pressurecoefficients from the following formulae:

K a D K Coulomb

a

D ([1 0.9 82 0.1 84] [1 0.3 8 3]) n

n

(2

[tan2 $ tan2 *]

2 tan 2 N ) sin N

) 2 tan 1 (*cotan ** cotan 2 * cotan 2 N

1 cosec N)

8 ) $ '

4N 2B () $ ' )


44/110


' sin 1 (sin $

sin N)

w here KaCoulomb is the value of Ka from C oulombs theory.

ReWaRD obtains Caquot and Kerisel's passive earth pressurecoefficients from a database of values taken from Clayton &Milititsky (1986).

Kerisel &AbsiKerisel and Absi (1990) improved upon the work by Caquot andKerisel (1948) in deriving active and passive earth pressurecoefficients using log spiral fa ilure surfaces.

ReWaRD obtains Kerisel and Absi's passive earth pressure

coefficients from a database.


45/110

Chapter 3: Required embedment 45

Chapter 3Req uired embedment

This chapter gives deta iled information ab out ho w ReWaRDcalculates the req uired embedment o f the wall.

O ut-of-ba lance momentReWaRD determines the required embedment of a retaining w allby calculating o verturning and restoring mo ments from the ea rthpressures acting on it.

The out-of-ba lance mo ment ( ) M) is given by:

) M M R M O

where M O is the overturning moment and M R the restoringmoment.

The significance of the o ut-of-ba lance moment is as follow s:

If ) M > 0, the wall is stableIf ) M = 0, the w all is in moment e quilibriumIf ) M < 0, the wall is unstable

Structural forces cannot be calculated for a wall that is not inmoment equilibrium.

Cantilever wallsReWaRD dete rmines the req uired embedment o f cantilever wallsunder fixed-earth co nditions.

Fixed-ea rth conditionsUnder fixed earth conditions, the retaining wa ll is assumed to rota teabout a pivot located a t some d epth (d o) below excavation level.The earth pressures acting on the w all in this situation are asfollows.


46/110


Rd o d

To simplify the a nalysis, the ea rth pressures a cting below the pivotare replaced by a single resultant force (R). The depth o f the pivotbelow excavation level (d o) is given by:

d o d

1 C d

where d is the total depth of embedment of the wall and C d is thecantilever toe-in . According to CIRIA Report 104 (1984), aconservative va lue o f C d is 20%.

The embedment needed to achieve equilibrium is determined bytaking moments about the pivot and occurs when the sum of the(clockwise) overturning moments equals the sum of the (anti-clockwise) restoring moments. The va lue o f R is found fromconsideration of horizontal equilibrium.

Single-propped wallsReWaRD dete rmines the required embedment o f single-proppedw alls under free-ea rth conditions.

Free-ea rth co nditionsUnder free-earth conditions, the reta ining w all is assumed to rota teab out the level of the suppo rt. The ea rth pressures act ing on thewall in this situation are as follows:


47/110

Chapter 3: Required embedment 47

P

d

The embedment needed to achieve eq uilibrium is determined bytaking moments about the pivot and occurs when the sum of the(ant i-clockwise) overturning mo ments eq uals the sum o f the(clockwise) resto ring mo ments. The resultant propping force (P) isfound from consideration of horizontal equilibrium.

Multi-propped wallsReWaRD a nalyses w alls w ith more than one prop using the hinge method described in the British Steel Piling Handboo k (1997) andBS 8002. In this method, pin joints are introd uced at all the supportpoints and the various sections of w all are analysed separately:

Sections between supports are treated as simply-supportedbeamsThe low est sec tion is trea ted as a single-propped cant ilever

Simply supported

Simply supported

Propped-cantilever


48/110


The simply-supported sections of the w all are inherently stable, b utthe propped cantilever section needs sufficient embedment in theground to prevent the w all toe from kicking into the excavation.

ReWaRD determines the required emb edment o f a multi-proppedwall from the stability of its propped-cantilever section, using themethod described above for single-propped walls.

If the propped-cantilever sect ion is unstable, then ReWaRD trea tsthe wall as simply supported (and hence inherently stable)throughout:

Simply supported

Simply supported


49/110

Chapter 4: Structural forces 49

Chapter 4Structural forces

This chapte r gives de tailed information about ReWaRDs structuralforce calculations.

Cantilever and single-propped wallsBefore calculating the structural forces acting in a cantilever orsingle-propped w all, it is necessary to find a set of earth pressuresand applied loads that are in force and moment equilibrium.ReWaRD provides three w ays o f do ing this:

At minimum safe embedmentWith maximum safety factorsAt failure

At minimum safe embedmentIn this method, equilibrium is achieved by reducing the depth ofembedment of the wall until the earth pressures acting on it are inmoment equilibrium. Fac tors of safety are introduced at a ppropriatepoints in the calculations.

Structural forces ca lculated by this method are regarded as fac tored(i.e. design) values (see Chapter 9).

With maximum safety factorsIn this method, equilibrium is achieved by increasing the factors ofsafety introduced into the calculations until the earth pressures

ac ting on the w all are in moment equilibrium. The de pth of


50/110


embedment of the wall is not reduced.

ReWaRD using the follow ing eq uation to enhance the safety fac torsspecified in the selected design standard above their normal values:

f f = +( )1 1

where f is the original safety factor, f , the enhanc ed safety factor,and , an enhancement factor. This has been spec ially formulatedto ensure that, when f = 1, f , = 1 and, w hen , = 1, f, = f.

Structural forces calculated by this method are regarded as factored(i.e. design) values (see Chapter 9).

At failureIn this method, equilibrium is achieved by reducing the depth ofembedment of the wall until the earth pressures acting on it are inmoment eq uilibrium. No fac tors of safety are applied to any part of

the calculations.

Structural forces calculated by this method are regarded as


51/110

Chapter 4: Structural forces 51

unfactored values and need to be multiplied by an appropriatesafety facto r to o bta in design values (see Chapter 9).

This is the recommended metho d (Method 1) from CIRIA Report104 (1984).

Multi-propped wallsThe structural forces ac ting in a multi-propped wall are calculatedby the hinge method described in the British Steel Piling Handbo ok(1997) and BS 8002. In this metho d, pin joints are introd uced at allthe support points and the various sections of wall are analysedseparately:

Sections between supports are treated as simply-supportedbeamsThe low est sec tion is trea ted as a single-propped cant ilever

Simply supported

Simply supported

Propped-cantilever

ReWaRD determines the structural forces in propped -ca ntileversection using one of the methods described above for cantileverand single-propped w alls.

A worked example showing how to use this method is given inCIRIA Special Publication 95 (1993).


52/110


Design structural forcesBending moments

Design bending moments (M d) are given by:

M d

f M M

where M is the unfactored bending moment and f M is anappropriate safety facto r (see Chapter 9).

Shear forcesDesign shear forces (S d) are given by:

S d f S S

w here S is the unfac tored shear force and f S is an appropriate safetyfactor (see Chapter 9).

Prop forcesDesign prop forces (P d) are given by:

P d f P P

w here P is the unfacto red prop force and f P is an appropriate safetyfactor (see Chapter 9). Different values of f P are sometimes used fordifferent props (for double-propped walls, CIRIA 104 recommendsa larger fP for the upper prop than for the low er prop).


53/110

Chapter 5: Pecks envelopes 53

Chapter 5Pecks envelopes

This chapter gives detailed information abo ut ReWaRDsimplementation of Peck's envelopes.

Distributed prop loadsPecks envelopes provide an empirical w ay o f estimating maximumprop loads fo r multi-propped w alls. The envelopes w ere derivedfrom measurements of strut loads in real excavations and give theapparent p ressure ac ting over the reta ined height of the wall (Peck,1968).

The term apparent p ressure has misled some people into thinkingthat Pecks envelopes represent the ac tual earth pressures acting onthe w all. For this reason, and in anticipation of the publica tion o fCIRIA Report RP526, the term distributed prop load is used inReWaRD instead of a pparent pressure.

ReWaRD ca lculates d istributed prop loads for multi-propped w allsduring short-term stages o nly. At present , only Pecks originalenvelopes are implemented in the program. When CIRIA ReportRP526 is published, support will be added for the envelopesdefined in that repo rt. Refer to ReWaRDs relea se no tes a nd o n-linehelp for further information.

Pecks envelopes Peck (1968) introduced enve lopes for the following gene ral soil

profiles:

SandStiff claySoft clay


54/110


H

H/4

H/4

Sand Soft clay Stiff clay

Envelope for sandPeck's envelope for sand is a rectangle (see the diagram above),w ith the ma ximum distributed prop load being given by:

DPLma x 0.65 K a (F

vH FvqH )

where Ka is the average active earth pressure coefficient in anydrained horizons existing over the retained height (H); FvH is thevertical effective stress at excavation level on the retained side ofthe wall; and Fvq H is the vertical surcharge at the same point.

Water pressures in the retained soil (when present) are added tothe envelope.

Envelope for stiff clayPeck's envelope for stiff clay is a trapezium (see the diagram

above), with the maximum distributed prop load b eing given by:

DPLma x 0.4 (FvH FvqH )

where FvH is the vertical total stress at excavation level on theretained side of the wall and Fvq H is the vertical surcharge at thesame point. (Pecks original envelope which suggested thatDPLma x might be as low as 0.2[ FvH + Fvq H] is now consideredunconservative.)

Pecks envelope for stiff clay includes the effect of any water


55/110

Chapter 5: Pecks envelopes 55

pressures acting on the retained side of the wall and hence waterpressures are not added to the envelope.

Peck's envelope for stiff clay can only be used when the stabilitynumber (N) is less than six, as given by:

N FvH FvqH

C u

w here C u is the average und rained shea r strength in any undra inedhorizo ns over the retained height.

Envelope for soft to medium claysPeck's envelope for soft to medium clays is a half-trapezium (seethe diagram above), w ith the maximum distributed prop load beinggiven by one of two formulae:

DPLma x (1 1.6

N ) (FvH FvqH )

DPLma x (1 4

N ) (FvH FvqH )

w here the symbols are as defined for the stiff clay envelope .

The first formula is used if the cutting is underlain by a deep depositof so ft clay (i.e. w hen the thickness of soft clay be low excavationlevel exceeds the retained height), otherw ise the seco nd equationis used. In this context, clay is considered soft if its undrainedstrength is less than 40 kPa.

Pecks envelope for soft to medium clays includes the e ffect o f anywater pressures acting on the retained side of the wall and hencew ater pressures are not added to the envelope.


56/110


Peck's envelope for soft to medium clays can only be used whenthe stability number N is greater than four.

Obtaining prop loads from Pecks envelopesProp loads are obtained from Pecks envelopes by dividing the

distributed prop load (DPL) diagrams into segments at themidpoints between the props. The load in any one prop is thenca lculated by integrating the D PL over its assoc iated segment.

The follow ing example illustrates this procedure.

aa + b

b + c

c + d

d

2c

2d

2b

The load carried by the top prop is equa l to the a rea o f the firstsegment, of thickness a + b.

The load carried by the middle prop is equa l to the a rea o f thesecond segment, of thickness b + c.

The load carried b y the bo ttom prop is eq ual to the a rea o f the third

segment, of thickness c + d.The load represented by the fourth segment is assumed to becarried b y the ground below excavation level.


57/110

Chapter 6: Base stability 57

Chapter 6Base stability

This chapter gives deta iled information abo ut ReWaRDs basestab ility ca lculations.

Factor-of-safety aga inst ba sal hea veBjerrum a nd Eide (1956) defined the facto r-of-safety against basalheave (Fbh) as follows:

F N C

bh c u

vH vqH ret

vqH exc

=+

where N c is a stability number; C u is the average undrained shear

strength of any undrained horizons within a depth 0.7H below excavation level; H is the retained height of the wall; is the vqH

ret

vertical total stress at excavation level on the retained side of the

w all; is the vertical total stress at excavation level on the vqH exc

excavated side of the wall; and FvH is the vertical surcharge at thesame point.

Stability numberThe stability number (N c) is given by:

for H/B # 2.5N B L H B

c =

+

+

9

1 0 2

12

1 0 2

15

. /

.

. /

.

for H/B > 2.5N B L

c =

+

9

1 0 2

12

. /

.

where H is the retained height; B is the breadth and L the length ofthe excava tion (see the section o n Excavations in Cha pter 10); and$ is the rigid layer correction (defined below ).


58/110


Rigid layer correctionThe rigid layer correction ( $) is derived from the bearing ca pac ityfactors given by Button (1953) and is given by:

= +

1 0 008

1 4

.

.

d

B

w here d is the depth b elow excavation level to the top o f the firstrigid layer and B is the bread th of the excavation.

ReWaRD treats a layer as rigid if it is flagged as such (see thesection on Layers in Chapter 10).


59/110

Chapter 7: Displacements 59

Chapter 7Displacements

This chapter gives detailed information abo ut ReWaRDsdisplacement calculations.

ReWaRD estimates the construction-induced (i.e. short-term)movement o f the retaining wall and the settlement o f the groundsurface behind it from an extensive data ba se of measureddisplacements. Long-term movements, which are generallyassoc iated w ith changes in pore w ater pressure in the soil, are notincluded in the database but are not usually damaging to theretaining structure. (An exception to this would be in soft clayssubject to long-term changes in pore w ater pressure.)

Displacements depend on a number of fac tors, of w hich the most

important a re the height of the excavation and the prevailing soiltype. Dimensionless displacement profiles are used to determinethe distribution of movement down and behind the wall.

ReWaRD allows you to view upper bound, average, and lowerbound displacements, based o n the case histories included in thedatabase.

Displacements are given for sections of wall that deform underplane strain conditions. Sections that are close to the corners of theexcavation or close to buttresses, etc., usually displace far less.

Database of wa ll movementsReWaRD's datab ase o f measured d isplacements comb ines the ca sehistories used by Clough and O'Rourke (1992) and St John et al.(1992) to determine co nstruction-induced wall movements.

The datab ase is split into three pa rts, depend ing on the prevailingsoil conditions:

SandStiff claySoft clay


60/110


In ea ch case, the measured displacements increase w ith increasingheight o f excavation (H), as de scribed below .

Surcharge loading fac torThe surcharge loading factor (fq ) that appears in many of the

eq uations below takes account o f the increase in vertica l stress thatresults from the presence of any surcharges acting on the retainedside of the wall.

For sand profiles, the surcharge loading factor is given by:

f q 1 FvqH

F

vH

where FvH is the vertica l effect ive stress at excavation level due tothe weight of soil and water and FvqH is the vertical stress at thesame point due to any surcharges.

For soft a nd stiff clay profiles, the surcharge load ing facto r is givenby:

f q 1 FvqH

FvH

where FvH is the vertical total stress at excavation level due to theweight of soil and water and Fvq H is as defined above.

Database for sandsThe data ba se for sand s is taken from Clough and O 'Rourke (1992)and includes 7 case histories for excavations up to 24m high.

Ca ntilever and propped w allsMaximum displacementsThe ma ximum set tlement behind the w all ( *vm) is given by:


61/110


*vm

H (0.003 0.001) f q

where fq is the surcharge loa ding factor (see abo ve). The values

represent upper and lower bounds to the data.

The ma ximum horizo ntal movement of the w all ( *hm) is given by:

*hm 4

3*vm

Displacement profilesClough and O 'Rourke (1992) proposed an envelope of no rmalized

settlement ( *v/ *vm) for sands which is triangular and extends for adistance eq ual to tw ice the height of the excavation (H).

Closer scrutiny of the data suggests that the bounds to themeasured settlements can be defined more closely than Cloughand ORourke propose. ReWaRD therefore calculatesdisplacements for sands using a modified form of the triangularsettlement profile proposed by Clough and O'Rourke, as shownbelow.


62/110


The settlement a t x = H ( *vH) is given by:

*vH

H 0.001 f q

and the ho rizontal displacement a t z = H ( *hH) is given by:

*hH 4

3*vH

The same profiles are used for ca ntilever and propped w alls.

Data base for stiff claysThe datab ase for stiff clays is taken from St John et al. (1992) andincludes 6 case histories involving cant ilever excavations up to 8mhigh and 13 case histories involving propped excavations up to25m high.

Cantilever wallsMaximum displacementsThe ma ximum horizo ntal movement ( *hm) of a ca ntilever wall in stiffclay is given by:

*hm

H 0.0015 f q (0.00035 0.00025) f

2q H

where fq is the surcharge loading factor (see abo ve). The valuesrepresent upper and lower bounds to the data.

The ma ximum settlement ( *vm) behind the wall is given by:

*vm 0.75 *hm


63/110


Displacement profilesClough and O 'Rourke (1992) propo sed an envelope o f normalizedsettlement ( *v/H) for stiff clays w hich is triangular a nd extends fora distance eq ual to three times the height of the excavation (H), asshow n below .

Propped wallsMaximum displacementsThe ma ximum ho rizo nta l moveme nt ( *hm) of a propped w all in stiffclay is given by:

*hm

H (0.003 0.001) f q

where fq is the surcharge loading factor (see abo ve). The valuesrepresent upper and lower bounds to *hm.


64/110


The ma ximum settlement ( *vm) behind the wall is given by:

*vm 0.75 *hm

Displacement profilesAs discussed for cantilever walls in stiff clays (above), Clough andO'Rourke (1992) proposed an envelope of normalized settlement(*v/H) for stiff clays which is triangular and extends for a distanceeq ual to three times the height of the excavation (H).

St John (1992, personal communication) has found that themaximum settlement behind the w all usually occurs near x = H andthat the settlement close to the w all ( *v0) is approximately 50% of*vm. ReWaRD therefore calculates displac ements for propped w allsin stiff clays using a modified profile, as shown below.

The table be low gives the co-ordinates o f the key points alongthese profiles.


65/110


x/H orz/H

0 0.65 1.0 1.5 3.0

*/ *m 0.5 1.0 1.0 0.5 0.0

Database for soft claysThe da taba se for soft clays is taken from C lough and O 'Rourke(1992) and includes 13 case histories for excavations up to 20mhigh.

Ca ntilever and propped w allsMaximum displacementsAccording to Clough et al. (1989), the horizontal movements ofretaining walls in soft clays is controlled by three main factors:

The height of the excavation (H)

The facto r-of-safety a ga inst basal hea ve (F bh , see Chapter 7)The systems st iffness (EI/ ( w sp

4, see below )

Clough et al. present design curves that allow the maximumhorizo ntal movement of the w all ( *hm) to b e estimated from H, F bh,and EI/ ( w sp

4 (see below ).

3.0

010 30 50 500100

System stiffness

h m

/ H ( % )

300 30001000

2.0

1.0

3.0

2.0

1.4

1.1

1.0

0.9 = Fb h


66/110


The ma ximum settlement ( *vm) behind a retaining wall in soft clayis equa l in magnitude to its maximum horizo ntal movement ( *hm)and is given by:

*vm

*hm

f q *

Clough

hm

where *hmClough is the maximum horizo ntal movement ob tained from

Clough et al .s chart.

Displacement profilesClough and O'Rourke propose an envelope of normalizedsettlement ( *v/ *vm) for soft clays which is trapezoidal in shape andextends for a distance equal to twice the height of the excavation(H).

The table be low gives the co-ordinates o f the key po ints alongthese profiles.

x/H or z/H 0 0.75 2.0

*/ *m 1.0 1.0 0.0

The same profiles are used for ca ntilever and propped w alls.


67/110


System stiffnessClough et al. (1989) defined system stiffness as follow s:

System stiffness EI

( w s 4p

where E is the Young's modulus of the wall and I its secondmoment of area; ( w is the unit weight of wa ter; and s p is the average spacing between props (a value that can only be calculated formulti-propped w alls).

Fernie and Suckling (1996) have suggested a method of definingsystem stiffness for cant ilever and single-propped walls:

For a cantilever: s p = retained height + depth o f fixityFor a single-propped wall: s p = (retained height below prop +depth of fixity) or retained height above prop (whichever islarger)

Fernie and Suckling further suggest that the depth o f fixity (d) in softsoils is given by:

For a cantilever, d = 1.4HFor a single-propped w all: d = 0.6H

w here H is the retained height.


68/110



69/110

Chapter 8: Durability 69

Chapter 8Durability

This chapter gives information ab out ReWaRDs durabilitycalculations.

Corrosion of steel piling in various environmentsBritish Steels Piling Handbook (1997) gives mean corrosion ratesfor steel piling in various environments:

Environment Description Mean corrosion rate(mm/year)

Atmospheric Above splash zone 0.035

Splash zone 0 to 1.5 m above tidalzone

0.075

Tidal zone Between mean highwater spring and meanlow water neap tides

0.035

Low w ater zone Between mean low water neap and lowestastronomical tide levels

0.075

Immersion zone Betw een lowestastronomical tide a nd

bed level

0.035

Soil Below bed level 0.015

ReWaRD calculates the tota l corrosion rate along a sheet pile w allby summing the mea n co rrosion rate (taken from the table ab ove)on each side of the wall. For example, a section of wall that is incontact with soil on one side and in the splash zone on the otherw ould have a tota l corrosion rate o f 0.015 + 0.075 = 0.09 mm/year.

For further information about durability of sheet pile, refer toChapter 3 of the Piling Handboo k.


70/110



71/110

Chapter 9: Safety factors 71

Chapter 9Safety factors

This chapter describes the safety factors that ReWaRD uses in itscalculation of earth pressures and structural forces.

The follow ing symbols are used throughout this chapter:

E = earth pressure

Subscripts:a = active mode of failured = design (i.e. factored) valuen = nettnom = nominal valuep = passive mode o f failure

r = revisedu = undrained

Superscripts:ret = retained side of w allexc = excavated side o f wall

Design a pproa chesCIRIA Report 104 (1984) discusses two distinct approaches todesigning embedded retaining w alls, based o n:

A. Moderately conservative soil parameters, loads, andgeometryB. Worst credible soil parameters, loads, and geometry

Lower factors of safety are appropriate when approach B isadopted.

CIRIA 104 recommends different factors of safety for temporaryand permanent works, depending on which design approach isadopted . The follow ing table indicates w here factors are quoted inthe report.


72/110


Design approach Works

Temporary Permanent

A. Moderatelyconservative

T Effective stress* Tota l stress

T Effective stress X Tota l stress

B. Worst credible T Effective stress X Tota l stress

T Effective stress X Tota l stress

T = values given; * = speculative va lues given; X = values not given

Safety factors in ea rth pressure ca lculationsThis section o f the Reference Manual gives details of the safetyfactors ReWaRD uses in the earth pressure calculations describedin Chapter 2, depending on which design method is adopted:

G ross pressure metho d

Nett pressure methodRevised (or Burland-Po tts) methodStrength facto r methodLimit state methods

G ross pressure methodIn the gross pressure metho d (described in Civil Engineering Co de-of-Practice CP2, 1951), a lumped factor-of-safety (F p) is applied tothe gross passive earth pressure:

E pd E

p

F p

Recommended values of F p taken from the Literature are givenbelow.


73/110


Design standard/approach orreference

Works

Temporary Permanent

CP2 2.0

Teng (1962) 1.5-2.0Canadian Foundation Engineering Manual (1978)

1.5

CIRIA 104 A. Mo dera telyconservative

Fp = 1.2-1.5 for N =20-30 E

Fpu = 2.0*

Fp = 1.5-2.0 for N =20-30 EFpu = X

B. Worstcredible

Fp = 1.0Fpu = X

Fp = 1.2-1.5 for N =20-30 EFpu = X

* = speculative; X = not given

Burland et al. (1981) have c riticized the G ross Pressure Metho dwhen applied to undrained analysis, because it can lead to twopossible required depths of embedment.

Nett pressure methodIn the nett pressure method (described in the British Steel PilingHandboo k, 1997), a lumped facto r-of-safety (F np) is applied to thenett passive earth pressure:

E npd E np

F np

Recommended values of F np taken from the Literature are givenbelow.


74/110


Design standard Wall type

Cantilever Propped

British Steel Piling Handbook 1.0* 2.0

*According to the Piling Handbook, the safety factor is introduced by theadoption of reasonably conservative soil strength parameters

Nett earth pressures are given by whichever of the followingeq uations applies:

E ret

n F

h

ret F

h

exc and E

exc n

0 (w hen E ret

n $ 0)

or:

E ret

n 0 and E

exc n

F

h

exc F

h

ret (w hen E

exc n > 0)

Likewise, nett water pressures are given by:

W ret

n u ret u exc and W

exc n

0 (w hen W ret

n $ 0)

or

W ret

n 0 and W

exc n

u exc u ret (w hen W exc

n > 0)

The ne tt pressure metho d ha s been c riticised for giving rap idlyincrea sing factors-of-safety w ith increa sing depth of embedment,and much higher factors-of-safety than other methods (Burland et al ., 1981; Potts &Burland, 1983). Results obtained with the nettpressure method should be compa red w ith those from o ne or moreof the o ther availab le methods.


75/110


Revised (or Burland-Potts) methodIn the revised (or Burland-Potts) method (described by Burland et al .,1981), a lumped fac tor-of-safety (F r) is applied to the revised passiveearth pressures below formation level:

E rpd E rp

F r

Recommended values of F r taken from the Literature are givenbelow.

Design standa rd/approa chor reference

Works

Temporary Permanent

Burland et al. (1981) 1.5-2.0

CIRIA 104 A. Moderate lyconservative

Fr = 1.3-1.5(usually 1.5)

Fru = 2.0

Fr = 1.5-2.0(usually 2.0)

Fru = X

B. Worst credible F r = 1.0*Fru = X

Fr = 1.5Fru = X


Drained horizonsRevised active earth pressures in drained horizons below excavation level are given by:

E rak (K a F

vH )ret

where Ka is the drained active earth pressure coefficient for thehorizon on the retained side of the wall and FNvH is the verticaleffective stress on the retained side o f the w all at excavation level.


76/110


Revised passive earth pressures below excavation level are givenby:

E rpk (K p F

v K pc c

)exc

(K a F

v K ac c

)ret (K a F

vH )ret

where Kp and Kpc are the drained passive earth pressure coefficientsfor the horizon on the excavated side of the wa ll; K a and Kac are thedrained active earth pressure coefficients for the horizon on theretained side of the w all; and FNvH is as defined above.

Undrained horizonsRevised active earth pressures in undrained horizons below excavation level are given by:

E rak

(K au FvH )ret

where Kau is the undrained active earth pressure coefficient for thehorizo n on the retained side of the wall and FvH is the vertical tota lstress on the retained side of the wall at excavation level.

Revised passive earth pressures below excavation level are givenby:

E rpk (K pu Fv K puc C u )exc (K au Fv K auc C u )

ret (K au FvH )ret

where Kpu and Kpuc are the undrained passive earth pressurecoefficients for the horizon on the excavated side of the wall; K auand Kauc are the undrained ac tive earth pressure coe fficients for thehorizon on the retained side of the wall; and FvH is as definedabove.

Strength factor methodIn the strength factor method (described in CIRIA Report 104,1984), a factor-of-safety (F s) is applied to the soils coefficient offriction (tan N) and effective cohesion (c N) and a different facto r-of-safety (Fsu) is applied to its undrained shea r strength (C u):


77/110


tan Nd tan N

F s , c

d

c

F s , C ud

C u

F su

The design earth pressures acting in the ground a re then ca lculatedfrom the design soil parameters:

E d E f (Nd , c

d , C ud , ...)

Recommended values of F s taken from the Literature are givenbelow.

Design standard/approach Works

Temporary Permanent

CIRIA 104 A. Moderatelyconservative

Fs = 1.1 for N > 30 Eelse Fs = 1.2

Fsu = 1.5*

Fs = 1.2 for N > 30 Eelse Fs = 1.5

Fsu = X

B. Worstcredible

Fs = 1.0Fsu = X

Fs = 1.2Fsu = X


Limit sta te metho dsIn design standards that employ limit state methods such asG eoguide 1, BS 8002, and Eurocode 7 partial factors ( ( ) areapplied at different stages in the earth pressure calculations.

Partial factors are typically applied to:

Actions (i.e. direct a nd indirect loads)Material propertiesGeometric properties

Partial factors on actionsDesign a ctions (Fd) are obtained from characteristic actions (F k) by

multiplying by the appropriate partial factor ( ( F):


78/110


F d ( F F k

where the value of ( F varies from one action to another anddepends on the selected design standard.

Recommended values of ( F taken from the Literature are givenbelow.

Design standard/case Action

Permanent Varia-ble Accid-ental

Unfav. Fav.

G eoguide 1 1.5 on surcharge on retained side of wall,otherw ise 1.0

BS 8002 1.0

Eurocode 7 A 1.0 0.95 1.5 1.0

B 1.35 1.0 1.5 1.0

C 1.0 1.0 1.3 1.0

Serviceability 1.0 1.0 1.0 1.0Unfav. = unfavourable; Fav. = favourable

In applying the partial factors from Eurocode 7, pressures arising

from the w eight of the so il are regarded as unfavourab le permanentactions, as are water pressures. Pressures arising from surchargesare regarded as permanent, variab le, or accidental and favourab leor unfavourable according to which flags are set for ea ch individualsurcharge.

Partial factors on material propertiesDesign material properties (X d) are obtained from characteristicmaterial properties (X k) by dividing by the a ppropriate pa rtial factor(( m):


79/110


X d X k

( m

where different values of ( m apply to each material property. Forsoil strength parameters, the specific equations used are:

tan Nd tan Nk

( N, c

d

c

k

( c , C ud

C uk

( Cu

where ( N, ( c, and ( Su depend on the selected design standard.

Recommended values of ( m taken from the Literature are given

below.

Design standard/case Partial factor

( N ( c ( Cu

G eoguide 1 1.2 2.0

BS 8002 1.2 1.5

Eurocode 7 A 1.1 1.3 1.2

B 1.0

C 1.25 1.6 1.4

Serviceability 1.0

Partial factors on geometric propertiesThe design retained height of the wall (H d) is obtained from theactual reta ined height (H k or H nom) by a dding an a ppropriate safetymargin () H):

H d H k ) H


80/110


Recommended values of ) H taken from the Literature are givenbelow.

Design standard/case Unplanned excavation ( ) H)

G eoguide 1 None

BS 8002 10% of the clear height*, buta minimum of 0.5m

Eurocode 7 A, B, &C 10% of the clear height*, buta maximum of 0.5m

Serviceability None*For propped w alls, clear height = height below bo ttom propFor ca ntilever w alls, clea r height = height of exca vation

Design earth pressures

Design earth pressures ac ting in the ground are ca lculated from thedesign parameters:

E d E k f (F d , Nd , c

d , C ud , H d , ...)

Safety factors for structural forcesThis section g ives de tails of the safety factors that a re applied to thestructural force calculations described in Chapter 4.

At minimum safe embedmentStructural forces calculated at minimum safe embedment (seeChapter 4) are regarded as factored (i.e. design) values.

Bending moments and shear forcesDesign bending moments (M) and shear forces (S) are given by:

M d M and S d S


81/110


82/110


Prop forcesThe design prop force (P) for a single-propped w all is given by:

P d f P P

Recommended values of f P taken from the Literature are given inthe table below .

Design standard Safety factor

fM fS fP

CP2 1.5 2.0 x 1.1* = 2.22.0 x 1.15 = 2.3

British Steel Piling

Handbook

1.5 2.0 x 1.15* = 2.3

CIRIA 104 1.5 2.0 x 1.25 1 = 2.52.0 x 1.15 2 = 2.3

Pa rtial facto rs to a cco unt for a rching *in co hesive so ils; in cohesionless soils; 1in upper level ofprops; 2in second level of props (single-a nd doub le-propped w alls only)


83/110

Chapter 10: Engineering objects 83

Chapter 10Engineering objects

This chapter gives de tailed informa tion abo ut how the variousengineering ob jects in ReWaRD affect its engineering calculations.

Co nstruction stagesCo nstruction stages ca n be designated a s short- or long-term. Theterm helps dete rmined w hether ReWaRD ca lculates ea rth pressuresusing total or effective stress theory (see the section entitled Total or effective stresses? in Chapter 2).

G round profilesSloping ground

When calculating earth pressure coefficients for horizons on the

retained side of the wa ll, ReWaRD determines the parameter $ thatappears in the eq uations for K a and Kp (see Chapter 2) as follows:

$ max ($ground , i layer )

where $ground is the slope of the ground profile and i layer is the d ip ofthe layer for which ea rth pressure coe fficients are being ca lculated .

Stepped groundThe effect o f a steppe d ground profile is to increase the vertica ltota l stress on the retained side o f the wall by a n amo unt that variesw ith depth as show n below .


84/110


AB

45 + /2C

The increase in vertical tota l stress dow n the w all ( )F v) is given by:

)F v 0 for z a # z # z b

)F v ( h z z b

z c z b for z b < z < z c

)F v ( h for z $ z c

where ( is the unit weight of soil at the ground surface and thedepths z b and z c are given by:

z b f tan N


85/110


z c (w f ) tan (45 EN

2) h

where N is the angle of friction of the soil. In these equations, h isthe height, w the width, and f the flat of the stepped groundsurface.

This approach is identical to the method (C) recommend ed inCIRIA Special Publication 95 (1993).

ExcavationsSloping excava tions

When calculating earth pressure coefficients for horizons on theexcavated side of the w all, ReWaRD dete rmines the pa rameter $that appears in the equations for K

a and K

p (see Chapter 2) as

follows:

$ min ($excavation , i layer )

where $excavation is the slope of the excava tion a nd i layer is the dip ofthe layer for which ea rth pressure coefficients are be ing calculated.

BermsReWaRD calculates the effects of a berm on the earth pressures

acting on the excavated side of the wall using the methodrecommended in CIRIA Special Publica tion 95 (1993).

The effect o f the berm is to increase the vertical total stress on theexcavated side of the wall by an amount that varies with depth asshow n below .


86/110


AB

45 /2C

The increa se in vertical total stress ( )F v) due to the presence of a

berm depends on w hether it is wide o r narrow .

Narrow bermsA berm is considered narrow when z b < h, in which case )F v isgiven by:

)F v ( z for z a # z # z b

)F v )F

ma x

v (z z b ) ( (h z )z b

h z b for z b < z < h

)F v )Fma x

v [z c z

z c h ] for h # z < z c

)F v 0 for z $ z c


87/110


where the largest increase in vertical total stress is:

)Fma x

v ( h (

z c h

z c z b )

In these equations, all depths are measured from the top of theberm. ( is the unit weight of soil in the berm and the depths z b andzc are given by:

z b f tan N

z c (w f ) tan (45 EN

2

) h

where N is the angle o f friction of the soil and h is the height, w thewidth, and f the flat o f the berm.

Wide bermsA berm is considered w ide w hen z b $ h, in w hich ca se )F v is givenby:

)F v ( z for z a # z # h

)F v ( h for h < z # z b

)F v ( h [z c z

z c z b ] for z b # z < z c


88/110


)F v 0 for z $ z c

w here the symbols are a s given for narrow berms.

Plan dimensionsThe plan dimensions o f an excavation a re used to ca lculate thefacto r of safety against basal heave (see Chapter 6).

SoilsSoil classification system

ReWaRD's soil classification system is based on a combination of:

The British Soil Classifica tion System (BSCS), as d escribed in BS5930:1981The Unified So il Classifica tion System (USCS), as described inASTM D2487-1069The G erman Soil Classifica tion System (DIN), as decribed in D IN18 196

In addition to the ba sic groupings of G ravel, Sand, Silt, and Claythat are common to all these systems, ReWaRD's Soil Classificationsystem includes co mmonly-encounte red soils under the headingsOrganic, Fill, Chalk, Rock, River Soil, and Custom.

The fo llow ing table lists the so ils that are included in ReWaRD's soilclassification system and give the corresponding group symbols

from each of the established systems listed above (w here they areavailable).

Class Sym-bo l

BSCS USCS DIN States

G r a v

e l

Unclassified*Well-gradedUniformly-gr'dG ap-gradedSiltyClayey*Very silty*

Very clayey*

GG WG PuG PgG -MG -CG M

G C

GG WG PuG PgG -MG -CG M

G C

GG WG PG P

G ?-G MG ?-G C

G M

G C

GG WG EG I

G UG TG U

G T

Unpecified (Unsp)Very loose (VL)Loose (L)Medium dense (MD)Dense (D)Very dense (VD)Poo rly compd (PC)

Well comp'd (WC)


89/110


Class Sym-bo l


S a n d Unclassified*

Well-gradedUniformly-gr'dG ap-gradedSiltyClayey*Very silty*Very clayey*

SSWSPuSPgS-MS-CSMSC

SSWSPuSPgS-MS-CSMSC

SSWSPSP

S?-SMS?-SCSMSC

SSWSESI

SUSTSUST

Same as GRAVEL

G r a n u

l a r s i l t

UnclassifiedG ravellySandyLow -plasticity

MMGMSML

MMGMSML

MML/MHML/MH

ML

U--

UL

Unpecified (Unsp)Very loose (VL)Loose (L)Medium dense (MD)Dense (D)Very dense (VD)

C o h e s i v

e s i l t

Unclassified*Int.-plast.*

High-plast.*

MMI

MH

MMI

MH-ME

MML

MH

UUM

-

Same as CLAY

C l a y

Unclassified*$G ravelly*Sandy*Low-plast.*Int.-plast.*$High-plast.*$Laminated*

CCGCSCLCI

CHLam

CCGCSCLCI

CH-CE-

CCL/CHCL/CH

CLCLCH

-

T--

TLTMTA-

Unspecified (Unsp)*$Very soft (VSo)Soft (So)Firm (F)*$Stiff (St)*$Very stiff (VSt)*$Hard (H)*$

O r g a n i c Unclassified

O rganic siltOrganic clayPeatLoam

OMOCOPt

Loam

OMLO/

HCLO /H

Pt-

OO LO HPt-

O(OU)O T

HN/HZ-

Same as CLAY

G r a n u

l a r f i l l

UnclassifiedRock fillSlag fillG ravel fillSand fillChalk fillBrick ha rdco reAshesPFA

MdGRockFSlag

GravFSandFChkFBrickAshPFA

UnspecifiedPoorly-co mp'd (PC)Well-compacted (WC)

Clay fill ClayFSame as CLAY


90/110


Class Sym-bo l


C h a l k Unclassified*

G rade I*G rade II*G rade III*G rade IV*G rade VG rade VI

ChkChk1Chk2Chk3Chk4Chk5Chk6

Unspecified (Unsp)

R o c k

Marl*Weatheredrock*

MarlRock

Unspecified (Unsp)

R i v e r s o i l

River mudDoc k siltAlluvium

RivMDock

SAlluv

Unspecified (Unsp)Very soft (VSo)Soft (So)

Custom*$ Cust Unspecified (Unsp)*$

G ? = G , GW, or G P; S? = S, SW, or SP; Int. = intermed iate; plast. = plasticity*may have effective cohesion (if symbol appears next to Class &State)may be undrained$may be fissured (if symbol appears next to Class &State)potential for liquefaction

Database of soil propertiesReWaRD uses a database of soil properties to check that anyparameters you enter for a soil are compatible with that soil'sengineering description.

ReWaRD's checking system is based on the concept that there arenormal and extreme ranges for each soil parameter.

If you enter a value that is outside the extreme range for a pa rticularsoil parameter, ReWaRD issues an error message a nd prevents youfrom proceeding until you have changed the o ffending value.

If you enter a value that is outside the normal range, ReWaRDissues a warning message and allows you to proceed only if youconfirm that the value entered is correct.

The default pa ramete rs are provided to assist in initial design studies

only, and should not be used as a substitute for measured


91/110


parameters. As in all forms of geotechnical design, parametersshould be chosen on the basis of adequate site investigation,including suitable laboratory and field measurements.

The publica tions that ha ve been referred to in compiling thedatabase include:

Terzaghi &Peck (1967)NAVFAC DM-7 (1971)Peck, Ha nson, &Thornburn (1974)Winterkorn &Fang (1975)Canadian Foundation Engineering Manual (1978)Reynolds &Steedman (1981)Bell (1983)Mitche ll (1983)TradeARBED's Spundwand-Handbuch Teil 1, Grund lagen (1986)Bolton (1986)

Clayto n &Militiski (1986)Clayton (1989)Tomlinson (1995)British Steel's Piling Handbook (1997)

Invaluable advice regarding the properties of various soils wasprovided b y Professors JB Burland , PR Vaughan, and DW Hight andby D r G Sills.

In the following table Dd = dry density; Dw = wet density; Npeak =peak angle of friction; Ncrit = critica l state angle o f friction; cpeak =peak effective co hesion; c

crit = critical state e ffective cohesion; S

u= undrained shea r strength; ) Su = rate o f increase in Su w ith depth.

Parameter Classification Minimum Default Maximum

Class Sta te Ext. Normal Normal Ext.

G r a v

e l

Dd (kg/m3) All Unsp

VLL

MDD

VDPC

WC

1200120013001400150017001200

1400

1400130014001500170020001400

1700

2050150016501850205022501650

2050

2200160018002000220024001800

2200

2500180020002200240025002200

2500


92/110


93/110


Npeak (deg )

Reducedto allow forpotentialliquefaction

All UnspVLL

MDD

VDPCWC

2020262933372329

3025303336403036

3226323437423237

4028353740453540

5530404550554555

Ncrit (deg) All All 23 30 32 35 40

cpeak (kPa)discountingnaturalcementation

SS_CSMSC

All 0 0 0 0 10

O thers All Not applicable

ccrit (kPa) SS_CSMSC

All 0 0 0 0 5

O thers All Not applicable

G r a n u

l a r s i l t

Dd (kg/m3) All All 1100 1275 1850 2150 2200

Ds (kg/m3) All All 1500 1800 2050 2150 2400

Npeak (deg )

Reducedto allow forpotentialli

reward reference manual 2.5

Documents