reward - geocentrix · reward 2.5 was designed and written by dr andrew bond and ian spencer of...

RETAINING WALL DESIGN

ReWaRDVersion 2.5

Reference Manual

2 ReWaRD 2.5 Reference Manual

Information in this document is subject to change without noticeand does not represent a commitment on the part of GeocentrixLtd. The software described in this document is furnished under alicence agreement or non-disclosure agreement and may be usedor copied only in accordance with the terms of that agreement. Itis against the law to copy the software except as specificallyallowed in the licence or non-disclosure agreement. No part of thismanual may be reproduced or transmitted in any form or by anymeans, electronic or mechanical, including photocopying andrecording, for any purpose, without the express written permissionof Geocentrix Ltd.

©1992-2000 Geocentrix Ltd. All rights reserved.

Geocentrix and ReWaRD are registered trademarks of GeocentrixLtd.

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 International BusinessMachines Corp. Other brand or product names are trademarks orregistered trademarks of their respective holders

Set in Optimum using Corel WordPerfect 8.0.

Service Release 2.53 (9/00).

Printed in the UK.

Acknowledgements 3

AcknowledgmentsReWaRD 2.5 was designed and written by Dr Andrew Bond andIan Spencer of Geocentrix Ltd. The program was originallycommissioned by British Steel Ltd.

The ReWaRD Reference Manual was written by Dr Andrew Bond.

Parts of ReWaRD were developed with the assistance of ProfessorDavid Potts of Imperial College of Science, Technology, andMedicine and Dr Hugh St John of the Geotechnical ConsultingGroup.

The following people assisted with the testing of this and previousversions of the program: Vassilis Poulopoulos (Geocentrix); RomainArnould (Geotechnical Consulting Group); Andy Fenlon (NonsuchVideographics); Joe Emmerson (British Steel); and Kieran Dineen(Imperial College).

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 11On-line help 11Tooltips 11Technical 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 with 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 25Perpendicular line surcharges 29


Area surcharges 30Point surcharges 32Design pressures 34Soil pressures 34Surcharge pressures 35Combined earth pressures 35Groundwater pressures 36Tension cracks 36Combined water pressures 38Total pressures 38Minimum active pressures 38Low-propped walls 38Earth pressure coefficients 41Coulomb 41Rankine 42Packshaw 43Caquot & Kerisel 43Kerisel & Absi 44

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

Out-of-balance moment 45Cantilever walls 45Fixed-earth conditions 45Single-propped walls 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

Table of contents 7

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

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

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

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

Database of wall movements 59Surcharge loading factor 60Database for sands 60Cantilever and propped walls 60Database for stiff clays 62Cantilever walls 62Propped walls 63Database for soft clays 65Cantilever and propped walls 65System stiffness 67

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

Corrosion of steel piling in various environments 69

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

Design approaches 71Safety factors in earth pressure calculations 72Gross 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


With maximum safety factors 81At failure 81

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

Construction stages 83Ground profiles 83Sloping ground 83Stepped ground 83Excavations 85Sloping excavations 85Berms 85Plan dimensions 88Soils 88Soil classification system 88Database of soil properties 90Critical state parameters 99Fissured soils 99Layers 100Dip 100Rigid layers 100Water tables 101Retaining walls 101Section properties 101Rowe’s parameter 103King-post (or soldier-pile) walls 103Surcharges 104Elastic reflection parameter 104Duration/effect 105Imposed loads 105Duration/effect 105

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

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 chapter 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 pressures� Chapter 3 Required embedment� Chapter 4 Structural forces� Chapter 5 Peck’s envelopes� Chapter 6 Base stability� Chapter 7 Displacements� Chapter 8 Durability� Chapter 9 Safety factors� Chapter 10 Engineering objects� Chapter 11 References


ConventionsTo help you locate and interpret information easily, the ReWaRDUser Manual uses the following typographical conventions.

This Represents

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

Item1 YYYY Item2 An item on a cascading menu. Item1 is the name of anoption on the main menu bar (such as File or Window);and Item2 is the name of an option on the cascadingmenu that appears when you select Item1 (such as Newor Open). Thus, File YYYY New represents the Newcommand from the File menu.

italic Place holders for information you must provide. Forexample, if you are asked to type filename, you shouldtype the actual name for a file instead of the wordshown in italics

Italic type also signals a new term. An explanationimmediately follows the italicized term

monospaced Anything you must type on the keyboard

CAPITALS Directory names, filenames, and acronyms

KEY1+KEY2 An instruction to press and hold down key 1 beforepressing key 2. For example, "ALT+ESC" means press andhold down the ALT key before pressing the ESC key.Then release both keys

KEY1, KEY2 An instruction to press and release key 1 before pressingkey 2. For example, "ALT, F" means press and release theALT key before pressing and releasing the F key

Chapter 1: Introduction 11

Where to go for helpYour first source of help and information should be the ReWaRDmanuals and the on-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 ReWaRD’sStockyard and Workbooks.

Reference manualThe ReWaRD Reference Manual (this book) gives detailedinformation about the calculations ReWaRD performs. The manualassumes you have a working knowledge of the geotechnical designof embedded retaining walls.

On-line helpThe on-line help system contains detailed information aboutReWaRD. Help appears in a separate window with its owncontrols. Help topics that explain how to accomplish a task appearin windows that you can leave displayed while you follow theprocedure.

To open the on-line help system:

� Press F1� Click the Help button in a dialogue box� Choose a command from the Help menu

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

TooltipsIf you pause while passing the mouse pointer over an object, suchas a toolbar button, ReWaRD displays the name of that object. Thisfeature, called Tooltips, makes it easier for you to identify what yousee and to find what you need.


Technical supportTechnical support for ReWaRD is available direct from Geocentrixor through your local distributor. If you require technical support,please contact Geocentrix by any of 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 Technical SupportGeocentrix 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 contactReWaRD Sales on the same numbers as above.

Chapter 2: Earth pressures 13

Chapter 2Earth pressures

This chapter gives detailed information about the theory andassumptions behind ReWaRD’s 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 water table� A maximum of one prop or anchor� An unlimited number of surcharges� An unlimited number of imposed loads

The results of ReWaRD’s earth pressure calculations are availableat the top and bottom of each horizon and (when present) at anyinternal sub-horizons within the horizon. ReWaRD inserts sub-horizons into an horizon when:

� Earth pressures increase with depth in a non-linear manner (suchas when a non-uniform surcharge is applied to the wall)

� Earth pressures are needed for structural force calculations (toensure sufficient accuracy in the bending moments)

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

� As built� At the minimum safe embedment� With maximum safety factors� At failure

The following paragraphs explains the assumptions that are madefor each of these conditions and the table below summarizes these.


Condition Wall length* Safetyfactors**

Inequilibrium?

As built L E No***

At minimumsafe embedment

< L E Yes

With maximumsafety factors

L > E Yes

At failure << L 1.0 Yes*L = specified wall length (as used in the construction stage)**E = specified safety factor (from the selected design standard)***Unless the wall length is selected accordingly

Earth pressures as builtReWaRD calculates as -built earth pressures for the specified walllength and safety factors using limiting earth pressure coefficients.As-built earth pressures are not normally in equilibrium: the wall iseither unstable (i.e. has too little embedment) or stable (i.e. hassufficient embedment) at limiting conditions.

Earth pressures at minimum safe embedmentReWaRD calculates earth pressures at minimum safe embedmentby reducing the wall length until the earth pressures are inequilibrium for the specified safety factors, using limiting earthpressure coefficients.

Earth pressures with maximum safety factorsReWaRD calculates earth pressures with maximum safety factors byincreasing the safety factors until the earth pressures are inequilibrium for the specified wall length, using limiting earthpressure coefficients.

Earth pressures at failureReWaRD calculates earth pressures at failure by reducing the walllength until the earth pressures are in equilibrium with safety factorsset to unity, using limiting earth pressure coefficients.


Stresses in the groundThis section describes the way ReWaRD calculates the stressesacting in the ground, owing to the weight of soil and water:

� Vertical total stress (cv)� Pore water pressure (u)� Vertical effective stress (ckv)� Horizontal effective stress (ckh)� Horizontal total stress (ch)

Total or effective stresses?The following table indicates when ReWaRD calculates earthpressures 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 vertical total stress in an horizon (cv) is calculated from the unitweight and thickness of any soil layers and standing water abovethe point being considered:

cv �

‹

z

0

E dz � Ew hsw

where z is the depth below the ground surface; E is the layer's bulkunit weight; Ew is the unit weight of water; and hsw is the height ofany standing water.

When there is no water table acting in the horizon or the watertable is Dry, E is equal to the soil's unsaturated unit weight;otherwise it is equal to the soil's saturated unit weight.


Pore water pressureDrained horizonsThe pore water pressure (u) at a depth (z) in a drained horizon iscalculated as follows.

If no water table is present or the water table is dry:

u � 0

If a water table is present and it is hydraulically connected to theoverlying water regime:

u � uT � (ju

jz)(z � zT)

where uT and zT are the pore water pressure and depth(respectively) at the top of the horizon; and ju/jz is the porepressure gradient.

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

u � uA � (ju

jz)(z � zW)

where uA is the ambient pore water pressure specified by the watertable; zW is the depth of the water table; and ju/jz is the porepressure gradient.

The value of ju/jz is determined by the type of water table presentin the horizon (see on-line Help).

Undrained horizonsThe pore water pressure in undrained horizons is calculated as fordrained horizons, but it is irrelevant to the calculation of total earthpressures and is therefore not displayed.


Vertical effective stressDrained horizonsThe vertical effective stress in the horizon (ckv) is given by Terzaghi'sequation:

c�

v � cv � u

where cv is the vertical total stress and u the pore water pressure atthe corresponding depth.

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

Horizontal effective stressDrained horizonsThe horizontal effective stress in a drained horizon (ckh) is obtainedfrom the vertical effective stress (ckv) via the equation:

c�

h � Kc�

v � Kcc�

where K and Kc are drained earth pressure coefficients and ck is thesoil's effective cohesion.

The value of K depends on the soil’s angle of friction (k), the angleof wall friction (G), the dip of the horizon (A) and the mode offailure (active or passive):

K � f (k, G, A, mode of failure)

See the section Earth pressure coefficients in this chapter for detailson the precise form of the function f.

Kc depends on the value of K and also the soil’s effective cohesion(ck), wall adhesion (a), and the mode of failure:


Kc � ±2 K (1 �

a

c �

)

where the + sign is used for active conditions and the > sign forpassive (Potts & Burland, 1983).

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

Undrained horizonsThe horizontal effective stress in undrained horizons is irrelevant tothe calculation of total earth pressures and is not displayed.

Horizontal total stressDrained horizonsIn drained horizons, the horizontal total stress (ch) is given byTerzaghi’s equation:

ch � c�

h � u

where ckh is the horizontal effective stress and u the pore waterpressure at the corresponding depth.

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

ch � Kucv � KucCu

where Ku and Kuc are undrained earth pressure coefficients and Cu

the soil’s undrained shear strength.

The value of Ku is 1 in all cases, whereas the value of Kuc dependson the soil’s undrained strength (Cu), the undrained wall adhesion


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

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

Kuc � ±2 1 �

au

Cu

where the + sign is used for active conditions and the > sign forpassive.

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

Pressures from surchargesThis section describes the way ReWaRD calculates earth pressuresarising from the presence of surcharges.

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

� Boussinesq’s theory (see Clayton & Militiski, 1986) [B]� Hybrid elastic method (ibid.) [HE]� Wedge analysis (see Pappin et al., 1985) [W]� Krey's method1 (British Steel Piling Handbook, 1988) [K]� Terzaghi’s 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


Surcharge type B HE W K T

Area q q q q

Parallel strip q q q q

Perpendicularstrip

q q

Parallel line q q q q q

Perpendicularline

q q

Point q q q

Uniform surchargesThe vertical stress resulting from a uniform surcharge (q) is given by:

cvq � q

For cantilever and high-propped walls, the corresponding horizontalstress is:

chq � Ka q

When the wall is low-propped, chq = Kaq for depths above the levelof the prop (or equivalent single-prop) and:

chq � Ki q

for depths below the level of the prop.

Parallel strip surchargesReWaRD provides four methods of calculating the effects of parallelstrip surcharges.


Boussinesq’s theoryThe vertical and horizontal stresses resulting from a parallel stripsurcharge of magnitude q are calculated from the equations:

cvq �

q

_[? � sin? cos (? � 2O)] eR

chq �

q

_[? � sin? cos (? � 2O)] eR

where tan (? + O) = (x + y)/z; tan O = x/z; eR is the elastic reflectionparameter (see the section entitled Surcharges in Chapter 10); z isthe depth below the surcharge; x is the perpendicular distancebetween the wall and the nearest edge of the surcharge; and y isthe width of the surcharge.

Hybrid elastic methodThe vertical stress is calculated from Boussinesq’s theory and thehorizontal stress is given by:

chq � Ka cvq

where Ka is the active earth pressure coefficient for the horizon.

Wedge analysisThe horizontal stress is calculated from plasticity theory, assumingzero wall friction and adhesion.

The horizontal stress depends on the width of the surcharge. A stripsurcharge is considered wide if:

2y

x¸ 1 � tan2 (45b �

k

2)


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

The horizontal stress varies with depth below the surcharge (z) asshown below.

a

c

b

xy

z a

b + c

xy

z

Wide Narrow

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

(chq)max � q tan2 (45b �

k

2)

and for narrow strip surcharges, it is given by:

(chq)max �

4 q tan2 (45b �

k

2)

2 �

x

y[1 � tan2 (45b �

k

2)]

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


cvq �

chq

tan2(45b �

k

2)

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

a � x tan k �

1

2b (1 � tan2(45 �

k

2))

b �

x

tan (45b �

k

2)

c �

y

tan (45b �

k

2)

Krey's methodThe horizontal stress is calculated from plasticity theory, assumingzero wall friction and adhesion.



a

b + c

xy

z

The maximum horizontal stress is given by:

(chq)max �

4 q tan2 (45b �

k

2)

2 �

x

y[1 � tan2 (45b �

k

2)]

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

The vertical stress is assumed to be:

cvq �

chq

tan2(45b �

k

2)

Perpendicular strip surchargesReWaRD provides two methods of calculating the effects ofperpendicular strip surcharges.

Boussinesq’s theoryThe vertical and horizontal stresses resulting from a perpendicularstrip surcharge of magnitude q are calculated from the equations:


cvq �

q

_[? � sin? cos (? � 2O)]

chq � 2qY?

_

where tan (? + O) = (x + y)/z; tan O = 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 Y is Poisson'sratio.

Hybrid elastic methodThe vertical stress is calculated from Boussinesq’s theory, and thehorizontal stress is given by:

chq � Ka cvq


Parallel line surchargesReWaRD provides five methods of calculating the effects of parallelline surcharges.

Boussinesq’s theoryThe vertical and horizontal stresses resulting from a perpendicularline surcharge of magnitude Q are calculated from the equations:

cvq � 2Qz 3

_R 4eR


chq � 2Qx 2z

_R 4eR

where R2 = x2 + z2; eR is the elastic reflection parameter (see thesection entitled Surcharges in Chapter 10); z is the depth below thesurcharge; and x is the perpendicular distance between the walland the surcharge.


chq � Ka cvq


Wedge analysisThe horizontal stress is calculated from plasticity theory, assumingzero wall friction and adhesion.


a

b

x

z



(chq)max �

4 Q tan2 (45b �

k

2)

x [1 � tan2 (45b �

k

2)]

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


cvq �

chq

tan2(45b �

k

2)

Krey's methodIn this method, the horizontal total stress increase is calculated fromplasticity theory, assuming zero wall friction and adhesion.


a

b

x

z



(chq)max �

4 Q tan2 (45b �

k

2)

x [1 � tan2 (45b �

k

2)]

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


cvq �

chq

tan2(45b �

k

2)

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

The vertical stress is calculated from Boussinesq’s theory.

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

x

H¶ 0.4

otherwise it is far from the wall. In this equation, x is theperpendicular distance between the wall and the surcharge; and 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:


chq � 0.20Q

H

(z

H)

(0.16 � [z

H]2)2

For far line surcharges, the horizontal stress varies with depth belowthe surcharge according to the formula:

chq � 1.28Q

H

(x

H)2 (

z

H)

([x

H]2 � [

z

H]2)2

Perpendicular line surchargesReWaRD provides two methods of calculating the effects ofperpendicular line surcharges.

Boussinesq’s theoryThe vertical and horizontal total stresses resulting from aperpendicular line surcharge of magnitude Q are calculated fromthe equations:

Fcvq � 2Qz 3

_R 4

Fchq � 2Qz

_R 2Y

where R2 = x2 + z2; z is the depth below the surcharge; x is thedistance along the wall to the surcharge; and Y is Poisson's ratio.



chq � Ka cvq


Area surchargesReWaRD provides four methods of calculating the effects of areasurcharges.

Boussinesq’s theoryThe vertical and horizontal stresses resulting from an area surchargeof magnitude q are calculated from the equations:

cvq �

q

2_[tan�1(

LB

zR) �

zLB

R(

1

R2

L

�

1

R2

B

)] eR

chq �

q

2_[tan�1(

LB

zR) �

zLB

R(

1

R2

L

)] eR

where z is the depth below the corner of a rectangular loaded areaof length L and breadth B; R2 = z2 + L2 + B2; RL

2 = z2 + L2 ; RB2 = z2 +

B2; and eR is elastic reflection parameter (see the section entitledSurcharges in Chapter 10).

The effect of an area surcharge which is offset from the wall iscalculated by superimposing the following surcharges:

� Add stress from area surcharge with B = x + y, L = v + w� Deduct stress from area surcharge with B = x, L = v + w� Deduct stress from area surcharge with B = x + y, L = v� Add stress from area surcharge with B = x, L = v


where x is the perpendicular distance between the wall and thenearest edge of the surcharge; y is the breadth of the surchargeperpendicular to the wall; v is the distance parallel to the wallbetween the cross-section being considered and the nearest edgeof the surcharge; and w is the length of the surcharge parallel to thewall.


chq � Ka cvq

where Ka is the active earth pressure coefficient.

Krey's method and Wedge analysisIn both these methods, the horizontal stress is calculated for a stripsurcharge running parallel to the wall, and is then reduced toaccount for the finite length of the surcharge.

For v @ x:

(chq)AREA � (chq)STRIP ÷ (2x

w� 1)

where v, x, and w are as defined above.

For v > x:

(chq)AREA � 0



cvq �

chq

tan2(45b �

k

2)

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

Boussinesq’s theoryThe vertical and horizontal stresses resulting from a point surchargeof magnitude P are calculated from the equations:

cvq �

3

2P

z 3

_R 5eR

chq �

P

2_R 2[

3z (v 2� x 2)

R 3� (1 � 2Y)

R

(R � z)] eR

where R2 = v2 + x2 + z2; eR is elastic reflection parameter (see thesection entitled Surcharges in Chapter 10); z is the depth below thesurcharge; v is the distance along the wall to the surcharge; x is theperpendicular distance between the wall and the surcharge; and Yis Poisson's ratio.


chq � Ka cvq

where Ka is the active earth pressure coefficient.


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

The vertical stress is calculated from Boussinesq’s theory.

The horizontal stress depends on the proximity of the surcharge tothe retaining wall. A point surcharge is considered near to the wallif:

x

H¶ 0.4

otherwise it is far from the wall. In this equation, x is theperpendicular distance between the wall and the surcharge; and His 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:

chq � 0.28P

H 2

(z

H)2

(0.16 � [z

H]2)3

cos2(1.1N)

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

chq � 1.77P

H 2

(x

H)2 (

z

H)2

([x

H]2 � [

z

H]2)3

cos2(1.1N)

In these equations, N = tan>1 (v/x), where v is the distance along the


wall to the surcharge.

Design pressuresDesign pressures acting on the wall are obtained from the series ofcalculations described below. Appropriate safety factors (seeChapter 9) are included in these calculations depending on whichdesign standard is selected.

Soil pressuresEarth pressures resulting from the weight of soil alone are termedsoil pressures in ReWaRD and given the symbol Es.

Drained horizonsUnfactored soil pressures in drained horizons are given by:

Es � c�

h

where ckh is the horizontal effective stress in the soil.

Design soil pressures are given by:

Esd �

Es

fEs

where fEs is the appropriate safety factor for the selected designstandard (see Chapter 9).

Undrained horizonsUnfactored soil pressures in undrained horizons are given by:

Es � ch

where ch is the horizontal total stress in the soil.

Design soil pressures are obtained in the same way as for drained


horizons.

Surcharge pressuresEarth pressures resulting from the presence of surcharges alone aretermed surcharge pressures in ReWaRD and given the symbol Eq.

Unfactored surcharge pressures are given by:

Eq � chq

where chq is the horizontal pressure resulting from any surcharges.

Design surcharge pressures are given by:

Eqd �

Eq

fEq

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

Combined earth pressuresThe combined earth pressures (E) from the weight of soil (Es) andthe presence of surcharges (Eq) are given by:

E � Es � Eq

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 (Pmin

ret, see


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

Ed � Pmin � Wd

where Wd is the design water pressure acting in the horizon on theretained side of the wall (see below).

Groundwater pressuresWater pressures resulting from pore water pressures in the soil aretermed groundwater pressures in ReWaRD and given the symbolWs.

Drained horizonsGroundwater pressures in drained horizons are given by:

Wsd � Ws � u

where u is the pore pressure in the soil.

Undrained horizonsGroundwater pressures in undrained horizons are given by:

Wsd � Ws � 0

Tension cracksTension cracks may form on the retained side of the wall when 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 on Layers in Chapter 10).

Tension cracks may be dry, wet, or flooded (see the section onLayers in Chapter 9) and are limited in extent to whatever depth isspecified in the selected design standard (see Chapter 9).

Water pressures resulting from tension cracks are termed tension


crack pressures in ReWaRD and given the symbol Wtc.

Dry tension cracksIn dry tension cracks:

Wtc � 0

Dry tension cracks should only be specified if there is noopportunity for water to collect in any tension crack that formsbetween the wall and the ground.

Wet tension cracksIn wet tension cracks:

Wtc � Ew(z � zwps)

where Ew is the unit weight of water, z is the depth below groundsurface, and zwps is the depth of the phreatic surface (i.e. the depthof the uppermost water table).

Flooded tension cracksIn flooded tension cracks:

Wtc � Ewz

where Ew and z are as given above. If the uppermost water table isabove ground level (in the case of standing water), then:

Wtc � Ew(z � zwps)

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


Combined water pressuresThe combined water pressures (W) from the soil (Ws) and anytension crack (Wtc) are given by:

Wd � W � maximum of Ws and Wtc

Total pressuresDesign total pressures are given by:

Pd � Ed � Wd

If, at any depth on the retained side of the wall, the design totalpressure is less than the minimum active pressure (see below), thenthe design earth pressure is increased so that Pd equals Pmin.

Minimum active pressuresThe minimum active pressure (Pmin) sets a lower limit to the designtotal pressure (Pd) acting on the retained side of the wall:

Pd ù Pmin

(CIRIA Report 104 uses the term minimum equivalent fluid pressure— “MEFP” — instead of minimum active pressure.)

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

Pmin � M z

where M is a constant specified by the selected design standard.

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


propped at or near excavation level are different to those assumedin conventional limit equilibrium calculations.

A single-propped wall is considered to be low-propped if theoverturning moment of the total pressures acting on the wall abovethe prop (Mabove) exceeds the restoring moment due to the totalpressures acting on the wall below the prop and above excavationlevel (Mbelow).

Ma b o v e

Mb e l o w

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

� Away from the soil above the prop� Into the soil below the prop on the retained side of the wall� Away from the soil below the prop on the excavated side

The corresponding horizontal stresses are calculated using thefollowing earth pressure coefficients:

� Above the prop: active� Below the prop on the retained side: intermediate between

active and passive� Below the prop on the excavated side: active

Drained horizonsThe earth pressure coefficients in drained horizons are given by:

� K = Ka and Kc = Kac above the level of the prop


� K = Ki and Kc = Kic below the level of the prop on the retainedside

� K = Ka and Kc = Kac below the level of the prop on the excavatedside

where the subscripts a and i denote active and intermediateconditions, respectively. Ki and Kic are given by:

Ki � Ka � (Kp � Ka)zp

dp

and

Kic � Kac � (�Kpc � Kac)zp

dp

where zp is the depth below the level of the prop and dp is thedepth of the wall toe below the level of the prop.

When zp = 0, Ki = Ka and Kic = Kac. When zp = dp, Ki = Kp and Kic =–Kpc. The negative sign in front of Kpc ensures that the horizontaleffective stress at the toe of the wall equals the full passive pressure,i.e. c’hi = Kpc’v – (–Kpc)c'.

Values of Ka and Kp are given in the section in this chapter entitledEarth pressure coefficients. Formulae for Kac and Kpc are given in thesection entitled Stresses in the ground, under the heading Horizontaleffective stress.

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

� Ku = 1 and Kuc = Kauc above the level of the prop� Ku = 1 and Ku = 1 and Kuc = Kiuc below the level of the prop on

the retained side� Ku = 1 and Kuc = Kauc below the level of the prop on the

excavated side


where the subscripts a and i denote active and intermediateconditions, respectively. Kiuc is given by:

Kiuc � �2 (1 � 2zp

dp

) (1 �

au

Cu

)

where zp is the depth below the level of the prop, dp is the depth ofthe wall toe below the level of the prop, Cu is the soil's undrainedshear strength, and au the undrained wall adhesion.

The formula for Kauc is given in the section in this chapter entitledStresses in the ground, under the heading Horizontal total stress.

Earth pressure coefficientsReWaRD calculates earth pressure coefficients according towhichever theory is specified in the selected design standard. Theearth pressure theories that have been implemented in ReWaRDare those due to:

� Coulomb� Rankine� Packshaw� Caquot & Kerisel� Kerisel & Absi

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

ReWaRD calculates Coulomb's earth pressure coefficients using theformulae given by Müller-Breslau (1906) for a frictionalcohesionless soil with sloping surface and a frictional wall:


Ka �

sin2 (90b� k) cos G

sin (90b� G) [1 �

sin (k � G) sin (k � A)

sin (90b� G) sin (90b� A)]2

Kp �

sin2 (90b� k) cos G

sin (90b� G) [1 �

sin (k � G) sin (k � A)

sin (90b� G) sin (90b� A)]2

where k = the soil's angle of friction; G = the angle of wall friction;and A = the slope of the soil surface (measured positive upwards).

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

ReWaRD calculates Rankine's earth pressure coefficients using thefollowing formulae:

Ka � cos2 Acos A � (cos2 A � cos2 k)

cos A � (cos2 A � cos2 k)

Kp � cos2 Acos A � (cos2 A � cos2 k)

cos A � (cos2 A � cos2 k)

where the symbols are as given above for Coulomb’s theory.

Rankine's theory assumes that the resultant force on a vertical planeacts parallel to the ground surface, and can only be used when theangle of wall friction (G) equals the ground slope (A).


The cos G term in these formulae is replaced by cos A.

PackshawReWaRD obtains Packshaw’s (1946) earth pressure coefficientsfrom a database of values taken from Code of Practice CP2 (1951).

Account is taken of sloping soil surfaces by increasing the value ofKa by 1% for every 1b of inclination above the horizontal (asrecommended in the British Steel Piling Handbook, 1997). Since Kac

is proportional to the square root of Ka (see the section entitledHorizontal effective stress above), it therefore increases by 0.5% forevery 1b of inclination.

Caquot & KeriselCaquot and Kerisel (1948) derived active and passive earthpressure coefficients using log spiral failure surfaces.

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

Ka � a KCoulomb

a

a � ([1 � 0.9U2� 0.1U4] [1 � 0.3U3])�n

n � (2 �

[tan2 A � tan2 G]

2 tan2 k

) sin k

F � 2 tan�1 (Gcotan GG � cotan 2 G � cotan 2 k

1 � cosec k)

U �

F � A � D

4k � 2_ (F � A � D)


D � sin�1 (sin A

sin k)

where KaCoulomb is the value of Ka from Coulomb’s 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 failure surfaces.

ReWaRD obtains Kerisel and Absi's passive earth pressurecoefficients from a database.

Chapter 3: Required embedment 45

Chapter 3Required embedment

This chapter gives detailed information about how ReWaRDcalculates the required embedment of the wall.

Out-of-balance momentReWaRD determines the required embedment of a retaining wallby calculating overturning and restoring moments from the earthpressures acting on it.

The out-of-balance moment (FM) is given by:

FM � MR � MO

where MO is the overturning moment and MR the restoringmoment.

The significance of the out-of-balance moment is as follows:

� If FM > 0, the wall is stable� If FM = 0, the wall is in moment equilibrium� If FM < 0, the wall is unstable

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

Cantilever wallsReWaRD determines the required embedment of cantilever wallsunder fixed-earth conditions.

Fixed-earth conditionsUnder fixed earth conditions, the retaining wall is assumed to rotateabout a pivot located at some depth (do) below excavation level.The earth pressures acting on the wall in this situation are asfollows.


R

do

d

To simplify the analysis, the earth pressures acting below the pivotare replaced by a single resultant force (R). The depth of the pivotbelow excavation level (do) is given by:

do �

d

1 � Cd

where d is the total depth of embedment of the wall and Cd is thecantilever toe-in. According to CIRIA Report 104 (1984), aconservative value of Cd 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 value of R is found fromconsideration of horizontal equilibrium.

Single-propped wallsReWaRD determines the required embedment of single-proppedwalls under free-earth conditions.

Free-earth conditionsUnder free-earth conditions, the retaining wall is assumed to rotateabout the level of the support. The earth pressures acting on thewall in this situation are as follows:

Chapter 3: Required embedment 47

P

d

The embedment needed to achieve equilibrium is determined bytaking moments about the pivot and occurs when the sum of the(anti-clockwise) overturning moments equals the sum of the(clockwise) restoring moments. The resultant propping force (P) isfound from consideration of horizontal equilibrium.

Multi-propped wallsReWaRD analyses walls with more than one prop using the hingemethod described in the British Steel Piling Handbook (1997) andBS 8002. In this method, pin joints are introduced at all the supportpoints and the various sections of wall are analysed separately:

� Sections between supports are treated as simply-supportedbeams

� The lowest section is treated as a single-propped cantilever

Simplysupported

Simplysupported

Propped-cantilever


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

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

If the propped-cantilever section is unstable, then ReWaRD treatsthe wall as simply supported (and hence inherently stable)throughout:

Simplysupported

Simplysupported

Chapter 4: Structural forces 49

Chapter 4Structural forces

This chapter gives detailed information about ReWaRD’s structuralforce calculations.

Cantilever and single-propped wallsBefore calculating the structural forces acting in a cantilever orsingle-propped wall, it is necessary to find a set of earth pressuresand applied loads that are in force and moment equilibrium.ReWaRD provides three ways of doing this:

� At minimum safe embedment� With maximum safety factors� At 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. Factors of safety are introduced at appropriatepoints in the calculations.

Structural forces calculated by this method are regarded as factored(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 pressuresacting on the wall are in moment equilibrium. The depth of


embedment of the wall is not reduced.

ReWaRD using the following equation to enhance the safety factorsspecified in the selected design standard above their normal values:

f fε ε= − +( )1 1

where f is the original safety factor, fI the enhanced safety factor,

and I an enhancement factor. This has been specially formulatedto ensure that, when f = 1, f

I = 1 and, when I = 1, f

I = 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 equilibrium. No factors of safety are applied to any part ofthe calculations.

Structural forces calculated by this method are regarded as

Chapter 4: Structural forces 51

unfactored values and need to be multiplied by an appropriatesafety factor to obtain design values (see Chapter 9).

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

Multi-propped wallsThe structural forces acting in a multi-propped wall are calculatedby the hinge method described in the British Steel Piling Handbook(1997) and BS 8002. In this method, pin joints are introduced at allthe support points and the various sections of wall are analysedseparately:

� Sections between supports are treated as simply-supportedbeams

� The lowest section is treated as a single-propped cantilever

Simplysupported

Simplysupported

Propped-cantilever

ReWaRD determines the structural forces in propped-cantileversection using one of the methods described above for cantileverand single-propped walls.

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


Design structural forcesBending moments

Design bending moments (Md) are given by:

Md � fM M

where M is the unfactored bending moment and fM is anappropriate safety factor (see Chapter 9).

Shear forcesDesign shear forces (Sd) are given by:

Sd � fS S

where S is the unfactored shear force and fS is an appropriate safetyfactor (see Chapter 9).

Prop forcesDesign prop forces (Pd) are given by:

Pd � fP P

where P is the unfactored prop force and fP is an appropriate safetyfactor (see Chapter 9). Different values of fP are sometimes used fordifferent props (for double-propped walls, CIRIA 104 recommendsa larger fP for the upper prop than for the lower prop).

Chapter 5: Peck’s envelopes 53

Chapter 5Peck’s envelopes

This chapter gives detailed information about ReWaRD’simplementation of Peck's envelopes.

Distributed prop loadsPeck’s envelopes provide an empirical way of estimating maximumprop loads for multi-propped walls. The envelopes were derivedfrom measurements of strut loads in real excavations and give theapparent pressure acting over the retained height of the wall (Peck,1968).

The term apparent pressure has misled some people into thinkingthat Peck’s envelopes represent the actual earth pressures acting onthe wall. For this reason, and in anticipation of the publication ofCIRIA Report RP526, the term distributed prop load is used inReWaRD instead of apparent pressure.

ReWaRD calculates distributed prop loads for multi-propped wallsduring short-term stages only. At present, only Peck’s originalenvelopes are implemented in the program. When CIRIA ReportRP526 is published, support will be added for the envelopesdefined in that report. Refer to ReWaRD’s release notes and on-linehelp for further information.

Peck’s envelopes Peck (1968) introduced envelopes for the following general soil

profiles:

� Sand� Stiff clay� Soft clay


H

H/4

H/4

Sand Soft clay Stiff clay

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

DPLmax � 0.65 Ka (c�

vH � cvqH)

where Ka is the average active earth pressure coefficient in anydrained horizons existing over the retained height (H); c’vH is thevertical effective stress at excavation level on the retained side ofthe wall; and cvqH 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 diagramabove), with the maximum distributed prop load being given by:

DPLmax � 0.4 (cvH � cvqH)

where cvH is the vertical total stress at excavation level on theretained side of the wall and cvqH is the vertical surcharge at thesame point. (Peck’s original envelope — which suggested thatDPLmax might be as low as 0.2[cvH + cvqH] — is now consideredunconservative.)

Peck’s envelope for stiff clay includes the effect of any water

Chapter 5: Peck’s 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 �

cvH � cvqH

Cu

where Cu is the average undrained shear strength in any undrainedhorizons over the retained height.

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

DPLmax � (1 �

1.6

N) (cvH � cvqH)

DPLmax � (1 �

4

N) (cvH � cvqH)

where the symbols are as defined for the stiff clay envelope.

The first formula is used if the cutting is underlain by a deep depositof soft clay (i.e. when the thickness of soft clay below excavationlevel exceeds the retained height), otherwise the second equationis used. In this context, clay is considered soft if its undrainedstrength is less than 40 kPa.

Peck’s envelope for soft to medium clays includes the effect of anywater pressures acting on the retained side of the wall and hencewater pressures are not added to the envelope.


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

Obtaining prop loads from Peck’s envelopesProp loads are obtained from Peck’s envelopes by dividing thedistributed prop load (DPL) diagrams into segments at themidpoints between the props. The load in any one prop is thencalculated by integrating the DPL over its associated segment.

The following example illustrates this procedure.

aa + b

b + c

c + d

d

2c

2d

2b

The load carried by the top prop is equal to the area of the firstsegment, of thickness a + b.

The load carried by the middle prop is equal to the area of thesecond segment, of thickness b + c.

The load carried by the bottom prop is equal to the area of the thirdsegment, of thickness c + d.

The load represented by the fourth segment is assumed to becarried by the ground below excavation level.

Chapter 6: Base stability 57

Chapter 6Base stability

This chapter gives detailed information about ReWaRD’s basestability calculations.

Factor-of-safety against basal heaveBjerrum and Eide (1956) defined the factor-of-safety against basalheave (Fbh) as follows:

FN C

bhc u

vH vqHret

vqHexc=

+ −σ σ σ

where Nc is a stability number; Cu is the average undrained shearstrength of any undrained horizons within a depth 0.7H below

excavation level; H is the retained height of the wall; is theσvqHret

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

wall; is the vertical total stress at excavation level on theσvqHexc

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

Stability numberThe stability number (Nc) is given by:

for H/B @ 2.5NB L H B

c =+

� �+�

��

��9

1 0 212

1 0 215

β. /.

. /.

for H/B > 2.5NB L

c =+

� �91 0 2

12β

. /.

where H is the retained height; B is the breadth and L the length ofthe excavation (see the section on Excavations in Chapter 10); andA is the rigid layer correction (defined below).


Rigid layer correctionThe rigid layer correction (A) is derived from the bearing capacityfactors given by Button (1953) and is given by:

β = + � �

−

1 0 00814

..d

B

where d is the depth below excavation level to the top of the firstrigid layer and B is the breadth of the excavation.

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

Chapter 7: Displacements 59

Chapter 7Displacements

This chapter gives detailed information about ReWaRD’sdisplacement calculations.

ReWaRD estimates the construction-induced (i.e. short-term)movement of the retaining wall — and the settlement of the groundsurface behind it — from an extensive database of measureddisplacements. Long-term movements, which are generallyassociated with changes in pore water 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 water pressure.)

Displacements depend on a number of factors, of which the mostimportant are 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 on 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 wall movementsReWaRD's database of measured displacements combines the casehistories used by Clough and O'Rourke (1992) and St John et al.(1992) to determine construction-induced wall movements.

The database is split into three parts, depending on the prevailingsoil conditions:

� Sand� Stiff clay� Soft clay


In each case, the measured displacements increase with increasingheight of excavation (H), as described below.

Surcharge loading factorThe surcharge loading factor (fq) that appears in many of theequations below takes account of the increase in vertical 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:

fq � 1 �

cvqH

c�

vH

where c’vH is the vertical effective stress at excavation level due tothe weight of soil and water and cvqH is the vertical stress at thesame point due to any surcharges.

For soft and stiff clay profiles, the surcharge loading factor is givenby:

fq � 1 �

cvqH

cvH

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

Database for sandsThe database for sands is taken from Clough and O'Rourke (1992)and includes 7 case histories for excavations up to 24m high.

Cantilever and propped wallsMaximum displacementsThe maximum settlement behind the wall (Gvm) is given by:


Gvm

H� (0.003 ±0.001) fq

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

The maximum horizontal movement of the wall (Ghm) is given by:

Ghm �

4

3Gvm

Displacement profilesClough and O'Rourke (1992) proposed an envelope of normalizedsettlement (Gv/Gvm) for sands which is triangular and extends for adistance equal to twice 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 O’Rourke propose. ReWaRD therefore calculatesdisplacements for sands using a modified form of the triangularsettlement profile proposed by Clough and O'Rourke, as shownbelow.


The settlement at x = H (GvH) is given by:

GvH

H� 0.001 fq

and the horizontal displacement at z = H (GhH) is given by:

GhH �

4

3GvH

The same profiles are used for cantilever and propped walls.

Database for stiff claysThe database for stiff clays is taken from St John et al. (1992) andincludes 6 case histories involving cantilever excavations up to 8mhigh and 13 case histories involving propped excavations up to25m high.

Cantilever wallsMaximum displacementsThe maximum horizontal movement (Ghm) of a cantilever wall in stiffclay is given by:

Ghm

H� 0.0015 fq � (0.00035 ±0.00025) f

2

q H

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

The maximum settlement (Gvm) behind the wall is given by:

Gvm � 0.75 Ghm


Displacement profilesClough and O'Rourke (1992) proposed an envelope of normalizedsettlement (Gv/H) for stiff clays which is triangular and extends fora distance equal to three times the height of the excavation (H), asshown below.

Propped wallsMaximum displacementsThe maximum horizontal movement (Ghm) of a propped wall in stiffclay is given by:

Ghm

H� (0.003 ±0.001) fq

where fq is the surcharge loading factor (see above). The ± valuesrepresent upper and lower bounds to Ghm.


The maximum settlement (Gvm) behind the wall is given by:

Gvm � 0.75 Ghm

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

St John (1992, personal communication) has found that themaximum settlement behind the wall usually occurs near x = H andthat the settlement close to the wall (Gv0) is approximately 50% ofGvm. ReWaRD therefore calculates displacements for propped wallsin stiff clays using a modified profile, as shown below.

The table below gives the co-ordinates of the key points alongthese profiles.


x/H orz/H

0 0.65 1.0 1.5 3.0

G/Gm 0.5 1.0 1.0 0.5 0.0

Database for soft claysThe database for soft clays is taken from Clough and O'Rourke(1992) and includes 13 case histories for excavations up to 20mhigh.

Cantilever and propped wallsMaximum 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 factor-of-safety against basal heave (Fbh, see Chapter 7)� The system’s stiffness (EI/Ewsp

4, see below)

Clough et al. present design curves that allow the maximumhorizontal movement of the wall (Ghm) to be estimated from H, Fbh,and EI/Ewsp

4 (see below).

3.0

010 30 50 500100

System stiffness

δ hm /

H (%

)

300 30001000

2.0

1.0

3.0

2.0

1.4

1.1

1.0

0.9 = Fb h


The maximum settlement (Gvm) behind a retaining wall in soft clayis equal in magnitude to its maximum horizontal movement (Ghm)and is given by:

Gvm � Ghm � fq GClough

hm

where GhmClough is the maximum horizontal movement obtained from

Clough et al.’s chart.

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

The table below gives the co-ordinates of the key points alongthese profiles.

x/H or z/H 0 0.75 2.0

G/Gm 1.0 1.0 0.0

The same profiles are used for cantilever and propped walls.


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

System stiffness �

EI

Ew s4

p

where E is the Young's modulus of the wall and I its secondmoment of area; Ew is the unit weight of water; and sp is the averagespacing between props (a value that can only be calculated formulti-propped walls).

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

� For a cantilever: sp = retained height + depth of fixity� For a single-propped wall: sp = (retained height below prop +

depth of fixity) or retained height above prop (whichever islarger)

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

� For a cantilever, d = 1.4H� For a single-propped wall: d = 0.6H

where H is the retained height.

Chapter 8: Durability 69

Chapter 8Durability

This chapter gives information about ReWaRD’s durabilitycalculations.

Corrosion of steel piling in various environmentsBritish Steel’s 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 water zone Between mean lowwater neap and lowestastronomical tide levels

0.075

Immersion zone Between lowestastronomical tide andbed level

0.035

Soil Below bed level 0.015

ReWaRD calculates the total corrosion rate along a sheet pile wallby summing the mean corrosion rate (taken from the table above)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 otherwould have a total corrosion rate of 0.015 + 0.075 = 0.09 mm/year.

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

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 following 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 of failurer = revisedu = undrained

Superscripts:ret = retained side of wallexc = excavated side of wall

Design approachesCIRIA Report 104 (1984) discusses two distinct approaches todesigning embedded retaining walls, based on:

� A. Moderately conservative soil parameters, loads, andgeometry

� B. 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 following table indicates where factors are quoted inthe report.


Design approach Works

Temporary Permanent

A. Moderatelyconservative

q Effective stress* Total stress

q Effective stressu Total stress

B. Worst credible q Effective stressu Total stress

q Effective stressu Total stress

q = values given; * = speculative values given; u = values not given

Safety factors in earth pressure calculationsThis section of 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:

� Gross pressure method� Nett pressure method� Revised (or Burland-Potts) method� Strength factor method� Limit state methods

Gross pressure methodIn the gross pressure method (described in Civil Engineering Code-of-Practice CP2, 1951), a lumped factor-of-safety (Fp) is applied tothe gross passive earth pressure:

Epd �

Ep

Fp

Recommended values of Fp taken from the Literature are givenbelow.


Design standard/approach orreference

Works

Temporary Permanent

CP2 2.0

Teng (1962) 1.5-2.0

Canadian FoundationEngineering Manual (1978)

1.5

CIRIA 104 A. Moderatelyconservative

Fp = 1.2-1.5 for k =20-30b

Fpu = 2.0*

Fp = 1.5-2.0 for k =20-30bFpu = u

B. Worstcredible

Fp = 1.0Fpu = u

Fp = 1.2-1.5 for k =20-30bFpu = u

* = speculative; u = not given

Burland et al. (1981) have criticized the Gross Pressure Methodwhen 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 PilingHandbook, 1997), a lumped factor-of-safety (Fnp) is applied to thenett passive earth pressure:

Enpd �

Enp

Fnp

Recommended values of Fnp taken from the Literature are givenbelow.


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 followingequations applies:

Eret

n � c�

h

ret� c

�

h

excand E

exc

n � 0 (when Eret

n A 0)

or:

Eret

n � 0 and Eexc

n � c�

h

exc� c

�

h

ret(when E

exc

n > 0)

Likewise, nett water pressures are given by:

Wret

n � u ret� u exc and W

exc

n � 0 (when Wret

n A 0)

or

Wret

n � 0 and Wexc

n � u exc� u ret (when W

exc

n > 0)

The nett pressure method has been criticised for giving rapidlyincreasing factors-of-safety with increasing depth of embedment,and much higher factors-of-safety than other methods (Burland etal., 1981; Potts & Burland, 1983). Results obtained with the nettpressure method should be compared with those from one or moreof the other available methods.


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

Erpd �

Erp

Fr

Recommended values of Fr taken from the Literature are givenbelow.

Design standard/approachor reference

Works

Temporary Permanent

Burland et al. (1981) 1.5-2.0


Fr = 1.3-1.5(usually 1.5)

Fru = 2.0

Fr = 1.5-2.0(usually 2.0)

Fru = u

B. Worst credible Fr = 1.0*Fru = u

Fr = 1.5Fru = u


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

Erak � (Kac�

vH)ret

where Ka is the drained active earth pressure coefficient for thehorizon on the retained side of the wall and ckvH is the verticaleffective stress on the retained side of the wall at excavation level.


Revised passive earth pressures below excavation level are givenby:

Erpk � (Kpc�

v � Kpcc�)

exc� (Kac

�

v � Kacc�)ret

� (Kac�

vH)ret

where Kp and Kpc are the drained passive earth pressure coefficientsfor the horizon on the excavated side of the wall; Ka and Kac are thedrained active earth pressure coefficients for the horizon on theretained side of the wall; and ckvH is as defined above.

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

Erak � (KaucvH)ret

where Kau is the undrained active earth pressure coefficient for thehorizon on the retained side of the wall and cvH is the vertical totalstress on the retained side of the wall at excavation level.

Revised passive earth pressures below excavation level are givenby:

Erpk � (Kpucv � KpucCu)exc

� (Kaucv � KaucCu)ret

� (KaucvH)ret

where Kpu and Kpuc are the undrained passive earth pressurecoefficients for the horizon on the excavated side of the wall; Kau

and Kauc are the undrained active earth pressure coefficients for thehorizon on the retained side of the wall; and cvH is as definedabove.

Strength factor methodIn the strength factor method (described in CIRIA Report 104,1984), a factor-of-safety (Fs) is applied to the soil’s coefficient offriction (tan k) and effective cohesion (ck) and a different factor-of-safety (Fsu) is applied to its undrained shear strength (Cu):


tan kd �

tan k

Fs

, c�

d �

c �

Fs

, Cud �

Cu

Fsu

The design earth pressures acting in the ground are then calculatedfrom the design soil parameters:

Ed � E � f(kd, c�

d, Cud, ...)

Recommended values of Fs taken from the Literature are givenbelow.

Design standard/approach Works

Temporary Permanent


Fs = 1.1 for k > 30belse Fs = 1.2

Fsu = 1.5*

Fs = 1.2 for k > 30belse Fs = 1.5

Fsu = u

B. Worstcredible

Fs = 1.0Fsu = u

Fs = 1.2Fsu = u


Limit state methodsIn design standards that employ limit state methods — such asGeoguide 1, BS 8002, and Eurocode 7 — partial factors (E) areapplied at different stages in the earth pressure calculations.

Partial factors are typically applied to:

� Actions (i.e. direct and indirect loads)� Material properties� Geometric properties

Partial factors on actionsDesign actions (Fd) are obtained from characteristic actions (Fk) bymultiplying by the appropriate partial factor (EF):


Fd � EF Fk

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

Recommended values of EF taken from the Literature are givenbelow.

Design standard/case Action

Permanent Varia-ble Accid-ental

Unfav. Fav.

Geoguide 1 1.5 on surcharge on retained side of wall,otherwise 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 arisingfrom the weight of the soil are regarded as unfavourable permanentactions, as are water pressures. Pressures arising from surchargesare regarded as permanent, variable, or accidental and favourableor unfavourable according to which flags are set for each individualsurcharge.

Partial factors on material propertiesDesign material properties (Xd) are obtained from characteristicmaterial properties (Xk) by dividing by the appropriate partial factor(Em):


Xd �

Xk

Em

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

tan kd �

tan kk

Ek

, c�

d �

c�

k

Ec

, Cud �

Cuk

ECu

where Ek, Ec, and ESu depend on the selected design standard.

Recommended values of Em taken from the Literature are givenbelow.

Design standard/case Partial factor

Ek

Ec ECu

Geoguide 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 (Hd) is obtained from theactual retained height (Hk or Hnom) by adding an appropriate safetymargin (FH):

Hd � Hk ± FH


Recommended values of FH taken from the Literature are givenbelow.

Design standard/case Unplanned excavation (FH)

Geoguide 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 walls, clear height = height below bottom propFor cantilever walls, clear height = height of excavation

Design earth pressuresDesign earth pressures acting in the ground are calculated from thedesign parameters:

Ed � Ek � f(Fd, kd, c�

d, Cud, Hd, ...)

Safety factors for structural forcesThis section gives details of the safety factors that are 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:

Md � M and Sd � S


Prop forcesDesign prop forces (P) are given by:

Pd � P

With maximum safety factorsStructural forces calculated with maximum safety factors (seeChapter 4) are regarded as factored (i.e. design) values.


Md � M and Sd � S

Prop forcesDesign prop forces (P) are given by:

Pd � P

At failureStructural forces calculated at failure (see Chapter 4) are regardedas unfactored values and need to be multiplied by an appropriatesafety factor to obtain design values. (This is equivalent to the“working stress” approach adopted in many of the older codes ofpractice and is the method recommended in CIRIA Report 104,1984.)


Md � fM M and Sd � fS S

Recommended values of fM and fS taken from the Literature aregiven in the table below.


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

Pd � fP P

Recommended values of fP 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 PilingHandbook

1.5 2.0 x 1.15*† = 2.3

CIRIA 104 1.5 2.0 x 1.251 = 2.52.0 x 1.152 = 2.3

Partial factors to account for arching *in cohesive soils; †in cohesionless soils; 1in upper level ofprops; 2in second level of props (single- and double-propped walls only)

Chapter 10: Engineering objects 83

Chapter 10Engineering objects

This chapter gives detailed information about how the variousengineering objects in ReWaRD affect its engineering calculations.

Construction stagesConstruction stages can be designated as short- or long-term. Theterm helps determined whether ReWaRD calculates earth pressuresusing total or effective stress theory (see the section entitled Totalor effective stresses? in Chapter 2).

Ground profilesSloping ground

When calculating earth pressure coefficients for horizons on theretained side of the wall, ReWaRD determines the parameter A thatappears in the equations for Ka and Kp (see Chapter 2) as follows:

A � max (Aground, ilayer)

where Aground is the slope of the ground profile and ilayer is the dip ofthe layer for which earth pressure coefficients are being calculated.

Stepped groundThe effect of a stepped ground profile is to increase the verticaltotal stress on the retained side of the wall by an amount that varieswith depth as shown below.


ABΦ

45=+=Φ/2C

The increase in vertical total stress down the wall (Fcv) is given by:

Fcv � 0 for za @ z @ zb

Fcv � Ehz � zb

zc � zb

for zb < z < zc

Fcv � Eh for z A zc

where E is the unit weight of soil at the ground surface and thedepths zb and zc are given by:

zb � f tan k


zc � (w � f ) tan (45b�k

2) � h

where k 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) recommended inCIRIA Special Publication 95 (1993).

ExcavationsSloping excavations

When calculating earth pressure coefficients for horizons on theexcavated side of the wall, ReWaRD determines the parameter Athat appears in the equations for Ka and Kp (see Chapter 2) asfollows:

A � min (Aexcavation, �ilayer)

where Aexcavation is the slope of the excavation and ilayer is the dip ofthe layer for which earth pressure coefficients are being calculated.

BermsReWaRD calculates the effects of a berm on the earth pressuresacting on the excavated side of the wall using the methodrecommended in CIRIA Special Publication 95 (1993).

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


ABΦ

45=−=Φ/2C

The increase in vertical total stress (Fcv) due to the presence of aberm depends on whether it is wide or narrow.

Narrow bermsA berm is considered narrow when zb < h, in which case Fcv isgiven by:

Fcv � Ez for za @ z @ zb

Fcv �

Fcmax

v (z � zb) � E(h � z)zb

h � zb

for zb < z < h

Fcv � Fcmax

v [zc � z

zc � h] for h @ z < zc

Fcv � 0 for z A zc


where the largest increase in vertical total stress is:

Fcmax

v � Eh (zc � h

zc � zb

)

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

zb � f tan k

zc � (w � f ) tan (45b�k

2) � h

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

Wide bermsA berm is considered narrow when zb A h, in which case Fcv isgiven by:

Fcv � Ez for za @ z @ h

Fcv � Eh for h < z @ zb

Fcv � Eh [zc � z

zc � zb

] for zb @ z < zc


Fcv � 0 for z A zc

where the symbols are as given for narrow berms.

Plan dimensionsThe plan dimensions of an excavation are used to calculate thefactor 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 Classification System (BSCS), as described in BS5930:1981

� The Unified Soil Classification System (USCS), as described inASTM D2487-1069

� The German Soil Classification System (DIN), as decribed in DIN18 196

In addition to the basic groupings of Gravel, Sand, Silt, and Claythat are common to all these systems, ReWaRD's Soil Classificationsystem includes commonly-encountered soils under the headingsOrganic, Fill, Chalk, Rock, River Soil, and Custom.

The following table lists the soils that are included in ReWaRD's soilclassification system and give the corresponding group symbolsfrom each of the established systems listed above (where they areavailable).

Class Sym-bol

BSCS USCS DIN States

Gra

vel

Unclassified*Well-gradedUniformly-gr'dGap-gradedSiltyClayey*Very silty*Very clayey*

GGWGPuGPgG-MG-CGMGC

GGWGPuGPgG-MG-CGMGC

GGWGPGP

G?-GMG?-GC

GMGC

GGWGEGIGUGTGUGT

Unpecified (Unsp)Very loose (VL)¶Loose (L)Medium dense (MD)Dense (D)Very dense (VD)Poorly comp’d (PC)Well comp'd (WC)


Class Sym-bol


Sand Unclassified*

Well-gradedUniformly-gr'dGap-gradedSiltyClayey*Very silty*Very clayey*

SSWSPuSPgS-MS-CSMSC

SSWSPuSPgS-MS-CSMSC

SSWSPSP

S?-SMS?-SCSMSC

SSWSESISUSTSUST

Same as GRAVELG

ranu

lar

silt Unclassified

GravellySandyLow-plasticity

MMGMSML

MMGMSML

MML/MHML/MH

ML

U--

UL

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

Coh

esiv

e si

lt Unclassified*†Int.-plast.*†High-plast.*†

MMIMH

MMI

MH-ME

MMLMH

UUM

-

Same as CLAY

Cla

y Unclassified*†$Gravelly*†Sandy*†Low-plast.*†Int.-plast.*†$High-plast.*†$Laminated*†

CCGCSCLCICHLam

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)*$

Org

anic Unclassified†

Organic clay†Organic silt†Peat†Loam†

OMOCOPt

Loam

OMLO/

HCLO/H

Pt-

OOLOHPt-

O(OU)OT

HN/HZ-

Same as CLAY

Gra

nula

r fil

l

UnclassifiedRock fillSlag fillGravel fillSand fillChalk fillBrick hardcoreAshesPFA

MdGRockFSlag

GravFSandFChkFBrickAshPFA

UnspecifiedPoorly-comp'd (PC)Well-compacted (WC)

Clay fill† ClayF Same as CLAY


Class Sym-bol


Cha

lk Unclassified*Grade I*Grade II*Grade III*Grade IV*Grade VGrade VI

ChkChk1Chk2Chk3Chk4Chk5Chk6

Unspecified (Unsp)

Roc

k Marl*Weatheredrock*

MarlRock

Unspecified (Unsp)

Riv

er s

oil

River mud†Dock silt†Alluvium†

RivMDock

SAlluv

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

Custom*†$ Cust Unspecified (Unsp)*$

G? = G, GW, or GP; S? = S, SW, or SP; Int. = intermediate; 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 particularsoil parameter, ReWaRD issues an error message and prevents youfrom proceeding until you have changed the offending 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 parameters are provided to assist in initial design studiesonly, and should not be used as a substitute for measured


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 publications that have been referred to in compiling thedatabase include:

� Terzaghi & Peck (1967)� NAVFAC DM-7 (1971)� Peck, Hanson, & Thornburn (1974)� Winterkorn & Fang (1975)� Canadian Foundation Engineering Manual (1978)� Reynolds & Steedman (1981)� Bell (1983)� Mitchell (1983)� TradeARBED's Spundwand-Handbuch Teil 1, Grundlagen (1986)� Bolton (1986)� Clayton & Militiski (1986)� Clayton (1989)� Tomlinson (1995)� British Steel's Piling Handbook (1997)

Invaluable advice regarding the properties of various soils wasprovided by Professors JB Burland, PR Vaughan, and DW Hight andby Dr G Sills.

In the following table ad = dry density; aw = wet density; kpeak =peak angle of friction; kcrit = critical state angle of friction; c’peak =peak effective cohesion; c’crit = critical state effective cohesion; Su

= undrained shear strength; FSu = rate of increase in Su with depth.

Parameter Classification Minimum Default Maximum

Class State Ext. Normal Normal Ext.

Gra

vel

ad (kg/m3) All UnspVLL

MDD

VDPCWC

12001200130014001500170012001400

14001300140015001700200014001700

20501500165018502050225016502050

22001600180020002200240018002200

25001800200022002400250022002500


as (kg/m3) All UnspVLL

MDD

VDPCWC

15001500170018001900200015001800

18001700180019002000220018002000

22001850200021002200225020002200

23001900210022002300240021002300

25002100220023002400250023002500

kpeak (deg) All UnspVLL

MDD

VDPCWC

2828303540452835

3532354045503545

3734374247523747

5038404550554050

6040455055605060

kcrit (deg) All All 28 35 37 40 45

c’peak (kPa) GG_CGMGC

All 0 0 0 0 10

Others All Not applicable

c’crit (kPa) GG_CGMGC

All 0 0 0 0 5


Sand ad (kg/m3) All Unsp

VLL

MDD

VDPCWC

12001200122512751350145012001275

12751225127513501450157512751450

16751450150015751675180015001675

18001550160017001800190016001800

22001750185019502050220019502200

as (kg/m3) All UnspVLL

MDD

VDPCWC

16001600175018001850195016001800

18001750180018501950205018001950

20751900195019752075217519502075

21501975200020502150225020002150

24002000205021502250240021502400


kpeak (deg)

†Reducedto allow forpotentialliquefaction

All UnspVLL

MDD

VDPCWC

2020†262933372329

3025†303336403036

3226†323437423237

4028†353740453540

5530†404550554555


c’peak (kPa)discountingnaturalcementation

SS_CSMSC

All 0 0 0 0 10


c’crit (kPa) SS_CSMSC

All 0 0 0 0 5


Gra

nula

r si

lt ad (kg/m3) All All 1100 1275 1850 2150 2200

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

kpeak (deg)

†Reducedto allow forpotentialliquefaction

All UnspVLL

MDD

VD

2020†23252730

2725†27282932

2826†28293033

3328†31323336

4530†35374045


c’peak (kPa) All All 0 0 0 5 10

c’crit (kPa) All All 0 0 0 0 5

Coh

esiv

e si

lt ad (kg/m3) All All 1100 1275 1850 2150 2200

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

kpeak (deg) MMIMH

All 171717

252520

282823

353530

454035


kcrit (deg) MMIMH

All 172017

222218

252519

303022

323225

c’peak (kPa) All VSo-So 0 0 0 0 0

Others 0 0 0 5 10

c’crit (kPa) All VSo-So 0 0 0 0 0

Others 0 0 0 0 5

Su (kPa) All UnspVSoSoFSt

VStH

11

103060100200

205

204075150300

20102550100200375

150204075150300500

10003060100200400

1000

FSu (kPa) All VSo-So -100 -10 0 4 100

Others -100 -10 0 8 100

Cla

ys ad (kg/m3) All UnspVSoSoFSt

VStH

1200120013001450160017501900

1500140015001650180019502100

2050165017501900205022002300

2200180019002050220023502400

2500200021002250240024502500

as (kg/m3) All UnspVSoSoFSt

VStH

1200120013001450160017501900

1500140015001650180019502100

2050165017501900205022002300

2200180019002050220023502400

2500200021002250240024502500

kpeak (deg) CCGCSCLCl

CHLam

All 15181820181515

20202024201616

20242427232019

33333333302725

39393939373139


kcrit (deg) CCGCSCLCl

CHLam

All 81818181888

20202020201512

23242423231816

33333328282020

39393930302222

c’peak (kPa) All UnspVSoSo

000

000

000

1000

1500

Others 0 0 2 10 15

c’crit (kPa) All VSo-So 0 0 0 0 0

Others 0 0 0 0 5

Cu (kPa) All UnspVSoSoFSt

VStH

11

103060100200

205

204075150300

20102550100200375

150204075150300500

10003060100200400

1000

FCu (kPa) All VSo-So -100 -10 0 8 100

Others -100 -10 0 8 100

Org

anic ad (kg/m3) Uncl

MOCOPt

Loam

All 80010001000800

1450

10001250125010001650

15001500150012001900

20501600160013002050

22501750175014002250

as (kg/m3) UnclMOCOPt

Loam

All 85014001400850

1450

105015001500950

1650

16501650165012501900

20501750175014002050

22501950195015002250

kpeak (deg) UnclMOCOPt

Loam

All 1818181820

2020202024

2323232327

3030303033

3937373739


kcrit(deg) UnclMOCOPt

Loam

All 1818181820

2020202024

2323232327

3030303033

3937373739

c’peak (kPa) All All Not applicable

c’crit (kPa) All All Not applicable


VStH

11

103060100200

205

204075150300

20102550100200375

150204075150300500

10003060100200400

1000

FCu (kPa) All VSo-So -100 -10 0 8 100

Others -100 -10 0 8 100

Gra

nula

r fil

l

ad (kg/m3) MdGRockFSlag


All 600140010001200120012501100600900

1225150012001400122513001300650

1000

160019001450195016001350160010001350

180021001600220018001400175010001500

250022001800250022001450190012001700

as (kg/m3) MdGRockFSlag


All 120017501400150016001700140012001350

165019001700180018001750165013001500

200021001850215020501825185014501750

215022001900230021501850195015001800

250023002000250024001900210018002000

kpeak (deg) MdGRockFSlag


All 233525282325353027

304030353030403530

354333403232423732

455040503537454037

606050604043504540


kcrit (deg) MdGRockFSlag


All 253025282325252727

303530353030303030

323732373232323332

354035403535353835

454545454040404240

Coh

esiv

e fil

l

ad (kg/m3) All All 950 1100 1550 1750 1900

as (kg/m3) All All 1300 1500 1850 2050 2250

kpeak (deg) All All 15 17 21 30 35





VStH

11

103060100200

205

204075150300

20102550100200375

150204075150300500

10003060100200400

1000

FCu (kPa) All VSo-So -100 -10 0 8 100

Others -100 -10 0 8 100

Cha

lk ad (kg/m3) ChkChk1Chk2Chk3Chk4Chk5Chk6

1255152513501275125012251225

1275165014001325130012751275

1450205015751450137513501350

2250225016501500142514001400

2500250017251550147514501450

as (kg/m3) ChkChk1Chk2Chk3Chk4Chk5Chk6

1725192518001750175017251725

1750202518501800177517501750

1900230019751900185018251825

2450245020251925187518501850

2600260020751950190019001900


kpeak (deg) ChkChk1Chk2Chk3Chk4Chk5Chk6

25252525252525

30303030303030

35353434333232

45454341393735

55555249464340

kcrit (deg) All 25 30 32 35 40

c’peak(kPa) ChkChk1Chk2Chk3Chk4Chk5Chk6

0000000

0000000

01055200

202020201000

10010050502000

c’crit(kPa) All 0 0 0 0 5

Roc

k ad (kg/m3) All 2050 2100 2250 2300 2500

as (kg/m3) All 2050 2100 2250 2300 2500

kpeak (deg) All 27 30 33 38 42

kcrit (deg) All 27 30 33 38 42

c’peak (kPa) All 0 0 5 10 20

c’crit (kPa) All 0 0 0 0 5

Riv

er S

oil

ad (kg/m3) All UnspVSoSo

120012001200

125012501400

160016001650

180018001800

200020002000

as (kg/m3) All UnspVSoSo

120012001200

125012501400

160016001650

180018001800

200020002000

kpeak (deg) All All 15 16 22 33 39




Cu (kPa) All UnspVSoSo

11

10

205

20

201025

402040

603060

FCu (kPa) All All -100 -10 0 4 100


Cus

tom ad (kg/m3) Uncl Unsp 600 1200 2000 2400 2500

as (kg/m3) Uncl Unsp 850 1200 2000 2400 2600

kpeak (deg) Uncl Unsp 10 20 30 50 60

kcrit (deg) Uncl Unsp 8 20 25 35 45

c’peak (kPa) Uncl Unsp 0 0 0 10 100

c’crit (kPa) Uncl Unsp 0 0 0 0 5

Cu (kPa) Uncl Unsp 1 5 20 300 1000

FCu (kPa) Uncl Unsp -100 -10 0 10 100

Critical state parametersWhen calculating earth pressures, ReWaRD applies a partial factorof one to the coefficient of friction and to the effective cohesion ofany soil that is flagged as having critical state parameters.

Fissured soilsSoils that are fissured are not allowed any effective cohesion.

LayersDip

When calculating earth pressure coefficients, ReWaRD determinesthe parameter A that appears in the equations for Ka and Kp (seeChapter 2) as follows:

Aret� max (Aground, ilayer)

Aexc� min (Aexcavation, �ilayer)

where Aret and Aexc are the values of A on the retained andexcavated sides of the wall, respectively; Aground is the slope of theground profile, Aexcavation is the slope of the excavation; and ilayer is thedip of the layer for which earth pressure coefficients are beingcalculated.


Rigid layersRigid layers below excavation level can help to increase the factorof safety against basal heave (see Chapter 6). A layer can beconsidered “rigid” if the ratio of its undrained strength (Cu) to thatof the overlying layer (Cu

over) is greater than the threshold valuesgiven in the following table. In this table, d is the depth to the topof the rigid layer and B is the breadth of the excavation.

d/B 1 0.75 0.4 0.3 0.2

Cu/Cuover > 1.2 > 1.5 > 2.0 > 2.5 > 3.0

Water tablesWater tables represent changes in the groundwater regime. Eachwater table affects the groundwater conditions in its underlyinghorizons. When there are several water tables on one side of thewall, the groundwater conditions in any particular soil horizon aredetermined by the water table at the top of the horizon orimmediately above it.

The type of water table that is present in an horizon determines thepore pressure gradient in that horizon and whether the soil istreated as dry or wet when calculating vertical total stresses (seeChapter 2).

Water table Pore pressuregradient (kPa/m)

Soil below istreated as...

Hydrostatic 9.80665 Wet

Constant 0 Wet

Hydrodynamic User-defined Wet

Linear seepage Programcalculates

Wet

Inverted User-defined Wet

Dry 0 Dry


Water table Pore pressuregradient (kPa/m)

Soil below istreated as...

Standing 9.80665 Wet

Retaining wallsSection properties

The cross-sectional area (A), second moment of area (I), andsection modulus (Z) of the various retaining walls ReWaRDsupports are determined as follows.

Sheet pile wallsValues of A, I, and Z for Larssen and Frodingham sections areobtained from a database of values supplied by Corus plc.

Secant bored-pile walls

A � (D 2

4S) (_ � sin 2O � 2O)

I � (D 4

384S) (6_ � sin 4O � 8 sin 2O � 12O)

Z � (D 3

192S) (6_ � sin 4O � 8 sin 2O � 12O)

where D and S are the pile's diameter and spacing respectively andO = cos>1 (S/D).


Contiguous bored-pile walls

A �

_D 2

4S, I �

_D 4

64S, Z �

_D 3

32S

where D and S are the pile's diameter and spacing respectively.

King-post (soldier pile) walls

A �

_D 2

4S, I �

_D 4

64S, Z �

_D 3

32S

where D and S are the pile's diameter and spacing respectively.

Diaphragm walls

A � W, I �

W 3

12, Z �

W 2

6

where W is the wall's width.

Rowe’s parameterRowe's parameter is used as a measure of wall flexibility, todetermine the effects of moment redistribution. Rowe's parameter(a) is defined as:

a �

(L � U)4

EI

where L is the overall length of the wall; U is the upstand; E is thewall's Young's modulus; and I is its second moment of area (orinertia) per unit run.


King-post (or soldier-pile) wallsKing-post (or soldier-pile) walls mobilize less passive resistance thancontinuous walls, owing to their horizontal spacing (S), which inReWaRD must be greater than or equal to 4.5D, where D is thediameter of the pile.

Earth pressure coefficients for king-post walls are calculated fromBroms’ (1965) theory, as follows.

Drained horizonsThe passive earth pressure coefficients (Kp and Kpc) are calculatedas described in Chapter 2 (see the section entitled Earth pressurecoefficients), and then multiplied by a factor b given by:

b �

D

S, for d < D

b �

3D

S, for d A D

where d is the depth below excavation level, D is the diameter ofthe pile, and S is the horizontal spacing of the piles.

Undrained horizonsThe passive earth pressure coefficients (Kpu and Kpuc) are given by:

Kpu � Kpuc � 0, for d < 1.5D

Kpu � 1, Kpuc �

9D

S, for d A 1.5D

where d is the depth below excavation level, D is the diameter ofthe pile, and S is the horizontal spacing of the piles.


SurchargesElastic reflection parameter

The elastic reflection parameter (eR) that appears in several of theformulae for surcharge pressures in Chapter 2 takes account of thedegree of yielding of the wall:

� If the wall is flexible, eR S 1� If the wall is rigid, eR S 2

The doubling of horizontal stress for rigid walls can be explained asfollows. In order to obtain zero horizontal displacements along theline of the wall, an imaginary surcharge is needed on the front sideof the wall equal in magnitude and position to the real surcharge onthe back. The principle of superposition implies that with twosurcharges chq will be double what it would have been with justone.

The elastic reflection parameter has been found in experiments tovary between 1.0 and 1.5, depending on how rigid the wall is.According to Schmitt & Gilbert (1992), it is common practice inFrance to use an elastic reflection parameter between 1.5 and 2.0.

The elastic solutions for perpendicular strip and line loads alreadyinclude an imaginary surcharge on the front of the wall, and henceimplicitly assume that eR = 2.

Duration/effectThe duration (Permanent, Variable, or Accidental) and effect(Favourable or Unfavourable) of a surcharge determine the partialfactors that are used in the calculation of design pressures forEurocode 7 (see Chapter 9).

Imposed loadsDuration/effect

The duration of an imposed load (Permanent, Variable, orAccidental) and its effect (Favourable or Unfavourable) determinethe partial factors that are used in the calculation of designpressures for Eurocode 7 (see Chapter 9).

Chapter 11: References 105

Chapter 11References

Bell FG (1983), Engineering properties of soils and rocks (2nd

edition), Butterworths, London, 149pp.

Bjerrum L and Eide O (1956), Stability of structted excavations inclays, Géotechnique, Vol. 6, No 1, pp32-47.

Bolton M (1986), The strength and dilatancy of sands, GéotechniqueVol. 36, No. 1.

British Standards Institution (1994), British Standard code ofpractice for Earth retaining structures, BS 8002:1994, 111pp.

British Steel, General Steels (1988), Piling handbook, 6th edition,British Steel plc.

British Steel, Sections Plates and Commercial Steels (1997), Pilinghandbook, 7th edition, British Steel plc.

Broms BB (1965), Lateral resistance of piles in cohesionless soils,Proc. Am. Soc. Civ. Engrs, J Soil Mech. Fdn Div., Vol. 90, SM3,pp123-156.

BS 8002. See British Standards Institution (1994).

Burland JB, Potts DM, and Walsh NM (1981), The overall stability offree and propped cantilever retaining walls, Ground Engineering,July, 28-38.

Canadian Foundation Engineering Manual. See CanadianGeotechnical Society (1978).

Canadian Geotechnical Society (1978), Canadian foundationengineering manual, The Foundations Committee, CanadianGeotechnical Society.

Caquot A and Kerisel J (1948), Tables for the calculation of passivepressure, active pressure and bearing capacity of foundations,


Gauthier-Villars, Paris.

Clayton CRI (1989), The mechanical properties of the Chalk, Proc.Int. Chalk Symp., Brighton.

Clayton CRI and Militisky J (1986), Earth pressure and earth-retainingstructures, Surrey University Press, 300pp.

Comité Européen de Normalisation (1994), Eurocode 7:Geotechnical design — Part 1: General rules, Brussels, 126pp.

CIRIA Report 104. See Padfield and Mair (1984).

CIRIA Special Publication 95. See Williams and Waite (1993).

Civil Engineering Code of Practice No 2. See Institution of StructuralEngineers (1951).

Clayton CRI and Militiski J (1986), Earth pressure and earth-retainingstructures, Surrey University Press, Glasgow and London, 300pp.

Clough WG and O'Rourke TD (1990), Construction inducedmovements of insitu walls, Proc. Speciality Conf. on Design andPerformance of Earth Retaining Structures, Cornell, ASCE,Geotechnical Special Publication No 25, Lambe PC and Hansen LA(eds), pp439-470.

Clough WG, Smith EM, and Sweeney BP (1989), Movement controlof excavation support systems by interactive design, Proc. ASCEFound. Engng, Current Principles and Practices, Vol. 2, pp869-884.

Coulomb CA (1776), Essai sur une application des règles de maximiset minimis à quelques problèmes de statique, relatifs à l'architecture,Mémoires de Mathématiques et de Physique présentés àl'Académie Royale des Sciences, Paris, 1773, Vol. 7, pp343-382.

Eurocode 7. See Comité Européen de Normalisation (1994).

Fernie R and Suckling T (1996), Simplified approach for estimatinglateral wall movement of embedded walls in UK ground, inGeotechnical Aspects of Underground Construction in Soft Ground,


ed. RJ Mair and RN Taylor, AA Balkema, Rotterdam, pp131-136.

Geoguide 1. See Geotechnical Control Office (1991).

Geotechnical Control Office (1991), Guide to retaining wall design(Geoguide 1), 2nd edition, Geotechnical Control Office,Engineering Development Dept, Hong Kong.

Institution of Structural Engineers (1951), Civil engineering Code ofPractice No 2, Earth retaining structures, Institution of StructuralEngineers, London.

Kerisel J and Absi E (1990), Active and passive earth pressure tables(3rd edition), AA Balkema, Rotterdam, 220pp.

Liao SSC and Neff TL (1990), Estimating lateral earth pressures fordesign of excavation support, Proc. Speciality Conf. on Design andPerformance of Earth Retaining Structures, Cornell, ASCE,Geotechnical Special Publication No 25, Lambe PC and Hansen LA(eds), 489-509.

Mayniel K (1808), Traité expérimental, analytique et pratique de lapoussée des terres et des murs de revêtement, Paris.

Mitchell (1983), Earth structures engineering, Allen & Unwin Inc.,Boston.

Müller-Breslau H (1906), Erddruck auf Stutzmauern, Alfred Kroner,Stuttgart.

NAVFAC DM-7. See US Dept of the Navy (1982).

Nyaoro DL (1989), Analysis of soil-structure interaction by finiteelements, PhD Thesis, University of London (Imperial College).

Packshaw S (1946), Earth pressure and earth resistance, J. Instn ofCiv. Engrs, Vol. 25, No 4, 233-256.

Padfield CJ and Mair RJ (1984), Design of retaining walls embeddedin stiff clay, Report 104, Construction Industry Research andInformation Association, London, 146pp.


Pappin JW, Simpson B, Felton PJ, and Raison C (1985), Numericalanalysis of flexible retaining walls, Proc. Conf. on NumericalMethods in Engineering Theory and Applications, Swansea.

Peck RB, Hanson WE, & Thornburn TH (1974), Foundationengineering, John Wiley, New York.

Potts DM and Burland JB (1983), A parametric study of the stabilityof embedded earth retaining structures, Transport and RoadResearch Laboratory, Supplementary Report SR 813.

Potts DM and Fourie AB (1985), The effect of wall stiffness on thebehaviour of a propped retaining wall, Géotechnique, Vol. 35, No3, pp347-352.

Puller M (1996), Deep excavations — a practical manual, ThomasTelford Publishing, London, 437pp.

Rankine WJM (1857), On the stability of loose earth, Phil. Trans.Roy. Soc., London, Vol. 147, No 2, 9-27.

Reynolds CE and Steedman JC (1981), Reinforced concretedesigner's handbook (9th edition), Viewpoint Publications, Slough,505pp.

Rowe PW (1952), Anchored sheet-pile walls, Proc. Instn Civ. Engrs,Vol 1., No 1, pp27-70.

Schmitt PJ and Gilbert CM (1992), Surcharge and elasto-plasticcomputations of earth retaining structures, in Retaining Structures,Thomas Telford, London, pp56-66.

St John HD, Harris DI, Potts DM, and Fernie R (1992), Design studyfor a cantilever bored pile retaining wall with relieving slabs, Proc.Conf. On Retaining Structures, in Retaining Structures, ThomasTelford, London, ppXXX-XXX.

Tamaro GJ and Gould JP (1992), Analysis and design of cast-in-situwalls (diaphragm walls), in Retaining Structures, Thomas Telford,London, pp343-352.


Teng WC (1962), Foundation design, Prentice Hall, New Jersey.

Terzaghi K & Peck RB (1967), Soil mechanics in engineeringpractice, (2nd edition), John Wiley, New York.

Tomlinson MJ (1995), Foundation design and construction (6th

edition), Longman Scientific & Technical, Harlow, Essex, 536pp.

TradeARBED's Spundwand-Handbuch Teil 1, Grundlagen (1986)

US Dept of the Navy (1982), Design manual: Soil mechanics,foundations and earth structures, NAVFAC DM-7, US Dept of theNavy, Washington, DC,

Williams BP and Waite D (1993), The design and construction ofsheet-piled cofferdams, Construction Industry Research andInformation Association, Special Publication 95, Thomas TelfordPublications, London, 198pp.

Winterkorn HF and Fang H-Y (1975), Foundation engineeringhandbook, Van Nostrand Reinhold Co., New York, 751pp.

reward - geocentrix · reward 2.5 was designed and written by dr andrew bond and ian spencer of...

Documents