CIRIA 123 Soil Reinforcement Using Geosynthetics

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j

Soil reinforcement

with

geotextiles

R.A.

Jewell

MA

PhD _CEng

CONSTRUCTION INDUSTRY RESEARCH AND INFORMATION ASSOCIATION

6 Storey's Gate London SW1P SAU E-mail switchboard©ciria.org.uk

CIRIA

and the

author

are

_grateful

_{for the help}

_given

to

this

_{project by the}

funders,

by the

members

of

the

_{Steering Group,}

and

_by

_{the many}

individuals who were consulted. The author particularly acknowledges

the

encouragement

he

received from

the late

Professor Peter Wroth

and the

_{helpful criticism}

on the

technical content

of

particular chapters from Dr M.D. Bolton,

Mr D.I.

Bush,

Dr J-P.

Giroud,

Dr

J.H. Greenwood, Professor C.J.F.P. Jones, Professor A. McGown, Dr G.W.E. Milligan

and Dr

R.T. Murray.

Soil

reinforcement with

geotextiles

Construction

_Industry

Research

and

Information Association CIRIA Special Publication 123, 1996

Keywords

Geotextiles, soil reinforcement.

Reader Interest

Geotechnical

and

_{structural engineers, local authorities, public utility engineers.}

All rights

reserved.

_{No part}

of

this

_{publication may}

be

_reproduced

or

transmitted

in

any form

_{or by}

_any

means,

including photocopying

and

recording, without

the

written permission

of the

copyright

holder,

application

for which

should

be

addressed

to

the publisher. Such written permission must also

be

obtained before

any part of

this

publication

is

stored

in

a

retrieval system

of

any nature.

CLASSIFICATION

AVAILABILITY Unrestricted

©

CIRIA 1996

CONTENT Subject area review ISBN

086017425

5

Thomas Telford ISBN STATUS _{Committee guided}

0

7277

2502 5

USER Structural and

geotechnical engineers

Published by CIRIA,

6 Storey's

Gate, Westminster, London SW1P 3AU

and

Thomas Telford

This report presents

the

results of

a

research

_project

carried

out

for

CIRIA

_by

Dr

R

A

Jewell, initially

of

the

University

of

Oxford

and

latterly

with

GeoSyntee Consultants of Brussels.

Following CIRIA's usual practice,

the

research

was

_guided

_by

a

_{steering group}

which comprised:

Mr

N A

Trenter (Chairman)

Sir

William Halcrow

and

Partners

Mr R

_{G V}

Green _{MRM Partnership (now}

Rust

_Consulting

Limited)

Dr

_J

_H

Greenwood

ERA

_{Technology Limited}

Lt

Col

L

J

_{Kennedy RARDE (Christchurch) and later}

of

RMCS Slirivenham

Professor A McGown _University

of

_Strathclyde

The late Mr E B

_MacKay Tarmac Construction Limited

Mr

G

R

A

Watts _{Transport Research Laboratory} CJRIA's research manager

for this

_project

was Mr

F

M

Jardine.

CIRIA gratefully acknowledges these organisations who provided

finding for the

project:

Department

of

the

Environment Ministry

of

Defence

Scottish Development Agency Transport Research Laboratory

BSP

Limited

Don

and

Low

Limited

Du Pont de

Nernours SA Godfreys

of

Dundee Limited

IC!

_{Fibres Geotextile Group}

MMG

_{Civil Engineering Systems}

Netlon Limited

Rhone-Poulene (UK) Limited

Contents

List

of

Tables ix

List

of

Figures xi

1 _{Engineering with geotextiles}

1.1

What are

_geotextiles? 2

1.2 Concepts

for

_{geotextile applications} 3

1.3 Examples

of

the

use

of

_geotextiles 6

1.4 Construction

with

_geotextiles 7

1.5 Geotextile capabilities 8

1.6 Geotextiles

as

_separators 9

1.7 Geotextiles

as soil

reinforcement 10

1.8 Geotextile compared

with

other solutions 12

1.9 Synopsis

of

Chapter 1 13

2

_Polymer

and

_{geotextile properties} 15

2.1 Polymer types 15

2.2

_{Polymer properties} 15

2.2.1

Index

_properties 17

2.2.2

_{Creep properties} 18

2.3

Strength

and

stiffness

of

geotextiles 18

2.3.1 Strength properties 19

2.3.2

_{Stiffness properties} 20

2.3.3

_{Extrapolation}

for

_{long-term properties} 21

2.3.4 Aged

life

of

_geotextiles 22

2.4

Measurement

of

reference properties 23

2.5

_Damage

and

_durability

_of

_geotextiles 25

2.5.1 Mechanical damage 25

2.5.2

_{Chemical and biological durability} 26

2.5.3

_{Material properties}

in the

_ground 29

2.6

_Synopsis

of

Chapter

2

29

3

_{Geotextile products} 31 3.1

Woven

_geotextiles 33

3.2

_Geogrids 35 3.2.1 Geogrid-like products 36

3.2.2

Geomeshes 36

3.3

Other

_{geotextile products} 37

3.3.!

Non-woven geotextiles 37

3.3.2 Knitted geotextiles 38

3.3.3 Sheathed materials 38

3.4

_{Comparing reinforcement materials} 38

3.4.1 Example cases 39

3.4.2

Data on

_{specific strength}

and

stiffness 39

3.4.3 Properties

for

_{woven geotextiles}

40

3.4.4 Properties

for

geogrid reinforcement 41

3.5

_Synopsis

of

Chapter 3

42

4

Reinforced soil behaviour 43

4.!

How reinforcement strengthens soil 43

4.2

Reinforcement orientation and stiffness 45

4.3

_{Strain compatibility} 46

4.4

Interaction between soil

and

reinforcement 48

4.5

Coefficient

of direct

sliding 50

4.6 Coefficient

of

bond 50

4.7

_{Example interaction coefficients} 54

4.7.! Woven

_geotextile 54

4.7.2 Geogrid 55

4.8 Synopsis

of

_Chapter

4

56

5

_{Soil strength}

and

_{bearing capacity} 59

5.!

_Angles

of

friction 59

5.1.!

_{Peak shearing resistance} 60

5.2 Strength

of

compact soils 61

5.2.1 Basic concepts 61

5.2.2 Granular soils 63

5.2.3 Testing granular soils 68

5.2.4

_Compact

clay

soils 71

5.2.5 Testing

clay

soils 73

5.3 Soft

_clay

foundations 74

5.3.1 Consolidation history 74

5.3.2 Lower

limit

to

undrained shear strength 76

5.3.3 Expected undrained shear strength 76

5.3.4

Testing soft

clay

foundations 77

5.4

_{Drained bearing capacity} 79

5.4.1 Influence

of

inclined loading 80

Contents

5.5 _{Undrained bearing capacity} 82

5.5.1 Influence

of

inclined loading 83

5.6

_Synopsis

of

Chapter 5 83

6

Design values and safety margins 87

6.1 Basis

of

calculations 87

6.1.1 Design situations 87

6.1.2

_{Design values}

of

parameters 88

6.1.3

_{Required and available forces} 88

6.2 Loadings 89

6.2.1 Self-weight loading 89

6.2.2

_{Surcharge loading} 89

6.2.3

Water

_pressures 89

6.3 Soil properties 90

6.3.1 Representative values

of

soil strength 90

6.3.2 Design values

of

soil strength 90

6.3.3 Drained analysis 90

6.3.4

Undrained analysis 91

6.4

_{Reinforcement properties} 91

6.4.1 Reinforcement properties

for

serviceability 93

6.5 Interaction properties 94

6.6

_Summary

of

_{design values} 94

6.7 Synopsis

of

Chapter

6

94

7

Limit

states 97

7.1 Design equilibrium 97

7.2

_{Ultimate limit states: design situations} 98

7.2.1 Internal

and

_{overall equilibrium}

99

7.2.2 External equilibrium 100

7.2.3 Construction over soft soil 100

7.3

_{Serviceability}

limit

states 101

7.3.1 Bounds

to likely

deflection 101

7.4 Synopsis

of

_Chapter 7 103

8

_{Steep reinforced slopes} 105

8.1 _{Internal equilibrium: idealised case} 105

8.1.1 Idealised equilibrium 107

8.1.2 Analysis

for

_{required stress} 108

8.1.3 Limit equilibrium analysis 109

8.2.1 Allowance

for

bond 111

8.2.2 Allowance

for

_{load-shedding} 112

8.3 Internal equilibrium: practical corrections 113

8.3.1 Allowance

for

bond 113

8.3.2 Allowance

for

_{compaction stresses} 114

8.4

_{External equilibrium} 115

8.4.1 Direct sliding 115

8.4.2

_{Bearing capacity} 116

8.4.3

_{External stability} 116

8.5 Design charts

for

steep reinforced slopes 116

8.6 Steps

for using the

design charts 117

8.7 Design example 120

8.7.1 Project

data and

design values 120

8.7.2 Design steps 122

8.8 General methods

of

stability analysis 124

8.8.1 Comment

on the

method

of

slices 125

8.9

_Synopsis

of

Chapter 8 127

9

Reinforcement

of

shallow

_slips

in

clay

embankments 131

9.1 Factors causing instability 132

9.1.1 Porewater pressures 133

9.1.2

_{Shearing resistance}

at

low

effective stress 133

9.2

_{Analysis for}

shallow slips 134

9.2.1 Assumed porewater pressure 134

9.2.2 Slip surface geometry 135

9.3 Results

for

shallow slips 136

9.3.1 Unreinforced case 136

9.3.2

Reinforced

case:

_{slip repair} 137

9.4

_{Design charts}

for

_{side-slope reinforcement} 139

9.4.1 Contrast with steep slopes 140

9.5

Selection

of

reinforcement 14!

9.5.1 Reinforcement types and materials 141

9.5.2 Reinforcement layout 141 9.5.3 Reinforcement bond 142 9.6 Construction expedients 143 9.7 Design example 143 9.8 Synopsis

of

Chapter 9 144 10 Retaining walls 147

Contents

10.2 Internal equilibrium: idealised case 150

10.3 _{Overall equilibrium} 151

10.3.1 Overall failure mechanisms 151

10.3.2 Allowance

for bond and

load-shedding 152

10.3.3 Equations

for

overall equilibrium 154

10.3.4

Line

of

thrust in the

reinforced zone 155

10.3.5 Minimum

_required

_length

for

_{overall equilibrium} 157 10.4 Internal equilibrium: practical corrections 158

10.5 External equilibrium 160 10.5.1 _{Direct sliding} 160 10.5.2 _{Excessive eccentricity} 162 10.5.3 _{Bearing capacity} 162 10.5.4 External stability 163 10.6 Deformation

of

walls 164

10.6.1 Deformation

of

the

reinforced fill 164

10.6.2 Deformation caused

by

foundation movement 166

10.7

Practical

_{aspects influencing design} 167

10.7.1

Thrust

from

the

backfill 167

10.7.2 Connections 168

10.7.3 Full-height facing 169

10.8 _{Design example for}

a

_{retaining wall} 170

10.8.1

Data and

_{design values} 170

10.8.2 Design

steps

(ultimate

limit

state) 172

10.8.3 Check

on

_{serviceability} 176

10.8.4 Design cross-section 178

10.9 Point loads 178

10.9.1 _{Internal equilibrium} 179

10.9.2 Allowance

for

bond 181

10.9.3 Overall

and

_{foundation equilibrium} 182

10.10 Sloping fill 183

10.11

_{'Loop-anchor'}

walls 184

10.12 Synopsis

of

Chapter 10 185

11 Embankments

on

soft soil 189

11.1 Stress

and

_{force equilibrium} 190

11.1.1 _Summary

of

mechanics 192

11.2 Slip mechanisms and deformation 193

11.2.1 _{Internal stability} 194

11.2.2 Overall stability 196

11.3.1 _{Construction period 201}

11.3.2 Drained

and

undrained shear 202

11.3.3 _{Design strategies 204}

11.3.4 Significance

of

_{foundation stability 204}

11.4 _{Concepts from plasticity analysis} 204

I

I .4. 1 _{Plasticity solutions 205}

11.4.2 Application

of

plastic theory 206

11.5

Limit

_{equilibrium analysis 207}

11.5.1 General considerations 208

11.5.2 _{Rotational stability: slip circle analysis} 208

11.5.3 _{Foundation and overall stability 210}

11.5.4 Limitations

of

_{slip circle analysis} 211 11.5.5 _{Translational stability:}

_wedge

_{analysis 212}

11.5.6 Methods

of

slices ₂₁₃

11.6 Analytical solutions 214

11.6.1 Foundation

of

uniform strength

and

_{limited depth} 215 11.6.2 Foundation

with

_{strength increasing with depth} 216

11.6.3 Reinforcement stiffness 217

11.7 Parameters for design 218

11.7.1 Limit states ₂₁₈

11.7.2 Ultimate limit sales 219

11.7.3 Analysis

for

_{serviceability} 223

11.7.4 Reinforcement mattress design 225

11.8 _{Design example 226}

11.8.1 Embankment details 226

11.8.2 Ultimate limit state 227

11.8.3 Serviceability limit state 230

11.8.4 Conclusions

_{for the design}

_example 232

11.9 Case histories 233

11.10 Synopsis

of

_Chapter 11 ₂₃₃

12 Working platforms and unpaved roads 235

12.1 Mechanics

of

reinforcement action ₂₃₆

12.2 _Analysis

for

_{working platforms 239}

12.2.1 _{Subgrade bearing capacity 239}

12.2.2 Stresses within

the

fill 240

12.2.3 _{Unreinforced design 241}

12.2.4 Reinforced design 242

12.2.5

Fill

_{bearing capacity 243}

Contents

12.2.7 _{Serviceability}

for

a

known applied loading 246

12.3 Procedure

for

_{working platform design} 246

12.3.1 Ultimate

limit

_{state analysis} 247

12.3.2 _{Serviceability}

limit

_{state analysis} 248

12.4 Design example: working platform 248

12.4.1 _Stability 248

12.4.2 _{Serviceability} 251

12.4.3 _{Reinforcement properties} 251

12.4.4 _{Comparative designs} 252

12.5

Static

_analysis

for

_{unpaved roads} 253

12.5.1 _{Subgrade bearing capacity} 253

12.5.2 Stresses within

the

fill 254

12.5.3 Unreinforced design 255

12.5.4 _{Reinforced design} 255

12.5.5

Fill

_{bearing capacity} 257

12.5.6 Serviceability 258

12.5.7 Design charts 258

12.6 Design example: static wheel loading 260

12.7 Allowance

for

traffic 263

12.7.1 Definition

of

failure 265

12.7.2 Rate effects 266

12.7.3 Fatigue relation 268

12.7.4 Permanent

road

thickness 268

12.7.5 _{Practical wheel loading} 269

12.7.6 Allowance

for

mixed traffic 270

12.8 Procedure

for

_unpaved

road

_design 271

12.8.! _{Unreinforced design} 271

12.8.2 Reinforced design 273

12.9 Comparisons

and

_{back-analysis} 275

12.9.1 _{Unreinforced unpaved road design (l-lammitt, 1970)} 276 12.9.2 _{Reinforced unpaved road design (Giroud}

and

_{Noiray, 1981)} 280 12.9.3 Back-analysis reinforced trafficking trials 282

12.10 Discussion ₂₈₇

12.11 _Synopsis

of

_Chapter 12 ₂₈₈

13 From

_{design to}

_{specification} 291

13.1 _{Future developments} 291

13.2 Designing reinforced soil structures 292

13.2.1 _Concept 292

13.2.3 _Timing

and

structural life 294

13.2.4 Foundation

and

fill materials 296

13.2.5 _Facings

and

_{slope protection} 296

13.3 _{Construction specification and}

_quality

assurance 297

13.3.1 Reinforcement materials 297

13.3.2

Site

_{preparation and construction control} 297

13.4 _Topics

of

_{special concern} 298

13.4.1 _{Limit state design} 298

13.4.2 Geotechnical properties 299 13.4.3 _{Geotextile properties} 300 13.4.4 Environmental considerations 300 13.4.5 Interaction properties 300 13.4.6 Combined applications 300 13.4.7 Unpaved roads 302 13.5 _{Concluding remarks} 302 13.6 Synopsis

of

Chapter 13 303 References 305 Index 317

List

of

Tables

2.1 Factors

to

allow

for

_{mechanical damage}

for

_{some geogrid reinforcements}

made from drawn HDPE 27

2.2

Factors

to

allow

for

_{mechanical damage}

for

_{some woven geotextiles and}

geogrids

made

from polyester 27

3.1 _{Typical reference properties}

for

_yarn

at

20°C and

_{65% relative humidity} 40 3.2 Geometric component

of

extension caused

_by

the weave in woven

geotextiles

40

3.3 Comparison

of

_{index strength}

of

three

_{woven geotextiles}

of

_{weight lOOg/m2}

in the

_{longitudinal direction}

and

_20g1m2

in the

transverse direction 41 3.4 Comparison

of

_{index elongation}

of

_{three woven geotextiles}

of

_weight 100

Wm2

in the

longitudinal direction

and 20

gIm2

in the

transverse direction 41 3.5 Typical geogrid reference properties

of

20°C

_{and 65% relative humidity} 42 4.1 Bearing stress

ratio for

soil reinforcement 52

4.2 Bond

coefficients

_{for grid}

reinforcement 53

5.1 Typical peak angles

of

friction

for

_compacted

_{granular fills in}

routine

applications 66

5.2

_{Peak strength and relative density index corresponding with FS}

=

1.3 68

5.3 Bearing

capacity

factors 81

6.1 Material factors

_(f,)

as

a

function

of

the

_{required extrapolation}

of

data

at

the

design temperature (Td) 93

6.2

_Summary

of

design

values

and

_{partial factors for}

the

_{main parameters in}

ultimate limit

state

_{calculations (drained analysis)} 95 8.1 _{Characteristic strength}

of

the

_{reinforcement grids}

in

_kN/m 122

8.2 Comparison

of

costs for

_{reinforcement layouts} 125

9.1 _{Gross required reinforcement force (kN/m slope)}

_to

_provide

_a

factor of

_safety

FS

=

1.2

and

1.3 138

9.2 Required reinforcement length

to

_provide

a

factor

of

_{safety FS}

=

1.2 and

1.3 ₁₃₈

10.1 _{Characteristic strengths}

for the

reinforcement

_{grids in}

_kN/m 171

10.2 Characteristic stiffnesses

of

the

reinforcement

grids in

kN/m 172 10.3 _{Available stress from reinforcement, 0AV}

in

kN/m2,

and in the

maximum

permissible depth for

each

reinforcement below

the crest,

7max

in

m 173

10.4 Summary

of

displacement calculations

for the

design example 177 11.1 _{Equations from simplified analysis}

for an

embankment on

a

foundation

of

11.2 _{Recommended soil properties}

for

_{ultimate limit state analysis} 220 11.3 _{Recommended reinforcement properties}

for

ultimate

limit

_{state analysis} 221

11.4

Two

_{available woven polyester geotextiles} 227

11.5 Ultimate limit state results

to

achieve

_FS

=

1.3

on

the

_clay

_strength 228 11.6 Ultimate limit state results

to

achieve _FSç

=

1.1

on the clay

_strength 228

1.7 _{Serviceability limit}

state

to

achieve

_FS

=

1.1 231 2.1

Ratio of

_{load-carrying capacity for reinforced}

and

_{unreinforced designs (two-}

dimensional loading case) 252

12.2 Variation

of

bearing capacity factor with outward shear stress for

plane

strain

(2D) and

axi-symmetric (3D) loading 254

12.3 _{Limiting bearing stress}

for

a

circular

load,

R

=

0.17m 263 12.4 Trafficking trials

on

a

crushed stone

fill

_{over clay subgrade, reinforced}

_by

a

List

of

_Figures

Figure 1.1 Geotextile functions:

(a)

separation and

(h)

reinforcement

Figure 1.2 Illustration

of

reinforcement

action in direct shear: (a) tensile and

compressive

strains in

soil,

and

(h)

resultant

reinforcement

forces

Figure 1.3 _{Reinforcement supporting}

_{load by}

membrane action:

(a) rutted

unpaved

road, (b) above

a

sinkhole

and

(c)

in

a

piled

embankment

foundation

Figure 1.4 Combined

use

_of

_{reinforcement}

to

st(ffrn

the

foundation beneath

a

reinforced

soil

wall

Figure 1.5

Local

_{tensile cracking}

at

the base

_of

a

loaded granular layer: (a)

unreinforced

case,

and

(b) reinforced case 7 Figure 1.6 Example applications

of

geotextile separators 9 Figure 1.7 _{Example applications}

_of

_geotextiles

as

soil

_{reinforcement} 10

Figure 1.8 Variation

of

required

reinforcement

force

with time:

(a) steep

slopes

and

walls,

(b)

embankments

on

_{soft soil,}

and

(c)

unpaved roads 11

Figure 2.1 DWerent types

of

creep behaviour

in materials:

(a)

in

a

metal

at

_high temperature,

and

(b)

in

a

polymer

at

ambient

temperature 17

Figure

2.2

Sustained-load

creep

tests on

a

_polyester

_geotextile 18

Figure 2.3 Sustained-load

creep

tests

_{causing failure in}

a

_polyester

_yarn 19 Figure

2.4

Yield

and

_{rupture points:}

_(a)

at

a

constant

_{rate of}

_elongation,

and

(h)

under sustained

load 19

Figure 2.5 Strength

properties

for

a

uniaxial

_{polyethylene geogrid} 20 Figure 2.6 Load-elongation relations

found from

creep

test data

21 Figure 2.7 Time

to

chemical breakdown

as

a

function

of

temperature

for

a

spunbonded polypropylene geotextile 23

Figure 2.8 Typical load-elongation response

from

index tests:

(a) linear

behaviour

and

(b) non-linear

behaviour 24

Figure

2.9

Creep-rupture

properties

for

a

geotextile material 25 Figure

2.10 Idealisation

of

mechanical damage reducing strength by

a

constant

factor

irrespective

of

time 26

Figure 2.11 _{Progressive influence with time}

_of

the soil

_{environment on strength} 28 Figure 3.1 _Requirements

_for

_{reinforcement:}

_(a)

_{axial load-carrying}

_capacity

_and,

for

geogrids,

(b)

an

adequate

transverse member

_arrangement

31 Figure 3.2 Significant reinforcement

in

two

_{perpendicular}

directions

is

best

Figure 3.3 Reinforcement

of

embankments

on

soft

soil: (a)

temporary

force

in

the direction offihling,

(b) jointed

layers

of

reinforcement

and

(c)

a

cellular mattress

Figure

3.4 Geometric components

of

deformation

caused by

straightening of load-

carrying

elements

in

a

woven geotextile

Figure 3.5 Uniaxial

_geogrid

_{reinforcement}

_formed

_by

a

_patented

_process

_of

punching holes

in

a

sheet followed by

drawing 35

Figure

3.6 Geogrid-like

products: (a)

connected

_{sheathed strips}

and

(b) inter- woven

_{bundled yarns}

with

a

_{protective coating} 36 Figure 3.7 Counter-rotating

die

for

manufacturing geomesh materials 37 Figure 4.1 _Effects

_of

_{reinforcement}

on

_equilibrium:

_(a)

_{unreinforced slope}

and

(b)

allowing

for

the

reinforcement force 44

Figure 4.2 Improvement

in

shearing

resistance as

a

function

of

the

_{reinforcement}

orientation 45

Figure 4.3 Optimum directions

for

reinforcement

in

soil: (a)

to

maximise bond,

and

(b)

to

maximise tensile

strain

45

Figure

4.4

Relations

for

strain

compatibility:

(a)

mohilised

soil shearing re-

sistance,

and

(b)

mobilised reinforcement force 47 Figure 4.5

The

compatibility curve

for

determining

the

equilibrium

in

reinforced

soil 47

Figure 4.6

Interactions

between

soil

and

reinforcement 48 Figure

4.7

Definition

of

dimensions

_for

_{reinforcement} 49 Figure

4.8

Bond between reinforcement

and

soil:

(a)

mechanisms

and

(b)

definitions

_for

analysis

Figure

4.9

Bearing

stresses

on reinforcement 54

Figure 4.10

Influence

of

particle

size

_{on soil bearing}

stress 55 Figure

5.!

Equilibrium stresses in

_frictional

soil 60 Figure 5.2 Relation between Kc,

and

peak angle

of

friction

for

normally

consolidated

_granular

soils

Figure

5.3 Trend

_of

_increasing

_{peak frictional}

resistance with distance

_from

the

critical state

line:

(a) critical state

line,

and

peak

strength versus

(b) initial

specific volume,

and

(c) initial

overcompression 62 Figure 5.4 Approximations

to

a

curved strength envelope 63 Figure 5.5 Variation of

peak angle

of

friction

with

mean

stress

_{in granular}

soil 64

Figure

5.6 Triaxial strength

data

_for

sands collected by Bolton (1986) 65 Figure 5.7

Peak angle

of

friction

for

sand in triaxial

compression 67 Figure 5.8 Definitions

for

the direct shear

test 69 Figure 5.9 Typical results from

a

direct shear test on

compact

granular

soil 70

List

of

_Figures

Figure

5.10

Normalised

peak

strength

data from triaxial

compression tests on

London clay 72

Figure

5.11

_{Peak angle}

_of

_friction

_for

London

_{clay (data from Figure}

_5.10) 72

Figure 5.12 Residual angle

of

friction

versus

_granular

_specific volume 74

Figure 5.13

Two

causes

_of

overconsolidation

in

_{a soft clay foundation} (a) reduction

in

_ground level

and

(b) previous lowering

of

groundwater 75 Figure

5.14

Values

of

the shear strength ratio s0/o,

for

normally consolidated

clays 76

Figure 5.15 Example

of

a

foundation

overconsolidated

_by

_{previously lowered} groundwater (a) effective vertical stresses, (b) overconsolidation

ratio

and

(c) undrained shear

strength 77

Figure

5.16

Interpretation

of

the relation

between

_shearing

resistance

and

vane correction

_factor

_Rfor

_{normally consolidated clays} 78 Figure 5.17 Relation between

undrained shearing

resistance

and

plasticity

index

from the

back-analysis

of

embankment

_failures

78 Figure 5.18 Definitions

for

the drained analysis

of

bearing

capacity 79

Figure

5.19 Reduction

in

_{bearing capacity}

due

to

load

inclination 81

Figure 5.20 Drained bearing capacity under

combined loading 82

Figure

5.21 Definitions

for

the analysis

of

undrained bearing

capacity 83

Figure 5.22

Undrained

_{bearing capacity under}

_{combined loading} 84

Figure

6.1 Reinforcement strength properties 92

Figure

7.1 Equilibrium

in

a

steep

reinforced

slope

expressed

in

terms

_of

_required

and available stresses 97

Figure

7.2

Equilibrium (foundation stability)

for

an

embankment

on

_{soft soil}

expressed

in

terms

of

required

and

available

forces 98 Figure 7.3

Internal

equilibrium

for a

steep

reinforced slope 99 Figure

7.4 Overall

equilibrium

for a

steep

slope

and

wall 99 Figure 7.5

External

equilibrium check

on

foundation capacity:

(a) direct

sliding,

(b)

bearing capacity,

and

(c)

eccentricity 100 Figure

7.6 External

equilibrium check on deep-seated

failure

mechanisms 100 Figure 7.7 Limits

to the

expected equilibrium shown

on

a

compatibility curve: (a)

soil

_{behaviour, (b) reinforcement behaviour, and}

_{(c) the}

_expected

equilibrium 102

Figure 8.1 Three types

of

reinforced slope 105

Figure 8.2 Steep slope definitions 106

Figure 8.3 Three zones

in

a

steep reinforced slope: zone

I,

bounded by

AB, zone

2,

to end

_of

reinforcement,

and

zone

3, the

unreinforced backfill 106

Figure 8.4

Idealised

equilibrium with uniform reinforcement

force in

zone

I

decreasing

to zero

at

the back

_of

zone 2 107

Figure 8.5 Maximum

required stress

in the

soil

exceeded everywhere by the

available

_{stress from reinforcement}

_arranged

at

two spacings 107

Figure 8.6 Stress characteristics illustrating

balanced

equilibrium

in

zone

/

108 Figure 8.7

(a)

Two-part wedge mechanism

and

(h) boundary

forces

109 Figure 8.8

(a)

Logarithmic

spiral

mechanism

and (h)

boundary

forces

109 Figure 8.9 Overall equilibrium check on

the required

reinforcement length 110 Figure

8.10

Maximum available reinforcement

force,

R'

to

maintain

overall

equilibrium

Figure 8.11 _Required

bond

_length

and

loss

_of

_{available force}

Figure

8.12

Additional reinfoirement. Kd> KReq.

to

mitigate

loss

of

available

force

due

to

bond

Figure

8.13

Additional reinforcement.

0mj'

to

allow

for

bond near the crest

of

a

steep

slope 113

Figure

8.14

Two-part wedge

analysis

for

direct

_sliding 115

Figure

8.15

Choice

of

pore-pressure

ratio to

allow

for a

phreatic

surface 117

Figure

8.16 (a)

Envelope

of

maximum

required

stress,

and

(h) locus

of

maximum

available

stress

in

a

_{steep reinforced slope} 118 Figure 8.17 Envelope

of

maximum

_required

stress

_for

the

_{design example} 123

Figure 8.18 Provision

of

available stress

_for

the

_{design example} 124

Figure

8.19 Cross-section

_for

the

_{design example using}

all

three

_{reinforcement}

grids

125

Figure 8.20 Illustration

of

the

method

_of

_{slices applied to}

_{reinforced soil} 126 Figure 8.21 Design

chart

I

for

steep

reinforced slopes,

r

=

0 127 Figure 8.22 Design

chart

2 for

steep

reinforced slopes, r11

=

015 128

Figure 8.23 Design

chart

3for

steep

reinforced slopes, r11

=

0.50 129

Figure 9.1 Shallow slope

failures in clay

slopes:

(a)

slip

sutface, (b) near-surface

porewater

pressures,

and

(c)

reduced

_{shearing resistance}

at

low

effective stress 131

Figure 9.2

Measured shearing resistance

for

London

Clay

at

low effective stress 134 Figure 9.3

(a)

Maximum

_{porewater pressure}

distribution

_{in clay}

embankment

side-slopes

and

(b)

the

idealisation

_for

_analysis 135

Figure

9.4

Slip mechanism

for

analysis 135

Figure 9.5 Variation

of

the

mobilised

_{friction angle}

_{with depth}

to

maintain

equilibrium

in

a

clay

side-slope 136

Figure

9.6

Required

shearing

resistance

_for

_{equilihirium compared with}

_{the peak}

and

critical state shearing

resistance

_of

_{London Clay} 137

Figure 9.7

Gross required

reinforcement

force

for

combinations

_of

_{slope height}

List

of

Figures

Figure 9.8 Required reinforcement length

for

combinations

of

slope

height

and

design

angle

of

friction

140

Figure

9.9 Typical reinforcement

arrangement in

a

clay

embankment side-slope 14!

Figure 9.10

Envelopes

of

required

and

available

_force

_in

_{reinforcement layers}

_for

a

1:2

_side-slope 142

Figure

9.11 Reinforcement layout

for

the

_{design example} 144 Figure 10.1 Two _examples

_of

_reinforced

soil wall

_systems 147

Figure 10.2 Definitions

_for

reinforced

soil

walls 148

Figure 10.3 Summary

of

steps in the

design of reinforced

soil

walls 149 Figure 10.4 Analysis

of

internal

_equilibrium

in

a

reinforced

soil

wall 150 Figure 10.5 Distribution

_of

available

stress

_for

balanced internal

_equilihi-ium 151

Figure 10.6 Analysis

for

overall

equilibrium

in

a

reinforced

soil

wall 152 Figure 10.7 Maximum available

force in

a

reinforcement layer

I

52 Figure 10.8

Forces acting on the

reinforced zone

for

overall

equilibrium 153 Figure 10.9 Eccentricity

of

the

resultant

_force

on

the

t,ial

wedge

0G.

at

an

angleO 155

Figure 10.10 Results

to

illustrate the line

of

thrust in

a

reinforced

soil

wall. (case

with

td

=

35°

and

no

_surcharge) I 56

Figure 10.11 _{Minimum reinforcement length}

_{for balanced}

_equilibrium

_(case:

_4bd

=

_trd'Yb

=

_Yr. level _backfill,

_{and A1}

=

_I/Ab) 158

Figure

10.12 Minimum reinforcement length

for

balanced

_equilibrium

_(case:

_thd

=

_trd

5°, Yb

=

Yr. level backfill,

and

A1

=

//Ab) 159

Figure

10.13

Direct

_sliding

at

_foundation level I 60 Figure 10.14 Possible

direct

sliding mechanisms when LdS

>

L 161

Figure 10.15 Equivalent

foundation

for

the analysis

of

bearing

capacity 162 Figure 10.16 Check

on foundation

stability:

(a)

bearing capacity analysis,

and

(h)

analysis

of

external slip

mechanisms 164

Figure 10.17

Chart

for

maximum horizontal movement

in

_reinforced

soil

walls 165

Figure 10.18 Resultant wall displacements following consolidation 167

Figure 10.19 Connections

at

the

_face

168

Figure 10.20

Forces

transmitted through

full-hei ght facing

169 Figure 10.21 _{Design example:}

wall details

and

required

stresses

_for

internal

equilibrium 173

Figure

10.22 Design example:

trial

reinforcement

layout to provide the

required stresses

(a) one

reinforcement

material

(h) use

of

stronger

grid at

base ₁₇₄

Figure

10.23 Design example:

_final

cross-section 178 Figure 10.24

inclined load on

a

reinforced

soil

wall 179 Figure 10.25 Additional

required stress

due

to

a

horizontal

_{point load}

180

Figure 10.26 Additional required stress due

to

a

vertical

point load

180

Figure

10.27

_{Required stress}

_for

internal

_{equilibrium with}

_point

loading 181

Figure 10.28 Wedge analysis

to

check

internal

equilibrium 182

Figure

10.29 Wall with sloping

fill

183

Figure 10.30 Active

earth pressure

coefficients

for

sloping

fills

184 Figure 10.31 Approximation

for

backfill stresses

due

to

a

broken slope 185

Figure 10.32

Details

for

loop-anchor walls 186

Figure 11.1 Reinforcement improving stability

during

construction

and

founda-

tion

consolidation 189

Figure 11.2 Disturbing

forces in

an

unreinforced embankment, with reinforcement

supporting

outward shear

stress 190

Figure 11.3 _{The influence}

_of

outward shear stress on bearing

capacity 191

Figure 11.4 Reinforcement providing

lateral restraint

on

the foundation

surface 192 Figure 11.5 improvement

in

bearing

capacity due

to

lateral restraint on

the

foundation suiface 193

Figure 11.6 Summary

of

mechanics

in

a

reinforced embankment

on

soft soil 194 Figure 11.7

internal

_stability:

direct

_sliding

_{failure in the fill}

195

Figure

11.8 Overall stability: slippage

across the foundation

surface 196

Figure

11.9 Foundation

_{stability: (a) applied}

stresses,

(b)

and

(c)

shear

on horizontal

_planes,

and

(d) resulting

shear

displacement,

for

the

case

c=O

197

Figure 11.10

Overall stability:

envisaged

rigid

body

failure

mechanism 199 Figure 11.11

Foundation

stability: limiting embankment cross-sections

and

pre-

failure' lateral

deflections

in the foundation

for

the

cases,

=

+1,

0,—!

200

Figure 11.12 Relation between

the

maximum

required

reinforcement

force

and

the

rate

_of

construction 201

Figure 11.13 The response

of

soft clay to rapid stage

2

loading beneath an

embankment 203

Figure 11.14 Beat-ing

capacity

expressed

in

terms

of

the

allowable vertical loading versus distance

from the

edge

of loading, relevant

to

embankment design 205

Figure 11.15 Plasticity solutions

for

strength increasing with depth 206 Figure 11.16 Solutions

for a

foundation

of

uniform strength

and

limited depth

above

a

_{rough stratum} 206

Figure 11.17

Practical

embankment cross-sections derived

from plasticity

solu-

tions 207

List

of

Figures

Figure 11.19 Slip circle

analysis

for

reinforced embankments:

(a)

foundation stability, with (b)

available

and

(c) required forces; (d)

overall

stability,

required forces

210

Figure

11.20 Comparison

of

slip

circle

analysis with

plasticity

solutions: (a) strength

increasing

with depth,

and

(b)foundation

of

limited depth 212 Figure 11.21 _Wedge

_analysis

_for

_{reinforced embankments:}

_(a)

_{exploded view}

_of

limiting stresses,

(b)

check

_{on foundation}

_stability,

and

(c) check on

overall

_stability 213

Figure 11.22 Assumed equilibrium

for

analytical solutions:

(a)

foundation

of

limited depth,

and

_{(b) foundation}

with strength increasing with

depth 214

Figure 11.23 Influence

of

reinforcement stiffness

on the

maximum values

_of

embankment displacement

and

_{reinforcement elongation} 224 Figure 11.24 Possible embankment cross-sections

fbr

the

design example 228 Figure 12.1 _Typical

_arrangement

_for

an

_unpaved

road

235 Figure 12.2 General definitions

for

the

two-dimensional loading on

a

working

platform 236

Figure 12.3 Combined _loading

on the

_subgrade

in the

_unreinJbrced

case

237 Figure 12.4 Action

of

the

_{reinforcement}

to

_{relieve subgrade}

_of

outward

shear

stress 238

Figure 12.5 _Envelope

_of

available

_{subgrade resistance}

_(ABCE)

and

the

stress

applied

by

suiface load

(GCH) 239

Figure

12.6 Elemental block

_of

_fill

_{beneath the surface pressure}

240

Figure

12.7 Horizontal

_forces

considered

in the

_{equilibrium analysis} 241 Figure 12.8 Outward

shear

stress

_{supported by the}

_{reinforcement} 242

Figure

12.9 Interaction

_diagram

_showing

the

_unreinforced

and

fully

reinforced

equilibrium 243

Figure

12.10 Limit imposed

by the bearing capacity

of

the

fill

(N

=

pyB/sB') 244 Figure 12.11 _{Limit imposed}

_{by the}

_{allowable reinforcement}

_force

_(aji

=

_taijB') 245 Figure 12.12 Required

and

available

stresses

_for

_working

_platform

_example 249 Figure 12.13 Design

chart

for

working platform example 250 Figure 12.14 General definitions

for

the

_{three-dimensional loading}

on

an

unpaved

road 253

Figure 12.15

Shear

loading

under axi

-symmetric conditions:

(a) shear

stresses,

(b)force

in

the

_{reinforcement,}

and

_{(c) average biaxial}

conditions 256 Figure 12.16 Design

chart

for

unreinforced

and

reinforced

stability

under

axi-

symmetric

loading: (a) required

fill

thickness,

and

(b) required

Figure 12.17 Design

charts

for

(s,IyR

=

10)

illustrating the

influence

of

load-

spread angle: (a)

and

(b) with

I

=

25',

(c)

and (d) with

I

=

45°

261 Figure 12.18 _Design

charts

_for

([3

= 35°)

illustrating

the

influence

of

the

fill:

(a)

and

_{(b) with sn/yR}

=

_{5, (c) and (d)}

_{with s0/1R}

=

20 262

Figure

12.19 Comparison between

static

and

repeated-load

tests on

unreinforced

unpaved roads 264

Figure 12.20 Definition

of

failure in an

unpaved

road under static

and

repeated

loading 265

Figure 12.21

Failure in

unreinforced

and

reinforced

unpaved roads subject

to

traffic 266

Figure 12.22 Vane correction

factors to

allow

_for

the

influence

of

strain rate

on

undrained shear

strength 267

Figure 12.23

Derivation

of

road capacity after

N

load

_repetitions

in

terms

_of

an

equivalent

static load

272

Figure

12.24 Design

chart

for

unreinforced unpaved

roads; applicable to

specific

values, se/yR,

and,

[3 273

Figure

12.25

Master

_design

chart

_for

_{reinforced unpaved roads} 274 Figure 12.26 Determination

of

the required

reinforcement

force

allowing

for

traffic 275

Figure 12.27

Correlation

for

unreinforced unpaved

roads proposed by

Hammitt

(1970) 276

Figure 12.28

Fit to

the

data

achieved

by the

equation

proposed

by Hammitt

(1970) 277

Figure 12.29 The

data

of

Hammitt (1970)

plotted as

an

equivalent static

load

278 Figure 12.30 Comparison between

the new

analysis,

the

relation

proposed

by

Hammitt (1970)

and

the

data

_for

_{unreinforced unpaved}

roads

279 Figure 12.31 Comparison of

the

new

analysis

with Giroud

and

Noiray (1981). 281 Figure 12.32 Results

for

the

hack-analysis

_of

the

_unreinforced

_{unpaved road}

tested

by Webster

and

Watkins (1977) 285

Figure 12.33 Illustration

of

the increasing

equivalent

load

due

to

fatigue

and

the limiting capacity caused by insufficient reinforcement modulus 287 Figure 13.1 _{Possible effect of sequence}

_of

_operations

at

a

_{soft-clay site: (a)}

proposed light bridge formed on

H-piles,

(b)

fill

placement

deforms

pre-installed piles,

(c)

piles installed alter

construction

_of

_approach

embankment 294

Figure

13.2 _{Possible effects of sequence}

_of

_{operations when installing}

a

culvert through

a

basally

reinforced embankment

on soft

clay 295

Notation

ab fraction

of grid

width available

for

bearing

fraction

of

reinforcement

_{plan area}

that

is

solid

bond

allowance

A1 load-shedding

(or

sharing) allowance

B width

of

a

transverse member

of

a

grid taking bearing

B

effective width

of

loaded area effective cohesion

/3 _depth

_of

_footing

_{below ground} level mean particle size

Dmax maximum particle size

e _{load eccentricity}

on

a

footing

e _eccentricity

of

foundation reaction from centre

of

reinforced block

e void ratio

efield

field

void

ratio

of

compacted fill Cmax void

ratio

at

loosest condition Cmin void

ratio

at

densest condition

fd partial factor

for

mechanical damage

fenv partial factor

for

chemical

and

biological environment fm overall material factor

F1 scale-effect factor

for

bearing stress ratio F2 shape-effect factor

for

bearing stress ratio

FS

factor

of

safety

FSa

factor

of

safety

in

a

'lumped-factor' design G, specific gravity

depth

where

critical wedge intersects width face height

of

phreatic surface above base

of

a

slope

H

slope

(or

wall) height

H' _{effective slope}

_(or

_{wall) height (allowing}

for

_{vertical surcharge)}

angle

of

backfill above

a

slope crest

reduction

factor

for

bearing capacity

under

inclined loading

i,, reduction factor

for

_{bearing capacity}

under

inclined loading

relative density

l,

plasticity index

relative

_density

index

reference stiffness

at

end

of

construction Jd reference stiffness

at

end

of

design

life

specific stiffness

of

a

polymer

k _empirical

constant in relation between

_{relative density}

_{and angle of}

friction

K0 coefficient

of

earth

pressure

at

rest

Kar active earth pressure coefficient corresponding

to design

angle

of

friction for reinforced fill

Kab active earth

pressure

coefficient corresponding

to

design angle

of

friction

for

backfill

Kad

design

active

earth

_{pressure coefficient}

Kd design value

of

earth

pressure coefficient

KReq required

value

of

earth

pressure coefficient

L

width

of

footing

or

block

of

reinforced soil

L

effective width

of

footing

for

inclined loading

bond

length

bond

_length

for

reinforcement

_layer

at

base

of

wall required reinforced length

to

prevent

direct

sliding Lr LR length

of

reinforcement

length

of

inclined trial wedge

in _power

to

which OCR is raised

_{in relating}

_(s/o')

for

_{normally and}

overconsolidated states

n _slope definition

in

1 vertical

to n

horizontal bearing capacity factor

Nq bearing capacity factor

bearing capacity factor OCR overconsolidation ratio

equivalent effective pressure with respect

to

normal consolidation line

P

tensile load

in

reinforcement

Av

available

force

_allowing

for

bond AvaiIable available reinforcement force

gross reinforcement force

"hase modified reinforcement

force

at

base

of

wall

bf

thrust

from backfill on reinforced block

design

strength

of

reinforcement

"darn reinforcement strength allowing

for

mechanical damage

env

reinforcement strength allowing

for

chemical

and

_{biological environment}

Pro

reinforcement force

at

_equilibrium

lateral

thrust from the

fill

Notation

(fieId)td,Td strength

of

reinforcement

in the field

at

design life, td,

and

design temperature, Td

mobilised

force in

reinforcement effective normal force

tensile

force

in

reinforcement

gross maximum

force

required

for

equilibrium gross available force

ref

reference strength

of

reinforcement

(fXd.

Td reference strength

of

reinforcement

at

design

time, td

and

temperature, Td

"Req required tensile reinforcement force required required reinforcement force

RL

gross reinforcement force,

likely lower

value

RU

gross reinforcement force,

likely upper

value

T1rupture tensile force

at

which

reinforcement ruptures

shear force

serviceability strength

of

reinforcement

(i.e.

at

max. allowable elongation vertical load

yieId tensile load

at

which

reinforcement yields

(R)l,2,

etc. horizontal resultant forces

on

wedges

in

stability analysis qb surcharge pressure above backfill

surcharge pressure above reinforced zone applied vertical surcharge

Q empirical constant

for

determining relative

density

index, 'R Q maximum _{compaction force}

_{per unit width}

of

roller

Qh horizontal component

of

applied

point

load

Q

vertical component

of

_applied

_point

load radius

of

_{slip circle}

pore pressure ratio

design

value

of

pore pressure ratio R reaction

on

a

foundation

R resultant thrust

R121221 etc. reactions between wedges

in

stability analysis Rh horizontal component

of

load on

footing

R

vertical component

of

_{load on footing}

mean effective stress

(=

(°'

+

o'3)/2)

Sh horizontal spacing

of

reinforcement elements

su undrained shear strength

Sud undrained shear strength

of

foundation

design

undrained shear strength

vertical spacing

of

reinforcement layers

S _{specific strength}

_(of

a

_polymer)

S _{spacing between transverse members taking bearing}

maximum shear stress

_(=(°'i

— _635/2)

time

_{in creep}

test design life

aged

life

T _temperature

design temperature

U _{porewater pressure}

Umax maximum

pore

pressure in

a

slope

U12 C. water upthrusts normal

to

sliding

face

of

wedges

Vg granular specific volume

specific volume

at

start

of

shearing

specific volume

at

critical

state

(constant volume) W _weight

of

reinforced

soil

block

etc. weight

of

wedge

W

width of

reinforcement

X distance

of

point load

edge

of

crest.

x

(dx) shear displacement

y

(dy) vertical displacement

z _{depth below ground surface}

effective

_depth

in

_slope

of

effective height

H'

depth

below slope surface

of

clay

embankment depth below slope crest

of

change

in

reinforcement

critical depth

where bond

_{length equals reinforcement length}

depth

to

groundwater level

load

inclination

(=

r/s1)

b

coefficient

_of

bond

ds

coefficient

of

direct

_sliding

slope angle from horizontal y

unit

weight

of

soil

design

value

of

unit

weight

of

soil

Yeff effective

unit

weight

of

foundation soil allowing

for

buoyancy

unit

_weight

of

foundation soil

yf

submerged weight

of

foundation soil

Ymax maximum

dry

density Yr

unit

weight

of

reinforced soil Yrd design

unit

weight

of

reinforced soil

Notation

o _angle

of

_{skin friction, soil}

on

_{planar reinforcement surface}

design

angle

of

friction between soil and reinforcement of inclination

of

_{inclined loading as}

_footing

₍₌

tan

_Rh/RV)

0rnax maximum horizontal displacement

Op peak friction

angle

between

soil and

reinforcement

maximum settlement

at

crest

of

wall wall roughness

AL'S improvement

in

shearing resistance Aqr increment

of

vertical surcharge

83 maximum

tensile

strain

in

soil

elongation

of

polymer

at

time t'

in

creep

test

EEQ tensile elongation

at

force equilibrium

8max maximum tensile strain

tensile elongation

of

reinforcement elongation

of

reinforcement

at

rupture

tensile elongation

of

reinforcement

at

force

_equilibrium

8RL tensile elongation

of

reinforcement,

_{likely lower}

value

tensile elongation

of

reinforcement,

likely upper

value tensile strain

in

soil

at

_{force equilibrium}

8sL

tensile

strain

in

soil, likely

lower

value 8su

tensile

strain

in

soil, likely

upper

value

Cyjeld elongation

of

reinforcement

at

yield

o inclination

of

reinforcement

to

vertical

angle

to

horizontal

of

_{trial wedge}

optimum reinforcement orientation

for

bond optimum orientation

of

reinforcement

05 optimum orientation

of

reinforcement

in

direction

of

maximum soil tensile strain

vane strength correction factor

a'

normal

effective

stress

equivalent vertical stress acting

at

level

of

footing base

Go maximum residual stress from compaction

major principal effective stress aS

minor

principal effective stress 0Av available stress

effective bearing stress

on

reinforcement

(oJ)

bearing stress ratio

bearing capacity

of

foundation soil

maximum effective bearing stress beneath rough

footing

of

effective width

I

0comp maximum horizontal stress caused

by

compaction

highest effective

stress experienced by

the

soil

design

normal

effective

stress

Of applied vertical stress acting

on

effective

footing

width

I

of

vertical stress applied across reinforced soil foundation

effective vertical stress below footing

Oax

maximum normal effective stress

on

reinforcement

0min minimum

direct

stress 0mob mobilised stress

normal

effective

stress preconsolidation pressure

0Req required stress

current vertical

effective

stress

direct

stress

_{on plane}

yy shear stress

tf

applied shear stress acting

on

effective

footing

width

£

shear stress

4) angle

of

shearing resistance

4)' angle

of

shearing resistance

in

terms

of

effective stress mobilised angle

of

shearing resistance,

at-rest

conditions

4)bd design

angle

of

friction

for

backfill

critical

state angle

of

_{shearing resistance}

constant volume (large strain)

angle

of

shearing resistance design

value

of

effective angle

of

shearing resistance 4? angle

of

friction

in

normalised plot

4? angle

of

shearing reistance

of

foundation soil 4? mobilised angle

of

shearing resistance

at

failuretb 4¾ design angle

of

shearing resistance

of

foundation soil

peak angle of

shearing resistance

of

foundation soil mobilised angle

of

friction

4)rnob mobilised effective angle

of

shearing resistance

peak

effective

_angle

of

shearing resistance,

i.e.

secant value

4)peak

constant

peak angle

of

friction,

i.e. c,

4/linear envelope

peak

angle

of

friction

in

plane

strain conditions

peak

angle

of

friction

for

reinforced fill angle

of

friction mobilised

in

reinforced soil

peak

angle

of

friction measured

in

triaxial compression angle

of

dilation

SOIL

REINFORCEMENT