Notes for Retaining Wall Design

8/11/2019 Notes for Retaining Wall Design

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RETAINING

•,IALL

DESIGN

NOTES

INDEX

SECTION

1

INTRODUCTION

1.1

Scope

1.2

Definitions

and

Symbols

1,3

Design

Principles

1,3,1

Free

Standing

Retaining

Walls

1,3,2

Other

Retaining

Structures

1,4 Lo•d

Cases

1,4,1

Basiq

Loadings

1,4,2

Other

onsiderations

SEG•ION

2

SOIL

PROPERTIES

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2°9

2.10

2.11

General

Selection

and

Use

of

Backfil

Density

Effective

Stress

and Pore

Pressures

Shearing

Strength

Base

Friction

Modulus

of

Elastici•and

Poisson's

Ratio

Coefficient

of

Subgrede

Reaction

Swelling

and

Softening

of

Clays

Permeability

Liquefaction

SECTION

3

STATIC

EARTH

PRESSURE

3;-1' States

of

Stress

3.2 Amount

and

•ype

of

Wall

Movement

3.3 Limiting

Equilibrium

onditions

3 3.1

The

Rankine Earth

Pressure

Theory

3.3.2

3.3.3

3.3.4

3.3.5.

3.3.6

3.4

The

Coulomb

Earth

Pressure

Theo[y

Passive Pressures

using

Equations.

The

Trial

Wedge

Method

Geometrical

Shape

of

the

Retaining

Structure

Limlte•-Backfill

Elastic

Equilibrium

onditions

3,4,1 At-rest Pressures

3.4,2

Over-consolidation

Pressures

3.4.3

Elestic

Theory

Methods

SECTION

4

EARTHQUAKE

EARTH

PRESSURE

4.1 Method

of

Analysis

4,2

Selection

of

Seismic

Coefficient

Page

I

1

1

i

2

2

2

3

3

4

4

6

7

7

10

I0

11

11

12

12

12

13

13

14

15

16

17

17

18

18

18

19

2O

20

20



4.3

4.4

Limiting

Equilibrium Conditions for Earthquake

Loading

4.3.1

General

•

4.3,2

Mononobe Okabe Equations

4.3.3

Trial

Wedge for

Earthquake

Seismic

At rest Pressures

SECTION 5 EFFECT

OF

SURCHARGES

5.1

Uniform

Surcharges

5.2

Line

Loads

5 3

Point

Loads

SECTION 6

EFFECTS

OF

WATER

6.1,

Static

Water Level

6.2

Seepage Pressure

6.3

Dynamic

Water

Pressuwe

6.4

Drainage

Provisions

SECTION

7 STABILITY

OF RETAINING

WALLS

Page

21

21

?_

21

22

23

23

23

23

24

24

25

25

27

7.1

General

7.2

Sliding

Stability

7.2.1

Base

Without

a

Key

7.2.2

Base Wit•

•..KRy

7.3

Overturning Stability

7.4

Foundation

Bearing Pressures

7.5

7.4.1

7.4.2

7.4.3

7.4.4

7.4.5

7.4.6

Slip

Vertical Central

Loads

Eccentric

Loads

Inclined

Loads

Eccentric

Inclined

Loads

Foundations

onZa

Slope

Effect

of Ground

Water Level

Circl.e.-Stab•l.ity

SECTION

8

STRUCTURAL

DESIGN

8.1

8.2

8.3

General.

8.1.1

8.1.2

8.1.3

8.1.4

8.1.5

Codes

Material

Strength

and Allowable

Stresses

Ultimate

Strength

Cover

to

Reinforcement.

Selection

of Wall

Type

Toe

Design

S em

Design

8.3.1

Stem

Loading

8.3.2

Lower

Section

of Counterfort

Stem

8.3.3

Horizontal

Moments

in

Counterfort

Stem

27

28

28

28

28

28

28

29

30

30

30

31

31

33

33

33

33

33

34

34

34

35

35

35

35



8 4

8 5

8 6

8 7

Heel Slab

Design

8 4 1

Loading

8 4 2

Heel

Slabs

for

Counterfort

Walls

Counterfort

Design

Key

Desig9

Control of

Cracking

SECTION

SPECIAL PROVISIONS

FOR

CRIB

WALLS

9 1

General

9 2

Design

L•ading

9 3

Foundation Depth

9 4

Drainage

9 5

Multiple

Depth

Walls

9 6

Walls

Curved

in

Plan

APPENDIX

.References

APPENDIX

II

Figures

Page

35

35

36

37

37

38

38

38

38

38

38

39

40

42



B

B

CF

C

Cb

c

D

dc,dq•dT

Is

Fs

H,H

,etc

SYMBOLS

effective

re

of base

base

width

of wall

effective

base

width

design

seismic

coefficient

including

importance

factor)

cohesion of

soil in

terms

of total

stress

dhesion

at

base

cohesion

of

soil in

terms

of

effective

stress

foundation

depth

foundetion

depth

correction

f ctors

modulus

of

elasticity

of

soil

eccentricity

of load

on

base

f ctor

•f

safety

vertical

height

of

plane

on

which

earth

pressure

is

c lcul ted

(from

underside

of base

or

bottom of

key

to

ground

surface)

vertical

height of

wa,ll

piezometric head

foundation

load

inclin tion

f ctors

coefficient

of

earth

pressure

at rest

..

coefficient

of

active

earth

pressure

coefficient of

ctive

earthquake

eaF•h

pressure

coefficient

of

passive

earth

pressure

coefficient

of

subgrad9

re ction

coefficient

of

permeability

length

of-b-•6

effective

length

of base

l@ngth of

f•ilure

surf ce

.'normal

reaction

on

a

soil

f ilure surf ce

bearing

capacity

f ctors

slope

stabi.lity

number

resultant

lateral

pressure

ctive

lateral

earth

pressure

active

lateral

earthquake'earth

pressure

(PA+APAE)

horizontal

component

of

later•l

earth

pressure

at-rest

earth

pressure

passive

earth

pressure

lateral

earth pressure

due to line

or

point surcharge

load

(per

Unit

length

of

wall)



ii)

Pv

APAE

PA

Pc

Pw

QL

Qp

q

qa

qult

qu

R,

RA, Rp,

Rw,

etc

S

S

Sc,Sq,Sy

T

U

U

V

W

Wb

Ww

Wt

Yo

•A

vertical

component

Of

lateral

ea th

pressure

hydrostatic

water

pressure

increment

in

active

earth

pressure

due

to

an

earthquake

intensity

of

active earth

pressure

consolidation

pressur•

intensity

af

water

pressure

total

load

line

load

point load

intensity

of

load

on

base

or

surcharge

load

allowable

soil bearing

pressure

intensity

ultimate

soil bearing

pressure

intensity

unconfined

compressive

strength

resultant

forces

total

shearing

resistance

at underside

o f

base

shearingstrength

of soil

foundation

shape

correction factors

tangential

force

along

a

fail•ure

surface

resultant

of

pore

water

pressures

intensity

of

pore water

pressure

.vertical

component

of

resultant

of

loading

on

the

base

weight

of

soil

wedge

used

in calculation

of

earth

pressgres

weight

of

backfill

ov r

heel

of wall

weight

of

wall

total

weight

of

wall,

soil

above

toe

and

soil

above

bee

vertical

depth

of tension

crack

in

cohesive

soil

angle

of failure

plane

from

the horizontal

for active

state

(degrees)

slope

of

back

of

the wall

(degrees)

density

of

Soil

(force

units

submerged

soil

density

Ysat

Yw

dry

soil

density

density

of

saturated

soil

density

of

water

increment;

settlement

angle

of wall

friction

(degrees)

angle

of

base

friction

(degrees)

angle

tan

-I

CF

Poisson's

ratio



iii)

angle measured

clockwise

from

vertical to

direction

ofP

A

total

normal stress

effective

normal

stress

shear

stre•s

angle

Of

shearing

resistance

in

terms

of total

stress

angle

of shearing resistance

in

terms

of

e fective stress

angle

of

inclination

of

loading

on

base

angle

of

ground

slope



1-

SECTION

NTRODUCTI

ON

I.

SCOPE

These

notes

are

intended

as a

guide

for

use

in

the

estimation

of

earth

pressure

forces

and

the

design

and

construction of

retaining

walls end

similar

earth

retaining

structures.

Recommended

methods

are

given

for

r•st

aspects of design,

however

if

a

more

detailed

knowledge

of

a

particular

subject

is

required,

the

references

given

should

prove

helpful.

Reference

is

also

made

to

standard texts for

detailed methods

such

as

the

construction

of-flow

nets.

for

pore

water

pressure

determination,

and

reinforced

concrete

design

methods.

Aspects

such

as:

the

use

of

classical earth

pressure

equations;

the

effect

of

earthquakes

on

earth

pressures;

and

allowable

bearing

pressures

under

inclined

loads,

which

are

not

readily

available

in

standard

texts

are

covered in

detail.

Engineering

judgement

must always

be

used when

applying the

theories

an•

methods

given

in

these

notes

and strict

notice

must

be taken

of the

limitations

of

the

various

assumptions.

1.2

DEFINITIONS

•ND

SYMBOLS

Throughout

these

n6•es,•'•tatic earth

pressure me ns

the

pressure

exerted

by

the

earth

due

to

gravity

forces.

Earthquake

earth

pressure

me ns

the

combined

static and

dynamic

earth

pressure

which

acts

during

or

because

of

an

earthquake.

A

list

of

symbols

used

with their meanings,

is

included

in

the

front

of

these

notes.

1o3

•_DES GN

PRINCIPLES

1.3.1

Free

Standing

Retaining

Walls

In

iZhe

design.of

free

standing

retaining

wails, the

following

aspects

need

to be

investigated:

a)

the

stability

of the

soil

containing the

wall;

b)

the

stability

of

the retaining

wall

itself;

and

the

structural

strength .of the

wall.

For

these

walls

it is

usual

to

a@sume

that

some

outward movement

of

the

wall takes

place

so

that the

lateral

earth

pressure

from the

retained

soil is

a

minimum

active

c•ndition)

for

both static and

earthquake

loadings.

However

the

designer

should check that the

required

movement

can

take

p•ace

and

that

it

does not affect the

serviceability

or

appearance

of.the

wall. If

the

deformation

that

is required

to

reduce

the

earth

pressure

to

the active

c se

is

not



1.3.2

available

due to

the

r gid

nature

of

the structureor

foundation,

either the

wall

must

be

designed

to .withstand

a

higher

pressure

or

some

change

made to

the

structure

or

foundation.

If cohesive

back-

fill

is

used the large

displacements

necessary

for the active

condition

means

that

the lataral

earth

pressure

will almost

al•ays

be higher

than the

active

value.

For the

determination

of

eai-•h

pressures

it

is usual

to consider

only

a

unit length

of the

cross•section

of

the wall

and

retained

Soil.

A unit length

is

also

used

in

the

structural

design

of

cantilever

walls

and

other

walls

with

a

uniform

cross-section.

Other

Retaining

Structures

Where

an

earth

retaining

wall

is

part

of

a

mor•

extensive

structure

(e.g.

a

basement

wall

in

a

building

or

an

abutment

wall

of

a

portal

structure

or

is

connected to

another

structuro

(e.g.

a

bridge

abutment

connected

to the

•uperstructure)

the

wall

is usually

subject

to static

earth

pressures

greater

than

active since

the

structure

does

not

allow

full

"yielding"

of

the

soil.

In these

cases,

the

main structure

generally

provides

the

stability

for

the

wall

which

then only

needs

to

have adequate

structural

strength.

The

earth

pressure

on

this

type

of

structure

under earthquake

conditions

depends

on

the

movements of

the structure

and the

forces

exerted

on

the wall

by

the

rest

of

the

structure

as

well

as

the

inertia

forces

from

the

soil.

1.4.1 Basic

Loadings

Twe

basic

earth

pressure

loadings

are

considered

for

design.

These

a)

b)

Normal

loading

Static

earth

pressure

+

water

pressure

+

pressure

due

to

live

loads

or

surcharge.

Earthquake

loading

Earthquake

earth

pressure

+

water

pressure

+

surcharge

but

not

live

loads).

However,

earth

retaining

structures

should

be designed

for

not

less

than

the

pressure

due

to

a

fluid

with

a

density

of

25

Ibs

per

cubic

-•oot.

400

kg/m3).

For

many

walls

of lesser

importance,

earthquake

loading

need

not

be

applied

see

section

4.

Other

Considerations

Consideration

should

als•

be

given

to the

possible

occurrence

of

other

design

cases

or

variations

within the

two

design

cases

given

bove,

caused

by construction

sequence

or

future

development

of

surrounding

areas

For

instance

additional

surcharges

should be

considered in

calculating

active

pressures

and

allowance

made for any

possible

future

removal

of

ground

i•

front

of

the

•all if the passive

resistance

of.this

material

is

included.



3

SECTION

2

SOIL

PROPERTIES

2.1

GENERAL

Tests

should

preferably be

carried out

on

the proposed backfill

material

and natural

ground

behind and

under

an

earth retaining

structure in

advance

of

design. It is

good

practice to make further soil

tests

on

the

material

exposed after

excavation.

For

all walls higher than

20 feet

(6

metres), e•pecially

those

with

sloping

backfill,

the

soil

properties

of

the natural

ground

and

backfill

should

be

estimated from tests

on

samples

of

the

m•terials

involved.

For

less

important

wails,

an

estimation

of

the

soil

properties

may

be

made from

previous

tests

on

similar

materials. However

a

careful

visual examination

of

the

material,

particularl•/

that

at the

proposed

foundation

level,

should

be

made

with

the

help of

identification tests to

ensure

that the assumed

•terial

type

is

correct.

2.2

SELECTION

AND USE OF BACKFILL

The

ideal backfill is

a

free

draining granular material o2

high

shearing

strength.

However

the

final choi0e

of

material should

be based

on

the costs

and

availability

balanced

against the desired

properties.

In

general the

use

of

cohesive

backfills

is

not recommended. Clays

"ar•subject

•o

seasonal

vaF•atiohs•

•welling

(see

2.9),

and

deteriorat on

which

all lead to

an

increase

in

pressure

on

a

wall. They

are

difficult

to

consolidate

and

long

te•m settlement

problems

are

considerably greater

than

with

cohesionless

materials.

For cohesive

backfills,

special attention

must

be

paid to the

provision

of drainage

to

prevent

the

build-up of

water

pressure.

Free draining

cohesionless materials

do

not rgquire the

same

amount

of

attention in

this respect•

The

wall

deflection

required to produce the active state

in

cohesive

•mterials

may

be

up

to •O ti• greateF•than

that for

cohesionless

materials.

• •,is, together

with

the fact

that the former

generally

have

lower values

of

shearing strength,

means

that the

amount of shearing

strength mobilised for

any

given

wall

movement •s

Considerably

lower

for cohesive materials

than

for

cohesionless

materialsZ The corresponding active earth

pressure

for

a

particular

wall

movement

•ill

therefore

be

higher'if

cohesive soil is used

for backfill.

In'cases•of

a

high

S•ismic

coefficient

and for

a

steeply

sloping

back-

fill,

the active

earth

pressure

will be

substantially

reduced

if the failure

plane

occurs

in

a

material with

a

high angle

of

shearing

resistance.

(See

figures

20 to

27).

In

some

circumstances

it

may

be economical

to

replace

weaker

material

so

that

the

above

situation

occurs.

However also

see

3.3.6.

It is

essential

to

•pecify

and supervise

the

placing

of backfill

to

ensure

tnat

its properties

•,

c

and

y)

agree

with

the design assumptions

bo•h

for

lateral

earth

pressure

and

d@ad

weight

calculations..



2.3

DENSITY

The

density

of •oil

depends

on

the

specific

gravity

of

the

solid

articles

and

the

propo•ions

of

solid,

air

and

water

in

the

soil.

The

verage

specific

gravity

of

the

soil

particles

is

about

2.65

for

sand

or

rock

and

2.70

for

clays,

however

this

will

va

y

• um

area

to

area.

The

roportion

of

the

total volume

that

is

made

up

of

this

solid

material

is

dependent

on

the

degree

of

compaction

or

consolidation.

An

estimate

of-the

density

of

backfill

material

•o

be

used

behind

a

retaining

structure

•y

be

obtained

from

standard

laboratory

compaction

ests

on

samples

of

the

material.

The

density

chosen

must

correseond

to

the

compaction

and

mo.isture

conditions.that

will

apply

in

the

actu•l

ituation.

The

density

of

natural

soll

should

be

obtained

from

undisturbed

samples

kept

at

the

field

moisture

cantent,

and

volume.

For

low,

relatively

nimportant,

walls

the

density

o•

the

soil

behind

the

wall

may

be

estimated

from

the

typical

values

given

in table • In

general

the

saturated

density

hould

be

used

in

calculations

involving

clay

filling.

•0•:

In

eaF-•h

pressure

calculations

using

metric

quantities,

density

m•s•

e

in

force

units,

i.e.

mass

densities

in

k•/m

•

must

be

multiplied

y

9.81

to

give

the

equivalent

force

in

N/m•).

2.4

EFFECTIVE

STRESS

AND

PORE

PRESSURES

An

effective

stress

is

the

stress

or

p•6s•u•e)

transmitted

through

•he

oints

of

contact

between

the

solid

particles

of

the

soil.

It

is

this

stress

that

determines

the

shearing

resistance of

the

soil.

T

tres•

at

any

point

in

the

soil

mass

•

•

•-•

he

effective

• • •.•u Dy suaTracting

the

ressure

transmitted

by

water

in

the

voids

pore

water

pressure)

from

the

otal

stress,

i.e.:

positive

pore

water

pressure

means

a

reduced

effective

stress

and

there-

fore

a

reduced

soil

shearing

strength

which

leads

to

an

increase

in

earth

pressure in

the

active

case. A

negative

pore

pressure

gives

an

increase

in

soil

strength.

Pore

water

pressures

result

from

a

number

of

factors.

ohesive

soils

may

retain

pore

pressures

due

to

a

previous

loading

since

the

dissipation

of

pore

pressures

in

these

materials

takes

months

or

even

yearsunder

some

conditions.

Negative

pore

ware

r•ssur

P

es

may

be

induced

by

capillary

tension

in

moist

sand.

This

particular

effect

is

however

transitory

as

it

is

destroyed

if

the

sand

dries

or

if

it

is

saturated

with

water.

Positive

pore

pressures

can

develop

due

to

static

water

pressure,

seep-

age

of

water,

the

effect

of

shock

or

vibration

in

Some

soils,

or

if

the

stress

increases

more

rapidly

than

the

pore

water

can

flow.

Pore

pressures

due

to

static

water

pressure

and

seepage of

water

are

covered

in

section

6.



5

TABLE

I

REPP•SENTATIVE

VALUES

FOR

DENSITIES

OF

SOILS

(Basic

Data

from

References

3 and

5)

MATERIAL

Clean

gravel

or

rock

loose

dense,

poorly

graded

dense, well

graded

Well graded, clean

sands,

m-avelly sands

•loose

dense

Poorly

graded

clean

sand,

sand-

gravel

mix

loose

dense

Clayey

sand

loose,

poorly

graded

dense,

poorly

graded

Fine

and silty

sands

and.

silt

loose

dense

Sand-si

It

clay

mixed

with

•gh_t• l_y

plas•tic

fines

C'layey

gravel,

psorly

graded

grave

l-sand

clay

Silty

gravel,

poorly

crade'd

gravel-sand

si

It

Glacial

t-ill

very

mixed

grained

Glacial

clay

soft

stiff

Organic

clay

so'ft

slightly

organic

sof

•ery

organ

c

DENSITIES

Dry,

Yd

Saturated,

Ysat

(Ib/ft

3

(kg/m•)

100-110

1600-1760

115-125

1840-2000

125-135

2000-2160

90-100 1440-1600

1107130

1760-2080

100-I 10

1600-1760

110-120

1760-1920

90-105

1440-1680

105-115

1680-1840

90-100

1440-1600

110-120

1760-1920

110-130

1760-2080

115-130

1840-2080

120-135

1920-216 0

130-135

2080-2160

(lb/ft 3

(kg/mS)

120-130

1920-2080

130-140

2080-2240

120

1920

130

208O

125

2000

135

2160

145

2320

I00-120

1600-1920

125-135

2000-2160

95-100

1520-1600

85-

90

1360-1440

Dams;Ties

must

be

converted

to force

units for

use

in

earth

pressure

alculations.



2.5

SHEARING

STRE;•GTH

The

sheari.ng

strength

of

a

sol

is

important

ateral

deformations

of

the

soil

boundary

occur

in

s tuatio•s

•here

The

maximum

shear

stress

hat

a

sample

of the

soil

can

sustain

under

different

normal

stresses

should

e

obtained

by

compression

or

shear

box

testing.

The

sample

must

be

at

a

density

and

moisture

content

corresponding

to

that

of

the

backfill

or

natural

ground.

The

plotted

results

of

these

tests

will

give

an

envelope

f

shearing

strength

at

failure

or

yielding

of

the

soil.

This

envelope

is

sually

represented

by

a

straight

line,

which

is

expressed

as:

s

c

+

•

tan

(in

terms

of

total

stress),

or

s

c'

+-•

tan

9T

(in

terms

of

effective

stress).

This

method.of

representing

the

shearing

strength

of the

soil,

is

usedn

these

notes.

An

effective

stress

analysis

should

generally

be

used.

In

this

case

c'

and

•

are

used

in

place

of

c

and

•

in all

calculations.

Tests

must

be

onducted

in

such

a

way

fhat

the

shearing

strength

is

given

in

terms

of

ffective

stress.

This

me ns

that,

either

the

test

loading

must

be

applied

lowly

and

drainage

provided

so

that

any

pore

water

can

adapt

itself

to"

the

hanged

stress

conditions

(drained

test),

or

measurements

of

pore

water

ressures

must

be

taken

during

consolidated-undrained

tests

and

the

normal

tress

adjusted

accordingly

(see

2.4).

If

c'

and

•

(effective

stress

soiltrength

parameters)

are

used

in

the

calculations

for

lateral

earth

pressure,

earing

pressure,

etc.,

the

effect

of

any

field

pore

water

pressures

must

be

ncluded

in

the

analysis.

In

certain

soils,

the

field

pore

water

pressures

may

be

simulated

by

he

undrained

tests

mentioned

above. In this

case

no

further allowance

eed

be

made

for

field

pore

water

pressures and

the

analysis

of

the

earth

ressure

forces

may

be

carried

out

in

terms

of

total

stress.

Saturated

undisturbed

soils

with

relatively

low

permeability,

such

as

silt

and

silty

sand,

ar@ likely

to

fail

in

the

field

under

conditions

imilar

to

those

under

which

the


tests

are

made,

and

hear

failuFe--in-saturated-sand

due

to

the

rapid

draw-down

of

the

water

able

also

corresponds

to

the


condition.

Therefore

n

these

cases,

the


shearing

strength

parameters

ould

be

usedwith

a

total

stress

analysis.

A

condition

that

may

be

approached

in

constructions

using clay

filling

hich

becomes

saturated

or

in

a

saturated

undisturbed

clay

m ss

is

that

of

he

stress

changing

m•re

rapidly

than

the

pore

water

can

flow.

If

the

hearing

strength

of

the

saturated

clay

in

this

condition

is

determined

by

sing

an

undrained

triaxial

t•st

it

is

usually

found

to

be

independent

of

he

normal

pressure

(i.e.

•

o).

Since

there

re

uncertainties

in

the

pplication

of

these

results,

an

unconfined

compression

test

is

usually

mployed,

where

theoretically

c

qu/2

if

•

o.

This

value

of

c

is

used

ith

a

total

stress

analys

s

for

the

situations

described.

Representative

values

for

the

angle

of

shearing

resistance

in

terms

of

ffective

stress,

•

and

total

stress

•

are

given

in

table

2.



7

For

any

particular

material,

the

shearing

resistance

depends

on

the

degree

Of

compaction

or

consolidation.

For loose

sand

•

is

approximately

equal

to

the

angle

of

repose

in the

dry

state.

TABLE

2

REPRESENTATIVE

VALUES

FOR

THE

ANGLE

OF

SHEARING

RESISTANCE

(Values

Obtained

Mainly

from

Reference

5

c

o

in

all

the

cases

except

clay

where

c

qu/2)

Material

Sandy

gravel

or

rock

filling

and

loose,

round

gr•ins,

uniform

dense,

round

grains,

uniform

-loose,

angular

grains,

well

graded

dense,

angular

grains,

well

graded

Silt

and

silty

s•nd

loose

dense

Clayey

sand

Clay,

normally

loaded

or

slightly

preconsolidated

(Degrees)

35-45

28

34

33

45

27-30

3O-35

20-25

22-30

•

(Degrees)

(Saturated)

20-22

25-30

14-20

2.6

BASE

FRICTION

•,

Typical

value•

of -f-ri•ib-h--•-ngle

T•b)

end

adhesion

(c

b)

for

calculating

ae

shearing

resistance

between

a

concrete

base

and

the

foundation

material

re

given

in

table

3.

These

values

may

be

used

for

low

walls

in

the

absence

f

specific

test

data.

Ifa--base

key

is

used

the

failure

plane

wi

enerally

be.

through

the

foundation

soil

and therefore

the

shearing

esistance

i•

that

of the

soil

•b

• and

Cb

c•.

2.7

MODULUS

OF

•LASTICITY-AND

POISSON S

RATIO

The

relations

between

stress

and

strain

in

soils

are

important

in

the

ettlement

of

soil-supported

foundation•.

They

also

determine

the

change

n

earth

pressure

due

to

small

movements

of retaining

walls

or

other

earth

upports.

These

relationships

are

complex

since

they

depend

on

stress,

train,

time,

inltiel

decree

of

saturation

and

Various

other

factors.

How-

ver

it

is

often

convenient

to

express

them

in

terms

of

•odulus

of

elasticity

nd

Poisson s

ratio,

since

for

small

stress

differences

the

soil

behaviour

losely

e•proxlmates

that

for

a

perfectly

elastic,

homog=neous

material.



8

The modulus

of elasticity of

the

soils

E

s

is

important

in

problems

where displacements

are

to

be calculated

The

value

is

usually

determined

from

triaxial

compression tests,

but plate bearing

tests

may

be

used.

Seismic

methods

may

be

used

to check

a

larger

mass

of

material,

however

the

values

obtained must

be

corrected

since

seismic

values

of E

s

are

always

onsiderably

higher •han

slatic

values particularly

•n jointed

rock,

and

ar•

not applicable

to

problems

o• static

loading.

For

all

soils the

elastic

mddulus

increases

with

increasing

onsolidation

p[essure,

Pc

For loose

sand

E

s

approximately

equals

100

Pc

A

range

of

values for

the modulus

of

elasticity

in

compression

for

selected

soils

is

given

in table

4.

TABLE 3

TYPICAL

FRICTION

•GLES •D

ADHESION

VALUES

FOR

BASES

WITHOUT

KEYS

(Valbes Taken

from

Reference

3)

Interface

Materials

Mass

concrete

on

the

following

foundation

material:

Clean

sound

rock

Cle

gravel,

gravel-sand

mixtures,

•:

coarse

sand

Clean

fine to

medium

sand,

silty

medium

to

coarse

sand, silty

or

clayey

gravel

Clean

fine

sand,

silty

or

clayey

fine

to.

medium

sand

Fine

sandy

silt,

non-plastic

silt

Very

stiff

and

hard

residua.l

or

preconsolidated

clay

Mediu•

stiff

and

Stiff

clay

and silty

clay

Formed

concrete

on

the

following

foundation

mater•al:

Clean

g•avel,

gravel-sand

mixtures,

well

graded

rock fill

with

spalls

Clean

sand,

silty

sand-gravel

mixture,

single

size

hard

rock

fill

Silty

sand,

gravel

or

sand

mixed

with

silt

or

clay

Fine

sandy

sil•,

non-plastic

silt

Soft

clay

and

clayey

silt

Stiff

and hard

clay

and

clayey

silt

Friction

Angle

6b)

Degrees

35

to

45

29

to

31

24 to

29

19

to 24

17

to 19

22

to

26

17

to

19

22

to

26

17

to

22

17

14

•Adhesion

Cb

Ib/ft

z

(kN/m 2)

200

to 700

(9.6

to

33.5)

700

to

1200

(33.5

to

57.5)



-9

Poisson s

ratio,

•

is

very

important

in

Stress

oriented

problems

(e.g.

tresses

on

retaining

walls

for

no

wall

moven•nt)

since

it

controls

the

Fela•ionship

between

orthogonal

stresses.

It

may

be

determined

from

triaxial

tests;•however

like

the

elastic

modulus,

it

is

dependent

on

the

confining

pressure

and rate

of

loading

amongst

other

factors.

For

granular

or

normally

consolidated

materials,

• may

be

estimated

from

the

relation-

ships

for

at-rest

pressure

coefficients

see

3.4.

Representative

values

are

given in

table

5.

TABLE_____•

t•DULUS

OF

ELASTICITY

FOR

SELECTED

SOILS

(COMPRESSION)

(Values

Taken

from

Reference

3)

Soil

Very

soft clay

Soft

clay

Medium

clay

Hard

clay

Sandy

clay

Silty

sand

Loose

sand

Dense

sand

E

s

psi)

Dense

•and

and

gravel

14,000-

Loess

• •i•,000

Sandstone

Limestone

Basalt

50-

400

250-

600

600-

1,200

I•000-

2,500

4,000-

6,000

1,000-

3,000

1,500-

3,500

7,000-

12,000

28,000

18,000

1,000,000- 3,000,000

2,000,000-

6,000,000

7,000,000-13,000,000

E

s

(•/m

z)

0.35

2.75

1.72

4.14

4.14

8.27

6.89

17.2

27.5

41.4

6.89

20.6

10.3

24.1

48.2

82.7

96.5

193

96.5

124

6

900

20

600

13

800

41 300

48

200

89

500

TABLE

5

TYPICAL

VALUES

FOR

POISSON S

RATIO

Va]ues

Taken

from

Reference

3)

Soil

Ciay,

saturated

Clay,

unsaturated

Sandy

clay

0.4

-0.5

0.1

-0.3

0.2

-0.3

Silt

Sand

dense

co rse

(void

ratio

0.4-0.7)

fine-grained

(void

ratib

0.4-0.7)

Rock

0.3

-0.35

0.2

-0.4

0.15

0.25

O.

-0.4



2.8

COEFFTCIENT

OF

SUBGRADE

REACTION

In

the design

of

footings

and

wall

f

subgrade

reaction

is

often

used

to

determine

foundation

pressures.

his

concept

is

based

on

the

assumption

that

the

settlement,

•

o•

any

element

of

a

loaded

re

is

entire ly

independent

of

the

load

on

the

djoining

elements.

It

is

further

assumed

that

the

ratio

•KS

=2_

foundations,

the

simplified

Concept

between

the

intensity,

p

of

the

foundation

pressure

on

the

element

and the

orresponding

settlement

is

a

constant,

Ks.

This

foundation

pressure is

alled

the

subgrade

reaction.

The

coefficient

K

s

;s

known

as

the

oefficient

of

subgrade

reaction.

Representative

values

of

K

s

for

oundation

design

ere

given

in

table

6.

NOTE:

TABLE

6

COEFFICIEN•

OF

SUBGRADE

REACTION

(VERTICAL)

Soil

Type

Dens•

gravel

and

gravelly

soils

(no

lay

fines)

•ense

sand

and

sandy

soils

including

layey

sand,

clayey

gravel

Silts,

clays

of

low

compressibility

Clays

of

high

compressibility

K

S

lblin2/in

>300

200-300

100-200

55-100

kN/m21mm

>8O

55-80

25-55..

15-25

For

clays

K

s

may

be

assumed

to

vary

linearly

with

qu,

from0

Ib/in2/in

for

qu

of

14.5

Ib•in

2

to

330

Ib/in2/in

for

qu

of

5

Ib/in

2

In

metric

units

K

s

varies

from

8

kN/m2/mm

for

qu

of

100

kN/m

z

to

0

kN/m2/mm

for

qu

of

380

kN/m

2.

2.9

SIqELLING

AND

SOFTENING

OF

CLA•S

Some

clays,

particularly

those

with

high

plasticity

(plasticity

index

exceeding

20)

tend

to

expand

in

the

presence

of

water

and

if

restrained

by

a

structure

can

develop

very

high

earth

pressures

e•ceeding

10,000

Ib/ft

2

480

kN/m2).

These

pressures

are

not

related

to

soil

strength,

but

to

the

mineralogy

and

initial,

moisture

of

the

clay.

Swelling

pressures

can

be

estimated

from

laboratory

swell

tests,

but

at

present

such

predictions

are

not

too

reliable.

These

pressures

usually

only

develop

in

the

zone

of

weathering

which

is

to

a

depth

of

3

to

5

feet.

(I

bove

pressures

should

be

con -

d•r•

•

.to

I.•

metres).

The

non-yieldina,

walls

•--•7

.-.cohesive

so•l

•s

to

be

used behind

eea

not

De

allowed

for

n

the

case

of fre•

sTanding

walls

t;here

a

small

yield

can

be

tolerated.



When

a

natural

deposit

of clay

or

silt

is disturbed

by

an

excavation

for

a

retaining

wall

the

change in stress

conditions

and

water

content

may

lead to

a

change

in

shearing

strength

with

time.

With

stiff

fissured

clays

it has been shown

that

progressive

softening

c n

reduce the

shearing strength

to

a

small

fraction

of its

original

value.

This

is

usually

d,,•

to

Water

percolating

into

the

fissures

which

open

at

the

time

of

excavation

for

the

wall.

Earth

pressures

should

therefore

be calculated

using

a

'residual'

strength to

allow

for this

deterioration.

References

5

and 28

should

be

consulted.

In

fissured

clays

and

clay

filling

the

rate

of

softening

is

reduced by

adequate

drainage

and

if the wall is

prevented

from

yielding

progressively.

However

the

latter

requirement

will

me n

that lateral

earth

pressures

higher

han

activewill

result.

•-•.•.10

PERMEABILITY

The

permeabiliti•s

of

soi

s

in

broad terms

are

givenin

table

7.

The

permeebiIities

of

granular

materials

are

given

in greeter

detai

in figure

5,

•ccording

to

the

pahticle

grading.

TABLE

7

PERMEABILITIES

OF

SOILS

Clean

gravel

Cl•an

sand,

clean

sand

andlgravel

mixture

Wery

fine

sand,

organic

and

inorganic

silt,

mixture

of

sandy

silt

and

clay,, glacial

till,

stratified

clay

deposits,

etc.

Homogeneous

clays

below

zone

of

weathering

Value•

Tgken

from

Reference

5

Soil

Type

Coefficient

of

Permeability,

k cm/sec)

100

-I.0

1.0-i0-3

2.11

LIQUEFACTION

In

materials

with

no

cohesion,

if the

pore

pressure

is

made

to

increase

so

as

to

reduce the

effective

stress

t•

zero,

a

condition

known

as

liquefaction

m•y

result

•here the

material has

no

shearing

strength

an•

there-

fore

behaves

like

a

fluid.

This

can

happen

in

saturated

loose

sands

and

silts

where

a

shock

or

vibration

c uses

spontaneous

collapse

of the

grain

•ructure

(densification)

and therefore

an

increase

in the

pore

water

•ressure.

Saturated

sandv

soil

layers

which

are

within

•0

#eat

9

metres)

f

the

ground

surface,

have

a

standard

penetratio•

temt

N-value

less than

•have

a

coefficient

of

uniformity

less

than

6 and

also

have

a

D20-value

be-

ween

0.04

mm

and 0.5

mm,

have

a

high

potential

for

liquefaction

during

earth-

uakes.

Saturated

sandy soil

l.ayers

which

have

a

D20

value

between

0.004

mm

and

0.04

mm

or

between

0.5

mm

and 1.2

mm

may

liquefy

during

earthquakes.



SECTION

3

STATIC

EARTH

PRESSURE

3.1

STATES

OF

STRESS

The

stresses

at

any

point

within

a

soil

m ss

may

be

represented

on

the

ohr

co-ordinate

system

in

terms

of

shear

stress,

•

and

effective

normal

tress,

o'

(see

references

or

6

for

the

plotting

of

stresses

and

use

of

the

system).

On

this

system,

the

shearing

strength

of

the

soil

at

various

ffective

normal

stresses

gives

an

envelope

of the

ossible

combinations

of

shear

end

normal

stress.

When

the

maximum

shearing

strength

is

fully

mobilised

along

a

surface

within

a

soil

mass,

a

failure

condition

known

as

a

state

of

plastic

(or

imiting)

equilibrium

is

reached.

Rankine's

active

and

passive

states

of

stress

result

when

Shear

stresses

equal

to

the

maximum

shearing

strength

of

the

soil

develop uniformly

and

unhindered

in

two

major

directions

through-

ut

a

soil

mass

due

to

lateral

extension

or

compression.

Where

the

combinations

of

shear

and

normal

stress

within

a

soil

m•s

ll

lie

below

the

limiting

envelope

the

soil

is

in

a

state

of

elasticquilibrium.

A

special

condition

of

elastic

equilibrium

is

the

at-rest

tate,

where

the

soil

is

prevented

from

expanding

or

compressing

laterally

ith

changes

in

the

vertical

stress.

3.2

AMOUNT

AND

TYPE

OF

NALL

MOVEMENT

.,•

The

limiting

eqdilibrium

theories

all

require

that

the

maximum

shearingtrength

of

the

soil

is

mobilised.

This

however

reouires

deformation

in

the

soil.

The

deformation

of

a

supporting

structure

only

has

a

local

effect

n

the

state

of

stress

in

the

soil.

The

remainder

of

the

soil

remains

in

state

of

elastic

equilibrium.

The

state

of

stress

in

the

locally

isturbed

zone

end the shape

of

this

zone

is

dependeqt

on

the

amount

and

.type

of

wall

deformation.

This

also

determines

the

shape

of

the

pressur•

istribution-on'the--wall

•n-d

the

intensity

of

the

pressure.

For

no mOvement

of

a

retai•ing

wall.system

at-rest

earth

pressures

(or

ressures

due

to.compaction)

ac,

on

the

•..all..

When

a

wall

moves

ou

ward,

the.

shearing

strength

of

the

retained

sell

resists

the

correspondina

outward

ovement

of

the

soil

and

reduces

the

earth

pressures

on

the wall.

The earth

pressure

calculate•

for the

active

state

is

the

absolute

minimum

value.

When

the

Wall

movement

is

towards

the

retained

soil

the

shearinc

streneth

of

the

soil

resists

the

corresponding

soil

movement

and

increases

•ne

earth

ressure

on

the

wall.

The

earth

pressure (or

resistance)

calculated

for

the

passive

state

is

the

maximum

value

that

can

be

developed.

TABLE

8

MOVEMENT

OF

WALL

NECESSARY

TO

PRODUCE

ACTIVE

PRESSURES

S0il

Cohesionless,

dense

Cohesionless,

loose

Clay,

firm

Clay,

soft

Wall

Y•eld

0.001

H

;

O.

O01-0.

002

0.01

-0.02

H

0.02

-0.05

H



The

amount

of

movement required to produce the active

or

passive•

states in the

soil

fs

dependent mainly

on

the type of

backfill material.

Table

8 gives the outward movement of

a

wail

which is

necessary

to produce

an

active state of stress in the

retained soil.

The movements

required to

produce

fell

•assive

resistance

are

considerably

larger,

especially in

cohesionless

material.

These

requirements

apply

whether

the

mevement

is

a

lateral

translation of •he whole

wall

or

a

rotation about the

base.

The

pressure

distributions for

full

active and passive states

are

basically

triengular

for constantly sloping ground

(see

3.3 .

If

a

wall

rotates

about its

top

in the direction

away

from

the

soil•

the

soil

between

the

wall

and

the surface

of sliding

does

not

all

pass

into

th•

active

state.

The soil

near

the top

of

the

wall

stays

near

the at-

res•

state.

This

condition

arises

in cuts

that

are

braced

as

excavation

proceeds

downwards

from

the

top.

The

distribution

of

pressure

may

be

represented

by

a

trepezium w•th

dimensions

which

vary

according to the

soil

type

see

figure 18.

(• •i

The amount Of wall

m•vement

which will

take

place depends mainly

upon

•The

foundation conditions

end the flexibility

of

the wall.

The designer

must

ensure

that

the

calculated

earth

pressures

correspond to the available

wall

movement.

A

free

standing

wall

need only be

designed for

active

each

pressure as

far

as

stability

is concerned since,

if it starts

to

slide

or

overturn

under

higher

pressures,

the

movement

will be

sufficient

to

reduce

the

pressures

to active.

Flowever if it

is

on

a

strong

foundation

or

otherwise

fixed

so

that adequate

stebility

is provided,

the

stem

may

be

subject

to

pressures

near

those for the

at-rest state.

The following

pressure

coefficlents shoul•be,

used for

rigid

foundation

cenditions unless

mere

exact

analysis of

movements

is made:

Ca)

(b)

(c)

CounterforT

or

gravity

type

walls founded

on

rock

or

piles

K

o

Cantilever

walls less than 16

feet

(5

metres)

high

founded

on

rock

or

piles

0.5 (Ko+K

A)

Any

wall

on

soil foundations

or

cantilever

walls higher

KA

han 16

feet

(5

me• •

Bridge abutment walls

tha•

are

not

included

in

the

above categories

should

be

designed

for at-rest

pressures.

Where

abutment walls

are

framed

in

with the

superstruclure, temperature

movements

may

produce

higher

pressures

•.see

reference 26.

T•e

tilting

movement that will

result

when earth

pressures

act

on

a

retaining

well

may

be

estimated

by

simulating

the

foundation

soil

as

a

series of

spFings with

an

appropriate coefficient

of

subgrade

reection

see

2.7.

The base rotation

(in

radians

is then given

by:

8

b

12Ve/KsL•

3.3

LIMITING

EQUILIBRIUM

CONDITIONS

3•3.1

The Rankine

Earth Pressure

Theory

If

Rahklne s•

active

or

passive states of stress

exist

throughout

a

zone

in

a

soil

mass

en

exact

solution (fully

satisfying

both static

equilibrium

and

the

condition

for failure)

may

be

obtained for

the



3.3.2

14

earth

pressure

from

that

zone

However,

useabie

equations

result

only

if

the

surfaces

of

failure

are

planar.

This

is

the

case

in

a

semi-infinite

mass

of

coheslonless

soil

with

the

ground

surface

at

any constant

slope,

and

also

in

cohesive

soil

with

a

horizontal

round

surface.

RangineSs

equations

give

the

earth

pressure

on

a

vertical

plane,

hich

is

sometimes

called

the

virtual

back

of

the

wall. The

equations

for

cohesionless

soil

are

giver

in

figure

2.

The

earth

pressure

on

the

vertical

plane

acts

in

a

direction

parallel

to

the

ground

surface

andis

directly

proportional

to

the

vertica.l

distance

below

the

ground

surface

(i.e.

a

triangular

pressure

distribution

ith

the

resultant

acting

at

I/3

Equations

for

Rankine s

conditions

in

cohesive

soils

with

a

horizontal

ground

surface

are

given

in

figure

iO.

The earth

ressure

on

tile

vertical

plane

acts

horizontally.

The

pressure

distribution

is

similaP

to

that

for

cohesionless

soil

except

that

a

zon•

of

tension

at

the

top

is

neglected

siace

soil

cannot

sustain

ension.

Rankine

active

earth

pressure

coefficients

for

cohesion-

less

soil

are

presented in

graphical

form

in

figure

3.

If

Rankine s

states

of

stress

exist

in

cohesive

soil

with

a

uniformly

sloping

ground

surface,

useable

equations

do

not

result,

since

the

failure

surfaces

are

curved,

and

the

pressure

distributio•

is

not

theoretical

y

a

linear

function

of

depth.

An

exact

o

ution

for

this

case

can

be

obtaine•

by

using

the

M•hr

diagram

ee

the

circle

of

stress

method

in

reference

I.

Rankiners

conditions

are

theoreticaIl.y.•nl•y

applicable

to

•etaining

alls

when

the

wall

does

net

interfere

with

the

formation

of

any

part

of

the

failure

wedges

that

form

on

either

side

of

the

vertical

plane,

or

where

an

imposed

boundary

produces

the

conditions

of

stress

that

would

exist

in

the

uninterrupted

soil

wedges.

The

vertical

plane

on

which

the

pressures

are

calculated

is

not

normally

a

failure

plane

(only

in

the

case

where

•

•).

However

a

vertical

wall

would

satisfy

the

Rankine

conditions

if

the

angle

of

wall

friction,

•

is

equal

to

the

backfi•ll

slope.

In

many

cases

this

would

not

represent

a

practical

situation

since

it

implies

a smooth

wall

for

horizontal

backfi-•l.

The

Coulomb

Earth

Pressure

Theory

This

theory

di•ectly

gives

the

resultant

pressure

against

the

back

of

e

retaining

structure

for

any

sI•pe

of

the

wall

and

for

a

range

of

wall

friction angles.

It

assumes that

the

soil

slides

on

the

back

of

the

wall

and

mobilises

the

shearing

resistance

between

the

back

the

wall

and

the

soil

as

well

as

that

on

the

failure

surface.

The

•oulomb

equations

reduce

to

those

of

the

Rankine

theory

if

a

vertical

wall

surface

with

an

angle

gf

wall

friction

equal

to

the

backfiI|

slope

is

used.

Other

Cases of

wall

slope

or

wa

•riction

require

CUrved

surfaces.of

sliding

to

satisfy

static

equilibrium.

The

degree

of curvature may

be

Quite

marked

especially

for

passive

conditions.

However

Coulomb•s

theory

aSSumes

that

the

failure

wedge

is

always

bounded

by

a

plane

surface,

and

.it

is

therefore

only

an

approximation

usuaJ.ly

on

the

unsafe

side).



15

d•rect•on

and

magnitude

for

the.wall

friction

angle

for

passive

pressure.

However

for

large

pos

tive backfill

sloes

or

la

rge

values

the

error

due

to

the

assumpTion

of

a

plane

fai

ure

surface

leads

to

a

large

over-estimat

on'

of th•

Dassive

resistan

Th•s

is

accentuated

further

when the

back

of

the

wall

has

a

negative

The

simplifying

assumption

also

me ns

that

static

equilibrium

.is

not

always

completely

satisfied,

i.e.

the

fQrces

actihg

on

the

soil

wedge

cannot

all

be

resolved

to

act

through

a

common

point. The

error

from

an

'exact'

solution

is

proportional

to

the

amount by which

static

equilibcium

is

not

satisfied.

Equations

for

Coulomb•s

conditions

in

cohesionless

soil with

e

constant

ground slope

re

given

in figure

4.

In the

active

c se

the

soil tends

to slip

downward

along

the

back

of

the wall

causing

the

resultant

earth

pressure

to

be inclined

at

a

positive

angle

(see

figure

4)

to

the

normal

to

the wall.

t

is

recommended

that

an

angle

of

wall

friction

of

+2/3

@ be

used

in

the

equation

for

active

pressure

for

concrete

walls which

have

been

cast

against

formwork.

Coulomb

active

earth

pressure

coefficients

re

given

in

figures

5 to

8

and the

corresponding

failure

planes

in

figure

9

for

selected

values

of

angle

of

internal

friction,

@.

Linear

interpolation

may

e

used to

fi.nd

the

earth

pressure

coefficient

or

failure

plane

angle

or

intermediate

values

of

@.

Passive

Pressures.Using

Equations

The

movement

required

to

produce

passive

pressure

leads

to

the

soil

sliding

upward

on

the

failure

surfaces

including

the

back

of

a

wall

or

anchor

block).

There'foce

Rankine's

equation

does

not

theoretic-

ally

apply

for

passive

resistance

of

soil

with

a

positive

ground

lope

against

a

vertical

wall because

it

ssumes

a

positive

angle

of

wall

friction

equal

to

the

ground

slope,

when

in

fact

the

wall

friction

angle

would

be

negative.

The

use of

Rankine's

equation

in

this

situation

gives

an

under-estimation

of

the

passive

resistance.

Equations

for

Coulomb s

conditions

allow

the

use

of

the

correct

slope.

In

the.ca•e•

of

a

vertical

wall

the

Rankine

equatiQn

should

e

used.instead

to

give

a

conservative

estimate

of

the

passive

esistance.

For

other

wall

slopes

the

passive

resistance

c n

be

aken

as

Rankine s

passive

pressure

on

the

ve•ical plane

plus

the

eight

of the

soil

wedge

between

the

vertical

plane

and the

pressure

urface.

Alternatively

methods

based

on

curved

failure

surfaces

such

as

the logarithmic

spiral

method

(references

and 5)

may

be

used.

eference

3

chapter

I0

gives

values,

of

KD based

on

the

logarithmic

piral

method

for

the

c se

of

a

vertical-wall

and

sloping

backfill

nd

for

a

sloping

wa•land

level

backfi•l.

For

negative

backfill

lopes,

the

conditions

for

Rankine's

passive

state

may

be

fuifilled

3c

that

a

good

estimation

of the

passive

resistance

may

be

obtained.

he

equation

for

Coulomb's

conditions

also

•ives

a

good

approximation

f.the

passive

resistance

in

this

case,

although

it

wil

generally

T,

I• be •light•y

on

the

unsafe

side.



For

;•ost

Cases

involving

passive

pressures

encountered

in

retaining

wall

design,

the

ground

surface

is

horizontal

and

the

pressure

surface

may

be

assumed

to

be

vertical.

If

the

angl&

of

wall

friction

is

taken

as

zero

under

these

conditions,

the

Rankine

and

Coulomb

equations

are

the

same

and

the

resulting

passive

resistance

is

on

the

•onservative

side

(since

there

would

be

some

wall

friction

Which

•nCreases

the

passive

resistance).

3.3.4

The

Trial

Wedge

Metho

d

Where

the

ground

surface

is

irregular

or

where

it

is

constantly

sloping

in

cohesive

soil

a graphical

procedure

USing

the

assumption

of

planar

failure

SUrfaces

is

the

simplest

approach.

This

procedure

is

known

as

the

trial

Wedge

method

(see

figures

The

backfill

is

divided

into

wedges

by

selecting

planes

through

th•

heel

of

the

wall.

The

forces

acting

on

each

of

these

wedges

ere

combined

in

a

force

polygon

so

that

the

magnitude

of

the

resultant

earth

pressure

can

be

obtained.

A

force

polygon

is

constructed

even

• •

although

She

forces

acting

on

the

wedge

are

often

not

in

•ment

' ',•_•

equilibrium.

This

method

is

therefore

an

apProximation

with

the

same

assumptions

as

the

equations

for

Coulomb•s

conditions

and,

for-

..•

a

ground

surface

with

a

constant

slope,

will

give

the

same

resu'It.

If

the

conditions

are

the

same

as

those

for

Rankine's

equations,

the

trial

wedge

earth

pressures

will

Correspond

to

these

also.

The

limitations

On

wall

friction

and

passive

pressures

mentioned

in

the

use

of

the

Rankine

and

Coulomb

equations

also

app:M

to

the

trial

wedge

method.

The

adhesion

of

the

soil

to

the

back

of

the

wall.in

cohesive

soils

is

neglected

since

it

increases

the

tension

crack

depth

and

hence

reduces

the

active

pressure.

i:

For

the

active

case

•he

maximum

va

ue

of

the

earth

pressure

.

calculated

for

the

ver

ous

wedees

is

nterpolating

between

required.

This

is

The

re

uired

values.

Fo

Y

i

q

m•nlmum

value

•s

similarly

obtained,

r

the

passive

case

The

direction

of

the

res ultant

earth

pressure

in

he

force

polygons

•..

should

be

obtained

from

he

considerations

of

3.3.1

to

3.3.3

(•)

the

cases

where

this

force

substitute

constant

•

•ct•

p•rallel

to

the

erou•

For

•

so

both

w•+h

•P•

snoula

be

used

as

•h•,.,• •

o•Tace

a

•

WITHOUT

cohesion.

in

Tlgure

15

for

For

cohesion•es•

material,

Culmann,s

graphical

construction

(figure

12)

provides

a

•compact

method

of

plotting

the

resultant

earth

pressures

for

the

various

wedges

and

obtaining

the

maximum

value with

the

COrresponding

failure

plane.

In

cohesive

soils,

according

to

theoretical

considerations,

tension

exists

to

a

depth

of

2c

o

•-tan

(45 °

+

•/2)

for

both

horizontal

and

slopin•

ground

surfaces.

Vertical

tension

Cracks

will

develop

in

this

Zoae

since

soil

cannot

sustain

tension.

One

of

these

cracks

will

extend.down

to

the

failure

Surface

and

so

reduce

the

length

on

which

Cohesion

acts.

The

effect

of

this,



3.3.5

17

3.3.6

together

with

the

slightly

smaller

wedge

weight

is

the same

as

neglecting

the

reduction

in

total

pressure

provided

by

the

tension

zone

according

to

the

Rankine

and

Coulomb

equations.

For

an

irregular

ground

surface

the

pressure

distribution

is

not

triangular.

However

if

the

ground

does

not

depart

significantly

from

a

plane

surface,

a

linear

pressure

distribution

may

be

assumed,

and

the

construction

given

in

figure

16

used.

A

more

accurate

method

is

given

in

figure

17.

The

latter

should

be

used

when

there

ere

abrupt

changes

in

the

ground

surface

or

there

are

non-uniform

surcharges.

Geometrical

Shape

of

the

Retaining

Structure

The

geometrical

shape

of

the

retaining

struct6re largely

determines

which

of

Rankine s

or

Coulomb s

conditions

are

satisfied

or

•ost

nearly

satisfied

for

a

particular

soil

and hence

how

the

pressure

should

be

determined.

Rankine s

conditions

may

be

taken

as

applying

to

cantilever

and

counterfort retaining

walls with

heel

lengths equal

to at

least

half

the

wall

height.

The

earth

pressure

is

calculated

on

the

vertical

plane

through

the

re r

of the

heel

which

is

sometimes

referred

to

as

the

Virtual

back

of

the

wall.

Coulomb s

conditions

may

be

applied

to

gravity

type

walls

and

walls

with

small

heels,

since

it

will

usually be

found

that

the

soil

siiUes

on

the

back

of

the

wall.

For

further

information

on

the

application

of

Rankine s

or

Coulomh s

conditions,

see

reference

I.

Limited Backfill

The

limiting

equilibrium

methods

given

above

ssume

that the

sol

is

homogeneous

for

a

sufficient

distance

behind

the

wall

to

enable

an

inner

failure

surface

lto

form

in

the

position

where

static

equilibrium

is

satisfied.

Where

an

excavation

is

made

to

accommodate

the

wall,

the

undis•r•ed

m•erial

may

have

a

different

strength

from

that

of

the

backfill.

If

equations

are

used

the

position

of

two

failure

planes

should

be

calculated

one

using

the

properties

of the

back-

fill

material

and

one

using

the

properties

of the

undisturbed

material.

If

both

fall

within

the

physical

limit

of the

backfill

the

critical

failure

plane

is

obviously

the

one

calculated

using

the

backfill

properties.

Similarly

if

they

both

come

within

the

undisturbed

material,

the

critical

one

is

that

for

the

undisturbed

material

properties.

Two

other

possible

situations

may

however

arise

one

where

critical

failure

planes

occur

in

both

materials

(the

one

gi•ng

the

maximum

earth

pressure

is

used),

and

the

other

where

the

failure

plane

calculated

with

the

backfill

properties

would

fall

within

the.

undisturbed

material

and

the

failure

plane

for

undisturbed

material

would

fall

within the

backfill.

In

the

latter

case,

which

occurs

when the

undisturbed

material

has

a

high

strength,

the

backfill

may

be

assumed

to

slide

on

the

physical

boundary

between

the

two

materials.

The

earth

pressure

equations

do

not

apply in

this

case,

but

The

trlcl

wedge

metho,

may

be

used

with the

already

selected

critical

faiiure

plane

and

the

backfill

soil

properties.

The

total

pressure

thus

calculated

will

be

less

than the full active

value

however

the

variation

of

pressure

with

depth

is

not

linear

it

should

be

deter-

mined by

the

procedure

given

in

figure

17.



18-

This

is

a

form

of

ever-consolidation.

In

Coarse

grained

soils

the

lateral

pressures

produced

are

equal

to

or

Slightly

higher

than

the

at-rest

pressures.

The

boundary

between

the

two

materials

should

b•

constructed

so

•h•

there

is

no

inherent

loss

of

friction

(or

cohesion)

on

the

failure

SUrface.

Benching

the

undisturbed

material

will

ensure

that

the

failure

surface

is

almost

entirely

through

solid

backfill

material.

ELASTIC

EQUILIBRIUM

CONDITIONS

At-rest

Pressures

The

special

state

of

elastic

equilibrium

known

as

the

at-rest

state

is

useful

as

a

reference

point

for

calculation

of

earth

pressures

Where

only

sma•l

wall

mOvements

occur.

For

the

Case

of

a

Vertical

wall

and

a

horizontal

ground

SUrface

the

coefficient

of

at-rest

earth

pressure

may

be

taken

as:

for

normally

consolidated

mater

als.

as

not

any

bu,,t

,n

Over conso.lidotio T oossume

that

the

material

ngles

and

backfi•l

slopes,

it

may

be

assumed

=- •ss.

rot

other

wall

roportional

to

KA.

At=rest

ea

that

K

o

varies

•re•s•

linearly

With

de•th

•__rth

pressures

may

be •SSumed

to

u•Terlals.

-.um

Zero

at

the

ground

surface

for

al

The

total

at-rest

earth

pressure

force

is

given

by:

o

½

K

o

y

H•

This

acts

at

H/3

from

the

base

of

the

wall

(or

bottom

of

th•

key

fQr

walls

with

ke•s).

For

gravity

type

retaining

walls

the

at-rest

pressure

should

be

taken

as

aC•ing

normal

to

the

back

of

the

wall

(i.e.

•

= o).

For

canti-

lever

and

Counterfort

walls

it

should

be

calculated

on

the

vertical

plane

through

the

rear

of

the

heel

and

taken

as

acting

parallel

with

the

ground

surface.

In

cohesionless

soils,

full

he

mos•

rigidly

•unaort=•

•a?•rest

pressures

will

occur

only

with

ressures

approa•hina

=

In

highly

plastic

clays,

ont•nu:'with

• •

•---esr

may

develop

Unless

wall

movement

can

Over conso]idat•on

Pressures

Several

factors

produce

a

coefficient

greater

than

that

given

in

3.4.1

above.

If

a

braced

excavation

is

Constructed

in

over-

Consolidated

clay,

the

built-in

ever-consolidation

produces

lateral

pressures

in

excess

of

those

that

would

be

obtained

by

USing

the

existing

depth

of

material.

This

is

a

rt

cu•arly

marked

at

shallow

existing

depths.

If

some

wall

mOvement

takes

place

these

high

pressures

dhop

rapidly.

Compaction

of

backfill

in

a Confined

wedge

behind

a

restrained

wall

also

tends

to

increase

lateral

pressures.

In

fine

grained

soils

the

lateral

pressures



all

ra

low

the

the

3 4 3

produced

by

compaction

may

be

higher

still.

Some

further

Information

on

actual

pressures

for

unyielding

retaining

structures

Is

given

in

references

and

8

Elastic

•heo•y

Methods

When

the

solution

of

a

lateral

pressure

problem

requires

the

estimate

of

some

deformations

or

the

relation

between

load and

deformation,

elastic

methods

of

analvsis

may

be

considered.

Usually

only

the

linear

theory

is

used.

Particular

care

and

judgement is

required

in

order

to

select

appropriate

elastic

constants

and

boundary

conditions.

Currently

available

general

computer

programs

based

on

the

finite

element

method

of

analysis

are

ICES=STRUDL-II

and

the

Ministry

of

Works' plane

stress

or

plane

strain

program

STQUAD2D,

From

elastic

theory

the

coefficient

of

at-rest

pressure

for

a

vertical

wall

and

horizon#al

ground

surface

is

given

by:

Ko

(for

plain

strain).



20

SECTION 4

EARTHQUAKE

EARTH

PRESSURE

4.1

IdETHOD

OF ANALYSIS

The

most

common

method

of

obtaining forces

due

to

earthquake

loading

is

the

pseudo-static

seismic

coefficient

method.

In this

method,

a

force

equal

to

the weight

of

a m ss

multiplied

by

a

specified

value

of

seismic

coefficient

is

assumed

to

act

statically

at the

centre

of

gravity of

the

m ss°

b)

This

approach

has been

extensively

used

to

determine the

pressure

on

earth

retaining

structures

under earthquakes

see references

9,

I0,

11

and

12)

and

at

this

stage

of

knowledge

it

is the

recommended method.

A

horizontal seismic

coefficient

only

need be

used

s•nce typical vertical

accelerations

have

a very

small

effect

on

earth

pressures

4.2

SELECTION

OF

SEISMIC

COEFFICIENT

The

design

seismic

coefficients

for

use

in

earth

pressure

calculations.

ere

given

in

table

9.

These

are

determined

without

regard

to

the

dynamic

haracteristics

of th•

retaining

structure

or

soil

•

They

are,

however,

dependent

on

the

seismic

zoning

of the

re

and the

importance

of

the

structure.

The

seismic

zone

should

be

determined

from

NZS 1900

chapter

8:

1965 reference

13).

Earth

retaining

structures

should

be placed

in

one

of the

three

importance

categories

as

follows

depend

ng

on

the

size of

the structure,

the

effect

of failure

in

The

structure,

and the

cost

of

reconstruction:

a)

Importance

category

1

Major retaining

walls

supporting

important

structures,

developed

property

or

services,

and the

like,

and

where

failure

would

have

disastrous

consequences

such

as

cutting

vital

communications

or

services,

serious

loss

of life,

etc

Importance

category 2

Free

standing

structures

of

at least

20

feet

6

metres)

in height

in

locations

other

•han

in a)

above

where

replacement

would

be

difficult

or

costly

and/or

where

other

consequences

of

failure

would

be serious.

Importanc•

category

3

For

all

other

retaining

structures

no

specific

provision

for

earthquake

loading

need

be

considered

except that

the

seismic

coefficient

to

be

applied

for

earth

pressure

on.bridge

members

should

be

in

accordance

with

the Highway

Bridge

Design

Brief

reference

14).

TABLE

9

SEISMIC

COEFFICIENTS,

CF FOR

EARTH

RETAL,

IrIG

STRUCTURES

Importance

Category

2

Zone

A

Zone

B

Zone

C

0.24

0.18

0.12

0.17

0.13

0.09





22

The

pressure

distribution

end

point

of

applicatioq

of

the

resultant

ressure

should

be

determined

by

superimposing

the

dynamic

increment

n

earth

pressure,

4PA•

on

the

static

pressure

diagram

similar

to

the

ethod

given

in

figure•19.

For

the

determination

of

PA

for

this

ase,

the

full

static

pressure

diagram

including

the

part

in

tension

hou

d

be

used

for

cohesive

soils.

For

an

irregular

ground

surface,

he

static

pressure

diagram

may

not

be

a

linear

variation

with

depth

i.e.

the

point of

application

of

PA

may

not

be

at

H/3).

However

he

dynamic

increment

PAE

should

always

be

applied

at

the

2/3H

oint

to

give

a

distribution

varying

linearly

from

a

maximum

at

the

op

to

zero

at the

bottom

of

the

wall (or

key,

for

walls

wi•h

keys).

4.4

SEISMIC

AT-REST

PRESSURES

For

a

completely

rigid

retaining

wall,

the

force

from

the

earthquake

arth

pressure

may

be

approximated

by:

PE

½

Y.H

2

(Ko

+

2

KAE)

where

•KAE

KAE

KA

Where

mevemeny

is

sufficient

for

the

fully

active

c se

to

develop

see

lause

3.2),

the

force

from

the

ea•hquake

earth

pressure

should

be

taken

as

PE

½

Y

H

•

(K

A

+4KAE)

For

wails

of

intermediate

rigidity,

the

earthquake

earth

pressure

should

be

etermined

by

estimating

the

displacement

of

the

top

of

the

wa•I

under

earth-

uake

loading

and interpolating

between

the

values

from

the

two

•quations

iven

above.

The

following

pressure coefficients

should

be

used

for

rigid

oundation

conditions

unless

a

more

exact

analysis

of

movements

is

made;.

(a)

Counterfor•

or

gravity

type

wails

founded

on

•ock

r

piles

Ko

+

AKAE

Cantilever

walls

le•s

than

16

feet

(5

metres)

igh

founded

on

rock

or

piles

(K

o

+

+

(C)

• y

wall

on

soil

foundations

or

cantilever

walls

igher

than

16

feet

(5

metres)

K

A

+ •KAE

The

point

of

application

of

the

resultant

of

the

ea'rth

pressure and

hence

he

pressure

distribution

shou

d

be

de•ermlned

similar

to

figure

19 with

•PAE

a•

2/3H).



be

23-

SECTION

5

THE

EFFECT

OF

SURCHARGES_

5.1

UNIFO•4

SURCHARGES

Uniform surcharge

loads

may

be

Converted

to

an

equivalent

height

of

fill

and

the

earth

pressures

calculated

for

the

correspondingly

greater

height.

The

equivalent

height

is

given

by:

be

•

cos

B

•

cos

6

•)

The

depth

of

the

tension zone

in

cohesive

material

is

calculated

from

the

top

of

the

equivalent

additional

fill.

The

distribution

of

pressure

for

the

greater

height

is

determined

from

the

procedures

given

in

sections

3

and

4.

The

total

lateral

earth

pressure

is

calculated

from

the

pressure

diagram

neglecting

the

part

in

tension

and/or

the

part

in

the

height

of

{ill

equivalent

to

the

surcharge.

Concrete

buildings may

be

represented

as

a

uniform

surcharge

of

200

Ib/ft2

(10

kN/m

2)

per

storey.

Timber

buildings

may

be

taken

as

half

the

above.

Traffic

Ioadina,

when

at

a

greater

distance

than

2/3

ti•es

the

height

of

the

wa•t

from

the

back

face

of

the

wa•l

may

be

represented

as

a

uniform

surcharge

of

250

lb/f

tz

[12

kN/m

2)-

The

two

loading

cases

shown

in

figure

29

need

to

be

considered.

5.2

LINE

LOADS

Where

there

is

a

superimposed

line

load

running

a

considerable

length

of

this

load

can

be

added

wed

e

to

which

it

is

applied

see

arallel

to

the

wall

the

weight

per

unit

length

hl

to

the

weight

of

the

part•c•l•r,t[•h

o

•ssur

will

be

given

fro•

t•e

[..;i

•n

The

increased

TOTa•

•r

-h=n•e

the

Do

nT OT

K

f•gure

line

load

wi•

a s

•

trial

wedge

procedur

rut

•

e

method

given

in

figure

17

may

be

•i•

application

of

th•s

TOTal

•,•==•'•

Th_

u•d

to

give

the

distributlon

ot

pressure.

•hen

the

line

load

is

small

in

comparison

with

active

earth

pressure,

the

effect

of

the

line

load

on

its

own

shguld

be

determined

by

the

method

given

in

figure

31.

This is based

on

stresses

in

an

elastic

medium

modified

by

experiment.

The

pressures

thus

determined

are

supeFimposed

on

those

due

to

active

earth

pressure

and

other

effects.

5.3

POINT

LOADS

Point

loads

cannot

be

taken

into

account by

trial

wedge

procedures.

•he

method

based

on

Boussinesq'S

equations

given

in

figure

31

should

be

used.

A

similar

method

is

given

in

appendix

H

of

reference

2.



24

SECTION

6

E•FFECTS

OF

WATER

6.1

STATIC

WATER

LEVEL

Where

part

or

all

of

the

soil

behind

a

wall

is

subm•rged

below

a

statig

ater

level,

the

earth

pressure

is

changed

due

to

the

hydrostatic

poreressures

set

up

in

the

soil.

The

water

itself

also

exerts

lateral

ressure

on

the wail

equal

to

the

depth

below

the

water

table

times

the

ensity

of

water.

If

cohesionless

soil

is

fully

saturated,

and

the

water

in

the

voids

is

ot

flowing,

the

pore

water

pressure

at

a

depth,

y

b'elow

the

water

table

is

equal

to

Yw

Y

where

Xw

is

the

density

of

water.

This

means

that

the

ffective

vertical

pressure

due

to

the

amount

of

soil

that

is

submerged

issat Y

Yw

Y

The

effect

of

the

h•dr

•

w aJlc

pore

water

pressure may

be

•Ken

•nTO

account

by

using

the

submerged

density

of

soil,

y',

for

f

the

earth

pressure

diagram

which

is

below

the

water

table

see

that

part

figure

2.

Alternatively

all

t:•e

forces

acting

on

e

soil

wedge

including

the

hydrostatic

normal

uplift

pressure

on

the

failure

plane

and

the

lateral

ydrostatic

pressure

may

be

included

in

the

trial

wedge

procedure

see

figure

14.

In

cohesive

soils

the

pore

water

pressures

set

up

during

construction

will

override

any

hydrostatic

pore

pressure

Where

tension

cracks

occur,

lateral

hydrostatic

water

pressure

should

be

included

for

the

full

depth

of

the

crack

as

given

in

3.3.4

or

for

H/2

•hichever

is less.

If however

shrinkage

cracks

are

l able

to

form

to

a

depth

greater

than

that

given

above,

water

pressure should

be

allowed

for

the

full

depth

of

such

shrinkage

cracks.

The

maximum

depth

varies

with

soil

and

climate

but

may

be

taken

as

5

feet

1.5

metres).

Full

lateral

ater

pressure

must

be

allowed

for

below

the

highest

level

of

the

soffit

of

the

weep

holes

or

other

drainage

outlets.

Static

water

pressure

always

acts

normal

to

the

surface

of

the

wall.

6.2

SEEPAGE

PRESSURE

If

the

water

in

the

soil voids

is

flowing,

the

pore

water

pressures

will

be

changed from

the

hydrostatic

values

by

an

amount

proportional

to

the

flow

of

water.

For

major

s

•ructures,

the

pore

water

pressures

under

seepage

conditions

should

be

determined

by

flow

he+

procedures

see

references

I

5

or

6.

The

pore

water

pressures

normal

to

the

failure

surface

of

active

or

passive

wedges

affects

the

earth

pressure

act

ng

on

a

wall.

The

resuliant

uplift

force

on

the

fai

ure

surface

determined

from

a

flow

net

is

applied

in

the

force

polygon

for

the

soil

wedge

together

with

any

lateral

water

pressure

at

the

wall

see

figure

14.

Fdr

an

approximate

analysis

the

uplift

intensity

may

be

taken

as

being

equa

to

the

pressure

of

the

vertical

height

of

water

between

ground

water

table

level

(may

be

sloping)

and

a

point

directly

beneath

on

the

failure

surface.

Figure

32

shows

a

flow

net

for

seepage

from

the

ground

surface

behind

a

wall

with

a

vertical

drain.

For

C

C

S



stat

c

is

is

s

be

rt

I-

H/2.

a

for

of

to

6.

passive

uplift

the

heigh•

for

For

25

cohesionless materials

sustained

seepage

under

the

conditions

shown

would

Increase

the

active

force

20

to 40

percent

over

that

for

dry

backfill,

depending

on

the

backfill shearing

strength.

6.3

DYNAMIC WATER

PRESSURE IN

EARTHQUAKES

Yhe

dynamic

pressure

of

any

water

in

the

backfill

should

be

taken into

account

by

applying the

seismic

coefficient

•o

the

weight

of

water

in

the

failure

wedge

as

well

as

to

the

soil.

If

the

•nonobe-Okabe

equations

are

used

with

the

Submerged

density

Of

the

soil below

the water

table,

the

seismic coefficient

must

be

scaled

up

by

Ysat/Y

to

allow fop

the

mass

of

the water.

The

dynamic

pressure

of

water in

front of

a

wall

e.g.

a

quay

wall)

is

usually

not

taken into

consideration

because

this

usually

acts

in

a

direction

opposite

to

the

pressures

from the

backfill material.

6.4

DRAINAGE PROVISIONS

Water

pressures

must

be

included in the forces acting

on

the

wall

unless

adequate drainage

is

provided.

For

walls

less than

6 feet

2

metres)

high, drainage

material

is

usually

only provided

on

the back face

of the

wall,

with

weep

holes

to

relieve water

pressure see

figure 34. In

these

circumstances

it

may

be

desirable

or

more

economic

to

design

for

hydrostatic

water

pressure.

In

general, if the drainage

system

shown in

figure

33 is

used

water

pressures

may

be

neglected both

on

the wall itself and

on

the soil

failure

plane.

Adequate

drainage

reduces the rate of

softening of

clay

filling

and of

stiff-fissured

clays

and

lessens

the

likelihood

of

reductions in

the

strength

of

the

foundations, and

is

therefore

very

desirable for

clay

soils.

It

Is worth noting

that in

cohesionless

soils,

the active force

on

a

wall with

static

water

level

at

the top

of the

backfill is approximately

double

that

for

a

dry

backfill. For walls

over

20

feet

6

metres) high,

particular

care

should be

taken

to

ensure

that the

drainage

system

will

control the effects

of water

according to

the

assumptions

made

in

design.

Many recorded wall

failures

seem

to

be the

result

of

inadequate drainage.

Water should

•Feferably

be

prevented

from

entering

the

backfill from

the

surface,

otherwise

any

resulting

seepage

pressures

must

be allowed for

in

design.

Drainage

material

should have

a

permeability

at least

100 times

that

of the material

it

is

meant

to

drain. If this

is achieved,

pore

water

pressures

due

to

seepage

will be

minimised

at the

boundary

and the

soil

mass

will drain

as

though it had

a

free

boundary.

Permeabilities of

granular

drainage)

materials

are

given

in figure

35.

The filter

principle

must be

used

when

seepage

is

from

fine

grained

to

coarser

grained

materials, to prevent movement

of the fines and

possible

choking

of

the

coarser more

permeable

material.

The following

particle

size

ratios should

generally

be

provided:



26

D15C

DSO

C

D15

C

-•SF

_•

5,

25,

• <

40

50

F

DIS

F

where

D15

C

size

at

which

15%

by

weight

of

the

coarse

material

is

fi•er

I5F

15$

-

fine

,,

,,

,,

DSOC

505

,,

,,

Coarse

,,

,,

,,

DSOF

,t

,,

50%

fine

.

.

D85F

85%

fine

,,

,,

,,

For

clay

soils

the

D15

C

size

should

not

be

less

than

0.2

mm

and

the

DSO

criterion

may

be

disregarded

but

•he

filter

(coarse)

material

must

be

well

graded

such

that:

D60C

20

io

C

The

filter

material

must

also

have

sufficient

permeabi

ity

so

that

the

seepage

can

pass

through

to

the

drainage

material

or

drain.

To

avoid

head

loss

in

the

filter

the

following

additional

provision must

be

met:

DI5C

------>5

I5F

To

avoid

internal

movement

of

•ines,

the

filter

should

have

0-5

passing

the

No.

200

s,eve,

and

to

avoid

segregation

it

should

not

contain

sizes

larger

than

3

inches.

The

above

criteria

mean

that the

following

grading

is

the

finest

equired

for

any

filter

materia

rotected:

regardless

of

the

material

that

is

being

Sieve

S•ze

3i16

No.

7

No.

14

No.

25

No.

52

No•

100

No.

200

Percent

Passing

100

92

74

5O

25

.8

0

Material

surrounding

a

perforated

subsoil

drain

pipe

must

have

a

D85

size

9reater

than

the

diameter

of

the

pipe

perforations•



net

D50

be

we

being

a

D85

27

SECTION 7

STABILITY

OF

RETAINING

WALLS

7.1 GENERAL

The stability

of

a

free

standing

retaining structure

end the

soil

containing

it is

determined

by

computing

factors

of

safety

or

stability

factors

which

may

be

defined

in

general terms

as:

Moments

or

forces

aiding

stabi.lity

s

Moments

or

forces

causing

instability

Factors

of

•afe•y

should

be

calculated

for the

following

separate

modes

of

failure:

a)

Sliding

of the

wall

outwards

from

the

retained

soil.

b)

Overturning of the

retaining

wall

about

its

toe.

c)

Foundation

bearing failure.

d)

Slip

circle failure

in the

surrounding

soil.

The

forces that

produce

overturning

and

sliding

are

also

producing

the

foundation bearing

pressures

and therefore

(a)

end

(b)

above

are

inter-

related

with foundation

bearing

failure

in most

soils.

In

c ses

where the

foundation is

soil,

overturning

stability

will

usually

be satisfied

if

bearing

criteria

are

satisfied.

However

it

may

be critical

for

strong

foundetion

materials

such

as

rock,

or

when

the base

of•the

wall

is

small,

which is

the

c se

with

crib walls.

From

settlement

and

•ilting

considerations in

soil

materials,

the

resultant of

the

loading

on

the

base should

be

within

the middle

third for

static

loading

and

within the

middle

half

for

earthquake

loading.

For

rock foundation

material,

the

resultant

should

be

within the

middle

half

of

the

base

for

both

static and

earthquake

loading.

When

ca-lculating

overall

stability

of the

wall.the

lateral

earth

pressure

is

calculated

to

the bottom

of the

blinding

layer,

or

in the

c se

of

a

basw

with

a

key, to

the

bottom

of the

key.

The

vertical

component

(if any)

of

the

resultant

earth

pressure

is

added

to the

weight

of the

wall

system

when

computing

stability

factors.

If

the

•essive resistance

of

the

soil in

front

of

a

wall

is

included in

calculations

for stability,

either

the

top 18

inches

(0.5

metres) of the

soil

should

be neglected,

or

only

2/3

of

the calculated

passive

resistance

should

be

used..

Stability

criteria

for free

standing

retaining

wal

fl•ure

36.

s

re

summarised in





7.4.2

The

recommended

method

of

calculating

the

bearing

capacity

applies

o

both

earthquake

loading

and

static

loading.

No

consideration

need

be

made for

the

cyclic

effects

of

dynamic

load

or

the

dynamic

roperties

of the

soil.

The

ultimate

bearing

capacity

for

a

shallow

(D

•

B)

strip

foundation

s

given

In

general

terms

by:

-Q-=

cN

c

s•d

c

+

D

Nq

Sqdq

+ BNy

sydy

ult

BL

Y

½

Y

The

bearing

capacity

factors

Nc,

Ng

and

Ny

(for

a

horizontal

strip

oundation

under

vertical

concentric

loading),

are

calculated

from

he

angle

of

shearing

resistance

of

the

foundation

material.

This

ssumes

that

the

material

is

reasonably

dense

so

that

failure

would

ccur

by

general

shearing.

If

the

material

is loose

c

and

¢

should

e

reduced

to

2/3

of

the

actual

values,

i.e.

c 2/3c

and tan

¢'

/3

tan

•. The

ultimate

bearing

capaqity

for

a

shallow

foundation

hat

is

not

a

continuous

•trip

is

obtained

by

multiplying

the

earing

capacity

factors

by

corresponding

empirical

shape

factors

s

c,

Sq

and

sy).

The

bearing

capacity

factors

may

be

further

multiplied

by

depth

actors

(dc,

dq

and dy)

which

take

into

account the

shearing

..resistance

of the

soil

above

foundation

level.

Bearl•g

capacity

factors,

shape

factors

and depth

factors

based

on

eyerhof s

assumptions

(references

16

or

19)

are

given

in

figure

37.

imilar

factors

according

to

Hansen

are

given

in

referenqe

27.

Eccentric

Loads

If

the

load

on

the

foundation

is

eccentric

this

can

substantially

educe

the

bearing

capacity.

To

allow

for

this

the

base

width,

B

s

reduced

to

an

effective

width B'

given

by:

B

t

B

2e

Where

e-is

the--load

eccentricity.

For

a

footing

eccentrically

loaded

in

two

directions

(el,

eb)

the

ffective

dimensions

of the

base

become

such

that

the

centre

of

an

rea

A

coincides

with

the

vertical

component

of the

applied

load,

A

B

x

L'

where L'

L 2e

B

B 2e

b

U

and

B

replace

L

and B

in

all

equations.

The

factor

of safety

is

given

by:

Fs

(bearing)

qul•t

where

q

A •

q

for

a

rectangular

footing

for

a

continuous

strip

footing.



7.4.3

7.4.4

?.4.5

Inclined

Loads

Where

the

load

on

a

horizontal

continuous

strip

foundation

is

inclined,

which

is

the

case

for

most

retaining

wails,

the

vertical

Component

of

the

ultimate

bearing

capacity

is

compared

with

the

bearing

pressure

from

the

vertical component

of

the

applied

loading

to

obtain

the

factor

of

safety.

According

to

Meyerhof,

the

vertical

component

of

the

ultimate

bearing

capacity

is

given

by:

qult(v).

CNcq

+

½

y

B

Nyq

where

Ncq

(depending

on

N

c

and

Nq

and

Nyq

(depending

on

Ny

and

Nq

are

beari.fig

c•)pacity

factors

n•odified

for

the

degree

of

inclination.

f

the

inclination

of

the

applied

loading

is

large

and the

oundation

depth,

D

is

small,

a

sliding

failure

may

occur

first.

variation

of

the

above

situation

is

where

the

base

is

inclined

so

that

the

applied

loading

is

normal

to

it.

In

this

ease

the

bearing

pressures

are

calculated

normal

to

the

base,

and

Meyerhof,s

ultimate

bearing

capacity

is

•iven

by:

qult

cNcq

+

½

y

B

Nyq

The

bearing

capacity

factors

Nc•

and

Nyg

for

the

two

cases

mentioned

are

given

in

figure

38

for

embe•ment

rafios,

D/B

of

0

and

I.

The

factors

for

intermediate

embedment

ratios

may

be

obtained

by

linear

interpolation.

In

the

particular

ase

where

@

o,

Meyerhof s

ultimate

bearing

Capaci.ty

(or

the

vertical

component

of

it)

is

given

by:

qult

or

qult. _9)•cN•_+

yD--

As

an

approximate

alternative

to

the

above

method,

the

terms

in

the

ultimate

bearing

C•pacity

equation

in

7.4.1

may

be

modified

by

inclination

factors

to

allow

for

the

inclined

load

see reference

19

(Meyerhof s

method)

and

27

(Hansen•s

method).

The

bearing

Capacity

of

a

rectangular

footing

is

approximately

the

same

as

a

strip

footing

at

a

load

inclination

angle

of

15

°

to

the

vertical.

ccentri•

Inclined

Loads

When

a

foundation

carries

an

eccentric

inclined

load,

an

estimate

of

the

ultimate

bearing

Capacity

may

be

obtained

by

combining

the

methods

given

in

7.4.2

and 7.4.3.

The

procedure

in

.the

ase of

a

horizontal

base

is

given

in

figure

38

but

it

also

applies

when

the

base

is

inclined

see reference

17.

Foundations

on

a

Slope

When

a

shallow

foundation

Is

located

on

the

face

of

a

slope

or

at

the

+op

of

a

slope,

ultimate

bearing

Capacity

is

reduced

see

reference

18.

For

slopes

less

than

30

°

the

decrease

in

bearing



7.4.6

capacity Is

small

for

clays

but

can

be

considerable

for

sands

and

gravels. However

in

clays

the

bearing capacity

of

a

shallow

foundatibn

may

be

limited by

the

stability of the

whole.slope.

The

ultimate

bearing

capacity

according to

Meyerhof'Is

given by:

qult

cNcq

+

Y

B

Nyq

•.

The'bearing

capacity

factors,

Ncq

and

•yq

for

a

strip

fo•,'•dation

wlth concentric vertical

load ng

re

g•ven

in

figure

39.

If the

foundation is

located

on

the face of

a

clay

slope

less

then

half

way

up

the

slope

the stability of the slope

will not

affect

the

bearing

capacity

and

a

stability number,

Ns,

of

zero

should

be used.

If

the

foundation

is

located

on

top of

the

•lope

the

bearing

capacity

varies

with the distance

from

the

slope.

When the

foundation

material is

cohesive, the

ultimate

bearing

capacity

also depends

on

the

slope stability,

number,

which must

be

calculated for

the

particular

situation

In the particular

c se

of

a

purely cohesive

soil @

o) the

slope

stability

number

is

given by:

N

s

¥

H/C

and

qult

=.

cNcq

+

yD

The

ultimate

bearing

capacity of

a

foundation located

more

than

half

way

up a

clay slope

may

be estimated by

using

a

slope stabiiity

number intermediate

between

zero

and

that

appropriate to

the

c se

of

a

foundation at

the top

of the slope.

Eccentric

applied

loads

may

be

taken

into

account

by

the

methods

of

7.4.2.

Effect of

Ground

Water

Level

The

equations

given'in

7.4.1 to 7.4.5

apply when

the

ground

water

table

is

at

a

distance

of

at

least

B below

the

base

of

the

foundatT•o•.

---•n

the--water

table

is

•t

the

s me

level

as

the

foundation, the

submerged

unit weight

of

the

soil

below

the

foundation

should be used.

For intermediate

levels of the

water

table the

Ultimate

bearing

Capacity should

be interpolated

between

the

above

limiting

values

7.5 SLIP CIRCLE FAILURE

For

walls

higher

than

30 feet (9

metres), slip

circle failure

in

the

soil

containing the wall should be investigated.

The

slip

circle

stability

factor:

F

s

(slip

circle)

N tan

•

+

cl

T

should

be

•t

least

1.5

for

static loading

and

at

least

1.3

for

earthquake

loading.

An

effective

stress

analysis

using

appropriate

pore

water

pressures

Is

recommended



Earthquake

loading

should

be

allowed

for

y

applying

a

static

orizontal

force

to

the

soil

m ss

s

described

in

4.1

using

the

design

eismic

coefficient

determined

from

4.2.

Computer

programs

currently

available

for

this

type

of

analysis

includeCES-LEASE

and

the

Ministry

of

Works

SOILS

program.

The

former

is

onsidered

to

be

mor

accurate

however

at

present

it

does

not

have

theapability

for

including

the

horizontal

force

for

the

earthquake

loading

hich

SOILS

allows.



8.1

GENERAL

SECTION 8

STRUCTURAL

DESIGN

8•1.1

Codes

Reinforced

concrete

design

should

be

in

accordance with NZS

3101P

(reference

20)

with

reference

to

ACI

3i8-71

reference

21)

for

those

requirements

not covered

by

the New Zealand

code.

8. .2 Material

Strengths

and

Allowable

Stresses

The

following

material

strengths (with

the

corresponding

allowable

stresses)

re

recommended.

However in

some

c ses

an

increased

concrete strength

with

correspondingly increased

allowable

stresses

may

give

some

economy:

Reinforcement,

Deformed

structural

grade

to

NZS i693:1962

Yield

stress,

fy

40,O00Ib/in

2

(275

MN/m

2

'Allowable

tensile

stress, fs 20,000 Ib/in

2

(138

MN/m•).

Concrete

Nominal

compressive strength,

f'c

3,000

Ib/in

2

(20

MN/m

2

Allowable

compressive

stress,

fc

1,350

Ib/in

2

(9.3

MN/m

2

Allowable

shear

stress,

fv

60

Ib/in

2

(0.41MN/m

2

Modular

ratio,

n

9.

For

earthquake

loading the

above

stresses

may

be increased

by

33%.

8.1.3

Ultimate

Strength

If

ult•n•a•e.•zength

d •ign

methods

are

used

for

proportioning

a

structural

section,

the

design

load•

shall

be

computed

so

thai the

capacity

of

the

section

shall

not

be

less

than:

U

1.35

(DL

+

1.35

EP

+

W);

or

U

1.08 (kDL

÷

I..25

(EQ

+

W))

where

DL

EP

dead

load

of

the

structural

element

static

earth

pressure

acting

on

the

element

(inclJdine

the

effects

of

any

surcharge

loads)

EQ

earthquake

earth

pressure

acting

on

the

element

W

hydrostatic

water

pressure

k ='1.2

or

0.8

whichever

is

more

severe,

to allow

for

vertical acceleration.

If

USD

is

used,

a

serviceability

check

on

"crack

widths

at

working

loads

shall

be

made

to

ensure

that

the limits

given

in

clause

3.1.9

of

NZS 3101P

are

not

exceeded.



q

8.1.4

8.1.5

8.2.2

Reference

23

gives

an

example

of

USD

of

a

cantilever

retaining

wall.

Cover

to

Reinforcement

a)

Concrete

below

ground

i)

ii)

. b)

cast

against

natural

ground

cast

egainst

formwork

or

blinding

concrete

Above

ground

inches

mm

3.0

75

2.0

50

i)

cast-in-situ

concrete

1.5

40

ii)

precast

components

•

1.25

30

•

CY/•:

•he

thickness

of

architectural

finishes

is

neglected

when

ca

culating

Fover

to

steel

or

stresses.

Selection

of

Hall

Type

For

walls

up

to

25

feet

7.5

m)

high

where

crib

walling

is

not

suit-

ble,

a

cantilever

wall

will

usually

be

found

@o

be

the

most

conomical.

For

higher

walls

en

investigation

should

be

made

for

the

relative

conomies

of

using

a

counterfort

or

cantilever

wall.

This

should.

ake

into

account

unit

costs

for

formwork,

reinforcing

steel,

and

oncrete,

end

not

just

all

in

cost per

cubic

yard

of

final

wall..

ounterfort

walls

should

have

approximately

a

30

ft.

(9

metre)

bay

ength

varied

to

suit

architectural

finish

etc.)

with

three

counter

orts

per

bay.

The

position

of

the

counterforts

is

obtained

by

onsidering

the

stresses

in

the

stem.

TOE

DESIGN

For

Length

of toe

Effective

depth

at

face

of

support

I,

design

according

to

NZS

3101P.

face

of

support.

Shear

may

be

taken

at

Wd'

out

from

LenQth

of

toe

Effective

depth

at

face

of

support

•

I,

design

as

a

0racket

in

accordance

with

section

II.14

of

ACI

318:71.



8.3

STEM

DESIGN

8.3.1

Stem

Leading

For

the stem

design in

cantilever

and

counterfort

walls,

t•e

earth

pressure

acting

on

the

vertical plene

through the

rear

of

the heel

Is•projected onto

the stem.

8.3.2

Lower

Section of

Counterfort

Wall

Stem

Th•

bottom

LS 2

of

the

stem

is

to

be

reinforced

fer

vertical

spanning action in

addition

to

horizontal spanning.

Bending

-re

M

re

M

wLs

2

-re

M

=-25--

where

w

is the

considered.

moments

per

unit

height

of

stem

may

be

assumed

as:

•Ls

14

WLs___•

22

horizontal

steel)

horizontal

steel)

vertical

steel)

lateral

design

pressur

e

at the level being

8.3.3

Horizontal Moments in Counterfort

Wall

Stem

Bending

moments

in

the

top part

of the

stem

may

be

celculated from:

-re

M

wLs

horizontal

steel)

+ve

M

wLs2

horizontal

steel)

16

Use continuous

horizontal steel

in

both

faces.

Horizontal

B.M.

variations

with

height should

be

catered

for

by

varying the

reinforcement spacing in preference

to

changing

the bar sizes.

When

caFculating-the bending

moments for

the

stem,

the

span

should

be

taken

as

.the clear

span

between

counterforts

Ls).

8.4

HEEL

SLAB

DESIGN

8.4.1

Loading

The

design

loading

on

fhe

heel

slab is shown

in

figure

40.

The

foundation

bearing

pressures

may

be calculated

by

using

the

theory

of

subgrade

reaction see 2.7).

For

a

rigid

base

slab this

theory

gives bearing

pressures

whlzh

vary

linearly

across

the

base

width.

The

pressures

for

use

in structural

design

are

not the

same

as

those

used

to check

the

factor

of safety

against ultimate

bearing

failure

section

7.4).



If

the

resultant

cuts

the

base

within

the

m•dd•e

third

the

toe

and

eel

pressures

for

structural

design

may

be

calculated

from:

p

V/BL

±

6

Ve/B2L

8.4.2

8.5

where

V

the

vertical

component

of

the

resultant

loading

on

the

base

B

the

base

width

L

the

length

of

wall

for

which

the

resultant

earth pressure

s

calculated

(usually

unity).

If

th•

resultant

lies

outside

the

middle

third:

2V

max

B/2

e)

L

Heel

Slabs

for

Counterfort

Walls

The

heel

siab

for

counterfori-

wails

shouI•

be

designed

as

a

•lab

panning

in

two

directions

if

a

key

is

included

at

the

rear

The

esig•

bending

moments

may

be

obtained

from

tables

in

reference

15.

Alternatively,

the

heel

slab

can

be

divided

into

or

5

strips,

of

pproximate

width

3.5

feet

(I

metre)

to

5

feet

(1.5

metres)

spanning

etween

counterforts.

The

outermost

strip

including

the

key

can

be

esigned

as

a•

L-beam

for

bending,

its

breadth

equal

to

the

strip

idth.

The

width

of the

key

strip

resisting

shear

should

be

ssumed

as

the

maximum

width

of the

key

plus

half

the

thickness

of

he

heel

slab.

Bending

moments

mey

be

calculated

as

in

8.3.3.

Each

strip

should

be

designed

for

the

average

load occurring.

Th•

ritical

section

is

at

the

face

of

the

counterforts

where

shear

tresses

are

not

to

exceed

stresses

in

section

8.1.2.

This

shearill

usually

govern

the

heel

thickness.

The

heel

slab

should

also

be

considered

as

strips

spanning

at

right

ngles

to

that

mentioned

above,

i.e.,

between

stem

line

and

keytrip.

Simple

aSsumptions

can

be

made

as

to

end

fixity

of

these

trips

and

an approximate

amount

of

reinforcing

provided.

COUNTERFORT

DESIGN

Vertical

steel

in

the

counterfort

is

required

to

carry

the

net

load

from

each

strip

of

the

heel

slab.

The

main

moment

reinforcement

for

the-

wall

is

usually

concentrated

at

the

back

of

the

counterfort.

Where

itoins

the

heel

slab, the

above

steel

should

be

considered

as

taking

only

that

load

o•currlng

on the

outermost

strip

incorporating

the

key,

as

defined

in

8.4.2

above.

Horizontal

steel

in

the

counterfort

is

required

to

carry

the

net

load

n

each

horizontal

strip

of

stem.

Cut-off

positions

for

the

main

tensile

steel

in

the

counterforts

is

shown

in

figure

41.



8.6 KEY

DESIGN

In

general

the depth

to

width

ratio of

the

key

should be

approximately

one

It

is difficult

to predict

what the force

acting

on

the

key

will

be.

An

epproxlmate design horizontal

load

on

the

hey

is:

•

horizontal

loads

causing

sliding

0.4

x

total

vertical

loads above

blinding

layer.

This

load

acts

at

I/3

key

height

frombottom

of key.

Design

the

key

as

e

bracket

refer 8.2

above.

Note

some

stresses

are

carried

from

the

key

lnto

the

bottom

of

the

heel

slab,

and

will

call

for

some

reinforcement

In that

area

8.7

CONTROL

OF

CRACKING

a)

To

mlnimise

cracking

in the

retaining

structure:

Provide

shrinkage

and

temperature

reinforcement

equal

to

0.25

of the

gross

concrete

area

as

a

minimum

in

both

directions

in

all

members.

In

the

stem:

b)

c)

d)

2/3

of

this

steel

to

be

on

the

outside

face

I/3

of

this

steel

to

be

on

the

earth

face.

Specify

that

the

coscrete

placing

and

temperature

is

to

be

kept

as

low

as

practical

especially

in

the

summer

period.

Specify

successive

bay

construction.

Specify

early

curing

for

the

purpose

of

cooling

so as

to

minimise

the

heat rise.

e)

f)

Place

the steel

in

bar

sizes

to

limit

crack

width to

0.01

inch (0.25

(see

code

requirements).

Added

protection

can

be

given

by

painting

the

earth

face

with

say

two

c•ats

of

Mulseal•J_or

F..intcoat

(reference

24).



38

SECTION

9

S•PECIAL

PROVISIONS

FOR

CRIB

WALLS

9.1

GENERAL

A

considerable

amount

of

llterature

is

available

from

Crlbwal

Unit

anufacturers

e.g.

Hume, I.C.B.,

Cement

Products)

and

also

Portland Cementssociation

on

the

design

of

crib

walls.

However,

care

must be

exercised

in

interpretatlon

of

this

data.

Crib

alls

must

be

checked

for

stability

in

accordance

with

section

7.

Figures

3 to

46

may

be

used

as

an

aid

In

determining

the

maximum

height

for

ifferent

well

thicknesses.

The

crib

units

and

wall

construction

should

be

in

eccordence

with

the

urrent

Ministry

of

Works

stendard

speclflcetion

for

this

work

MOW

7562).

9,2

DESIGN

LOADING

The

pressures

ecting

on

a

typical

crib

well

are

shown

In

figure

42.

hese

pressures

are

calculated

by

the

methods

of

sectlon

3.

Earthquake

oeding

will

usually

not

be

applied

to

crib

wells,

but

if

it

is

the

methodsf

section

4

should

be

used.

9.3

FOUNDATION

DEPTH.

The

minimum

•epth

of

foundation

shall

be

as

shown

in

figure

42

which

ncludes

a

continuous

concrete

foundation

slab.

A

minimum

slab

thickness

f

6

inches

150

ram)

reinforced

with

one

layer

of

655

mesh

is

recommended

o

prevent

differential settlement

of

the

wali

structure.

The

onsequences

of

such

settlement

are

described

in

reference

25.

F•] 9.4

DRAINAGE

A

continuous

6

In•cb__ •5.0_•)

diameter

minimum)

subsoil

drain

should

e

provided

at

the

reer

of

the

foundetion

slab,

to

ensure

a

dry

foundatlcn.

(•-• •

This

should

be

provided

for

all

heights

of

crib

wall.

Adequate

drainage

Of

the

whole

crib

structure

is

essential.

Many

of

the

failures

in

crib

walls

heve

oCcurred

because

material

of

low

permeability

as

used

as

backfill

thus

developing

high

static

or

seepage

water

ressures

.A free

draining

backfill

should

always

be

used

if

possible,

therwise

the

effect

of

water

should

be

allowed

for.

Unless

effectively

drained

ov r

the

full

height•

crib

walls

should

be.

esigned

to

resist

lateral

hydrostatic

pressures in

addition

to

sell

ressures

9.5

MULTIPLE

DEPTH

WALLS

Walls

of

more

than

single

depth

should

be

checked

at

the

changes

from

Single

to

double

and

double

to

triple

depth

to

satlsfy

the

followingtabillty

crlterla:



For

normal

conditions

resultant

to be within

middle

I/3.

This

will

ensure

that

no

part

of

the wall

structure

is in tension

For

earthquake

conditions

resultant

to

be within

the

section

of

the

wall

The

appropriate overturning

factor

of

safety

must

also

be

met at

these

s•ctions

9.6

HALLS

CURVED

IN

PLAN

Crlb

walls

with

a convex

front

face

re

much more

susceptible

to

m ge

by transverse

deformations

than

are

conc ve

walls

see

reference

25



•

40

AhPENDIX

REFERENCES

4.

5.

6.

7.

Huntington,

W.

C.

(1957):

John

Wiley

and

Sons.

Earth

Pressures

and

Retaining

Institution

of

Structural

Engineers

(1951):

Earth

Retaining

Structures .

Civll

Engineering

Code

of

Prectice No.

2.

Prepared by

Civil

Engineering

Codes

of

Practice

Joint

Committe•.

US

Department

of

the Navy

(1971):

Design

Manual

Soil

Mechanics,

Foundations,

and

Earth

Structures . Navfac

DM-7.

TschebotariofF,

G.

P.

(1951):

Soil

Mechanics,

Foundations,

and

Earth

Structures .

McGraw-Hill Book

Co.

Terzaghi,

K.'and

R.

B.

Peck

(1967):

Soil

Mechanics

in

Engineering

Practice .

2nd

Edition.

John

Wiley

and

Sons..

Scott,

R.

F.

(1963):

Publishing

Co.

Principles of

Soil

Mechanics .

Addison-Wesley

Gould,

J.

P.

(1970):

Lateral Pressures

on

Rigid

Permanent

Structures . ASCE

Speciality

Conference

Lateral

Stresses

in

the

Ground

and

Earth

Retaining

Structures.

8.

Broms,

B.

(1971):

Lateral

Earth Pressures

due to

Compaction of

Cohesionless

•oils

Pro.

4th

Budapest

Conference

on

Soi'l

Mechanics

and

Foundation

Engineering.

9.

Tennessee

Valley

Authority 1951):

The

Kentucky

Project .

Technical

•eport No.

13..

10.

Kuesel,

T. R.

(1969):

Earthquake

Design

Criteriafor

Subways .

Proc.

ASCE

Structural

Division,

ST6,

pp.

1213-i231.

11.

lZ.

Japan

Society_o•_§•Engiqg•rs

(1968):

Earthquake

Resistant

Design

for

Civil Engineering

Structures, Earth

Structures

and

Foundations in

Japan .

Seed,

H.

B.

and

R.

V.

Whitman

(1970):

Design

of

Earth

Retaining

Structures

for

Dynamic

Loads .

ASCE Speciality

Conference

Lateral Stresses

in the

Ground and

Earth

Retaining

Structures.

13.

Standards

Association

of

New

Zealand

(1965):

NZS 1900

•del

Building.Bylaw

Chapter

8

Basic Design

Loads .

14.

N.Z.

Ministry

of Works

(1972):

Highway

Bridge

Design

Brief .

Issue B

with amendments

to

July

1973

or

Issue C

(metric

version).

15. Bowles, J. E.,

(1968):

Foundation

Analysis and

Design .

McGraw-Hil

Book CO.

16.

Meyerhof,

G.

G.

(1951):

The Ultimate

Bearing Capacity

of

Foundations

Geotechnique Volume

II.



17.

18.

19.

20.

21.

23.

Meyerhof,

G.

G.

(1953):

The

Bearing

Capacity

of

Foundations

under

Eccentric

and Inclined

Loads .

Proc.

3rd

International

onference

on

Soil

Mechanics

and

Foundation

Engineering.

Meyerhof;

.G.

6.

(1957):

The

Ultimate

Bearing

Capacity

of

Foundations on

Slopes .

Proc.

4th

International Conference

on

oil

Mechanics

and Foundation

Engineering.

Meyerh0f,

G.

G.

1963):

So6e

Recent

Research

on

the

Bearing

apacity

of

Foundations .

Canadian

Geotechnical

Journal,

olume

1,

No...].

Standards

Association

of

New

Zealand

1970):

NZS

3101P

Code

of

ractice

for

Reinforced

Concrete

Design .

American

Concrete

Institute (1971):

Building

Code

Requirements

for

einforced

Concrete

(ACI

31•-71) o

Urquhart,

L. C.;

C.

E.

O'Rourke;

and

G.

Winter

1958):

Design

of

oncrete

Structures .

6th

Edition.

McGraw-Hill.Book

Co.

Fergus0n,

P.

M.

(1958):

Reinforced

Concrete

Fundamentals .

2nd

dition.

John

Wiley

and

Sons.

Evans,

E.

P.

and

B. P.

Hughes

(1968):

Shrinkage

and

Thermal

racking

in

a

Reinforced

Concrete

Retaining

Wall .

Proc.

nstitution

of.

Civil

Engineers,

Volume

39.

Tschebotari0ff,

G.

P.

1965):

Analysis

of

a

High

Crib

Wall

Failure .

roc.

6th

International

Conference

on

•oil

Mechanics

and

oundation

Engineering.

Br0ms,

B.

B.

and

I.

Ingels0n

(1971):

Earth

Pressure

against

the

butments

of

a

Rigid

Frame

Bridge .

Geotechnique

Vol.

21,

No.

1.

Hansen,

J.

B.

1970):

A

Revised

and

Extended

Formula

for

Bearing

apacity

'';--

-The-Danish'Geotechnical

Institute,

Bulletin

No.

28.

Cullen,

R. M.

and

I.

B.

Donald

(1971):

Residual

Strength

etermination

in

Direct

Shear .

Proc.

Ist

Australian-New

Zealand

onference

on

Geomechanics.



1

2

3

4

5

6

7

8

9,

10

11.

12

13

14

15

16.

17

18

19

2O

21

22

¸23

24

25

26

28

29

APPENDIX

II

FIGURES

Loading

on

typical

retaining

wall

Rankine

earth

pressure,

cohesionless

soil,

constant

backfil

slope

•Rankine

active

earth

pressure

coefficients

Coulomb.

earth

pressure,

cohesionless

soil•

constant

backfill

slope

Coulomb

active

earth

pressure

coefficients,

@

25

Coulomb

failure

plane for

active

pressure,

cohesionless

soil

with

uniform

slo•ing

backfill

Rankine

earth

pressure,

soil

with

cohesion,

horizontal

ground

surface

Trial wedge

method,

cohesionless

soil

Trial

wedge

method,

cohesionless

soil,

Culmann s

construction

Trial

wedge

method,

soil

with

cohesion

Trial

wedge

method,

layered

soil and

pore

water

pressures

Approximate

method

for

direction

of

Rankine

earth

pressure

Point of

application

of

active

pressure

Point

of

application

of

resultant

pressure

and

pressure

distribution

Braced

excavation

pressure

distributions

Mononobe-Okabe

earthquake

earth

pressure

Active

earthquake

earth

pressure

coefficients

for

pressure on a

vertical

plane,

@

25

°

Active

earthquake

earth

pressure

coefficients

for

pressure on

a

vertical

planes @

3•

Active

earthquake

earth

pressure

coefficients for

pressure on a

vertical

plane,

35

°

Active

earthquake

earth

pressure

coefficients

for

pressure

on a

vertical

plene,@

40

°

Active

earthquake

earth pressure coefficients

for

pressure

on

wall

with

B

•14

°

@

25o

Active

earthquake

earth

pressure

coefficients

for

pressure on

wall

with

B

-14

°

@

30

°

Active

earthquake

earth

pressure

coefficients for

pressure on

wall

wi•h

B

= 14

°

@

35

°

Active

earthquake

earth

pressure

coefficients

for

pressure

on

wall

wlth

B

-14

°

40

°

Earfhquake

loading,

trial

wedge

method,

soil with

or

without

cohesion

Uniform

surcharge

load

c ses







RANKINE

EARTH

PRESSURE:

:'Io

H ESI

O

NLESS

SO•L

,

CONSTANT

BACKFILL

SLOPE:

•• - -.

FAILURE

PEANES

FOR

•

RANKIN•

•CTIVE

STATE

•

PRESSURE

ON

VERT

LANE

The

followin

9

equations

require

That

The

each

pressure

acts

af

he

backfi

1.

ACTIVE

PRgSSU•

H

•

PA

KAY

•

KA

cos

•

(cos

•

/•os

2

•

T

cos

2

eA

45

•

¢/2

•(•-•)

where

sin

•

•wifh

O<

•

<90

°

For

m

0

KA

•I-

sln

¢

÷

sin

¢

PASSIVE

PRESSURE

H

2

p

Kp

y

•

•A

45°

•/2

Kp

cos

•

2

•

cos2

)

ap

45

° ¢/2

½

•)

Note

the

angle

between

the

failure

planes

for

the

passive

pressure

case

is

90

°

•.

sin

s•

ep

45

°

•/2

For

•

0

Kp

sin

¢

FFI

GURE

2.



R NKINE

CTIVE

E RTH

PRESSURE

COEFFICIENTS

FOR

COHESlONLESS

SOIL

WITH

UNIFORM

SLOPING

BACKFILL.

PRESSURES

ON

A

VERTICAL

PLANE :

0 90

0

-80

H

PA

•

H2

KA

cos •

7(COS

z

•

cosZ

¢) .

0.50

0 30

0

°

5

°

10

°

15

°

BACKFILL

SLOPE

20

°

25

°

50

°

IFIGURE



COULOMB

EARTH

PRESSUR

COHESIONLESS

SOIL

CONSTANT

BACKFILL

SLOPE

•umed

fa•ure

plane

B

•---- i'•e,•

°

•

actual

failure

surface

FAILURE

WEDGE

FOR

AgTIVE

STATE

ACTIVE

PRESSURE

ON

BACK

OF

WALL.

The

following

equations

give

only

an

approximate

solution

for

the

earth

ressure

when

static

equilibrium

is

not

fully

satisfied.

The

departure

rom

an

exact

solution

is

usually

very

small

for

the

active

pressure

case

but

passive

resistance

may

be

da.ngerously

overestimated°

ACTIVE

PRESSURE

H•

cos

2

(•-IB)

cos(•+•)

•

(e-•)J-

cot

C•A-•)

-tan

(•+•+•-•)

+

sec

(•+•+•-•)

•

(•+6)

sin

(•+6)

cos

(•-•)

sin

(•-m)

If

the

pressure

su.rface

AB

is

projected

on

to

a

ve•ical

plane,

the

pressure

per

unit

of

ve•

cal

distance

at

a

ve•ical

depth,

y

below

the

top

of

the

wall

is p'

K

A

y

y.

for 6

m

and

•

O,

K

A

•

Rankine s

value.

PASSIVE

PRESSURE

Pp

I<p

T

2

Kp

cos•

•cos

(•+B)•1

L cos(•+8) cos(m-•)J

for

6

•

and

6

0,

Kp

•

Rankine s

value

FIGURE



COULOMB

ACTIVE

EARTH

PRESSURE

COEFFI.CIENTS

COHESIONLESS

SOIL

WITH

UNIFORM

SLOPING

BACKFILL

0;8

0 5

0.4.

0.:5

0.2

20

I0

BACKFILL

SLOPE

0

I0

20



Wt ILUIVI•

CTIVE

EIARTH

FOR

COHESIONLESS

SOIL

WITH

UNIFORM

SLOPING

BACNFILL.

0 9•

1-20

-I0

CKFILL

,0

SLOPE

I0

20

D

°

6



r

COULOM

ACTIVE EARTI4

PRESSURE

COEFFI.C E NTS

FOR

COHESIONLESS SOIL

WITH

UNIFORM

SLOPING

BACKFILL.

•=

55

°

0"9

0"7

0; 2

20

-I0

BACKFILL

0

SLOPE

I0

20

50

40

I

GLIIE

7



CuuILoMB

ACTIVE

EARTH

PRESSURE

COEFFIICtENTS

FOR

CONESIONLESS

SOIL

WITH

UNIFORM

SLOPIN

BACKFILL.

K

O

20

iO

BACKFILL

O

IO 20

SLOPE

.D

°



COULOMB

FAILURE PLANE

COHESIONLESS

SOIL

WITH

BACKFILL

OR ACTIVE PRESSURE

UNIFORM

SLOPING



•ANKINE

E RTH

PRESSURF

•OIL

WITH

COHESION

•ORIZONTAL

GROUND

SURFACF

A'

_Tension

zone

•

7]

/.j•

°

neglected.

i i

.

/

A

•-

KAY(H-y

J

FAILURE

PLANES

FOR

PRESSURE

ON

VERTICAL

ANKINE S

ACTIVE

STATE

PLANE

A-A

Water

pressure should

also

be

added

on

ALA

..

ACTIVE

PRESSURE

PA

½KA

•

(H

yo 2

sin

{

Yo

2•c

tan

(450

+

{

unit

pressure at

depth

y

below

top

of

wall,

p

KA

y(y

Yo

PASSIVE

PRESSURE

unit

pressure

at

depth

y

below

top

of

wall

p

Kp

y

y

+

2c/•

The

angle

between

the

failure

planes

for

the

passive

case

is

90

°

+

4-

FIGURE

I0



TRIAL

WEDGE

METHOD

.COHESIONLESS

SOIL

IRREGULAR

GROUND

SURFACE

A

FORCES

ACTING

ON

WEDGE

FOR

ACTIVE

AND

PASSIVE

STATES

NOTES

FORCE

TRIANGLE

ACTIVE

(FULL

LINES)

PASSIVE

(DOTTED)

i.

The

lateral

earth

pressure

is obtained

by

selecting

a

number

of

trial

failure

planes

and

determining

corresponding

values

of PA

(or

.Pp).

For the

active

pressure

case,

the

minimum

value

of

PA

is

required.and

for the

passive

case,

the

maximum

PD

is

required.

These

.. limiting

values

are

obtgined

by

interpolating

between•

the

values

for

the

wedges

selected

2.

Culmann s

construction

(figure

12)

may

be

used to

determine

the

maximum value

of

PA

and

critical

failure

plane

for

cohesionless

soils.

•

3.

Lateral

earth

pressure

may

be

calculated

on

any

surface,

or

plane

hrough

the

soil.

4.

See clauses

3.3.1

to

3.3.4

for

the

direction

of

the

earth

pressure

-5..

See

figure

16

for

the

point

of application

of

PA

6.

T•etrial

wedge

method

ma•

also

be

use

for

a

level

or

constantly

loping

ground surface,

in which

c se

it should

yield

the

same

result

as

that

given

by

Ran.kine s

or

Coulomb s

equations,

whichever

is

applicable.

GUR

EI

II



I T IIR

A

L

WEDGE

COHESIONLESS

CULMANN S

METHOD

SOIL

CONSTRUCTION

FOR:

STATIC

EARTH

PRESSURE

ONLY)

Failure

Plane

D

Pressure

Surface

c

4

W

PROCEDURE

I.

Draw

line

A-G

at

an

angle

of

{o

to

the

horizontal

for

active

pressure

2.

Draw

trial

wedges

ABCDI,

ABCD2,

etc.

a

minimum

o•

four

will

usually

uffice.

3.

Calculate

the

weights

of

the

wedges

say

wl

w•,

etc.,

and

plot

these

to

a

suitable

scale

on

A-G,

each

measured from

A.

4. Through

Wl,

w

etc.,

draw

lines

at

an

angle

•,

(see

text

for

direction

f

PA

and

hence

6),

to

intersect

A-l,

A-2,

etc.,

at

H,

J,

et•.

5.

Draw

a

urve

through

A,

H,

J,

etc.

6.

PA

is

obtained

by

drawing

a

tangent

to

the

curve,

parallel

to

A-G

tO

touch

at

T.

PA

is

the

line

W-T,

to

the

sa•e

scale

as

w•,

etc.

7.

The

failure

plane

is

the

line

through

A

and

T.

, ¸

FF GURE



TRIAL

WEDGE

METHOD SOIL

WITH

COHESION

IRREGULAR

GROUND SURFACE

surface

.on

which

pressure

is

coloulo ed..

-,x&

/

7

/

2

3

/

/

/

/

NOTES

TRIAL

WEDGES FOR

ACTIVE

PRESSURE

.PA

FORCE

POLYGON

FOR

TYPICAL

WEDGE.

yo

Depfh

of

Tension

zone

2c

tan(45o+•}

COMBINATION

OF

FORCE

POLYGONS

TO

OBTAIN

MAX.P

A

The

above example

show

Rankine•s

conditions

But

the

s me

principle

applies

for

CoUlomb's

conditions.

Adhesion

on

the

back of the

wall

ignored .

For

direction

of

PA

see

figure

15

(Rankine's

conditions)

or

figure

16

(Coulomb's

conditions .

3.

See figure

16

for point

of application.

See

figure

17 for

resultant

pressure

diagram.

5.

The

trial

wedge

method

may

be used for

a

level

or

constantly

sloping

ground

surface.





tt J





POINT OF APPLICATION

OF

RESULTANT

PRESSURE

AND PRESSURE

DISTRIBUTION

surcharge

B

.///

A

TRIAL

WEDGES

h

B

A

PRESSURE

ON A-B

Use

when

t•e

ground

surface is

very

irregular

or

when

a

non-uniform

surcharge

is

carried.

PROCEDURE

.1.

Subdivide

th•

l•ne

A-4 into

about 4

equal

parts h

I

below

the

depth

Yo

of

tension cracing).

Compute

the

active

earth

pressures

PI;

P

P3'

etc.

as

if

each

of

the

points

I, 2, 3,

etc.,

w r

the base

of

the

wall.

The trial

wedge

method

is

Used

for

each computation.

Determine

the

pressure

distribution

by

working

down

from

point

4.

A

linear

variation

of

pressure

may

be assumed between

the

points

where

pressure

has

been

calculated.

Determine

the elevation

of the

centroid

of

the

pressure

diagram,

•.

This

is

the approximate

elevation

of

the point,

of

application

of

the

resultant

earth

pressure

PA

FIGURE

17



BRACED

EXCAVATION

DEFLECTED

/

/

•F ILURE

SURFACE

POSITION

PRESSURE

DISTRIE UTION;3

H

EXCAVATION

I N

CLAY

The

above

apparent

pressure

diagrams

may

b•

used

{or

determining

the

s•r,.,

oads

in

braced

excavations.

EXCAVATION

IN

SAND

Area

abcd

is

the

pressure

distribution.

acts

at

0.50

H

above

the

base.

See

figures

5

to

8

for

K

A.

EXCAVATION

IN

CLAY

The

resultant,

PH

0.65

K

A

y

•:

Area

abcd

is

the

pressure

distribution,

The

shape

of

this

diagram

he,magnitude

of

the

pressures

depend

on

the

value

of

the

stability

umber

Ns

yH

C

PH

2<:,

N

s

•<

5

5<

N

s

.75

H

PH

87

H

O'4 /H

'TH-4

C

°25H

0

50H

-75H

50H

.4Z•H

lO<Ns<

20

20<Ns

'(1.25-

-O38Ns)Hp

H

,SH

PH

•'H- (8-

.•.N

C

qrH

O

O

(1 5-'075

N

s

)H

0



MONONOBE-OKABE

EARTHQUAKE

EARTH

PRESSURE

COHESIONLESS

SOIL

CONSTANT

BACKFILL

SLOPE

H

A

FAI

L U RE

EARTHQUAKE

PLANE FOR

LOADI

N

G

ACTIVE EARTHQUAKE

PRESSURE

ON A B

ACTIVE

PRESSURE

PAE

½

KAE

Y

H2.

cos

2

(q-B-e)

l

(•os(a+•+0)

cos(•-•)J

e

tan

-1

CF

CF

E•L•I•-

•f

•AE-•)'=

-tan

(•+•+•-•)

•

sec

C•+•+•-•)

cos

•+•+e) sin (•+•

cos

p-•9

sin

NOTES

1.

The

above

equations

re

based

on a

resolution

of the forces

acting

on

awedge

of

soil.

The

effect

of

an

earthquake

is

represented

by.a

static horizontal

force

equal to

the

design

seismic

coefficient

times

the

weight of

the wedge.

2.

Where

the

earthquake

earth

pressure

is

calculated

on a

vertical

plane

through

the

re r

of the

heel,

B is

zero

and •

is equal

to

•.

3.

For

the determination of the point

of

application

of

PAE, the

total

active

earthquake

pressure

is divided

into

two

coEB•ents,

PA

from

static loading)

and the

dynamic

increment,

•'APAEi=

PAE

PA

PA

is

applied

at

I/3H

up

the

wall

and

•PAE

at

2/3•LG•;the-'•all.

The point of application of PAE is then calculatedby

taking

moments,

and the

pressure

diagram

is determined

accordingly.

FIGURE

19



ACTIVE

EARTHQUAKE

EARTH

PRESSURE

COEFFICIENTS

FOR

COH[-SIONLEoS

SOIL

_1 2

UNIFORM

SLOPING

BACKFILL.

PLANE

KAE

.0-3.

-20

0 25

0-20

I

0ol5

i

O-IO

J

0

-05

IO

O

B,4CKFILL

SLOPE

• °

IO

WITH.

LT.L

2O

FIGURE

30



ACTIVE

EARTHQUAKE

EARTH

PRESSURE

COEFFICIENTS

FOR

COHESIONLESS

SOIL

UNIFOR[VI

SLOPING

BACKFILL

•ITH

PRESSURE

ON

VERTICAL

PLANE

KAE

• 20

10

0

I0

20

30

4.0

0

BACKFILL

SLOPE

•

FIGURE

2



ACTIVE

EARTt4QJAKE

EARTH

PRESSURE

COEFFICIENTS

FOR

COHESIONLESS

SOiL

WITH

UNIFO - IL

SLOPING

BACNFILL

PRE_• _SUR'•::

011

VERTICAL

PLANE

0o6

IO-

SLOI•E

•°

20

•0



ACTIVE

E RTHQU KE

E RTH

PRESSURE

COEFFICIENTS

FOR

UNIFORM

SLOPING

PRESSURE

•

H

COHESIONLESS

SOIL

BAC KF

LL

ON

VERTICAL

PLANE

WITH

-I0

0

I0

BACKFILL SLOPE

.0

°

2O 30

40



ACTIVE

EARTHQUAKE

BACK

FIL

I

EARTH

PRESSURE

..C.OEFFICIENTS

FOR

COHESIONLESS

SOIL

WITI•

UNIFORM

SLOPING

PRESSURE

ON

WALL

WITH

14°

•

=

25°

H

K

E

-I0°

0

BACKFILL

SLOPE

20

°

50

°

FIGURE

2





.ACTIV

E RTHQU KE

E RTH

PRESSURF

COEFFICIENTS

FOR

COHESIONLESS

SOIL

FORM

SLOPING

BACK

FILl

PRESSURE.

ON

WALL

WITH

WITH

0 1

20

°

-I0

°

BACKFI

LL

0

I0 °

SLOPE

•

°

20

°

30

o

FIGURE

26



r

ACTIVE

EARTHQUAKE

EARTH

PRESSURE

COEFFICIENTS

FOR

COHESIONLESS

SOIL

WITH_

UNIFORM

--SSURE

SLOPING

BACKFILL_

ON

WALL

WITH

,•

-14 °

-20

°

qO

°

BACKFILL

SLOPE

I0

°

•°

50

°

[FIGUR

27



EARTHQUAKE

LOADING

TRIAL

WEDGE

METHOD

SOIL

WITH

OR

WITHOUT

COHESION

IRREGULAR

GROUND

SURFACE

2 5

4

5

CFW

FORCES

ACTING.

ON

•

TRIAL

WEDGES

FOR

/

Z

EARTHQUAKE

•

M•X.PA

E

PAE

FORCE

POLYGON

FOR

TYPICAL

WEDGE

2

\•CFW

COMBINATION

OF

•CX

FORCE

POLYGONS

TO

OBTAIN

MAX.

PAE.

The

ab ve

example

is

drawn

for

Rankine's

conditions

but

the

principle

pplies

also

for

Coulomb's

conditions.

For

direction

of

PAE

s

figure

15

(Rankine's

conditions)

or

figure

16

Coulomb's

conditions).

For

construction

of

pressure

diagram

and

point

of

application

of

resultant

see

figure

9• also

clause

4.3.3

for

cohesive

soils.

For

cohesionless

soil

the

vector

c

x

is

omitted

from

the

force

olygons,

iFIGUR

28





d

_

Z

Z

Z



I 00

m

R

//

0-4.

-60H

R

0.5

.•6H

•

o.•

.Ts

.59H

0.2

0.4.

0 6

0 8.

VALUE

OF

PQ

QL

For

m

S

0.4

0.20n

PQ(

(0.16

+

n2) 2

PRESSURES

LINE

LOAD

PQ

0.55QL

For m

>

0.4

FROM

1.28m2

n

QL

pQ •L

)

(m

2

+

n2)2

0.64q

L

•__

PQ__=__

m•

+

PQ

=

KA

QL

FROM

LINE

FORCE

LOAD

QL

(approx.

method

for

low

retaining wails)

LINE

LOAD

0 5..60

.54H

0 6 -46

48H

5

1 0

1'5

H

2

VALUE

OFPQ

(•)

For

m

_ <

0.4

d

p^•

H2)

0.28n2

q'Qp

(0.16

+

n2) 3

For

m

>

0.4

H

2

1.77m2n

2

pQ •-•-•)

(m2

+

n2)

3

E m

H

SECTION

A-A

p'Q=pQ

cos

2

(l.10a)

PRESSURES

FROM

POINT

LOAD

Qp

POINT

LOAD

LATERAL

PRESSURE

DISTRIBUTION

ON

WALL

TO

POINT

AND

LINE

LOADS

DUF

IFIGURE

31



0

.

o|

•• -

•

I,O

l .

o..

•/•o_•o

•

.0

O t

O

•:;

¢0

,•

•

0

1--

6

o

6

6

2

0

0

z

0

0

0 0

z

H

•J.,z4/n

OI.LV•I

LU



]

Z







TYPE

OF

WALL

GRAVITY

SEMI

GRAVITY

CANTI

.EVER

COUNTER

FORT.

LOAD

DIAGRAM

7

TOE

STABILITY

CRITERIA

FOR

RETAINING

STABILITY

CRITERIA

SLIDING

S

(W

t

+ pv

tan

6

b

+

CbB

Fs

(sliding)

S

+

p

PH

•

1.5

(static

loading)

or •

1.2

(earthquake

loading)

OVERTURNING

Moments

about

the

toe

of

the

base

Fs

(overturning)

Wt

a

+

Pv

f

PHb

•

2 0

(static

loading)

or

•

1.5

(earthquake

loading)

Also

check

overturning

at

selected

orizontal

planes

up

the

wal

for

gravity

type

walls.

BEARING

PRESSURE

Point

where

R

w

intersects

base,

rom

toe,

d

Wt

a

+

Pv

f

PHb

Wt

+

Pv

assuming

pp

0

For

soil

foundation

material,

d

should

be

within

middle

third

of

the

base

(static

loading)

or

middle

hal#

(earthquake

loading).

For

a

rock

foundation,

d

should

be

ithin

middle

half

for

both

static

and

earthquake

loading.

Fs

(bearing)

•

3.0

(static

loading)

r •

2.0

(earthquake

loading).

See

section

7.4

for

calculation

of

actor

of•safety

for

bearing.

W

t

total

•eight

of

the

wall

in-

cluding

soil

on

toe

plus

soil

bove

heel

(for

cantilever

and

counterfort

walls

only)

v

vertical

component

of PA

H

horizontal

component

of

PA

w

resultant

of

W

t

and

PA

IWALLS

36



SHAPE

FACTORS

s

c

+

0.2 N@

B/L

Sq)=

1.00 for

@

0

sy)

I

+

0.1

N@

B/L

for

For

continuous

strip

footi.ng

s

c

=.Sq

sy

1.0

DEPTH FACTORS

for

D/B

<

d

c

+

0.2•

D/B

dq)

ii.00

for

•

0

dy)

I

+

0.1

N•r•@

D/B,

fob

@

>

10

o

t•O•: Ny=O

for

•=0

5 I0 15 20

25

50

55

40

ANGLE

OF

INTERNAL

FRICTION,

•,

DEGREES

N@ =

tan

2

45

°

+

3

L FOOTING

LENGTH

D

| •

=•D

ASSUMED

CONDITIONS

i.

2.

3.

5.

D

•

B

Soil

is

uniform to

a

depth

do

>

B

Water

level

is

lower than

d

o

below

the base

of

the

footing

The

applied

load is vertical

and concentric

Friction

and

on

the vertical

sides

of the

footi,ng

are

neglected

ULTIF•TE

BEARING

CAPACITY

qult

E-Q--=BL

cNc

sc

dc

+

•

Nq

Sq

dq.

+

½

X

B Ny

sy

dy

BEARING

CAPACITY

OF SHALLOW

FOOTINGS

WITH CONCENTRIC LOADS

FIGURE

57



INCLI

20•

Z

<

I00

'

I0

20

•-0

60

80

NATION

OF

LOA__D

•

DEGREES

Q=

total

inclined

load

•B

HORIZONTAL

BASETINCtclNED

ECCENTRIC

LOAD

NOTES

]

Calculate

effective

base

width

B

=

B-2e

;2

Obtain

Nyq

and

from

chart

above.

Ncq

3.

Vertical

component

of ultimate

bearing

capacity

quit v)

CNcq

+

½yB

NTq

4.

Bearing

pressure

from

vertical

component

of

applied

loading

qCv)

B

qblt(v)

s

•(v)

BEARING

CAPACITY

6

0

20

40

60

80

INCLI______NATION

OF__FOOTING

@

DEGREE•

q=

normal

pressure(load/area)

INCLINED

BASE

WITH

NORMAL

LOAD.

NOTES

1.

Obtain

and

from

chart

bove.

Nyq

Nc

q

2.

Ultimate

bearing

capacity

qult

-=

CNcq

+.½yB

Ny•

3.

Fs

qul•t

q

FOR

AN

INCLINED

LOAD

HIGHER Q

ULT.

IS

OBTAINED

WITH

AN

INCLINED

BASE,

A

FOR.

INCLINED

LOADS

FIGURE

38



roundel/on

depth/width

3 B=O

Linear

interpolation

lot

termed[ale depth•

4O

0

tO 20

30

40

50

Incliner;on of •lope

e•

FOUNDATION ON

FACE

OF

SLOPE

In

general

qult

cNcq

+

½yBNyq F

S

qult

q

for

0

quit

CNcq

+'YD

BEARING

DIB

lactarNs

I

0

2

3

4

5

D•slonce

of

[oundel•on

from

edge

of Slope

9/B=I

•

Linear

interpolation

0

Dislance

of

[oundat•on

[ram

edge

of

FOUNDATION ON

TOP

OF

SLOPE

@OEE: The

charts

given

are

for

vertical loading.

The base

Ns

xH

wldth

is

reduced

for

eccentric

c

loads.

CAPACITY FOR

FOUNDATIONS ON

SLOPES

FIGURE

•B



TOE

MOMENT

EFFECT

ON

HEEL

The

toe

support

moment

produces

a

oading

on

the

heel.

If

it

is

assumed

that

no

moment

is

trans-

i.tted

into

the

stem,

an

equivalent

arabolic

heel

loading

is

as

shown

elow,

with

the

maximum

ordinate

iven

by

Pt

2.4

MT/a2

where

M

T

is

the

toe

support

moment.

WEIGHT

OF

BACKFILL

BOVE

HEEL

SELF

WEIGHT

OF

HEEL

LOADING

FROM

TOE

MOMENT

SSUMED

FOUNDATION

BE RING

PRESSURES

VE

RESULTANT

LOADING

ON

HEEl_

May

be

fully

positive)

Note:

Pressure

diagrams

not

to

scale.

D__ESIGN

LOADING

ON

HEEL SLAB

FIGURE



SSUMED

45

°

CRACK

LINE

FROM

B.

ASSUMED

a,5•

CRACK

LINE

F•

A.

ANCHORAGE

LENGTH

EQUIVALENT

jd

FOR

B

AT

B.

45

o

A

MOMENT

EQUIVALENT

jd

FOR

MOMENT

AT

A.

MAIN

TENSILE

STEEL

'IN

COUNTERFORT.

Point

of maximum

mor•nt (maximum

allowable

stress

in

all

main

tenslle

rein

forcement).

B Section

of

lesser

moment

than

at

Ao

If

some

of

the

reinforcing

bars

of

the

main

tensile

steel

were

eliminated

then

there

would

be

maximum

allowable

stress

in

the

remainin

9

bars.

The

Icut

off

position

for

some

of

the

bars

of

the

main

tensile

reinforcement

is

to

be

the

greater

of:

a)

Anchorage

I-•h• •

the-•ssumed

45

°

crackline

from

A.

b)

12"

past the

assumed 45

°

cracked

li•e

from

8.

'jd'

c n

be

taken

as

the

perpendicular

distance

from

the

centroid

of

the

steel

to the

midpoipt

of

the

stem

slab.

'CUT

OFF'

POSITIONS

OF

MAIN

TEN,SIL_F•

STEEL

IN

COUNTERFORT

FIGURE.





SINGLE

W LL

DOUBLE W LL

TRIPLE W LL

25

ASSUMPTIONS

Soil Properties

•

30

°

c O

y

125

Ib/ft

3

Wall

Properties 8 20

°

W

w

=

I00

Ib/ft

3

Wall Slope

B

14

°

I

in 4)

Water

table below

base of

wall

Live

load

surcharge

equal

to

2

ft.

F

s

sliding)

1.5 min

I0

0

5

i0

15

20

BACKFILL SLOPE

•°

FIGURE

4-:5



CRIBWALL

DESIGN

CURVES

NORM L

LOADING

=40

°

see

figure43for

diagrams

ASSUMPTIONS

Soil

PropePfies

•

40

°

c=O

T

125Ib/ft

3

Wall

•roperties

6

26.6

°

W

w

100

Ib/ft

3

Wall

Slope

•

-14° I

in

4)

Water

table

below

base

of

wall

Live

load

surcharge

equal

to

2

ft

f

soil

included

Fs

sliding)

1.5

min

Fs

°verturning)

2.0

min

5

I

15

BACKFILL

SLOPE,•°

2O



SINGLE

WALl-.

DOUBLE

W LL TRIPLE WALL

ASSUMPTIONS

15

I0

Soil Properties

{

30

°

•

125

Ib/ft

3

Wall Properties 6

20

°

W

w

100

Ib/ft

3

Wall

Slope

•

-14

°

I

in

4

Water

table

below base

of

wall

F

s

sliding) 1.2 min

F

s

overturning)

1.5

min

15 20

SLOPE

•0

°

|FIGUR



CRIBWALL

DESIGN

CURVE£

_EARTHQUAKE

LOADING

SEISMIC

COEFFICIENT

0•20

See

figure

4.5

for

diagroms)

ASSUMPTIONS

•oil

Properties

Wall

Properties

•

40

°

c

0

y

125 Ib/ft

3

6

26 6

°

W

w

I00 Ib/ft

3

Wall

Slope

•

-14

°

I

in

4)

Water

table

below

base

of

wall

Fs

slidi.ng)

1.2

min

Fs

Overturning)

1.5

min

Documents

Notes for Retaining Wall Design