Maria M

avro

ulidou, 2

014

1

The principle of

Effective Stress

Karl Terzaghi

(1883-1963)

All measurable

effects in soils

are associated

with changes in

effectivestress

Maria M

avroulidou, 2

014

Maria M

avro

ulidou, 2

014

2

Lecture Plan

Defin

itions

The concept o

f effe

ctiv

e

stress

Pore pressure

Effe

ctiv

e stress calculatio

n

Effe

ct o

f static

water above

ground level

Effe

ct o

f capilla

ry rise

Summary

Maria M

avro

ulidou, 2

014

3

Questio

n

uw

uw

w

W,

If stress has not changed in problem

2, why these

changes in the soil?

Problem

1

Problem

2

Maria M

avro

ulidou, 2

014

4

Defin

itions

Total Stress

Force

CrossSectio

nalArea

=

Effective stress

wu

'=

Note:

The dash is not optional !!!!!!

The effective stress cannot be m

easured directly,

it is calculated by Eqn (2)

Since, according to Terzaghi soil behaviour

(strengths and deformations) is related to effective stresses

it is important to decide if stress is total or effective

where

uw

: Pore w

ater pressure , i.e. the pressure of the water

in the pore spaces

(2)

(1)

Maria M

avro

ulidou, 2

014

5

The concept o

f effe

ctiv

e stress

is transmitte

d by:

1)Interpartic

lecontacts

2)Pore water pressure actin

g in

pore voids (of equal intensity in all directions)

uwarising in pores does not

contribute to

the soils

shear

resistance =>(neutral)

Only 1) gives m

echanical resistance

to shearing=> effe

ctiv

e in

mobilisin

g sh

ear resistance

govern

ing vo

lume ch

ange /d

eform

ation

Maria M

avro

ulidou, 2

014

6

What is

effe

ctiv

e stress?

=

N

A=PA

A

Aw =

area of water (w

hile A is total area)

A

=N

A

PA+uw

=

+uw

The particle contact area is relatively very sm

all A~

Aw

For equilibrium

normal to x-x: Load P

=

N+

uw A

Particle contact area A

s

We can represent

the principle as:

Maria M

avro

ulidou, 2

014

7

Answer

It is the norm

al force

carried by the soil skeleto

n,

divided by the w

hole

cross sectional area of the soil

It does not represent the exact contact stress between

particles but the distribution of load carried by the soil

solids (skeleton) over the cross-sect area considered.

ie:

It is the averageinterparticle

stress on the x-x plane

=>

not to be confused with intergranular

contact stress:

NB: T

he effe

ctiv

e stre

ss is a prin

ciple and

not a

law:

i.e. It is

an empiric

al, w

orking hypothesis

Effective stress cannot be m

easured directly=>

always

through uw

and m

easurements

Advan

tage o

f the p

rincip

le:in the lab there is no

need to apply field uw

and values.

Only the difference (

-u

w) needs to be considered

Maria M

avro

ulidou, 2

014

8

Now we can note th

at

uw

uw

w

W,

Maria M

avro

ulidou, 2

014

9

Pore pressure (1)

Reminder: soils contain water in

pores(voids)

Water exerts isotropic stress

(i.e

. the same in

all d

irectio

ns)

This is th

e pore pressure

Groundwater level

Ground level

hw

borehole

Groundwater level : level o

f water in

open

borew

hole

Pore p

ressure u

w = (level o

f water in

open

borew

hole)

x (unit w

eight o

f water)

uw = h

w

w g

=hw x

w

w =9.81kN

/m3

z

Maria M

avro

ulidou, 2

014

10

Pore pressure (2)

If th

ere is no flo

w, u

wis

hydrostatic

uw

uw 1

1.Piezo

meter: p

lastic tube m

easurin

g th

e pressu

re head

at a specific p

oint

Maria M

avro

ulidou, 2

014

11

Pore pressure (3)

Pore pressure m

ay not b

e

hydrostatic

Artesian pressure

e.g

. assum

e a

sand la

yer o

verla

in b

y c

lay

(clay confines sand as it has low perm

eability):

The level of w

ater in the borehole rises higher than

the layers surface (can be higher than ground surface)

Underdrainage (dow

nward flow

)

Pore pressure changes due to

external lo

ads (=>flo

w)

In th

is lecture we will m

ainly fo

cus

on hydrostatic

conditio

ns

Maria M

avro

ulidou, 2

014

12

Calculatio

n of T

otal V

ertic

al S

tress

Example: W

hat is

vat th

e base?

q v

z1

z2

zz

v= q

+

1z1+

2z2+

3( z -

z1 -z2)

Questio

n:

Which

are w

e talking about?

1.If so

il is totally

dry, =

d

2.If so

il is fully satu

rated =

sat

Maria M

avro

ulidou, 2

014

13

Calculatio

n of p

ore water pressure

Example: W

hat is

uwat p

oint A

?

Soil w

ith a static

water ta

ble

Uw(A

)=

w g

z =

w

z

Wate

r table

z

A

: uw= 0

Using hydrostatic

s prin

ciples,

water p

ressure at A

is:

w

:m

ass d

ensity

of w

ate

r

g: a

ccele

ratio

n d

ue to

gra

vity

w

: unit w

eig

ht o

f wate

r

Where:

Maria M

avro

ulidou, 2

014

14

Calculatio

n of v

ertic

al effe

ctiv

e stress

Example: W

hat is

vat th

e base?

2m

6m

wt

d

d =15.6kN/m

3

sat =

19.56kN/m

3

Maria M

avro

ulidou, 2

014

15

Pore pressure and stress profile

s

050

100

150

0m

2m

4m

6m

8m

kP

a

pore

wate

r

pre

ssure

Effe

ctiv

e

stre

ss

Tota

l

Stre

ss

Depth

Vertical stress an

d pore p

ressure v

ariation

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avro

ulidou, 2

014

16

Effe

ct o

f water above soil s

urface

(For hydrostatic

conditio

ns)

Questio

ns:

1. A sand of 20kN

/m3

lies under a 1m deep river. W

hat is the vertical effective stress 4m

below the top of the sand?

2. The N

orth Sea is 200m

deep. The sea bed consists of sand of

20kN/m

3. What is the vertical effective stress 4m

below the top

of the sand?

3. Consider a soil m

ass with the w

ater table at surface level. The

soil is a sand of 20kN/m

3. What is the vertical effective stress

4m below

the top of the sand?

uw

uw

Maria M

avro

ulidou, 2

014

17

Water ta

ble (w.t.)

:level at w

hich pore

pressure is atm

ospheric, ie

uw=0

Below th

e water ta

ble, p

ore pressures are

positiv

e.

Above th

e water ta

ble,pore pressure are

negativ

e: u

w= -

w*hc

Capilla

ry rise: th

e height a

bove th

e water

table to

which th

e soil is

saturated

Effe

ct o

f capilla

ry rise

uw=0

uw

uw

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ulidou, 2

014

18

Why is water rising above w.t.?

=>surface te

nsion

(visualise void spaces as capilla

ry tu

bes of

varia

ble cross-sectio

n)

The sm

aller the voids, the higher the capillary rise

in coarse sands: 0

.12-0.18m

in fin

e sands:

0.3-1.2m

in silts

:0.76-7.6m

in clays : 7

.6-23m

Effe

ct o

f capilla

ry rise

a) Rise of w

ater in capillary tube b) Pressure w

ithin the capillary rise height)

Maria M

avro

ulidou, 2

014

19

Effe

ct o

f capilla

ry rise

uw

z

2m8m

Assume

1.a soil la

yer where water ta

ble is at th

e

ground surface (fully saturated)

2.The same soil la

yer with

the water ta

ble

2m below ground surface, and a capilla

ry

rise of 2

m

In both cases, soil is

fully saturated.

Diffe

rence in to

tal stress= NONE (as unit

weight is

the same, ie

sat )

Diffe

rence in pore pressure:In 2, a reductio

n

by 20kN/m

2( w*2m).

This m

eans th

at effective stress is increased

by th

e

same am

ount, ie. b

y 20kN/m

2

Maria M

avro

ulidou, 2

014

20

Summary

To calculate th

e effe

ctiv

e stress in

hydrostatic

conditio

ns:

1. C

alculate to

tal vertic

al stress

Be careful about selectio

n of

if a

bove th

e saturated zone:

=

=

=

=d

if b

elow th

e saturated zone:

=

=

=

=sat

2. C

alculate hydrostatic

water

pressure:uw

=zw w

3. C

alculate effe

ctiv

e vertic

al stress:

=

=

=

=

z

=

=

=

=

uw

NB:T

he latter is not affected by static water above ground surface

Maria M

avro

ulidou, 2

014

21

Tutorial

Exercise 1

Aconfin

edaquife

rconsists

ofa5m

layerofsand

overla

inby

a4m

layer

of

clay.

The

sand

isunderla

inbyim

perm

eable

rock.Thewaterlevelin

astandpipedriv

eninto

thesandlayeris

3m

above

thesoil(clay)surfa

ce.Thebulk

unitweighsofthe

clay

and

sand

are

18kN/m

3and

20kN/m

3

respectiv

ely.

Determ

ine

the

vertic

al

effe

ctiv

estre

ssatthe

top

and

botto

mofthe

sand

layer.

(Take

w=9.81kN/m

3)

NB: In

this case th

e water in

the sand is

under

arte

sian pressure (ie

. not h

ydrostatic

)

(Answ

er: A

t the top of the sand:v =3.33kN

/m2

At the bottom

of the sand:v =54.28kN

/m2

)

Exercise 2

A la

yer o

f fine sand 3m th

ick overlie

s a th

ick clay

layer. T

he w

ater ta

ble is in

the sand, a

t a depth of

1.8m below th

e surfa

ce. In

the zone above th

e

water ta

ble th

e average degree of s

aturatio

n of th

e

sand is 70%. T

he porosity

of th

e sand is 35% and

its specific

gravity

is 2.65. T

he w

ater c

ontent o

f the

clay is 40% and its

specific

gravity

is 2.7. C

alculate

the vertic

al to

tal a

nd effe

ctiv

e stre

ss at a

depth of

6.7m below th

e clay surfa

ce. (T

ake w=9.81kN/m

3)

(Answ

er: total stress: 178.98kN/m

2 ; effective stress: 99.98kN

/m2)

Maria M

avro

ulidou, 2

014

22

Tutorial

Exercise 3

A soil profile consists o

f three layers. T

he soil is su

bject to

a uniformly distrib

uted load of q=80kPa. Layer I w

hose

depth is 3

m is fu

lly dry above the water ta

ble. Layers II

and III, w

hose depths are 3m and 6m respectiv

ely are

fully saturated, lying below the water ta

ble (i.e

. the w.t. is

at 3m below ground level).T

he properties of th

e three

layers a

re:

Layer I:

Dry unit w

eight

d = 17 kN/m

3

Layer II:

Saturated unit w

eight

sat=19.5 kN/m

3.

Layer III:

Saturated unit w

eight

sat =18 kN/m

3

Determine the pore pressure and the total and effectiv

e

stresses at 0m, 3m, 6m and 12m below the ground

surface. Ta

ke the unit w

eight of water

w=9.81 kN/m

3

Maria M

avro

ulidou, 2

014

23

Tutorial

Exercise 4

A soil profile consists o

f two layers: a

layer of silty

sand 5m

deep, underlain by a 4m layer of sa

turated clay. T

he

properties of th

e two layers a

re:

Layer I (silty

sand):

Saturated unit w

eight

sat=18.5 kN/m

3. Layer II (cla

y):

Saturated unit w

eight

sat =17.7 kN/m

3

Determine and plot th

e pore pressure and the total and

effectiv

e stre

sses against d

epth for th

e following two cases: a

) the water ta

ble is a

t the surface; b) th

e water ta

ble is a

t 2.5m

below surface but th

e silty

sand is sa

turated with capillary

water to

a height up to the soil su

rface. (Ta

ke w=9.81kN/m

3)

Exercise 5

A soil profile consists o

f two layers: a

layer of sa

nd 5m deep,

underlain by a 4m layer of sa

turated cla

y. The water ta

ble is

at 3m below the ground surface. The properties of th

e two

layers a

re:

Layer I (sa

nd):

Dry unit w

eight

d = 17 kN/m

3

Saturated unit w

eight

sat=20 kN/m

3.

Layer II (cla

y):

Saturated unit w

eight

sat =19 kN/m

3

Determine and plot th

e pore pressure and the total and

effectiv

e stre

sses against d

epth for th

e following two cases: a

) capillary rise

in the sand above the water ta

ble is n

egligible; b)

there is ca

pillary water to

a height of 1m above the water

table. (Ta

ke w=9.81kN/m

3)