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Mechanical Soil Properties

39

Chapter III

Mechanical Soils Properties

3.1.Compression and consolidation

3.1.1 Definition phenomena

Under load application due to buildings or other kinds of superstructures,

physical deformations of the subsoil will occur.

The nature and amount of deformation occurring is a function of not only

the applied load but also of the soil properties and time.

a) stiff structure b) elastic structure

Figure 3.1 Deformations of the soils

h

h

h

h

h

h

com

presion

com

presion

relaxation

relaxation

r r

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Chapter 3

40

The mechanisms will be evoked the deformations of soils are:

- volume changes due to the extrusion of pore air and pour water;- shear distortions producing particle and fabric unit displacement or yield

phenomena with or without measurable pore water extrusion and with

development of slip planes.

Compressibility describes the volumetric response behaviour of the soil

mass, and recent and common usage of the term has restricted it to describing

behaviour characteristics under compression.

The change in volume of a soil mass with time due to the extrusion of pore

water is said to be a process of consolidation

The overall load-volume change performance is identified as a stress -

strain -time phenomenon and can be called rheological behaviour.

3.1.2 The compression tests

The tests that characterise the soil deformations are:- Laboratory compressibility tests;- In situ tests (with plate).3.1.2.1 Laboratory tests

A one-dimensional consolidation process can be simulated in laboratory by

compressing a soil specimen in a special testing apparatus called oedometer or

consolidometer.

Porous stone

Soil specimen

Brass ring

Porous stone

Water level

Load

Dial gauge

Figure 3.2 Oedometer

This apparatus models the behavior of a soil volume at a certain depth

beyond the axis of a foundation.

The load is applied step by step and after the application of a certain load

one waits until the deformation due to this load stops.

The result of the oedometer test is plotted in the compression - settlement

curve. Compressibility tests of soils are carried out in devices with rigid walls

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41

(oedometers) in order to ensure that the soil is compacted in one direction only

(to prevent lateral expansion).

The relationship between moisture content and pressure can be represented

in the diagram which is called the compression curve (Figure 3.3).

0

p

p

p

p1 p2 logp(daN/cm )

1

2

M=tg p

2p

Figure 3.3 Compression-settlement curve

The mechanism will be evoked the deformations of soils are:

- volume changes due to the extrusion of pore air pour water- shear distortions

2 1

p2 p1

pM=

p p

h

h

I I(

!( (

[kPa] (3.1)

The compression curve can be easily reconstructed into void ratio

pressure coordinates (figure 3.4).

Result the compression void ratio curves (e p and e log p).

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Chapter 3

42

0 p

e

e1

e2

p1 p2

(1)

(2)

p

e

logp

e

av = - e p = - tg

a b

c

logp2logp1

ei

e

e

log (logp)

log( p+ i)

Cc = - tg =- e (logp)

(a)e - p

(b)e - log p

0

Figure 3.4Compression - void ratio curvey Coefficient of compressibility

0

v v 0

1(1 )

100a m (1 )

ee

ep p

I( (! ! !

( ( (3.2)

where: - Initial void ratio

p

h

h

Figure 3.5 Mechanical model

The correlation between pressure and void ratio can be deduced in the

following way.

For the sample having the transversal section equal to A and the volume

V, we can write:

V A h! (3.3)

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43

Loading this sample which the pressure p its volume will decrease.

(1 ) (1 )! ! ! VS V S S

S

VV V V V V e

V

(3.4)

where: V = total volume []

A= total surface []

Vs = volume of the skeleton []

Vv = volume of voids []

For the pressure p1, the volume results:

1 1 1 1(1 )! ! !

S SV A h V V V e (3.5)

1(1 ) (1 )

1 S S SV=V-V V e V e V e( ! ! (

(3.6)

1 11

1 1 1 1 1

- (1 ) - (1 )-

(1 ) 1

( (! ! ! !

h h s s

h s

A A V e V eV VV e

V V A V e e (3.7)

1 1 1

1 1 1

- 1 -1- -

1 1

! !

h h e e e e

h e e (3.8)

1

1 1

h

h 1

e e

e

(!

or 1 1

1

h h1

e e

e

( !

(3.9)

where:

1 2 1

1 2 1

h

h 1

e e p p

e p p

(!

(3.10)

1

1 2 1

2 1

h 1

1h

e e

e p p

p p

(!

(3.11)

Result:

v1v

2 1 1 1

a1 1m

1 1 M

e e

p p e e

! ! !

2cm

daN

-

(3.12)

The Compression Index Cc can be determined with relation:

1 2 1 2c

2 22 1

1 1

( ) ( )C

(log log ) log log

e e e e e

p pp pp p

(! ! !

(3.13)

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44

where: - are the void ratios at the end of consolidation under

pressures respectively.

The value of Cc can vary widely depending on the soil Skemton (1944) has

given an empirical correlation for the compression index in which:Cc=0.009 (LL-10) clay is normally consolidated (3.14)

where: LL liquid limit

The Swelling Index

The value of the swelling index, Cs, is in most cases, 1/4 to 1/5 of the

compression index. This is the slope of the unloading portion of the e log p

curve (figure 3.5) and can be defined as:

3 4

S4

3

( )C

loglog

e e e

p p

p

(! !

( ( (3.15)

3.1.2.2 In situ test

y The establishing of compressibility "in situ" with plateballast

rod

jack

loading platebench mark rods

Df

D

Figure 3.6 Loading plate

The test results are plotted in a diagram which contains:

- The variation of clear pressure (pn) functions of time;

- The variation of settlement (s) functions of time;

- The variation of settlement (s) functions of clear pressure.

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45

pl0

sl

p

s

pi0

si

p

s

pi-1 pi+1

si-1

si+1

Figure 3.7 - The establishing of the limit pressure of proportionality.

With this diagram, we establish the limit pressure of proportionality (p1)

until there is proportionality betweenp ands.

n ef f p p DH! (3.16)

- rigidity factorl

S

l

pk tg

sE! ! (3.17)

iS

i

pk tg

sE! ! (3.18)

1 11.5( )i i i i s s s s " (3.19)

- linear deformation module2

2

s

(1 ) DE=k D(1 ) l

l

p

s

R

R [

! (3.20)

[ = form factor

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47

Figure 3.8 The diagrams for the plate tests

3.1.2.3 General case of compression relationship.

In the general case, variations of void ratio, e, in compression depend not

only on the vertical normal stresses ZW , but also on horizontal stresses yW and

XW . Let us determine the sum of principal stresses in the case of a soil layer

being compressed without lateral expansion. From the condition of equilibrium

result:

z pW ! and x y p1

R

W ! W ! R (3.21)

xx y z

0 0

( )E E

W RI ! W W

and

x y 0I ! I ! (3.22)

Result:

x y 0k pW

!W

! (3.23)

where:0

k1

R!

R (3.24)

0k - is called the coefficient of lateral pressure of soil at rest

t x y z c3pW ! W W W ! . (3.25)

The sample is loaded one dimensional with an effort

2 3 oW ! W ! Increase until falling out. We measure the vertical () and

horizontal () maximum deformations and we plot the characteristic curves of

one dimensional compression. With these amounts we can establish:

1) The Poissons ratio:2

1

IQ

I! (3.26)

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Chapter 3

48

0

5

10

15

0,5 1,0p(daN/cm )2

1

2

(%)

v=1/m= 2/ 1

Figure 3.9 The characteristics curves of

one dimensional compression. Poissons ratio.

2)

In line deformation modulus (E), which has many forms:- tangent(or initial) modulus - - secant(or middle) modulus - (3.27)- hysteresis modulus -

0

p(daN/cm )2

(%)

p=p /3 p

l

r

s

h

r

E0=ctg 0

Es=ctg s

Eh=ctg h

cl c

Figure 3.10 In line deformation modulus

3.1.3 Consolidation refers to fully saturated clays, it means that the porepressures generated by compression are dissipated to reach finally the value of

zero. Consolidation is not the full extent of the compressibility of the clay under

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49

load since a further compression in time is generally recorded under the same

load.

This has been termed as secondary compression or secondary

consolidation, to distinguish it from the primary mechanism governing

consolidation behavior.

t1 t2 t3

S

t

I

II

III

extrusion of airchemical - colloidal

proceses and others

extrusion of water

primary

consolidation

secundary

consolidation

extrusion of air

secundary consolidation

primary consolidation

Figure 3.11 Phenomenon of consolidation

Casagrande graphical method determining the preconsolidation pressure:

Natural soil deposits can be:

- Preconsolidation pressure- Normal consolidation- Overburden consolidation3.1.3.1.Preconsolidation mechanisms

Based on laboratory tests, a graph can be plotted showing the variation of

the void ratio, e, at the end of consolidation against the corresponding stress

(e vs. log p).

During the laboratory tests, after the desired consolidation pressure is

reached, the specimen can be gradually unloaded.

This will result in the swelling of the specimen.Three parameters that will be necessary for calculation of the settlement in

the field can be determined.

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Preconsolidation pressure, pc , is the maximum past effective overburden

pressure to which the soil specimen has been subjected.

The procedure for determining de preconsolidation pressure using a

method proposed by Cassagrande (1936), has following steps (figure 3.2).

- Determine the point O on the (e log p) curve that has the highestcurvature;

- Draw a horizontal line OA;- Draw a line OB that is tangent to the (e log p)curve at O;- Draw a line OC that bisects the angle AOB;- Produce the straight line portion of the (e log p) curve backwards to

intersect OC (point D).

The pressure that corresponds to this point is the preconsolidation pressure,

pc .

101.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

100 400

Slope =C2

(e3,p3)

(e4,p4)(e2,p2)

Slope =C1

(e1,p1)

B

C

AD0

Pc

Pressure, p(kN/m)

V

oidratio,e

20 30 40 50 60 70 80 90 200

Figure 3.12 The diagram of the consolidation test

When , effective overburden pressure is equal to the

preconsolidation pressure, the soil is normally consolidated.

However, if the soil is over consolidated.

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Consolidation coefficient:2 2

50% 50%v

50% 50%

T H 0.197 HC

t t

! !

(3.28)where: T - time factor, equal to 0,197

- length of longest drainage- time for a percent 50% of consolidation [sec]

lav

p

(!

(-coefficient of compressibility

0

50%

0 50%

h 1 hH 1

2 100 h

(!

- (3.29)

- sample initials height3.1.4 Degree of consolidation

The consolidation is the result of gradual dissipation of the excess pore

water pressure from a clay layer. This pressure increases the effective stress,

which induces settlement.

To estimate the degree of consolidation of a clay layer at sometime t after

the load application, one should know the rate of dissipation of the excess pore

water pressure.

For a vertical drainage condition from the clay layer, Terzaghi has derived

the following differential equation:2

v 2

( u) ( u)c

t z

H ( H (!

H H

(3.30)

v

v ww

av

k kc

em

p(1 e )

! !( K

K(

(3.31)

where: vc - coefficient of consolidation

k = coefficient of permeability of the clay

e - total change of void ratio caused by a stress increase of p

ave = average void ratio during consolidation

v

av

e 1m

p (1 e )

(!

(

= volume coefficient of compressibility (3.32)

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Result:2N 2N

00 0

0 0

( u ) 2N ( u)dz ( u)dzU 1

( u ) 2N 2N ( u )

( ( (! !

( (

(3.33)

2v

nM Tt

2n 0max

S 2U 1 ( ) eS M

!g

!

! ! (3.34)

The variation of U with Tv can be calculated from equations (3.35) and is

plotted in Figure 3.10 These are also valid when an impermeable layer is

located at the bottom of the clay layer.

In such a case, excess pore water pressure dissipation can take place in one

direction only. So, the length of the maximum drainage path is equal to H = Hc.

The variation of Tv with U, can be approximated by the following

relations:2

v

U%T

4 100

T

! forU 0 60%

!

(3.35)

andvT 1.781 0.933 log(100 U%)! for U 60%"

3.2.Yield and Field Criterion

3.2.1. General Introduction

By applying the Mohr Coulomb failure criteria one can determine the

shear strength of a soil (s).

The effective stress is calculated with the equation:

'

tans c!

W J (3. 36)where:

- effective normal stress on plane of shearing;

- cohesion(or apparent cohesion);

J - internal friction angle.

For the most day to day work, the shear strength parameters of a soil are

determined by standard laboratory tests: the direct shear test, the triaxial test,the

unconfined compression test.

The normal and shear stresses at failure can be determined as:

and

(3. 37)

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53

where:

A = area of the failure plane soil

For sand for s tg X ! J

(3. 38)

clay for s tg cX ! J

dz

ds

90

-

dx

dx

dz

dzds

ds

M

o +

convention of sign

xz

zf

zx

z

Figure 3.13 Stress state in the soil mass

The locus of all ( ) referring to all plans passing through L point is

Mohrs circle.

Several tests of this type can be conducted by varying the normal load. The

angle of friction of the sand can be determined by plotting a graph of s vs.

sigma. As shown in Figure..

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Chapter 3

54

s(or )

o

P

o

90-o

s(or ')

'

'1

P2

'3o

'

90-o

u u( 1- 3)=( '1- '3)

'3

3

1

'1

Figure 3.14 Mohrs circle

If we have to know the main directions knowing the efforts, we plot theMohrs circle: A and B points have these efforts as co ordinates. Then we plot

the point by drawing parallels to the co ordinate.

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(s)

1

P

303 1

xz

xz

zx

zx

z

x

x

z

B( )zxz

A xzx

3

3

1

Figure 3.15 The establishing of the principal stresses

This theory may be applied also to the case spatial state of stresses.

o

B

C

R( )

23 1

1

3

1

1

3

*

Figure 3.16 Mohrs representation of stresses in three dimensional systems

For sands, the angle of friction usually ranges from 260

to 450. It

increases with relative density of compaction .The approximate range of

relative density of compaction and the corresponding range of the angle of

friction for various sands are given in Table 2.4, chapter two.

Mohr envelopes are often curves.

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3.2.3 The principle of triaxial test:

By referring to a triaxial test, the strength parameters can be obtained by

means of:

y Consolidated Drained test (C.D.)y Consolidated Undrained test(C.U.)y Unconsolidated Undrained test(U.U.)

W1

W3

W3

W1

Lucitechamber

Chamber

fluid

Porous

stone

Piston

Porous

stone

Rubber

membrane

Soilspecimen

Chamber

fluidTo drainage and/or pore

water pressure device

Base

plate

a) b) Figure 3.19 Schematic diagram of triaxial test equipment

For clays, three main types of test can be conducted by means of

triaxial equipment:

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Chapter 3

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y Consolidated drained tests:

Normal

stress

Shear

s stress

'3 3 '1 1'3

'1

c'

'

Figure 3.20 a) Consolidated drained test

The shear strength parameters ( ) can now be determined by

plotting Mohrs circle at failure as shown in Figure 3.20 (a).

(3. 40)

- major principal effective stress

- minor principal effective stress

Consolidated Undrained Testes:

The total stress Mohrs circles of test this type and effective stress can be

presented in Figure 3.20, (b).

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'

Normal stress

Shears stress

'3 3 '1 1

Effective stress

failure envelope

Figure 3.20 (b) Consolidated undrained test

(3. 41)

Normalstress

Shears stress

'3 3 '1 1

ccu

cu

Total stressfailure envelope

Figure 3.20 (c) Unconsolidated Undrained test

where: ( ) are the shear strength parameters from the

consolidated undrained cohesion. Kenny (1959) has given a correlation

between the friction angle , and the plasticity index (PI) of normally

consolidated clays. This correlation is shown in Figure 3.20, (c).

y The Unconsolidated Undrained Test:The total stress Mohrs circle at failure can be determined with the relation:

- the major principal total stress

- the minor principal total stress

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Chapter 3

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when :

= constant

=0 and Coulombs line is horizontal

The shear stress for this condition can be given as:

(3. 42)

Normalstress

Shears stress

'3 3 '1 1

Total stressfailure envelope

( =0 )0

s=cu

3

1

Figure 3.20 (d) Unconsolidated Undrained Ttest

3.2.4 The Unconfined Compression test

The unconfined compression test is a special type of unconsolidated-undrainedtest. In this test, , the major principal total stress is applied vertical to cause

failure (Figure 3.21 ,a ) and stresses .

The corresponding Mohrs circle is shown in (Figure 3.21, c)

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W

Normalstress

Shear

s(X stress

W3=0sr Degree of

saturation

Unconfined compressive

qu strength

W!(Wf=qu

(b) (c)(a)

(Wf=qu=W

Figure 3.21 Unconfined compression test

a) soil specimen b)Variation of qu with the degree ofsaturation

c) Mohrs circle for the test;

The shear strength of saturated clays can be given as:

for

where: = the axial stress at failure

s = shear strength

= cohesion forceThe unconfined compression strength can be used with the specifications

on the consistency of clays from the table below (Table3.1)

Table 3.1

Standard

penetration

number N

Consistency of clays

Unconfined compression

strength

0 - 2 Very soft 0 25

2 - 5 Soft 25 50

5 - 1 Medium soft 50 100

10 20 Stiff 100 200

20 - 30 Very stiff 200 400

>30 Hard >400

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As an indicator to relate the consistency of clays. This is shows in Table on

page.

Are sometimes conducted on unsaturated soils. With the void ratio of a soil

specimen remaining constant, the unconfined compression strength rapidles de

creases with degree of saturation (Fig.).

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