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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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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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Mechanical Soil Properties
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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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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Mechanical Soil Properties
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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Chapter 3
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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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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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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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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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Mechanical Soil Properties
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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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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
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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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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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