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of Soils
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Shear failureSoils generally fail in shear
embankment
strip footing
failure surface mobilised shear
resistance
At failure, shear stress along the failure surfacereac es e s ear s reng .
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Shear failure
The soil grains slide over
failure surface
failure surface.
No crushing ofindividual grains.
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Shear failure
At failure, shear stress along the failure surface
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reac es e s ear s reng f .
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Mohr-Coulomb Failure Criterion
tan cf
c
cohesionfriction angle
f
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f is the maximum shear stress the soil can take
without failure, under normal stress of .
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Mohr-Coulomb Failure Criterion
Shear strength consists of two
components: cohesive and frictional.
tanc
f tan frictionalcomponent
f
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c and are measures of shear stren th.
Higher the values, higher the shear strength.
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Mohr Circles & Failure Envelope
Y
X
Y Soil elements at
X
different locationsX ~ failure
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Mohr Circles & Failure Envelope
The soil element does not fail if
the Mohr circle is contained
GL
c
Y cc c+
Initially, Mohr circle is a point
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Mohr Circles & Failure EnvelopeAs loading progresses, Mohr
circle becomes larger
GL
c
Y cc
.. and finally failure occurs
when Mohr circle touches the
envelope
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Orientation of Failure Plane
Failure plane
oriented at 45 + /2Y
GL
to horizontal
45 + /2
c
Y cc c+
90+
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Mohr circles in terms of &
v v u
X X Xh h u= +
effective stresses
total stresses
vhvhu
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Envelopes in terms of & Identical specimens
initially subjected to
different isotropic stresses
and then loaded
f
axially to failure
c
c
c
c
Initially Failure
f
c,
in terms of ,
3 = c; 1 = c+ f
= u ; = - u
c,
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1-3 Relation at Failure
X 3
1
X
3
2
anan31 c2 13
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arning,Inc.Thomso
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/Cole,a
divisionofThomsonLe
2001Brooks
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Soil strength
Soils are essentially frictional materials
the strength depends on the applied stress
Strength is controlled by effective stresses
Soil strength depends on drainage different strengths will be measured for a given soil that
(a) deforms at constant volume (undrained) and
pressures (drained)
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Mohr-Coulomb failure criterion
n
The limiting shear stress (soil strength) is given by
= c + n tan =
= friction angle
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Mohr-Coulomb failure criterion
The parameters c, are in general not soil constants. Theydepend on
d
the type of loading (drained or undrained)
The Mohr-Coulomb criterion is an empirical criterion, and the
failure locus is only locally linear. Extrapolation outside therange o norma s resses or w c as een e erm ne s
likely to be unreliable.
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Effective stress failure criterion
I t e so s at a ure t e e ect ve stress a ure cr ter on w
always be satisfied.
c n' tan '
cand are known as the effective (or drained) strengtharameters.
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Effective stress failure criterion
I t e so s at a ure t e e ect ve stress a ure cr ter on w
always be satisfied.
c n' tan '
cand are known as the effective (or drained) strengtharameters.
effective strength parameters are the fundamental strength
parameters. But they are not necessarily soil constants.
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Total stress failure criterion
If the soil is taken to failure at constant volume (undrained) then the
failure criterion can be written in terms of total stress as
cu n utan
cu and u are known as the undrained strength parameters
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Total stress failure criterion
If the soil is taken to failure at constant volume (undrained) then the
failure criterion can be written in terms of total stress as
cu n utan
cu and u are known as the undrained strength parameters
These parameters are not soil constants, they depend strongly on the
moisture content of the soil.
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Total stress failure criterion
If the soil is taken to failure at constant volume (undrained) then the
failure criterion can be written in terms of total stress as
cu n utan
cu and u are known as the undrained strength parameters
These parameters are not soil constants, they depend strongly on the
moisture content of the soil.
The undrained strength is only relevant in practice to clayey soilsthat in the short term remain undrained. Note that as the pore
failure criterion cannot be used.
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Tests to measure soil strength
.
Normal load
Load cell to
op p a en
Motor
drive
measure
Shear Force
Soil
Porous plates
Rollers
Measure relative horizontal displacement, dx
vertical displacement of top platen, dy
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Shear box test
Usually only relatively slow drained tests are performed in shear
box apparatus. For clays rate of shearing must be chosen to
.
gravels tests can be performed quickly
Tests on sands and ravels are usuall erformed dr . Water
does not significantly affect the (drained) strength.
If there are no excess pore pressures and as the pore pressure
identical.
The failure stresses thus define an effective stress failure
envelope from which the effective (drained) strength parametersc, can be determined.
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Typical drained shear box results
Load
(F)
Normal
load
Shea
Horizontal displacement (dx)
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Typical drained shear box results
= F/APeak
Ultimate
= N/AN1 N2
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Figure 11.6 Plot of
shear stress and
ooks/Cole,adivisionofThoms
change in height of
specimen against shear
20
01Br
and dense dry sand
(direct shear test)
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A eak and an ultimate failure locus can be obtained from the
Interpretation of shear box tests
results each with different c and values.
All soils are essentially frictional and continued shearing results
.
Normally consolidated clays (OCR=1) and loose sands do not
show se arate eak and ultimate failure loci and for soils in
these states c = 0.
Overconsolidated clays and dense sands have peak strengthsw c .
Note that dense sands do not possess any true cohesion
bonds the a arent cohesion results from the tendenc of soil
to expand when sheared.
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Shear box test - advantages
Easy and quick test for sands and gravels
Lar e deformations can be achieved b reversin shear
direction. This is useful for determining the residual strength of a
soil
Large samples may be tested in large shear boxes. Small
samples may give misleading results due to imperfections
fractures and fissures or the lack of them.
Samples may be sheared along predetermined planes. This is
planes are required.
Sh b di d
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Shear box test - disadvantages
- .stress-strain behaviour cannot be determined. The estimated
stresses may not be those acting on the shear plane.
There is no means of estimating pore pressures so effectivestresses cannot be determined from undrained tests
Undrained strengths are unreliable because it is impossible to
prevent localised drainage without high shearing rates
In practice shear box tests are used to get quick and crude
estimates of failure parameters
T t t il t th
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Tests to measure soil strength
2. The Triaxial TestDeviator load
Confining
cylinder
Rubber
membrane
-
seals
Porous filterSoil
Celldisc
pressure
and volume
change
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Triaxial Test A aratuspiston (to apply deviatoric stress)
O-ring
failure plane
porous
membrane
soil sample at
failure
stoneperspex cell
water
cell pressure
back pressurepore pressure or
volume chan e
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T es of Triaxial Testsdeviatoric stress ()
n er a -aroun
cell pressure c
ear ng oa ng
Is the draina e valve o en? Is the draina e valve o en?
yes no yes no
samplenconsolidated
sample
ra ne
loading loading
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T es of Triaxial TestsDepending on whether drainage is allowedor not during
initial isotropic cell pressure application, and
shearing,
there are three special types of triaxial teststhat have practical significances. They are:
Consolidated Drained (CD) test
Unconsolidated Undrained (UU) test
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For unconsolidated
undrained test in
terms of total
stresses, u = 0
Granular soils have
no cohesion.
For normally consolidated
clays, c = 0 & c = 0.c = 0 & c= 0
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CD, CU and UU Triaxial Tests
Consolidated Drained (CD) Test
very slow shearing to avoid build-up of pore
Can be days!
not desirable
situations (e.g., long term stability,very slow loading)
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CD, CU and UU Triaxial Tests
Consolidated Undrained (CU) Test
pore pressure eve ops ur ng s ear
Measure
gives c and
faster than CD (preferred way to find c and )
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CD, CU and UU Triaxial Tests
Unconsolidated Undrained (UU) Test
pore pressure eve ops ur ng s ear
Not measured
unknown= 0; i.e., failure envelope is
horizontal
analyse in terms of gives cu and u
Use cu and u for analysing undrained
situations (e.g., short term stability,quick loading)
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1-3 Relation at Failure
X 3
1
X
3
2
anan31 c2 13
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Stress PointvXh
q stress point stress point
-
p
or
h v
v
p(
v
+h
)/2
2
hvq
2
hvp
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Stress Path
During loading
q
is the locusof stressoints
Stress path
p
or
p
Stress path is a convenient way to keep track of the
ro ress in loadin with res ect to failure envelo e.
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Failure Envelo es
q failure
tan-1 (sin )
p
During loading (shearing).
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Pore Pressure Parameters
A simple way to estimate the pore
pressure change in undrained
loading, in terms of total stresschan es ~ after Skem ton 1954
1 )( 313 ABuY 3
u = ? Skemptons pore pressure
parameters A and B
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=
If soil is saturated B=1, therefore,
u = 3 + A (1 -3)
3 ,
A = u / (1 - 3)
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Pore Pressure Parameters
B-parameter
For saturated soils, B 1.
,..
A-parameter at failure (Af)
For normally consolidated clays Af 1.
f
For heavily overconsolidated clays Af is negative.
Stresses in triaxial specimens
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Stresses in triaxial specimens
=r
=r r
pressure)
a
= x a s ress
Stresses in triaxial specimens
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p
=r
=r r
pressure)
a
= x a s ress
Fa r
Arom equ r um we ave
Stresses in triaxial specimens
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p
,
q a r ( ) ( ) 1 3
The axial and radial stresses are principal stresses
If q = 0 increasing cell pressure will result in
volumetric compression if the soil is free to drain. The
effective stresses will increase and so will the strength increasing pore water pressure if soil volume is constant
(that is, undrained). As the effective stresses cannot change
o ows a u = r
Increasing q is required to cause failure
Strains in triaxial specimens
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p
, ,volume dV we can determine
dh
Volume strain
ah0
VdV
where h0 is the initial height and V0 is the initial volume
0
Strains in triaxial specimens
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p
, ,volume dV we can determine
dh
Volume strain
ah0
VdV
where h0 is the initial height and V0 is the initial volume
0
It is assumed that the specimens deform as right circular cylinders.
The cross-sectional area, A, can then be determined from
1 +dV
V 1 - v0
1 +dh
h
1 -
o o
a
0
Advantages of the triaxial test
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pec mens are su ecte to approx mate y un orm stressesand strains
The complete stress-strain-strength behaviour can be
investigated
Drained and undrained tests can be performed
,allowing effective stresses to be determined
applied
Typical triaxial results
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Increasing cell
pressure
a
Interpretation of Laboratory results
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. ra ne s ear oa ng
In laboratory tests the loading rate is chosen so that no excess
water pressures will be generated, and the specimens are free
to drain. Effective stresses can be determined from the applied
total stresses and the known pore water pressure.
relevance to drained tests.
It is possible to construct a series of total stress Mohr circles but
e n erre o a s ress un ra ne s reng parame ers are
meaningless.
Interpretation of Laboratory results
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Effective strength parameters are generally used to check thelong term stability (that is when all excess pore pressures have
dissipated) of soil constructions.
For sands and gravels pore pressures dissipate rapidly and theeffective strength parameters can also be used to check the
short term stability.
In rinci le the effective stren th arameters can be used tocheck the stability at any time for any soil type. However, to do
this the pore pressures in the ground must be known and in
general they are only known in the long term.
Interpretation of Laboratory results
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In undrained laboratory tests no drainage from the sample must occur,
nor should there be moisture redistribution within the sample.
In the shear box this requires fast shear rates. In triaxial tests slowerloading rates are possible because conditions are uniform and
drainage from the sample is easily prevented.
In a triaxial test with ore ressure measurement the effectivestresses can be determined and the effective strength parameters c,
evaluated. These can be used as discussed previously to evaluatelong term stability.
Interpretation of Laboratory results
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undrained) strength parameters cu, u. If these parameters are to berelevant to the ground the moisture content must be the same. This can
be achieved either b erformin UU tests or b usin CIU tests and
consolidating to the in-situ stresses.
The total (undrained) strength parameters are used to assess the short
erm s a y o so cons ruc ons. s mpor an a no ra nage
should occur if this approach is to be valid. For example, a total stress
analysis would not be appropriate for sands and gravels.
For clayey soils a total stress analysis is the only simple way to assess
stability
o e a un ra ne s reng s can e e erm ne or any so , u ey
may not be relevant in practice
Relation between effective and total stress criteria
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triaxial tests. Each sample is subjected to a different cell pressure. No
water can drain at any stage.
Relation between effective and total stress criteria
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triaxial tests. Each sample is subjected to a different cell pressure. No
water can drain at any stage. At failure the Mohr circles are found to
e as s own
13
Relation between effective and total stress criteria
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triaxial tests. Each sample is subjected to a different cell pressure. No
water can drain at any stage. At failure the Mohr circles are found to
e as s own
13
We find that all the total stress Mohr circles are the same size,and therefore u = 0 and = su = cu = constant
Relation between effective and total stress criteria
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,stress failure condition must also be satisfied. As all the circles
have the same size there must be only one effective stress Mohr
circle c n' tan '
1313
Relation between effective and total stress criteria
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,stress failure condition must also be satisfied. As all the circles
have the same size there must be only one effective stress Mohr
circle c n' tan '
1313
1 3 1 3 2 cuWe have the following relations
1 3 = N + 2 c N
Relation between effective and total stress criteria
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The different total stress Mohr circles with a single effectivestress Mohr circle indicate that the pore pressure is different for
each sample.
As discussed previously increasing the cell pressure withoutallowing drainage has the effect of increasing the pore pressure
by the same amount (u = r) with no change in effectivestress.
The change in pore pressure during shearing is a function of the
initial effective stress and the moisture content. As these are
identical for the three samples an identical strength is obtained.
Significance of undrained strength parameters
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It is often found that a series of undrained tests from a particular
site give a value of u that is not zero (cu not constant). If thisha ens either
the samples are not saturated, or
the samples have different moisture contents
If the samples are not saturated analyses based on undrained
behaviour will not be correct
The undrained strength cu is not a fundamental soil property. If
the moisture content changes so will the undrained strength.
Example
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In an unconsolidated undrained triaxial test the undrainedstrength is measured as 17.5 kPa. Determine the cell pressure
used in the test if the effective stren th arameters are c = 0
= 26o and the pore pressure at failure is 43 kPa.
Example
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In an unconsolidated undrained triaxial test the undrainedstrength is measured as 17.5 kPa. Determine the cell pressure
used in the test if the effective stren th arameters are c = 0
= 26o and the pore pressure at failure is 43 kPa.
Analytical solution
= = 1 3 1 3
. 2 2
Example
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In an unconsolidated undrained triaxial test the undrainedstrength is measured as 17.5 kPa. Determine the cell pressure
used in the test if the effective stren th arameters are c = 0
= 26o and the pore pressure at failure is 43 kPa.
Analytical solution
= = 1 3 1 3
.
Failure criterion 1 3 = N + 2 c N
2 2
Example
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In an unconsolidated undrained triaxial test the undrainedstrength is measured as 17.5 kPa. Determine the cell pressure
used in the test if the effective stren th arameters are c = 0
= 26o and the pore pressure at failure is 43 kPa.
Analytical solution
= = 1 3 1 3
.
Failure criterion 1 3 = N + 2 c N
2 2
Hence = 57.4 kPa, = 22.4 kPa
and cell pressure (total stress) = + u = 65.4 kPa
Graphical solution
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26
17.5
Graphical solution
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26
17.5
13
Graphical solution
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26
17.5
1313
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= + +
Ms
= (dh)cu
x d/2
T = c [( d2h/2) +(d3/4)]
= for triangular mobilization of undrained shear
strength
= or un orm mo zat on o un ra ne s ear
strength
=
strength