Shear Strength
of Soils
Duration: 17 min: 04 sec
N. Sivakugan
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Shear failure
Soils generally fail in shear
embankment
strip footing
failure surface
mobilised shear
resistance
At failure, shear stress along the failure surface
reaches the shear strength.
Shear failure
failure surface
The soil grains slide over
each other along the
failure surface.
No crushing of
individual grains.
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Shear failure
At failure, shear stress along the failure surface
() reaches the shear strength (f).
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Mohr-Coulomb Failure Criterion

 f  c   tan 

friction angle
cohesion
f
c

f is the maximum shear stress the soil can take
without failure, under normal stress of .
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
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Mohr-Coulomb Failure Criterion
Shear strength consists of two
components: cohesive and frictional.

 f  c   f tan 
f
f tan 

c
frictional
component
c
f

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c and  are measures of shear strength.
Higher the values, higher the shear strength.
Mohr Circles & Failure Envelope

Y
X
Y
X

Soil elements at
different locations
X ~ failure
Y ~ stable
Mohr Circles & Failure Envelope
The soil element does not fail if
the Mohr circle is contained
within the envelope
GL

c
Y
c
c
Initially, Mohr circle is a point

c+
Mohr Circles & Failure Envelope
As loading progresses, Mohr
circle becomes larger…
GL

c
Y
c
c
.. and finally failure occurs
when Mohr circle touches the
envelope
Orientation of Failure Plane
Failure plane
oriented at 45 + /2
to horizontal
Y
45 + /2
GL
45 + /2

c
Y

c
90+
c
c+
Mohr circles in terms of  & ’
v
X
v’
h
=
X
u
 h’
effective stresses
 h’
v’  h
+
X
total stresses
u
v
u
Envelopes in terms of  & ’
Identical specimens
initially subjected to
different isotropic stresses
(c) and then loaded
axially to failure
f
c
c
c
c
Initially…
At failure,
3 = c; 1 = c+f
3’ = 3 – uf ; 1’ = 1 - uf
uf
Failure
c, 
in terms of 
c’, ’
in terms of ’
Triaxial Test Apparatus
piston (to apply deviatoric stress)
failure plane
O-ring
impervious
membrane
soil sample at
failure
porous
stone
perspex cell
water
cell pressure
pore pressure or
back pressure
pedestal
volume change
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Types of Triaxial Tests
deviatoric stress ()
Under all-around
cell pressure c
Is the drainage valve open?
yes
no
Shearing (loading)
Is the drainage valve open?
yes
no
Consolidated
Unconsolidated
Drained
Undrained
sample
sample
loading
loading
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Types of Triaxial Tests
Depending on whether drainage is allowed
or not during
 initial isotropic cell pressure application, and
 shearing,
there are three special types of triaxial tests
that have practical significances. They are:
Consolidated Drained (CD) test
Consolidated Undrained (CU) 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.
c = 0 & c’= 0
For normally consolidated
clays, c’ = 0 & c = 0.
CD, CU and UU Triaxial Tests
Consolidated Drained (CD) Test
 no excess pore pressure throughout the test
 very slow shearing to avoid build-up of pore
pressure
Can be days!
 not desirable
 gives c’ and ’
Use c’ and ’ for analysing fully drained
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 develops during shear
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 develops during shear
= 0; i.e., failure envelope is
Not measured
horizontal
’ unknown
 analyse in terms of   gives cu and u
 very quick test
Use cu and u for analysing undrained
situations (e.g., short term stability,
quick loading)
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1- 3 Relation at Failure
1
3
X
X
soil element at failure
3
1
 1   3 tan (45   / 2)  2c tan( 45   / 2)
2
 3   1 tan (45   / 2)  2c tan( 45   / 2)
2
Stress Point
v
h
X

t
stress point
stress point
(v-h)/2
v 
h
(v+h)/2
t
s
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v h
2
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s
v h
2
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Stress Path
During loading…

t
Stress path
is the locus
of stress
points
Stress path

s
Stress path is a convenient way to keep track of the
progress in loading with respect to failure envelope.
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Failure Envelopes

t

failur
e
tan-1 (sin )
c cos 
c
stress path

s
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 stress
changes ~ after Skempton (1954)
1
Y
u  B 3  A(  1   3 )
3
u = ?
Skempton’s pore pressure
parameters A and B
Pore Pressure Parameters
B-parameter
B = f (saturation,..)
For saturated soils, B  1.
A-parameter at failure (Af)
Af = f(OCR)
For normally consolidated clays Af  1.
For heavily overconsolidated clays Af is negative.