Complete Soil Mech. Undestanding Pakage: ABHAY)

1. 1
Shear Strength
of Soils
N. Sivakugan
Duration: 17 min: 04 sec

2. Shear failure
Soils generally fail in shear
strip footing
embankment
failure surface mobilised shear
resistance
At failure, shear stress along the failure surface
reaches the shear strength.

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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).

5. Mohr-Coulomb Failure Criterion
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

  c  tan f
c

cohesion
friction angle
f

f is the maximum shear stress the soil can take
without failure, under normal stress of .

6. Mohr-Coulomb Failure Criterion
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  tan f f  c 
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Shear strength consists of two
components: cohesive and frictional.
f
f



c
f tan 
c
frictional
component

7. c and  are measures of shear strength.
Higher the values, higher the shear strength.

8. Mohr Circles & Failure Envelope
X
Y Soil elements at
different locations
X
Y
X
Y
~ failure
~ stable



9. Mohr Circles & Failure Envelope
Y
Initially, Mohr circle is a point
c
c
c

c+

The soil element does not fail if
the Mohr circle is contained
within the envelope
GL

10. Mohr Circles & Failure Envelope
c
Y
c
c

GL
As loading progresses, Mohr
circle becomes larger…
.. and finally failure occurs
when Mohr circle touches the
envelope

11. Orientation of Failure Plane
c
Y
c
c

GL
Failure plane
oriented at 45 + /2
to horizontal
c+
90+
45 + /2

45 + /2
Y

12. Mohr circles in terms of  & ’
v
h
v’
h’
X X X
u
u = +
total stresses
effective stresses
v h v h ’ ’
u

13. Envelopes in terms of  & ’
Identical specimens
initially subjected to
different isotropic stresses
(c) and then loaded
axially to failure
c
c
c
c
f
Initially… Failure
uf
At failure,
3 = c; 1 = c+f
3’ = 3 – uf ; 1’ = 1 - uf
c, 
in terms of 
c’, ’
in terms of ’

14. Triaxial Test Apparatus
failure plane
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piston (to apply deviatoric stress)
O-ring
impervious
membrane
porous
stone
pedestal
perspex cell
cell pressure
back pressure
pore pressure or
volume change
water
soil sample at
failure

15. Types of Triaxial Tests
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deviatoric stress ()
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Under all-around
cell pressure c
Shearing (loading)
Is the drainage valve open? Is the drainage valve open?
yes no yes no
Consolidated
sample
Unconsolidated
sample
Drained
loading
Undrained
loading

16. Types of Triaxial Tests
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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

17. Granular soils have
no cohesion.
c = 0 & c’= 0
For normally consolidated
clays, c’ = 0 & c = 0.
For unconsolidated
undrained test, in
terms of total
stresses, u = 0

18. 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
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pressure
 gives c’ and ’
Can be days!
 not desirable
Use c’ and ’ for analysing fully drained
situations (e.g., long term stability,
very slow loading)

19. CD, CU and UU Triaxial Tests
Consolidated Undrained (CU) Test
Measure  ’
 gives c’ and ’
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 pore pressure develops during shear
 faster than CD (preferred way to find c’ and ’)

20. CD, CU and UU Triaxial Tests
Unconsolidated Undrained (UU) Test
Not measured
’ unknown
 analyse in terms of   gives cu and u
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 pore pressure develops during shear
 very quick test
= 0; i.e., failure envelope is
horizontal
Use cu and u for analysing undrained
situations (e.g., short term stability,
quick loading)

21. - 3
1
Relation at Failure
X
soil element at failure
1
X 3
3 1
tan (45 / 2) 2 tan(45 / 2) 2
1 3     c 
tan (45 / 2) 2 tan(45 / 2) 2
3 1     c 

22. stress point
(v-h)/2
 

v h s
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Stress Point
t
s

  h v
(v+h)/2
stress point
2
 

v h t
2
X
v
h

23. During loading…
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Stress Path
t
s
Stress path
is the locus
of stress
points
Stress path
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
s
c

c cos 
failur
e
tan-1 (sin )
During loading (shearing)….
stress path

25. Pore Pressure Parameters
Y
1
3
u = ?
A simple way to estimate the pore
pressure change in undrained
loading, in terms of total stress
changes ~ after Skempton (1954)
 ( ) 3 1 3 u  B   A   
Skempton’s pore pressure
parameters A and B

26. 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.