Shear Strength of Soils

1
Shear Strength of Soils

• Dr. Nalin De Silva

2
Strength of different materials
3
Shear failure of soils

• Soils generally fail in shear

At failure, shear stress along the failure
surface (mobilized shear resistance) reaches the
shear strength.
4
Shear failure of soils

• Soils generally fail in shear

5
Shear failure of soils

• Soils generally fail in shear

Retaining wall
At failure, shear stress along the failure
surface (mobilized shear resistance) reaches the
shear strength.
6
Shear failure mechanism
The soil grains slide over each other along the
failure surface.
No crushing of individual grains.
7
Shear failure mechanism
At failure, shear stress along the failure
surface (?) reaches the shear strength (?f).
8
Mohr-Coulomb Failure Criterion(in terms of total
stresses)
?
?f is the maximum shear stress the soil can take
without failure, under normal stress of ?.
9
Mohr-Coulomb Failure Criterion(in terms of
effective stresses)
u pore water pressure
?f is the maximum shear stress the soil can take
without failure, under normal effective stress of
?.
10
Mohr-Coulomb Failure Criterion
Shear strength consists of two components
cohesive and frictional.
11
c and ? are measures of shear strength.
Higher the values, higher the shear strength.
12
Mohr Circle of stress
Resolving forces in s and t directions,
13
Mohr Circle of stress
14
Mohr Circle of stress
15
Mohr Circles Failure Envelope
?
?
16
Mohr Circles Failure Envelope
The soil element does not fail if the Mohr circle
is contained within the envelope
GL
?c
17
Mohr Circles Failure Envelope
GL
Y
?c
18
Orientation of Failure Plane
Failure envelope
f
s
19
Mohr circles in terms of total effective
stresses

20
Failure envelopes in terms of total effective
stresses

If X is on failure
21
Mohr Coulomb failure criterion with Mohr circle
of stress
22
Mohr Coulomb failure criterion with Mohr circle
of stress
23
Determination of shear strength parameters of
soils (c, f or c, f)
Other laboratory tests include, Direct simple
shear test, torsional ring shear test, plane
strain triaxial test, laboratory vane shear test,
laboratory fall cone test
24
Laboratory tests
How to take undisturbed samples
25
Laboratory tests
Field conditions
26
Laboratory tests
Simulating field conditions in the laboratory
Step 2 Apply the corresponding field stress
conditions
27
Direct shear test
Schematic diagram of the direct shear apparatus
28
Direct shear test
Direct shear test is most suitable for
consolidated drained tests specially on granular
soils (e.g. sand) or stiff clays
Preparation of a sand specimen
29
Direct shear test
Preparation of a sand specimen
30
Direct shear test
Test procedure
31
Direct shear test
Step 2 Lower box is subjected to a horizontal
displacement at a constant rate
32
Direct shear test
33
Direct shear test
Analysis of test results
Note Cross-sectional area of the sample changes
with the horizontal displacement
34
Direct shear tests on sands
Stress-strain relationship
35
Direct shear tests on sands
How to determine strength parameters c and f
36
Direct shear tests on sands
Direct shear tests are drained and pore water
pressures are dissipated, hence u 0
Sand is cohesionless hence c 0
Therefore, f f and c c 0
37
Direct shear tests on clays
In case of clay, horizontal displacement should
be applied at a very slow rate to allow
dissipation of pore water pressure (therefore,
one test would take several days to finish)
Failure envelopes for clay from drained direct
shear tests
38
Interface tests on direct shear apparatus
In many foundation design problems and retaining
wall problems, it is required to determine the
angle of internal friction between soil and the
structural material (concrete, steel or wood)
39
Advantages of direct shear apparatus

• Due to the smaller thickness of the sample, rapid
  drainage can be achieved

• Can be used to determine interface strength
  parameters

• Clay samples can be oriented along the plane of
  weakness or an identified failure plane

Disadvantages of direct shear apparatus

• Failure occurs along a predetermined failure plane

• Area of the sliding surface changes as the test
  progresses

• Non-uniform distribution of shear stress along
  the failure surface

40
Lets do some examples
41
Triaxial Shear Test
42
Triaxial Shear Test
Specimen preparation (undisturbed sample)
43
Triaxial Shear Test
Specimen preparation (undisturbed sample)
44
Triaxial Shear Test
Specimen preparation (undisturbed sample)
45
Triaxial Shear Test
Specimen preparation (undisturbed sample)
In some tests
46
Types of Triaxial Tests
Is the drainage valve open?
Is the drainage valve open?
47
Types of Triaxial Tests
48
Consolidated- drained test (CD Test)
Step 1 At the end of consolidation
Step 2 During axial stress increase
Step 3 At failure
49
Consolidated- drained test (CD Test)
Deviator stress (q or Dsd) s1 s3
50
Consolidated- drained test (CD Test)
Volume change of sample during consolidation
51
Consolidated- drained test (CD Test)
Stress-strain relationship during shearing
52
CD tests
How to determine strength parameters c and f
53
CD tests
Therefore, c c and f f
Since u 0 in CD tests, s s
cd and fd are used to denote them
54
CD tests
Failure envelopes
For sand and NC Clay, cd 0
Therefore, one CD test would be sufficient to
determine fd of sand or NC clay
55
CD tests
Failure envelopes
For OC Clay, cd ? 0
56
Some practical applications of CD analysis for
clays
1. Embankment constructed very slowly, in layers
over a soft clay deposit
t in situ drained shear strength
57
Some practical applications of CD analysis for
clays
2. Earth dam with steady state seepage
58
Some practical applications of CD analysis for
clays
3. Excavation or natural slope in clay
t In situ drained shear strength
Note CD test simulates the long term condition
in the field. Thus, cd and fd should be used to
evaluate the long term behavior of soils
59
Consolidated- Undrained test (CU Test)
Step 1 At the end of consolidation
Step 2 During axial stress increase
Step 3 At failure
60
Consolidated- Undrained test (CU Test)
Volume change of sample during consolidation
61
Consolidated- Undrained test (CU Test)
Stress-strain relationship during shearing
62
CU tests
How to determine strength parameters c and f
63
CU tests
How to determine strength parameters c and f
uf
Effective stresses at failure
Mohr Coulomb failure envelope in terms of total
stresses
fcu
ccu
64
CU tests
Shear strength parameters in terms of effective
stresses are c and f
Shear strength parameters in terms of total
stresses are ccu and fcu
c cd and f fd
65
CU tests
Failure envelopes
For sand and NC Clay, ccu and c 0
Therefore, one CU test would be sufficient to
determine fcu and f( fd) of sand or NC clay
66
Some practical applications of CU analysis for
clays
1. Embankment constructed rapidly over a soft
clay deposit
t in situ undrained shear strength
67
Some practical applications of CU analysis for
clays
2. Rapid drawdown behind an earth dam
Core
t Undrained shear strength of clay core
68
Some practical applications of CU analysis for
clays
3. Rapid construction of an embankment on a
natural slope
Note Total stress parameters from CU test (ccu
and fcu) can be used for stability problems
where, Soil have become fully
consolidated and are at equilibrium with the
existing stress state Then for some reason
additional stresses are applied quickly with no
drainage occurring
69
Lets do an example
70
Unconsolidated- Undrained test (UU Test)
Data analysis
Initial volume of the sample A0 H0
Volume of the sample during shearing A H
Since the test is conducted under undrained
condition,
A H A0 H0
A (H0 DH) A0 H0
A (1 DH/H0) A0
71
Unconsolidated- Undrained test (UU Test)
Step 1 Immediately after sampling
Step 2 After application of hydrostatic cell
pressure


Duc B Ds3
Note If soil is fully saturated, then B 1
(hence, Duc Ds3)
72
Unconsolidated- Undrained test (UU Test)
Step 3 During application of axial load


Dud ABDsd
73
Unconsolidated- Undrained test (UU Test)
Combining steps 2 and 3,
Total pore water pressure increment at any stage,
Du
Du Duc Dud
Du B Ds3 ADsd
74
Unconsolidated- Undrained test (UU Test)
Derivation of Skemptons pore water pressure
equation
75
Derivation of Skemptons pore water pressure
equation
Step 1 Increment of isotropic stress
Increase in effective stress in each direction
Ds3 - Duc
76
Derivation of Skemptons pore water pressure
equation
Step 2 Increment of major principal stress
Increase in effective stress in s1 direction
Ds1 - Dud
Increase in effective stress in s2 and s3
directions 0 - Dud
Average Increase in effective stress (Ds1 - Dud
- Dud Dud)/3
77
Typical values for parameter B
78
Typical values for parameter A
NC Clay (High sensitivity) (A gt 1.0)
NC Clay (low sensitivity) (A 0.5 1.0)
Collapse of soil structure may occur in high
sensitivity clays due to very high pore water
pressure generation
79
Typical values for parameter A
OC Clay (Heavily overconsolidated) (A -0.5 -
0.0)
OC Clay (Lightly overconsolidated) (A 0.0
0.5)
During the increase of major principal stress
pore water pressure can become negative in
heavily overconsolidated clays due to dilation of
specimen
80
Typical values for parameter A
81
Unconsolidated- Undrained test (UU Test)
Step 1 Immediately after sampling
Step 2 After application of hydrostatic cell
pressure
Step 3 During application of axial load
Step 3 At failure
82
Unconsolidated- Undrained test (UU Test)
Mohr circle in terms of effective stresses do not
depend on the cell pressure.
Therefore, we get only one Mohr circle in terms
of effective stress for different cell pressures
83
Unconsolidated- Undrained test (UU Test)
Mohr circles in terms of total stresses
84
Unconsolidated- Undrained test (UU Test)
Effect of degree of saturation on failure envelope
S lt 100
S gt 100
85
Some practical applications of UU analysis for
clays
1. Embankment constructed rapidly over a soft
clay deposit
t in situ undrained shear strength
86
Some practical applications of UU analysis for
clays
2. Large earth dam constructed rapidly with no
change in water content of soft clay
87
Some practical applications of UU analysis for
clays
3. Footing placed rapidly on clay deposit
Note UU test simulates the short term condition
in the field. Thus, cu can be used to analyze the
short term behavior of soils
88
Unconfined Compression Test (UC Test)
s1 sVC Ds
s3 0
Confining pressure is zero in the UC test
89
Unconfined Compression Test (UC Test)
Note Theoritically qu cu , However in the
actual case qu lt cu due to premature failure of
the sample
90
Lets do an example
91
Stress Invariants (p and q)
p (or s) (s1 s3)/2
q (or t) (s1 - s3)/2
p and q can be used to illustrate the variation
of the stress state of a soil specimen during a
laboratory triaxial test
92
Stress Invariants (p and q)
p (or s) (s1 s3)/2
q (or t) (s1 - s3)/2
GL
93
Mohr Coulomb failure envelope in terms of stress
invariants
p (or s) (s1 s3)/2
q (or t) (s1 - s3)/2
94
Mohr Coulomb failure envelope in terms of stress
invariants
p (or s) (s1 s3)/2
q (or t) (s1 - s3)/2
Therefore, sinf tana
95
Stress path for CD triaxial test
In CD tests pore water pressure is equal to zero.
Therefore, total and effective stresses are equal
q (or t) 0
p, p (or s, s) s3
p, p (or s, s) s3 Dsd/2
q (or t) Dsd/2
96
Stress path for CU triaxial test
In CU tests pore water pressure develops during
shearing
q (or t) 0
p, p (or s, s) s3
p (or s) s3 Dsd/2
q (or t) Dsd/2
97
Lets do some example
98
Other laboratory shear tests

• Direct simple shear test

• Torsional ring shear test

• Plane strain triaxial test

99
Other laboratory shear tests

• Direct simple shear test

• Torsional ring shear test

• Plane strain triaxial test

100
Direct simple shear test
Direct shear test
Direct simple shear test
101
Other laboratory shear tests

• Direct simple shear test

• Torsional ring shear test

• Plane strain triaxial test

102
Torsional ring shear test
103
Torsional ring shear test
Preparation of ring shaped undisturbed samples is
very difficult. Therefore, remoulded samples are
used in most cases
104
Other laboratory shear tests

• Direct simple shear test

• Torsional ring shear test

• Plane strain triaxial test

105
Plane strain triaxial test
106
In-situ shear tests

• Vane shear test

• Torvane

• Pocket Penetrometer

• Pressuremeter

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT)

• Standard Penetration Test, SPT

107
In-situ shear tests

• Vane shear test (suitable for soft to stiff
  clays)

• Torvane

• Pocket Penetrometer

• Pressuremeter

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT)

• Standard Penetration Test, SPT

108
Vane shear test
This is one of the most versatile and widely used
devices used for investigating undrained shear
strength (Cu) and sensitivity of soft clays
Rate of rotation 60 120 per minute Test can
be conducted at 0.5 m vertical intervals
109
Vane shear test
T Ms Me Me Ms 2Me
Me Assuming a uniform distribution of shear
strength
Since the test is very fast, Unconsolidated
Undrained (UU) can be expected
110
Vane shear test
T Ms Me Me Ms 2Me
Ms Shaft shear resistance along the
circumference
Since the test is very fast, Unconsolidated
Undrained (UU) can be expected
111
Vane shear test
T Ms Me Me Ms 2Me
Me Assuming a triangular distribution of shear
strength
Since the test is very fast, Unconsolidated
Undrained (UU) can be expected
Can you derive this ???
112
Vane shear test
T Ms Me Me Ms 2Me
Me Assuming a parabolic distribution of shear
strength
Since the test is very fast, Unconsolidated
Undrained (UU) can be expected
Can you derive this ???
113
Vane shear test
After the initial test, vane can be rapidly
rotated through several revolutions until the
clay become remoulded
Since the test is very fast, Unconsolidated
Undrained (UU) can be expected
114
Some important facts on vane shear test
The above reduction is partially regained after
some time
Insertion of vane into soft clays and silts
disrupts the natural soil structure around the
vane causing reduction of shear strength
Cu as determined by vane shear test may be a
function of the rate of angular rotation of the
vane
115
Correction for the strength parameters obtained
from vane shear test
Bjerrum (1974) has shown that as the plasticity
of soils increases, Cu obtained by vane shear
tests may give unsafe results for foundation
design. Therefore, he proposed the following
correction.
Cu(design) lCu(vane shear)
Where, l correction factor 1.7 0.54 log
(PI) PI Plasticity Index
116
In-situ shear tests

• Vane shear test

• Torvane (suitable for very soft to stiff clays)

• Pocket Penetrometer

• Pressuremeter

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT)

• Standard Penetration Test, SPT

117
Torvane
Torvane is a modification to the vane
118
In-situ shear tests

• Vane shear test

• Torvane

• Pocket Penetrometer (suitable for very soft to
  stiff clays)

• Pressuremeter

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT)

• Standard Penetration Test, SPT

119
Pocket Penetrometer
Pushed directly into the soil. The unconfined
compression strength (qu) is measured by a
calibrated spring.
120
Swedish Fall Cone (suitable for very soft to soft
clays)
Cu 8 Mass of the cone 8 1/(penetration)2
Soil sample
The test must be calibrated
121
In-situ shear tests

• Vane shear test

• Torvane

• Pocket Penetrometer

• Pressuremeter (suitable for all soil types)

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT)

• Standard Penetration Test, SPT

122
Pressuremeter
123
Pressuremeter
124
In-situ shear tests

• Vane shear test

• Torvane

• Pocket Penetrometer

• Pressuremeter

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT) (suitable for all soil
  types except very course granular materials)

• Standard Penetration Test, SPT

125
Static Cone Penetrometer test
Cone penetrometers with pore water pressure
measurement capability are known as piezocones
126
Static Cone Penetrometer test
Force required for the inner rod to push the tip
(Fc) and the total force required to push both
the tip and the sleeve (Fc Fs) will be measured
Point resistance (qc) Fc/ area of the tip
Sleeve resistance (qs) Fs/ area of the sleeve
in contact with soil
Friction Ratio (fr) qs/ qc 100 ()
Various correlations have been developed to
determine soil strength parameters (c, f, ect)
from fr
127
In-situ shear tests

• Vane shear test

• Torvane

• Pocket Penetrometer

• Pressuremeter

• Static Cone Penetrometer test (Push Cone
  Penetrometer Test, PCPT)

• Standard Penetration Test, SPT (suitable for
  granular materials)

128
Standard Penetration Test, SPT
SPT is the most widely used test procedure to
determine the properties of in-situ soils
Number of blows for the first 150 mm penetration
is disregarded due to the disturbance likely to
exist at the bottom of the drill hole
Various correlations have been developed to
determine soil strength parameters (c, f, ect)
from N
The test can be conducted at every 1m vertical
intervals
Standard penetration resistance (SPT N) N2 N3
129
Standard Penetration Test, SPT
SPT (Manual operation)
130
Various correlations for shear strength
For NC clays, the undrained shear strength (cu)
increases with the effective overburden pressure,
s0
For OC clays, the following relationship is
approximately true
For NC clays, the effective friction angle (f)
is related to PI as follows
131
Shear strength of partially saturated soils
In the previous sections, we were discussing the
shear strength of saturated soils. However, in
most of the cases, we will encounter unsaturated
soils in tropical countries like Sri Lanka
Pore water pressure can be negative in
unsaturated soils
132
Shear strength of partially saturated soils
Bishop (1959) proposed shear strength equation
for unsaturated soils as follows

• Where,
• sn ua Net normal stress
• ua uw Matric suction
• a parameter depending on the degree of
  saturation
• (c 1 for fully saturated soils and 0 for
  dry soils)

Fredlund et al (1978) modified the above
relationship as follows
Where, tanfb Rate of increase of shear
strength with matric suction
133
Shear strength of partially saturated soils
Therefore, strength of unsaturated soils is much
higher than the strength of saturated soils due
to matric suction
134
How it become possible build a sand castle
135
THE END