Shear Strength of Soils

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Shear Strength of Soils

• Dr. Nalin De Silva

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Strength of different materials
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Shear failure of soils

• Soils generally fail in shear

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

• Soils generally fail in shear

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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.
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Shear failure mechanism
The soil grains slide over each other along the
failure surface.
No crushing of individual grains.
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Shear failure mechanism
At failure, shear stress along the failure
surface (?) reaches the shear strength (?f).
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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 ?.
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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
?.
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Mohr-Coulomb Failure Criterion
Shear strength consists of two components
cohesive and frictional.
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c and ? are measures of shear strength.
Higher the values, higher the shear strength.
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Mohr Circle of stress
Resolving forces in s and t directions,
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Mohr Circle of stress
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Mohr Circle of stress
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Mohr Circles Failure Envelope
?
?
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Mohr Circles Failure Envelope
The soil element does not fail if the Mohr circle
is contained within the envelope
GL
?c
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Mohr Circles Failure Envelope
GL
Y
?c
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Orientation of Failure Plane
Failure envelope
f
s
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Mohr circles in terms of total effective
stresses

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Failure envelopes in terms of total effective
stresses

If X is on failure
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Mohr Coulomb failure criterion with Mohr circle
of stress
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Mohr Coulomb failure criterion with Mohr circle
of stress
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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
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Laboratory tests
How to take undisturbed samples
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Laboratory tests
Field conditions
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Laboratory tests
Simulating field conditions in the laboratory
Step 2 Apply the corresponding field stress
conditions
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Direct shear test
Schematic diagram of the direct shear apparatus
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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
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Direct shear test
Preparation of a sand specimen
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Direct shear test
Test procedure
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Direct shear test
Step 2 Lower box is subjected to a horizontal
displacement at a constant rate
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Direct shear test
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Direct shear test
Analysis of test results
Note Cross-sectional area of the sample changes
with the horizontal displacement
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Direct shear tests on sands
Stress-strain relationship
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Direct shear tests on sands
How to determine strength parameters c and f
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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
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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
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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)
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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

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Lets do some examples
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Triaxial Shear Test
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Triaxial Shear Test
Specimen preparation (undisturbed sample)
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Triaxial Shear Test
Specimen preparation (undisturbed sample)
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Triaxial Shear Test
Specimen preparation (undisturbed sample)
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Triaxial Shear Test
Specimen preparation (undisturbed sample)
In some tests
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Types of Triaxial Tests
Is the drainage valve open?
Is the drainage valve open?
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Types of Triaxial Tests
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Consolidated- drained test (CD Test)
Step 1 At the end of consolidation
Step 2 During axial stress increase
Step 3 At failure
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Consolidated- drained test (CD Test)
Deviator stress (q or Dsd) s1 s3
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Consolidated- drained test (CD Test)
Volume change of sample during consolidation
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Consolidated- drained test (CD Test)
Stress-strain relationship during shearing
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CD tests
How to determine strength parameters c and f
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CD tests
Therefore, c c and f f
Since u 0 in CD tests, s s
cd and fd are used to denote them
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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
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CD tests
Failure envelopes
For OC Clay, cd ? 0
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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
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Some practical applications of CD analysis for
clays
2. Earth dam with steady state seepage
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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
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Consolidated- Undrained test (CU Test)
Step 1 At the end of consolidation
Step 2 During axial stress increase
Step 3 At failure
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Consolidated- Undrained test (CU Test)
Volume change of sample during consolidation
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Consolidated- Undrained test (CU Test)
Stress-strain relationship during shearing
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CU tests
How to determine strength parameters c and f
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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
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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
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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
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Some practical applications of CU analysis for
clays
1. Embankment constructed rapidly over a soft
clay deposit
t in situ undrained shear strength
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Some practical applications of CU analysis for
clays
2. Rapid drawdown behind an earth dam
Core
t Undrained shear strength of clay core
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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
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Lets do an example
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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
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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)
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Unconsolidated- Undrained test (UU Test)
Step 3 During application of axial load


Dud ABDsd
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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
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Unconsolidated- Undrained test (UU Test)
Derivation of Skemptons pore water pressure
equation
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Derivation of Skemptons pore water pressure
equation
Step 1 Increment of isotropic stress
Increase in effective stress in each direction
Ds3 - Duc
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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
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Typical values for parameter B
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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
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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
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Typical values for parameter A
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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
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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
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Unconsolidated- Undrained test (UU Test)
Mohr circles in terms of total stresses
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Unconsolidated- Undrained test (UU Test)
Effect of degree of saturation on failure envelope
S lt 100
S gt 100
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Some practical applications of UU analysis for
clays
1. Embankment constructed rapidly over a soft
clay deposit
t in situ undrained shear strength
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Some practical applications of UU analysis for
clays
2. Large earth dam constructed rapidly with no
change in water content of soft clay
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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
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Unconfined Compression Test (UC Test)
s1 sVC Ds
s3 0
Confining pressure is zero in the UC test
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Unconfined Compression Test (UC Test)
Note Theoritically qu cu , However in the
actual case qu lt cu due to premature failure of
the sample
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Lets do an example
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Stress Invariants (p and q)
p (or s) (s1 s3)/2
q (or t) (s1 - s3)/2
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Mohr Coulomb failure envelope in terms of stress
invariants
p (or s) (s1 s3)/2
q (or t) (s1 - s3)/2