shear strength of soil
TRANSCRIPT
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Shear Strength of Soil
Prof. Samirsinh P ParmarAssistant Professor, Department of Civil Engineering,Dharmasinh Desai University, Nadiad, Gujarat, INDIAMail: [email protected]
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Disclaimer
• The presentation slides produced here from the presentations of A Sivakugan, and Author feels hearty respect to him. This material is reproduced for just education purpose of students as well as faculty members for academic use only.
• It is expressed that getting copy right activity is characteristics of selfish personality and if anybody is thinking to disbelieve this fact, kindly do research on the copy right of English language.
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DEFINITIONS OF KEY TERMS• Shear strength of a soil (τf) is the maximum internal resistance to applied shearing forces.• Effective friction angle (Ø´) is a measure of the shear strength of soils due to friction.• Cementation (Ccm) is a measure of the shear strength of a soil from forces that cement the
particles.• Soil tension (Ct) is a measure of the apparent shear strength of a soil from soil suction
(negative pore water pressures or capillary stresses).• Cohesion (Co) is a measure of the intermolecular forces.• Undrained shear strength (Su) is the shear strength of a soil when sheared at constant
volume.• Apparent cohesion (C) is the apparent shear strength at zero normal effective stress.• Critical state is a stress state reached in a soil when continuous shearing occurs at constant
shear stress to normal effective stress ratio and constant volume.• Dilation is a measure of the change in volume of a soil when the soil is distorted by shearing.
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Strength of different materials
Steel
Tensile strength
Concrete
Compressive strength
Soil
Shear strength
Presence of pore waterComplexbehavior
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TYPICAL RESPONSE OF SOILS TO SHEARING FORCES
Simple shear deformation of Type I and Type II soils
Ref: Muni Budhu
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Embankment
Strip footing
Shear failure of soilsSoils generally fail in shear
Failure surface
Mobilized shear resistance
At failure, shear stress alongthe failuresurface
(mobilized shear resistance) reaches the shear strength.
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Retaining wall
Shear failure of soilsSoils generally fail in shear
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Retaining wall
Shear failure of soils
At failure, shear stress along the failuresurface(mobilized shear resistance) reaches the shear strength.
Failuresurface
Mobilized shear resistance
Soils generally fail in shear
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Shear failure mechanism
failure surface
The soil grains slide over each other along the failure surface.
Nocrushing
of individual grains.
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Shear failure mechanism
At failure, shear stressalongreaches the shear strength (f).
thefailure
surface()
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INTERPRETATION OF THE SHEAR STRENGTH OF SOILS
Contribution of sliding friction, dilatancy,crushing, and rearrangement of particles onthe peak shear strength of soils.
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Mohr-Coulomb Failure Criterion
f is the maximum shear stress the soil can takewithout failure, under normal stress of .
c
(in terms of total stresses)
f
c tan
Cohesion
Friction anglef
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Mohr-Coulomb Failure Criterion
f is the maximum shear stress the soil can takewithout failure, under normal effective stress of ’.
(in terms of effective stresses)
’
f c' ' tan '
’
c’
Effective cohesion
Effectivefriction angle
f
’
' uu = pore water
pressure
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Mohr-Coulomb Failure Criterion
tan' f c' ' f
’f
’
Shear strength consists of two components: cohesive and frictional.
f
'
c’
’f tan ’
c’
frictionalcomponent
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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
Soil element
’1
’
’1
Resolving forces in and directions,
’3’3
Cos2 '
Sin2
22
2
' ' 13
' ' 13
' 3
' 1
2 ' 3
'
1
2' 3
' 12
'22
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Mohr Circle of stress
2 ' 3
'
1
2
' '
13 2
' 22
’2
' 3
'1
2
' 3
'1
' 3
' 1
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Mohr Circle of stress
2 ' 3
'
1
2
' '
13 2
' 22
’2
PD = Pole w.r.t. plane
' 3
'1
2
' 3
'1
' 3
' 1
’,
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Soil elements at different locations
Failure surface
Mohr Circles & Failure Envelope
X X
Y ~ stable
X ~ failure
Y Y
’
f c' ' tan '
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Mohr Circles & Failure Envelope
Y
Initially, Mohr circle is a point
+c
GL
c
c
c
The soil element does not fail if the Mohr circle is contained within the envelope
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Mohr Circles & Failure Envelope
Y
GL
c
c
c
As loading progresses, Mohrcircle becomes larger…
.. and finally failure occurs when Mohr circle touches the envelope
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’2
PD = Pole w.r.t. plane
' 3
'1
' 3
' 1
’, f
Orientation of Failure Plane
’
’
’1
’1
’3’3
’
Failure envelope
–
Therefore,
– ’ =
45 + ’/2
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Mohr circles in terms of total & effective stresses
= X
v v’
h’ X
u
u+
v’ hh’
effective stresses
uv
Xh
total stresses
or ’
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Failure envelopes in terms of total & effective stresses
= +X
v’ hh’
effective stresses
uv
v v’
h’ X
u
uXh
total stresses
or ’
If X is onfailure
c’ c
Failure envelopein terms of total stresses’
Failure envelope in terms of effective stresses
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Mohr Coulomb failure criterion with Mohr circle of stress
X
’v = ’1
’h = ’3
X is on failure ’1c’’3
effective stresses
’’
Failure envelope in terms of effective stresses
c’ Cot’ ’ ’
’ ’
Sin '
'
' 3
c'Cot '
'
221
' 31
Therefore,
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Mohr Coulomb failure criterion with Mohr circle of stress
Sin '
'
' 3
c'Cot '
'
221
' 31
Sin' '2c'Cos
''1 3
''1 3
' 1 Sin' ' 1 Sin' 2c'Cos'
1 31 Sin ' '
1 Sin '
2c' Cos ' 1 Sin
'
3 '
1
2
' 2c'Tan 45
2
' ' Tan2 45
3 '
1
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Other laboratory tests include, Direct simple shear test, torsional ring shear test, plane strain triaxial test, laboratory vaneshear test, laboratory fall cone test
Determination ofsoils (c, or c’ ’
shear strength parameters of
Laboratory specimens
testson
taken fromrepresentativesamples
undisturbed
Field tests
Most common laboratory tests to determine the shear strength parameters are,
1.Direct shear test 2.Triaxial shear test
1. Vane shear test2. Torvane3. Pocket penetrometer4. Fall cone5. Pressuremeter6. Static cone penetrometer7. Standard penetration test
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LABORATORY TESTS
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Laboratory testsHow to take undisturbed samples
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Laboratory testsField conditions
zA representativesoil sample
vc
vc
hchc
Before construction
z + vc
hchc
After and duringconstruction
vc +
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Laboratory testsSimulating field conditions in the laboratory
Step 1
Set the specimen inthe apparatus and
initialapply thestress condition
vc
vc
hchc
Representative soil sample taken from the site
0
00
0
Step 2
Applycorresponding
thefield
stress conditions
vc +
hchc
vc +
vc
vc
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Direct shear testSchematic diagram of the direct shear apparatus
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Direct shear testPreparation of a sand specimen
Porous plates
Components of the shear box Preparation of a sand specimen
Direct shear test is most suitable for consolidated drained tests specially on granular soils (e.g.: sand) or stiff clays
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Direct shear test Mould
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Direct shear test
Leveling the top surface of specimen
Preparation of a sand specimen
Specimen preparation completed
Pressure plate
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Direct shear testTest procedure
Step 1: Apply a vertical load to the specimen and wait for consolidation
Pressure plate
Porousplates
S
Steel ballP
Proving ring to measure shear force
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Direct shear test
Step 1: Apply a vertical load to the specimen and wait for consolidation
Step 2: Lower box is subjected to a horizontal displacement at a constant rate
PTest procedurePressure plate
Porousplates
S
Steel ball
Proving ring to measure shear force
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Direct shear testShear box
Loading frameto apply vertical load
Dial gauge to measure vertical displacement
Dial gauge to measure horizontal displacement
Proving ring to measure shear force
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Direct shear testAnalysis of test results
Area of crosssection of the sample
Normalforce(P) Normalstress
Shear stress Shear resistance developedat the sliding surface
(S)Area of cross section of the sampleNote: Cross-sectional area of the sample changes with the horizontal
displacement
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Shea
r str
ess,
Shear displacement
Dense sand/ OC clay
fLoose sand/NC clayf
Dense sand/OC Clay
Direct shear tests on sandsStress-strain relationship
Shear displacementLoose sand/NC Clay
Cha
nge
in h
eigh
tof
the
sam
ple
Expa
nsio
nC
ompr
essi
on
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f1Normal stress = 1
Direct shear tests on sands
Shea
r str
ess,
How to determine strength parameters c and
Normal stress = 3
Normal stress = 2
Shear displacement
f2f3
Shea
r str
ess
at fa
ilure
, f
Normal stress,
Mohr – Coulomb failure envelope
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Direct shear tests on sands
Some important facts on strength parameters c and of sand
Sand is cohesionlesshence c = 0
Direct shear tests are drained and pore water pressuresare dissipated, hence u = 0
Therefore,
’ = and c’ = c = 0
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Direct shear tests on clays
Failure envelopes for clay from drained direct shear testsSh
ear s
tres
s at
failu
re,
f
Normal force,
Normally consolidated clay (c’ = 0)
’
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)
Overconsolidated clay (c’ ≠ 0)
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Interface tests on direct shear apparatusIn 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)
f ca ' tan
Where,
ca = adhesion,
= angle of internal friction
Soil
Foundation materialFoundation material
Soil
P
S
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Advantages of direct shear apparatus
Due to the smaller thickness of the sample, rapid drainage canbe 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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Triaxial Shear Test
Soil sample at failure
Failure plane
Porous stone
impervious membrane
Piston (to apply deviatoric stress)
O-ring
pedestal
Perspexcell
Cell pressure Back pressure Pore pressure or
volume change
Water
Soil sample
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Triaxial Test Equipment
The Cell (Chamber)
Loading Frame Control Panel
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Triaxial Test Equipment
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Triaxial Shear TestSpecimen preparation (undisturbed sample)
Sampling tubes
Sample extruder
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Triaxial Shear TestSpecimen preparation (undisturbed sample)
Edges of the sample are carefully trimmed
Setting up the sample in the triaxial cell
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Triaxial Shear Test
Cell is completely filled with water
Specimen preparation (undisturbed sample)
Sample is coveredwith amembrane an
rubber d sealed
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Triaxial Shear TestSpecimen preparation (undisturbed sample)
Proving ring to measure the deviator load
Dial gauge to measure vertical displacementIn some tests
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Types of Triaxial TestsDepending 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
Consolidated
Drained (CD) test
Undrained (CU) testUnconsolidated Undrained (UU) test
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Types of Triaxial Tests
Is the drainage valve open?
yes no
Consolidatedsample
Unconsolidatedsample
Is the drainage valve open?
yes no
Drainedloading
Undrainedloading
Under all-around cell pressure c
cc
c
cStep 1
deviatoric stress ( = q)
Shearing (loading)
Step 2
c c
c+ q
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Types of Triaxial Tests
Is the drainage valve open?
yes no
Consolidatedsample Unconsolidated
sample
Under all-around cell pressure c
Step 1
Is the drainage valve open?
yes no
Drainedloading
Undrainedloading
Shearing (loading)
Step 2
CD test
CU test
UU test
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Consolidated- drained test (CD Test)
Step 1: At the end of consolidationVC
hC
Total, = Neutral, u Effective, ’+
0
Step 2: During axial stress increaseVC +
’VC = VC
’hC =hC
hC 0
’V = VC + =’1
’h = hC = ’3
Drainage
Drainage
Step 3: At failureVC + f
hC 0
’Vf = VC + f = ’1f
’hf = hC = ’3fDrainage
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1 = VC +
3 = hC
Deviator stress (q or d) = 1 – 3
Consolidated- drained test (CD Test)
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Volu
me
chan
ge o
f th
e sa
mpl
e
Expa
nsio
nC
ompr
essi
on
Time
Volume change of sample during consolidation
Consolidated- drained test (CD Test)
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Dev
iato
r str
ess,
d
Axial strain
Dense sand or OC clay
Axial strain
Loose sandor NC clay
Stress-strain relationship during shearing
Dense sand or OC clay
d)f
Volu
me
chan
geof
the
sam
ple
Expa
nsio
nC
ompr
essi
on
Consolidated- drained test (CD Test)
Loose sandor NC Clayd)f
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CD tests How to determine strength parameters c and
Dev
iato
r str
ess,
d
Axial strain
Mohr – Coulomb failure envelope
Shea
r str
ess,
or ’
d
)fa
Confining stress = 3a
)
d fb
Confining stress = 3c
Confining stress = 3b
d
)fc
3c
1c
3a
1a( d
)fa
3b
1b( )
d fb
1 = 3
+ ( )
d f
3
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CD tests
Strength parameters c and obtained from CD tests
Since u = 0 in CDtests, = ’
Therefore, c = c’and = ’
cd and d are used to denote them
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CD tests
Failure envelopes
Shea
r str
ess,
σ or ’
dMohr – Coulomb failure envelope
σ1a
( d)fa
For sand and NC Clay, cd = 0
Therefore, one CD test would be sufficient to determine d
of sand or NC clay
σ3a
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CD tests
Failure envelopes
For OC Clay, cd ≠ 0
or ’
3
1(
d)f
cc
OC NC
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Some practical applications of CD analysis for clays
= in situ drained shear strength
Soft clay
1. Embankment constructed very slowly, in layers over a soft clay
deposit
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Some practical applications of CD analysis for clays
2. Earth dam with steady state seepage
Core
=
drained
shear
strength of clay core
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Some practical applications of CD analysis for clays
3. Excavation or natural slope in clay
= In situ drained shear strength
Note: CD test simulates the long term condition in the field. Thus, cd and d should be used to evaluate the long term behavior of soils
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SHEAR STRENGTH OF SOIL
SELECTION OF TRIAXIAL TESTSoil type Type of construction Type of tests and shear strength
Cohesive Short term (end ofconstruction time)
Triaxial UU or CU for Undrained Strength with appropriatelevel of insitu strength
Staging Construction Triaxial CU for Undrained Strength with appropriate level of insitu strength
Long term Triaxial CU with pore water pressure measurement or Triaxial CD for effective shear strength parameter
Granular All Strength parameter ’ which is got from field investigation ordirect shear test
Material c- Long Term Triaxial CU with pore water pressure measurement or TriaxialCD for effective shear strength parameter
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Consolidated- Undrained test (CU Test)
Step 1: At the end of consolidation VC
hC
Total, = +Neutral, u Effective, ’
0
Step 2: During axial stress increase VC +
’VC = VC
’hC
= h
C
hC
±u
Drainage
Step 3: At failure VC + f
hC
No drainage
No drainage
±uf
’V = VC
+ ± u = ’1
’h = hC
u = ’3
±
’Vf = VC + f
uf = ’1f
±
’hf =
hC ±
uf = ’3f
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Volu
me
chan
ge o
f th
e sa
mpl
e
Expa
nsio
nC
ompr
essi
on
Time
Volume change of sample during consolidationConsolidated- Undrained test (CU Test)
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Dev
iato
r str
ess,
d
Axial strain
Loose sand/NC Clay
Axial strain
Dense sand or OC clay
Stress-strain relationship during shearing
Dense sand or OC clay
d)f
u+
-
Consolidated- Undrained test (CU Test)
Loose sandor NC Clay
d)f
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CU tests How to determine strength parameters c and
Dev
iato
r str
ess,
d
Axial strain
Shea
r str
ess,
or ’
d
)fb
3b
1b
3a
1a( d
)fa
cuMohr – Coulomb failure envelope in terms of total stresses
ccu
Total stresses at failure
Confining stress = 3b
Confining stress = 3a
1 = 3 + ( d)f
3 d
)fa
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( d)f
a
CU tests
Shea
r str
ess,
or ’
3b
1b
’3b
’3a
3a
ufb
’1b 1a
’1a( d)f
a
cu
Mohr – Coulomb failure envelope in terms of effective stresses
Mohr – Coulomb failure envelope in terms of total stresses
ccu
’
C’ ufa
How to determine strength parameters c and ’1 = 3 + ( d)f - uf
’ = 3 - uf
Effective stresses at failure
uf
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CU testsStrength parameters c and obtained from CD tests
Shearstrengthparameters intermsof total stressesare ccu and cu
Shearstrength parameters in terms of effective stresses are c’ and ’
c’ = cd and ’ = d
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CU tests Failure envelopesFor sand and NC Clay, ccu and c’ = 0
Therefore, one CU test would be sufficient to determinecu and ’= d) of sand or NC clay
Shea
r str
ess,
or ’
cuMohr – Coulomb failure envelope in terms of total stresses
3a 3a
1a 1a
( d)fa
’
Mohr – Coulomb failure envelope in terms of effective stresses
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Some practical applications of CU analysis for clays
= in situ undrained shear strength
Soft clay
1. Embankment constructed rapidly over a soft clay deposit
![Page 76: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/76.jpg)
Some practical applications of CU analysis for clays
2. Rapid drawdown behind an earth dam
• • Core
• = 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 cu) 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
= In situ undrained shear strength
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Unconsolidated- Undrained test (UU Test)Data analysis
C = 3 C =
3
No drainage
Initial specimen condition
3 + d3
No drainage
Specimen conditionduring shearing
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 – H) = A0 × H0
A ×(1 – H/H0) = A0 z
AA
1
0
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Unconsolidated- Undrained test (UU Test)Step 1: Immediately after sampling
0
0
= +
Step 2: After application of hydrostatic cell pressure
uc = B 3
C = 3 C =
3
uc
’3 = 3 - uc
’3 = 3 - uc
Nodrainage
Increase of pwp due to increase of cell pressure
Increase of cell pressure
Skempton’s pore waterpressure parameter, BNote: If soil is fully saturated, then B = 1 (hence, uc = 3)
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Unconsolidated- Undrained test (UU Test)
Step 3: During application of axial load
3 + d
3
No drainage
’1 = 3 + d - uc
ud
’ = - u u3 3 c d
uc ± ud
ud = AB d
= +
Increase of pwp due toincrease of deviator stress
Increase stress
ofdeviator
Skempton’s pore waterpressure parameter, A
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Unconsolidated- Undrained test (UU Test)Combining steps 2 and 3,
uc = B 3 ud = AB d
Total pore water pressure increment at any stage, u
u = uc + ud
u = B [ 3 + A d]Skempton’s pore water pressure equation
u = B [ 3 + A( 1 – 3]
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Unconsolidated- Undrained test (UU Test)
Derivation of Skempton’s pore water pressure equation
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Step 1 :Increment of isotropic stress
Derivation of Skempton’s pore water pressure equation
2
3
1
No drainage
1 + 3
3 + 3
2 + 3
No drainage
uc
Increase in effective stress in each direction = 3 - uc
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Step 2 :Increment of major principal stress
Derivation of Skempton’s pore water pressure equation
2
3
1
No drainage
1 + 1
3 + 0
+ 0
2
No drainage
uc
Increase in effective stress in 1 direction = 1 - ud
Increase in effective stress in 2 and 3 directions = - ud
Average Increase in effective stress = ( 1 - ud - ud – ud)/3
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Typical values for parameter B
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Typical values for parameter A 1 – 3
u
Axial strain
NC Clay (low
sensitivity) (A = 0.5 –
1.0)
NC Clay (High sensitivity)
(A > 1.0)
Axial strain
u
1 – 3
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 1 – 3
Axial strain
OC Clay (Lightly overconsolidated)
(A = 0.0 – 0.5)
OC Clay (Heavily overconsolidated)
(A = -0.5 - 0.0)
During the increase of major principal stress pore water pressure can become negative in heavily overconsolidated clays due to dilation of specimen
Axial strain
uu
1 – 3
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Typical values for parameter A
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Unconsolidated- Undrained test (UU Test)
Step 1: Immediately after sampling
0
0
Total, = +Neutral, u Effective, ’
-ur
Step 2: After application of hydrostatic cell pressure
’V0 = ur
’h0 = ur
C
C
-ur uc = -ur c
(Sr = 100% ; B = 1)
Step 3: During application of axial load
C +
C
No drainage
No drainage -u ±
ur c
’VC = C + ur - C = ur
’h = ur
Step 3: At failure
’V = C + + ur - c u
’=
h C r c
+ u - u
’hf = C + ur - c
uf
= ’3f
’Vf = C + f + ur - c
uf = ’1f
-u ± u
r c fC
C + f
No drainage
![Page 90: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/90.jpg)
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3a
b
a
3c 3b
Unconsolidated- Undrained test (UU Test)Effect of degree of saturation on failure envelope
c
or ’
S < 100% S > 100%
![Page 93: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/93.jpg)
Some practical applications of UU analysis for clays
= in situ undrained shear strength
Soft clay
1. Embankment constructed rapidly over a soft clay deposit
![Page 94: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/94.jpg)
Some practical applications of UU analysisfor clays2. Large earth dam constructed rapidly with
no change in water content of soft clay• • Core
• = Undrained shear
• strength of clay core
![Page 95: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/95.jpg)
Some practical applications of UU analysisfor clays3. Footing placed rapidly on clay deposit
= In situ undrained shear strength
Note: UU test simulates the short term condition in the field.Thus, cu can be used to analyze the short
termbehavior of soils
![Page 96: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/96.jpg)
True Triaxial Apparatus
FIGURE : Schematic of true triaxial cell and stresses imposed on a sample of soil.
• The purpose of a true triaxial test is to determine soil behaviour and properties by loading the soil in three dimensions.
• In a true triaxial test, a cuboidal sample is subjected to independent Displacements or stresses on three Cartesian axes.
• Displacements are applied through a system of rigid metal plates moving perpendicularly and tangentially to each face, as shown by the arrows in Figure
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Unconfined Compression Test (UC Test)
1 = VC +
3 = 0
Confining pressure is zero in the UC test
![Page 98: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/98.jpg)
Unconfined Compression Test (UC Test)
1 = VC + f
3 = 0
qu
Normal stress, Sh
ear s
tres
s,
Note: Theoritically qu = cu , However in the actual case qu < cu due to premature failure of the sample
![Page 99: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/99.jpg)
Stress Invariants (p and q)p (or s) = ( 1 + 3)/2 q (or t) = ( 1 - 3)/2
( 1 - 3)/2
3 1( 1 + 3)/2
c
p and q can be used to illustrate the variation of the stress state of a soil specimen during a laboratory triaxial test
![Page 100: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/100.jpg)
GL
c
c
Stress Invariants (p and q)
c
p (or s) = (1 + 3)/2 q (or t) = (1 - 3)/2
or
q or p
![Page 101: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/101.jpg)
Mohr Coulomb failure envelope in terms of stress invariants
p (or s) = (1 + 3)/2 q (or t) = (1 - 3)/2
Sin '
' '
c 'Cot
'
' '
221 31 3
'
Sin 'c'Cos '
223
' 1
'3
'1
3 1(1 + 3)/2
(1 - 3)/2
c
q pSin 'c'Cos '
![Page 102: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/102.jpg)
p (or s) = (1 + 3)/2 q (or t) = (1 - 3)/2
or
q
or p
Mohr Coulomb failure envelope in terms of stress invariants
c cos
Therefore, sin = tan = sin-1(tan
![Page 103: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/103.jpg)
Stress path for CD triaxial test
3
p, p’ (or s, s’) = (1 + 3)/2
= (’1 + ’3)/2
q (or t) = (1 - 3)/2
or
q or p
In CD tests pore water pressure is equal to zero. Therefore, total and effective stresses are equal
Step 1 3
3
p, p’ (or s, s’) = 3 q (or t) = 0
Step 2 3 + d
3
p, p’ (or s, s’) = 3 + d/2 q (or t) = d/2d
450
![Page 104: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/104.jpg)
Stress path for CU triaxial test
450
3 = ’3
p (or s) = (1 + 3)/2
p’ (or s’) = (1 + 3)/2 - uq (or t) = (1 - 3)/2
In CU tests pore water pressure develops during shearing
Step 1 3
3
p, p’ (or s, s’) = 3 q (or t) = 0
p (or s) = 3 + d/2d
ud
Step 2 3 + d
3ud
q ’ or p, p’q (or t) = d/2
![Page 105: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/105.jpg)
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
![Page 106: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/106.jpg)
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
![Page 107: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/107.jpg)
Direct simple shear test
Direct shear test = 80 mm
Soil specimenPorousstones
Spiral wire in rubber membrane
Direct simple shear test
![Page 108: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/108.jpg)
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
![Page 109: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/109.jpg)
Torsional ring shear test
’max
’res
PeakResidual
Shear displacement
f
’
![Page 110: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/110.jpg)
Torsional ring shear test
N
Preparation of ring shaped undisturbed samples is very difficult. Therefore, remoulded samples are used in most cases
![Page 111: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/111.jpg)
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
![Page 112: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/112.jpg)
Plane strain triaxial test
’1, 1
’2, 2
’3, 3
Plane strain test
’2 ≠ ’3
2 = 0
’1
’2
’3
’2
Rigid platens
Specimen
![Page 113: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/113.jpg)
FIELD TESTS
![Page 114: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/114.jpg)
In-situ shear tests
Vane shear test
Torvane
Pocket Penetrometer
Pressuremeter
Static Cone Penetrometer test (Push Cone Penetrometer Test, PCPT)
Standard Penetration Test, SPT
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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
![Page 116: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/116.jpg)
PLAN VIEW
Vane shear testThis is one of the most versatile and widely used devices used for investigating undrained shear strength (Cu) and sensitivity of soft clays
Bore hole(diameter = DB)
h > 3DB)
Vane
D
H
Applied Torque, T
Vane T
Rupture surface
Disturbed soil
Rate of rotation : 60 – 120 per minute
Test can be conducted at 0.5m vertical intervals
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Vane shear test
Since the test is very fast, Unconsolidated Undrained (UU) can be expected
Cu
Cu
T = Ms + Me + Me = Ms + 2Me
Me – Assuming a uniformdistribution of shear strength
3 0
u
0
r 2 dr 2C
M 2C
u e
12 8 32C C d
3 d 3 M
uue
d/2
d/2d2
M e (2rdr).C u r
0
r 3 2
d2
d
Cu
h
![Page 118: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/118.jpg)
Vane shear test
Since the test is very fast, Unconsolidated Undrained (UU) can be expected
Cu
Cu
Ms – Shaft shear resistance along the circumference
22d 2h
Cu
dM s dhCu
2122
32
d h Cu dT C
u
6
d 3 T Cu
d 2
h 2
6
d 3 d 2 h
Cu
2
T
T = Ms + Me + Me = Ms + 2Me
![Page 119: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/119.jpg)
Vane shear test
Since the test is very fast, Unconsolidated Undrained (UU) can be expected
Cu
Cu
T = Ms + Me + Me = Ms + 2Me
Me – Assuming a triangulardistribution of shear strength
hd/2d/2
Cu
8
d 3
d 2 h
C
2
T u
Can you derive this ???
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Vane shear test
Since the test is very fast, Unconsolidated Undrained (UU) can be expected
Cu
Cu
T = Ms + Me + Me = Ms + 2Me
Me – Assuming a parabolicdistribution of shear strength
h
2 20
3d 3 d 2 h
C
Tu
Can you derive this ???
d/2d/2
Cu
![Page 121: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/121.jpg)
Vane shear test
Since the test is very fast, Unconsolidated Undrained (UU) can be expected
Cu
Cu
h
After the initial test, vane can be rapidly rotated through several
the claybecome
revolutions until remoulded
peakultimate
Shear displacement
UltimateStengthPeak StengthSensitivity
![Page 122: Shear strength of soil](https://reader035.vdocuments.us/reader035/viewer/2022062400/589e58c61a28ab16348b4eab/html5/thumbnails/122.jpg)
Some important facts on vane shear test
Insertion of vane into soft clays and silts disrupts the natural soil structure around the vane causing reduction of shear strength
The above reduction is partially regained after some time
Cu as determined by vane shear test may be a function of the rate of angular rotation of the vane
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Correction for the strength parameters obtained from vane shear test
Cu(design) = Cu(vane shear)
Where, = correction factor = 1.7 – 0.54 log (PI)
PI = Plasticity Index
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.
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TorvaneTorvane is a modification to the vane
FIELD VANE SHEAR TEST
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Pocket PenetrometerPushed directly into the soil. The unconfined compression strength (qu) is measured by a calibrated spring.
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Swedish Fall Cone (suitable for very soft to soft clays)
The test must be calibrated
Soil sample
Cu ∞ Mass of the cone
∞ 1/(penetration)2
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PressuremeterAir
Coaxial tube
Water
Pre – bored or self – bored holeGuard cell
Measuring cell
Guard cell
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Pressuremeter
Pre – bored or self – bored hole
Guard cell
Measuring cell
Guard cell
Coaxial tube
Water
Air Pres
sure
Volu
met
ric e
xpan
sion Time
PressureVolu
met
ric e
xpan
sion
Pseudo- elastic phase
Elastic phase
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Static Cone Penetrometer test
Cone penetrometers with pore water pressure measurement capability are known as piezocones
40 mm
40 mm
40 mm
40 mm
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Static Cone Penetrometer testForce 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, ect) from fr
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Standard Penetration Test, SPTSPT is the most widely used test procedure to determinethe properties of in-situ soils
63.5 kg
The test can be conducted at every 10.76 m vertical intervals
Drill rod0.15 m0.15 m0.15 m
Number of blows = N1
Number of blows = N2
Number of blows = N3
Standard penetration resistance (SPT N) = N2 + N3
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 soilm strength parameters (c, ect) from N
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Standard Penetration Test, SPT
SPT (Manual operation)
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Various correlations for shear strengthFor NC clays, the undrained shear strength (cu) increases withthe effective overburden pressure, ’0
0.11 0.0037(PI ) '
0
cu Skempton (1957)
Plasticity Index as a %For OC clays, the following relationship is approximately true
(OCR)0.8
' 0
' 0
cc
Overconsolidated Normally Consolidated
uu
Ladd (1977)
For NC clays, the effective friction angle (’) is related to PI as follows
Sin ' 0.814 0.234 log(IP)
Kenny (1959)
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Shear strength of partially saturated soilsIn 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
Solid
Water
Saturated soils Unsaturated soils
Pore waterpressure, u
Effective stress, ’ Solid
Pore waterpressure, uw
Effective stress, ’
Water
AirPore airpressure, ua
Pore water pressure can be negative in unsaturated soils
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Shear strength of partially saturated soilsBishop (1959) proposed shear strength equation for unsaturated soils as follows
c'( u ) (u u)tan'
n a aw
f
Where,n – ua = Net normal stressua – uw = Matric suction= a parameter depending on the degree of saturation
( = 1 for fully saturated soils and 0 for dry soils)
Fredlund et al (1978) modified the above relationship as follows
b f c'( n ua ) tan '(ua uw ) tanWhere,tanb = Rate of increase of shear strength with matric suction
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Shear strength of partially saturated soils
b f c'( n ua ) tan '(ua uw ) tan
Same as saturated soils Apparent cohesion due to matric suction
Therefore, strength of unsaturated soils is much higher than the strength of saturated soils due to matric suction
’
- ua
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’
- ua
How it become possible build a sand castle ?
b f c'( n ua ) tan'(ua uw ) tan
Same as saturated soils Apparent cohesiondue to matric suction
Apparent cohesion
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Ranges of Friction Angles for Soils (degrees)
*Higher values (32°–37°) in the range are for sands with significant amount of feldspar (Bolton, 1986). Lower values (27°–32°) in the range are for quartz sands.
Ref: Muni Budhu, page no. 282
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Summary of Equations for the Four Failure Criteria
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Correlation of N, N60, γ, Dr, and Ø´ for Coarse-Grained Soils
Correlation of N60 and su for Saturated Fine-Grained Soils
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Empirical Soil Strength Relationships
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Some practical cases and the laboratory strength tests to specify.
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Some practical cases and the laboratory strength tests to specify.
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Some practical cases and the laboratory strength tests to specify.
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Questions ???