Shear Strength of Soils Fars Science and Research Branch, Islamic Azad University
Dec 23, 2015
Shear Strength of Soils
Fars Science and Research Branch,
Islamic Azad University
2
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 .
tancf
c
failure envelope
Cohesion
Friction anglef
3
Mohr-Coulomb Failure Criterion(in terms of effective stresses)
f is the maximum shear stress the soil can take without failure, under normal effective stress of ’.
’
'tan'' cf
c’
’
failure envelope
Effective
cohesion
Effectivefriction angle
f
’
u '
u = pore water pressure
4
Mohr-Coulomb Failure Criterion
'tan'' ff c
Shear strength consists of two components: cohesive and frictional.
’f
f
’
'
c’ c’cohesive
component
’f tan ’ frictional component
s’
2
'3
'1 '
3 '1
PD = Pole w.r.t. plane
q
(s’, tf)
Orientation of Failure Plane
f’
’1
’1
’3’3
’
’1
’1
’3’3
’
Failure envelope
(90 – )q
Therefore,
90 – + q f’ = q = q 45 + f’/2
6
Other laboratory tests include,Direct simple shear test, torsional ring shear test, plane strain triaxial test,
Determination of shear strength parameters of soils (c, f or c’, f’)
Laboratory tests on specimens taken from representative undisturbed samples
Field tests
Most common laboratory tests to determine the shear strength parameters are,
1.Direct shear test2.Triaxial shear test
1. Vane shear test2. Torvane3. Pocket penetrometer4. Pressuremeter5. Static cone penetrometer6. Standard penetration test
7
Laboratory tests
Field conditions
z svc
svc
shcshc
Before construction
A representative soil sample
z svc + Ds
shcshc
After and during construction
svc + Ds
8
Laboratory testsSimulating field conditions in the laboratory
Step 1
Set the specimen in the apparatus and apply the initial stress condition
svc
svc
shcshc
Representative soil sample taken from the site
0
00
0
Step 2
Apply the corresponding field stress conditions
svc + Ds
shcshc
svc + DsTraxial t
est
svc
svc
t
t
Direct shear test
9
Direct shear testSchematic diagram of the direct shear apparatus
10
Direct shear test
Preparation of a sand specimen
Components of the shear box Preparation of a sand specimen
Porous plates
Direct shear test is most suitable for consolidated drained tests specially on granular soils (e.g.: sand) or stiff clays
11
Direct shear test
Leveling the top surface of specimen
Preparation of a sand specimen
Specimen preparation completed
Pressure plate
12
Direct shear test
Test procedure
Porous plates
Pressure plate
Steel ball
Step 1: Apply a vertical load to the specimen and wait for consolidation
P
Proving ring to measure shear force
S
13
Direct shear test
Step 2: Lower box is subjected to a horizontal displacement at a constant rate
Step 1: Apply a vertical load to the specimen and wait for consolidation
PTest procedure
Pressure plate
Steel ball
Proving ring to measure shear force
S
Porous plates
14
Direct shear test
Shear box
Loading frame to apply vertical load
Dial gauge to measure vertical displacement
Dial gauge to measure horizontal displacement
Proving ring to measure shear force
15
Direct shear testAnalysis of test results
sample theofsection cross of Area
(P) force Normal stress Normal
sample theofsection cross of Area
(S) surface sliding at the developed resistanceShear stressShear
Note: Cross-sectional area of the sample changes with the horizontal displacement
16
Direct shear tests on sands
Sh
ear
str
ess
, t
Shear displacement
Dense sand/ OC clay
tfLoose sand/ NC claytf
Dense sand/OC Clay
Loose sand/NC Clay
Ch
ang
e in
hei
gh
t o
f th
e sa
mp
le Exp
ansi
on
Co
mp
ress
ion Shear displacement
Stress-strain relationship
17
tf1
Normal stress = s1
Direct shear tests on sandsHow to determine strength parameters c and f
Sh
ear
stre
ss,
t
Shear displacement
tf2
Normal stress = s2
tf3
Normal stress = s3
Sh
ear
stre
ss a
t fa
ilu
re,
tf
Normal stress, s
fMohr – Coulomb failure envelope
18
Direct shear tests on sandsSome important facts on strength parameters c and f of sand
Sand is cohesionless hence c = 0
Direct shear tests are drained and pore water pressures are dissipated, hence u = 0
Therefore,
f’ = f and c’ = c = 0
19
Direct shear tests on clays
Failure envelopes for clay from drained direct shear tests
Sh
ear
stre
ss a
t fa
ilu
re,
tf
Normal force, s
f’
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)
20
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
21
Triaxial Shear Test
Soil sample at failure
Failure plane
Porous stone
impervious membrane
Piston (to apply deviatoric stress)
O-ring
pedestal
Perspex cell
Cell pressureBack pressure Pore pressure or
volume change
Water
Soil sample
22
Triaxial Shear TestSpecimen preparation (undisturbed sample)
Edges of the sample are carefully trimmed
Setting up the sample in the triaxial cell
23
Triaxial Shear Test
Sample is covered with a rubber membrane and sealed
Cell is completely filled with water
Specimen preparation (undisturbed sample)
24
Triaxial Shear TestSpecimen preparation (undisturbed sample)
Proving ring to measure the deviator load
Dial gauge to measure vertical displacement
25
Types of Triaxial Tests
Is the drainage valve open?
yes no
Consolidated sample
Unconsolidated sample
Is the drainage valve open?
yes no
Drained loading
Undrained loading
Under all-around cell pressure c
cc
c
cStep 1
deviatoric stress ( = q)
Shearing (loading)
Step 2
c c
c+ q
26
Types of Triaxial Tests
Is the drainage valve open?
yes no
Consolidated sample
Unconsolidated sample
Under all-around cell pressure c
Step 1
Is the drainage valve open?
yes no
Drained loading
Undrained loading
Shearing (loading)
Step 2
CD test
CU test
UU test
27
Consolidated- drained test (CD Test)
Step 1: At the end of consolidationsVC
shC
Total, s = Neutral, u Effective, s’+
0
Step 2: During axial stress increase
s’VC = sVC
s’hC = shC
sVC + Ds
shC 0
s’V = sVC + Ds = s’1
s’h = shC = s’3
Drainage
Drainage
Step 3: At failuresVC + Dsf
shC 0
s’Vf = sVC + Dsf = s’1f
s’hf = shC = s’3fDrainage
28
Deviator stress (q or Dsd) = s1 – s3
Consolidated- drained test (CD Test)
s1 = sVC + Ds
s3 = shC
29
Vo
lum
e ch
ang
e o
f th
e sa
mp
le
Exp
ansi
on
Co
mp
ress
ion
Time
Volume change of sample during consolidation
Consolidated- drained test (CD Test)
30
De
via
tor
str
ess
, D
sd
Axial strain
Dense sand or OC clay
(Dsd)f
Dense sand or OC clay
Loose sand or NC clay
Vo
lum
e ch
ang
e o
f th
e sa
mp
le Exp
ansi
on
Co
mp
ress
ion Axial strain
Stress-strain relationship during shearing
Consolidated- drained test (CD Test)
Loose sand or NC Clay(Dsd)f
31
CD tests How to determine strength parameters c and fD
evia
tor
stre
ss,
Ds
d
Axial strain
Sh
ear
stre
ss,
t
sor s’
fMohr – Coulomb failure envelope
(Dsd)fa
Confining stress = s3a(Dsd)fb
Confining stress = s3b
(Dsd)fc
Confining stress = s3c
s3c s1cs3a s1a
(Dsd)fa
s3b s1b
(Dsd)fb
s1 = s3 + (Dsd)f
s3
32
CD tests
Strength parameters c and f obtained from CD tests
Since u = 0 in CD tests, s = s’
Therefore, c = c’ and f = f’
cd and fd are used to denote them
33
CD tests Failure envelopesS
hea
r st
ress
, t
sor s’
fd
Mohr – Coulomb failure envelope
s3a s1a
(Dsd)fa
For sand and NC Clay, cd = 0
Therefore, one CD test would be sufficient to determine fd
of sand or NC clay
34
CD tests Failure envelopes
For OC Clay, cd ≠ 0
t
sor s’
f
s3 s1
(Dsd)f
csc
OC NC
35
Some practical applications of CD analysis for clays
t t = in situ drained shear strength
Soft clay
1. Embankment constructed very slowly, in layers over a soft clay deposit
36
Some practical applications of CD analysis for clays
2. Earth dam with steady state seepage
t = drained shear strength of clay core
t
Core
37
Some practical applications of CD analysis for clays
3. Excavation or natural slope in clay
t = In situ drained shear strength
t
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
38
Consolidated- Undrained test (CU Test)
Step 1: At the end of consolidationsVC
shC
Total, s = Neutral, u Effective, s’+
0
Step 2: During axial stress increase
s’VC = sVC
s’hC = shC
sVC + Ds
shC ±Du
Drainage
Step 3: At failuresVC + Dsf
shC
No drainage
No drainage ±Duf
s’V = sVC + Ds ± Du = s’1
s’h = shC ± Du = s’3
s’Vf = sVC + Dsf ± Duf = s’1f
s’hf = shC ± Duf = s’3f
39
Vo
lum
e ch
ang
e o
f th
e sa
mp
le
Exp
ansi
on
Co
mp
ress
ion
Time
Volume change of sample during consolidation
Consolidated- Undrained test (CU Test)
40
De
via
tor
str
ess
, D
sd
Axial strain
Dense sand or OC clay
(Dsd)f
Dense sand or OC clay
Loose sand /NC Clay
Du
+-
Axial strain
Stress-strain relationship during shearing
Consolidated- Undrained test (CU Test)
Loose sand or NC Clay(Dsd)f
41
CU tests How to determine strength parameters c and fD
evia
tor
stre
ss,
Ds
d
Axial strain
Sh
ear
stre
ss,
t
sor s’
(Dsd)fb
Confining stress = s3b
s3b s1bs3a s1a
(Dsd)fa
fcuMohr – Coulomb failure envelope in terms of total stresses
ccu
s1 = s3 + (Dsd)f
s3
Total stresses at failure(Dsd)fa
Confining stress = s3a
42(Dsd)fa
CU tests How to determine strength parameters c and fS
hea
r st
ress
, t
sor s’s3b s1bs3a s1a
(Dsd)fa
fcu
Mohr – Coulomb failure envelope in terms of total stresses
ccus’3b s’1b
s’3a s’1a
Mohr – Coulomb failure envelope in terms of effective stresses
f’
C’ ufa
ufb
s’1 = s3 + (Dsd)f - uf
s’3 = s3 - uf
Effective stresses at failure
uf
43
CU tests
Strength parameters c and f obtained from CD tests
Shear strength parameters in terms of total stresses are ccu and fcu
Shear strength parameters in terms of effective stresses are c’ and f’
c’ = cd and f’ = fd
44
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
Sh
ear
stre
ss,
t
sor s’
fcuMohr – Coulomb failure envelope in terms of total stresses
s3a s1a
(Dsd)fa
s3a s1a
f’
Mohr – Coulomb failure envelope in terms of effective stresses
45
Some practical applications of CU analysis for clays
t t = in situ undrained shear strength
Soft clay
1. Embankment constructed rapidly over a soft clay deposit
46
Some practical applications of CU analysis for clays
2. Rapid drawdown behind an earth dam
t = Undrained shear strength of clay core
Core
t
47
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
t = In situ undrained shear strength
t
48
Unconsolidated- Undrained test (UU Test)Data analysis
sC = s3
sC = s3
No drainage
Initial specimen condition
s3 + Dsd
s3
No drainage
Specimen condition during 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 – DH) = A0 × H0
A ×(1 – DH/H0) = A0z
AA
10
49
Unconsolidated- Undrained test (UU Test)
Step 1: Immediately after sampling0
0
= +
Step 2: After application of hydrostatic cell pressure
Duc = B Ds3
sC = s3
sC = s3 Duc
s’3 = s3 - Duc
s’3 = s3 - Duc
No drainage
Increase of pwp due to increase of cell pressure
Increase of cell pressure
Skempton’s pore water pressure parameter, B
Note: If soil is fully saturated, then B = 1 (hence, Duc = Ds3)
50
Unconsolidated- Undrained test (UU Test)
Step 3: During application of axial load
s3 + Dsd
s3
No drainage
s’1 = s3 + Dsd - Duc Dud
s’3 = s3 - Duc Dud
Dud = ABDsd
Duc ±
Dud
= +
Increase of pwp due to increase of deviator stress
Increase of deviator stress
Skempton’s pore water pressure parameter, A
51
Unconsolidated- Undrained test (UU Test)
Combining steps 2 and 3,
Duc = B Ds3 Dud = ABDsd
Du = Duc + Dud
Total pore water pressure increment at any stage, Du
Du = B [Ds3 + ADsd]
Skempton’s pore water pressure equation
Du = B [Ds3 + A(Ds1 – Ds3]
52
Unconsolidated- Undrained test (UU Test)
Step 1: Immediately after sampling
0
0
Total, s = Neutral, u Effective, s’+
-ur
Step 2: After application of hydrostatic cell pressure
s’V0 = ur
s’h0 = ur
sC
sC
-ur + Duc = -ur + sc
(Sr = 100% ; B = 1)Step 3: During application of axial load
sC + Ds
sC
No drainage
No drainage
-ur + sc ± Du
s’VC = sC + ur - sC = ur
s’h = ur
Step 3: At failure
s’V = sC + Ds + ur - sc Du
s’h = sC + ur - sc Du
s’hf = sC + ur - sc Duf
= s’3f
s’Vf = sC + Dsf + ur - sc Duf = s’1f
-ur + sc ± Duf
sC
sC + DsfNo drainage
53
Unconsolidated- Undrained test (UU Test)
Total, s = Neutral, u Effective, s’+Step 3: At failure
s’hf = sC + ur - sc Duf
= s’3f
s’Vf = sC + Dsf + ur - sc Duf = s’1f
-ur + sc ± Duf
sC
sC + DsfNo drainage
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
t
s’s’3 s’1Dsf
54s3b s1bs3a s1aDsfs’3 s’1
Unconsolidated- Undrained test (UU Test)
Total, s = Neutral, u Effective, s’+Step 3: At failure
s’hf = sC + ur - sc Duf
= s’3f
s’Vf = sC + Dsf + ur - sc Duf = s’1f
-ur + sc ± Duf
sC
sC + DsfNo drainage
t
s or s’
Mohr circles in terms of total stresses
uaub
Failure envelope, fu = 0
cu
55
s3b s1b
Unconsolidated- Undrained test (UU Test)
Effect of degree of saturation on failure envelope
s3a s1as3c s1c
t
s or s’
S < 100% S > 100%
56
Some practical applications of UU analysis for clays
t t = in situ undrained shear strength
Soft clay
1. Embankment constructed rapidly over a soft clay deposit
57
Some practical applications of UU analysis for clays
2. Large earth dam constructed rapidly with no change in water content of soft clay
Core
t = Undrained shear strength of clay core
t
58
Some practical applications of UU analysis for clays
3. Footing placed rapidly on clay deposit
t = 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 term behavior of soils
59
Unconfined Compression Test (UC Test)
s1 = sVC + Ds
s3 = 0
Confining pressure is zero in the UC test
60
Unconfined Compression Test (UC Test)
s1 = sVC + Dsf
s3 = 0
Sh
ear
stre
ss, t
Normal stress, s
qu
Note: Theoritically qu = cu , However in the actual case qu < cu due to premature failure of the sample
61
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
62
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
63
Direct simple shear test
Direct shear testf = 80 mm
Soil specimenPorous stones
Spiral wire in rubber membrane
Direct simple shear test
64
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
65
Torsional ring shear test
PeakResidual
t
Shear displacement
tf
s’
f’max
f’res
66
Torsional ring shear test
sN
Preparation of ring shaped undisturbed samples is very difficult. Therefore, remoulded samples are used in most cases
67
Other laboratory shear tests
Direct simple shear test
Torsional ring shear test
Plane strain triaxial test
68
Plane strain triaxial test
s’1, e1
s’2, e2
s’3, e3
Plane strain test
s’2 ≠ s’3
e2 = 0
s’1
s’2
s’3
s’2
Rigid platens
Specimen
69
In-situ shear tests
Vane shear test
Torvane
Pocket Penetrometer
Pressuremeter
Static Cone Penetrometer test (Push Cone Penetrometer Test, PCPT)
Standard Penetration Test, SPT
70
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
71
PLAN VIEW
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
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 0.5 m vertical intervals
72
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 uniform distribution of shear strength
2
0
).2(
d
ue rCrdrM
2
0
32
0
2
322
d
u
d
ue
rCdrrCM
1283
2 33 dCdCM uu
e
d/2d/2
Cu
h
73
Vane shear test
Since the test is very fast, Unconsolidated Undrained (UU) can be expected
Cu
Cu
Ms – Shaft shear resistance along the circumference
22
2hdC
ddhCM uus
2122
32
dChd
CT uu
62
32 dhdCT u
62
32 dhd
TCu
T = Ms + Me + Me = Ms + 2Me
74
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 triangular distribution of shear strength
h
d/2d/2
Cu
82
32 dhd
TCu
Can you derive this ???
75
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 parabolic distribution of shear strength
h
203
2
32 dhd
TCu
Can you derive this ???
d/2d/2
Cu
76
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 revolutions until the clay become remoulded
tpeak tultimate
t
Shear displacement
StengthUltimate
StengthPeakySensitivit
77
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
78
Torvane
Torvane is a modification to the vane
79
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
80
Pocket Penetrometer
Pushed directly into the soil. The unconfined compression strength (qu) is measured by a calibrated spring.
81
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
82
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
83
Pressuremeter
Pre – bored or self – bored hole
Guard cell
Measuring cell
Guard cell
Coaxial tube
Water
Air
84
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
85
Static Cone Penetrometer test
Cone penetrometers with pore water pressure measurement capability are known as piezocones
40 mm
40 mm
40 mm
40 mm
86
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
87
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)
88
Standard Penetration Test, SPT
SPT is the most widely used test procedure to determine the properties of in-situ soils
63.5 kg
0.76 m
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
The test can be conducted at every 1m vertical intervals
Various correlations have been developed to determine soil strength parameters (c, , f ect) from N
89
Standard Penetration Test, SPT
SPT (Manual operation)
90