# STRESSES IN A SOIL ELEMENT - SOIL MECHANICS - Shear Strength of Soil

Mechanics

Jul 18, 2012 (5 years and 10 months ago)

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Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 1 of 55
STRESSES IN A SOIL ELEMENT
Analyze Effective Stresses (
σ
´)

Stresses in a Soil Element
after Figure 8.1a.
Das FGE (2005).
τ

σ
´
v
σ
´
v
σ
´
H
σ
´
H
τ

τ

τ

Where:

σ
´
= Normal Effective Stress on
Failure Plane


τ
f
= Shear Stress on Failure Plane

σ
´
v
= Vertical Effective Stress

σ
´
H
= Horizontal Effective Stress

τ
= Shear Stress
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 2 of 55
MOHR FAILURE ENVELOPE
MOHR (1900):
Theory of Rupture in Materials.
A material fails due to because of
a critical combination of normal
and shear stress, not from
maximum normal or shear stress.
Functional Relationship:

Mohr Functional Relationship
after Figure 8.1b.
Das FGE (2005).
)
(
σ
τ
ʹ′

f
f
Where:

τ
f
= Shear Stress on Failure Plane

σ
´

= Normal Stress on Failure Plane
Normal Effective Stress (
σ
´)
τ
f
= f(
σ
´
)
Failure Envelope
Failure –
Cannot Exist
Stable
Shear Stress (
τ
)
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 3 of 55
MOHR-COULOMB (MC) FAILURE CRITERIA
Failure Envelope is approximated by
a linear relationship
MC Failure Criteria
(Effective Stresses)
MC Failure Criteria
after Figure 8.1b.
Das FGE (2005).
φ
σ
τ
ʹ′
ʹ′

ʹ′

tan
c
f
Where:
τ
f
= Shear Stress on Failure Plane

σ
´

= Normal Effective Stress on Failure Plane

= Effective Cohesion

φ
´
= Effective Friction Angle
Normal Effective Stress (
σ
´)
Failure
Envelope
Stable
Shear Stress (
τ
)
MC Failure
Criteria

φ
σ
τ
tan

c
f
MC Failure Criteria
(Total Stresses)
Where:

σ

= Normal Total Stress on Failure Plane

c
= Cohesion

φ
= Friction Angle

Failure –
Cannot Exist
NOTE:
c´ ≈ 0 for sands, inorganic silts,& NC clays
φ

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 4 of 55
FACTORS AFFECTING EFFECTIVE FRICTION ANGLE (
φ
´)

Cohesionless
Soils (
c´ ≈
0)
MC Failure Criteria
after Figure 8.1b.
Das FGE (2005).
φ
σ
τ
ʹ′
ʹ′

ʹ′

tan
c
f
Normal Effective Stress (
σ
´)
Stable
Shear Stress (
τ
)
MC Failure
Criteria
SANDS: Peak effective friction angle (
φ
´
p
) a
function of particle mineralogy, level of
effective confining stresses, and the
packing arrangement (Bolton, 1986).
Failure –
Cannot Exist
c´ ≈ 0 for sands, inorganic silts,& NC clays
Factor
Effect
Void Ratio (
e
)
e
φ

Angularity (A)
A
φ

Grain Size Distribution
C
u

φ

Water Content (
w
)
w
φ

(slightly)
Particle size
No effect (with
constant
e
)
Overconsolidation or
prestress
Little Effect
Table 11-3.
Holtz and Kovacs (1981).

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 5 of 55
TYPICAL DRAINED FRICTION ANGLES (
φ
´)
Soil
D
r
φ
´ (°)
Sand
(Rounded)
Loose
27 – 30
Medium
30 – 35
Dense
35 - 38
Sand
(Angular)
Loose
30 – 35
Medium
35 – 40
Dense
40 - 45
Gravels
(w/ some sands)
34 – 48
Silts
26 - 35
Table 8.1.
Das FGE (2005).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 6 of 55
TYPICAL DRAINED FRICTION ANGLES (
φ
´)
Coarse Grained Soils
Figure 7.
NAVFAC DM 7.01 (1986).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 7 of 55
INCLINATION OF FAILURE PLANE – PRINCIPAL STRESSES
Where:

σ
´
1
= Major Principal Stress

σ
´
3
= Minor Principal Stress
σ
´
1
σ
´
1
σ
´
3
σ
´
3
Normal Stress (
σ
´)
Shear Stress (
τ
)
MC Failure
Criteria
c
´

θ

a
σ
´
1
σ
´
3
Normal Stress (
σ
´)
Inclination of Failure Plane with Major Principal Plane
Figure 8.2.
Das FGE (2005).
f
d
h
b
e
g
θ

φ

O
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 8 of 55
INCLINATION OF FAILURE PLANE – PRINCIPAL STRESSES
Normal Stress (
σ
´)
Shear Stress (
τ
)
MC Failure
Criteria
c
´

a
σ
´
1
σ
´
3
Normal Stress (
σ
´)
Figure 8.2.
Das FGE (2005).
f
d
h
b
e
g
θ

φ

2
cot
2
sin
2
2
cot
sin
2
45
3
1
3
1
3
1
3
1
σ
σ
φ
σ
σ
φ
σ
σ
σ
σ
φ
φ
φ
θ
ʹ′

ʹ′

ʹ′
ʹ′
ʹ′

ʹ′

ʹ′
ʹ′

ʹ′

ʹ′

ʹ′

ʹ′
ʹ′

ʹ′

ʹ′

c
c
Oa
fO
fa
fa
o
Angle dab = 2
θ
= 90° +
φ
´ or
From Figure 8.2
Substituting
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 9 of 55
INCLINATION OF FAILURE PLANE – PRINCIPAL STRESSES
Normal Stress (
σ
´)
Shear Stress (
τ
)
MC Failure
Criteria
c
´

a
σ
´
1
σ
´
3
Normal Stress (
σ
´)
Figure 8.2.
Das FGE (2005).
f
d
h
b
e
g
θ

φ

⎟
⎠
⎞
⎜
⎝
⎛
ʹ′

ʹ′

⎟
⎠
⎞
⎜
⎝
⎛
ʹ′

ʹ′

ʹ′
⎟
⎠
⎞
⎜
⎝
⎛
ʹ′

ʹ′

ʹ′
⎟
⎠
⎞
⎜
⎝
⎛
ʹ′

ʹ′

ʹ′

⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ʹ′

ʹ′
ʹ′

⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ʹ′

ʹ′

ʹ′

ʹ′
ʹ′

ʹ′

ʹ′
ʹ′
ʹ′

ʹ′

ʹ′
2
45
tan
2
2
45
tan
2
45
tan
sin
1
cos
2
45
tan
sin
1
sin
1
sin
1
cos
2
sin
1
sin
1
2
cot
2
sin
2
3
1
2
3
1
3
1
3
1
φ
φ
σ
σ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
σ
σ
σ
σ
φ
σ
σ
φ
o
o
o
o
c
c
c
From Previous Slide

or
Trigonometry Identities
and
Therefore
MC Failure Criteria in Terms of
Failure Stresses
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 10 of 55
SHEAR STRENGTH LABORATORY TESTING
SUMMARY
Test
ASTM
Pore Pressure
Soil Types
Drained
Undrained
Coarse
Grained
Fine
Grained
Direct Shear
D3080
Y
N
Y
See Note 1
Triaxial
CD
- WK3821
CU
– D4767
UU
– D2850
Y
Y
Y
Y
Unconfined
Compression
D2166
N
Y
N
Y
NOTES:
1. Possible, but not recommended. Takes 2 -5 days to allow for drained conditions.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 11 of 55
DIRECT SHEAR TESTING
Figure 8.3.
Das FGE (2006).
τ

τ

σ
´ = Confining Stress
= Normal Force/Area

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 12 of 55
DIRECT SHEAR TESTING
ASTM D3080

Oldest, Simplest Shear Test

Typically performed on
coarse grained soils

Drained conditions (i.e. no
pore pressure buildup)

Failure occurs on fixed plane

Shear stress distribution not
uniform

Can be Stress or Strain
Controlled (typically strain)

Measure Shear Force,
Horizontal Displacement,
Vertical Displacement
Figure 8.3.
Das FGE (2006).
σ
´
= Confining Stress
= Normal Force/Area

τ

τ

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 13 of 55
DIRECT SHEAR TESTING
Figure 8.3.
Das FGE (2006).
Area

sectional
-
Cross
Force
Shear
Stress
Shear

Area

sectional
-
Cross
Force

Normal
Stress

Normal

ʹ′

τ
τ
σ
σ
σ
Normal Stress
Shear Stress
τ

τ

σ
´
= Confining Stress
= Normal Force/Area

NOTE: Cross-sectional Area (A)
is from start of test
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 14 of 55
DIRECT SHEAR TESTING
Figure 8.5.
Das FGE (2006).
Direct Shear Test Results – Dry Sands

Components of Shear Strength for
Cohesionless Soils (Rowe, 1962)

Friction Resistance:
Resistance due to particle sliding and
possibly rolling.

Dilation:

Expansion required to overcome
particle interlocking. Increase in volume.

Interference:

Due to particle interlocking (like dilation),
but occurs even at a constant volume
condition (unlike dilation). Particles
cannot go in straight line, must go around
each other.
Ultimate =
Residual
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 15 of 55
DIRECT SHEAR TESTING
Typical Direct Shear Results – Dry Sand (
c = 0
)
Peak Results Only
Figure 8.3.
Das FGE (2006).

Test typically
performed at a
minimum of three (3)
confining stresses.

Density of sample
should be within ± 2%
of field value.

Plots of peak (
φ
p
) and
residual (
φ
r
) MC criteria
should be presented.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 16 of 55
Test

Confining Stress
(
σ
)

(psi)

Shear Stress (
τ
)

(psi)

Peak

Residual

1
14.4
11.1
8.4
2
17.5
14.0
11.8
3
23.1
18.4
16.7
Determine the peak friction angle (
φ
peak
) and
residual
Friction angle
φ
residual
) for this material.
DIRECT SHEAR TESTING – EXAMPLE #1
GIVEN:
REQUIRED:
A Poorly Graded Sand (SP) from a Local Sand Pit with the
following Direct Shear Test Results.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 17 of 55
DIRECT SHEAR TESTING – EXAMPLE #1
0
5
10
15
20
25
30
35
40
C
o
n
f
i
n
i
n
g

S
t
r
e
s
s

(
σ
)

(
p
s
i
)
0
5
10
15
20
S
h
e
a
r

S
t
r
e
s
s

(
τ
)

(
p
s
i
)
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 18 of 55
DIRECT SHEAR TESTING – EXAMPLE #1
SOLUTION
0
5
10
15
20
25
30
35
40
C
o
n
f
i
n
i
n
g

S
t
r
e
s
s

(
σ
)

(
p
s
i
)
0
5
10
15
20
S
h
e
a
r

S
t
r
e
s
s

(
τ
)

(
p
s
i
)
D
i
r
e
c
t

S
h
e
a
r

P
e
a
k

V
a
l
u
e
s
P
e
a
k

B
e
s
t

F
i
t

L
i
n
e
(
φ

=

3
8
°
,

c

=

0
)
D
i
r
e
c
t

S
h
e
a
r

R
e
s
i
d
u
a
l

V
a
l
u
e
s
R
e
s
i
d
u
a
l

B
e
s
t

F
i
t

L
i
n
e
(
φ

=

3
4
°
,

c

=

0
)
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 19 of 55
Test

Confining Stress
(
σ
)

(psf)

Shear Stress (
τ
)

(psf)

Peak

Residual

1
604
657
549
2
926
875
734
3
1248
1092
920
Determine the peak friction angle (
φ
peak
) and
residual
Friction angle
φ
residual
) for this material.
DIRECT SHEAR TESTING – EXAMPLE #2
GIVEN:
REQUIRED:
A Clayey Sand (SC) from a Local Sand Pit with the following
Direct Shear Test Results.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 20 of 55
0
400
800
1200
1600
2000
2400
C
o
n
f
i
n
i
n
g

S
t
r
e
s
s

(
σ
)

(
p
s
f
)
0
200
400
600
800
1000
1200
S
h
e
a
r

S
t
r
e
s
s

(
τ
)

(
p
s
f
)
DIRECT SHEAR TESTING – EXAMPLE #2
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 21 of 55
DIRECT SHEAR TESTING – EXAMPLE #2
SOLUTION
0
400
800
1200
1600
2000
2400
C
o
n
f
i
n
i
n
g

S
t
r
e
s
s

(
σ
)

(
p
s
f
)
0
200
400
600
800
1000
1200
S
h
e
a
r

S
t
r
e
s
s

(
τ
)

(
p
s
f
)
D
i
r
e
c
t

S
h
e
a
r

P
e
a
k

V
a
l
u
e
s
B
e
s
t

F
i
t

L
i
n
e

(
φ
p

=

3
4
°
,

c
p

=

2
5
0

p
s
f
)
D
i
r
e
c
t

S
h
e
a
r

R
e
s
i
d
u
a
l

V
a
l
u
e
s
B
e
s
t

F
i
t

L
i
n
e

(
φ
r

=

3
0
°
,

c
r

=

2
0
0

p
s
f
)
P
l
o
t

o
f

P
r
o
v
i
d
e
d

D
a
t
a
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 22 of 55
DIRECT SHEAR TESTING
INTERFACIAL SHEAR
SOIL
FOUNDATION
τ

τ

Interfacial Shear between
Foundation and Soil
after Figure 8.7.
Das FGE (2006).
APPLICATION EXAMPLES:
Deep
Foundations
Retaining
Walls
δ
σ
τ
ʹ′
ʹ′

ʹ′

tan
a
f
c
Where:

τ
f
= Shear Stress on Failure Plane

σ
´

= Normal Effective Stress on Failure Plane

c
a
´

δ
´
= Effective Interfacial Friction Angle
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 23 of 55
Direct Shear Interfacial Testing for
Geomembranes

(after
Mofiz
, 2000)
ASTM D5321-08
Standard Test Method for Determining the Coefficient of Soil and
Geosynthetic
or
Geosynthetic
and
Geosynthetic
Friction by the Direct Shear Method

BS EN 13738:2004
Geotextiles and geotextile-related products. Determination of pullout
resistance in soil (British Standard)
ISO 12957-1:2005
Geosynthetics
- Determination of friction characteristics - Part 1: Direct
Shear Test
DIRECT SHEAR TESTING
INTERFACIAL SHEAR STANDARDS
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 24 of 55
INTERFACIAL FRICTION ANGLE
Table 1.
NAVFAC DM 7.02 (1986).
General Rule of Thumb
Relating
δ
and
φ

1/3
φ
<
δ
< 2/3
φ

Other Interfacial Testing Methods:
The Dual Interface Apparatus -
Paikowsky et al. (1995)

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 25 of 55
TRIAXIAL SHEAR TESTING
Considered to be the most
reliable soil shear test

stress-strain behavior than
direct shear testing

Allows soil to fail along
preferred failure plane

Provides more flexibility in

Allows measurement of
vertical stress, confining
stress, vertical displacement,
pore pressure, and volume
change.
Figure 7-7a.
FHWA NHI-01-031.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 26 of 55
TRIAXIAL SHEAR TESTING
Test Samples:

Diameter: 35 to 75 mm
2 ≤ D/L Ratio ≤ 2.5

D = Diameter
L = Length
Figure 7-7d.
FHWA NHI-01-031.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 27 of 55
TRIAXIAL SHEAR
TEST SETUP
Pressure
Source
Triaxial
Cylinder
(Plexiglass)
Soil Sample
Base
Inlet for
Filling
Drainage
Connection
Pore Pressure
Measurement
Figure 8.9.
Das FGE (2006).
Membrane
Porous
Stone
Porous
Stone
Chamber
Filled w/ water
or glycerine
Chamber Pressure:
σ
3

(a.k.a.
σ
c
)

Applied Axial Stress:
Δσ
d

(a.k.a. Deviator Stress,
Δσ
1
)
Stress applied two ways:

1.

Stress controlled:

increments until specimen
fails.
1.

Strain controlled:

Application of axial
deformation at constant rate
until specimen fails.
Valve
Valve
Connection determines
cheap or good
triaxial

setup
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 28 of 55
TRIAXIAL SHEAR TESTING
Figure 5.
NAVFAC DM 7.01 (1986).
σ
3
σ
1
= P/A
Applied Stress

Soil
u
u
Measurement
Instrumentation
σ
1
Axial Deformation
ε
v
Dial Gauges,
LVDT’s, DCDT’s
Confining Pressure
σ
3

Pressure Transducers,
Water Levels
Pore Pressure
u
Pressure Transducers,
Water Levels
Volume Change
Δ
w
Δσ
d
σ
1

-
σ
3
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 29 of 55
TRIAXIAL SHEAR TESTING
Figure 5.
NAVFAC DM 7.01 (1986).
σ
3
σ
1
Soil
u
u
BASIC TRIAXIAL TESTS
Test Type
ASTM
Simple
Abbr.
Letter
Consolidated Drained
WK3821
CD
S
“Slow”
Consolidated Undrained
D4767
CU
R
“Rapid”
Unconsolidated Undrained
D2850
UU
Q
“Quick”
Full Test Abbreviations (Example):
C
I

D

C

(L)
Consolidation State
(Consolidated/Unconsolidated)
Consolidation Condition
(Isotropic, Anisotropic (e.g. K
o
))
Compression/Extension
Drained/Undrained
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 30 of 55
3
σ
c
u
B

Where:

B
= Skempton’s Pore Pressure Parameter

B
≈ 1 for Saturated Soils (see Table 8.2 below)

u
c
= Pore Pressure Increase due to Confining Stress

σ
3
= Confining Stress
CONSOLIDATED DRAINED (CD) TEST
σ
3
σ
3
u
c

= 0
(Drained
prior to
test)
After Isotropic
Consolidation
σ
3
σ
3
Prior to

Drainage
u
c

σ
3

(i.e.
B

1)
Check for Saturation
(
Skempton’s
Pore Pressure Parameter
B
)
Table 8.2.
Theoretical Values of B at S = 100% (Das FGE 2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 31 of 55

f
f
f
d
f
f
f
1
1
3
3
3
σ
σ
σ
σ
σ
σ
ʹ′

Δ

ʹ′

Where:

σ
3f
= Minor Principal Stress at Failure

σ
´
3f

= Minor Principal Effective Stress at Failure

(
Δ
σ
d
)
f

= Deviator Stress at Failure

σ
1f

= Major Principal Stress at Failure

σ
´
1f

= Major Principal Effective Stress at Failure
CONSOLIDATED DRAINED (CD) TEST
σ
3
σ
3
Δ
u
d

= 0
During Axial
Compression
σ
3
σ
3
S “Slow” Test
Δσ
d
Δσ
d
Allow drainage of sample during testing. Therefore, no
pore pressures within the soil sample buildup during shear
(i.e.
Δ
u
d
= 0).

Since pore pressure developed during the test is
completely dissipated:
and
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 32 of 55
CONSOLIDATED DRAINED (CD) TEST RESULTS
Sands and Normally Consolidated Clays
Normal Stress
(
σ
´)
Shear Stress (
τ
)
φ
´
σ
´
1f
σ
´
3f
σ
´
3f
σ
´
1f

σ
´
3f
σ
´
1f
Test 1
Test 2
Test 3
(
Δσ
d
)
f
c´ ≈ 0
Total Stress Envelope = Effective Stress Envelope
τ
f

=

σ
´tan
φ
´
+

c
´
Total and Effective Stress Failure Envelope from CD Tests
Figure 8.13.
Das FGE (2006).
Should use a Minimum of Three Tests
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 33 of 55
CONSOLIDATED DRAINED (CD) TEST RESULTS
Overconsolidated
Clays
Normal Stress
(
σ
´)
Shear Stress (
τ
)
c
´
σ
´
1f
σ
´
3f
σ
´
3f
σ
´
1f

σ
3f
´
σ
´
1f
Test 1
Test 2
Test 3
(
Δσ
d
)
f
φ
´=
φ
´
NC

Test 4
σ
3f
´
σ
´
1f

σ
´
vm

OC
NC
φ
1
´
=

φ
OC
´

τ
f

=

σ
´tan
φ
´
+

c
´
τ
f

=

σ
´tan
φ
´
Total and Effective Stress Failure Envelope from CD Tests
Figure 8.14.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 34 of 55
CONSOLIDATED DRAINED (CD) TEST RESULTS
CD Test – Volume Change with Time during Consolidation (
Δ
V
c
)

Figure 8.11a.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 35 of 55
CONSOLIDATED DRAINED (CD) TEST RESULTS
Loose Sands and Normally Consolidated Clays
Change in Deviator Stress
(
Δσ
d
) vs. Axial Strain (
ε
v
)

Figure 8.11b.
Das FGE (2006).
Volume Change (
Δ
V
d
) vs.
Axial Strain (
ε
v
)

Figure 8.11d.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 36 of 55
CONSOLIDATED DRAINED (CD) TEST RESULTS
Dense Sands and
Overconsolidated
Clays
Change in Deviator Stress
(
Δσ
d
) vs. Axial Strain (
ε
v
)

Figure 8.11c.
Das FGE (2006).
Volume Change (
Δ
V
d
) vs.
Axial Strain (
ε
v
)

Figure 8.11e.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 37 of 55
d
d
u
A
σ
Δ
Δ

Where:

Ā
= Skempton’s Pore Pressure Parameter

Δ
u
d
= Pore Pressure Increase due to Deviator Stress

Δ
σ
d
= Deviator Stress
CONSOLIDATED UNDRAINED (CU) TEST
Skempton’s
Pore Pressure Parameter
Ā

σ
3
σ
3
Δ
u
d
≠ 0
σ
3
σ
3
Δσ
d
Δσ
d
Setup same as CD Test. Check for Saturation (
B

parameter). Close drainage valve prior to test to
make undrained (i.e. allow pore pressure buildup
within sample). Pore pressure can be measured
during test to determine effective stresses.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 38 of 55

3
1
3
1
1
1
3
3
1
3
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
ʹ′

ʹ′

ʹ′

Δ

ʹ′

Δ

Δ

f
f
d
f
f
f
d
f
f
f
d
f
u
u
Where:

σ
3f
= Minor Principal Stress at Failure

σ
´
3f

= Minor Principal Effective Stress at Failure

(
Δ
σ
d
)
f

= Deviator Stress at Failure

(
Δ
u
d
)
f

= Pore Pressure Increase at Failure

σ
1f

= Major Principal Stress at Failure

σ
´
1f

= Major Principal Effective Stress at Failure
CONSOLIDATED UNDRAINED (CU) TEST
σ
3
σ
3
During Axial
Compression
σ
3
σ
3
R “Rapid” Test
Δσ
d
Δσ
d
DO NOT
allow drainage of sample during testing.
Therefore, pore pressures within the soil sample buildup
during shear (i.e.
Δ
u
d

0). Therefore:
Δ
u
d
≠ 0
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 39 of 55
Normal Stress (
σ
´)
Shear Stress (
τ
)
φ

(
Δσ
d
)
f
c &

≈ 0
Total Stress Envelope
τ
f

=

σ
tan
φ

+

c

φ
´
Effective Stress Envelope
τ
f

=

σ
tan
φ
´

+

c
´
σ
3f
´
σ
3f

σ
1f
´
σ
1f

(
Δ
u
d
)
f
CONSOLIDATED UNDRAINED (CU) TEST RESULTS
Sands and Normally Consolidated Clays
* Still Need a Minimum of Three Tests!
(
Δσ
d
)
f
(
Δ
u
d
)
f
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 40 of 55
CONSOLIDATED UNDRAINED (CU) TEST RESULTS
Overconsolidated
Clays
Normal Stress
(
σ
´)
Shear Stress (
τ
)
c
´
σ
´
1f
σ
´
3f
σ
´
3f
σ
´
1f

σ
3f
´
σ
´
1f
Test 1
Test 2
Test 3
(
Δσ
d
)
f
φ
´=
φ
´
NC

Test 4
σ
3f
´
σ
´
1f

σ
´
vm

OC
NC
φ
1
´
=

φ
OC
´

Effective Stress Failure Envelope from CU Tests
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 41 of 55
CONSOLIDATED UNDRAINED (CU) TEST RESULTS
Overconsolidated
Clays
Normal Stress (
σ
)
Shear Stress (
τ
)
c

σ
3f
σ
1f

φ

φ
1

=

φ
OC

Total Stress Failure Envelope from CU Tests
Figure 8.19.
Das FGE (2006).
Total Stress Envelope
τ
f

=

σ
tan
φ
OC

+

c

Total Stress Envelope
τ
f

=

σ
tan
φ

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 42 of 55
CONSOLIDATED UNDRAINED (CU) TEST RESULTS
CU Test – Volume Change with Time during Consolidation (
Δ
V
c
)
(Still allowing drainage during Consolidation)

Figure 8.17a.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 43 of 55
CONSOLIDATED UNDRAINED (CU) TEST RESULTS
Loose Sands and Normally Consolidated Clays
Change in Deviator Stress
(
Δσ
d
) vs. Axial Strain (
ε
v
)

Figure 8.17b.
Das FGE (2006).
Pore Pressure Change
(
Δ
u
d
) vs. Axial Strain (
ε
v
)

Figure 8.17d.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 44 of 55
CONSOLIDATED UNDRAINED (CU) TEST RESULTS
Dense Sands and
Overconsolidated
Clays
Change in Deviator Stress
(
Δσ
d
) vs. Axial Strain (
ε
v
)

Figure 8.17e.
Das FGE (2006).
Pore Pressure Change
(
Δ
u
d
) vs. Axial Strain (
ε
v
)

Figure 8.17g.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 45 of 55
)
(
3
1
3
3
σ
σ
σ
σ
σ

Δ

Δ

A
B
A
B
u
u
u
u
d
d
c
Where:

σ
3
= Minor Principal Stress

σ
1

= Major Principal Stress

Δ
σ
d

= Deviator Stress

Δ
u
d

= Pore Pressure Increase due to Deviator Stress

Β

=
Skempton’s
Pore Pressure Parameter

Ā

=
Skempton’s
Pore Pressure Parameter
UNCONSOLIDATED UNDRAINED (UU) TEST
σ
3
σ
3
σ
3
σ
3
Q “Quick” Test
Δσ
d
Δσ
d
Drainage of sample not permitted during application of
confining stress
σ
3
or during testing (i.e. application of
Δσ
d
). Therefore, pore pressures within the soil sample at
any stage of testing is:
u

≠ 0
Therefore:
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 46 of 55
UNCONSOLIDATED UNDRAINED (UU)
TEST RESULTS
Normal Stress
(
σ
)
Shear Stress (
τ
)
σ
1f
σ
3f
σ
3f
σ
1f

σ
3f

σ
1f
Test 1
Test 2
Test 3
Failure Envelope
φ
= 0
Total Stress Mohr’s
Circles at Failure
c
u
c
u
=
S
u

Undrained Shear
Strength

(
Δσ
d
)
f

(
Δσ
d
)
f
constant regardless of confining stress (
σ
3
)

Figure 8.21.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 47 of 55
UNCONSOLIDATED UNDRAINED (UU)
TEST RESULTS
σ

τ

σ
´
1f
σ
´
3f
σ
3f
σ
1f

σ
3f

σ
1f
Test 1
Test 2
Total Stress Mohr’s
Circles at Failure
c
u
(
Δσ
d
)
f

Figure 8.22.
Das FGE (2006).
Failure Envelope
φ
= 0
Δσ
3

=
Δ
u
c

(
Δ
u
d
)
f

(
Δσ
d
)
f

(
Δσ
d
)
f

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 48 of 55
Figure 11.34 .
Das PGE (2006).
UNCONFINED COMPRESSION TEST
Cohesive Soils
UC Test Setup
(Courtesy of Durham Geo)
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 49 of 55
UNCONFINED COMPRESSION TEST
Cohesive Soils
Normal Stress (
σ
´)
Shear Stress
(
τ
)
σ
3
σ
1
=
q
u
q
u
Soil
σ
1
σ
1
Total Stress Mohr’s
Circle at Failure
c
u
=
q
u
/2

Where:

q
u
= Unconfined Compression Strength
c
u
= Undrained Shear Strength

Figure 8.23.
Das FGE (2006).
Failure Envelope
φ
= 0
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 50 of 55
UNCONFINED COMPRESSION TEST
General Relationship between Consistency and
q
u
of Cohesive Soils
Table 8.3
Das FGE (2006)
Consistency
q
u
(tsf)
q
u
(kN/m²)
Very Soft
0 – 0.25
0 – 25
Soft
0.25 – 0.5
25 – 50
Medium
0.5 – 1
50 – 100
Stiff
1 – 2
100 – 200
Very Stiff
2 – 4
200 – 400
Hard
> 4
> 400
1
tsf
= 95.8
kPa
≈ 100
kPa

Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 51 of 55
UNCONFINED COMPRESSION (UC) &
UNCONSOLIDATED UNDRAINED (UU)
TEST COMPARISON
Normal Stress
(
σ
´)
Shear Stress (
τ
)
φ
´ = 0
q
u
=
σ
1f
σ
3
σ
1

σ
3

σ
1
Test 1 - UC
Test 2 - UU
Test 3 - UU
c
u
Theoretical Failure Envelope
Actual Failure Envelope
Figure 8.25.
Das FGE (2006).
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 52 of 55
SENSITIVITY OF COHESIVE SOILS

Unconfined Compression Strength for
Undisturbed and Remolded Clays
Figure 8.26.
Das FGE (2006).
)
(
)
(
disturbed
u
d
undisturbe
u
t
q
q
S

Strength

Shear

Disturbed
Strength

Shear

d
Undisturbe

t
S
Sensitivity (
S
t
)
Disturbed = Remolded
Example: Unconfined Compression
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 53 of 55
SENSITIVITY OF COHESIVE SOILS

Sensitivity Classification of Clays
Figure 11.36.
Das PGE (2006).
Strength

Shear

Disturbed
Strength

Shear

d
Undisturbe

t
S
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 54 of 55
THIXOTROPY OF COHESIVE SOILS

Thixotropy
:
Time dependent
reversible process in
which soil gains
strength with time after
being remolded if left
undisturbed.
Revised 4/2012
14.330 SOIL MECHANICS
Shear Strength of Soil
Slide 55 of 55
ANISOTROPY OF COHESIVE SOILS

)
(
)
(
H
u
V
u
c
c
K

Where:

K
= Coefficient of Anisotropy
c
u(V)
=
Undrained
Shear Strength in Vertical Direction
c
u(H)
=
Undrained
Shear Strength in Horizontal Direction

Strength Anisotropy in Cohesive Soils
Figure 8.27.
Das FGE (2006).
Direction Variation of Undrained Shear
Strength in Cohesive Soils
Figure 8.27.
Das FGE (2006).
Vertical/Horizontal
c
u
Ratio