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Soil Mechanics II
(Teuku Faisal Fathani)
1. Application of soil mechanics
2. Stress Distribution
3. Consolidation
4. Settlement
5. Shear Strength Parameter of Soil
6. Slope Stability
References:
- Principles of Geotechnical Engineering (Braja M.
Das, 2002)
- Soil Mechanics (R. F. Craig, 1987)
- Mekanika Tanah I (Hary Christady H., 2002)
Shear Strength Parameters
Shear strength parameter:
Internal resistant force per unit area
Failure of shear at a slip surface due to applied force to the soil.
Shear resistant:
1. Cohesion (c): depend on the type of soil and its density,
independent from normal stress ( ) at the shear surface.
2. Friction inter material ( tan ): depend on the normal
stress ( ) at the shear surface and internal friction angle ( )
3. Combination of c and
MOHR-COULOMB Failure Criteria
Mohr (1900): Failure of a material due to the combination of critical
condition between normal stress ( ) and shear stress ( )
Coulomb (1776) f ( ) :
N
F
A
= shear strength (kN/m2)
c = cohesion (kN/m2)
= internal friction angle ( 0)
= normal stress at the failure
surface (kN/m2)
MOHR-COULOMB Failure Criteria
Mohr
Mohr-Coulomb
c
A
B
C
y
x
f
A Failure does not occur
B Failure occurs
C Failure never happen
In effective stress condition (Terzaghi, 1925):
= shear strength (kN/m2)
c’ = effective cohesion (kN/m2)
’ = effective internal friction angle ( 0)
’ = effective normal stress on the failure plane (kN/m2)
u = pore water pressure (kN/m2)
Saturated soil
Mohr’s Circle and failure envelope
’
Failure
envelope
c f
3’ 1’ f’
2
1’
1’
3’ 3’ f’
f
1’ = effective major principle stress
3’ = effective minor principle stress
= theoretical angle between the failure plane and
major principal plane
Relationship between effective principle
stress at failure and shear strength
parameter c - :
Laboratory Test for Determination of
Shear Strength Parameter
1. Direct shear test
2. Triaxial test UU, CU CD
3. Unconfined compression test
4. Vane shear test
Direct Shear Test
N
T
Shear box
Porous stone
Sample
Loading
plate
h
L
Method of test :
Stress-controlled Test
Peak shear strength
Strain-controlled Test
Peak shear strength and Residual shear strength
Direct test is appropriate to be used for sandy soil.
Shearing the sample up to failure or the maximum strain
reaches max = 20%
Direst shear tests are repeated on similar specimens at
various normal stresses (min. 3 times).
1
2
3
c
1 2 3
Pure sand c = 0 ; maka
Dry condition :
Stress-strain characteristics of sand:
L
= constant
dense
loose
L H
+
-
Exp
an
sio
n
Co
mp
ressio
n
Dense sand
Loose sand
Peak shear strength
Residual shear strength
Shear displacement
Factors affected shear strength of sand:
- Particle size
- Water inter the particle
- Roughness of the surface of particle
- Grain size distribution
- Shape of particle
- Pore number (e) or relative density (Dr)
- Main principal stress
- Stress history
Example
Direct shear test on a clean compacted sand. Shear box with
dimension of 250 x 250 mm2. The results as follow:
Calculate shear strength parameter of the sand in dense condition
and loose condition
m dense sand peak stress
t loose sand residual stress
Normal force (kN) 5,00 10,00 11,25
Peak shear force (kN) 4,90 9,80 11,00
Residual shear force (kN) 3,04 6,23 6,86
Normal stress (kN/m2) 80 160 180
Peak shear stress (kN/m2) 78,4 156,8 176
Residual shear stress (kN/m2) 48,6 99,7 109,8
(kN/m2)
(kN/m2)
Peak stress
Residual
stress
From the above figure
m dense sand = 450
t loose sand = 320
Triaxsial Test
• The most reliable method to determine the shear strength
parameter of soil
• Commonly use for site investigation for civil construction and for research
h
h h
v
v
Applied stresses:
1 = major principal stress
3 = minor principal stress
2 = 3 = confining stress
= 1 - 3 = deviator stress
z
y
x 3
1
1
2
Correction of the sample area at a
certain strain (A)
Diagram of Triaxsial Test Equipment
Axial Load and Confining Pressure
3 3
3
3
3 3
3 + = 1
3 + = 1
L
Loading on vertical direction:
1. Apply the dead load gradually until failure. Axial deformation
is measured by dial gage.
2. Apply the axial deformation with a constant increment (strain-
controlled). Axial load is measured by proving ring.
Types of Standard Triaxial Test
Test condition 3 (confining
pressure)
Deviator stress,
Output
U.U.
(Unconsolidated-
Undrained)
Drainage
connection close
Drainage
connection
close
Total stress
C.U.
(Consolidated-
Undrained)
3 consolidation
Drainage
connection open
Drainage
connection
close
u
Total stress
Effective
stress
C.D.
(Consolidated-
Drained)
3 consolidation
Drainage
connection open
Drainage
connection
open
Effective
stress
The Results of Triaxsial test
(%)
31
32
33
c
3 1 1
f1
1 3 3
3 3
3 + = 1
3 + = 1
C.D. Test
3 3
3
3
uc=0 3 3
ud=0
3 + = 1
3 + = 1
B = pore pressure parameter by
Skempton (1954)
B = 1 for saturated soft soil
Confining
pressure Deviator
stress
t Vc
+
-
= constant
Dense sand / NC
Loose sand / OC
Vd
+
-
f
f
Dense sand / NC
Loose sand / OC
Because of the pore water pressure (u) during the
implementation of deviator stress is totally dissipated
Total stress = Effective stress
The same test is conducted at the same soil sample with
different 3 (confining pressure).
After getting 1 and 3 Mohr’s circle + failure envelope can be drawn
Failure envelope of Triaxsial CD
For sand dan clay NC
Failure envelope
3= 3’
2
1
1
3 3
f
f
2
1= 1’
A
B
f
f
Failure envelope of Triaxial CD
for clay OC
OC
BC
3= 3’
1
1
3 3
f
f
1= 1’
A
B
c
C
AB
NC
c= c’
C.U. Test
3 3
3
3
uc=0 3 3
ud 0
3 + = 1
3 + = 1
A = pore water pressure parameter
by Skempton (1954)
Confining
pressure Deviator
stress
t Vc
+
-
Dense sand / NC
Loose sand / OC
ud
+
-
f
f
Dense sand / NC
Loose sand / OC
Pore water pressure during the application of deviator stress = ud
Total stress Effective stress
Pore water pressure at failure can be measured = udf
Major principal stress at failure (total) :
Minor principal stress at failure (total) :
Pore water pressure at failure :
Major principal stress at failure (effective) :
Minor principal stress at failure (effective) :
In order to determine the shear strength parameter triaxial test
on soil samples should be done with different confining pressure 3
(%)
31
32
33
c
3 1 1
f1
1 3 3
3 3
3 + = 1
3 + = 1
Failure envelope of Triaxsial CU
For sand dan clay NC
Failure envelope
of effective stress
3
1
1
3 3
f
f
1
A
B
udf
C
D
cu
1’ 3’
udf
Failure envelope
of total stress
OC
2
3
1
1
3 3
f
f
1
A
B
c
C
1
NC
c
Failure envelope of Triaxial CU
for clay OC
A parameter for clay:
• Lempung NC : 0,5 – 1
• Lempung OC : -0,5 – 0
A value depends on OCR
c’ = c = maximum confining pressure when the soil sample consolidates
A = pore water pressure parameter by Skempton
(1954) at failure:
U.U. Test
3 3
3
3
uc 0 3 3 ud 0
3 + = 1
3 + = 1
Confining
pressure Deviator
stress
Total pore water pressure =
and
Hence
Triaxial UU test on saturated clay :
f will be the same for different confining pressure 3
Failure envelope
1
1
3 3
f
f
cu
3 1 1 3 3 1
The application of Triaxial UU, CU and CD:
UU :
• Foundation on soft soils
• Embankment on soft soils
• Dam on soft soils
The loading apply so fast, hence the consolidation and drainage
did not occur yet at the soil layers end of construction
CU :
• Slope stability, where the soil has been consolidated and stable
• Rapid draw-down at of reservoir
• Embankment construction (several phase / stage)
CD :
• Embankment long time construction
• Earth dam affected by steady
• Clay excavation
• Practically, it is difficult to implement this test for clay,
because the time to get u = 0 will be too long,
p = need to be small it takes a long time and very easy to seep out.
Example 1
Triaxial CD has been done for normally consolidated clay.
The result of test as follow:
3 = 276 kN/m2
f= 276 kN/m2
Calculate :
a. Internal friction angle,
b. The angle between failure surface and major principal plane,
c. Normal stress ’ and shear stress f at failure surface
For Normally Consolidated Clay, the failure envelope equation
Principal stress:
Failure envelope
3’=276 kN/m2
2
’1
’1
’3 ’3
f
f
B
1’=552 kN/m2 A O
Failure
envelope
3’=276 kN/m2
2
B
1’=552 kN/m2 A O
At failure
plane
Example 2
Consolidated-Drained Triaxial test for example no. 1 :
a. Calculate effective normal stress ( ’) acting on the plane with
maximum shear stress ( ).
Maximum shear stress occurs at the plane with = 450
b. Why does the failure occur at the plane of = 54,730, not at the
plane having maximum shear stress?
Shear stress that causes the failure at = 450:
Shear stress acting on that plane :
Example 3
The result of triaxial test (UU) as follow:
Calculate the shear strength parameter by using Mohr’s circle.
No of test Confining pressure
(kg/cm2)
Deviator stress (kg/
cm2)
1 1 0,57
2 1,4 0,71
3 1,8 0,76
4 2,2 0,84
(kg/cm2)
Failure envelope
c
33 13 14 34 32 12
1 2 3
(kg/cm2)
1
No test 3 (kg/cm2) (kg/cm2) 1= 3+
(kg/cm2)
( 1+ 3)/2
(kg/cm2)
1 1 0,57 1,57 1,285
2 1,4 0,71 2,11 1,753
3 1,8 0,76 2,56 2,182
4 2,2 0,84 3,04 2,620
From the figure :
Example 4
Triaxial test (CU) for normally consolidated clay, with the result:
3 = 260 kN/m2
Deviator stress : f= 200 kN/m2
Pore water pressure : udf = 120 kN/m2
Calculate :
a. Internal friction angle at Consolidated-Undrained (CU)
condition
b. Internal friction angle at Consolidated-Drained (CD) condition
Unconfined Compression
Test
(Uji Tekan Bebas)
Unconfined
Compression Test
as a special type of
Triaxial UU for
saturated clay
ASTM D2166
AASHTO T208
1
1
3=0 cu
3=0 1=qu
qu = unconfined compression
strength
Consistency qu (kN/m2)
Very soft 0 – 25
Soft 25 – 50
Medium 50 – 100
Stiff 100 – 200
Very stiff 200 – 400
Hard >400
Theoretical failure envelope
of total stress
cu
3 1 1 3 0 1=qu
The real failure envelope
of total stress
1 2
3
Result of Unconfined Compression Test (Mohr’s circle-1)
vs. Triaxial UU (Mohr’s circle- 2 and 3) for saturated clay
Vane shear Test
To determine shear strength at undrained condition cu ( = 0)
for saturated clay.
Method:
• Vane shear equipment is driven to
the borehole with minimum depth of
3 x borehole diameter
• Rotate with the velocity of 6o – 12o per minute.
• Every 15-30 seconds, record T value
h
d
Ms
Me
Me cu
cu
cu
Shear strength mobility at 2
cylindrical edge surface
Bjerrum (1974) : cu form vane shear test is too high, because of
the shear zone expanded.
Vane shear result in the field need to be corrected: