shear strength.pptx GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

Questions to guide your reading
What is shear strength of soil?
What are the major types of shear strength?
Which soil parameters represent shear strength?
What is the significance of the shear strength of soil.
Discuss the mode of shear failure.
2

Questions to guide your reading
What are the major shear characteristics of soil
How can the shear strength parameters of soil can be determined in
the field and in the laboratory.
Discuss the design use of shear strength parameters of soil.
Enlist some of the common engineering issues that triaxial tests can
be used.
3

introduction
In general, resistance to deformation is known as stiffness and
resistance to failure is known as strength.
Stiffness is an indicator of the tendency for an element to return to
its original form after being subjected to a force.
Strength measures how much stress can be applied to an element
before it deforms permanently or fractures.
4

SHEAR STRENGTH OF SOIL
Shear strength is a term used in soil mechanics to describe the
magnitude of the shear stress that a soil can sustain. The shear
resistance of soil is a result of friction and interlocking of particles, and
possibly cementation or bonding at particle contacts.
8

Types of shear strength
there are three commonly identified shear strengths for a soil
undergoing shear:
Peak strength p
Critical state or constant volume strength Peak strength cv
Residual strength r

9

Critical state shear strength
The theoretical state at which the shear stress and density remain
constant while the shear strain increases may be called the critical
state.
11

Residual state shear strength
The minimum and constant drained shear strength at which a soil
experiences a large shear displacement under a given normal stress
may be called as residual strength.
12

Peak state shear strength
The highest level of shear strength measured under a given normal
load is defined as the peak strength.
13

Shear strength parameters
According to the Mohr-Coulomb failure criterion, the shear strength
of soils consists of two components, cohesion (c) and frictional angle
(φ) and is also dependent on the normal effective stress (σ').
14

Factors affecting shear strength
The shearing strength of a compacted cohesive soil is primarily
affected by the water content, gradation, dry density, soil structure,
thixotropy and the normal effective stress acting on the failure plane.
15

Effect of shear strength
Shear strength is a very important property of soils.
Higher the shear strength higher would be the stability of soil against
failure.
The concept is used by geotechnical engineers in estimating the
bearing capacity of foundations and in assessing the stability of
retaining walls, slopes, and embankments and the design and
construction of highway and airfield pavements.
16

Shear strength measurement
The following are the methods to determine the shear strength of soil:
Direct Shear Test
Triaxial Compression Test
Unconfined Compression Test
Vane Shear Test
Bore Hole Shear Test
17

Shear strength conditions
Effective and total stress shear strength
 Drained and undrained shear strength
Principal stress difference Vs. principal stress ratio as failure criterion
18

MODE OF SHEAR FAILURE
Shear failures of foundations can be grouped into three categories:
General shear failure
Local shear failure
Punching shear failure
19

Punching shear failure
In weak compressible soils, and soils of low relative density,
considerable vertical settlement may take place with the yield surfaces
restricted to vertical planes immediately adjacent to the sides of the
foundation; the ground surface may be dragged down. After the first
yield has occurred the load-settlement curve will steepened slightly,
but remain fairly flat. This is referred to as a punching shear failure.
20

22
Punching Shear Failure
Loose or
Soft Soils
No surface
heave Settlement
q

Local shear failure
In moderately compressible soils, and soils of medium
relative density, significant vertical settlement may take
place due to local shear failure, i.e. yielding close to the
lower edges of the footing. The yield surfaces often do not
reach the surface. Several yield developments may occur
accompanied by settlement in a series of jerks. The
bearing pressure at which the first yield takes place is
referred to as the first-failure pressure qf (1) - the term
first-failure load Qf (1) is also used.
23

25
Local Shear Failure
Medium dense
or firm soils
minor surface
heave only
Settlement
q

General shear failure
When a load (Q) is gradually applied on a foundation, settlement occurs
which is almost elastic to begin with. At the ultimate load, general
shear failure occurs when a plastic yield surface develops under the
footing, extending outward and upward to the ground surface, and
catastrophic settlement and/or rotation of the foundation occurs.
26

28
Generalized Shear Failure
Soil Failure
Lines
rigid
radial
shear
passive
log spiral
Settlement
q

Bearing failure patterns
29
GENERAL SHEAR FAILURE LOCAL SHEAR FAILURE PUNCHING SHEAR FAILURE

Effective stress concept is valid only for normal stress σ, since the shear
stress τ is not transferred by the water so that it is effective.
32

Effective and total stress
Assume conditions Drained layer Undrained layer
short - term effective stress total stress
long - term effective stress effective stress
33

Drained and undrained soil behavior
34

• Porous materials like soils have different design properties under
drained and undrained conditions. As you all know in drained
condition, the pore water can easily drain out from the soil matrix
while in undrained condition the pore water is unable to drain out or
the rate of loading is much quicker than the rate at which the pore
water is able to drain out.
35

The existence of either a drained or an undrained condition in a soil
depends on:
Soil type (e.g. sand, gravel, silt, clay)
Geological formation (fissures, embedded sand layers in clay, etc.),
Rate of loading.
36

Experiments have shown that the drained condition almost always
exists for coarse-grained material such as gravels and sands under
static/monotonic loading. This is because of the large permeability of
the material so that the pore water can quickly drain out. Note that
under seismic loading condition due to the quick rate of loading
saturated loose sands can experience undrained loading condition
resulting in liquefaction.
37

On the other hand, due to the low material permeability, undrained
condition almost always exist for clays and silts when subjected to quick
static loads and earthquake loads.
38

STRENGTH THEORIES FOR SOILS
A number of theories have been proposed for explaining the shearing
strength of soils. Of all such theories, the Mohr’s strength theory and
the Mohr-Coulomb theory, a generalisation and modification of the
Coulomb’s equation, meet the requirements for application to a soil in
an admirable manner.
40

Laboratory tests for shear strength
1) Direct shear test
2) Triaxial test
3) Simple shear test
4) Plane strain triaxial test
5) Torsional ring shear test
6) Unconfined Compression Test
7) Laboratory Vane Shear Test
41

Motor
drive
Load cell to
measure
Shear Force
Normal load
Rollers
Soil
Porous plates
Top platen
Measure relative horizontal displacement, dx
vertical displacement of top platen, dy
SHEAR BOX TEST

The limiting shear stress (soil strength) is given by
t = c + sn tan f
where c = cohesion (apparent)
f = friction angle
t
sn
MOHR-COULOMB FAILURE
CRITERION

Normal and shear stress
45
n 
1 1
2 2
3 3
4 4
5 5

46
t
sn
Shear parameters (c, )

47
t
sn

48
t
sn

49
t
sn

50
t
c
  
 
c tan
f
sn

Maximum shear and shear at failure (max , f)

52
t   
 
c tan
f
sn

53
t   
 
c tan
f
sn

54
t   
 
c tan
f
sn
m
ax
f

n

example
The stresses at failure on the failure plane in a cohesionless soil mass
were:
Shear stress = 4 kN/m2
; normal stress = 10 kN/m2
. Determine the
resultant stress on the failure plane, the angle of internal friction of the
soil and the angle of inclination of the failure plane to the major
principal plane.
55

Graphical solution
The procedure is first to draw the σ-and τ-axes from an origin O and
then, to a suitable scale, set-off point D with coordinates (10,4), Joining
O to D, the strength envelope is got. The Mohr Circle should be
tangential to OD to D. DC is drawn perpendicular to OD to cut OX in C,
which is the centre of the circle. With C as the centre and CD as radius,
the circle is completed to cut OX in A and B.
56

exercise
The following results were obtained in a shear box text. Determine the
angle of shearing resistance and cohesion intercept:
Normal stress (kN/m2
) 100 200 300
Shear stress (kN/m2
) 130 185 240
58

example
Clean and dry sand samples were tested in a large shear box, 25 cm ×
25 cm and the following results were obtained :
Normal load (kN) 5 10 15
Peak shear load (kN) 5 10 15
Ultimate shear load (kN) 2.9 5.8 8.7
Determine the angle of shearing resistance of the sand in the dense
and loose states.
60

solution
The value of  obtained from the peak stress represents
the angle of shearing resistance of the sand in its initial
compacted state; that from the ultimate stress
corresponds to the sand when loosened by the shearing
action.
The area of the shear box = 25 × 25 = 625 cm2
.
= 0.0625 m2
.
Normal stress in the first test = 5/0.0625 kN/m2
= 80 kN/m2
61

solution
Similarly the other normal stresses and shear stresses are obtained by
dividing by the area of the box and are as follows in kN/m2
:
Normal stress, σ 80 160 240
Peak shear stress, max 80 160 240
Ultimate shear stress, f 46.4 92.8 139.2
62

65
y = 0.5706x
R² = 0.8253
0
10
20
30
40
50
0 10 20 30 40 50
Shear
Stress

(kN/m
2
)
Normal Stress n (kN/m2)
BH7-SPT04
 = 29.70
C = 0
PRACTICAL WORKED EXAMPLE

66
Borehole
No.
Sample
No.
Depth
(m)
Strength
parameters
Bulk
Density
(
)
(kN/m³)
Moisture
Content
(

)
(%
)
Dry
Density
(

d)
(kN/m
3
)
c
(kPa)

(degree)
BH14 SPT2 2.0 0.0 17.3 19.2 13.1 17.0
BH14 SPT3 3.0 1.7 22.9 19.2 34.3 14.3
BH14 SPT6 6.0 3.9 26.4 19.2 37.0 14.0
PRACTICAL WORKED EXAMPLE

example
The following data were obtained in a direct shear test. Normal
pressure = 20 kN/m2
, tangential pressure = 16 kN/m2
. Angle of internal
friction = 20°, cohesion = 8 kN/m2
.
Represent the data by Mohr’s Circle and compute the principal stresses
and the direction of the principal planes.
67

Example-2
From a direct shear test on an undisturbed soil sample, the
following data have been obtained. Evaluate the undrained
shear strength parameters. Determine shear strength,
major and minor principal stresses and their planes in the
case of specimen of same soil sample subjected to a
normal stress of 100 kN/m2
. :
sn (kN/m2
) 70 96 114
t (kN/m2
) 138 156 170
69

Unconfined compression test
71

72

73
0
1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Stress
(N/mm2)
0 10
1 2 3 4 5 6 7 8 9
Stroke Strain (%)
Max

Example-3
A cylindrical sample of saturated clay 4 cm in diameter and 8 cm high
was tested in an unconfined compression apparatus. Find the
unconfined compression strength, if the specimen failed at an axial load
of 360 N, when the axial deformation was 8 mm. Find the shear
strength parameters if the angle made by the failure plane with the
horizontal plane was recorded as 50°.
74

Mcq’s
For sands the residual strength is the same as the critical state
strength.
Critical state is between peak state and residual state.
The theoretical state at which the shear stress and density remain
constant while the shear strain increases may be called the critical
state.
77

Mcq’s
The minimum and constant drained shear strength at which a soil
experiences a large shear displacement under a given normal stress
may be called as residual strength.
The highest level of shear strength measured under a given normal
load is defined as the peak strength.
78

Mcq’s
Triaxial compression test is used for the determination of shear
parameters of all types of soil under any drainage condition.
79

triaxial shear test
A triaxial shear test is a common method to measure the mechanical
properties of many deformable solids, especially soil (e.g. sand, clay)
and rock, and other granular materials or powders. There are several
variations on the test.
82

triaxial shear test
The principle behind a triaxial shear test is that the stress applied in the
vertical direction (along the axis of the cylindrical sample) can be
different from the stresses applied in the horizontal directions
perpendicular to the sides of the cylinder, i.e. the confining pressure).
In a homogeneous and isotropic material this produces a non-
hydrostatic stress state, with shear stress that may lead to failure of the
sample in shear.
83

triaxial shear test
In homogeneous and anisotropic samples (e.g. bedded or jointed
samples) failure may occur due to bending moments and, hence, failure
may be tensile. Also combinations of bending and shear failure may
happen in inhomogeneous and anisotropic material.
84

Potential applications
Determining the mechanical properties of soils is a very important
step to design foundations, embankments and other soil
structures. Building constructions, excavations, tunneling and
similar applications have several effects on the subsoil structures
and these effects are successfully simulated with Triaxial Tests
where the stress-strain relation of undisturbed soil specimen are
investigated by subjecting the soil sample to different stress levels
and drainage conditions.
85

TRIAXIAL TEST
Cell
pressure
Pore pressure
and volume
change
Rubber membrane
Cell water
O-ring seals
Porous filter disc
Confining cylinder
Deviator load
Soil

sr sr = Radial stress (cell
pressure)
sa = Axial stress
F = Deviator load
sr
STRESSES IN TRIAXIAL SPECIMEN

sr sr = Radial stress (cell
pressure)
sa = Axial stress
F = Deviator load
sr
 
a r
F
A
 
From equilibrium we have
STRESSES IN TRIAXIAL SPECIMEN

Type of Triaxial tests
Depending on the nature of loading and drainage condition, triaxial
tests are conducted in three different ways
Unconsolidated Undrained test (UU-test)
Consolidated Undrained test (CU-test)
Consolidated Drained test (CD-test)

Use of triaxial tests
Field Problem Type of Analysis Type of Test
First Time Slope
Failure
Effective Stress CU or CD Triaxial
Cut Slope Failure Effective Stress CU Triaxial
Earth Dams Total Stress
Effective Stress
UU Triaxial
CU Triaxial
Triaxial Permeability
Tunnel Linings Total Stress
Effective Stress
UU Triaxial
CU Triaxial
91

Sample preparation for Triaxial testing
92

SAND CEMENT PROPORTION
The following is the procedure for the
determination of the void ratio of a cemented
specimen, Determine
The specific gravity of sand G sand
The specific gravity of cement G cement
The dry mass of specimen M dry i.e., the mass of
solid M solid
Specimen dimensions i.e., height H and diameter
D

AVERAGE SPECIFIC GRAVITY
The average specific gravity of the specimen G (taking cement content
= C %)
cement
soil G
C
G
C
G 




100
100
100

INITIAL VOID RATIO
The volume of solid (i.e., sand + cement) V solid
The total volume of the specimen V total
The volume of voids V voids
w
solid
solid
G
M
V



solid
total
voids V
V
V 


INITIAL VOID RATIO
The initial void ratio of the specimen e
solid
voids
V
V
e 

CONSTANT DRY DENSITY WITH INCREASING CEMENT CONTENT
The mass of sand M sand and mass of cement M cement can be calculated
as follow:
total
sand M
C
M 







100
100
total
cement M
C
C
M 







100

SAND CEMENT MIXING BUCKET
Once dry sand and cement
mixed thoroughly, water of
required percent must be added
and mixed to get a uniform and
consistent sand-cement paste.

SAND CEMENT MIXING
The targeted dry unit weight of the material for a
standard size specimen can be maintained by
varying the weight of the moist sample using the
following equation.
The required weight of mixture should be taken for
specimen preparation





1
d

MEMBRANES
Rubber membranes: (a) Latex; (b) Neoprene.

Concrete sand
Gs = 2.65
D50 = 0.35
Cu= 2.2
emax = 0.79
emin = 0.46
Polypropylene fibre
Length= 22mm
Diameter = 0.023mm
Gs = 0.9
Elastic modulus = 8 GPa
Ordinary Portland cement
TS EN 197-1-CEM 1
Gs = 3.15
MATERIALS

SPECIMEN PREPARATION ACCESSORIES

CEMENTED SPECIMEN PREPARATION
Grine, K. and Glendinning, S. (2007) Geotech Geol Eng 25, 441–448
Grine & Glendinning (2007)

Ismail, M. A., Joer, H. A., and Randolph, M. F., (2000) Sample Preparation Technique for Artificially
Cemented Soils,” Geotechnical Testing Journal, 23( 2),, pp. 171–177.
Ismail, et al (2000)

Ladd, R. S. (1978) Preparing test specimens using undercompaction," Geotechnical Testing Journal, 1(1),
16-23.
Ladd, (1978)

Bradshaw, A. S. and Baxter, C. D. P. (2007) Sample preparation of silts for liquefaction testing,
Geotechnical Testing Journal, 30(4), 1-9.
Bradshaw and Baxter (2007)

UNCEMENTED SPECIMEN PREPARATION

Uncemented specimen preparation

Pore pressure
control
Back pressure /
volume control
Porous stones
Top cap
Top drainage
valve
Bottom drainage
valve
Cell chamber
Load cell
Pore pressure valve
Spacers
Computer
Cell pressure /
volume control
Displacement
control
Specimen
Cross beam

Triaxial testing procedure
Docking
Flushing
Saturation ramp
B-check
Consolidation
Shearing

terminology
Back pressure —a pressure applied to the specimen pore-water to
cause air in the pore space to compress and to pass into solution in the
pore-water thereby increasing the percent saturation of the specimen.
Effective consolidation stress —the difference between the cell
pressure and the pore-water pressure prior to shearing the specimen.
123

terminology
Failure—the stress condition at failure for a test specimen. Failure is
often taken to correspond to the maximum principal stress difference
(maximum deviator stress) attained or the principal stress difference
(deviator stress) at 15 % axial strain, whichever is obtained ﬁrst during
the performance of a test.
124

docking
Bring the axial load piston into contact with the specimen cap several
times to permit proper seating and alignment of the piston with the
cap. During this procedure, take care not to apply an axial load to the
specimen exceeding 0.5% of the estimated axial load at failure. When
the piston is brought into contact, record the reading of the
deformation indicator to three digits.
125

flushing
Under an effective stress of at least 13 kPa (2 lb/in2
) allow water to
percolate from bottom to the top of the specimen under a differential
pressure of less than 20 kPa (3 lb/in2
).
126

Uu triaxial test
ASTMD2850—15 is the standard test method for unconsolidated
undrained triaxial compression test on cohesive soils. This test method
covers determination of the strength and stress-strain relationship of a
cylindrical specimen of either undisturbed or remoulded cohesive soil.
131

Uu-Triaxial test
The unconsolidated undrained (UU) test is the simplest and fastest
procedure, with soil specimens loaded whilst only total stresses are
controlled and recorded. This allows the undrained shear strength cu to
be determined, which is suitable for assessing soil stability in the short-
term (e.g. during or directly following a construction project). Note this
test is generally performed on cohesive soil specimens.
132

Uu-Triaxial test
If the test specimens is 100 % saturated, consolidation cannot
occur when the confining pressure is applied nor during the shear
portion of the test since drainage is not permitted. Therefore, if
several specimens of the same material are tested, and if they are
all at approximately the same water content and void ratio when
they are tested, they will have approximately the same
unconsolidated-undrained shear strength.
133

Uu-Triaxial test
If the test specimens are partially saturated, or
compacted/reconstituted specimens, where the degree of saturation is
less than 100 %, consolidation may occur when the confining pressure
is applied and during application of axial load, even though drainage is
not permitted. Therefore, if several partially saturated specimens of the
same material are tested at different confining stresses, they will not
have the same unconsolidated-undrained shear strength.
134

Uu-Triaxial test
135
The failure envelopes will usually be a horizontal line for saturated specimens and a
curved line for partially saturated specimens

Uu-Triaxial test
The unconsolidated-undrained shear strength is applicable to situations
where the loads are assumed to take place so rapidly that there is
insufficient time for the induced pore-water pressure to dissipate and
for consolidation to occur during the loading period (that is, drainage
does not occur).
136

Scope of UU Triaxial test
This test method covers determination of the strength
and stress-strain relationships of a cylindrical specimen
of either intact, compacted, or remolded cohesive soil.
This test method provides data for determining
undrained strength properties and stress-strain
relations for soils. This test method provides for the
measurement of the total stresses applied to the
specimen, that is, the stresses are not corrected for
pore-water pressure.
137

ASTM D 2664 – 95a. This test method covers the determination of the
strength of cylindrical rock core specimens in an undrained state under
Triaxial compression loading. The test provides data useful in
determining the strength and elastic properties of rock, namely: shear
strengths at various lateral pressures, angle of internal friction, (angle
of shearing resistance), cohesion intercept, and Young’s modulus.
138

It should be observed that this method makes no provision for pore
pressure measurements. Thus the strength values determined are in
terms of total stress, that is, not corrected for pore pressures.
139

t t = in situ undrained
shear strength
Soft clay
1. Embankment constructed rapidly over a soft clay deposit
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
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
CLAYS

CU Triaxial test
ASTM D4767 - 11 is the standard test method for
Consolidated Undrained Triaxial Compression Test for
Cohesive Soils. In a consolidated undrained test the
specimens are isotropically consolidated and sheared in
compression without drainage at a constant rate of axial
deformation (strain controlled). The shear characteristics
are measured under undrained conditions and the sample
is assumed to be fully saturated.
144

CU Triaxial test
This method determines the angle of internal friction (f) and cohesion
(c) strength parameters of soils by triaxial compression testing.
When pore pressures are measured, the effective values of internal
friction and cohesion, (f') and (c') respectively, can be calculated.
145

CU Triaxial test
This test method provides for the calculation of total and effective
stresses, and axial compression by measurement of axial load, axial
deformation, and pore-water pressure.
146

example
147
0% 5% 10% 15% 20% 25%
0
1000
2000
3000
4000
5000
6000
7000
(19.8, 5791)
(20.0, 3356)
(20.0, 2239)
Sample 1
Sample 2
Sample 3
Vertical Strain, εv
Deviator
Stress,
Δσd
(psf)
0% 5% 10% 15% 20% 25%
0
500
1000
1500
2000
2500
3000
3500
4000
(19.8, 2848)
(20.0, 1489)
(20.0, 572)
Sample 1
Sample 2
Sample 3
Pore
Water
Pressure,
Δu
(psf)

148
0% 5% 10% 15% 20% 25%
0
500
1000
1500
2000
2500
3000
3500
4000
(19.8, 2848)
(20.0, 1489)
(20.0, 572)
Sample 1
Sample 2
Sample 3
Pore
Water
Pressure,
Δu
(psf)

149
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000
0
1000
2000
3000
4000
Normal Stress, σ (psf)
Shear
Stress,
τ
(psf)
φ' = 30.3°, c' = 140 psf
φcu = 18.9°, cu = 230 psf

150
0% 5% 10% 15% 20% 25%
0
1000
2000
3000
4000
5000
6000
7000
(19.8, 5791)
(20.0, 3356)
(20.0, 2239)
Sample 1 Sample 2
Sample 3
Deviator
Stress,
Δσd
(psf)

CU test stages
Initial specimen conditions
Length
Diameter
Humid mass
Moisture content
Specific gravity
Bulk unit weight and dry unit weight
151

Saturation stage
Percolation stage ( flushing stage)
Saturation method (saturation ramp…)
Initial cell pressure 50 kPa
Moisture content at saturation (depends on void ratio)
152

• Final specimen condition
156

example
A specimen of saturated sand was consolidated under
an all-round pressure of 60 lb/ft2
. the axial stress was
then increased and drainage was prevented. The
specimen failed when the axial deviator stress reached
50 lb/in2. The pore water pressure at failure was 41.35
lb/in2. determine:
Consolidated-undrained angle of shearing
resistance, f
Drained friction angle, f`
Deviator stress at failure qf
157

example
A normally consolidated clay was consolidated under a
stress of 3150 lb/ft2
, then sheared undrained in axial
compression. The principal stress difference at failure was
2100 lb/ft2
, and the induced pore pressure at failure was
1848 lb/ft2
. Determine (a) the Mohr-Coulomb strength
parameters, in terms of both total and effective stresses
analytically, (b) compute (s1/s3), and (s’1/s’3), and (c)
determine the theoretical angle of the failure plane in the
specimen.
158

example
The following results were obtained at failure in a series of
consolidated-undrained tests, with pore
pressure measurement, on specimens of saturated clay. Determine the
values of the effective stress parameters c’ and ’ by drawing Mohr
circles.
159

Cd triaxial test
Standard Test Method for Consolidated Drained Triaxial
Compression Test for Soils ASTM D7181- 11. This test method
covers the determination of strength and stress-strain
relationships of a cylindrical specimen of either intact or
reconstituted soil. Specimens are consolidated and sheared in
compression with drainage at a constant rate of axial deformation
(strain controlled).
161

Cd triaxial test
This test method provides for the calculation of principal stresses and
axial compression by measurement of axial load, axial deformation, and
volumetric changes.
This test method provides data useful in determining strength and
deformation properties such as Mohr strength envelopes. Generally,
three specimens are tested at different effective consolidation stresses
to define a strength envelope.
162

Example
A CD triaxial compression test was conducted on a sand specimen using
a conﬁning pressure of 42 kPa. Failure occurred at a deviator stress of
53 kPa. Calculate the normal and shear stresses on the failure plane at
failure. Also calculate the angle made by the failure plane with the
horizontal. (a) Solve the problem graphically and (b) conﬁrm your
solution analytically.
167

Example
Three CD triaxial compression tests were conducted on three over
consolidated clay specimens using three conﬁning pressures: 4, 20, and
35 kPa. Failure occurred at the deviator stresses of 19, 36 and 54 kPa,
respectively. Determine the shear strength parameters of the soil.
169

Stress path in cd Triaxial test
171

Example-1
A series of shear tests were performed on a soil. Each test was carried
out until the sample sheared and the principal stresses for each test
were :
Test No. (kN/m2
) (kN/m2
)
1 200 600
2 300 900
3 400 1200
173

example
A cylindrical sample of soil having a cohesion of 80 kN/m2
and an angle
of internal friction of 20° is subjected to a cell pressure of 100 kN/m2
.
Determine: (i) the maximum deviator stress
(s1- s3) at which the sample will fail, and (ii) the angle made by the
failure plane with the axis of the sample.
181

Stress path
Stress path is used to represent the successive states of stress in a test
specimen of soil during loading or unloading. Series of Mohr circles can
be drawn to represent the successive states of stress.
The successive states of stress can be represented by a series of stress
points and a locus of these points (in the form of straight or curve) is
obtained.
183

Stress path
The locus stress points is called stress path.
184

Stress path
185
Stress point on Mohr circle and on p-q

Stress path in CU Triaxial test
186
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000
0
500
1000
1500
2000
2500
3000
3500
Stress Path, p' (psf)
Stress
Path,
q
(psf)

CU Triaxial compression test
187

Example-i
Plot the total and effective stress paths for the following stress changes
188

Exercise-I
The following results were obtained from a series of undrained triaxial
tests carried out on undisturbed samples of a compacted soil:
189

Exercise-II
Each sample, originally 76mm long and 38 mm in diameter,
experienced a vertical deformation of 5.1 mm. Draw the strength
envelope and determine the Coulomb equation for the shear strength
of the soil in terms of total stresses.
190

Exercise-III
A sample of clay was subjected to an undrained triaxial test with a cell
pressure of 100kN/m2
and the additional axial stress necessary to cause
failure was found to be 188kN/m2
. Assuming that u = 0°, determine
the value of additional axial stress that would be required to cause
failure of a further sample of the soil if it was tested undrained with a
cell pressure of 200 kN/m2
.
192

Exercise-IV
A series of drained triaxial tests were performed on a soil. Each test was
continued until failure and the effective principal stresses for the tests
were:
194

Exercise-V
Plot the relevant Mohr stress circles and hence determine the strength
envelope of the soil with respect to effective stress.
195

Exercise-vI
A series of undisturbed samples from a normally consolidated clay was
subjected to consolidated undrained test. The results were:
197

Exercise-ViI
Plot the strength envelope of the soil (a) with respect to total stresses
and (b) with respect to effective stresses.
198

Exercise-ViiI
A series of shear tests were performed on a soil. Each test was carried
out until the sample sheared and the principal stresses for each test
were :
Test No. (kN/m2
) (kN/m2
)
1 200 600
2 300 900
3 400 1200
200

Stress hardening and stress softening
Strength and stiffness
Theory of plasticity
Theory of elasticity
Associated and non associated flow model
Plastic potential surface
Cam-clay model
Elasto-plastic model
204

quasi steady state (QSS)
ultimate steady state (USS)
the state of phase transformation
Flow failure
Failure line (FL)
Peak state
Failure state
205

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