Unit IV Shear Strength

1. SHEAR STRENGTH OF SOILS
Er.D.Mythili
Assistant Professor
Department of Civil Engineering
Excel Engineering College
1

2. OUTLINE
 Shear strength
 Introduction
 Shear failure
 Principal Stresses and Principal Planes
 Mohr-Coulomb failure criterion
 Laboratory tests
 Direct Shear test
 Unconfined Compression test
 Tri axial Compression test
 Vane Shear test
 Problems
2

3. Strength of different
materials
Steel
Tensile
strength
Concrete
Compressive
strength
Soil
Shear
strength
Presence of pore water
Complex
behavior
3

4. SHEAR STRENGTH
 The resistance to shearing stresses and a
consequent tendency for shear deformation.
 Maximum shear stress that a soil can sustain without
failure.
 Soil derives its shear strength from:
 Interlocking of particles
 Frictional resistance (sliding & rolling friction)
 Cohesion.
4

5. SHEAR FAILURE
 Soils generally fail in shear
 At failure, shear stress along the failure surface
reaches the shear strength.
 The soil grains slide over each other along the failure
surface.
5

6. SHEAR FAILURE MECHANISM IN AN
EMBANKMENT
Where, σ = normal stress
 = shear stress
At failure, shear stress along the failure surface ()
reaches the shear strength (f).
6

7. 7
SHEAR FAILURE MECHANISM IN
RETAINING WALL
Retaining
wall

8. 8
SHEAR FAILURE MECHANISM OF
RETAINING WALL
Retaining
wall
At failure, shear stress along the failure surface
(mobilized shear resistance) reaches the shear strength.
Failure
surface
Mobilized
shear
resistance

9. SHEAR FAILURE OF FOUNDATION
 Depending on the stiffness of foundation soil and
depth of foundation, the following are the modes of
shear failure experienced by the foundation soil.
 General Shear Failure
 Local Shear Failure
 Punching Shear Failure
9

10. GENERAL SHEAR FAILURE
 Continuous, well defined and distinct failure surface develops
between the edge of footing and ground surface.
 Dense or very stiff soil that of low compressibility experiences
this failure.
 Continuous bulging of shear mass adjacent to footing is
visible.
 Failure is accompanied by tilting of footing.
 Failure is sudden and catastrophic with pronounced peak
in curve.
 The length of disturbance beyond the edge of footing is large.
 State of plastic equilibrium is reached initially at the footing
edge and spreads gradually downwards and outwards.
 General shear failure is accompanied by low strain (<5%) in a
soil with ø>36o and large N (N > 30) having high relative
density (ID> 70%).
10

11. GENERAL SHEAR FAILURE
11

12. LOCAL SHEAR FAILURE
 This type of failure is seen in medium dense sand and stiff
clays.
 A significant compression of soil below the footing and partial
development of plastic equilibrium is observed.
 Failure is not sudden and there is no tilting of footing.
 Failure surface does not reach the ground surface and slight
bulging of soil around the footing is observed.
 Failure surface is not well defined.
 Failure is characterized by considerable settlement.
 Well defined peak is absent in curve.
 Local shear failure is accompanied by large strain (> 10 to
20%) in a soil with considerably low (ø<28o) and low N (N < 5)
having low relative density (ID> 20%)
12

13. LOCAL SHEAR FAILURE
13

14. PUNCHING SHEAR FAILURE
 This type of failure is seen in loose and soft soil.
 This type of failure occurs in a soil of very high
compressibility.
 Failure pattern is not observed.
 Bulging of soil around the footing is absent.
 Failure is characterized by very large settlement.
 Failure surface is vertical or slightly inclined.
 The failure surface never reaches the ground
surface.
 There is no heaving at the ground surface and no
tilting of the footing.
14

15. PUNCHING SHEAR FAILURE
15

16. FACTORS AFFECTING SHEAR STRENGTH
 Soil composition
 Mineralogy, Grain size and Grain size distribution, Shape of
particles.
 Initial state
 Defined by the initial void ratio, effective normal stress and
shear stress (stress history).
 Soil structure
 Arrangement of particles within the soil mass
 Packed or distributed.
 Layers, joints, fissures, voids, pockets, etc.
 Drainage conditions
 Drained or undrained
 Total or effective stresses
 Loading conditions
 Magnitude, rate, method of application (static, dynamic),
16

17. 17
CONCEPT OF PRINCIPAL STRESSES AND
PRINCIPAL PLANES

18. 18
Cont.....

19. MOHR CIRCLE
19

20. OBSERVATIONS FROM MOHR
CIRCLE
20
 The planes which are subjected to only normal
stress and no shear stress acts on them are called
as principal planes.
 The stresses on these planes are called as principal
stresses.
 The plane at which the shear stress is equal to shear
strength, shear failure takes place. This is called
incipient failure condition.
 The plane at which the shear stress is maximum
need not be the failure plane.
 The ultimate strength is determined by the stresses
on the failure plane (plane of shear).

21. ADVANTAGES OF MOHR CIRCLE
21
 No Equation to be remembered.
 Location of different planes are clear.

22. SOILS SUBJECTED TO STRESS
CONDITION- PRACTICAL CASE
22

23. MOHR CIRCLE
23

24. EXPRESSION OF NORMAL AND SHEAR
STRESS
24

25. MOHR-COULOMB FAILURE CRITERIA
25
 Mohr (1900) proposed a hypothesis for failure of
materials which suggested shear strength, τf is not a
constant but a function of normal stress, σ.
 The shear stress at failure or shear strength can be
expressed as:
τf = f(σ).
 The failure envelope described
by the above equation is a curve.
Mohr’s failure envelope

26. MOHR-COULOMB FAILURE CRITERIA
26
 But Coulomb (1776) found that shear strength of
rupture plane had two components namely cohesion
and frictional resistance.
 Cohesion was found to be constant and independent
of normal stress.
 Shearing resistance was found to be a function of
normal stress.
 Combining the hypothesis of Mohr and findings of
Coulomb, the shear stress at failure is approximated
as a linear function of normal stress expressed as:

27. MOHR-COULOMB FAILURE CRITERIA
Where, c = cohesion
σ = normal stress on the failure plane
ø = angle of internal friction
 Theory states that
“material fails essentially
by shear because of a
critical combination of
normal and shear
stresses alone”.
27
Mohr-Coulomb failure envelope

28. POSSIBILITIES OF MOHR’S CIRCLE
FOR THE GIVEN STRESS
28

29. LOCATION OF FAILURE PLANE AT
FAILURE
29
Failure plane
Major principal plane
Minor principal plane

30. 30
Cont.....

31. 31
Cont.....

32. 32
Cont.....

33. 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 .



 tan

 c
f
c

Cohesion
Friction angle

34. 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
'
' 

 
 c
f
c’
’
Effective
cohesion Effective
friction angle
u

 
 '
u = pore water
pressure
34

35. FAILURE ENVELOPES IN TERMS OF
TOTAL AND EFFECTIVE STRESSES
= X
1’
3’
X
u
u
+
1’
3’
effective stresses
u 1
3
X
1
3
total stresses

 or ’
If X is on
failure
c

Failure envelope in
terms of total stresses
’
c’
Failure envelope in terms
of effective stresses
35

36. MOHR’S CIRCLE FOR DIFFERENT SOILS
36

37. FAILURE ENVELOPE BASED ON
DRAINAGE CONDITIONS
37

38. Soil elements at different locations
Failure surface
FAILURE OF SOIL ELEMENT
X X
X ~ failure
Y
Y
Y ~ stable

’
'
tan
'
' 

 
 c
f
38

39. SIGNIFICANCE OF SHEAR STRENGTH
PARAMETERS
39
 c and ø are measures of shear strength.
 Higher the values, higher the shear strength.
 c and ø are mathematical parameters rather than
fundamental parameters -------- Why?
If the undrained test is performed on a sandy
soil in the laboratory, øu=0 with a large cu value.
If a drained test is conducted on clayey soil, c’=0
with a large ø’ value.

40. IMPORTANCE OF SHEAR STRENGTH
 Evaluation of bearing capacity for foundation design.
 Analysis of stability of the slope.
 Design of earth retaining structures like retaining
walls, sheetpile and other underground structures.
40

41. 41
Determination of shear strength parameters of
soils (c,  or c’, ’)
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 test
2.Unconfined Compression test
3.Triaxial Compression test
4.Vane Shear test
1. Vane Shear test
2. Penetration test

42. SUITABILITY OF TESTS
42
TESTS SUITABILITY
DIRECT SHEAR TEST COHESIONLESS SOIL
TRIAXIAL COMPRESSION TEST ALL TYPE OF SOILS
UNCONFINED COMPRESSION
TEST
COHESIVE SOIL
VANE SHEAR TEST SOFT, SATURATED & SENSITIVE
CLAYS

43. DIRECT SHEAR TEST
 The direct shear test is the simplest method of shear test
for determining the shear strength of soil.
 In this test soil sample, undisturbed or remoulded, is
placed in a metal box having square or circular in section.
 The shear box can be split in two half horizontally.
 The size of the box normally used for clays and sand is 6
cm square and the sample is 2 cm thick.
 The large size shear box is 30 cm square with sample
thickness of 15 cm, used for gravelly soil.
 The lower half of the box can slide relative to the upper
half when pushed by a hand operated or motorized drive
unit, while a yoke supporting a load hanger provides the
normal pressure.
43

44. DIRECT SHEAR TEST
44
 The lower half of the box can slide relative to the
upper half when pushed by a hand operated or
motorized drive unit, while a yoke supporting a load
hanger provides the normal pressure.
 The normal load is maintained throughout the test
and shear stress is gradually applied causing the two
halves of the box to slide relative to each other.
 The shearing displacement is recorded by a dial
gauge.
 Shear stress is applied in such a way that we get a
shear displacement of 1.25 mm/min. If the soil does
not fail then 12 mm strain is taken as failure point.

45. DIRECT SHEAR TEST
45
 Shear application can be of two types:
 Stress controlled
 Strain controlled.
 A number of samples of the soil are tested each
under different vertical loads and the value of shear
stress at failure is plotted against the normal stress
for each test.
 Provided there is no excess pore water pressure in
the soil, the total and effective stresses will be
identical.
 From the stresses at failure, the failure envelope can
be obtained.

46. DIRECT SHEAR TEST
 By dividing the normal load and the maximum
applied shearing force with the cross-sectional area
of the specimen at the shear plane gives
respectively the normal stress and shear stress at
failure.
 In order to obtain sufficient points to draw the
coulomb graph, the test is repeated with different
normal stresses on a number of identical samples.
 The value of each tests are plotted with normal
stress on the x-axis and shear stress on Y-axis. The
shear strength parameters are then obtained from
the best line fitting the test points.
46

47. SHEAR BOX APPARATUS
47

48. 48

49. Direct shear test
Analysis of test results
sample
the
of
section
cross
of
Area
(P)
force
Normal
stress
Normal 


sample
the
of
section
cross
of
Area
(S)
surface
sliding
at the
developed
resistance
Shear
stress
Shear 


49

50. DIRECT SHEAR TEST
Shear
Stress,
τ
(kPa)
Normal Stress, σ (kPa)
First Test
τf
Second Test
τf
Third Test
τf
Fitting a best fit line through these points
Mohr Coulomb’s failure envelope
c

50

51. 51
Direct shear tests
Dense sand/OC Clay
Loose sand/NC Clay
Change
in
volume
Expansion
Compression
Shear displacement
Stress-strain relationship

52. ADVANTAGES
 Simple and cheap.
 Easy and quick test for sands and gravels.
 Concept of Shear failure could be easily understood.
 Sample thickness is small-drainage is quick and pwp
dissipation is rapid.
 Large deformations can be achieved by reversing
shear
direction. This is useful for determining the residual
strength of soil.
52

53. LIMITATIONS
 The plane of shear failure is predetermined, which may
not be the weakest one.
 Failure along the horizontal failure plane is
progressive.
 Non-uniform deformations and stresses in the
specimen. The stress-strain behaviour cannot be
determined.
 The estimated stresses may not be those acting on the
shear plane.
 There is no means of estimating pore pressures. So
effective stresses cannot be determined from
undrained tests.
 There is an effect of lateral restraint by the side walls
53

54. UNCONFINED COMPRESSION TEST
 It is a special case of triaxial compression test where the
confining pressure is zero.
 The test is performed on a cylindrical sample having
height to diameter ratio of 2 to 2.5
 The usual size of the specimen is 38 mm.
 Since the specimen is laterally unconfined, the test is
known as ‘unconfined compression test’.
 No rubber membrane is necessary to encase the
specimen.
 The vertical compressive stress is the major principal
stress.
 The test is suitable for undisturbed and remoulded
cohesive soils.
54

55. UNCONFINED COMPRESSION TEST
 This test is a quick and undrained test where the failure
plane is not predetermined and takes place along the
weakest plane.
 The proving ring measures the vertical resistance
offered by the soil.
 When a proving ring is used, the vertical load is applied
by rotating a handle to produce an axial strain of 2% per
minute.
 The compressive force is recorded from the proving ring
and the strain from the dial gauge.
55

56. 56

57. SPECIMEN DEFORMATION
57

58. INTEPRETATION OF RESULTS
 The deformation is continued till the sample fails.
 The values of axial strain corresponding to various
deformation readings are calculated and then the deformed
cross-sectional areas corresponding to these strain values
are calculated.
 The compressive stress at any strain is calculated by
dividing the load at the stage with the corresponding
deformed area (A2).
 The stress – strain curve is plotted.
58

59. Cont.....
59
 The stress at the peak of the curve represents the
failure condition. If there is no definite peak in the
curve, then stress corresponding to 20% strain is
arbitrarily taken as the failure condition which is
termed as ‘Unconfined Compressive Strength’
(UCS).

60. 60
Cont.....
Cont.....

61. 61
Cont.....

62. 62
Cont.....

63. 63
Cont.....

64. MERITS
 The test is convenient, simple and quick.
 Ideally suitable for measuring shear strength of
saturated clays.
 Useful in determining the sensitivity of soil using
undisturbed and remoulded sample.
 The cost involved in this test is much less than the
triaxial test due to simpler testing requirement.
64

65. DEMERITS
 Suitable for intact homogeneous clays and not
suitable for fissured clays.
 The test may be misleading for soils for which the
angle of shearing resistance is not zero.
 As no covering or lateral support is provided to the
sample in this test, it is applicable to soil which can
stand unsupported and are impervious to maintain
the un-drained condition throughout the test.
 The test under estimates in-situ strength because of
the sampling disturbance
65

66. SENSITIVITY
 Some clays have a property due to which their
strength in a remoulded or highly disturbed state is
less than that in an undisturbed state at the same
moisture content. This property is called sensitivity.
 St = qu (undisturbed)/qu (remoulded)
 Sensitivity of natural deposits ranges from less than
1.0 to as high as 100. High sensitivity is observed in
clays known as “Quick clays”.
66

67. CLASSIFICATION OF SENSITIVITY
67
CLASSIFICATION SENSITIVITY
Insensitive Less than 1
Slightly Sensitive 1-2
Medium Sensitive 2-4
Very Sensitive 4-8
Slightly Quick 8-16
Medium Quick 16-32
Very Quick 32-64
Extra Quick Greater than 64

68. TRIAXIAL COMPRESSION TEST
 First introduced by Casagrande and Terzaghi in 1936.
 This is the most widely used and is suitable for all types of
soils.
 A cylindrical specimen, generally having a length to
diameter ratio of 2 to 2.5 is used in the test and is
stressed under conditions of axial symmetry.
 The usual size is 76 mm x 38 mm.
 Three principal stresses are applied to the soil sample,
out of which two are applied water pressure inside the
confining cell and are equal.
 The third principal stress is applied by a loading ram
through the top of the cell and is different to the other two
principal stresses.
68

69. TRIAXIAL COMPRESSION TEST
 The soil sample is placed inside a rubber sheath which
is sealed to a top cap and bottom pedestal by rubber
O-rings.
 For tests with pore pressure measurement, porous
discs are placed at the bottom, and at the top of the
specimen.
 Filter paper drains may be provided around the outside
of the specimen in order to speed up the consolidation
process.
 Pore pressure generated inside the specimen during
testing can be measured by means of pressure
transducers.
69

70. TRIAXIAL COMPRESSION TEST
70
 The triaxial compression test consists of two stages:
 First stage: In this, a soil sample is set in the triaxial
cell and confining pressure is then applied.
 Second stage: In this, additional axial stress (also
called deviator stress) is applied which induces
shear stresses in the sample. The axial stress is
continuously increased until the sample fails.
 During both the stages, the applied stresses, axial
strain, and pore water pressure or change in sample
volume can be measured.

71. 71
TRIAXIAL COMPRESSION TEST

72. TRIAXIAL CELL
72

73. 73

74. FAILURE PATTERN OF SPECIMEN
74

75. TYPES OF TRIAXIAL TEST
 Fine grained soils are tested for shear strength when
they are fully saturated.
 Shear tests for saturated soils are designed for three
types of drainage conditions.
 The choice of a particular type of drainage condition
depends upon the field conditions.
 The drainage conditions are generally designated by
two letter symbol.
 The first letter refers to what happens before shear
(i.e., whether the sample is consolidated) and
second letter refers to the drainage conditions during
shear.
75

76. TYPES OF TRIAXIAL TEST
TYPE OF TEST SYMBOL ALSO KNOWN AS
Unconsolidated
Undrained
UU Quick test
Consolidated
Undrained
CU ---
Consolidated
Drained
CD Slow test
76

77. UNCONSOLIDATED UNDRAINED TEST
(UU TEST)
77
 In this test, drainage is prevented throughout the
test. For this, valve A is closed and valve B is kept
open.
 The pressure gauge measures the pore water
pressure developed and since drainage is not
allowed, there is no volume change in the specimen.
This is a quick test.

78. CONSOLIDATED UNDRAINED TEST
(CU TEST)
78
 During the first stage (application of cell pressure),
drainage is allowed and hence the soil specimen is
consolidated under the applied cell pressure.
 But during the second stage (application of deviator
stress), the drainage is prevented.
 Accordingly, the appropriate valve is opened and
volume change is measured during consolidation
and pore water pressure is measured in the second
stage of the test.

79. CONSOLIDATED DRAINED TEST
(CD TEST)
79
 In this test, drainage is permitted throughout the test.
 For this, valve A is kept open and valve B is closed.
 The change in water level in the burette indicates the
change in volume of the soil.
 This is a slow test.

80. MOHR CIRCLE DURING APPLICATION
OF CELL PRESSURE
80

81. MOHR CIRCLE DURING APPLICATION
OF DEVIATOR STRESS
81

82. MOHR CIRCLE AT INCIPIENT
FAILURE
82

83. MOHR CIRCLES FOR TOTAL
PRINCIPAL STRESSES
83

84. MOHR CIRCLES FOR EFFECTIVE
PRINCIPAL STRESSES
84

85. ADVANTAGES
 The soil samples are subjected to uniform stresses
and strains.
 Different combinations of confining and axial
stresses can be applied.
 Complete control over drainage conditions.
 The stresses induced on any plane and at any stage
of the test can be determined.
 Pore water pressures and volumetric changes can
be measured directly.
 Stress distribution on failure plane is uniform and the
specimen fails on the weakest plane.
 The complete stress-strain behaviour can be
determined
85

86. LIMITATIONS
 The apparatus is elaborate, costly and bulky.
 The drained test takes a longer period of time than
other tests.
 The test suffers from end restraint.
86

87. SKEMPTON’S PORE PRESSURE
PARAMETERS
87
 The change in pore pressure due to change in the
applied stress, during an undrained shear is
explained in terms of empirical coefficients called the
pore pressure parameters.
 A pore pressure parameter may be defined as a
dimensionless number that indicates the fraction of
total stress increment that show up an excess pore
pressure.
 Considering a soil mass subjected to major and
minor principal stresses, Δσ1 and Δσ3 with an
increase in pore pressure of Δu.
 The empirical coefficients ‘A’ and ‘B’ are called the
Skempton’s pore pressure parameters.

88. SKEMPTON’S PORE PRESSURE
PARAMETERS
88
 Δu = B[Δσ3+A(Δσ1- Δσ3)] where Δu = Δu1+ Δu2
 Hence comparing equations
 B = (Δu1/ Δσ3) and Δu2 = AB (Δσ1- Δσ3) = ̄A (Δσ1- Δσ3)
Where A = ̄A/B
Therefore, A = (Δu- Δσ3)/(Δσ1- Δσ3)

89. VANE SHEAR TEST
 Vane shear test is a quick test used to determine the
insitu undrained shear strength of soft and sensitive
clays which are difficult to sample.
 The test can conducted in laboratory and in the field at
the bottom of the borehole.
 A vane shear test equipment consists of a four bladed
vane.
 The height of the vane is usually twice its diameter. The
vane is welded orthogonally to a steel rod.
89

90. VANE SHEAR TEST
90
 A boring is made to the depth at which the test is to
be performed and the vane is inserted at the bottom
of the boring.
 After inserting the vane in the ground it is slowly
rotated (usually 0.1° per second).
 The torque is applied until the soil fails in shear, then
the undrained shear strength is computed from this
torque.

91. 91

92. 92
 Let H = Height of the vane
D = Diameter of the vane
 Assuming that the shear resistance Su is constant
over the cylinder of soil sheared by vane.
 Maximum resistance offered to shearing along the
cylindrical surface = (πDH)Su ………………(i)

93. 93
Cont.....

94. MERITS
 This test is simple and quick.
 It is ideally suited for determination of in-situ
undrained shear strength of non-fissured, fully
saturated clay.
 The test can be conveniently used to determine the
sensitivity of the soil.
94

95. DEMERITS
 The test cannot be conducted on fissured clay or
clay containing sand or silt laminations.
 The test does not give accurate results when the
failure envelope is not horizontal.
95

96. 96
NUMERICAL PROBLEMS

97. EXAMPLE 1:
97
PROBLEMS

98. EXAMPLE 2 :
A soil sample in a triaxial test is subjected to a major and minor principal stress of
300kPa
And 100kPa respectively. Draw the Mohr circle of stresses and determine the
state of stresses on a plane inclined to 350 with the major principal plane.
Solution For normal stress and shear stress, same scale should be selected
To draw Mohr circle, first the centre of circle is located
σcentre = (100 + 300)/2 = 200
Radius of circle = (300-100)/2 = 200
98

99. EXAMPLE 3:
Hence deviator stress Δσ = 252kPa
99

100. EXAMPLE 4:
A sample of cohesionless sand in a direct shear test fails under a shear stress of
160kPa when the normal stress was 240 kPa. Find the angle of shearing
resistance of the sand. Find the principal stresses and locate the principal planes.
Solution Mark point P with coordinates of (240, 160) on the shear stress-normal
stress plot.
100

101. 101

102. EXAMPLE 5:
102

103. 103

104. EXAMPLE 6:
Two identical specimens of a soil are tested in a triaxial apparatus. The first
specimen failed at a deviator stress of 770 kPa when the cell pressure was 200
kPa, while the second specimen failed at a deviator stress of 1370 kPa under a
cell pressure of 400 kPa. Determine the shear strength parameters. Also, find the
deviator stress at failure when the cell pressure was 600 kPa. If the same soil is
tested in a direct shear apparatus, estimate the shear stress at which the sample
will fail under a normal stress of 600 kPa.
104

105. 105

106. Graphical Method :
106

107. EXAMPLE 7:
107

108. Graphical method :
With σ3 = 100 and 45+ø/2 = 550, Mohr circle is drawn. Diameter of
Mohr circle gives the deviator stress.
108

109. EXAMPLE 8:
109

110. 110
Graphical Method:

111. EXAMPLE 9:
111

112. EXAMPLE 10:
112

113. EXAMPLE 11:
113

114. TEXT BOOKS
114
 P.C. Varghese, ‘Foundation Engineering’, Prentice
Hall of India Pvt. Ltd.
 Shashi K. Gulhati and Manoj Datta, ‘Geotechnical
Engineering’, Mc.Graw Hill Company.
 M.J. Smith, ‘Soil Mechanics’, fourth edition, ELBS
Publishers.
 R.F. Craig, ‘Soil Mechanics’, ELBS Publishers.
 C. Venkatramaiah, ‘Geotechnical Engineering’, New
Age International Publishers.
 A.V. Narasimha Rao and C. Venkatramaiah,
‘Geotechnical Engineering’, University Press (India)
Ltd.

115. TEXT BOOKS
115
 Braja M. Das, ‘Geotechnical Engineering’, Cengage
Learning India Pvt. Ltd., New Delhi.
 Iqbal H. Khan, ‘Geotechnical Engineering’, PHI
Learning Pvt. Ltd., New Delhi.
 V.N.S Murthy, ‘Principles of Soil Mechanics and
Foundation Engineering’, UBS Publishers and
distributors Ltd.
 Gopal Ranjan and Rao, ‘Basic and Applied Soil
Mechanics’, New Age International Publishers.
 Hasmukh Oza and Gautam Oza, ‘Soil Mechanics
and Floundation Engineering’,Charotar Publishing
House Pvt.Ltd.

116. THANK YOU
116