Detailed content on shear strength of soils, principles of effective stresses, tests conducted to determine the shear strength of soils and its applications, dilatancy, thixotropy and sensitivity.

1. SHEAR STRENGTH OF SOILS

2. CONTENTS
• Shear strength of soils
• Stress condition at a point in a soil mass
• Relationship between principal stresses and cohesion
• Mohr circle of stresses
• Mohr coulumb failure theory
• Effective stresses
• Factors effecting shear strength of soils
• Tests on soil
1. Direct shear
2. Triaxial test
3. Unconfined compressive strength
4. Vane shear test
• Shear strength characteristics of sands
• Critical Void ratio
• Sensitivity and thixotrophy of cohesive soils

3. SHEAR STRENGTH OF SOILS:
• Soils consist of individual particles that can slide and roll
relative to one another.
• Shear strength of a soil is equal to the maximum value of
shear stress that can be mobilized within a soil mass without
failure taking place.
• The shear strength of soil is a function of stresses applied to
it as well as the manner in which these stresses are applied.
• Acknowledge of shear strength of soils is necessary to
determine the bearing capacity of foundations, the lateral
pressure exerted on retaining walls and the stability of
slopes.

4. STRESS CONDITION AT A POINT IN A SOIL MASS
• Through every point in a stressed body there are three planes at right angles
to each other which are unique as compared to all the other planes passing
through the point, because they are subjected only to normal stresses with no
accompanying shearing stresses acting on the planes.
• These three planes are called principal planes, and the normal stresses
acting on these planes are principal stresses.
• Ordinarily the three principal stresses at a point differ in magnitude. They
may be designated as the major principal stress the intermediate
principal stress , and the minor principal stress
• Principal stresses at a point in a stressed body are important because, once
they are evaluated, the stresses on any other plane through the point can be
determined. Many problems in foundation engineering can be approximated
by considering only two-dimensional stress conditions.
• The influence of the intermediate principal stress on failure may be
considered as not very significant.

5. A Two-Dimensional Demonstration of the Existence of
Principal Planes:
• Consider the body (Fig. 8.6(a)) is subjected to a system of
forces such as F1,F2,F3 and F4 whose magnitudes and lines
of action are known.

8. RELATIONSHIP BETWEEN THE PRINCIPAL STRESSES
AND COHESION c
If the shearing resistance s of a soil depends on both friction and
cohesion, sliding failure occurs in accordance with the Coulomb Eq.
(8.3), that is, when

10. MOHR CIRCLE OF STRESS

12. MOHR-COULOMB FAILURE THEORY
• Various theories relating to the stress condition in engineering
materials at the time of failure are available in the engineering
literature.
• Each of these theories may explain satisfactorily the actions of
certain kinds of materials at the time they fail, but no one of them
is applicable to all materials.
• The failure of a soil mass is more nearly in accordance with the
tenets of the Mohr theory of failure than with those of any other
theory and the interpretation of the triaxial compression test
depends to a large extent on this fact.
• The Mohr theory is based on the postulate that a material will fail
when the shearing stress on the plane along which the failure is
presumed to occur is a unique function of the normal stress acting
on that plane.
• The material fails along the plane only when the angle between
the resultant of the shearing stress and the normal stress is a
maximum, that is, where the combination of normal and shearing
stresses produces the maximum obliquity angle .

13. According to Coulomb's Law, the condition of failure is that
the shear stress

14. • In Fig 8.1 l(b) MoN and MoN1 are the lines that satisfy
Coulomb's condition of failure.
• If the stress at a given point within a cylindrical specimen
under triaxial compression is represented by Mohr circle 1,
it may be noted that every plane through this point has a
shearing stress which is smaller than the shearing strength.
• For example, if the plane AA in Fig. 8.1 l(a) is the assumed
failure plane, the normal and shear stresses on this plane at
any intermediate stage of loading are represented by point b
on Mohr circle1 where the line Pob is parallel to the plane
AA
• The shearing stress on this plane is ab which is less than the
shearing strength ac at the same normal stress Oa.

15. • Under this stress condition there is no possibility of failure.
On the other hand it would not be possible to apply the
stress condition represented by Mohr stress circle 2 to this
sample because it is not possible for shearing stresses to be
greater than the shearing strength.
• At the normal stress Of, the shearing stress on plane AA is
shown to be fh which is greater than the shear strength of the
materials fg which is not possible.
• Mohr circle 3 in the figure is tangent to the shear strength
line MoN and MoN1 at points e and e respectively.
• On the same plane AA at normal stress Od, the shearing
stress de is the same as the shearing strength de. Failure is
therefore imminent on plane AA at the normal stress Od and
shearing stress de.

16. • The equation for the shearing stress de is
• where 0 is the slope of the line MQN which is the
maximum angle of obliquity on the failure plane.
• The value of the obliquity angle can never exceed <5m
= 0, the angle of shearing resistance, without the
occurrence of failure.
• The shear strength line MQN which is tangent to Mohr
circle 3 is called the Mohr envelope or line of rupture.
• The Mohr envelope may be assumed as a straight line
although it is curved under certain conditions. The
Mohr circle which is tangential to the shear strength line
is called the Mohr circle of rupture.

17. • Thus the Mohr envelope constitutes a shear diagram and is a
graph of the Coulomb equation for shearing stress. This is
called the Mohr-Coulomb Failure Theory.
• The principal objective of a triaxial compression test is to
establish the Mohr envelope for the soil being tested.
• The cohesion and the angle of shearing resistance can be
determined from this envelope.
• When the cohesion of the soil is zero, that is, when the soil
is cohesionless, the Mohr envelope passes through the
origin.

18. EFFECTIVE STRESSES
• So far, the discussion has been based on consideration of
total stresses. It is to be noted that the strength and
deformation characteristics of a soil can be understood
better by visualizing it as a compressible skeleton of solid
particles enclosing voids.
• The voids may completely be filled with water or partly
with water and air. Shear stresses are to be carried only by
the skeleton of solid particles. However, the total normal
stresses on any plane are, in general, the sum of two
components.
Total normal stress = component of stress carried by solid
particles + pressure in the fluid in the void space.

19. This visualization of the distribution of stresses between solid
and fluid has two important consequences:
When a specimen of soil is subjected to external pressure, the
volume change of the specimen is not due to the total normal
stress but due to the difference between the total normal stress
and the pressure of the fluid in the void space.
• The pressure in the fluid is the pore pressure u.
• The difference which is called the effective stress d may now
be expressed as
The shear strength of soils, as of all granular materials, is largely
determined by the frictional forces arising during slip at the
contacts between the soil particles.
• These are clearly a function of the component of normal stress
carried by the solid skeleton rather than of the total normal
stress.
• For practical purposes the shear strength equation of Coulomb
is given by the expression

20. • The effective stress parameters c' and 0' of a given sample of
soil may be determined
provided the pore pressure u developed during the shear
test is measured.
• The pore pressure u is developed when the testing of the soil
is done under undrained conditions.
• However, if free drainage takes place during testing, there
will not be any development of pore pressure.
• In such cases, the total stresses themselves are effective
stresses.

21. Factors Effecting shear strength of soils
soil composition (basic soil material):
• mineralogy, grain size and grain size distribution,
shape of particles, pore fluid type and content, ions
on grain and in pore fluid.
state (initial):
• Defined by the initial void ratio, effective normal
stress and shear stress (stress history).
• State can be described by terms such as: loose,
dense, overconsolidated, normally consolidated,
stiff, soft, contractive, dilative, etc.

22. structure:
• Refers to the arrangement of particles within the soil
mass
• the manner the particles are packed or distributed.
Features such as layers, joints, fissures, slickensides,
voids, pockets, cementation, etc., are part of the
structure.
• Structure of soils is described by terms such as:
undisturbed, disturbed, remolded, compacted,
cemented; flocculent, honey-combed, single-grained;
flocculated, deflocculated; stratified, layered,
laminated; isotropic and anisotropic.
Loading conditions: Effective stress path, i.e., drained,
and undrained; and type of loading, i.e., magnitude, rate
(static, dynamic), and time history (monotonic, cyclic)

23. TESTS ON SOIL

24. DIRECT SHEAR STRENGTH

46. TRI-AXIAL

76. UNCONFINED COMPRESSIVE STRENGTH

79. • The unconfined compression test is a special case of a
triaxial compression test in which the allround pressure = 0
• The tests are carried out only on saturated samples which
can stand without any lateral support
• The test, is, therefore, applicable to cohesive soils only.
• The test is an undrained test and is based on the assumption
that there is no moisture loss during the test.
• The unconfined compression test is one of the simplest and
quickest tests used for the determination of the shear
strength of cohesive soils.
• These tests can also be performed in the field by making use
of simple loading equipment.
• Any compression testing apparatus with arrangement for
strain control may be used for testing the samples . The
axial load may be applied mechanically or pneumatically.

80. • Specimens of height to diameter ratio of 2 are normally
used for the tests.
• The sample fails either by shearing on an inclined plane (if
the soil is of brittle type) or by bulging. The vertical stress at
any stage of loading is obtained by dividing the total
vertical load by the cross-sectional area.
• The cross-sectional area of the sample increases with the
increase in compression.
• The cross-sectional area A at any stage of loading of the
sample may be computed on the basic assumption that the
total volume of the sample remains the same. That is

82. • The unconfined compression test (UC) is a special case of
the unconsolidated-undrained (UU) triaxial compression test
(TX-AC).
• The only difference between the UC test and UU test is
that a total confining pressure under which no drainage
was permitted was applied in the latter test.
• Because of the absence of any confining pressure in the UC
test, a premature failure through a weak zone may terminate
an unconfined compression test.
• For typical soft clays, premature failure is not likely to
decrease the undrained shear strength by more than 5%. Fig
8.23 shows a comparison of undrained shear strength values
from unconfined compression tests and from triaxial
compression tests on soft-Natsushima clay from Tokyo Bay.

83. • The properties of the soil are:
• There is a unique relationship between remolded undrained shear strength
and the liquidity index,as shown in Fig. 8.24 (after Terzaghi et al., 1996).
• This plot includes soft clay soil and silt deposits obtained from different parts
of the world.

89. VANE SHEAR TESTS
• From experience it has been found that the vane test can
be used as a reliable in-situ test for determining the
shear strength of soft-sensitive clays.
• It is in deep beds of such material that the vane test is
most valuable, for the simple reason that there is at
present no other method known by which the shear
strength of these clays can be measured.
• Repeated attempts, particularly in Sweden, have failed
to obtain undisturbed samples from depths of more than
about 10 meters in normally consolidated clays of high
sensitivity even using the most modern form of thin-
walled piston samplers.
• In these soils the vane is indispensable.

90. • The vane should be regarded as a method to be used under
the following conditions:
1. The clay is normally consolidated and sensitive.
2. Only the undrained shear strength is required.
• It has been determined that the vane gives results similar to
those obtained from unconfined compression tests on
undisturbed samples.
• The soil mass should be in a saturated condition if the vane
test is to be applied.
• The vane test cannot be applied to partially saturated soils to
which the angle of shearing resistance is not zero.

91. Description of the Vane
• The vane consists of a steel rod having at one end four small
projecting blades or vanes parallel to its axis, and situated at
90° intervals around the rod.
• A post hole borer is first employed to bore a hole up to a
point just above the required depth.
• The rod is pushed or driven carefully until the vanes are
embedded at the required depth.
• At the other end of the rod above the surface of the ground
a torsion head is used to apply a horizontal torque and this is
applied at a uniform speed of about 0.1° per sec until the
soil fails, thus generating a cylinder of soil.

92. • The area consists of the peripheral surface of the cylinder
and the two round ends.
• The first moment of these areas divided by the applied
moment gives the unit shear value of the soil. Fig. 8.32(a)
gives a diagrammatic sketch of a field vane.
Determination of Cohesion or Shear Strength of Soil
• Consider the cylinder of soil generated by the blades of the
vane when they are inserted into the undisturbed soil in-situ
and gradually turned or rotated about the axis of the shaft or
vane axis.
• The turning moment applied at the torsion head above the
ground is equal to the force multiplied by the eccentricity.

95. Shear Strength Characteristics of Sand
Shear strength characteristics of sandy soils depend on the
drainage conditions in addition to several other parameters as
discussed in the following subsections.
1. Shear Strength Characteristics of Saturated Sands
during Drained Shear:
• It is nearly impossible to test undisturbed samples of
cohesionless soils in either the direct shear or the triaxial
compression test.
• Only the remolded samples are, therefore, used and the
samples are to be compacted approximately to the in situ
density.
• The direct shear test, being simpler and more rapid, is most
commonly used.

96. • The shear strength characteristics of dry and saturated sands
are the same, provided the excess pore pressure is zero for
saturated sands during the test.
• Hence, to conduct drained tests, dry sands are commonly
used, as it is somewhat more difficult to test saturated sands.
• Typical curves relating principal stress difference and axial
strain for dense and loose sand specimens in drained triaxial
compression tests are shown in Fig. 13.25.
• Similar curves are obtained relating shear stress and shear
displacement in direct shear tests. For dense sand, the
deviator stress increases with increase in axial strain until a
maximum deviator stress is reached.

97. • After reaching the peak stress, the deviator stress decreases
with further increase in the strain.
• For loose sand, there is no peak stress and the deviator
stress increases continually with increase in axial strain.
• However, the rate of increase of stress per unit strain
(modulus) for loose sand is less than that of dense sand.
• The ultimate deviator stress is approximately the same for
both dense sand and loose sand.

99. • Figure 13.26 shows the volumetric strain as a function of
axial strain for dense sand and loose sand.
• The volume of soil specimen decreases with increase in
axial strain for loose sand. In case of dense sand, the
volumetric strain initially decreases with increase of axial
strain until the sample attains some minimum volume.
• The volume then increases with further increase of axial
strain.

100. • In a properly carried out drained triaxial test, a common
tangent can be drawn for all the Mohr’s circles of stress as
shown in Fig. 13.27.
• The failure plane for each of the samples makes an angle a
with the horizontal as shown, which is approximately given
by

101. In AOCD of Fig. 13.27, alternate expression for ɸ in terms of
the principal stress ratio may be written as
• The shear strength of sands is derived basically from sliding
friction between soil grains.
• In addition to the frictional component, the shear strength of
dense sand has another component which is influenced by
arrangement of soil particles.
• The soil grains are highly irregular in shape and have to be
lifted over one another for sliding to occur.
• This effect is known as interlocking.

102. • In dense sand, there is a considerable degree of interlocking
between particles and this interlocking must be overcome
before shear failure can take place.
• This is in addition to the frictional resistance due to sliding
between particles.
• The characteristic stress-strain curve for dense sand shows a
peak stress at a relatively low strain and thereafter as the
interlocking is overcome, the stress necessary for additional
strain decreases rapidly and becomes constant with
increasing strain
• The degree of interlocking will be greatest in the case of
very dense, well-graded sands consisting of angular
particles.

103. • As strain increases beyond the peak point on the stress-
strain diagram, the interlocking stress is overcome.
• The ultimate shear strength (principal stress difference in
the case of a triaxial test) and void ratio for dense and loose
sand specimens are essentially equal under the same all-
round pressure as indicated in Fig. 13.25.
• Thus, at the ultimate state, shearing takes place at constant
volume, the corresponding friction angle being denoted as
ɸCV‘.
• The reduction in the degree of interlocking produces an
increase in volume of the specimen during shearing as
shown in Fig. 13.26, by the relationship between the
volumetric strain and axial strain.

104. • In the case of loose sand, there is no significant particle
interlocking to be overcome, because of lesser particle
interference, and the principal stress difference increases
gradually to an ultimate value without a prior peak.
• Thus, the shear strength of loose sands is essentially due to
sliding friction between soil particles.
• It is a function of effective normal stress at the point of
contact and increases linearly with the same.
• The failure of loose sands at large strains may be described
as progressive failure compared to the relatively sudden
failure of dense sands at low strains.

105. • Only the drained strength of sand is normally relevant in
practice and typical values of the friction angle for loose
sands and dense sands are given in Table 13.3.
• In the case of dense sands, peak value of in-plane strain can
be 4° or 5° higher than the corresponding value obtained by
conventional triaxial tests.
• This increase is negligible in the case of loose sands.
2. Effect of Void Ratio and Confining Pressure on Volume
Change:
• The initial void ratio of the soil specimen has a significant
effect on the volume change during shear.
• Loose sands, having high initial void ratio, tend to decrease
in volume, since they do not have any interlocking effect
and permit closer particle movement during shear.

106. • Dense sands with low initial void ratio have high degree of
interlocking, which when overcome, produce an increase in
the volume of the specimen during shear.
• The effect of confining pressure is to increase the density of
the soil specimen and hence reduce the void ratio.
• Dense sand under low confining pressure behaves similar to
loose sand under high confining pressure.
3. Characteristics of Saturated Sands during Undrained
Shear:
• There is no advantage in using undrained test on
cohesionless soils, since they tend to drain very fast in situ
in most cases, as the permeability is high and the loads are
applied relatively gradually.

107. • A consolidated quick test on samples of sand may be
performed in a triaxial compression apparatus, since the box
shear apparatus is not suitable for this purpose.
• A sample of sand completely saturated is consolidated under
an all-round pressure at a known initial void ratio.
• The sample is then sheared by keeping the drainage valve
open and applying the deviator stress at a slow rate.
• Typical Mohr’s circles of stress of samples subjected to c-q
test are shown in Fig. 13.28.
• The Mohr’s failure envelope is curved at low pressure and
approaches a straight line with a slope angle of ɸcq.
• Pore pressures are usually measured and the effective
Mohr’s stress circles are drawn as shown by dashed lines.
• A straight Mohr-Coulomb failure envelope is obtained with a
slope angle of ɸ’cq.

109. Critical void ratio
• Casagrande (1936) performed drained, strain-controlled
triaxial tests on initially loose and initially dense sand
specimens.
• The results (figure 6.5) which form the cornerstone of modern
understanding of soil strength behavior showed that all
specimens tested at the same effective confining pressure
approached the same density when sheared to large strains.
• Initially loose specimens contracted, or densified, during
shearing and initially dense specimens first contracted, but
then very quickly began to dilate.
• At large strains, all specimens approached the same density
and continued to shear with constant shearing resistance.
• The void ratio corresponding to this constant density was
termed the critical void ratio

110. • By performing tests at different effective confining pressures,
Casagrande found that the critical void ratio was uniquely
related to the effective confining pressure, and called the locus
the critical void ratio (CVR) line (figure 6.9) by defining the
state of the soil in terms of void ratio and effective confining
pressure the CVR line could be used to mark the boundary
between loose (contractive) and dense (dilative) states.
Figure 6.5 (a) Stress-strain and (b) stress-void curves for loose
and dense sands at the same effective confining pressure.

111. • Loose sand exhibits contractive behavior (decreasing void ratio)
and dense sand exhibit dilative behavior (increasing void ratio)
during shearing. by the time large strains have developed both
specimens have reached the critical void ratio and mobilize the
same large strain shearing.
Sensitivity of cohesive soils:
• Cohesive soils upon remoulding, lose a part of shear strength.
• The loss of strength of clay soils from remoulding is caused
primarily by the destruction of the clay particle structure that
was developed during the original process of sedimentation and
also disturbance to water molecules in adsorbed layer.
• Sensitivity is the measure of loss of strength with remoulding.
Sensitivity, St is defined as the ratio of unconfined compressive
strength of clay in undisturbed state to unconfined compressive
strength of a same clay in remoulded state at unaltered water
content.

112. Clays are classified according to their sensitivity values
as shown in Table

113. • Highly over consolidated clays are classified as insensitive.
St is mostly 1 or >1, but for fissured clays St <1 because
drawback in undisturbed soil is rectified in remoulded state.
• The sensitivity of most clays ranges from about 1 to 8;
however, highly flocculent marine clay deposits may have
sensitivity ratios ranging from about 10 to 80. Some clay
turn to viscous liquids upon remoulding, and these clays are
referred to as “quick” clays.
Thixotropy of cohesive soils:
• When clays with flocculent structure lose strength due to
disturbance or remoulding.
• Loss of strength is partly due to permanent destruction of
structure and reorientation of molecules in adsorbed layer.
• Strength loss with destruction of structure can’t recovered
with time.

114. • However, remoulded soil left undisturbed at same water
content, regain part of strength due to gradual reorientation
of adsorbed molecules of water.
• This phenomenon of strength loss-strength gain, with no
change in volume or water content, is called
‘Thixotropy’(from the Greek thix, meaning ‘touch’
and tropein, meaning ‘to change’).
• This may also be said to be “a process of softening caused
by remoulding, followed by a time-dependent return to the
original harder state”.
• Higher the sensitivity, larger thixotropic hardening.
• Extent of strength gain depends on type of the clay mineral.

115. • Mineral that absorb large quantity of water in lattice structure,
such as Montmorillonite has greater thixotropic gain compared
to other stable clay minerals.
• Figure.1. shows the gain in strength of soil due to thixotropic
effect.
• Thixotropy has important applications in connection with pile-
driving operations. The immediate frictional strength of
thixotropic clay in driven piles is less compared to frictional
strength after one month, because strength gain with passage of
time.
Thixotropy of clays

116. THANKYOU
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