SHEAR STRENGTH OF SOILS INTRODUCTION MOHR’S STRENGTH THEORY MOHR COLOUMBS THEORY MODIFIED MOHR COLOUMB’S THEORY

1. SOIL MECHANICS
SHEAR STRENGTH OF SOILS

2. -: CREATED BY :-
 ALAY MEHTA 141080106011
 SHIVANI PATEL 141080106021
 KAVIN RAVAL 141080106026
 KUNTAL SONI 141080106028
-:CONTENT:-
 INTRODUCTION
 MOHR’S STRENGTH THEORY
 MOHR COLOUMBS THEORY
 MODIFIED MOHR COLOUMB’S
THEORY

3. INTRODUCTION
 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.
 Due to interlocking, particulate material may expand or contract in
volume as it is subject to shear strains.
 If soil expands its volume, the density of particles will decrease and
the strength will decrease; in this case, the peak strength would be
followed by a reduction of shear stress.
 The stress-strain relationship levels off when the material stops
expanding or contracting, and when antiparticle bonds are broken.
 The theoretical state at which the shear stress and density remain
constant while the shear strain increases may be called the critical
state, steady state, or residual strength.

4. MOHR’S STRENGTH THEORY
 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 a soil is a function of the stresses
applied to it as well as the manner in which these
stresses are applied. A knowledge 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.

5. MOHR’S STRENGTH THEORY
 Mohr Circle of Stresses
In soil testing, cylindrical
samples are commonly used in
which radial and axial stresses
act on principal planes.
 The vertical plane is usually
the minor principal plane
whereas the horizontal plane
is the major principal plane.
 The radial stress (sr) is the
minor principal stress (s3),
and the axial stress (sa) is the
major principal stress (s1).

6. MOHR’S STRENGTH THEORY
 To visualize the normal and
shear stresses acting on any
plane within the soil
sample, a graphical
representation of stresses
called the Mohr circle is
obtained by plotting the
principal stresses.
 The sign convention in the
construction is to consider
compressive stresses as
positive and angles measured
counter-clockwise also
positive.

7. MOHR’S STRENGTH THEORY
 Draw a line inclined at
angle with the horizontal
through the pole of the
Mohr circle so as to
intersect the circle.
 The coordinates of the
point of intersection are
the normal and shear
stresses acting on the
plane, which is inclined at
angle within the soil
sample.
 Normal stress
 Shear stress

8. MOHR’S STRENGTH THEORY
 The plane inclined at an angle of 45⁰ to the horizontal
has acting on it the maximum shear stress equal to ,
and the normal stress on this plane is equal to .
 The plane with the maximum ratio of shear stress to
normal stress is inclined at an angle of to the
horizontal, where a is the slope of the line tangent to
the Mohr circle and passing through the origin.

9. MOHR COLOUMBS THEORY
 This theory states that a material fails because of a
critical combination of normal stress and shear stress,
and not from their either maximum normal or shear
stress alone.
 Shear failure occurs when the Mohr circle is large enough
to touch the failure envelope.
 Therefore, no failure will occur at the stress states
represented by circle A, but failure will occur at the
stress states represented by circle B.

10. MOHR COLOUMBS THEORY

11. MOHR COLOUMBS THEORY
 Failure Envelope
 The failure envelope for a
saturated soil is obtained by
plotting a line tangent to a series
of Mohr circles representing the
stress state at failure.
 The slope of the line defines the
effective angle of internal friction,
j ’, and its intercept on the
ordinate is called the effective
cohesion, c’.
 The tangent point on the Mohr
circle at failure represents the
stress states on the failure plane.

12. MODIFIED MOHR COLOUMB’S
THEORY
 The Modified Mohr-
Coulomb plasticity
model is particularly
useful to model frictional
materials like sand .
However, many
enhancements have been
provided so that it is
suitable for all kinds of
soil. The main extensions
compared to DIANA's
regular Mohr-Coulomb
model are