SOIL MECHANICS

SHEAR STRENGTH OF SOILS

-: 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

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.

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.

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).

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.

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 

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. 

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.

MOHR COLOUMBS THEORY

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.

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