Shear Strength of Soil Part 1

By Shreya Laddha|Updated : November 29th, 2021

Through Champion Study Plan for GATE Civil Engineering (CE) 2022, we are providing Shear Strength of Soil study notes and other important materials on every topic of each subject.

These topic-wise study notes are useful for the preparation of various upcoming exams like GATE CivilIESBARCISROSSC-JEState Engineering Services examinations and other important upcoming competitive exams.

The article contains fundamental notes on the "Shear Strength of Soil"  topic of the "Geotechnical Engineering" subject.

Shear Strength of Soil - 1

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 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).

byjusexamprep

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.

byjusexamprep

Draw a line inclined at angle θ 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 θ within the soil sample.

  • Normal stress

byjusexamprep

  • Shear stress

byjusexamprep

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

Mohr-Coulomb Failure Criterion

When the soil sample has failed, the shear stress on the failure plane defines the shear strength of the soil. Thus, it is necessary to identify the failure plane. Is it the plane on which the maximum shear stress acts, or is it the plane where the ratio of shear stress to normal stress is the maximum?

For the present, it can be assumed that a failure plane exists and it is possible to apply principal stresses and measure them in the laboratory by conducting a triaxial test. Then, the Mohr circle of stress at failure for the sample can be drawn using the known values of the principal stresses.

If data from several tests, carried out on different samples upto failure is available, a series of Mohr circles can be plotted. It is convenient to show only the upper half of the Mohr circle. A line tangential to the Mohr circles can be drawn, and is called the Mohr-Coulomb failure envelope.

byjusexamprep

If the stress condition for any other soil sample is represented by a Mohr circle that lies below the failure envelope, every plane within the sample experiences a shear stress which is smaller than the shear strength of the sample. Thus, the point of tangency of the envelope to the Mohr circle at failure gives a clue to the determination of the inclination of the failure plane. The orientation of the failure plane can be finally determined by the pole method.

byjusexamprep

Mohr-Coulomb failure criterion can be written as the equation for the line that represents the failure envelope. The general equation is

byjusexamprep

Where byjusexamprep= shear stress on the failure plane 
c = apparent cohesion 
byjusexamprep = normal stress on the failure plane
= angle of internal friction 

The failure criterion can be expressed in terms of the relationship between the principal stresses. From the geometry of the Mohr circle,

byjusexamprep 
Rearranging, 

byjusexamprep

where byjusexamprep 

Methods of Shear Strength Determination

  1. Direct Shear Test

The test is carried out on a soil sample confined in a metal box of square cross-section which is split horizontally at mid-height. A small clearance is maintained between the two halves of the box.The soil is sheared along a predetermined plane by moving the top half of the box relative to the bottom half. The box is usually square in plan of size 
60 mm x 60 mm. A typical shear box is shown. 

byjusexamprep

If the soil sample is fully or partially saturated, perforated metal plates and porous stones are placed below and above the sample to allow free drainage. If the sample is dry, solid metal plates are used. A load normal to the plane of shearing can be applied to the soil sample through the lid of the box.

Tests on sands and gravels can be performed quickly, and are usually performed dry as it is found that water does not significantly affect the drained strength. For clays, the rate of shearing must be chosen to prevent excess pore pressures building up.

As a vertical normal load is applied to the sample, shear stress is gradually applied horizontally, by causing the two halves of the box to move relative to each other. The shear load is measured together with the corresponding shear displacement. The change of thickness of the sample is also measured.

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.

The test has several advantages:

  • It is easy to test sands and gravels.
  • Large samples can be tested in large shear boxes, as small samples can give misleading results due to imperfections such as fractures and fissures, or may not be truly representative.
  • Samples can be sheared along predetermined planes, when the shear strength along fissures or other selected planes are needed.

The disadvantages of the test include:

  • The failure plane is always horizontal in the test, and this may not be the weakest plane in the sample. Failure of the soil occurs progressively from the edges towards the centre of the sample.
  • There is no provision for measuring pore water pressure in the shear box and so it is not possible to determine effective stresses from undrained tests.
  • The shear box apparatus cannot give reliable undrained strengths because it is impossible to prevent localised drainage away from the shear plane. 

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