Shear strength of soil may be defined as the resistance to shearing stresses and a consequent tendency for shear deformation. Soil derives its shearing strength from the following

- Resistance due to interlocking of particles
- Frictional resistance between the individual soil grains
- Adhesion between soil particles or cohesion

**Principal Planes and Principal Stresses of Soil**

At a point in a stressed material, every plane will be subjected to a normal or direct stress and a shearing stress. A principal plane is defined as a plane on which the stress is fully normal or one which does not carry shearing stress.

The normal stress acting on this principal planes are known as principal stresses. There exist three principal planes at any point in a stressed material. These three principal planes are mutually perpendicular.

In the order of decreasing magnitude the principal planes are designated as major principal plane, minor principal plane and intermediate principal plane and the corresponding principal stresses are designated in the same manner.

From this figure,

These equations will give the stresses on the inclined plane making an angle with the major principal plane.

**Mohr’s Circle of Stress for Soils**

Otto Mohr, a German scientist devised a graphical method for the determination of stresses on a plane inclined to the major principal planes. The graphical construction is known as Mohr’s circle. In this method, the origin O is selected and the normal stresses are plotted along the horizontal axis and the shear stresses on the vertical axis.

To construct a Mohr circle, first mark major and minor principal stress on X axis, Mark the centre point of that as C. A circle is drawn with c as centre and CF as radius. Each point on the circle gives the stresses ? and ? on a particular plane. The point E is known as the pole of the circle.

- Mohr’s circle can be drawn for stress system with principal planes inclined to co-ordinate axes
- Stress system with vertical and horizontal planes are not the principal planes

**Mohr-Coulomb Theory **

The soil is a particulate material. The shear failure in soils is by slippage of particles due to shear stresses. According to Mohr, the failure is caused by a critical combination of normal and shear stresses. The soil fails when the shear stress on the failure plane at failure is a unique function of the normal stress acting on that plane.

Since the shear stress of the failure plane is defined as the shear strength (s) the equation for that can be written as

S= f ()

The Mohr theory is concerned with the shear stress at failure plane at failure. A plot can be made between the shear stresses and the normal stress at failure. The curve defined by this is known as the failure envelope.

The shear strength of a soil at a point on a particular plane was expressed by Coulomb as a linear function of the normal stress on that plane as,

In this C is equal to the intercept on Y axis and phi is the angle which the envelope make with X axis

**Different Types of Shear Tests and Drainage Conditions**

The following tests are used to measure the shear strength of the soil

- Direct shear test
- Triaxial compression test
- Unconfined compression test
- Vane shear test

Depending upon the drainage conditions, there are three types of tests

- Unconsolidated-Undrained condition
- Consolidated – Undrained condition
- Consolidated-Drained condition

**Direct Shear Test on Soil**

**Apparatus**

The test is conducted in a soil specimen in a shear box which is split into two halves along the horizontal plane at its middle. The size of the shear box is 60 x 60 x 50 mm. the box is divided horizontally such that the dividing plane passes through the centre.

The two halves are held together by locking pins the box is also provided with gripper plates plain or perforated according to the testing conditions

**Test**

A soil specimen of size 60 x 60 x 25 mm is taken. It is placed in the direct shear box and compacted. The upper grid plate, porous stone and pressure pad is placed on the specimen. Normal load and shear load is be applied till failure

**Presentation of results**

- Stress – strain curve
- Failure envelope
- Mohr’s circle

**Merits**

- the sample preparation is easy
- as the thickness of the sample is very less, the drainage is quick
- it is ideally suited for conducting drained tests on cohesionless soils
- the apparatus is relatively cheap

**Demerits**

- the stress conditions are known only at failure
- the stress distribution on the failure plane is not uniform
- the area of shear gradually decreases as the test progresses
- the orientation of the failure plane is fixed
- control of drainage conditions is very difficult
- measurement of pore water pressure is not possible

** Triaxial Compression Test**

It is used for the determination of shear characteristics of all types of soils under different drainage conditions. In this a cylindrical specimen is stressed under conditions of axial symmetry. In the first stage of the test, the specimen is subjected to an all round confining pressure on the sides, top and bottom.

This stage is known as the consolidation stage. In the second stage of the test called shearing stage, an additional axial stress and deviator stress is applied on the top of the specimen through a ram. Thus the total stress in the axial direction at the time of shearing is equal to the confining stress plus the deviator stress.

The vertical sides of the specimen are principal planes. The confining pressure is the minor principal stress. The sum of the confining stress and deviator stress is the major principal stress. Triaxial apparatus consists of a circular base with a central pedestal. The specimen is placed on the pedestal.

The pedestal has one or two holes which are used in the drainage function or pore pressure measurement. A triaxial cell is placed to the base plate. It is a Perspex cylinder. There are three tie rods which support the cell. A central ram is there for applying axial stress. An air release valve and an oil release valve are attached to the cell.

The apparatus also have special features like,

- Mercury control system
- Pore water pressure measurement device
- Volume changes measurement

**Triaxial test on cohesive soil**

CU, UU and CD tests can be conducted on soil specimen. The specimen is placed in the pedestal inside a rubber membrane. The confining pressure and axial pressure is applied till failure.

**Triaxial test on cohesionless soil**

The procedure is same as that in the cohesive soil only the sample preparation is different. A metal former, a membrane and a funnel are used for the sample preparation.

**Merits**

- There is complete control over the drainage conditions
- Pore pressure changes and volumetric changes can be measured directly
- The stress distribution in the failure plane is uniform
- The specimen is free to fail on the weakest plane
- The state of stress at all intermediate stages up to failure is known
- The test is suitable for accurate research work

**Demerits**

- The apparatus is elaborate, costly and bulky
- The drained test takes a longer period as compared with that in a direct shear test
- The strain condition in the specimen are not uniform
- It is not possible to find out the cross sectional area of the specimen accurately under large strains
- The test simulates only axi symmetric problems
- The consolidation of the specimen in the test is isotropic whereas in the field, consolidation is generally anisotropic.

**Computation of various parameters**

Post consolidation dimensions

Cross sectional area during shearing stage

**Stresses**

Deviator stress=P/A

Principal stresses

**Compressive strength**

The deviator stress at failure is known as the compressive strength of soil

**Presentation of results of triaxial test**

- Stress-strain curves
- Mohr envelopes in terms of total stress and effective stress

**Unconfined Compression Test on Soil**

The unconfined compression test is a special form of triaxial test in which the confining pressure is zero. The test can be conducted only on clayey soils which can stand without confinement. There are two types of UCC machines machine with a spring and machine with a proving ring

A compressive force is applied to the specimen till failure. The compressive load can be measured using a proving ring..

**Presentation of results**

In this test the minor principal stress is zero. The major principal stress is equal to the deviator stress. The Mohr circle can be drawn for stress conditions at failure.

**Merits**

- The test is convenient, simple and quick
- It is ideally suited for measuring the unconsolidated undrained shear strength of intact saturated clays
- The sensitivity of the soil can be easily determined

**Demerits**

- The test cannot be conducted on fissured clays
- The test may be misleading for soils of which the angle of shearing resistance is not zero.

**Vane Shear Test**

The undrained strength of soft clays can be determined in a laboratory by vane shear test. The test can also be conducted in the field on the soil at the bottom of bore hole. The apparatus consists of a vertical steel rod having four thin stainless steel blades or vanes fixed at its bottom end.

Height of the vane should be equal to twice the diameter. For conducting test in a laboratory, a specimen of diameter 38mm and height 75mm is prepared and fixed to the base of the apparatus.

The vane is slowly lowered into the specimen till the top of the vane is at a depth of 10 to 20 mm below the top of the specimen. The readings of the strain indicator and torque indicator are taken

Shear strength S

Where T =Torque applied

D = Diameter of vane

H_{1}= Height of vane

**Merits**

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

**Demerits**

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