# Shearing strength of soils and tests

We can define Shearing strength as the resistance to shearing stresses and a resultant propensity for shear deformation.

Soil takes after its shearing strength from the following factors:

1. resistance because of the interlocking of particles
2. frictional resistance amongst the individual soil grains
3. bond between soil particles or cohesion

The principal planes and principal stresses

At a specific point in a stressed material, each one of the plane will be exposed to a regular or direct stress and additionally, shearing stress as well. We can define the principal plane as a plane on which case the stress is totally regular or normal or at least one which would not carry any extent of shearing stress. The normal stress acting which function on these principal planes are also called principal stresses. There are basically 3 principal planes at any given point in a stressed material. Those three principal planes are equally vertical. On the basis of diminishing magnitude, the principal planes are chosen as major principal plane, minor principal plane and lastly, the intermediate principal plane. Similarly, the corresponding principal stresses are also elected in the same process.

From the figure, we can ascertain

The above mentioned equations will provide the stresses on the sloped plane creating an angle   with the major principal plane.

### MOHR’s Circle

German scientist named Otto Mohr invented a graphical technique for the ascertain of stresses on a plane sloped to the major principal planes. We call the graphical construction as Mohr’s circle. In the following technique, the origin O is chosen and the normal stresses are plotted in succession alongside the flat axis and the shear stresses on the perpendicular axis.

For the construction of Mohr circle, first of all note the major and minor principal stress on X axis, note down the mid point of that as C. After that a circle is illustrated with c as focal point and CF as radius. All of the point on the circle yields the stresses ? and ? on a specific plane. The point E is also called as the pole of the circle.

1. Mohr’s circle could be illustrated for stress system with principal planes sloped to co-ordinate axes
2. Stress system with perpendicular and horizontal planes aren’t the principal planes.

### Mohr-Coulomb Theory

The soil is a particulate substance. The shear failure inside the soils is caused by slippage of particles because of the shear stresses. As per Mohr, the breakdown is instigated by an acute blend of normal and shear stresses. The soil fails when the shear stress on the breakdown plane at breakdown is an exclusive purpose of the normal stress functioning on that plane. Subsequently, the shear stress of the failure plane is also called as the shear strength (s) and the equation for it can be expressed as:

S= f ( )

he Mohr theory is basically related along 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 some given point on a specific plane was illustrated by Coulomb as a linear function of the normal stress on that plane as,

In this case, the C is equivalent to the intercept on Y axis and phi is the angle which the envelope makes with X axis

Different kinds of shear tests and drainage conditions

The following tests are utilized for measurement of the shear strength of the soil

1. Direct shear test
2. Triaxial compression test
3. Unconfined compression test
4. Vane shear test

Based on the drainage conditions, there are three kinds of tests

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

## Direct Shear Test

Apparatus

The test is carried out in a soil sample in a shear box which is divided in to two halves along the parallel plane at its central point. The volume of the shear box has to be60 x 60 x 50 mm. Then the box is cut into half horizontally in such a way that the dividing plane passes through the focal point. Then those two halves are held organized by locking pins the box is also given with gripper plates plain or perforated in accordance to the testing circumstances.

Test

A soil sample of size 60 x 60 x 25 mm is chosen. It is positioned in the direct shear box and compressed. The upper grid plate, porous stone and pressure pad are also positioned on the sample. Normal load and shear load is exerted till breakdown.

Presentation of results

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

Merits

1. The sample preparation is simple
2. Since the density of the sample is minimum, the drainage is rapid
3. It is preferably suitable for showing drained tests on cohesion less soils
4. The apparatus is comparatively inexpensive

Demerits

1. the stress conditions are identified only at failure
2. the stress distribution on the failure plane is of varying nature
3. the portion of shear gradually diminishes as the test progresses
4. the orientation of the failure plane is secure
5. control of drainage conditions is hard
6. measurement of pore water pressure is not feasible

## Triaxial Compression Test

It is basically utilized for the ascertaining of shear properties of all kinds of soils under wide assortment of drainage conditions. In this a cylindrical shaped sample is stressed under the factors of axial symmetry. In the initial step of the test, the sample is exposed to an all-round restraining pressure, on the sides, the crest and the foundation as well. This step is called the consolidation stage. After that, we move on to the second of the test known as shearing stage, an auxiliary axial stress known as deviator stress is exerted on the apex of the sample with the help of a ram. Consequently, the aggregate stress in the axial direction at the time of shearing is equivalent to the confining stress plus the deviator stress. The perpendicular sides of the sample are principal planes. The restraining pressure is the minor principal stress. The aggregate of the confining stress and additionally deviator stress is the major principal stress. Triaxial apparatus comprises of a spherical foundation with a central pedestal. The sample is positioned on the pedestal. The pedestal need to have at least one or two holes which are mainly utilized in the drainage function or pore pressure determination. A triaxial cell is positioned to the base plate. It is a Perspex cylinder. There are three tie rods which back the cell. A central ram is there for exerting axial stress. An air release valve and similarly an oil release valve are connected to the cell. The apparatus also come with different special properties like,

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

Triaxial test on Cohesive soil

CU, UU and CD tests could be carried out on soil sample. The sample is positioned in the pedestal within a rubber membrane. The restraining pressure and axial pressure is exerted till the point of failure.

### Triaxial test on cohesionless soil

The process is similar to that of the cohesive soil and just the specimen groundwork is dissimilar. A metal former, a membrane and a funnel are utilized for the specimen preparation.

Merits

1. There is total regulation over the drainage conditions
2. Pore pressure alters and volumetric alterations could be computed directly
3. The stress distribution in the failure plane is completely even
4. The sample is free to fail on the frailest plane
5. The state of stress at all transitional stages up to failure is identified
6. The test is appropriate for precise research work

Demerits

1. The apparatus is extravagant, expensive and massive
2. The drained test consumes a longer time- period in comparison with that in a straight shear test
3. The strain condition in the sample are not even
4. It is not feasible to ascertain out the cross sectional area of the sample precisely under larger strains
5. The experimentation simulates just the axi symmetric problems
6. The consolidation of the sample in the test is isotropic meanwhile in the field, consolidation is usually anisotropic.

Computation of different parameters

1. Post Consolidation dimensions

Cross sectional area while in shearing stage

1. Stresses

Deviator stress=P/A

Principal stresses

1. Compressive strength
2. The deviator stress at failure is called 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

The unconfined compression test refers to a specified form of triaxial test in which the restraining pressure is nil. The experimentation could be carried out only on the surface of the clayey soils which could stance exclusive of confinement. There are two kinds of UCC machines, one with a spring and another machine with a proving ring.

A compaction force is exerted to the sample till failure. The compressive load could be calculated with utilization of a proving ring.

Presentation of results

In this experimentation, the minor principal stress is nil. Similarly, major principal stress is equivalent to the deviator stress. The Mohr circle could be drawn for stress conditions at point of failure.

Merits

1. The test is suitable, simple and fast
2. It is preferably suited for measuring the unconsolidated undrained shear strength of intact saturated clays
3. The sensitivity of the soil can be effortlessly ascertained

Demerits

1. The experimentation cannot be undertaken on fissured clays
2. The experimentation might be deceptive for soils of which the angle of shearing resistance is not nil.

## Vane Shear Test

The undrained strength of soft clays could be ascertained in a laboratory with the utilization of the vane shear test. The experimentation could also be conducted in the field on the soil at the base of bore hole. The apparatus comprises of a perpendicular steel rod containing four thin stainless steel blades or vanes attached at its base end. Stature of the vane has to be equivalent to twice the diameter. For undertaking the test in a laboratory, a sample of diameter 38mm and height 75mm is created and attached to the foundation of the apparatus. The vane is slowly lowered in to the sample till the apex of the vane is at a stature of 10 to 20 mm below the apex of the sample. The readings of the strain indicator and torque indicator are marked.

Shear Strength S

Where T =Torque applied

D = Diameter of vane

H1= Height of vane

Merits

1. The test is simple and fast
2. It is preferably suitable for determination of the in-situ undrained shear strength of non fissured, fully saturated clay
3. The experimentation could be suitably utilized to regulate the sensitivity of the soil

Demerits

1. The test cannot be undertaken on the fissured clay or the clay comprising silt or sand laminations
2. The test does not yield precise results when the failure envelope is not parallel

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