The shear strength of soils can be defined as the resistance to shear stresses and a consequent tendency to deformation by shear. Soil derives its shear strength from the following.
- Resistance due to the interlocking of particles.
- Frictional resistance between individual soil grains.
- Adhesion between soil particles or cohesion
Main planes and main soil stresses
At a point in a stressed material, each plane will be subjected to normal or direct stress and shear stress. A principal plane is defined as either a plane in which the stress is completely normal or one that has no shear stress.
The normal stress acting on these principal planes is known as principal stresses. There are three principal planes at any point in a stressed material. These three principal planes are mutually perpendicular.
In decreasing order of magnitude, the principal planes are designated the major principal plane, minor principal plane, and intermediate principal plane, and the corresponding principal stresses are designated in the same way.
These equations will give the stresses in the inclined plane making an angle θ with the principal principal plane.
Mohr’s Stress Circle for Soils
Otto Mohr, a German scientist, devised a graphical method for determining stresses in a plane inclined to the principal principal planes. The graphical construction is known as Mohr’s circle. In this method, the origin O is selected and the normal stresses are are plotted along the horizontal axis and the shear stresses along the vertical axis.
- Mohr’s circle can be drawn for the stress system with principal planes inclined to coordinate axes
- The tension system with vertical and horizontal planes are not the principal planes.
Mohr–Coulomb theory
Soil is a particulate material. Shear failure in soils is due to sliding of particles due to shear stresses. According to Mohr, failure is caused by a critical combination of normal and shear stresses. Soil fails when the shear stress in the failure plane at failure is a single function of the normal stress acting in that plane.
Since the failure plane shear stress is defined as the shear strength(s), the equation can be written as
S = f(θ)
Mohr’s theory refers to the shear stress in the failure plane at failure. A diagram can be made between the shear stresses and the normal stress at failure. The curve defined by this is known as the failure envelope.
Coulomb expressed the shear strength of a soil at a point in a particular plane as a linear function of the normal stress in that plane as,
S=C+σ tanφ
In this case, C is equal to the intersection on the Y axis and phi is the angle that the envelope makes with the X axis.
Different types of shear tests and drainage conditions
The following tests are used to measure the shear strength of soil.
- direct shear test
- Triaxial compression test
- Unconfined compression test
- Paddle cut test
Depending on the drainage conditions, there are three types of tests.
- Unconsolidated-undrained condition
- Consolidated condition – not drained
- Drained condition – consolidated
Direct shear test on the ground
tool or appliance
The test is carried out on a soil sample in a shear box that is divided into two halves along the horizontal plane at its center. The size of the shear box is 60 x 60 x 50 mm. is divided horizontally so that the dividing plane passes through the center.
The two halves are held together by locking pins. The box is also provided with either flat or perforated grip plates depending on test conditions.
Proof
A soil sample of size 60 x 60 x 25 mm is taken. It is placed in the direct shear box and compacted. The top grid plate, porous stone and pressure pad are placed on the sample. The normal load and shear load are applied until failure
Results presentation.
- Stress – deformation curve
- fail envelope
- Mohr’s circle
Advantage
- sample preparation is easy
- Since the thickness of the sample is much less, the drainage is fast
- It is ideal for performing drainage tests on cohesionless soils.
- the device is relatively cheap
Disadvantages
- stress conditions are known only in case of failure
- the stress distribution in the failure plane is not uniform
- the cut area gradually decreases as the test progresses
- the orientation of the fault plane is fixed
- control of drainage conditions is very difficult
- Pore water pressure cannot be measured.
Triaxial compression test
It is used to determine the shear characteristics of all types of soils under different drainage conditions. In this, a cylindrical sample is stressed under conditions of axial symmetry. In the first stage of the test, the sample is subjected to a confining pressure on all sides, above and below.
This stage is known as the consolidation stage. In the second stage of the test called the shear stage, additional axial stress and deflection stress are applied to the top of the sample through a ram. Therefore, the total stress in the axial direction at the moment of shear is equal to the confinement stress plus the diverter stress.
The vertical sides of the specimen are principal planes. The limiting pressure is the minor principal stress. The sum of the confining stress and the deviator stress is the principal principal stress. The triaxial apparatus consists of a circular base with a central pedestal. sample is placed on the pedestal.
The pedestal has one or two holes that are used in the drain function or pore pressure measurement. A triaxial cell is placed on the base plate. It is a Perspex cylinder. There are three tie rods that support the cell. There is a central ram to apply axial tension. An air release valve and an oil release valve are attached to the cell.
The appliance also has special features like,
- Mercury control system
- Pore water pressure measuring device
- Measurement of volume changes
Triaxial test on cohesive soil
The CU, UU and CD tests can be performed on soil samples. The sample is placed on the pedestal inside a rubber membrane. Confining pressure and axial pressure are applied until failure.
Triaxial test on cohesionless soil
The procedure is the same as for cohesive soil, only the sample preparation is different. A metal former, membrane, and funnel are used for sample preparation.
Advantage
- There is complete control over 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 in the weakest plane.
- The stress state at all intermediate stages up to failure is known
- The test is suitable for precise research work.
Disadvantages
- The apparatus is elaborate, expensive and bulky.
- The drain test takes a longer period compared to the direct shear test.
- The strain condition in the sample is not uniform.
- It is not possible to find the cross-sectional area of the sample accurately under high stresses.
- The test simulates only axial symmetric problems
- Sample consolidation in the test is isotropic, whereas in the field, consolidation is generally anisotropic.
Calculation of several parameters.
Post Consolidation Dimensions
V0=L0 (πD0ˆ2/4)
D0=[V0/((π/4)L0))]ˆ1/2
Cross sectional area during the cutting stage
A=A0/(1-ξ1)
tensions
Front derailleur tension = P / A
Main tensions
σ1= σ3+( σ1- σ3)
compressive strength
The diverter stress at failure is known as the compressive strength of the soil.
Presentation of results of the triaxial test.
- Stress-strain curves
- Mohr envelopes in terms of total stress and effective stress
Unconfined compression test in soil
The unconfined compression test is a special form of triaxial test in which the confining pressure is zero. The test can be performed only on clayey soils that can remain unconfined. There are two types of UCC machines: spring-loaded machine and machine with test ring.
A compressive force is applied to the specimen until failure. The compressive load can be measured with a test ring.
Results presentation.
In this test, the minor principal stress is zero. The principal principal stress is equal to the diverter stress. Mohr’s circle can be drawn for failure stress conditions.
Advantage
- The test is convenient, simple and fast.
- It is ideal for measuring the unconsolidated undrained shear strength of intact saturated clays.
- Soil sensitivity can be easily determined
Disadvantages
- The test cannot be performed on fissured clays.
- The test can be misleading for soils whose angle of shear resistance is not zero.
Pallet Cut Test
The undrained strength of soft clays can be determined in a laboratory by paddle shear test. The test can also be performed in the field in the soil downhole. The apparatus consists of a vertical steel rod having four thin stainless steel blades or paddles attached to its lower end.
The height of the paddle must be equal to twice the diameter. To carry out the test in a laboratory, a sample of diameter 38 mm and height 75 mm is prepared and fixed to the base of the apparatus.
The paddle is slowly lowered into the sample until the top of the paddle is to a depth of 10 to 20 mm below the top of the sample.Tension gauge and torque gauge readings are taken.
Shear strength S
S=(T)/π{[(Dˆ2H1)/2]+[Dˆ3/12]}
Where T = applied torque
D = diameter of the blade
h1= height of the paddle
Advantage
- The test is simple and fast.
- It is ideal for the determination of the in situ undrained shear strength of fully fissured and unfissured clay.
- The test can be conveniently used to determine the sensitivity of the soil.
Disadvantages
- The test cannot be performed on fissured clay or clay containing silt or sand laminations.
- The test does not give accurate results when the failure envelope is not horizontal