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# Shear Strength of Soil

Shear Strength of Soil

Contents

Define Shear strength of Soil 1

Recall the Parameters of the Shear Strength 2

Describe the concept of Mohr’s Stress Circle 2

Recall the Mohr-Coulomb theory 4

Describe the direct shear test and its limitations 5

Recall the Mohr’s Circle for direct shear test 6

Describe the Triaxial compression test 7

Recall the advantages and limitations of the triaxial compression test 8

Recall the Sensitivity and Thixotropy 9

Describe the Unconfined Compression Test 10

Describe the Vane Shear Test 11

Recall the Typical Stress-Strain Curves for different Soils 12

Describe the Consolidated undrained and the Consolidated drained tests 13

Recall the terms Critical Void Ratio and Stress Path 14

Describe the Skempton’s pore pressure coefficients 14

Recall the Sensitivity and Thixotropy 15

# Define Shear strength of Soil

Shear strength of soil refers to the resistance of soil to sliding or shearing forces. It is a measure of the maximum stress that soil can withstand before it begins to fail or deform. Shear strength is an important factor in determining the stability of soil, and is used in the design of foundations, slopes, and retaining walls.

1. Cohesionless soil: Cohesionless soil, also known as granular soil, is composed of individual particles that do not stick together. The shear strength of cohesionless soil is primarily determined by the internal friction between the particles. The internal friction is a result of the roughness and irregularity of the soil particles, and the strength of the bond between the particles.
2. Cohesive soil: Cohesive soil, also known as clay soil, is composed of particles that stick together due to the presence of clay minerals and other fine-grained materials. The shear strength of cohesive soil is primarily determined by the cohesion or the bonding strength between the particles. The cohesion is a result of the chemical and mineralogical composition of the soil, and the water content of the soil.
3. Shear strength parameters: To determine the shear strength of soil, two main parameters are used: the cohesion (c) and the internal friction angle (ϕ). The cohesion is a measure of the bonding strength between the soil particles, while the internal friction angle is a measure of the resistance to sliding between the particles. Together, these parameters can be used to calculate the shear strength of soil using the Mohr-Coulomb failure criterion.
4. Shear strength test: To determine the shear strength of soil, several laboratory tests can be performed such as Direct shear test, Triaxial test, and Unconfined compression test. These tests are performed on soil samples that are taken from the field and are used to determine the shear strength parameters of the soil.
5. Factors affecting shear strength: Several factors can affect the shear strength of soil, including the type of soil, the water content, the density, the grain size, and the degree of compaction. These factors can all affect the internal friction and cohesion of the soil, and therefore the shear strength. Understanding how these factors affect the shear strength of soil is important for designing stable foundations, slopes, and retaining walls.

# Recall the Parameters of the Shear Strength

1. Cohesion (c): Cohesion, also known as bonding strength, is the measure of the resistance of soil to failure due to the strength of the bonds between the soil particles. It is a measure of the vertical component of the shear strength and is typically measured in units of force per unit area (kPa or psi). Cohesion is a characteristic of cohesive soils and is often used in the design of slopes, retaining walls, and foundations.
2. Internal Friction Angle (ϕ): Internal friction angle, also known as angle of internal friction, is the measure of the resistance of soil to failure due to sliding between the soil particles. It is a measure of the horizontal component of the shear strength and is typically measured in degrees. Internal friction angle is a characteristic of both cohesive and cohesionless soils and is often used in the design of slopes, retaining walls, and foundations.
3. Angle of Repose (θ): Angle of repose is the angle between the surface of the soil and the horizontal plane at which soil will remain stable without sliding. It is determined by the internal friction angle and the density of soil. It is used in the design of slopes, embankments, and stockpiles, and also helps in understanding soil stability.
4. Dilatancy Angle (δ): Dilatancy angle is the angle between the vertical and the tangent to the failure plane at the point of failure. It is a measure of the change in volume of soil particles when shear stress is applied. It is used in the design of slopes, embankments and foundations.
5. Pore water pressure: Pore water pressure is the pressure of water present in the pores of soil. It is used to calculate the effective stress in soil and can have an effect on the shear strength of soil. Increase in pore water pressure can reduce the shear strength of soil and make it more susceptible to failure. It is important to take into account the pore water pressure when determining the shear strength of soil in saturated or partially saturated conditions.

# Describe the concept of Mohr’s Stress Circle

Mohr’s stress circle is a graphical representation of the state of stress at a point in a soil or rock mass. It is a powerful tool for visualizing the distribution of stresses and strains in a material and is used to understand the behavior of soil and rock under different loading conditions. The concept of Mohr’s stress circle is based on Mohr’s circle theorem, which states that the normal and shear stresses on any plane can be represented by a circle.

1. Principal stresses: The Mohr’s stress circle is constructed using the principal stresses, which are the maximum and minimum normal stresses acting on a plane. The principal stresses are represented by the center of the circle and the radius of the circle, respectively. The center of the circle is the average of the maximum and minimum normal stresses, while the radius of the circle is half the difference between the maximum and minimum normal stresses.
2. Shear stress: The Mohr’s stress circle also represents the shear stress on a plane. Shear stress is represented by the tangent of the angle between the normal stress and the shear stress. The angle is known as the Mohr’s angle and is used to determine the direction of the shear stress on a plane.
3. Stress space: The Mohr’s stress circle is plotted in a stress space, which is a three-dimensional space that represents the three principal stresses. The stress space is divided into two regions, one representing the compressive stress and the other representing the tensile stress. The Mohr’s stress circle is used to determine the state of stress in a material and identify whether it is in a state of compression or tension.
4. Failure criterion: Mohr’s stress circle is also used to determine the failure criterion of a material. The failure criterion is the point at which the material will fail under a given set of stresses. The Mohr-Coulomb failure criterion is a common failure criterion that is used to determine the shear strength of soil.
5. Mohr’s stress circle has several practical applications in geotechnical engineering, rock mechanics, and structural engineering. It is used to determine the stability of slopes, foundations, and retaining walls, and also used in the design of underground excavations and tunnels. It also used to understand the behavior of soil and rock under different loading conditions and to predict the failure of soil or rock.

# Recall the Mohr-Coulomb theory

The Mohr-Coulomb theory is a failure criterion for soil and rock that describes the shear strength of a material as a function of the normal stress and the angle of internal friction. It is based on the concept of Mohr’s stress circle, which is a graphical representation of the state of stress at a point in a soil or rock mass.

Mohr-Coulomb equation: The Mohr-Coulomb theory is described by the equation:

σ t = c + σn * tan(φ)

Where:

σt is the shear stress

c is the cohesion

σn is the normal stress

1. φ is the angle of internal friction
2. Cohesion: Cohesion is the shear strength of a soil or rock in the absence of an angle of internal friction. It is the force that holds particles of a soil or rock together. It is represented by the y-intercept of the Mohr-Coulomb equation.
3. Angle of internal friction: The angle of internal friction is the angle between the shear stress and the normal stress on a plane. It represents the resistance of a soil or rock to shearing. It is represented by the slope of the Mohr-Coulomb equation.
4. Shear strength: The Mohr-Coulomb theory describes the shear strength of a soil or rock as the sum of the cohesion and the shear stress caused by the angle of internal friction. The shear strength is the maximum stress that a soil or rock can withstand before failure.
5. Limitations: The Mohr-Coulomb theory is based on the assumption that the soil or rock behaves in a linear elastic manner and that the failure surface is planar. However, in practice, soils and rocks often exhibit nonlinear behavior and the failure surface is not always planar. Therefore, the Mohr-Coulomb theory should be used with caution and in combination with other methods to determine the shear strength of soil and rock.
6. Mohr-Coulomb theory is widely used in geotechnical engineering and civil engineering for the design of slopes, foundations, and retaining walls. It is also used in the design of underground excavations and tunnels, and to understand the behavior of soil and rock under different loading conditions.

# Describe the direct shear test and its limitations

The direct shear test is a laboratory test used to determine the shear strength of soil. It is used to measure the shear strength of soil when the soil is subjected to a normal load and a shear load at the same time. It is typically used to determine the shear strength of cohesive soils and can be used to determine the shear strength of granular soils when the soil is saturated.

1. Test setup: The direct shear test is typically performed using a direct shear box, which is a device that consists of two parallel metal plates with a gap in between. The soil sample is placed in the gap and a normal load is applied to the top plate. A shear load is then applied to the bottom plate, causing the soil to shear along a plane that is perpendicular to the direction of the shear load. The shear strength of the soil is determined by measuring the shear load and the normal load at failure.
2. Test procedure: The soil sample is placed in the direct shear box, and a normal load is applied to the top plate. The normal load is then increased until the soil fails. The shear load is then increased until the soil fails again. The shear strength is determined by measuring the shear load and the normal load at failure.
3. Limitations: The direct shear test has some limitations:
• Only a small soil sample is tested at a time, so the results may not be representative of the entire soil deposit.
• The test is performed under controlled laboratory conditions, so the results may not be representative of the field conditions.
• The test is typically performed on saturated soil samples, so the results may not be representative of unsaturated soil conditions.
• The test does not take into account the effects of soil structure or soil fabric on the shear strength.
1. Conclusion: The direct shear test is a commonly used method for determining the shear strength of cohesive soils. However, it has some limitations and should be used in combination with other methods, such as the triaxial test, to determine the shear strength of soil.

# Recall the Mohr’s Circle for direct shear test

Mohr’s Circle is a graphical representation of the normal and shear stresses acting on a soil sample during a direct shear test. It is used to analyze the results of the test and to determine the shear strength of the soil.

1. Mohr’s Circle: Mohr’s Circle is a graphical representation of the normal and shear stresses acting on a soil sample. It is based on the concept of the Mohr-Coulomb theory, which states that the shear strength of a soil is equal to the normal stress multiplied by the coefficient of internal friction.
2. Construction: Mohr’s Circle is constructed by plotting the normal and shear stresses on a graph. The normal stress is plotted along the horizontal axis and the shear stress is plotted along the vertical axis. The center of the circle is the mean normal stress, and the radius of the circle is the difference between the maximum and minimum normal stresses. The shear strength is equal to the tangent of the angle of internal friction, which is the angle between the horizontal axis and the line representing the shear stress.
3. Analysis: Mohr’s Circle is used to analyze the results of a direct shear test by comparing the shear stress and the normal stress at failure. The shear strength of the soil can be determined by drawing a line through the point representing the failure condition and the center of the circle. The angle of this line represents the angle of internal friction, and the length of the line represents the shear strength of the soil.
4. Limitations: Mohr’s Circle is limited in that it is only applicable to soils that have a linear relationship between the shear stress and the normal stress. It does not take into account the effects of soil structure or soil fabric on the shear strength.
5. Conclusion: Mohr’s Circle is a useful tool for analyzing the results of a direct shear test and determining the shear strength of a soil. However, it has some limitations and should be used in combination with other methods, such as the triaxial test, to determine the shear strength of soil.

# Describe the Triaxial compression test

The triaxial compression test is a laboratory test used to determine the shear strength of soil. The test is designed to simulate the conditions of in-situ soil and measure the shear strength of soil under controlled laboratory conditions. It is considered one of the most reliable and widely used methods for determining the shear strength of soil.

1. Test setup: The test setup consists of a cylindrical soil sample that is placed inside a triaxial cell. The sample is surrounded by a rubber membrane, which is filled with water. The cell is then pressurised with air to apply an axial load to the soil sample. The load is applied to the top of the sample, while the bottom of the sample is supported by a load-bearing ring. The cell is also equipped with pressure transducers to measure the pore water pressure and the confining pressure.
2. Test procedure: The test procedure consists of three main stages: the preconsolidation stage, the isotropic compression stage, and the shear stage. During the preconsolidation stage, the sample is consolidated by applying a confining pressure to the sample. During the isotropic compression stage, the confining pressure is increased and the sample is compressed. During the shear stage, the sample is sheared by applying a shearing force to the top of the sample. The shearing force is increased until the sample fails.
3. Data analysis: The data obtained from the test is analyzed to determine the shear strength of the soil. The shear strength of the soil is calculated using the Mohr-Coulomb equation, which relates the shear stress to the normal stress and the angle of internal friction. The test results also provide information about the stress-strain behavior of the soil, the deformation characteristics of the soil, and the pore water pressure.
4. Limitations: The triaxial compression test is a laboratory test and may not accurately reflect the conditions of in-situ soil. Additionally, the test is time-consuming and expensive, and it requires a large amount of soil.
5. Conclusion: The triaxial compression test is a reliable and widely used method for determining the shear strength of soil. However, it has some limitations and should be used in combination with other methods, such as the direct shear test and the vane shear test, to determine the shear strength of soil.

# Recall the advantages and limitations of the triaxial compression test

The triaxial compression test is a widely used method for determining the shear strength of soil in laboratory conditions. However, it has some advantages and limitations that should be considered when using this test.

1. High accuracy: The triaxial compression test is considered one of the most reliable methods for determining the shear strength of soil. It provides a high level of accuracy and precision when compared to other laboratory tests.
2. Simulates in-situ conditions: The test setup simulates the in-situ conditions of soil, which allows the test results to be more representative of the actual soil conditions.
3. Provides detailed information: The test results provide detailed information about the stress-strain behavior of the soil, the deformation characteristics of the soil, and the pore water pressure. This information can be used to design and analyze engineering structures, such as foundations and retaining walls.
4. Widely used: The triaxial compression test is widely used by engineers, geologists, and soil scientists, making it a well-established and accepted method.

Limitations:

1. Laboratory test: The triaxial compression test is a laboratory test and may not accurately reflect the conditions of in-situ soil.
2. Time-consuming and expensive: The test is time-consuming and requires a large amount of soil, making it an expensive method.
3. Complex equipment: The test requires specialised equipment, which can be expensive and difficult to operate.
4. Limited to small samples: The test is limited to small soil samples, which can be a limitation when testing large or complex soil formations.
5. Conclusion: The triaxial compression test is a reliable and widely used method for determining the shear strength of soil. However, it has some limitations and should be used in combination with other methods, such as the direct shear test and the vane shear test, to determine the shear strength of soil. Additionally, it is important to consider the limitations of this test when interpreting the results and applying them to real-world situations.

# Recall the Sensitivity and Thixotropy

Sensitivity and thixotropy are important properties of soils that can affect the shear strength of the soil.

Sensitivity: Sensitivity is a measure of the soil’s ability to change its shear strength when subjected to changes in water content. A soil that is sensitive to changes in water content will have a large change in shear strength as the water content changes, while a soil that is not sensitive will have little change in shear strength. Sensitive soils are typically more susceptible to changes in moisture content and are therefore more prone to failure when subjected to changes in water content.

Thixotropy: Thixotropy is a property of a soil that describes its ability to change its consistency when subjected to changes in shear rate. A thixotropic soil will change its consistency when sheared, becoming more fluid and less viscous, and will then return to its original consistency when the shearing forces are removed. Thixotropy can affect the shear strength of a soil, as a thixotropic soil may have a higher shear strength when it is not being sheared and a lower shear strength when it is being sheared.

Both of these properties are important to consider when evaluating the shear strength of soil, as they can affect the behavior of the soil under different conditions. For example, a soil that is sensitive to changes in water content may have a lower shear strength when it is wet than when it is dry, while a soil that is thixotropic may have a higher shear strength when it is not being sheared than when it is. Engineers and geologists must take these properties into account when evaluating the shear strength of soil and designing structures that will be built on or in soil.

# Describe the Unconfined Compression Test

The Unconfined Compression Test (UCT) is a laboratory test that is used to determine the unconfined compressive strength of a soil. The test is also known as the Unconsolidated-Undrained (UU) Test.

The UCT is performed by compacting a soil sample into a cylindrical mold, and then applying an axial load to the top of the soil sample using a loading device, such as a hydraulic jack. The load is applied at a constant rate, and the deformation of the soil sample is measured. The test is typically conducted at a constant rate of strain, typically 1% per minute.

The unconfined compressive strength (q u ) of the soil can be determined from the load-deformation data obtained from the test. The unconfined compressive strength is calculated as the maximum load applied to the soil sample divided by the cross-sectional area of the soil sample. The unconfined compressive strength is a measure of the maximum stress that a soil can withstand before failure in an unconfined condition.

The UCT is commonly used to evaluate the strength of cohesive soils, such as clay and silt. The test is also used to evaluate the strength of granular soils in the laboratory. However, the UCT is not suitable for evaluating the strength of soils that are sensitive to changes in water content, such as expansive soils.

The UCT is a simple and relatively inexpensive test, and it is widely used in the geotechnical engineering field. The test results are used to design foundations, slopes, and retaining walls, and to evaluate the stability of natural and man-made slopes. The results of the UCT are also used to evaluate the strength of soil samples used in laboratory research.

The test has some limitations, it does not account for the effects of drainage, confining pressure, and stress history on the soil. Also, the test can be affected by variations in the density of the soil sample, and the test results may not be directly applicable to in-situ conditions.

# Describe the Vane Shear Test

The Vane Shear Test (VST) is a laboratory test that is used to determine the in-situ shear strength of a soil. The test is also known as the Torvane test.

The VST is performed by installing a cylindrical vane into the soil at a specific depth, and then applying a torque to the vane using a torque wrench. The torque is applied at a constant rate, and the rotation of the vane is measured. The test is typically conducted at a constant rate of rotation, typically 1 degree per minute.

The shear strength (t) of the soil can be determined from the torque-rotation data obtained from the test. The shear strength is calculated as the torque applied to the vane divided by the circumference of the vane. The shear strength is a measure of the maximum shear stress that a soil can withstand before failure in an in-situ condition.

The VST is commonly used to evaluate the shear strength of cohesive soils, such as clay and silt. The test is also used to evaluate the shear strength of granular soils in the laboratory. The VST is suitable for evaluating the shear strength of soils that are sensitive to changes in water content, such as expansive soils.

The VST is a simple and relatively inexpensive test, and it is widely used in the geotechnical engineering field. The test results are used to design foundations, slopes, and retaining walls, and to evaluate the stability of natural and man-made slopes. The results of the VST are also used to evaluate the shear strength of soil samples used in laboratory research.

The test has some limitations, it does not account for the effects of drainage, confining pressure, and stress history on the soil. Also, the test can be affected by variations in the density of the soil sample, and the test results may not be directly applicable to in-situ conditions. Also, the vane is a relatively small specimen, so the results of the test may not be representative of the entire soil mass.

# Recall the Typical Stress-Strain Curves for different Soils

Stress-strain curves are graphical representations of the relationship between stress and strain in a soil. These curves are used to understand the mechanical behavior of soils and to predict the behavior of soils under different loading conditions.

There are four typical stress-strain curves for different types of soils:

1. Cohesive soils: These soils, such as clay, have a high degree of internal cohesion and exhibit a linear elastic behavior up to a certain point. After this point, the soil will start to deform plastically and the curve will become non-linear. The peak strength of cohesive soils is known as the “unconfined compression strength” (qu) or the “unconfined yield strength” (qu).
2. Cohesionless soils: These soils, such as sand, have little or no internal cohesion and exhibit a linear elastic behavior up to a certain point. After this point, the soil will start to deform plastically and the curve will become non-linear. The peak strength of cohesionless soils is known as the “unconfined compression strength” (qu) or the “unconfined yield strength” (qu).
3. Stiff soils: These soils, such as stiff clay or dense sands, have a high degree of internal cohesion and exhibit a linear elastic behavior. These soils are not affected by plastic deformation and the stress-strain curve will remain linear.
4. Soft soils: These soils, such as loose sands or soft clays, have low internal cohesion and exhibit a linear elastic behavior up to a certain point. After this point, the soil will start to deform plastically and the curve will become non-linear. The peak strength of soft soils is known as the “unconfined compression strength” (qu) or the “unconfined yield strength” (qu).

It’s important to note that the stress-strain curves are not always a perfect representation of the soil behavior, and they can be affected by factors such as soil type, density, water content, and the loading conditions.

# Describe the Consolidated undrained and the Consolidated drained tests

Consolidated undrained (CU) and Consolidated drained (CD) tests are used to determine the shear strength of soil.

1. Consolidated undrained (CU) test: This test is used to measure the undrained shear strength of a soil. In this test, the soil sample is placed in a triaxial cell, and then the cell is filled with water to the top of the soil sample. The confining pressure is then applied to the soil sample and the pore water pressure is held constant while the axial load is applied. The test is considered undrained because the pore water pressure is not allowed to change during the test. The undrained shear strength is measured by the ratio of the confining pressure to the axial deformation.
2. Consolidated drained (CD) test: This test is used to measure the drained shear strength of a soil. In this test, the soil sample is placed in a triaxial cell, and then the cell is filled with water to the top of the soil sample. The confining pressure is then applied to the soil sample and the pore water pressure is allowed to change during the test. The drained shear strength is measured by the ratio of the confining pressure to the axial deformation.

The CU test and the CD test can provide different results, as the undrained and drained tests are measuring the shear strength of the soil under different conditions. The undrained test is used to determine the strength of a soil in its natural state, while the drained test is used to determine the strength of a soil that has been drained of excess water.

It’s important to note that these tests are performed in laboratory conditions and the results obtained from these tests are highly dependent on the soil type, density, water content, and the loading conditions, so the results may not be the same as in the field conditions.

# Recall the terms Critical Void Ratio and Stress Path

1. Critical Void Ratio: The critical void ratio is a concept used in soil mechanics to describe the maximum dry density of a soil at which it will begin to collapse and compact under an applied load. It is a measure of the compressibility of a soil and is typically determined through laboratory testing. The critical void ratio is a fundamental parameter used in soil behavior and engineering design.
2. Stress Path: A stress path is a graphical representation of the change in stress state of a soil or rock mass over time. It is used to describe the changes in stress that occur in a soil or rock mass due to changes in loading conditions, such as changes in the magnitude or direction of applied loads. Stress paths are typically represented using Mohr circles, which provide a visual representation of the changes in stress state. Stress paths are important in understanding the behavior of soils and rocks under different loading conditions and are used in soil and rock mechanics to predict the response of these materials to changes in loading conditions.

# Describe the Skempton’s pore pressure coefficients

Skempton’s pore pressure coefficients are a set of coefficients used to estimate the pore water pressure that develops in a soil or rock mass under an applied load. These coefficients are used in the analysis of soil behavior and are based on the concept of effective stress, which is the difference between the total stress in a soil and the pore water pressure. Skempton’s pore pressure coefficients are used to estimate the pore water pressure that develops in a soil or rock mass under an applied load, and are defined as the ratio of the pore water pressure to the effective stress.

There are three types of Skempton’s pore pressure coefficients:

1. The coefficient of volume compressibility (Cv): represents the change in pore water pressure per unit change in volume due to loading. It is used to estimate the pore water pressure that develops in a soil or rock mass under an applied load.
2. The coefficient of lateral pressure (Cl): is used to estimate the pore water pressure that develops in a soil or rock mass due to changes in the horizontal stress. It is used to estimate the pore water pressure that develops in a soil or rock mass due to changes in the horizontal stress.
3. The coefficient of vertical pressure (Cz): is used to estimate the pore water pressure that develops in a soil or rock mass due to changes in the vertical stress. It is used to estimate the pore water pressure that develops in a soil or rock mass due to changes in the vertical stress.

These coefficients are determined through laboratory testing and are used in the analysis of soil behavior and engineering design. The values of these coefficients can vary depending on the soil type, and it is important to use the appropriate coefficients when analyzing the behavior of a soil or rock mass under different loading conditions.

# Recall the Sensitivity and Thixotropy

1. Sensitivity: Sensitivity is a measure of the ease with which a soil or clay changes its shape or volume in response to changes in applied stress. It is a measure of the soil’s plasticity and is typically determined through laboratory testing. A soil that is sensitive will change its shape or volume easily in response to changes in applied stress, while a less sensitive soil will be more resistant to changes in shape or volume. Sensitivity is an important parameter in understanding the behavior of soils and clays and is used in soil mechanics and engineering design.
2. Thixotropy: Thixotropy is the property of certain materials to become more fluid when agitated and to return to a more solid state when at rest. This type of behavior is commonly observed in some types of clays and soils, and is caused by the presence of small particles or fibres that can align or reorient in response to changes in applied stress. Thixotropy is an important parameter in understanding the behavior of soils and clays and is used in soil mechanics and engineering design, particularly in the design of foundations, slopes, and embankments.

Sensitivity and Thixotropy are related in that a thixotropic soil is also sensitive because it changes its behavior depending on the applied stress. The degree of Thixotropy and Sensitivity of a soil can be determined through laboratory testing using shear box, vane shear and other test methods. These properties are important to take into account when designing structures and foundations, as they can affect the stability and settlement of the soil.