Shear Strength: Direct Shear, Vane, Triaxial Tests, Compaction, Maximum Dry Density, Optimum Moisture Content

Introduction to Shear Strength of Soil

Shear strength is a fundamental property of soil that defines its ability to resist deformation and failure when subjected to shear stresses. It is the maximum resistance per unit area that the soil can offer to the sliding or shearing surfaces. Understanding shear strength is crucial for the design of foundations, retaining walls, slopes, and other geotechnical structures, as the failure of these structures is often governed by the soil's shear strength.

The shear strength of a soil is primarily dependent on the friction between soil particles and the cohesion between them. For granular soils like sands and gravels, cohesion is negligible, and shear strength is mainly due to inter-particle friction. For cohesive soils like clays, both friction and cohesion contribute to shear strength.

Factors Affecting Shear Strength

Several factors influence the shear strength of a soil:

• Type of soil (grain size, shape, and distribution)
• Soil density and void ratio
• Water content
• Effective stress (normal stress acting on the failure plane)
• Drainage conditions during shearing
• Soil structure and fabric
• Presence of cementing agents

Mohr-Coulomb Failure Criterion

The most widely used criterion for predicting the shear strength of soils is the Mohr-Coulomb failure criterion. This empirical criterion states that the shear strength ($\tau_f$) of a soil at a point is a linear function of the effective normal stress ($\sigma'$) acting on the failure plane. The equation is expressed as:

$\tau_f = c' + \sigma' \tan \phi'$

Where:

• $\tau_f$ is the shear strength at failure.
• $c'$ is the effective cohesion, representing the shear strength at zero effective normal stress.
• $\sigma'$ is the effective normal stress acting perpendicular to the failure plane.
• $\phi'$ is the effective angle of internal friction, representing the frictional resistance of the soil.

For soils with no cohesion (e.g., dry sand), $c' = 0$, and $\tau_f = \sigma' \tan \phi'$.

The Mohr-Coulomb criterion is often represented graphically using Mohr's circles of stress. A series of Mohr's circles representing different stress states are drawn, and the 'failure envelope' tangent to these circles represents the failure condition according to the Mohr-Coulomb criterion.

Laboratory Methods for Determining Shear Strength

Shear strength parameters ($c'$ and $\phi'$) are typically determined through laboratory tests on soil samples. The most common methods are the Direct Shear Test, Vane Shear Test, and Triaxial Shear Test.

Direct Shear Test

Principle and Procedure

The Direct Shear Test is one of the oldest and simplest methods for determining the shear strength of soils. The test involves applying a normal load and a shear load to a soil sample contained within a shear box. The soil sample is typically square or circular and is divided into two halves by a horizontal plane.

The procedure involves:

1. A soil sample of a specific size is placed in the shear box. For cohesive soils, the sample might be consolidated under a normal load before shearing.
2. A normal load is applied to the top of the sample, simulating the overburden pressure.
3. The shear box is then placed in a testing machine, and the two halves of the box are moved horizontally relative to each other at a constant rate of strain.
4. The shear force required to cause failure (sliding of the two halves) is measured.
5. The test is repeated on identical samples under different normal loads to obtain a series of shear strengths.

Calculation of Shear Strength Parameters

For each test, the shear stress ($\tau$) at failure is calculated as the maximum shear force divided by the area of the failure plane. The effective normal stress ($\sigma'$) is calculated based on the applied normal load and the area.

$\tau_f = \frac{\text{Shear Force at Failure}}{\text{Area of the shear box}}$

$\sigma' = \frac{\text{Normal Load}}{\text{Area of the shear box}}$

By plotting $\tau_f$ against $\sigma'$ for several tests, the shear strength parameters $c'$ and $\phi'$ can be determined from the intercept and slope of the best-fit line (the failure envelope).

Advantages and Disadvantages

Advantages:

• Simple to perform and relatively inexpensive.
• Provides a direct measure of shear strength.
• Suitable for granular soils and compacted cohesive soils.

Disadvantages:

• The failure plane is predetermined and may not correspond to the critical failure surface in a real structure.
• Drainage conditions are not easily controlled, making it difficult to test under drained or undrained conditions accurately.
• For cohesive soils, the rapid shearing can lead to pore water pressure buildup, giving misleading results if not properly interpreted.
• The test tends to overestimate the angle of internal friction for dense sands.

Vane Shear Test (VST)

Principle and Procedure

The Vane Shear Test is primarily used to determine the undrained shear strength ($c_u$) of soft, saturated cohesive soils in situ (in the ground) or in the laboratory. It is particularly useful for very soft clays where obtaining undisturbed samples is difficult.

The test involves inserting a four-bladed vane into the soil. The vane is then rotated at a slow, constant rate, and the torque required to cause failure is measured. The failure occurs along a cylindrical surface defined by the rotation of the vane.

The procedure is as follows:

1. A vane apparatus, typically consisting of four thin rectangular blades welded to a central rod, is pushed into the soil.
2. Torque is applied to the rod, causing the vane to rotate.
3. The maximum torque ($T_{max}$) registered by the torque indicator is recorded.
4. The vane is then rotated rapidly (about 10 revolutions) to remold the soil, and the torque required to cause failure in the remolded soil ($T_{remolded}$) is measured.

Calculation of Undrained Shear Strength

The undrained shear strength ($c_u$) is calculated from the maximum torque using the following formula:

$c_u = \frac{T_{max}}{K}$

Where $K$ is the vane factor, which depends on the geometry of the vane. For a standard vane with height $H$ and diameter $D$:

$K = \frac{\pi D^3}{2} \left(1 + \frac{H}{3D}\right)$

For a standard vane where $H = 2D$:

$K = \frac{\pi D^3}{2} \left(1 + \frac{2}{3}\right) = \frac{5\pi D^3}{6}$

The undrained shear strength of the remolded soil is calculated using the same formula with $T_{remolded}$. The ratio of the undisturbed shear strength to the remolded shear strength provides an indication of the sensitivity of the clay.

Advantages and Disadvantages

Advantages:

• Can be performed in situ, providing results on undisturbed soil.
• Quick and relatively inexpensive for field testing.
• Suitable for soft to medium-stiff clays.

Disadvantages:

• Only suitable for cohesive soils.
• Results can be affected by the insertion of the vane, especially in firm clays.
• The test measures undrained shear strength only.
• Not reliable in highly sensitive clays or soils with significant sand content.

Triaxial Shear Test

Principle and Procedure

The Triaxial Shear Test is the most versatile and widely used laboratory method for determining the shear strength parameters of soils. It allows for the control of drainage conditions and stresses, providing a more realistic simulation of field conditions. The test can be performed on undisturbed or remolded samples.

A cylindrical soil sample is placed inside a rubber membrane and then enclosed in a triaxial cell filled with water. The cell pressure (confining pressure) is applied to the outside of the membrane, simulating the ambient stress in the ground. A deviator stress is then applied axially by a loading ram, causing the sample to fail. Pore water pressure can also be measured.

There are three main types of triaxial tests, classified based on drainage conditions:

1. Consolidated-Drained (CD) Test: The sample is first consolidated under a given cell pressure with drainage allowed. Then, the deviator stress is applied slowly enough to allow pore water pressure to dissipate, and drainage is permitted throughout the shearing phase. This test determines the effective stress parameters ($c'$ and $\phi'$).
2. Consolidated-Undrained (CU) Test: The sample is consolidated under a given cell pressure with drainage allowed. However, during the shearing phase, drainage is prevented. Pore water pressure is measured. This test is faster than the CD test and determines the effective stress parameters by analyzing the pore water pressure changes, or can be used to determine the total stress parameters ($c_u$ and $\phi_u$) if pore pressure is not measured.
3. Unconsolidated-Undrained (UU) Test: The sample is subjected to cell pressure and deviator stress without any drainage allowed at any stage. This is a rapid test and is suitable for cohesive soils where undrained conditions prevail in the short term. It determines the undrained shear strength parameters ($c_u$ and $\phi_u$).

Calculation of Shear Strength Parameters

In a triaxial test, multiple samples are tested under different cell pressures. For each test, the axial stress ($\sigma_1$) and cell pressure ($\sigma_3$) are known, and the pore water pressure ($u$) is measured (for CU and CD tests).

The principal stresses at failure are:

• Major principal stress: $\sigma_{f1} = \sigma_3 + \Delta\sigma_f$ (where $\Delta\sigma_f$ is the deviator stress at failure)
• Minor principal stress: $\sigma_{f3} = \sigma_3$

For effective stress parameters ($c'$ and $\phi'$), the effective stresses are used:

• Effective major principal stress: $\sigma'_{f1} = \sigma_{f1} - u$
• Effective minor principal stress: $\sigma'_{f3} = \sigma_{f3} - u$

Mohr's circles are drawn using these effective principal stresses. The failure envelope tangent to these circles gives $c'$ and $\phi'$.

For total stress parameters ($c_u$ and $\phi_u$), Mohr's circles are drawn using the total principal stresses ($\sigma_{f1}$ and $\sigma_{f3}$). The failure envelope gives $c_u$ and $\phi_u$.

Advantages and Disadvantages

Advantages:

• Allows for control of drainage conditions (drained, undrained).
• Can simulate in-situ stress conditions more realistically.
• Provides effective stress parameters ($c'$, $\phi'$).
• Pore water pressure can be measured (CU test).
• Suitable for all types of soils.

Disadvantages:

• More complex and expensive than direct shear or vane shear tests.
• Sample preparation can be difficult, especially for undisturbed samples.
• The rubber membrane can cause errors in results, particularly for dense or coarse-grained soils.

Compaction of Soil

Definition and Purpose

Compaction is the process of increasing the density of a soil by mechanically expelling air from the void spaces. It is achieved by applying energy to the soil, such as rolling, tamping, or vibration. Compaction is a crucial step in many civil engineering projects, including the construction of embankments, dams, roads, and building foundations.

The primary purposes of soil compaction are to:

• Increase the soil's shear strength and bearing capacity.
• Reduce its compressibility and settlement.
• Decrease its permeability, making it less susceptible to frost action and water damage.
• Improve its stability and durability.

Factors Affecting Compaction

The degree of compaction achieved depends on several factors:

• Soil Type: Granular soils (sands, gravels) are generally easier to compact than cohesive soils (clays).
• Water Content: This is the most critical factor. There is an optimum water content at which the soil can be compacted to its maximum density for a given amount of compactive effort.
• Compactive Effort: The amount of energy applied to the soil. Higher compactive effort generally leads to higher density.
• Type of Compaction Equipment: Different types of equipment (e.g., smooth wheel rollers, sheepsfoot rollers, vibratory compactors) are effective for different soil types.
• Thickness of the compacted layer: The compactive energy needs to penetrate the entire layer.

Standard Proctor Test and Modified Proctor Test

Objective

The Standard Proctor Test (ASTM D698) and the Modified Proctor Test (ASTM D1557) are laboratory procedures used to determine the relationship between the water content, compactive effort, and the resulting dry density of a soil. These tests establish the compaction characteristics of a soil, specifically its maximum dry density and optimum moisture content.

Procedure

Both tests involve compacting a soil sample in a standard mold (typically 1/30 cubic foot for Standard Proctor, and 1/30 or 1/60 cubic foot for Modified Proctor) using a standard rammer. The key differences lie in the compactive effort applied:

Standard Proctor Test:

• Uses a 5.5 lb (2.5 kg) rammer.
• Rammer is dropped from a height of 12 inches (305 mm).
• Soil is compacted in 3 layers.
• Each layer receives 25 blows.
• The compactive effort is approximately 568 kJ/m³.

Modified Proctor Test:

• Uses a 10 lb (4.5 kg) rammer.
• Rammer is dropped from a height of 18 inches (457 mm).
• Soil is compacted in 5 layers.
• Each layer receives 25 blows.
• The compactive effort is approximately 2700 kJ/m³, which is about 4.6 times greater than the Standard Proctor.

In both tests, the soil is prepared at different water contents, compacted, and the dry density is determined for each water content.

Compaction Curve

A plot of dry density versus water content is generated. This plot typically shows a curve that rises to a peak and then falls.

• The peak of the curve represents the maximum dry density ($ \rho_{d,max} $ or $ \gamma_{d,max} $) achievable for that soil under the specific compactive effort.
• The water content at which this maximum dry density occurs is called the optimum moisture content ($ OMC $ or $ w_{opt} $).

Theoretical Explanation of Compaction Curve

At very low water content, the soil is stiff, and it's difficult to expel air, leading to low density. As water content increases, the water acts as a lubricant, allowing particles to rearrange into a denser state, and air is more easily expelled. This increases the dry density.

Beyond the optimum moisture content, adding more water increases the total mass of the soil but also increases the volume occupied by water. This leads to a decrease in dry density because the same compactive effort is now trying to push out both air and excess water, and the presence of more water increases the void ratio rather than reducing it.

The theoretical maximum dry density is achieved when all the air is expelled from the voids (zero air voids line). This occurs at a water content known as the zero air voids water content ($w_{zv}$). The zero air voids curve is always above the compaction curve.

The relationship for zero air voids is:

$ \rho_{sat} = \frac{G_s \rho_w}{1 + \frac{w G_s}{100}} $

Where:

• $ \rho_{sat} $ is the density at zero air voids.
• $ G_s $ is the specific gravity of soil solids.
• $ \rho_w $ is the density of water.
• $ w $ is the water content (as a decimal).

At zero air voids, $ \rho_{d,zv} = \frac{G_s \rho_w}{1 + w_{zv} G_s} $.

Maximum Dry Density (MDD) and Optimum Moisture Content (OMC)

Maximum Dry Density ($ \rho_{d,max} $ or $ \gamma_{d,max} $): This is the highest dry density achievable for a soil under a specific compactive effort. It represents the densest state the soil can attain when compacted. Higher MDD is generally desirable for structural fills as it implies higher strength and lower compressibility.

Optimum Moisture Content ($ OMC $ or $ w_{opt} $): This is the water content at which the maximum dry density is achieved for a given compactive effort. At the OMC, the soil particles are arranged in the most efficient way, with the water acting as a lubricant and helping to expel air.

The Modified Proctor test is generally preferred for materials used in highway and airfield construction because it simulates the heavier rolling equipment used in the field, resulting in a higher MDD and a lower OMC. A lower OMC is advantageous as it means less water needs to be added (or removed) during construction, making the process more economical and faster.

Field Compaction

In the field, compaction is achieved using various types of rollers (e.g., smooth wheel, pneumatic tired, sheepsfoot, vibratory). The choice of equipment depends on the soil type and the required degree of compaction. Field compaction is monitored by checking the in-situ density and water content of the compacted soil, often comparing them to the results of the Proctor tests. Field densities are typically specified as a percentage of the MDD obtained from the relevant Proctor test (e.g., 95% of Standard Proctor MDD).

Relationship between Shear Strength and Compaction

There is a direct correlation between the degree of compaction and the shear strength of a soil. As the dry density increases (up to the MDD), the shear strength generally increases because the soil particles are packed more closely together, leading to higher inter-particle friction and potentially higher cohesion. Compacting soil at or near its OMC is crucial for achieving optimal shear strength and stability in engineered fills.

Compacting soil wet of optimum (i.e., at a water content higher than OMC) can lead to lower shear strength and higher compressibility, making the compacted layer less stable.

Summary of Shear Strength Tests and Compaction

Shear strength tests (Direct Shear, Vane Shear, Triaxial) are essential for determining how a soil will behave under load and resist failure. Compaction tests (Proctor tests) are vital for achieving optimal soil properties for construction purposes, influencing shear strength, settlement, and permeability. The MDD and OMC from compaction tests are key parameters for field control.