Direct Shear Test: Shear Stress and Normal Stress at Failure

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Introduction

In the field of civil engineering, the direct shear test is commonly used to determine the shear strength parameters of soil. This test provides valuable information about the behavior of soil under shear loading conditions. By analyzing the shear stress and normal stress at failure, engineers can understand the soil's internal friction angle, which is a key parameter in designing foundations, slopes, and other geotechnical structures.

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Shear Stress and Normal Stress

Shear stress (τ) is the force per unit area acting parallel to the cross-sectional area of a material. It is a measure of the resistance of a material to shear deformation. Normal stress (σ) is the force per unit area acting perpendicular to the cross-sectional area of a material. It is a measure of the pressure or compression applied to the material.

In a direct shear test, a soil sample is subjected to a shearing force until failure occurs. At failure, the shear stress and normal stress values are recorded. In this case, the shear stress at failure is 0.6 kg/cm2 and the normal stress at failure is 1 kg/cm2.

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Internal Friction Angle

The internal friction angle (ϕ) is a fundamental parameter in soil mechanics that characterizes the shear strength and resistance to sliding of the soil. It is defined as the angle between the shear plane and the normal to the shear plane at failure. The internal friction angle is determined using the following equation:

ϕ = tan^(-1)(τ / σ)

where τ is the shear stress and σ is the normal stress.

In this case, the shear stress at failure is 0.6 kg/cm2 and the normal stress at failure is 1 kg/cm2. Plugging these values into the equation, we can calculate the internal friction angle:

ϕ = tan^(-1)(0.6 / 1) = tan^(-1)(0.6) = 30.96 degrees

Therefore, the internal friction angle of the dry sand sample at failure is approximately 30.96 degrees.

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Conclusion

In summary, the direct shear test provides valuable information about the shear strength of soil. By analyzing the shear stress and normal stress at failure, engineers can determine the internal friction angle of the soil. In this case, the shear stress at failure is 0.6 kg/cm2 and the normal stress at failure is 1 kg/cm2, resulting in an internal friction angle of approximately 30.96 degrees. This information is crucial in designing geotechnical structures and ensuring their stability and safety.