Drained Direct Shear Test on Clayey Soil

Introduction
In geotechnical engineering, the drained direct shear test is commonly used to determine the shear strength properties of soils. This test provides valuable information about the angle of internal friction and cohesion of the soil specimen. In this particular case, the test was conducted on a clayey soil.

Given Data
- Normal stress (σn) = 50 kPa
- Shear stress (τ) = 35 kPa

Calculating the Angle of Internal Friction
The angle of internal friction (φ) can be calculated using the formula:

tan(φ) = τ/σn

Substituting the Given Values
tan(φ) = 35/50

Calculating the Angle
To find the angle of internal friction, we need to find the inverse tangent of the value obtained from the above calculation.

φ = atan(35/50)

Calculating the Angle in Degrees
The result obtained from the previous step is in radians. To convert it to degrees, we multiply the value by 180/π.

φ (in degrees) = atan(35/50) * (180/π)

Calculating the Result
Using a scientific calculator, we can find the inverse tangent of the ratio 35/50 and multiply it by 180/π to get the angle in degrees.

φ ≈ 38 degrees (rounded off to the nearest integer)

Explanation
The angle of internal friction is a measure of the resistance of a soil to shearing. It represents the frictional forces between the particles of the soil. In the drained direct shear test, the excess pore water pressure is allowed to dissipate during the test, simulating the conditions of a drained slope or foundation.

In this case, the clayey soil specimen failed at a shear stress of 35 kPa under a normal stress of 50 kPa. By calculating the angle of internal friction using the formula tan(φ) = τ/σn, we find that the angle is approximately 38 degrees.

The angle of internal friction provides important information about the shear strength and stability of the soil. It is used in various geotechnical calculations, such as determining the bearing capacity of foundations and the stability of slopes. The higher the angle of internal friction, the greater the shear strength of the soil.

In conclusion, the angle of internal friction of the clayey soil sample, as determined from the drained direct shear test, is approximately 38 degrees. This value represents the resistance of the soil to shear and is crucial in geotechnical engineering calculations for designing safe and stable structures.