Question

If a sample of clay has a cohesion of 80 kPa and an angle of shearing resistance of 10°, the shear strength of clay at a normal stress of 100 kPa will be:

• A. 97.63 kPa
• B. 98.48 kPa
• C. 78.78 kPa
• D. 95.34 kPa

Hint:

The shear strength of clay can be calculated using the Mohr-Coulomb equation, involving cohesion, normal stress, and the angle of shearing resistance.

Answer 1

The Correct Option is A

The shear strength of clay is given by the Mohr-Coulomb equation: \[ \tau = c + \sigma \cdot \tan(\phi) \] Where: - \( \tau \) = shear strength - \( c \) = cohesion - \( \sigma \) = normal stress - \( \phi \) = angle of shearing resistance Given: - \( c = 80 \, \text{kPa} \) - \( \phi = 10^\circ \) - \( \sigma = 100 \, \text{kPa} \) Now, we calculate the shear strength: \[ \tau = 80 + 100 \cdot \tan(10^\circ) \] \[ \tau = 80 + 100 \cdot 0.1763 \] \[ \tau = 80 + 17.63 = 97.63 \, \text{kPa} \]
Step 2: Conclusion.
Thus, the correct answer is 97.63 kP(A)

Final Answer: \[ \boxed{97.63 \, \text{kPa}} \]