Question

In a Mohr--Coulomb failure criterion, the ratio of the uniaxial compressive strength to the tensile strength is

• A. \(\dfrac{1+\sin\phi}{1-\sin\phi}\)
• B. \(\dfrac{1-\sin\phi}{1+\sin\phi}\)
• C. \(C\left(\dfrac{1-\sin\phi}{1+\sin\phi}\right)\)
• D. \(2C\left(\dfrac{1-\sin\phi}{1+\sin\phi}\right)\)

Hint:

For the Mohr--Coulomb criterion, \[ \boxed{ \frac{\sigma_c}{\sigma_t} = \frac{1+\sin\phi}{1-\sin\phi} } \] where \(\phi\) is the angle of internal friction.

Answer 1

The Correct Option is A

Step 1: Recall the Mohr--Coulomb strength relation. For a material obeying the Mohr--Coulomb failure criterion, the ratio of uniaxial compressive strength \((\sigma_c)\) to uniaxial tensile strength \((\sigma_t)\) is \[ \frac{\sigma_c}{\sigma_t} = \frac{1+\sin\phi}{1-\sin\phi}, \] where \(\phi\) is the angle of internal friction.

Step 2: Identify the correct option. Thus, \[ \boxed{ \frac{\sigma_c}{\sigma_t} = \frac{1+\sin\phi}{1-\sin\phi} } \] Hence, \[ \boxed{(A)} \] is the correct answer.