Question

As per Rankine's theory of earth pressure, the inclination of failure planes is \[ \left( 45^\circ + \frac{\phi}{2} \right) \] with respect to the direction of the minor principal stress. The above statement is correct for which one of the following options?

• A. Only the active state and not the passive state
• B. Only the passive state and not the active state
• C. Both active as well as passive states
• D. Neither active nor passive state

Hint:

Rankine's earth pressure theory applies the same formula for failure plane inclination in both active and passive conditions.

Answer 1

The Correct Option is C

Rankine's theory of earth pressure provides a relationship for the angle of inclination of the failure plane with respect to the direction of the minor principal stress. The formula applies to both active and passive states in earth pressure, as the failure plane's angle of inclination is the same for both states. Therefore, the correct answer is both active and passive states.

Step 1: Understand the formula.
The angle of inclination of the failure planes is determined using \( 45^\circ + \frac{\phi}{2} \), where \( \phi \) is the angle of internal friction. This is true for both active and passive conditions.

Step 2: Verify the options.
- (A) Only the active state: Incorrect, as the formula applies to both states.
- (B) Only the passive state: Incorrect, as the formula applies to both states.
- (C) Both active and passive states: Correct, as it applies to both conditions.
- (D) Neither active nor passive state: Incorrect.

Final Answer: (C) Both active as well as passive states