The GATE Grind

GATE 2022 CE (CE1) – Question 41

Geotechnical Engineering · Earth pressure theories: Rankine and Coulomb, sheet piles · 2 marks · Multiple choice

As per Rankine’s theory, failure planes are inclined at $45^\circ+\phi/2$ to the minor-principal-stress direction. For which state is this correct?

  1. Only the active state and not the passive state
  2. Only the passive state and not the active state
  3. Both active as well as passive states
  4. Neither active nor passive state

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) Both active as well as passive states

Explanation

The Mohr–Coulomb failure-plane angle relative to the **minor-principal-stress direction** is $45^\circ+\phi/2$ irrespective of whether the soil is in the active or passive Rankine state.

The principal directions interchange between those states, which changes the angle relative to horizontal, but not the angle specified in the question. **Answer: C, both states**.