Earth Retaining Structures MCQ with answer and solution

Concept

Rankine theory finds stresses in a soil mass that is in a state of plastic equilibrium, which means it is just at the point of shear failure everywhere.

Formula

K_a = (1 - sin φ)/(1 + sin φ), K_p = (1 + sin φ)/(1 - sin φ)

Step-by-step solution

1. Rankine (1857) studied the stresses in a semi-infinite soil mass. 2. He considered the soil at the point of shear failure at every point. 3. This condition is called plastic equilibrium. 4. It gives the active and passive earth pressures. Answer is (D).

Explanation

Rankine theory assumes the whole soil mass is just about to fail in shear. This condition is called plastic equilibrium. The active and passive earth pressures are found from this state.

Why the other options are wrong

A: 'General state of equilibrium' is not a defined term in earth pressure theory. B: Local equilibrium means failure only at some points, but Rankine assumes failure in the whole mass. C: 'Limited equilibrium' is not the standard term. The correct term is plastic equilibrium.

Shortcut

Rankine means plastic equilibrium. Coulomb means wedge theory.

Common mistake

Mixing up 'limit equilibrium' (used in slope or wedge methods) with Rankine's plastic equilibrium.