The passive earth pressure for a soil is ______.

Asked in SSC JE 06/06/2024 (Morning)

Detailed Explanation

Lateral earth pressure depends on how the wall moves relative to the soil:

Active: wall moves away from the soil; the soil ‘relaxes’ and pressure falls to a minimum.
At rest: no movement.
Passive: wall is pushed into the soil; the soil resists and pressure rises to a maximum.

\[ K_a = \frac{1-\sin\phi}{1+\sin\phi} \qquad K_p = \frac{1+\sin\phi}{1-\sin\phi} \]

For \(\phi = 30^\circ\): \(K_a = 1/3\), \(K_p = 3\), so passive pressure is 9 times the active pressure.

Why “always greater than active earth pressure” Is Correct

In the active case the soil's shear strength helps hold it up, reducing the pressure. In the passive case the shear strength has to be overcome, increasing it. So passive pressure is always greater than active (and than at-rest) pressure.

Earth pressure depends on how the wall moves. With no movement the soil is at rest (K₀). A very small movement away from the soil drops the pressure to the active value (K_a); a much larger movement into the soil raises it to the passive value (K_p). For φ = 30°: K_a = 1/3, K₀ ≈ 0.5, K_p = 3.

Why the Other Options Are Wrong

A. equal to active earth pressure: Active and passive pressures are equal only if φ = 0 and c = 0, which is not a real soil.
C. always less than the earth pressure at rest: Passive pressure is greater, not less, than the at-rest pressure.
D. equal to earth pressure at rest: It equals the at-rest pressure only with no movement, which is not the passive state.

Key Point

Ka < K0 < Kp. Passive is the largest.

Key Concepts for Students

Mobilising full passive pressure needs much more movement than active.
Passive resistance in front of a wall's toe helps resist sliding.
Kp/Ka = Kp² for Rankine's theory with level fill.

Practice more: this is question 3 in Earth Pressure and Retaining Wall MCQs – Part 1. Try the whole set and check every answer instantly.