When the movement of a wall under the earth pressure from the backfill was prevented, the coefficient of earth pressure was recorded as 0.5. The ratio of the coefficients of passive and active earth pressures of the backfill is
- A1/3
- B3
- C1/9
- D9Correct
Solution
Concept
At-rest, active and passive earth pressure coefficients
Formula
K0 = 1 − sin φ; Ka = (1 − sin φ)/(1 + sin φ); Kp = 1/Ka
Step-by-step solution
1. Wall movement prevented → at-rest condition: K0 = 0.5. 2. K0 = 1 − sin φ = 0.5 → sin φ = 0.5 → φ = 30°. 3. Ka = (1 − 0.5)/(1 + 0.5) = 1/3; Kp = 1/Ka = 3. 4. Kp / Ka = 3 / (1/3) = 9.
Explanation
When the wall cannot move, the pressure is the at-rest pressure. Using K0 = 1 − sin φ gives φ = 30°. Then the ratio of passive to active coefficients is 1/Ka² = 9.
Shortcut
Kp/Ka = 1/Ka² = ((1 + sin φ)/(1 − sin φ))² = 9 for φ = 30°.
Common mistake
Giving Kp (3) instead of Kp/Ka.
Correct answer: D) 9