Question Bank • QB_SWCE_ADV_108 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Active and passive earth pressures

Question Statement:

For a cohesionless backfill with an angle of internal friction $\phi = 30^\circ$, the ratio of Rankine's coefficient of passive earth pressure ($K_p$) to active earth pressure ($K_a$) is:

Options:

  • (A) 9.0
  • (B) 3.0
  • (C) 1.0
  • (D) 6.0

Answer Key:

A

Step-by-Step Solution & Explanation

1. Active coefficient: $K_a = \frac{1 - \sin 30^\circ}{1 + \sin 30^\circ} = \frac{1 - 0.5}{1 + 0.5} = \frac{1}{3}$ 2. Passive coefficient: $K_p = \frac{1 + \sin 30^\circ}{1 - \sin 30^\circ} = \frac{1 + 0.5}{1 - 0.5} = \frac{1.5}{0.5} = 3$ 3. Ratio: $\frac{K_p}{K_a} = \frac{3}{1/3} = 9.0$ Option A is correct.
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