Question Bank • QB_SWCE_EXP_014 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Active and passive earth pressures

Question Statement:

A vertical retaining wall of height $5.0\text{ m}$ retains dry cohesionless backfill with unit weight $\gamma = 18\text{ kN/m}^3$ and angle of internal friction $\phi = 30^\circ$. According to Rankine's theory, the total active thrust per meter run of the wall in $\text{kN/m}$ is ________ (round off to 1 decimal place).

Answer Key:

75

Step-by-Step Solution & Explanation

1. Coefficient of active earth pressure $K_a$: $K_a = \frac{1 - \sin 30^\circ}{1 + \sin 30^\circ} = \frac{1 - 0.5}{1 + 0.5} = \frac{0.5}{1.5} = \frac{1}{3}$ 2. Total Rankine active thrust $P_a$: $P_a = \frac{1}{2} K_a \gamma H^2 = \frac{1}{2} \times \frac{1}{3} \times 18 \times 5.0^2 = 3 \times 25 = 75.0\text{ kN/m}$
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