Question Bank • QB_SWCE_SM_005 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Active and passive earth pressures

Question Statement:

A vertical smooth retaining wall of height $5.0\text{ m}$ supports a cohesionless sand backfill with unit weight $\gamma = 18\text{ kN/m}^3$ and internal friction angle $\phi = 30^\circ$. The ground surface is horizontal. The total Rankine active thrust per metre length of the wall in $\text{kN/m}$ is ________ (answer in integer).

Answer Key:

75

Step-by-Step Solution & Explanation

1. Rankine active earth pressure coefficient ($K_a$): $K_a = \frac{1 - \sin \phi}{1 + \sin \phi} = \frac{1 - \sin 30^\circ}{1 + \sin 30^\circ} = \frac{0.5}{1.5} = \frac{1}{3}$ 2. Total active thrust ($P_a$): $P_a = \frac{1}{2} K_a \gamma H^2 = \frac{1}{2} \times \frac{1}{3} \times 18 \times (5.0)^2 = 3 \times 25 = 75\text{ kN/m}$
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