Section 4: Soil and Water Conservation Engineering
Soil Compaction, Consolidation & Earth Pressures
Subtopic: Rankine active thrust on retaining wall
Question Statement:
A smooth vertical retaining wall of height $H = 5.5\text{ m}$ retains cohesionless sand with unit weight $\gamma = 18.0\text{ kN/m}^3$ and angle of internal friction $\phi = 30^\circ$. Assuming a horizontal backfill surface, the total Rankine active thrust per meter run of the wall is ________ $\text{kN/m}$ (round off to two decimal places).
Answer Key:
90.66
Step-by-Step Solution & Explanation
Rankine active earth pressure coefficient:
$K_a = \frac{1 - \sin 30^\circ}{1 + \sin 30^\circ} = \frac{1 - 0.5}{1 + 0.5} = \frac{1}{3} \approx 0.3330$
Total active thrust per unit length of wall:
$P_a = \frac{1}{2} K_a \gamma H^2 = \frac{1}{2} \times \frac{1}{3} \times 18.0 \times (5.5)^2 = 90.66\text{ kN/m}$