Earth Retaining Structures MCQ with answer and solution

Concept

Total active earth thrust on cantilever wall

Formula

P_a = 0.5 × K_a × γ × H², K_a = (1 - sinφ) / (1 + sinφ)

Step-by-step solution

1. Active earth pressure coefficient Ka = (1 - sin 30°) / (1 + sin 30°) = (1 - 0.5) / (1 + 0.5) = 1/3. 2. Unit weight γ = 18 kN/m³ and backfill height H = 4.5 m. 3. Active lateral pressure at base = Ka × γ × H = (1/3) × 18 × 4.5 = 27 kN/m². 4. Total active earth thrust Pa = 0.5 × (Ka × γ × H) × H = 0.5 × 27 × 4.5 = 60.75 kN/m. Answer: A

Explanation

According to Rankine's earth pressure theory for cohesionless soil with φ = 30 degrees, the active earth pressure coefficient Ka is (1 - sin 30) / (1 + sin 30) = 1/3. Total active thrust per unit run equals 0.5 × Ka × γ × H² = 0.5 × (1/3) × 18 × 4.5² = 60.75 kN/m.

Why the other options are wrong

B) 75 kN/m is an incorrect rounding or miscalculated Ka. C) 91.13 kN/m uses an incorrect soil friction angle. D) 101.25 kN/m uses passive coefficient or neglects 1/3 factor.

Shortcut

P_a = 0.5 × (1/3) × 18 × 4.5² = 3 × 20.25 = 60.75 kN/m.

Common mistake

Forgetting the 0.5 factor for triangular pressure distribution, giving 121.5 kN/m.