A gravity retaining wall of top width 1 m and base width 3 m and total height of 1.90 m is retaining dry cohesionless backfill of unit weight of 20 kN/m³ and angle of shearing resistance 30°. Then factor of safety against sliding will be (take γsoil = 22 kN/m³, tan 30 = 0.5)
- A2.3Correct
- B2.4
- C2.5
- D2.7
Solution
Concept
Sliding stability of a gravity wall
Formula
FS = μ ΣW / Pa; Pa = ½ Ka γ H²
Step-by-step solution
1. Ka = (1 - 0.5)/(1 + 0.5) = 1/3 2. Pa = 0.5 × (1/3) × 20 × 1.9² = 12.03 kN/m 3. Area of wall = (1 + 3)/2 × 1.9 = 3.8 m² 4. W = 3.8 × 22 = 83.6 kN/m (22 kN/m³ is taken as the wall unit weight) 5. μ = (2/3) × tan30° = (2/3) × 0.5 = 0.333 6. Resisting force = 0.333 × 83.6 = 27.87 kN/m 7. FOS = 27.87 / 12.03 = 2.32 ≈ 2.3
Explanation
The ratio of resisting to driving force depends on the height.
Shortcut
FS = μW/Pa.
Correct answer: A) 2.3