For cohesionless sand at a depth of 6 m and with an angle of internal friction of 30°, the active lateral pressure intensity will be (take unit weight of dry sand as 19600 N/m³)
- A43·4 kN/m²
- B39·2 kN/m²Correct
- C36·4 kN/m²
- D33·2 kN/m²
Solution
Concept
Rankine active earth pressure
Formula
pa = Ka γ H, Ka = (1 − sinφ)/(1 + sinφ)
Step-by-step solution
1. Ka = (1 − 0.5)/(1 + 0.5) = 1/3. 2. pa = (1/3) × 19.6 × 6 = 39.2 kN/m².
Explanation
For a dry cohesionless backfill the active pressure intensity at depth H is Ka γ H.
Why the other options are wrong
The other values do not equal γH/3.
Shortcut
φ = 30° → Ka = 1/3.
Common mistake
Using Kp = 3 (gives 352.8 kN/m²).
Correct answer: B) 39·2 kN/m²