The total active pressure due to dry backfill, acting at h/3 above the base, is directly proportional to:
Try it first: pick an option, then read the explanation.
Correct answer: C. H²
Asked in SSC JE (previous year paper)
Detailed Explanation
The pressure at depth z is p = Kaγz. The total force is the area of the triangular pressure diagram.
\[ P_a = \frac{1}{2} \times H \times K_a\gamma H = \frac{1}{2}K_a\gamma H^2 \]
Why “H²” Is Correct
Because the base of the triangle (KaγH) and its height (H) both grow with H, the area grows with H². Doubling the wall height makes the total thrust four times as large.
Why the Other Options Are Wrong
- A. 1/H²: The thrust increases with height; it is not inversely proportional.
- B. 1/H: Again it increases, not decreases, with H.
- D. H: Pressure at the base is proportional to H; the total thrust is proportional to H².
Key Point
Pressure ∝ H; thrust ∝ H²; overturning moment ∝ H³.
Key Concepts for Students
- Thrust acts at H/3 above the base.
- A uniform surcharge adds a term proportional to H (KaqH).
- Water pressure adds ½γwH² if the backfill is undrained.
Practice more: this is question 9 in Earth Pressure and Retaining Wall MCQs – Part 1. Try the whole set and check every answer instantly.