If a cantilever retaining wall is to retain soil to its full height H, for the analysis of bending moment at its base, the distance from the base where the total force due to backfill acts is:

Asked in SSC JE 09/10/2023 (Morning)

Detailed Explanation

For a level, dry, cohesionless backfill, the lateral pressure at depth z is p = K_aγz. It is zero at the top and largest at the base, so the pressure diagram is a triangle.

\[ P_a = \tfrac{1}{2}K_a\gamma H^2 \quad\text{acting at } \frac{H}{3} \text{ above the base} \]

\[ M_{\text{base}} = P_a \times \frac{H}{3} = \frac{K_a\gamma H^3}{6} \]

Why “0.33 H” Is Correct

The resultant of a triangular load acts through the triangle's centroid, which is one third of the height from the wide end. So the total force acts at H/3 = 0.33H above the base, and that lever arm is used for the stem's bending moment.

Active earth pressure on a smooth vertical wall retaining dry cohesionless soil of height H. Pressure grows linearly with depth to K_aγH at the base, so the diagram is a triangle. Its area gives the total thrust P_a = ½K_aγH², acting through the centroid at H/3 above the base.

Why the Other Options Are Wrong

A. H: At H (the top) the pressure is zero.
B. 0.5 H: 0.5H is the line of action for a uniform (rectangular) pressure, such as a surcharge.
D. 0.25 H: 0.25H does not correspond to the centroid of a triangle.

Key Point

Triangular pressure → resultant at H/3. Uniform surcharge pressure → at H/2.

Key Concepts for Students

Base moment grows with H³, so tall cantilever walls quickly need counterforts.
With water behind the wall, the water pressure triangle adds γwH²/2 at H/3.
Cohesion reduces the pressure near the top (tension zone).

Practice more: this is question 6 in Earth Pressure and Retaining Wall MCQs – Part 1. Try the whole set and check every answer instantly.