Question

To have zero active pressure intensity at the top of a wall in a cohesive soil, one should apply a uniform surcharge intensity of: (Where $C =$ cohesion and $\alpha =$ angle of failure plane with major principal plane)

• A. $2C \tan \alpha$
• B. $2C \cot \alpha$
• C. $-2C \tan \alpha$
• D. $-2C \cot \alpha$

Hint:

For cohesive soils, a surcharge is often needed to neutralize negative active pressure at the top of retaining walls.

Answer 1

The Correct Option is A

Step 1: Active earth pressure in cohesive soil.
The general expression for active earth pressure at depth $z$ is: \[ p_a = \gamma z K_a - 2C \sqrt{K_a}, \] where $K_a = \tan^2\left(45^\circ - \frac{\phi}{2}\right)$ and $C$ is cohesion.

Step 2: Pressure at top of wall ($z=0$).
At $z=0$: \[ p_a = -2C \sqrt{K_a}. \] This becomes negative, meaning tension at top, which is not realistic.

Step 3: Apply surcharge $q$.
The modified expression is: \[ p_a = q K_a - 2C \sqrt{K_a}. \]

Step 4: Condition for zero pressure at top.
For $p_a = 0$: \[ q K_a = 2C \sqrt{K_a}. \] \[ q = \frac{2C}{\sqrt{K_a}} = 2C \tan \alpha. \]

Step 5: Conclusion.
Thus, the required uniform surcharge intensity is $2C \tan \alpha$.