Question

The total active thrust on a vertical wall 3m high retaining a horizontal sand backfill (unit weight ${\gamma }_t=20KN/m^3$, angle of shearing resistance ${\varphi }^{\prime }={30}^{\circ }$) when the water table is at the bottom of the wall, will be:

• A. 30 KN/m
• B. 35 KN/m
• C. 40 KN/m
• D. 45 KN/m

Answer 1

The correct option is A 30 KN/m


$K_a=\frac{1-sin\varphi }{1+sin\varphi }=\frac{1-sin{30}^{\circ }}{1+sin{30}^{\circ }}=\frac{1}{3}$

Active earth pressure

$P_a=K_a\gamma Z-2C\sqrt{K_a}$

For sand, c = 0

$P_a=K_a\gamma Z$

$=\frac{1}{3}\times 20Z$

$=6.67Z:0\le$ Z $\le 3$ ... (i)

Plot expression (i)

Total active thrust

= Area under active earth pressure diag.

$=\frac{1}{2}\times 20\times 3=30KN/m$