Question

A vertical retaining wall of 5m height has to support soil having unit weight of $18KN/m^3$, effective cohesion of $12KN/m^2$, and effective friction angle of ${30}^{\circ }$, As per Rankine's earth pressure theory and assuming that a tension crack has occured, the lateral active thrust on the wall per meter length (in KN/m, round off to two decimal places), is

• A. 21.71

Answer 1

The correct option is A 21.71
If tension crack occur then -ve area of pressure diagram not considered.

Depth at which the pressure will be zero (Z)

$K_a\gamma Z-2C\sqrt{Ka}=0$

$\frac{1}{3}\times 18\times Z=2\times 12\times \sqrt{\frac{1}{3}}\{\begin{array}{c}{K}_a=\frac{1-sin30}{1+sin30}\\ =\frac{1}{3}\end{array}$

Z = 2.309 m

Preasure at bottom of soil

$=\frac{1}{3}\times 18\times 5-2\times 12\sqrt{\frac{1}{3}}$

= 16.14 kPa

So, lateral active thrust per meter

$=\frac{1}{2}\times 2.69\times 16.14$

= 21.71 kN/m