Question

A 6m height retaining wall having smooth vertical face and horizontal backfill. Top 3 m thick layer is sand $\varphi ={30}^{\circ }$ while the bottom layer is 3 m thick clay (C = 20 kPa). Assume unit weight for both sand and clay as $18kN/m^3$. The total active earth pressure per unit length of the wall (in K=kN/m) is

• A. 150
• B. 216
• C. 156
• D. 196

Answer 1

The correct option is A 150


$K_{a_1}=\frac{1-sin\varphi }{1+sin\varphi }=\frac{1}{3}$

$K_{a_2}=1$

$P_B=K_{a_1}\gamma z=\frac{1}{3}\times 18\times 3=18kN/m^2$

$P_{B^{\prime }}=K_{a_1}\gamma z-2c\sqrt{K_{a_2}}=14kN/m^2$

$P_c=K_{a_2}\gamma z-2c\sqrt{K_{a_2}}$

$=18\times 6-2\times 20\sqrt{1}=68kN/m^2$

Total active earth pressure 1 m length of wall,

$P_a=\frac{1}{2}\times 18\times 3+\frac{1}{2}(14+68)\times 3$

$=27+123=150kN/m^2$