Question

Determine the total thrust on the back of a smooth vertical wall, 8m high, which is supporting granular backfill with bulk unit weight 18kN/m3 and angle of friction of 33 degrees. The soil surface is horizontal and the water table lies 2.2m below ground level. Assume the saturated unit weight of backfill is 22kN/m3 below water table. 

Answer 1

$k_a= \frac{1-sin 33}{1+sin 33}= 0.2948$

vertical pressure= $k_a. \gamma H$

1. 0.2948 $\times 18 \times 2.2 = 11.6741 KN/m^2$

$0.2948 \times 22 \times 5.8 = 37.616 KN/m^2$

pressure due to $\gamma_w . H_2= 9.81 \times 5.8 = 56.898 KN/m^2$

Total vertical thrust = $( \frac{1}{2} \times 11.6741 \times 2.2 ) + (11.6741\times 5.8) +(\frac{1}{2} \times 37.616\times 5.8) +(\frac{1}{2} \times 56.898\times 5.8)$

$P_a= 12.84151 +67.707978 +109.0864 +165.004= 354 KN$