Question

Two different soil types (soil 1 and soil 2) are used as backfill behind a retaining wall as shown in the figure, where ${\gamma }_t$ is total unit weight, and C' ${\varphi }^{\prime }$ are effective cohesion and effective angle of shearing resistance. The resultant active earth force per unit length (in kN/m) acting on the wall is:

• A. 31.7
• B. 35.2
• C. 51.8
• D. 57.0

Answer 1

The correct option is A 31.7

For soil - 1

$K_{a_1}=\frac{(1-sin{30}^{\circ })}{(1+sin{30}^{\circ })}=\frac{1}{3}$

For soil - 2

$K{a}_2=\left(\frac{1-sin{40}^{\circ }}{1+sin{40}^{\circ }}\right)$

= 0.217

$\therefore F=(F_{a_1}+F_{a_2})$

$=\frac{1}{2}\times 10\times 2+\frac{(8.64+6.51+6.51)}{2}\times 2\times 1$

= 10 + 21.7

= 31.7 kN/m