Question

A retaining wall of 10 m with a smooth vertical back retains a purely cohesive fill unit weight of $18kN/m^3$ , cohesion is $30kN/m^2$. If the Backfill is fully submerged with unit weight of $20kN/m^3$ and additional pressure of $20kN/m^2$ is applied over large area on surface of Backfill, the percentage reduction in tension crack depth is ?

• A. 42%
• B. 40%
• C. 45%
• D. 32%

Answer 1

The correct option is B 40%


Initial dry state:
At Z =$Z_c$ :

${\sigma }_v=\gamma Z_c$ $\varphi =0^{\circ }$

$P_a=0$ $K_a=1$

$K_a{\sigma }_v-2c\sqrt{K_a}=0$

${\sigma }_v=\frac{2C}{\sqrt{K_a}}$

$Z_c=\frac{2C}{\gamma \sqrt{K_a}}=\frac{2\times 30}{18\times \sqrt{1}}=3.33mm$


Submerged condition:

At Z=$Z_c$:
$p_a=0$

$K_a({\gamma }^{\prime }{Z}_c+q)+{\gamma }_w{Z}_c=2C\sqrt{K_a}$

$q+{\gamma }_{sat}{Z}_c=2_c$

$Z_c=\frac{2c}{{\gamma }_{sat}}-\frac{q}{{\gamma }_{sat}}$

$=\frac{2\times 30}{20}-\frac{20}{20}$

$Z_c=2m$

$\therefore$ % reduction in tensile crack depth =$\frac{3.33-2}{3.33}\times 100=39.94\%\approx 40\%$