Question

An unsupported excavation is made to the maximum possible depth in a clay soil having ${\gamma }_t$ = $18kN/m^3$, $C=100kN/m^2$, $\varphi ={30}^{\circ }$. The active earth pressure, according to Rankine's theory, at the base level of the excavation is

• A. $115.47kN/m^2$
• B. $54.36kN/m^2$
• C. $27.18kN/m^2$
• D. $13.0kN/m^2$

Answer 1

The correct option is A $115.47kN/m^2$

In an unsupported excavation maximum possible depth in a clay soil

$z=\frac{4c}{\gamma \sqrt{K_a}}$

$Given,{\gamma }_t=18kN/m^3$

$C=100kN/m^2$

$\varphi ={30}^{\circ }$

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

$z=\frac{4c}{\gamma \sqrt{K_a}}=\frac{4\times 100}{18\sqrt{\frac{1}{3}}}$

= 38.49 m

Active earth pressure at depth z

$P_a=K_a\gamma z-2c\sqrt{K_a}$

$=\frac{1}{3}\times 18\times 38.49-2\times 100\times \sqrt{\frac{1}{3}}$

$=115.47KN/m^2$