Question

An infinite slope is to be constructed in a soil. The effective stress strength parameters of the soil are c' = 0 and $\varphi ={30}^{\circ }$, the saturated unit weight of the slope is 20 $kN/m^3$ and the unit weight of water is 10$kN/m^3$. Assuming that seepage is occurring parallel to the slope, the maximum slope angle for a factor of safety of 1.5 would be

• A. ${10.89}^{\circ }$
• B. ${11.30}^{\circ }$
• C. ${12.48}^{\circ }$
• D. ${14.73}^{\circ }$

Answer 1

The correct option is A ${10.89}^{\circ }$

$FOS=\frac{Resistingforce}{Actuatingforce}$

$=\frac{c+\sigma tan\varphi }{\tau }=\frac{0+\gamma zco{s}^2\beta tan\varphi }{\gamma zsin\beta cos\beta }$

$FOS=\frac{{\gamma }_{sub}}{{\gamma }_{sat}}\times \frac{tan\varphi }{tan\beta }$

$1.5=\frac{(20-10)}{20}\times \frac{tan{30}^{\circ }}{tan\beta }$

$\beta ={10.89}^{\circ }$

Note: In calculation of resisting force we always take effective stress while in case of actuating force or destabilizing force we always take total stress.