Question

A fully submerged infinite sandy slope has an inclination of ${30}^{\circ }$ with the horizontal. The saturated unit weight and effective angle of internal friction of sand are $18KN/m^3$ and ${38}^{\circ }$, respectively. The unit weight of water is 10 KN/$m^3$. Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is

• A. 0.6014

Answer 1

The correct option is A 0.6014
$\text{Inclination of slope}\beta ={30}^{\circ }$

$\text{Friction angle}\varphi ={38}^{\circ }$

${\gamma }_{sat}=18KN/m^3$

${\gamma }_w=10KN/m^3$

Factor of safety against shear failure when seepage is parallel to the slope

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

${\gamma }_{sub}={\gamma }_{sat}-{\gamma }_w$

= 18 - 10

$=8KN/m^3$

$=\frac{8\times tan{38}^{\circ }}{18\times tan{30}^{\circ }}$

= 0.6014