Question

A 10 m high slope of dry clay soil (unit weight = $20KN/m^3$), with a slope angle of ${45}^{\circ }$ and the circular slip surface, is shown in the figure (not drawn to the scale). The weight of the slip wedge is denoted by W. The undrained unit cohesion $\left(c_u\right)$ is 60 kPa.

The factor of safety of the slope against slip failure is

• A. 3.685
• B. 1.57
• C. 0.58
• D. 1.67

Answer 1

The correct option is A 3.685

Resisting moment per unit width

$=(C_u\times \theta \times r)\times r$

$=60\times \frac{\pi }{2}\times 10\times 10$

= 9424.778 kN-m/m

Overturning moment per unit width

= (Area of soil $\times$ Unit weight) $\times$ lever arm

$=(\frac{\pi }{4}\times {10}^2-\frac{1}{2}\times 10\times 10)\times 20\times 4.48$

= 2557.167 kN-m/m

$FOS=\frac{resistingmoment}{overturningmoment}$

$=\frac{9424.778}{2557.167}=3.685$