GATE 2020 CE (CE2) – Question 45
A 10 m high dry-clay slope has unit weight 20 kN/m³ and inclination 45°. The circular slip surface and wedge weight W are shown; undrained cohesion is 60 kPa. Find safety factor against slip.
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Correct answer: MTA
Explanation
For the indicated quarter-circle of radius 10 m, sliding area is $\pi10^2/4-10^2/2=28.5398$ m². Weight is 570.796 kN/m. Cohesive resisting moment is $60(5\pi)(10)=9424.778$ kN·m/m. Dividing by $W(4.48)$ gives about 3.69, absent from choices. The official key awards **marks to all**.