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GATE 2021 CE (CE1) – Question 57

Geotechnical Engineering · Stability of slopes · 2 marks · Numerical answer

For a 15 m purely cohesive slope, cu=75 kPa. A trial circle of radius 25 m subtends 60°; the sliding mass weighs 2500 kN/m with line of action 10 m horizontally from the toe, vertically below the circle centre. Find undrained factor of safety to two decimals.

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Correct answer: 1.94 to 1.98

Explanation

Slip arc length is $r\theta=25\pi/3$ m. Resisting moment is $c_u(r\theta)r=75(25\pi/3)(25)$. Driving moment about the circle centre is W×10=25000 kN·m/m. Their ratio is **1.96350≈1.96**. The slope angle and height are already reflected in the supplied trial-circle geometry.