GATE 2023 CE (CE1) – Question 56
A soil having the average properties, bulk unit weight = 19 kN/m$^3$; angle of internal friction = 25° and cohesion = 15 kPa, is being formed on a rock slope existing at an inclination of 35° with the horizontal. The critical height (in m) of the soil formation up to which it would be stable without any failure is _____ (round off to one decimal place).
[Assume the soil is being formed parallel to the rock bedding plane and there is no ground water effect.]
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 4.97 to 5.03
Explanation
For an infinite slope with cohesion, the critical height is $H_c = \frac{c}{\gamma\cos^2 i(\tan i - \tan\phi)} = \frac{15}{19 \times \cos^2 35° \times (\tan 35° - \tan 25°)} = \frac{15}{19 \times 0.671 \times (0.7002 - 0.4663)} = \frac{15}{2.982} = 5.0$ m.