Question

The critical height for an unsupported vertical cut in cohesive soil is given by _____________

(a) \(H_c=\frac{q-2c cot⁡α}{γ} \)

(b) \(H_c=\frac{4c tan⁡α}{γ} \)

(c) \(H_c=\frac{4 cot⁡α}{γ} \)

(d) \(H_c=\frac{cot⁡α}{γ} \)

I got this question in an international level competition.

Question is taken from Active Earth Pressure of Cohesive Soils topic in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Correct answer is (b) \(H_c=\frac{4c tan⁡α}{γ} \)

For explanation: If a tension crack is developed at the top of wall to a depth Zo in cohesive soils, then the total net pressure is zero for a depth of 2Zo. This means that the soil will be able to stand with a vertical face up to a depth of 2Zo.

∴ The critical height  \(H_c=\frac{4c tan⁡α}{γ}. \)