GATE 2016 CE (CE1) – Question 23
A vertical cut is made in soil of cohesion $c$, friction angle $\phi$ and unit weight $\gamma$. With active and passive earth-pressure coefficients $K_a,K_p$, the maximum unsupported depth is ______.
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Correct answer: (D) $4c/(\gamma\sqrt{K_a})$
Explanation
Rankine active pressure is σh=Kaγz−2c sqrt(Ka). Integrating over height H gives resultant Pa=KaγH²/2−2cH sqrt(Ka). At the limiting unsupported height the resultant becomes zero, giving Hc=4c/(γ sqrt(Ka)). This is **D**, under the ideal homogeneous-soil assumptions of the model.