GATE 2021 CE (CE1) – Question 33
Soil has cohesion c=15 kPa, friction angle φ=20° and unit weight γ=17.5 kN/m³. Find maximum unsupported excavation depth in m, to two decimals.
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Correct answer: 4.8 to 5
Explanation
For a vertical cut in cohesive-frictional soil, $H_c=4c/(\gamma\sqrt{K_a})$, where $\sqrt{K_a}=\tan(45^\circ-\phi/2)$. Substitution gives $H_c=60/[17.5\tan35^\circ]=4.89651$ m. **Answer: 4.90 m**.