GATE 2020 CE (CE1) – Question 56
A 5 m high vertical retaining wall supports soil with unit weight 18 kN/m³, effective cohesion 12 kPa and effective friction angle 30°. Using Rankine theory and assuming a tension crack has occurred, find active thrust per wall length (kN/m), to two decimals.
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Correct answer: 21 to 23
Explanation
Rankine coefficient is $K_a=(1-\sin30^\circ)/(1+\sin30^\circ)=1/3$. Tension-crack depth is $z_c=2c/(\gamma\sqrt{K_a})=2.3094$ m. Base pressure is $K_a\gamma H-2c\sqrt{K_a}=16.1436$ kPa. Positive thrust is triangular: $(H-z_c)(16.1436)/2=\mathbf{21.72}$ kN/m.