GATE 2021 CE (CE1) – Question 55
A 10 m retaining wall weighs 5000 kN/m. Clay backfill has γ=17.2 kN/m³, c=30 kPa and φ=0°. Base friction angle is 20°. The tension crack fills with water (γw=9.81). Ignore passive pressure from the 2 m clay in front. Find sliding factor of safety to two decimals.
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Correct answer: 4.20 to 4.35
Explanation
Rankine Ka=1 and tension-crack depth $z_c=2c/\gamma=3.48837$ m. Soil thrust is $\tfrac12\gamma(H-z_c)^2=364.651$ kN/m; crack-water thrust is $\tfrac12\gamma_wz_c^2=59.6856$ kN/m. Base friction resistance is $5000\tan20^\circ=1819.851$ kN/m. Therefore FS=$1819.851/(364.651+59.6856)=\mathbf{4.29}$.