GATE 2020 CE (CE2) – Question 56
A 2 m × 2 m footing transfers pressure 200 kPa at depth 1.5 m as shown. Clay is normally consolidated, with specific gravity 2.65 and compression index 0.3. Using 2:1 vertical-to-horizontal load spread and water unit weight 10 kN/m³, find clay primary consolidation settlement (mm), to two decimals.
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Correct answer: 74 to 76
Explanation
Clay midpoint is 1.75 m below the footing base. Initial effective stress is $2(15)+0.5(18-10)+0.75(17-10)=39.25$ kPa. Saturated-clay void ratio is $(26.5-17)/(17-10)=1.357143$. The 2:1 spread gives $\Delta\sigma=200(2\cdot2)/(2+1.75)^2=56.88889$ kPa. Then $$S=\frac{0.3(1.5)}{1+1.357143}\log_{10}\frac{39.25+56.88889}{39.25}.$$ This yields **74.27 mm**.