GATE 2024 CE (CE1) – Question 53
The total primary consolidation settlement ($S_c$) of a building constructed on a 10 m thick saturated clay layer is estimated to be 50 mm. After 300 days of the construction of the building, primary consolidation settlement was reported as 10 mm. The additional time (in days) required to achieve 50% of $S_c$ will be ______________________ (rounded off to the nearest integer).
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Correct answer: 1575
Explanation
After 300 days the degree of consolidation is $U = \frac{10}{50} = 20\%$. For $U < 60\%$ the time factor is $T_v = \frac{\pi}{4}U^2$, so $t \propto U^2$. The time for 50% is $t_{50} = 300 \times \left(\frac{0.5}{0.2}\right)^2 = 300 \times 6.25 = 1875$ days. The additional time is $1875 - 300 = 1575$ days.