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GATE 2022 CE (CE1) – Question 55

Geotechnical Engineering · Compaction and one-dimensional consolidation · 2 marks · Numerical answer

A raft foundation of 30 m × 25 m is proposed to be constructed at a depth of 8 m in a sand layer. A 25 m thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50 % consolidation settlement in 10 minutes. The time (in days) required for 25 % consolidation settlement of the raft foundation will be ____________________. (round off to the nearest integer)

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Correct answer: 1736

Explanation

Both the clay layer and lab sample have double drainage, so their drainage paths are 12.5 m and 0.0125 m, a ratio of 1000. For U≤60%, $T_v=\pi U^2/4$, giving $T_{25}/T_{50}=(.25/.5)^2=1/4$.

Since $t=T_vH_d^2/c_v$, field time is $10(1000)^2/4=2500000$ minutes = 1736.111 days. **Answer: 1736 days**.