GATE 2020 CE (CE1) – Question 58
A submerged 10 m clay layer rests on 3 m sand over an impervious stratum as shown. A 2 m fill of unit weight 20 kN/m³ is placed above the clay. Clay $c_v=9\times10^{-2}$ m²/year and $m_v=2.2\times10^{-4}$ m²/kN. Use Taylor’s time-factor/average-consolidation relation. Find settlement after 10 years (mm), to two decimals.
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Correct answer: 18.4 to 19.5
Explanation
Final settlement is $m_v\Delta\sigma H=0.00022(40)(10)=0.088$ m. Double drainage gives $H_{dr}=5$ m. Then $T_v=c_vt/H_{dr}^2=0.036$, and Taylor’s low-U relation gives $U=\sqrt{4T_v/\pi}=0.214095$. Settlement is $88U=\mathbf{18.84}$ mm.