GATE 2025 CE (CE2) – Question 32
A 6 m thick clay stratum has drainage at both its top and bottom surface due to the presence of sand strata. The time to complete 50% consolidation is 2 years. The coefficient of volume change ($m_v$) is $1.51 \times 10^{-3}$ m$^2$/kN and unit weight of water is 9.81 kN/m$^3$.
The coefficient of permeability (in m/year) is ______ (round off to three decimal places).
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Correct answer: 0.003 to 0.023
Explanation
With drainage at both faces, the drainage path is $H_{dr} = \frac{6}{2} = 3$ m. For 50% consolidation the time factor is $T_v = 0.197$. Then $c_v = \frac{T_vH_{dr}^2}{t} = \frac{0.197 \times 9}{2} = 0.8865$ m²/year. The permeability is $k = c_vm_v\gamma_w = 0.8865 \times 1.51 \times 10^{-3} \times 9.81 = 0.0131$ m/year.