Question

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 the unit weight of water is \(9.81\ {kN/m}^3\).
The coefficient of permeability (in m/year) is __________ (round off to three decimal places).
 

Hint:

For consolidation with double drainage, use half the thickness of the layer as the drainage path and apply time factor equations accurately.

Answer 1

For double drainage (top and bottom), the drainage path length: \[ d = \frac{H}{2} = \frac{6}{2} = 3\ {m} \] Time factor for 50\% consolidation: \[ T_v = \frac{\pi}{4} \times (0.5)^2 = 0.196 \] The time factor is also defined as: \[ T_v = \frac{C_v \cdot t}{d^2} = \frac{k \cdot t}{m_v \cdot \gamma_w \cdot d^2} \] Rearranging for permeability \(k\): \[ k = \frac{T_v \cdot m_v \cdot \gamma_w \cdot d^2}{t} \] Substitute the values: \[ k = \frac{0.196 \times 1.51 \times 10^{-3} \times 9.81 \times 3^2}{2} \approx 0.013\ {m/year} \] Hence, the coefficient of permeability is \( \boxed{0.013\ {m/year}} \).