Question

The average permeability parallel to the bedding planes is given by________

(a) \(k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}*\frac{1}{2} \)

(b) \(k = \frac{1}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}} \)

(c) \(k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}} \)

(d) \(k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z} \)

This question was addressed to me in an interview for job.

My question is from Permeability of Stratified Soil Deposits topic in section Permeability of Geotechnical Engineering I

Answer 1

The correct choice is (d) \(k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z} \)

To explain I would say: For flow parallel to the bedding plane,

Total discharge=sum of discharge through the individual layers

q=q1+q2+…+qn

q=kiz=k1 z1+k2 z2+⋯.+kn zn

∴ \(k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}. \)