Question

The average permeability perpendicular 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.

I would like to ask this question from Permeability of Stratified Soil Deposits in division Permeability of Geotechnical Engineering I

Answer 1

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

Best explanation: For flow perpendicular to the bedding plane,

The head loss through the individual layers is different,

h=h1+h2+….+h3

Since the velocity is given by,

V=ki=kh/L

∴h=vz/k

vz/k=v1z1/k1+ v2z2/k2+….+ vnzn/kn

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