Question

What will be its average permeability perpendicular to the bedding plane if a soil deposit has three layers of soil? The permeability of the second layer is 1/2 that of the first layer and the permeability of the third layer is 1/3 that of the first layer. The thickness of each layer is equal.

(a) k

(b) 1/2k

(c) 1/3k

(d) 1/4k

The question was posed to me in final exam.

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

Answer 1

The correct option is (b) 1/2k

Easiest explanation: Given,

Let the permeability of the three layers be k1, k2, and k3.

K1=k

K2=1/2k

K3=1/3k

And z1=z2=z3=z

For flow perpendicular to the bedding plane,

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

\(K_z = \frac{z}{\frac{z}{k}+\frac{2z}{k}+\frac{3z}{k}}=\frac{1}{2}k.\)