Question

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. What will be its average permeability parallel to the bedding plane?

(a) 11k

(b) 18k

(c) \(\frac{11}{18}k\)

(d) \(\frac{18}{11}k\)

I had been asked this question in an interview.

My doubt stems from Permeability of Stratified Soil Deposits in chapter Permeability of Geotechnical Engineering I

Answer 1

The correct choice is (c) \(\frac{11}{18}k\)

The explanation is: 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 parallel to the bedding plane,

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

\(K_x=\frac{zk+\frac{zk}{2}+\frac{zk}{3}}{3z}\)

∴ Kx=\(\frac{11}{18}k\).