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 twice that of the first layer and the permeability of the third layer is thrice that of the first layer. The thickness of each layer is 5m.

(a) 11k

(b) 18k

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

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

I have been asked this question in my homework.

The above asked question is from Permeability of Stratified Soil Deposits topic in division Permeability of Geotechnical Engineering I

Answer 1

The correct answer is (d) \(\frac{18}{11}k\)

Easy explanation: Given,

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

K1=k

K2=2k

K3=3k

And z1=z2=z3=5m

 For flow perpendicular to the bedding plane,

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

\(K_z = \frac{15}{\frac{5}{k}+\frac{5}{2k}+\frac{5}{3k}} = \frac{18}{11} k. \)