Question

The coefficient of permeability of the two soil layers 1 and 2 in soil deposit is 9*10^-7 cm/s and 4*10^-7 cm/s respectively. The thickness of the layers is equal. The value of average permeability perpendicular to bedding planes is ________

(a) 4.5*10^-7 cm/s

(b) 5.5*10^-7 cm/s

(c) 6.5*10^-7 cm/s

(d) 7.5*10^-7 cm/s

The question was asked by my college professor while I was bunking the class.

I'm obligated to ask this question of Permeability of Stratified Soil Deposits in section Permeability of Geotechnical Engineering I

Answer 1

Right option is (b) 5.5*10^-7 cm/s

Easy explanation: Given,

K1=9*10^-7 cm/s

K2=4*10^-7 cm/s

Let the thickness of each layer be z,

Therefore the total thickness is 2z.

For flow perpendicular to the bedding plane,

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

\(K_z = \frac{2z}{\frac{z}{9*10^{-7}}+\frac{z}{4*10^{-7}}}\)

∴ Kz = 5.5*10^-7 cm/s.