Question

A homogeneous anisotropic earth dam which is 20 m high, is constructed on an impermeable foundation. The coefficients of permeability of the soil used for the construction of the dam, in the horizontal and vertical directions are 4.8 $\times$ ${10}^{-8}m/s$ and 1.6 $\times$ ${10}^{-8}m/s$ respectively. The water level on the reservoir side is at 18m from the base of the dam; downstream side is dry. It is seen that there are 4 flow channels and 18 equipotential drops in a square flow net drawn in the transformed dam section. The quantity of seepage per unit length is _____ $\times$ ${10}^{-8}$ $m^3/s/m$ through the dam.

• A. 11.08

Answer 1

The correct option is A 11.08

Permeability in horizontal direction,

$k_x=4.8\times {10}^{-8}m/s$

Permeability in vertical direction,

$k_z=1.6\times {10}^{-8}m/s$

$N_f=4$

$N_d=18$

For the transformed section

k = $\sqrt{k_x{k}_z}$

= $\sqrt{4.8\times {10}^{-8}\times 1.6\times {10}^{-8}}$

or k = 2.77 $\times$ ${10}^{-8}m/s$

Seepage per unit length

$q=kh\frac{N_f}{N_d}$

$=2.77\times {10}^{-8}\times 18\times \frac{4}{18}$

$q=11.08\times {10}^{-8}{m}^3/s/m$