Question

The coefficient of permeability of a soil in x and y direction is
2.3x10 cm/sec and 1.8x10-3 cm/sec. Given the equivalent
permeability for a 3-D flow is 1.94x10 cm/sec, estimate the
permeability of soil in z direction.

Answer 1

Answer:

The correct question is : The coefficient of permeability of a soil in x and y direction is 2.3x10-3 cm/sec and 1.8x10-3 cm/sec.the equivalent permeability for a 3-D flow is 1.94x10-3 cm/sec, estimate the permeability of soil in z direction

Explanation:

kx = 2.3*10-3 cm/sec

ky = 1.8*10-3 cm/sec

keq = 1.94*10-3 cm/sec

to fine:

Coefficient of permeability of a soil in z direction.

Solution :

Consider thickness of soil sample in x , y and z directions be H.

Parallel system

keq = Eki zi

Zzi

1.94*10-3 = (2.3*10-3*H) + (1.8*10-3*H) + (kz*H) 3H 1.94*10-3 = 2.3*10-3 + 1.8*10-3 + kz 3 kz = (1.94*10-3)*3 (2.3*10-3 +1.8*10-) kz = 5.82*10-3 - 4.1*10-3 kz = 1.72*10-3 cm/sec

Therefore, the coefficient of permeability of a soil in z direction is 1.72*10-3 cm/sec.