Find the ratio of average ( equivalent ) permeability in the horizontal direction to that of vertical direction of the soil deposit of three layers whose thickness ratio is 1:2:3. Assume the ?

To find the ratio of average permeability in the horizontal direction to that in the vertical direction, we need to consider the thickness ratio of the three layers.

Let's assume the thickness of the three layers is x, 2x, and 3x respectively.

The average permeability in the horizontal direction can be calculated by taking the harmonic mean of the permeabilities of the three layers. Let's denote the permeabilities of the three layers as k1, k2, and k3.

The average permeability in the horizontal direction (Kh) is given by:

Kh = 3 / (1/k1 + 1/k2 + 1/k3)

Similarly, the average permeability in the vertical direction (Kv) is given by:

Kv = 3 / (x/k1 + 2x/k2 + 3x/k3)

To find the ratio of Kh to Kv, we can divide Kh by Kv:

Kh/Kv = (3 / (1/k1 + 1/k2 + 1/k3)) / (3 / (x/k1 + 2x/k2 + 3x/k3))

Simplifying the expression:

Kh/Kv = (x/k1 + 2x/k2 + 3x/k3) / (1/k1 + 1/k2 + 1/k3)

Since the thickness ratio is 1:2:3, we can substitute x = 1, 2x = 2, and 3x = 3 into the expression:

Kh/Kv = (1/k1 + 2/k2 + 3/k3) / (1/k1 + 1/k2 + 1/k3)

Therefore, the ratio of average permeability in the horizontal direction to that in the vertical direction is (1/k1 + 2/k2 + 3/k3) / (1/k1 + 1/k2 + 1/k3).