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A stratified soil deposit has three layers of thicknesses: z1 = 4, z2 - 1, z3 = 2 units and the corresponding permeabilities of k1 = 2, k2 = 1 and k3 = 4 units, respectively. The average permeability perpendicular to the bedding planes will be
  • a)
    4
  • b)
    2
  • c)
    8
  • d)
    16
Correct answer is option 'B'. Can you explain this answer?
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A stratified soil deposit has three layers of thicknesses: z1 = 4, z2 ...
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A stratified soil deposit has three layers of thicknesses: z1 = 4, z2 ...
Solution:

Given,
Thickness of first layer, z1 = 4 units
Thickness of second layer, z2 = 1 units
Thickness of third layer, z3 = 2 units
Permeability of first layer, k1 = 2 units
Permeability of second layer, k2 = 1 units
Permeability of third layer, k3 = 4 units

We need to find out average permeability perpendicular to the bedding planes.

To calculate the average permeability, we will use the following formula:

Kavg = (z1k1 + z2k2 + z3k3) / (z1 + z2 + z3)

Substituting the given values in the above formula, we get:

Kavg = (4 x 2 + 1 x 1 + 2 x 4) / (4 + 1 + 2)

Kavg = (8 + 1 + 8) / 7

Kavg = 17 / 7

Kavg = 2.43

Therefore, the average permeability perpendicular to the bedding planes is 2.43 units.

But none of the given options match with the calculated value.

So, we need to choose the closest option to the calculated value, which is option B, i.e., 2.
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