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Permeability in Layered Soils - Vertical Flow

A stratified ...

Question

A stratified soil deposit has three layers of thicknesses : $z_{1} = 4, z_{2} = 1, z_{3} = 2$ units and the corresponding permeabilities of $k_{1} = 2, k_{2} = 1 a n d k_{3} = 4$ units, respectively. The average permeability perpendicular to the bedding planes will be

A

4

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B

2

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C

8

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D

16

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Solution

The correct option is B 2
$k_{e v} = \frac{z_{1} + z_{2} + z_{3}}{\frac{z_{1}}{k_{1}} + \frac{z_{2}}{k_{2}} + \frac{z_{3}}{k_{3}}}$

$= \frac{4 + 1 + 2}{\frac{4}{2} + \frac{1}{1} + \frac{2}{4}} = \frac{7}{3.5} = 2$

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