Stratification of soil is nothing but arranging it into

different layers based on similar properties. In general, natural soil deposits

are formed in stratified manner. Permeability of stratified soils or layered

soils is explained in this article.

In stratified soils, it is assumed that each individual layer is homogeneous and isotropic. The coefficient of permeability of each layer is different from other layers. So for this type of soils, the average coefficient of permeability for whole soil deposit is to be determined.

The average coefficient of permeability varies according to

the direction of flow. The direction of flow can be of two types as follows.

- Flow Parallel to Bedding Planes
- Flow Perpendicular to Bedding Planes

In both the cases assume a stratified soil mass of 3 layers

which thickness are Z_{1}, Z_{2 }and Z_{3} with coefficient

of permeability values K_{1}, K_{2} and K_{3} respectively.

## 1. Flow Parallel to Bedding Planes

Let Q be the total discharge through soil deposit and q_{1},

q_{2} and q_{3} are the discharges of individual layers.

When flow is parallel to the bedding planes, Total discharge

is the sum of individual layer discharges

Hence, Q = q_{1} + q_{2} + q_{3 }———–

Eq (1)

We know discharge is the product of area and velocity. Assume

Area of each layer is A_{1}, A_{2}, and A_{3}.

Area of entire soil deposit by considering width of soil

layer as unity.

A= A_{1} + A_{2} + A_{3} = (Z_{1} + Z_{2 }+ Z_{3}) x 1 = (Z_{1} + Z_{2 }+ Z_{3})

From Darcy’s law velocity is the product of the coefficient of permeability (k) and hydraulic gradient (i). When the flow is parallel to the bedding planes, Head loss (h) is constant for all layers hence the hydraulic gradient also constant for all the layers.

h = h_{1} = h_{2} = h_{3}

Hence, i_{1} = i_{2} = i_{3} = i

Let k_{H} = be the Average horizontal coefficient of

permeability for entire soil deposit.

Q = k_{H }. i . A

Similarly, q_{1 }= k_{1 }. i_{1}. A_{1}

q_{2 }= k_{2}. i_{2} . A_{2}

q_{3 }= k_{3 }. i_{3} . A_{3}

From equation (1),

k_{H }. i . A = k_{1 }. i_{1}. A_{1 }+ k_{2}. i_{2} . A_{2 }+ k_{3 }. i_{3} . A_{3 }————– equation (2)

By substituting and solving above expressions in equation

(2), average coefficient of permeability when flow is parallel to bedding plane

is obtained and it is expressed as

## 2. Flow Perpendicular to Bedding Planes

When flow is perpendicular to the bedding planes, Total head

loss is the sum of head loss through individual layers varies

h = h_{1} + h_{2} + h_{3 }———————

Equation (3)

Hence hydraulic gradient, i = i_{1} + i_{2} +

i_{3}

We know i = h/Z,Since Z is the length of flow in

this case.

Therefore head loss becomes h = i_{1}.Z_{1} + i_{2}. Z_{2} + i_{3}.Z_{3 }

If k_{v} = average vertical coefficient of permeability

Then from Darcy’s law, v = k_{v}.i = k_{v} .

(h/Z)

h

= vZ/k_{v}

Similarly, h_{1} = vZ_{1}/k_{1}

h_{2} = vZ_{2}/k_{2 }

and _{ }h_{3} = vZ_{3}/k_{3}

By substituting and solving above expressions in equation (3), The average vertical coefficient of permeability when flow is perpendicular to bedding planes in obtained and it is expressed as,