Permeability of Stratified Soil Deposits

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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.

Layers of Stratified Soil
Fig 1: Layers of Stratified Soil

The average coefficient of permeability varies according to
the direction of flow. The direction of flow can be of two types as follows.

  1. Flow Parallel to Bedding Planes
  2. Flow Perpendicular to Bedding Planes

In both the cases assume a stratified soil mass of 3 layers
which thickness are Z1, Z2 and Z3 with coefficient
of permeability values K1, K2 and K3 respectively.

1. Flow Parallel to Bedding Planes

Let Q be the total discharge through soil deposit and q1,
q2 and q3 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 = q1 + q2 + q3 ———–
Eq (1)

We know discharge is the product of area and velocity. Assume
Area of each layer is A1, A2, and A3.

Area of entire soil deposit by considering width of soil
layer as unity.

A= A1 + A2 + A3 = (Z1 + Z2 + Z3) x 1 = (Z1 + Z2 + Z3)

Flow Parallel to Bedding Planes
Fig 2: Flow Parallel to Bedding Planes

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 = h1 = h2 = h3

Hence, i1 = i2 = i3 = i

Let kH = be the Average horizontal coefficient of
permeability for entire soil deposit.

Q = kH . i . A

Similarly, q1 = k1 . i1. A1

q2 = k2. i2 . A2

q3 = k3 . i3 . A3

From equation (1),

kH . i . A = k1 . i1. A1 + k2. i2 . A2 + k3 . i3 . A3 ————– 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 = h1 + h2 + h3 ———————
Equation (3)

Hence hydraulic gradient, i = i1 + i2 +
i3

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

Therefore head loss becomes h = i1.Z1 + i2. Z2 + i3.Z3

Flow Perpendicular to Bedding Planes
Fig 3: Flow Perpendicular to Bedding Planes

If kv = average vertical coefficient of permeability

Then from Darcy’s law, v = kv.i = kv .
(h/Z)

                                                h
= vZ/kv

Similarly, h1 = vZ1/k1

h2 = vZ2/k2

and  h3 = vZ3/k3

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,



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