Geotechnical Engineering

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136 GEOTECHNICAL ENGINEERING

kn

k 3

k 2

k 1

hn

h 3

h 2

h 1

v hh
q

v
q

q 1

q 2

q 3

qn

Fig. 5.11 Flow parallel to the bedding planes
With the same notation as in the first case, the hydraulic gradient i will be the same for
all the layers as for the entire deposit. Since v = ki, and k is different for different layers, v will
be different for the layers, say, v 1 , v 2 , ... vn.


Also, v 1 = k 1 i ; v 2 = k 2 i ... and so on.
Considering unit dimension perpendicular to the plane of the paper, the areas of flow
for each layer will be plane of the paper, the areas of flow for each layer will be h 1 , h 2 , ... hn
respectively, and it is h for the entire deposit.
The discharge through the entire deposit is equal to the sum of the discharge through
the individual layers. Assuming kx to be the average permeability of the entire deposit parallel
to the bedding planes, and applying the equation :
q = q 1 + q 2 + ... + qn,


we have, kx · ih = k 1 i · h 1 + k 2 i · h 2 + ... kni · hn.


∴ kx =

kh kh k h
h

F 11 ++ 22 nn
HG

I
KJ
...(Eq. 5.35)

where h = h 1 + h 2 + ... + hn.


In other words, kx is the weighted mean value, the weights being the thickness for each
layer.
It can be shown that kx is always greater than kz for a given situation.

*5.9 Capillarity

The phenomenon in which water rises above the ground water table against the pull of grav-
ity, but is in contact with the water table as its source, is referred to as ‘Capillary rise’ with
reference to soils. The water associated with capillary rise is called ‘capillary moisture’. The
phenomenon by virtue of which a liquid rises in capillary tubes is, in general, called ‘capillarity’.
All voids in soil located below the ground water table would be filled with water (except
possibly for small pockets of entrapped air or gases). In addition, soil voids for a certain height
above the water table will also be completely filled with water. This zone of saturation above
the water table is due to capillary rise in soil. Even above this zone of full saturation, a condi-
tion of partial saturation exists. The zone of soil above the water table in which capillary water
rises is denoted as the ‘capillary fringe’.
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