Geotechnical Engineering

DHARM

SEEPAGE AND FLOW NETS 177

lB

bB

aA

aB aB

kB

b lA

k A

A

Fig. 6.11 Flow at the boundary between two soils

qA = qB

But qA = kA. ∆h

lA

. bA

qB = kB. ∆h

lB

. bB

∴ kA. ∆h

lA

. bA = kB. ∆h
lB
. bB

l

b

l

b

A

A A

B

B B

==tanαα$$tan

kkA

A

B

tanαα$$tan B

=

tan

tan

$

$

α

α

A

B

A

B

k

k

=

Anisotropic Soil

Laplace’s equation for flow through soil, Eq. 6.4, was derived under the assumption that per-
meability is the same in all directions. Before stipulating this condition in the derivation, the
equation was:

kx. ∂

∂

∂

∂

2

2

2

2 0

h

x

k h

z z

+=. ...(Eq. 6.3)

This may be reduced to the form:

∂

∂

∂

∂

2

2

2

2

h

z

h

k

k

z x

x

+

F

HG

I

KJ

= 0 ...(Eq. 6.10)

By changing the co-ordinate x to xT such that xT =

k

k

z

x

. x, we get

∂

∂

∂

∂

2

2

2

2

h

z

h

xT

+ = 0 ...(Eq. 6.11)

which is once again the Laplace’s equation in xT and z.

In other words, the profile is to be transformed according to the relationship between x
and xT and the flow net sketched on the transformed section.