Geotechnical Engineering

DHARM

SEEPAGE AND FLOW NETS 187

d

x

F

AB

Top flow line

ht E

a z

a sina

a

J

Fig. 6.22 Schaffernak and Iterson’s solution for α < 30°

But dz/dx = tan α and z = a sin α

∴ q = k. a sin α tan α ...(Eq. 6.24)

Also,

k.

dz

dx. z. dx = ka sin α tan α. dx

or a sin α tan α dx = zdz

Integrating between the limits x = d to x = a cos α

and z = ht to z = a sin α

We have a sin α tan α

d

a

h

a

dx z dz

t

cos sin

αα

zz=

a sin α tan α (a cos α – d) =

(sinah^22 t^2 )

2

α−

From this, we have:

a =

dd ht

cosα cos ααsin

2

2

2

− 2 ...(Eq. 6.25)

*6 .7 Radial Flow Nets

A case of two-dimensional flow, called ‘radial flow’, occurs when the flow net is the same for all
radial cross-sections through a given axis. This axis may be the centre line of a well, or any
other opening that acts as a boundary of cylindrical shape to saturated soil. The direction of
flow at every point is towards some point on the axis of symmetry. The flow net for such a
section is called ‘radial flow net’.
A well with an impervious wall that extends partially through a previous stratum con-
stitutes an example of radial flow and is shown in Fig. 6.23.
The width of flow path, b, multiplied by the distance normal to the section, 2πr, is the
area of the flow 2πrb. The flow through any figure of the flow net is

∆Q = k. ∆h

l

. 2πrb

or ∆Q = 2πk(∆h) (rb/l) ...(Eq. 6.26)