Civil Engineering Reference
In-Depth Information
14.5 Flownet for two-dimensional seepage
A solution to any problem in two-dimensional steady state seepage can be found by
drawing a flownet with curvilinear squares. This must be a proper scale drawing with
the correct boundary conditions. The solution gives the rate of flow from Eq. (14.9)
and the distribution of pore pressure from Eq. (14.1). Techniques for constructing
flownets by sketching, by electrical models and by numerical analysis are covered in
textbooks on hydraulics. All I will do here is find solutions to two simple cases to
illustrate the general principles.
In Fig. 14.7 water seeps from a river into a trench supported by walls and which is
pumped dry. The geometry is symmetric about the centre-line. The flow is confined so
there is no phreatic surface. If a standpipe is placed with its tip just at the ground level,
such as at G or at C, water will rise to the river level or the pumped level: therefore AG
is an equipotential with value
P
1
and similarly CF is an equipotential with value
P
2
.
Any impermeable boundary, such as the wall and the rock surface, must be a flowline
and so is the axis of symmetry; therefore, ABC and DEF are flowlines because flowlines
cannot cross. A roughly sketched flownet is shown in Fig. 14.7(b). This satisfies the
boundary conditions in Fig. 14.7(a); flowlines and equipotentials are orthogonal and
each element is more or less 'square' with approximately equal length and breadth.
For this flownet the total number of flow channels is
N
f
=
8 (i.e. four on each side of
the centre-line) and the number of equipotential drops is
N
d
=
10.
In Fig. 14.8 water seeps through a soil embankment dam to a drain in the down-
stream toe. The flow is unconfined and there is a phreatic surface in a position
approximately as shown by the broken line. If a standpipe is placed with its tip
anywhere on the upstream face, water will rise to the reservoir level so AB is an
equipotential with value
P
1
. Similarly, the drain CD is an equipotential with value
P
2
.
Figure 14.7
Flownet for steady state flow into a trench excavation.
