Geotechnical Engineering

DHARM

168 GEOTECHNICAL ENGINEERING

heads at elevations 700 mm and 300 mm are 100 mm and – 140 mm, respectively, as shown at
the left of the flow net.

Finally, let us see how to use the flow net to determine the hydraulic gradient at any
point in the flow net. The gradient for any square is given by h/l, where h is the head lost for
the square and l is the length in which it is lost. Thus for all the squares in the flow net which
are of the same size, the hydraulic gradient is given by (H/10) × (1/l) or

1600

10

1

100

× = 1.6.

The example selected is so simple that these quantities could have been obtained easily
even without the flow net. For complex two-dimensional flow situations, the techniques just
described may be applied even for complex flow net patterns.

The values of flow, head, and gradient are exactly correctly when obtained from an
exactly correct flow net ; thus, the results can be only as accurate as the flow net itself is. The
flow net is a valuable tool in that it gives insight into the flow problem.

6.3 FLOW NET FOR TWO-DIMENSIONAL FLOW

It may be necessary to use flow nets to evaluate flow, where the directions of flow are irregu-
lar, or where the flow boundaries are not well-defined. Flow nets are a pictorial method of
studying the path of the moving water.

In moving between two points, water tends to travel by the shortest path. If changes in
direction occur, the changes take place along smooth curved paths. Equipotential lines must
cross flow lines at right-angles since they represent pressure normal to the direction of flow.
The flow lines and equipotential lines together form the flow net and are used to determine the
quantities and other effects of flow through soils.

During seepage analysis, a flow net can be drawn with as many flow lines as desired.
The number of equipotential lines will be determined by the number of flow lines selected.
Generally speaking, it is preferable to use the fewest flow lines that still permit reasonable
depiction of the path along the boundaries and within the soil mass. For many problems, three
or four flow channels (a channel being the space between adjacent flow lines) are sufficient.

In this section the flow nets for three situations involving two-dimensional fluid flow
are discussed. The first and second—flow under a sheet pile wall and flow under a concrete
dam—are cases of confined flow since the boundary conditions are completely defined. The
third—flow through an earth dam—is unconfined flow since the top flow line is not defined in
advance of constructing the flow net. The top flow line or the phreatic line has to be deter-
mined first. Thereafter, the flow net may be completed as usual.

6.3.1 Flow under Sheet Pile Wall

Figure 6.2 shows a sheet pile wall driven into a silty soil. The wall runs for a considerable
length in a drirection perpendicular to the paper; thus, the flow underneath the sheet pile wall
may be taken to be two-dimensional.

The boundary conditions for the flow under the sheet pile wall are; mb, upstream
equipotential; jn, downstream equipotential; bej, flow line and pq, flow line. The flow net