Geotechnical Engineering

DHARM

172 GEOTECHNICAL ENGINEERING

6.3.3 Flow through Earth Dam

The flow through an earth dam differs from the other cases in that the top flow line is not know

in advance of sketching the flow net. Thus, it is a case of unconfined flow. The determination of

the top flow line will be dealt with in a later section.

The top flow line as well as the flow net will be dependent upon the nature of internal

drainage for the earth dam. Typical cases are shown in Fig. 6.8; the top flow line only is shown.

Assuming that the top flow line is determined, a typical flow net for an earth dam with

a rock toe, resting on an impervious foundation is shown in Fig. 6.9:

B

A

Impervious D

Rock toe

CC

Fig. 6.9 Flow net for an earth dam with rock toe (for steady state seepage)
AB is known to be an equipotential and AD a flow line. BC is the top flow line; at all
points of this line the pressure head is zero. Thus BC is also the ‘phreatic line’; or, on this line,
the total head is equal to the elevation head. Line CD is neither an equipotential nor a flow
line, but the total head equals the elevation head at all points of CD.

6.4 Basic Equation for Seepage

The flow net was introduced in an intuitive manner in the preceding sections. The equation for

seepage through soil which forms the theoretical basis for the flow net as well as other meth-

ods of solving flow problems will be derived in this section.

The following assumptions are made:

1. Darcy’s law is valid for flow through soil.


2. The hydraulic boundary conditions are known at entry and exit of the fluid (water)
   into the porous medium (soil).


3. Water is incompressible.


4. The porous medium is incompressible.
   These assumptions have been known to be very nearly or precisely valid.
   Let us consider an element of soil as shown in Fig. 6.10, through which laminar flow of
   water is occurring:
   Let q be the discharge with components qx, qy and qz in the X-,Y- and Z-directions
   respectively.
   q = qx + qy + qz, obviously.