Civil Engineering Reference
In-Depth Information
14.3 Essentials of steady state seepage
Darcy's law governing flow of water through soil is very like Ohm's law for the flow
of electricity through a conducting material, and an electrical flow model can be used
to solve problems in groundwater seepage. In both cases a potential causes a current
to flow against a resistance so that electrical conductivity is analogous to permeability.
We have already seen that hydraulic potential is not the same as pore pressure and it
is necessary to include a term to take account of elevation.
To define hydraulic potential it is necessary to have a datum as in Fig. 14.3(a). Since
it is only changes of potential that matter the datum could be anywhere, but it is best to
put it low down to avoid negative values of potential. From Fig. 14.3(a), the potential
atAis
u
γ
P
=
h
w
+
z
=
w
+
z
(14.1)
(Note that this is simply Bernoulli's expression for total head since, in groundwater
seepage, the velocity terms are small compared with the pressure and elevation terms.)
In Fig. 14.3(b) the points A and B are
δ
s
apart on the same flowline and the hydraulic
gradient between A and B is
=−
δ
P
δ
i
(14.2)
s
The negative sign is introduced into Eq. (14.2) so that the hydraulic gradient is positive
in the direction of flow. (Note that in Fig. 6.12 and in Eq. (6.19) the hydraulic potential
and the hydraulic gradient were defined in terms of
h
w
only. This was allowable in that
case because the flowlines in Fig. 6.12 were horizontal and so the
z
term in Eq. (14.1)
remains constant. From now on we will work with potentials and hydraulic gradients
using Eqs. (14.1) and (14.2), taking account of pore pressure and elevation terms.)
Figure 14.4 shows part of a flownet with two flowlines AB and CD at an average
distance
δ
b
apart. The points A and C have the same potential and so do the
Figure 14.3
Pore pressure and potential.
