Civil Engineering Reference
In-Depth Information
Figure 14.4
Flowlines and equipotentials.
points B and D. The lines AD and BD are called equipotentials (because they are
lines of equal potential) and the average distance between them is
s
. Flowlines and
equipotentials intersect at 90
◦
as shown. (The proof of this is given in textbooks on
hydraulics.)
Figure 14.4 represents two-dimensional seepage through isotropic soil in which the
value of
k
is the same in all directions and through a slice of unit thickness normal
to the page; all the discussion in this chapter is for two-dimensional seepage through
isotropic soil. The rate of flow (in cubic metres per second) between the two flowlines
is
δ
δ
q
and the mean seepage velocity (in metres per second) is
=
δ
q
V
(14.3)
δ
b
Darcy's law states that
V
=
ki
(14.4)
where
k
is the coefficient of permeability which has the units of velocity. Typical
values of
k
for soils were given in Sec. 6.10. Remember that for coarse-grained
soils
k
10
−
8
m/s; these very large dif-
ferences mean that coarse-grained soils with high permeability can act as drains
while fine-grained soils with very low permeability can be used as nearly watertight
barriers.
Notice that the seepage velocity
V
given by Eq. (14.4) is not the velocity of a drop
of water as it seeps through the pore spaces. From Fig. 14.5 the velocity of the drop
of water is
V
w
=
δ
10
−
2
m/s while for fine-grained soils
k
>
<
q
/
δ
w
, where
δ
w
is the area occupied by the pore spaces in an area
