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required to let all water infiltrate is determined. At time
t
in the interval (0
,
t
e
), the
specific discharge is
q = k
(
h-d
)/
d
. Conservation of mass states that the total
volume of water remains unchanged; so,
V
= 0
=
(
h
n
d
)
A
, or
h = -n
d
. The
velocity of the infiltrating waterfront is
v = q/n =
d/
t
(
d
is the coordinate of the
t
e
0
n
moving front). Thus
t = n
d/q
and integration, according to
0
t =
h
0
d/q
,
yields after some elaborations
kt
e
=
h
0
f
(
n
), with
f
(
n
) = (1
n
).
Noticing that
f
is about 0.7 for 0.3 <
n
< 0.4, the final result becomes a simple
formula to estimate the permeability of an unsaturated soil layer in the field:
k =
0.7
h
0
/t
e
. Make a sketch of
f
(
n
) versus
n
. What is the effect of the capillary head?
n
log(
n
)/(1
n
))/(1
A
A
A
A
A
A
A
A
A
A
u
u
= 0
= 0
= 0
= 0
h
h
h
h
0
0
0
0
0
0
0
0
0
0
q
q
q
q
q
q
q
q
d
d
d
d
d
d
d
d
v
v
v
v
v
v
v
v
u
u
p = 0
u
= 0
p = 0
p = 0
u
= 0
p = 0
= 0
= 0
= 0
= 0
Figure 4.9 Field infiltration test
application 4.3
Consider a horizontal confined aquifer, i.e. a sandy layer with thickness
B
and
on top and underneath a relatively impervious layer. Somewhere a building pit is
required, the depth of which reaches in the sandy layer, and in order to create a dry
excavation with a surrounding of sheet piling, some pumping wells are being
applied. In the aquifer a natural seepage flow exists. The horizontal flow pattern is
calculated and visualised using a square net of flow lines and equipotentials, shown
in Fig 4.10. Making use of the geohydrological conditions, the use of three wells is
suitable to create a more or less equal drawdown at the proposed location of the
building pit.
The theory of square flow net provides a practical formula to determine the local
discharge using (4.13). Given
k =
10 m/day and layer thickness
B =
5 m, the
discharge of the large scale virtual well (Fig 4.10a) becomes
Q =
4
kB
(2.0-0.8)/3 =
80 m
3
/day. Note, that
M
= 4 (use all the flow lines towards the well) and that
h
and
N
are related (the drop over the chosen intervals). The discharges of the real
wells (Fig 4.10b) can be determined in the same way.
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