Geoscience Reference
In-Depth Information
0 . 4
θ
0 . 3
0 cm
3 9 c m
−
0 . 2
0 . 1
−
6 0 c m
0
0
1
2
xt
−
1 / 2
( c m m i n
−
1 / 2
)
Fig. 9.9 Comparison between soil moisture profiles during sorption, namely water content
θ
as a
function of
φ
(
≡
xt
−
1
/
2
), computed with the exact solution of Equation (9.27) (solid lines) and
experimental data after Peck (1964) (dashed lines), for different values of the pressure in the
water supply at
x
=
0 expressed as equivalent height of water column. For the case of
atmospheric pressure
H
=
0 in the source of water, the sorptivity was measured to be
A
0
=
0
.
7cmmin
−
1
/
2
. (After Brutsaert, 1968.)
A comparison is shown in Figure 9.9 between soil water profiles calculated with this
result and experimental data of Peck (1964). The curve for a water supply pressure of 0 cm
at
x
=
0isgivenby
φ
=
2
.
09(1
−
S
n
)cmmin
−
1
/
2
(Brutsaert, 1968); the curves for
−
39 cm
and
−
60 cm (at
x
=
0) were obtained by renormalizing
S
n
with the water content at those
pressures.
Although Equation (9.27) is an exact solution, its main shortcoming is that the required
diffusivity (9.26) may not be flexible enough to provide a precise representation of the
actual soil water diffusivity. The main advantage of (9.27) is that it can be used in testing
the accuracy of other methods of solution. The sorptivity for this exact solution is readily
found by means of (9.17),
A
0
=
(
θ
0
−
θ
i
) [2
D
w0
/
(
m
+
1)]
1
/
2
(9.28)
By combining (9.27) with (9.28) the water content profiles obtained with this exact solution
can be expressed in dimensionless form, as shown in Figure 9.10. It can be seen that the
wetting front becomes steeper with increasing values of
m
. The fractional values of
m
,
namely
m
=
0
.
25 and 0
.
50 result in solutions with a shape, which is not very different from
that of the linear case (9.56) (see below).
The position of the wetting front can be taken as the value of
φ
at
S
n
=
0; thus one
obtains from (9.27)
φ
f
=
[2
D
w0
(1
+
m
)
/
m
2
]
1
/
2
(9.29)
Comparing this result with (9.28) one sees that the cumulative volume of infiltration is
directly proportional with the position of the wetting front, or
m
(
m
+
1)
x
f
F
=
(
θ
0
−
θ
i
)
(9.30)
