Geoscience Reference
In-Depth Information
Table 8.1 Example of the F distribution of the independent domain approach for the porous
material studied by Poulovassilis (1962). F is expressed as drainable porosity in percent
per (4 cm) 2
H w (cm)
28
0.95
24
2.38
0.01
20
1.90
2.38
0.95
16
1.43
4.29
6.19
1.90
12
0.01
4.76
17.14
9.05
0.95
8
0.95
4.29
8.57
8.57
3.81
0.95
4
3.81
3.33
5.24
2.86
1.90
0.48
0.95
0
H d
(cm)
0
4
8
12
16
20
24
28
(see also Equation (8.10) for a given H d , F is the slope of the curve DE. Table 8.1 shows
an example of the F function obtained experimentally by Poulovassilis (1962); another
example is presented in Problem 8.3.
The independent domain model was concluded to compare favorably with experimental
data by Poulovassilis (1962) and Talsma (1970), but not so favorably by Topp (1971). An
early example of the application of this model to the problem of intermittent infiltration with
redistribution of soil water can be found in the numerical study of Ibrahim and Brutsaert
(1968).
It is not easy to obtain the experimental data needed to estimate the F function. For
this reason several attempts have been made to simplify the independent domain model
with various similarity assumptions by, among others, Parlange (1976), Mualem and Miller
(1979), and Braddock et al . (2001). In what follows a brief description is presented of
Parlange's (1976) proposal, which has been useful in many practical applications.
The main assumption is that F is independent of H w , so that F ( H d , H w ) can be replaced
by F ( H d ). This means that, for example in Table 8.1, the F values in each column can be
replaced by their averages. In Table 8.1, the values in the column between H d values 20
and 24 cm, all become equal to 4.05%. It also means that, for example in Figure 8.18, DE
would be represented by a straight line. The main advantage of this simplification is that
it becomes possible to calculate all the scanning curves from the boundary drying curve,
which is also the easiest to determine experimentally. For instance, the function F ( H d ) can
be determined immediately by integration of Equation (8.9) as
1
H d
∂θ
H d
F =
(8.12)
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