Geoscience Reference
In-Depth Information
Fig. 8.26 Capillary conductivity as a
function of negative pressure
k
=
k
(
−
p
w
) for the drainage
(desorption) cycle for different
soils: (1) Pachappa sandy loam,
(2) Indio sandy loam, (3) Fort
Collins loam, (4) Aiken clay
loam, (5) Chino clay (10 kPa is
roughly equivalent to 1.02 m of
water column). (After Gardner
and Miklich, 1962.)
100
k
10
(cm d
−
1
)
1
0.1
2
0.01
1
5
4
3
0.001
0 0 0 0 0 0 0
Suction,
−
p
w
(kPa)
and water suction
H
(
=−
p
w
/γ
) displays hysteresis; however, the relationship between
conductivity and water content
θ
is fairly free of hysteresis. Many studies in the literature
have confirmed that
k
) exhibits very little, if any, hysteresis (see Jackson
et al
.,
1965; Talsma, 1970; Topp, 1971). Some additional examples of
k
=
k
(
θ
=
k
(
H
) are presented
in Figure 8.26.
For the purpose of simulating flow problems in nature, however, it is clearly preferable
to determine
k
(
) for the undisturbed soil profile. To date most experimental determi-
nations have been restricted to vertical flow. Various studies, consisting mostly of the
inverse application of finite difference forms of the governing differential equation (see
Section 8.4.1), in the absence of precipitation and by preventing evaporation at the sur-
face, have been carried out, for example, by Ogata and Richards (1957), Nielsen
et al
.
(1973), Davidson
et al
. (1969), Baker
et al
. (1974), Libardi
et al
. (1980) and Katul
et al
.,
(1993). However, measurements of soil water content and water pressure, at several
levels in the profile and over extended periods of time, are not easy and require many
precautions. Thus, field methods are usually hard, if not impossible, to apply when one of
the following conditions is present: a water table close to the surface, frequent and large
precipitation, non-negligible or unknown net lateral inflows, a large vertical drainage
rate at the lower end of the profile, and large variability in the soil properties. Because
field methods are only feasible under exceptionally favorable conditions, many attempts
have also been made to develop conceptual prediction methods. Some of these methods
will be touched upon in Section 8.3.4.
θ
Soil water diffusion formulation
In the solution of certain flow problems in partly saturated soils, it has been found
convenient to reformulate Darcy's law as a diffusion equation. Thus the pressure gradient
in (8.19) is replaced by a water content (i.e. concentration) gradient, and Darcy's law
can be written as
D
w
∂θ
∂
k
∂
x
3
q
i
=−
x
i
−
(8.31)
∂
x
i
