Environmental Engineering Reference
In-Depth Information
In order to model the more complex flow phenomena under unsaturated
conditions, an extended formulation of Darcy's law is applied. The hydraulic con-
ductivity for water decreases with the water content. Here the
volumetric water
content
as a generalization of porosity is denoted by
. Its maximum value is equal
to the porosity of the porous medium. As an alternative parameter, the effective
saturation
S
e
can be used.
S
e
takes values between 0 (gas phase only) and 1 (aqueous
phase only):
y
S
e
¼
y y
r
y
s
y
r
(11.19)
where
y
r
is the residual water content and
y
s
the water content in the saturated
situation.
Several mathematical relationships have been proposed for the dependency
between hydraulic conductivity and water content. Mualem (
1976
) suggests
a power law:
KðS
e
Þ¼KS
e
n
(11.20)
with a soil specific exponent
n
. The value for
K
on the right side of the equation is
the conductivity of the saturated soil. For most soil types the exponent takes values
between three and four (Brooks and Corey
1964
). van Genuchten (
1980
) proposed
a formula, which is frequently found in publications :
h
m
i
2
S
p
1
S
e
1
=m
KðS
e
Þ¼K
1
(11.21)
The application in the vadose zone requires the hydraulic head to be split into
a term representing the effect of total pressure
p
and buoyancy, as it was done in
(
11.17
) already. With pressure head
as a measure of total pressure in a length unit
(representing the height of a corresponding water column), the (
11.18
) for 1D gets
the form:
c
@y
@t
¼
@
@z
K ðÞ
@
@z
c z
ð
Þ
(11.22)
On the left side of (
11.22
) storage of water is described by the change of water
content.
The code for the retention curve visualization is included in the accompanying
software under the name
“retention.m”.
In the unsaturated zone the pressure head takes negative values. Sometimes the
term
suction head
is used for the negative of pressure head.
c
becomes zero at the
groundwater
table. The saturation-suction relationship, often referred to as
