Environmental Engineering Reference
In-Depth Information
retention curve
, is an empirical relationship, which has to be considered in soil
modeling. Van Genuchten (
1980
) uses the mathematical form:
n
m
S
e
¼
1
=ð
1
þ ac
j
j
Þ
(11.23)
with parameters
is [1/L]. Parameter
m
is identical
to the one introduced in (
11.21
). Figure
11.8
depicts some example retention
curves. There are various other formulations of the retention curve, which are not
repeated here. A problem that is seldom tackled is the hysteresis of the retention
curve, which means that the curve is not unique. In fact, experiments have shown
that the saturation-suction curve for dewatering is often very different from the
curve for re-wetting.
There are two possible ways to compute problems of unsaturated flow, based on
(
11.22
) and the retention curve
a
and
n ¼
1
1
=m
. The unit of
a
cðyÞ
. Some authors prefer to use the retention curve
to rewrite the term on the right side of (
11.22
) as function of
y
. A MATLAB
®
implementation, using that approach, is presented by Hornberger and Wiberg
(
2005
). The alternative approach is to rewrite the left side as follows:
@y
@c
@c
@t
¼
@
@z
K ðÞ
@
@z
c z
ð
Þ
(11.24)
Volumetric water content [-]
Hygiene sandsto
n
e
Touchet Silt Loam
Silt Loam
Guelph Loam
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0
50
100
150
200
Suction head [cm]
Fig. 11.8 Examples of retention curves, data from Hornberger and Wiberg (
2005
); produced
using MATLAB
®
