Environmental Engineering Reference
In-Depth Information
10
−
7
10
−
8
10
−
9
Predicted coefficient of
permeability
Measured coefficient of
permeability
10
−
10
10
−
11
10
−
12
0.1
1
10
100
Soil suction, kPa
Figure 8.11
Computed and measured coefficients of permeability plotted as conventional water
permeability function (modified from Gonzalez and Adams, 1980).
1.0
0.8
Soil-water characteristic curve
0.6
0.4
Coefficient of
permeability
function
0.2
0
10
6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 8.12
Typical SWCC and permeability function for a silt soil.
where:
van Genuchten SWCC equation could be reduced to a two-
parameter equation. A closed-form permeability equation
was obtained from the Burdine integration procedure when
n
vb
and
m
vb
SWCC fitting parameters were related as
follows:
m
vb
=
q
=
a constant assumed to be equal to 2, and
n
=
normalized water content
(i.e., equal
to [(
θ
−
2
/n
vb
. It was then possible to perform
the integration of the Burdine (1953) equation and arrive
at the following closed-form equation for the permeability
function:
1
−
θ
r
)/(
θ
s
−
θ
r
)] with
θ
s
equal to saturated volumetric
water content and
θ
r
equal to residual volumetric
water content).
−
a
vb
ψ
n
vb
−
2
1
+
a
vb
ψ
n
vb
−
m
vb
The square of the normalized water content is meant to
account for the effect of tortuosity of the water flow path.
This model appears to be significantly more accurate than
the same equation used without the correction factor,
n
.
In 1980, van Genuchten proposed a three-parameter
equation for the SWCC. It was then noted that a closed-
form solution could be obtained from the Burdine
integration procedure provided the three parameters in the
1
k
w
(ψ)
k
s
k
r
(ψ)
=
=
1
+
a
vb
ψ
n
vb
2
n
vb
(8.12)
where:
m
vb
=
fitting parameter set equal to 1
−
2
/n
vb
,
n
vb
=
fitting parameter from the van Genuchten (1980)
equation best fit to the SWCC,
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