Environmental Engineering Reference
In-Depth Information
the correlation study. The correlations cannot be transferred
to other permeability functions.
Probably the most general correlation that has been under-
taken for permeability functions is related to the functional
form suggested by Leong and Rahardjo (1997a). Details
of parameters for various soil types are presented below
along with statistical variation of the single required fitting
parameter.
10
−
5
10
−
6
8.2.8.1 Leong and Rahardjo (1997a) Permeability
Function
Leong and Rahardjo (1997a) suggested using a dimension-
less equation for the SWCC that was then raised to a power
q
to obtain the permeability function. The permeability func-
tion was written in the following form:
10
−
7
10
−
8
k
s
d
(ψ)
q
Predicted coefficient
of permeability (drying)
k
r
(ψ)
=
(8.29)
Predicted coefficient
of permeability (wetting)
where:
10
−
9
d
(ψ)
=
dimensionless water content form
θ/θ
s
for
Measured coefficient
of permeability (drying)
SWCC, and
q
=
correlation-based soil fitting parameter.
Measured coefficient
of permeability (wetting)
10
−
10
Equation 8.29 is attractive for estimating the permeability
function due to its simplicity. The equation is easy to use
and reflects the relationship between the SWCC and the
permeability function. It is necessary to know the value to
use for the
q
soil fitting parameter when using Eq. 8.29.
Leong and Rahardjo (1997a) used the data from six soils
to assess the magnitude of the
q
soil fitting parameter. The
results of the fitting exercise are shown in Table 8.2.
A later study undertook the analysis of approximately 300
permeability data sets (Fredlund et al., 2001a). Each data set
consisted of (i) experimental results where the SWCC was
measured, (ii) experimental results where the coefficient
of permeability under various applied soil suctions was
measured, and (iii) the saturated coefficient of permeability
was measured. All experimental results were extracted
from the SoilVision knowledge-based system. The soils
were divided into a number of categories dependent upon
20
30
40
50
60
Volumetric water content
Figure 8.24
Comparisons of predicted and measured coefficients
of permeability for Guelph silt. (Data from Elrick and Bowman,
1964.)
permeability estimation equation. Therefore, a more ac-
curate estimation permeability equation can be written
using the following modification to Eq. 8.21:
θ
e
y
dy
b
θ(e
y
)
−
θ(ψ)
q
(ψ)
k
r
(ψ)
=
e
y
ln
(ψ)
b
θ(e
y
)
θ
e
y
dy
−
θ
s
(8.28)
e
y
ln
(ψ
aev
)
Table 8.2 Summary of Typical
q
Parameters from
Study by Leong and Rahardjo (1997a)
Kunze et al. (1968) suggested that the value of the power
q
could be set equal to 1.
8.2.8 Correlation of Soil Parameters for Permeability
Function
A number of possible correlations have been undertaken
which assist in the estimation of an unsaturated soil perme-
ability function. Correlations have been undertaken between
the fitting parameters for a particular permeability function
or SWCC and soil classification properties. Unfortunately,
the correlations related to a particular permeability equation
can only be used with the equation used when performing
a
f
(kPa)
n
f
m
f
Soil Type
q
Beit Netofa clay
389
0.69
1.176
52.12
Rehovot sand
2.25
4.32
1.235
6.04
Touchet silt
7.64
7.05
0.506
4.55
Columbia sandy silt
5.81
10.59
0.381
5.79
Superstition sand
2.66
6.86
0.525
6.21
Yolo light clay
2.93
2.11
0.379
9.57
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