Environmental Engineering Reference
In-Depth Information
Table 8.5 Statistics of Permeability Fitting Parameter q for Various Soil Textures
Clay
Sandy clay
Silty clay
Silt
Sandy
Loam
Statistics
Clay
loam
Loam
Sand
loam
Silty clay
loam
loam
loam
sand
Mean
4.34
3.58
3.78
2.37
2.80
5.59
3.22
3.52
2.86
2.67
Median
4.71
2.62
3.56
2.36
2.62
4.77
3.18
3.46
2.85
2.59
Mode
3.00
2.80
3.25
2.20
2.75
4.60
4.05
3.15
2.75
4.63
Standard deviation
1.50
1.81
1.16
0.49
1.00
1.31
1.36
1.09
0.84
0.68
Sample variance
2.25
3.29
1.34
0.24
0.99
1.73
1.86
1.19
0.71
0.46
Range
5.42
5.92
4.14
2.25
4.71
6.33
4.97
5.99
4.20
4.01
Minimum
1.52
1.84
1.63
1.25
0.64
1.11
1.28
0.83
1.02
1.41
Maximum
6.94
7.76
5.76
3.49
5.35
7.44
6.25
6.82
5.22
5.42
Number of sets
21
18
12
49
17
34
18
74
30
29
where:
k w u a
study (Ebrahimi-Birang et al., 2004) has suggested that
there should be a lower limit for the water coefficient of
permeability and that the magnitude of potential vapor
diffusion be taken into consideration.
Figure 8.30 shows the results of the method proposed
by Ebrahimi-Birang et al. (2004) applied to silty sand. The
lower limit that was suggested for liquid water flow was
1
u w =
coefficient of permeability as a function
of soil suction,
k s
=
saturated coefficient of permeability,
a g
=
fitting parameter related to the inverse of
the air-entry value,
n g
=
fitting parameter related to the rate of
desaturation of the soil,
10 14 m/s. It was suggested that the same lower limit
for the coefficient of permeability might be applicable for
all soils. The lower limit for the water coefficient of perme-
ability is of importance with respect to numerical modeling
of water flow. The lack of a lower limit for the water coeffi-
cient of permeability can give rise to numerical convergence
problems during seepage modeling.
×
u a
u w =
matric suction,
ρ w =
density of water, and
g
=
acceleration due to gravity.
The second Gardner (1958a) permeability equation has
the following form:
k w u a
8.2.11 Water Storage Modulus for Transient Modeling
The water storage property of a soil, m 2 , is defined as
the relationship of the slope of the (volumetric) water con-
tent and soil suction. The water storage variable is required
whenever a transient seepage analysis is performed. The
water storage modulus can be obtained through the (arith-
metic) differentiation of any of the equations designated for
the SWCC (Fig. 8.31).
u w =
k s exp
c g u a
u w
(8.31)
where:
c g
=
soil parameter related to the exponential decrease in
permeability with respect to soil suction.
Inherent in the form of the latter equation is the assump-
tion that the air-entry value for the soil is near zero. Equation
8.31 should only be used when it is known that the air-
entry value of the soil under consideration is approaching
zero. Neither of the above permeability functions should be
used unless it has been possible to determine the a g and
n g fitting parameters through use of an independent anal-
ysis or through direct measurements of the coefficient of
permeability at various applied soil suction values.
8.3 APPLICATION TO
SATURATED-UNSATURATED WATER FLOW
PROBLEMS
Steady- and unsteady-state water seepage through a
saturated-unsaturated soil system can be analyzed by solv-
ing the governing partial differential equation of seepage.
The solution is obtained through use of the numerical mod-
eling methods such as finite difference and finite element
methods. The approach is similar for steady-state seepage
and unsteady-state seepage with the exception that unsteady-
state seepage is time dependent, requiring discretization
of time (i.e., elapsed time is handled in an incremental
elapsed time manner for unsteady-state water seepage).
8.2.10 Estimation of Minimum Coefficient
of Permeability
Limited research has been undertaken on the form that
the permeability function should take once residual water
content conditions are reached and exceeded. A recent
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