Environmental Engineering Reference
In-Depth Information
e
=
irrational constant equal to 2.71828,
a number of soils from Japan. Laboratory measurements on
the soils were compared to estimations of the air permeabil-
ity functions based on measured SWCCs. The results were
interpreted using the residual degree of saturation as well as
a zero degree of saturation.
ψ
=
any soil suction value, and
ψ
r
=
soil suction at residual conditions.
The air permeability equation is obtained by substituting
Eq. 9.87 [i.e., Fredlund and Xing (1994) SWCC equation]
into Eq. 9.57.
Other empirical relationships between the coefficient of
air permeability and the degree of saturation have also been
suggested. Different air permeability functions can also be
obtained by using different equations to describe the SWCC.
The reliability of various proposed air permeability functions
can best be validated through comparisons with experimen-
tal measurements of air permeability. However, data from
air permeability measurements are scarce.
9.9.4.1 Samingan et al. (2003) Results
Samingan et al., (2003) conducted a series of air permeabil-
ity tests and made SWCC measurements on four Singapore
residual soil samples. The soil consisted of 43% sand, 45%
silt, and 12% clay. The initial void ratio and saturated vol-
umetric water content of the specimen were 1.05 and 0.51,
respectively. The air permeability test results on soil spec-
imen UP-2 showed hysteresis; however, only the drying
curve results are presented.
The Fredlund and Xing (1994) equation and the van
Genuchten (1980) equation were used to fit the experimental
results using a least-squares method. The residual volumet-
ric water content was estimated at 3.5% and the residual
suction was estimated at 10,000 kPa for the Samingan soil
specimen. The SWCC for the Samingan sample is shown
in Fig. 9.2a.
The best-fit soil parameters for both soils are listed in
Table 9.1. The fitting parameters for the SWCC data are
shown for the case where the observed residual conditions
were used as well as the case where the minimum degree of
saturation was zero. Dry air permeability values
k
d
are also
presented along with an estimated value for the
q
parameter.
The volumetric air content for the Samingan et al., (2003)
soil as well as the Moldrup et al., (2003) soil is shown in
Fig. 9.25. At low soil suctions the graphs show zero air
content and the air-entry value indicates the point at which
free air commences flowing through the soil sample.
Substituting Eq. 9.87 [i.e., Fredlund and Xing (1994)
SWCC equation] into Eq. 9.85 yields the functional relation-
ships for the air coefficient of permeability and soil suction.
Other functional relationships between the air coefficient of
permeability and soil suction can be calculated using the
9.9.4 Comparison of Estimated and Measured Air
Permeability Functions
The results obtained from indirect computation of the
air permeability (i.e., through use of the SWCC) can be
compared with published experimental data (Ba-Te et al.,
2005). Laboratory data from SWCC tests can be best fit
with the Fredlund and Xing (1994) SWCC equation or the
van Genuchten (1980) SWCC equation. The relationship
between the air content of the soil and soil suction (i.e.,
SACC) can then be calculated. The SACC results are then
substituted into the proposed air permeability functions
to give the relationship between the coefficient of air
permeability and soil suction. A comparison can then be
made between the experimental data and the estimates made
using the indirect, empirical air permeability functions.
Two data sets on air permeability measurements were ana-
lyzed by Ba-Te (2005). The results of the analysis can be
used to compare the measured and estimated air permeability
functions. One set of results is from a series of air per-
meability tests undertaken by Samingan et al., (2003) on
Singapore residual soils. The second set of air permeability
measurements was undertaken by Moldrup et al., (2003) on
Table 9.1 Parameters for Fitting Test Data from Samingan et al. (2003)
θ
r
(
S
res
)
(decimal)
Model
a
n
m
ψ
r
(kPa)
k
d
(m/s)
q
10
−
5
Fredlund and Xing
+
k
a
(S)
1.79
×
2.923
30.68
0.80
1.54
10,000
10
−
6
0.035
Fredlund and Xing
+
k
a
(S
e
)
6.92
×
2.850
10
−
4
(0.068)
van Genuchten
+
k
a
(S)
3.38
×
3.528
0.07
16.62
0.02
—
10
−
4
van Genuchten
+
k
a
(S
e
)
1.01
×
3.430
10
−
5
Fredlund and Xing
+
k
a
(S)
1.70
×
2.914
30.68
0.80
1.54
10,000
10
−
5
Fredlund and Xing
+
k
a
(S
e
)
1.73
×
2.917
0(0)
10
−
4
van Genuchten
+
k
a
(S)
1.71
×
3.320
0.06
2.53
0.13
—
10
−
4
van Genuchten
+
k
a
(S
e
)
1.68
×
3.317
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