Environmental Engineering Reference
In-Depth Information
1.0
Best-fit curve
Experimental data
0.8
0.6
a
= 1.948
n
= 2.708
m
= 1.084
ψ
r
= 3000
0.4
0.2
0
10
6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 5.34
Best-fit Fredlund and Xing (1994) equation applied to experimental data on silt.
100
80
Best-fit curve
Experimental data
60
a
= 15150
n
= 1.101
m
= 0.865
ψ
r
= 1,000,000
40
20
0
10
6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 5.35
Best-fit Fredlund and Xing (1994) equation applied to experimental data on initially
slurry Regina clay (Data from Fredlund, 1964).
can be used to fit the experimental data reasonably well over
the entire suction range from 0.1 to 10
6
kPa.
If the SWCC needs to only be fit between saturated condi-
tions and residual conditions, another form of Eq. 5.48 can be
used to best fit to the data, as shown in the following equation:
that only fit the experimental data between saturated and
residual water content conditions.
5.4 REGRESSION ANALYSIS ON SWCC
EQUATIONS
θ
s
−
θ
r
θ
=
θ
r
+
ln[
e
(ψ/a
f
)
n
f
]
m
f
(5.61)
The desorption (or drying) branch of the SWCCs is most
commonly measured in the laboratory. SWCCs are pre-
sented in terms of one of three variables to describe the
amount of water in the soil: gravimetric water content, volu-
metric water content, or degree of saturation (D.G. Fredlund,
2002a; 2006). Various regression analysis studies have been
performed to assess the closeness of fit of the proposed
SWCC equations to experimental data sets.
+
where:
θ
r
=
residual volumetric water content.
The volumetric water contents
θ
r
and
θ
s
can be
treated as two additional parameters. The five parameters
a
f
,n
f
,m
f
,
θ
s
, and
θ
r
in Eq. 5.61 can be systematically
identified through a best-fit analysis on experimental data.
Equation 5.61 is for the Fredlund and Xing (1994) fit of
the data; however, the form is similar to that often shown
for the van Genuchten (1980) equation and other equations
5.4.1 Equations for the SWCC
Several of
the commonly used SWCC equations are
sigmoidal
in character and as such do not provide a
Search WWH ::
Custom Search