Environmental Engineering Reference
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where
70
w
sat
= 50;
S
1
= 1;
S
2
= 30;
ψ
aev
= 500;
ψ
r
= 2000
w
sat
= 50;
S
1
= 1;
S
2
= 30;
ψ
aev
= 100;
ψ
r
= 700
w
sat
= 30;
S
1
= 2;
S
2
= 30;
ψ
aev
= 100;
ψ
r
= 700
ψ
t
aev
ψ
t
aev
+
ψ
t
2
60
r
A(ψ)
=
B(ψ)
=
ψ
t
2
ψ
t
1
+
ψ
t
2
50
r
and
40
30
t
1
,t
2
are curve-fitting parameters that control the transi-
tions of the curve.
20
10
The slope of the curve at and beyond residual soil suction
is of particular interest in geotechnical engineering when
considering problems involving the calculation of actual
evaporation. The variable
S
3
can be replaced by a more
meaningful variable,
w
s
(i.e., gravimetric water content at a
soil suction of 1 kPa). The relationship between
S
3
and
w
s
can be written as follows:
0
10
6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 5.56
Sample plots of the meaningful parameter SWCC
equation using various curve-fitting parameters (after Pham, 2005).
w
sat
+
(S
2
−
S
1
)
log
(ψ
aev
)
−
S
2
log
(ψ
r
)
S
3
=
log
10
6
ψ
r
(5.71)
undertaking a curve-fitting process (e.g.,
t
1
=
5).
Higher values for
t
1
and
t
2
result in more distinct breaks
along the SWCC. When best fitting the degree-of-saturation
SWCC, the curve-fitting parameter
S
1
can be set to
zero. The curve-fitting parameter
w
s
(i.e., saturated water
content) should be replaced by a constant value (i.e., 100%
for the degree of saturation).
5 and
t
2
=
Equation 5.70 can now be reduced to the form shown in
Eq. 5.72. Figure 5.56 shows typical plots of Eq. 5.72 for
various soil properties (i.e., curve-fitting parameters). The
transition parameters used for plotting Fig. 5.56 are
t
1
=
5
and
t
2
=
5:
5.6.2 Pham and Fredlund (2009) Simplified Equation
forEntireSWCC
The simplified SWCC equation for high-volume-change
soils also has curve-fitting parameters that are independent
of one another; however, the parameters may not have
physical meaning. The equation has two parts: (i) a part of
the simplified SWCC equation that is for soil suction values
less than residual soil suction (i.e.,
ψ
r
) and (ii) a part that
makes use of the Fredlund and Xing (1994) correction factor.
The equation has the following form:
w
(ψ)
=
w
s
(M
1
+
M
3
)
+
S
1
[
−
log
(ψ
aev
)(M
1
+
M
3
)
−
M
2
]
S
2
M
1
log
10
6
ψ
aev
log
ψ
r
ψ
aev
M
3
+
M
2
(5.72)
+
−
−
where
log
ψ
ψ
r
ψ
t
2
ln
(
10
)
2
t
2
r
−
(
1
−
ψ
t
2
ψ
t
2
+
r
ψ
t
2
r
[
w
s
−
w
r
×
ψ
t
2
a
+
ψ
t
2
r
w
(ψ)
=
S
1
log
(ψ)
−
w
r
]
a
+
M
1
(ψ)
=
log
10
6
ψ
r
ψ
b
+
1
ln[1
+
ψ/ψ
r
]
×
−
(5.73)
log
ψ
ψ
aev
ln[1
+
10
6
/ψ
r
]
ψ
t
ae
ψ
t
aev
+
ln
(
10
)
2
t
1
−
(
1
−
where:
ψ
t
1
M
2
(ψ)
=
ψ
t
aev
ψ
t
2
r
w
s
=
gravimetric water content at 1 kPa soil suction,
(ψ
t
aev
ψ
t
1
)(ψ
t
2
+
+
ψ
t
2
)
r
S
1
=
slope of the portion of the curve in the low soil suc-
tion,
log
(
10
6
)
−
log
(ψ)
M
3
(ψ)
=
w
r
=
residual water content,
log
(
10
6
)
−
log
(ψ
r
)
a, b
=
curve-fitting parameters,
The curve-fitting parameter
t
1
controls the radius of
curvature at the air-entry value and curve-fitting parameter
t
2
controls the radius of curvature at residual suction.
These two curve-fitting parameters have little influence on
the shape of the remainder of the SWCC. The transition
parameters
t
1
and
t
2
can be chosen as constants prior to
ψ
b
=
soil suction at the
b
fitting parameter, and
ψ
r
=
residual soil suction [i.e., can be approximated as
(
2
.
7
a)
1
/b
]
The water content of a soil at a soil suction of 1 kPa is
used as a reference starting point for the SWCC. The slope
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