Environmental Engineering Reference
In-Depth Information
2.5
κ
[Han (1996) drying]
κ
[Han (1996) wetting]
κ
(Escario and Juca, 1989)
κ
(Miao et al., 2002)
2.0
κ
[Thu et al. (2006) drying]
κ
[Thu et al. (2006) wetting]
κ
(Kayadelen et al., 2007)
1.5
1.0
0.5
0
0
100
200
300
400
Matric suction (
u
a
-
u
w
), kPa
Figure 12.12
Trend of the back-calculated
κ
with respect to matric suction for various soils.
(after Goh, 2012).
written as follows
The subscripts
d
and
w
were used to designate whether
the controlling parameters were related to the drying and
wetting SWCC, respectively (i.e.,
y
d
,b
d
, and
y
w
,b
w
). The
regression analysis showed that the parameter
y
d
(i.e.,
y
d
is on the drying curve) was related to plasticity index
I
p
of the soil, following a natural logarithm (ln) scale. The
parameter
b
d
(i.e.,
b
for the drying curve) was related to
I
p
and the fitting parameter
n
d
[i.e.,
n
fitting for the drying
curve of the Fredlund and Xing (1994) SWCC equation].
The
y
d
parameter is graphically shown in Fig. 12.13 and
can be written as follows:
c
+
u
a
)
tan
φ
+
u
w
)
tan
φ
b
τ
=
(σ
−
(u
a
−
(12.16)
where:
φ
b
φ
when
(u
a
−
=
u
w
)<(u
a
−
u
w
)
b
.
The following shear strength equation is used once the
air-entry value of the soil is exceeded
c
+
(σ
u
w
)
tan
φ
τ
=
−
u
a
)(u
a
−
+
(u
a
−
u
w
)
b
b
κ
n
tan
φ
u
w
)
−
(u
a
−
(12.17)
y
d
=
0
.
502 ln
(P I
+
2
.
7
)
−
0
.
387
(12.19)
u
w
)
b
The
κ
parameter is zero for suction values lower than
the air-entry value and increases nonlinearly as soil suction
increases in accordance with the following equation.
κ
=
log
(u
a
−
when
(u
a
−
u
w
)
≥
(u
a
−
The
b
d
parameter is graphically shown in Fig. 12.14 and
can be written as follows:
2
b
d
=−
0
.
245
{
ln[
n
d
(
PI
+
4
.
4
)
]
}
u
w
)
b
y
u
w
)
−
log
(u
a
−
(12.18)
+
2
.
114
{
ln[
n
d
(
PI
+
4
.
4
)
]
}−
3
.
522
(12.20)
where:
The shear strength equation corresponding to the wetting
SWCC was also predicted using the
y
w
and
b
w
(i.e.,both
y
w
and
b
w
are on the wetting curve). The wetting curve parame-
ters were found to be related to the parameters for the drying
SWCC (i.e.,
y
d
and
b
d
) as well as the soil properties. The
parameters
y
w
and
b
w
were found to adhere to the following
relationships:
y
and
b
=
controlling parameters.
It should be noted that the
κ
parameter used by Goh et al.
(2010) and the
κ
parameter used by Fredlund et al. (1996)
are defined differently. The
κ
parameter in the Fredlund
et al. (1996) equation is a best-fit variable obtained from
the drying shear strength experimental data along with the
drying SWCC results. The
κ
parameter used by Goh et al.
(2010) is used together with the variable
b
for estimating
the drying and wetting shear strengths along with drying and
wetting SWCCs.
y
w
=
3
.
55
y
d
−
3
.
00
(12.21)
0
.
542
b
d
n
d
n
w
b
w
=
+
0
.
389
(12.22)
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