Environmental Engineering Reference
In-Depth Information
soil suction is difficult to measure using conventional
soil-testing equipment. However, the volume change
versus soil suction relationship can be obtained through use
of a SWCC and a shrinkage curve for the soil.
The shrinkage limit of a soil was originally used as one of
the plasticity classification properties for a soil. The shrink-
age limit is defined as the water content corresponding to
the minimum shrinkage volume for the initially slurry soil.
While the shrinkage limit is a classification soil property of
interest, it is the entire drying curve from some initial con-
dition to completely dry conditions that is of greater interest
when attempting to model unsaturated soil behavior.
The shrinkage curve describes the ratio of the water
content change to void ratio change for a specific change
in soil suction. Typical shrinkage curve data are shown
in Fig. 14.1. M.D. Fredlund et al., (2002b) proposed the
following equation to fit shrinkage curve data:
Let us suppose that the SWCC has been measured or esti-
mated for a soil and can be represented by the Fredlund and
Xing (1994) SWCC equation (i.e., Eq. 14.10):
1
ln
1
ψ
ψ
r
+
ln
1
10
6
ψ
r
w
(ψ)
=
w
s
−
+
1
×
(14.10)
ln
exp
(
1
)
+
ψ
a
f
n
f
m
f
where:
w
s
=
gravimetric saturation water content,
ψ
=
soil suction, kPa,
ψ
r
=
residual suction, kPa,
a
f
=
fitting parameter corresponding to the soil suction
at the inflection point,
a
sh
w
c
sh
1
1
/c
sh
n
f
=
fitting parameter designating the rate of desatura-
tion, and
e(
w
)
=
sh
+
(14.9)
b
c
sh
m
f
=
third fitting parameter for the SWCC.
where:
The curve for void ratio versus soil suction can be com-
puted by combining the equation for the SWCC (Eq. 14.10)
with the equation for the shrinkage curve (Eq. 14.9). The
relationship between void ratio and soil suction represents
the limiting boundary condition on the void ratio constitu-
tive surface. The void ratio change can be written in the
form of volumetric strain [i.e.,
dε
v
=
e
=
void ratio,
w
=
gravimetric water content,
a
sh
=
minimum void ratio,
e
min
,
b
sh
=
slope of the line of tangency, and
c
sh
=
curvature of the shrinkage curve.
e
0
)
], corre-
sponding to a particular soil suction change. In other words,
the slope of the volumetric strain plot versus soil suction is
a compressibility modulus designated by the compressibility
variable
m
2
. There is no Poisson ratio effect associated with
a change in soil suction since the stress change is always
isotropic and the soil has been assumed to behave in an
isotropic manner.
The elasticity modulus associated with a change in soil
suction is designated by the
H
parameter. The soil modu-
lus
m
2
can be written in terms of the elasticity parameter
H
for particular stress path conditions. Soil suction change
can occur under one-dimensional
K
0
loading conditions if
a soil sample is allowed to swell under lateral confinement
(e.g., confined within a steel ring). The compressibility (or
swelling) modulus and the elasticity modulus are related as
follows:
de
/(
1
+
The fitting parameters for the shrinkage curve shown in
Fig. 14.1 are as follows:
a
sh
=
0
.
27, and
c
sh
=
9
.
57. A procedure for the estimation of the shrinkage curve
was described in Chapter 2.
0
.
765,
b
sh
=
3.0
2.5
2.0
1.5
1
+
μ
1.0
m
2
=
(14.11)
H(
1
−
μ)
If soil suction change occurs under isotropic conditions,
the soil sample is allowed to change volume in all direc-
tions and the compressibility (or swelling) modulus and the
elasticity modulus can be related as follows:
0.5
100% saturation
Fredlund PTF
Experimental data
0
0
10
20 30 40
Gravimetric water content, %
50
60
3
H
Figure 14.1
Function for shrinkage curve for heavy clay. (Data
from Russam, 1958.)
m
2
=
(14.12)
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