Environmental Engineering Reference
In-Depth Information
w
w
C
c
/
G
s
C
s
/
G
s
10
6
10
6
y
aev
y
aev
Logarithmic soil suction
Logarithmic soil suction
(a) Slurry soil specimen
(b) Highly consolidated specimen
w
C
s
/
G
s
C
c
/
G
s
p
c
10
6
y
aev
Logarithmic soil suction
(c) Normally consolidated specimen
Figure 5.53
Typical shapes for SWCCs (i.e., gravimetric water content) of a soil subjected to
various stress histories (after Pham, 2005).
Several typical forms for the gravimetric water content ver-
sus soil suction curve are shown in Fig. 5.53. A clay soil, for
example, can be subjected to different stress histories with the
result that the SWCC changes; however, the general form of
the equation remains the same. A slurry soil will be highly
compressible in the low-effective-stress range. Preconsoli-
dated soils may have been subjected to a stress state that is
higher than the air-entry value of the soil. Most originally
proposed empirical equations for the SWCC are sigmoidal in
shape. Consequently, these equations cannot adequately rep-
resent the SWCC in the region below the air-entry value since
the equations are asymptotic to a horizontal line. The sig-
moidal equations are more suitable for best fitting the degree
of saturation form of the SWCC. It is prudent to have a
curve-fitting equation that can be applied to soils that exhibit
significant volume change (Mbonimpa et al., 2006).
w
2
(
y
)
S
1
w
sat
w
aev
This line presented by
equation:
w
1
(
y
)
t
1
w
3
(
y
)
S
2
t
2
w
r
S
3
y
aev
1
y
r
10
6
y
(kPa)
Logarithmic soil suction
Figure 5.54
Typical SWCC for a soil that changes volume along
with a designation of the variables required to define the curve
(after Pham, 2005).
S
3
. The water content at a soil suction of 10
6
kPa is assumed
to be equal to zero (Fredlund and Xing, 1994). Parameters
t
1
and
t
2
can be used to control the transitions between various
portions of the SWCC. Three equations correspond to the
three sloping lines that can be written as three mathematical
functions [i.e.,
w
1
(ψ),
w
2
(ψ)
, and
w
3
(ψ)
]:
5.6.1 SWCC Equation with Meaningful Parameters
for Entire Suction Range
It is useful to have SWCC equations written in terms of vari-
ables that have physical significance (e.g., air-entry value;
residual soil suction; residual water content; maximum slope
of the SWCC). Such an equation is particularly useful when
conducting sensitivity studies where the fundamental prop-
erties of the soil can be varied. The basic properties of
a SWCC are shown in Fig. 5.54. Most SWCCs can be
represented by three straight lines with slopes of
S
1
,S
2
, and
S
1
log
ψ
1
S
3
log
(
10
6
)
w
1
(ψ)
=
w
s
−
=
+
(S
1
−
S
2
)
×
log
(ψ
aev
)
+
(S
2
−
S
3
)
log
(ψ
r
)
−
S
1
log
(ψ)
(5.64)
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