Environmental Engineering Reference
In-Depth Information
where:
procedures have been proposed for the quantification of air-
entry value and residual conditions.
The empirical procedure for defining residual water con-
tent and residual soil suction is shown in Fig. 5.19 (Fredlund,
1997; Vanapalli et al., 1998). A tangent line is drawn through
the inflection point of the SWCC. The SWCC relationship
in the high-suction range is approximated using another line
that extends through zero water content and 10 6 kPa. The
residual water content θ r is approximated as the ordinate of
the point at which the two lines intersect (Fig. 5.19).
The total suction corresponding to zero water content
appears to be essentially the same for all porous materials. A
value slightly below 10 6 kPa has been experimentally sup-
ported for a variety of soils (Croney and Coleman, 1961).
The 10 6 kPa value is also supported by thermodynamic con-
siderations (Richards, 1965).
The main curve shown in Fig. 5.19 is a desorption curve.
The adsorption curve differs from the desorption curve as a
result of hysteresis related to wetting and drying. The end
point of the adsorption curve may differ from the starting
point of the desorption curve because of air entrapment in
the soil. The drying and wetting SWCCs have similar forms
(i.e., are essentially congruent).
Typical SWCCs (i.e., desorption curves) for soils ranging
from sands to clays are shown in Fig. 5.20. The saturated
water content and the air-entry value (or bubbling pressure),
(u a
w (ψ)
=
water content at any soil suction, ψ ,
correction factor directing the SWCC to 10 6 kPa
at zero water content,
C(ψ)
=
e
=
irrational constant equal to 2.71828, used when
taking the natural logarithm,
a f
=
fitting parameter indicating the inflection point
that bears a relationship to and is greater than
the air-entry value,
n f
=
fitting parameter related to the rate of desatura-
tion, and
m f
=
fitting parameter related to the curvature near
residual conditions.
Laboratory studies have shown that there is a relationship
between the SWCC for a particular soil and the unsatu-
rated soil properties (Fredlund and Rahardjo, 1993a). For
example, the permeability function for an unsaturated soil
bears a relationship to the SWCC. It has become accept-
able practice in geotechnical engineering (and other disci-
plines) to empirically estimate the permeability function for
an unsaturated soil by using the saturated coefficient of per-
meability and the SWCC (Marshall, 1958; Mualem, 1986;
van Genuchten, 1980; Fredlund et al., 1994a). Similar pro-
cedures have been proposed for estimating the shear strength
properties of an unsaturated soil (Vanapalli et al., 1996a) as
well as other unsaturated soil property functions.
Figure 5.19 shows a typical SWCC for a silt soil along
with identification of some of its main characteristics. The
air-entry value of the soil is the matric suction where air
starts to displace water in the largest pores in the soil. The
residual water content is the water content where a larger
suction change is required to remove additional water from
the soil. In other words, there is a change in the rate at which
water can be extracted from the soil (on a logarithm scale).
These definitions are quite vague and empirical construction
u w ) b , generally increase with the plasticity of the soil.
Other factors such as stress history and secondary soil struc-
ture also affect the shape of the SWCCs.
5.3.1 Comments on Some Empirical SWCC Equations
Gardner (1958b), proposed an empirical equation for the
permeability function. The equation emulates the SWCC and
has subsequently been used to best fit the SWCC:
1
d =
(5.17)
a g ψ n g
1
+
60
θ s
Air
Air-entry value
50
Residual air content
40
Desorption curve
30
20
Adsorption
curve
10
Residual water
content, θ r
0
10 6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 5.19 Typical SWCC for silt soil.
 
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