Environmental Engineering Reference
In-Depth Information
100
80
Clay soil
(initially slurry)
60
40
Silt soil
20
Sand soil
0
10 6
0.1
1
10
100
1000
10,000
100,000
Soil suction, kPa
Figure 5.20 Comparative desorption SWCCs for sand, silt, and clay soils.
where:
1983; McCuen et al., 1981). The equation was proposed for
describing moisture movement in agricultural soils.
McKee and Bumb (1984) suggested an exponential
function (i.e., Boltzmann distribution) for the relationship
between the normalized water content and soil suction:
d
=
dimensionless volumetric water content, equal to
θ/θ s where θ
=
any volumetric water content and
θ s =
saturated volumetric water content.
exp a m 1
a g
=
curve-fitting parameter
related to the air-entry
ψ
value of the soil and
n =
(5.19)
n m 1
n g
=
curve-fitting parameter related to the slope at the
inflection point on the SWCC.
where:
Among the earliest equations proposed for the SWCC is
the power law proposed by Brooks and Corey (1964). The
proposed equation represents desaturation of the soil when
the soil suction is greater than the air-entry value:
a m 1 and n m 1 =
fitting parameters.
Equation 5.19 is valid for suction values greater than the
air-entry value of the soil but is not valid near maximum
desaturation or under fully saturated conditions. McKee and
Bumb (1987) and Bumb (1987) suggested the following
equation to overcome some of the mathematical concerns
of Eq. 5.19:
ψ
ψ aev
λ bc
n =
(5.18)
where:
1
n =
(5.20)
1
+
exp[
a m 2 )/n m 2 ]
n =
normalized volumetric water content [e.g., n =
θ r ) , where θ s and θ r are the sat-
urated and residual volumetric water contents,
respectively] and the fit can also be made on
the degree of saturation or the gravimetric water
content SWCC if there is negligible volume
change when measuring the SWCC,
θ r )/(θ s
where:
a m 2 ,n m 2 =
fitting parameters.
The McKee and Bumb (1987) equation provides a better
approximation of the SWCC in the low-suction range but
it is not suitable in the high-suction range where the curve
drops exponentially to zero.
The Brooks and Corey (1964) equation as well as other
proposed equations suggest that there is a sharp discontinu-
ity in the soil suction versus water content near the air-entry
value for the soil. Although some coarse-grained sands may
have a rapid change in water content at low soil suctions,
most medium- and fine-textured soils show a gradual cur-
vature in the air-entry region of the SWCC.
ψ
=
soil suction,
ψ aev =
air-entry value (or bubbling pressure), and
λ
=
pore-size distribution index.
The degree of saturation S can be used in place of the nor-
malized water content. Equation 5.18 describes the SWCC
in the region between the air-entry value and residual condi-
tions (Campbell, 1974; Clapp and Hornberger, 1978; Gard-
ner et al., 1970a, 1970b; Rogowski, 1971; Williams et al.,
 
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