Geoscience Reference
In-Depth Information
Fig. 8.20 Soil water characteristic curve for a fine sand
(Oso Flaco) during drainage, showing the
effective saturation,
S
e
=
(
θ − θ
r
)
/
(
n
0
− θ
r
),
against negative pressure in the
water
H
=
−
p
w
/γ
w
, expressed in cm of
equivalent water column. The curve represents
Equation (8.15) with
n
0
=
0
.
405,
θ
r
=
0
.
0381,
a
=
0
.
0280 cm
−
1
, and
b
=
6
.
7; the circles
represent the experimental curve, already
shown in Figure 8.5.
1
S
e
0.1
0.01
0.001
10
100
50
H (cm)
in the values of soil water flow parameters and from ignoring hysteresis altogether, as is
currently still almost universal practice.
8.2.4
Some expressions for the soil water characteristic function
Several empirical functions have been proposed in the literature to describe the soil water
characteristic. Among the better known is the power function introduced by Brooks and
Corey (1964),
S
e
=
1
for 0
<
H
<
H
b
(8.14)
H
b
)
−
b
S
e
=
(
H
/
for
H
≥
H
b
where as usual
H
[
=
(
−
p
w
/γ
w
)
=−
ψ
w
] denotes the suction expressed as height of water
column, where
S
e
is defined in (8.6), and where
b
and
H
b
are constants which are charac-
teristic for a given soil; the latter is also referred to as the
bubbling
or
air entry
suction.
Finer textured soils tend to have smaller values of
b
and larger values of
H
b
than coarser
textured soils. A disadvantage of Equation (8.14) is its two-part structure and the singular
behavior of its derivative at
H
w
=
H
b
.
In order to obtain a smooth transition from
S
e
=
1 (or
θ
=
θ
0
)downto
S
e
=
0
(or
θ
=
θ
r
), Brutsaert (1966) proposed instead
S
e
=
(1
+
(
aH
)
b
)
−
1
(8.15)
where again
a
and
b
are constants for a given soil. In Equation (8.15) the constant
a
has
the dimensions of inverse length [L
−
1
], which represents the inverse of negative capillary
pressure expressed as height of water column; observe that the value of
a
−
1
happens to be the
capillary suction where the effective degree of saturation
S
e
is at 50%. Figure 8.20 illustrates
the shape of Equation (8.15) for Oso Flaco sand, when plotted with logarithmic scales;
the parameters used for this were found to be
n
0
=
0
.
405,
S
r
=
0
.
094,
a
=
0
.
0280 cm
−
1
and
b
=
6
.
7. Equation (8.15) was extended by Van Genuchten (1980) by introducing an
