Geoscience Reference
In-Depth Information
Fig. 8.16 Example of the
independent
domain
function
F
=
F
(
H
d
,
H
w
).
H
w
F
δ
H
w
45
o
H
d
δ
H
d
H
m
The independent domain approach
In brief, this concept involves the assumption that each element (or pore) of the total pore
space is specified completely by the (negative) pressure range over which it is emptied,
and that over which it is filled. Implicit in this is that any such element is either full or
empty, with a transition sometimes referred to as a Haines jump. With this assumption,
one can define a function
F
=
F
(
H
d
,
H
w
), which represents the fraction of the pore space,
which drains at a negative pressure or suction
H
d
and wets or is filled at a suction
H
w
. This
function can be represented graphically by the isometric projection shown in Figure 8.16.
All pores require either the same or a larger suction to be emptied than that required to
fill them, so that
H
d
≥
H
w
. The symbol
H
m
denotes the maximal tension to be experienced
in the soil water. The function
F
can now be related to the soil water characteristic as
follows.
As illustrated in Figure 8.15, the fluid volume that enters the soil during wetting between
H
w
+
δ
H
w
and
H
w
amounts to
∂θ
δθ
=
H
w
δ
H
w
∂
On the other hand, as shown in Figure 8.16, in terms of
F
this volume equals
⎡
⎣
⎤
⎦
δ
H
w
H
m
δθ
=
F
(
x
,
H
w
)
dx
(8.7)
x
=
H
w
in which
x
is the dummy variable of integration. Thus, one obtains for the slope of the
wetting boundary curve of the soil water characteristic
H
m
∂θ
∂
H
w
=
F
(
x
,
H
w
)
dx
(8.8)
x
=
H
w
Similar equalities can be obtained by considering the amount of water drained between
H
d
and
H
d
+
δ
H
d
, which yield the slope of the drying boundary curve of the soil water
