Geoscience Reference
In-Depth Information
H
d
δ
A
θ
B
δθ
A´
C
B´
E
δθ
D
0
H
d
H
d
+
δ
H
d
H
Fig. 8.18 Illustration of how the fractional volume of water
δθ
, which is extracted during drying (BC),
re-enters the soil during wetting, as the soil water suction decreases from
H
+
δ
H
to 0. The
vertical difference between the primary wetting scanning curve CA and the curve CB
A
is
shown as the curve DE.
the successive water contents
0
0
H
1
x
θ
1
=
θ
0
−
F
(
x
,
y
)
dy dx
H
2
H
1
H
1
θ
2
=
θ
1
+
F
(
x
,
y
)
dx dy
x
=
y
(8.11)
H
2
H
3
H
2
x
θ
3
=
θ
2
−
F
(
x
,
y
)
dy dx
H
2
H
4
H
3
H
3
H
2
H
1
θ
4
=
θ
3
+
F
(
x
,
y
)
dx dy
+
F
(
x
,
y
)
dx dy
x
=
y
x
=
y
The hysteresis function
F
can be determined from the primary wetting scanning curves
on the basis of the following considerations. In Figure 8.18,
δθ
is the water content drained
between
H
d
and
H
d
+
δ
H
d
) is the rate of drainage, that is the amount of
water content drained per unit drainage suction increase. The primary wetting scanning
curve BA shows how the water content which drained between 0 and
H
d
is redistributed
during rewetting; similarly, the primary wetting scanning curve CA shows how the water
content that drained between 0 and
H
d
+
δ
H
d
is redistributed during rewetting. Hence,
subtraction of the amount of water entering the pore space as described by curve BA from
the amount entering, as described by curve CA, shows how the amount
δθ
redistributes
itself during rewetting. Graphically, this difference is the vertical (in Figure 8.18) distance
between curves CA and CB
A
, which is also shown as the curve DE. It follows that the rate
of change of this rate of drainage, namely
δ
(
δθ/δ
H
d
)
/δ
H
w
is the increase in refilled water
content per unit wetting suction decrease. In other words, for a given
H
d
,
F
is the value
of the increase in refilled water content for each increment
δ
H
w
. Therefore, in Figure 8.18
H
d
and (
δθ/δ
