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Scanning drying curve
Main drying curve
Scanning wetting curve
Main wetting curve
0
Volumetric water content
θ
0
Figure 4.15
Water retention curve with hysteresis, showing the main wetting, main
drying and scanning curves.
4.5 Darcy's Law
4.5.1 Saturated Soil
Darcy, a French engineer working for the drinking water supply of Dijon, measured
the volume of water
Q
lowing per unit time through water-saturated packed sand col-
umns of length
L
(m) and cross section
A
(m
2
) at constant hydraulic head differences
Δ
H
=
H
1
-
H
2
between the inlow and outlow (
Figure 4.16
). Darcy derived a linear
relation between discharge
Q
(m
3
d
-1
) and hydraulic head gradient:
HH
L
−
QAk
=
1
2
(4.12)
s
where
k
s
is the saturated hydraulic conductivity (m d
-1
) which is constant for rigid,
saturated soil. Darcy's law may be generalized to apply between any two points of
a saturated porous medium provided that the total hydraulic head difference of the
water between the two points is known. We will assume that the soil is rigid and sat-
urated and that no solute membranes exist within the water low paths. Under these
restrictions, the total water hydraulic head in saturated soil consists of the sum of the
hydrostatic pressure and gravitational potential components. We may eliminate the
soil cross section
A
, and write Darcy's law simply as:
∂
=−
∂
( )
hz
x
qk
H
x
=−
∂
(4.13)
k
s
s
∂
where
q
is the soil water lux density (m d
-1
) and
x
is the spatial coordinate (Jury
et al.,
1991
). A sign is needed as the velocity is a vector. The minus sign denotes that
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