Environmental Engineering Reference
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engineered structures, such as capillary barriers (finer-textured soils above coarser-
textured soils) in landfill covers to divert water from flowing through the underlying
waste (e.g., Mallants et al.
1999
), or having narrow sand or gravel layers at the soil
surface to prevent or limit evaporation.
Similarly as for the water retention curve, analytical models are often used also
for the hydraulic conductivity function. Many of these functions were derived using
the pore-size distribution models of Burdine (
1953
) or Mualem (
1976
) in combina-
tion with one of the retention functions given earlier. The Brooks and Corey (
1964
)
retention (Eq. (
18.4
)) is commonly associated with Burdine's pore-size distribution
model, leading to the hydraulic conductivity function:
K
s
S
2
/λ
+
l
+
1
K
=
(18.5)
e
in which
K
s
is the saturated hydraulic conductivity [LT
−
1
],
S
e
=
θ
r
)is
effective saturation, and
l
a pore-connectivity parameter assumed to be 2.0 in the
original study of Brooks and Corey (
1964
).
The Van Genuchten (
1980a
) retention function (Eq. (
18.3
)) is similarly coupled
mostly with the model of Mualem (
1976
)togive
(
θ
-
θ
r
)/(
θ
s
-
K
s
S
l
e
[1
S
1
/
m
e
)
m
]
2
K
(
h
)
=
−
(1
−
(18.6)
where
m
=
1
−
1
/
n
,
n
>
1
(18.7)
The pore-connectivity parameter
l
in (Eq. (
18.7
)) was estimated by Mualem
(
1976
) to be about 0.5 as an average for many soils. However, more recently, Schaap
and Leij (
2000
) recommended using
l
equal to -1 as an appropriate value of most
soil textures.
The saturated hydraulic conductivity
K
s
can be measured in the laboratory using
either the constant or falling head method, and in the field using single or double
ring infiltrometers, a constant head well permeameter, the auger-hole method, or the
piezometer method (Dane and Topp
2002
). Many laboratory and field methods are
also available for measuring unsaturated hydraulic conductivities (Dane and Topp
2002
).
18.2.2 Mass Balance Equation
Water flow in variably saturated rigid porous media (such as soils) is usually
formulated in terms of a mass balance equation of the form
∂θ
∂
t
=−
∂
q
z
−
S
(18.8)
∂
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