Environmental Engineering Reference
In-Depth Information
and allowing the sample to imbibe (rather than
drain) water at different pressures. The proced-
ure requires special equipment, and it can take
weeks to measure a complete water-retention
curve. Water-retention curves also can be deter-
mined with simultaneous field measurements
of water content and pressure head with meth-
ods described in Sections
5.2.1
and
5.2.2
.
Unsaturated hydraulic conductivity,
K
(
h
), is
expressed as the product of saturated hydrau-
lic conductivity,
K
s
, and relative hydraulic
conductiv it y,
K
r
(
h
):
similar to that of the zero-flux plane method).
By relating fluxes to measured head gradients,
K
(
h
) can be calculated. The instantaneous pro-
file method requires intensive instrumenta-
tion and monitoring, and it can take up to
months to complete. In addition, it provides
information for only the top part of the unsat-
urated zone under relatively wet conditions.
The steady-state centrifuge method (SSCM)
is a laboratory method for determining unsatu-
rated hydraulic conductivity that relies on
centrifugal force to move water through soil
core samples (Nimmo
et al
.,
2002a
). The SSCM
can provide relatively rapid (within a few days)
measurements of
K
(
h
) for a range of water con-
tents, from very dry to fully saturated condi-
tions. However, the size of the samples that can
be analyzed is small (about 50 mm in diameter
by 50 mm in length), and centrifuges for run-
ning the analyses are available only in a small
number of laboratories.
Empirical equations, such as those of van
Genuchten (
1980
) and Brooks and Corey (
1964
),
are often used to represent the water-retention
and hydraulic conductivity curves. The van
Genuchten equations are given by:
Kh
()
=
sr
KK h
()
(5.1)
where
h
is pressure head. Relative hydraulic
conductivity has its maximum value of 1
under saturated conditions; values decrease
toward 0 as pressure head decreases. As with
water-retention curves, shapes of hydraulic-
conductivity curves are influenced by soil
texture (
Fig ure 5.1b
). A sandy soil may have
a much higher hydraulic conductivity than a
silt-loam soil at saturation (pressure head of
0 m); however, at a pressure head of -0.5 m,
the hydraulic conductivity of the silt-loam
soil may be orders of magnitude greater than
that of the sandy soil (
Fig ure 5.1b
). The cap-
ability of the sandy soil to transmit water
at a pressure head of -500 mm is greatly
reduced relative to that at saturation because
of the reduced water content at -500 mm.
Methods for measuring or estimating unsat-
urated hydraulic conductivity are described
in Dane and Topp (
2002
); they include field,
laboratory, and empirical approaches. These
methods can consume considerable time and
require expensive instrumentation. The esti-
mates that they produce may also contain
large uncertainties. The instantaneous profile
method (Vachaud and Dane,
2002
) can encom-
pass a larger sample size than most methods
(up to several square meters). It is conducted
by ponding water on land surface until a
steady infiltration rate is established; the
ponded water is allowed to drain, and water
content and pressure head are measured at
multiple depths beneath the ponded area. A
flux is determined for each depth increment
from changes in water content (an approach
θ θθ α θ
(5.2)
( )
h
=− +
(
)[1
(
h
) ]
nm
−
+
s
r
r
1(
−
α
h
)
[1(
+
α
h
) ]
}
n1
−
n
−
m 2
Kh
()
=
(5.3)
r
[1
+
(
α
h
) ]
n
m/2
where θ is volumetric water content,
h
is pres-
sure head, θ
s
is saturated water content, θ
r
is
residual water content, α and
n
are referred
to as the van Genuchten parameters, and
m
is
taken equal to 1 - 1/
n
. The Brooks and Corey
equations are given by:
θ θθ
( )
h
=−
(
)[
hh
/
]
λ
+
θ
(5.4)
s
r
b
r
Kh
() [(()
=
θ θθθ
(23)/
h
−
)/(
−
λλ
)]
+
(5.5)
r
r
s
r
where
h
b
is the bubbling pressure and λ is the
pore-size distribution index. An alternative to
laboratory or field measurement of water-reten-
tion and hydraulic conductivity curves (which
can be time consuming and problematic) is
to approximate the curves with pedotransfer
functions (e.g. Briggs and Shantz,
1912
; Arya
