Environmental Engineering Reference
In-Depth Information
cases where horizontal flow in the unsaturated
zone is important (such as with layered or het-
erogeneous soils; generally, simulation models
ba se d on t he R ic h a r d s e qu at ion (
Section 3.3.2
) a r e
used to study two- or three-dimensional flow in
the unsaturated zone). The Darcy method allows
monitoring of individual recharge events and
therefore can provide insight into the mechan-
ics of the recharge process. Concerns associated
with the method include the highly variable
nature of hydraulic conductivity and the limited
accuracy with which unsaturated hydraulic con-
ductivity curves and hydraulic gradients can be
measured.
Tensiometers are usually used to measure
the hydraulic gradient, as discussed in
Section
5.2.2
(Stephens and Knowlton,
1986
; Healy,
1989
). Because the hydraulic gradient can vary
greatly with depth and time, it is desirable to
have head measurements at several depths.
Steenhuis
et al
. (
1985
) installed tensiometers at
seven depths between land surface and 2.13 m.
Stephens and Knowlton (
1986
) installed eight
tensiometers at 0.3-m depth intervals down to
2.4 m. The frequency with which head meas-
urements are made may also be important.
Electronic recording facilitates a high fre-
quency of measurement. As with the zero-flux
plane method, if frequent readings are not
taken, there is a possibility of a wetting front
passing undetected.
Instruments other than tensiometers are
occasionally used to measure hydraulic gradi-
ents for application of the Darcy method. Flint
et al
. (
2002
) measured pressure heads with heat-
dissipation probes to apply the Darcy method
near Yucca Mountain, Nevada. Also in the vicin-
ity of Yucca Mountain, Kwicklis
et al
. (
1993
)
applied the Darcy method with pressure-head
data measured with thermocouple psychrom-
eters installed at multiple depths within the
500-m thick unsaturated zone. Sophocleous
et al
. (
2002
) applied the Darcy method with the
hydraulic gradient determined with heat dis-
sipation probes at three sites in southwestern
Kansas. Schwartz
et al
. (
2008
) measured water
content with TDR probes in field plots near
Bushland, Texas; water contents were con-
verted to pressure heads by means of computed
0
1
2
3
4
5
Fall
Winter
Summer
Spring
6
7
8
0.20
0.25
0.30
0.35
0.40
Water content (m
3
/m
3
)
Figure 5.10
Hypothetical water-content profiles at four
different times of the year. As depth increases, the seasonal
variation in water content decreases (after Healy
et al
.,
2007
).
soil-water retention curves, and the drainage
was calculated with the Darcy equation.
Precipitation and evapotranspiration pat-
terns usually produce large variations in pres-
sure head and water content near land surface
over a period of a year. These fluctuations tend
to be dampened with depth (
Fig ure 5.10
). If the
unsaturated zone is deep enough, fluctuations
can be almost completely damped out at some
depth and a region of uniform pressure head
and water content can exist over some depth
interval. Within this depth interval the verti-
cal pressure-head gradient will be 0, flow will
be constant and driven strictly by gravity, and
the vertical hydraulic gradient will be equal to
-1. The concept of the unit hydraulic gradient
in natural systems was described more fully by
Gardner (
1964
), Childs (
1969
), and Nimmo
et al
.
(
1994
). Black
et al
. (
1969
) proposed use of the
unit-gradient assumption for estimating drain-
age rates from soils. The assumption greatly
simplifies application of the Darcy method by
removing the need to measure the hydraulic
gradient. Substituting -1 for the gradient in
Equation (
5.13
) gives:
q
=
sr
( )
KK h
(5.14)
The drainage rate is equal to the value of
hydraulic conductivity at the ambient pressure
