Kouli_etal_2008_Groundwater modelling_BOOK.pdf - Pantelis ...

Contaminants in Groundwater and the Subsurface 171
contaminant transport along pathways in the soil and groundwater is crucial to contamination
prevention and remediation.
Movement of water through soil as a steady flow can be described with Darcy's equation:
Q
= q = -
A
∂h
K( θ )
(1)
∂z
where Q is the volumetric flow rate (cm 3 /day), A is the cross-sectional area (cm 2 ), q is the
volumetric flow rate per unit surface area (cm/day), K(θ) is the hydraulic conductivity
(cm/day), θ is the volumetric water content (cm 3 /cm 3 ), h is the hydraulic head, and z is
distance (cm). The specific discharge q in the saturated zone or groundwater is a superficial or
apparent velocity because water only moves through the pore openings making up the surface
area (Domenico and Schwartz, 1990). The more realistic velocity (v) is a volumetric flow rate
per unit area of connected pore space: v = q / n e , where n e is the effective porosity.
Thousands of measurements of hydraulic conductivity have been obtained in the field and
laboratory over the years. Values of hydraulic conductivity can range over 11 orders of
magnitude from 1x10 -8 cm/day in unfractured igneous and metamorphic rocks to tens or
thousands of meter per day in gravels and some karstic or reef limstones (Davis, 1969).
Various direct and indirect field and laboratory methods are available for measuring hydraulic
conductivity. In unsaturated soils, the hydraulic conductivity is a function of saturated
hydraulic conductivity and soil water content. The soil water content can be measured by
simply drying samples, by neutron probe, or by time domain reflectometry (TDR).
Various schemes are available for parameterizing soil hydraulic properties (Clapp and
Hornberger, 1978; van Genuchten, 1980; Cosby et al., 1984), and have been widely used in
different soil and hydrological applications. They conceptualize hydraulic conductivity and
soil-water metric potential as functions of the normalized volumetric water content (S e ),
which is defined as:
θ -θ
r
=
θ s -θ
r
S e
(2)
where θ s is the soil water content at saturation, and θ r is the residual soil water content. A
simple equation by Clapp and Hornberger (1978) and Cosby et al. (1984) can be used for
relating hydraulic conductivity to soil water content:
3+1/ λ
K( θ )= K s ( S e )
(3)
where K s is the saturated hydraulic conductivity (cm/day), and λ is a pore size parameter. A
more versatile equation by Rawls and Brakensiek (1985), relating the hydraulic conductivity
to soil water content, is the following:
1/2
K( θ )= K s ( S e ) [1-(1- S ) ]
(4)
e
1/m m 2