where α (m1) and λ (dimensionless) are empirical parameters. The reduced water content
is defined by
(θ - θr )
Θ=
(84)
(θs - θr )
where θ is the volumetric water content (dimensionless), and θs and θr are the saturated
and residual volumetric water contents (dimensionless). The resulting empirical equations
for volumetric water content are:
for unsaturated, unfrozen soils
λ -1
λ
1
θ = θr + (θs - θr )
(85)
(Ψα)λ + 1
and, by extension, for frozen, saturated soils:
λ -1
λ
1
θ = θr + (θs - θr )
(86)
.
λ +1
( ftα)
Similarly, the following equations may be used to calculate changes in relative permeabil-
ity:
for unsaturated, unfrozen soils:
2
(αψ)λ -1
1 -
λ -1
[
]
1 + (αψ)λ λ
Kr (Ψ) =
(87)
λ -1
[
]
1 + (αΨ)λ 2λ
and for frozen, saturated soils:
2
(-αft)λ -1
1 -
λ -1
[
]
1 + (-αft)λ λ
Kr (t) =
.
(88)
λ -1
[
]
λ 2λ
1 + (-αft)
RESEARCH PRIORITIES
The literature survey presented here has revealed important gaps in scientific informa-
tion that will impede the development of contaminant-transport models for cold regions:
1. The Pitzer model provides a powerful method by which to model the thermophysical
behavior of electrolyte solutions below the freezing point of water. Unfortunately, there are
few measurements with which to apply this tool. Physicalchemical properties of aqueous
electrolyte solutions at subzero temperatures: isobaric heat capacities, molar volumes and
viscosities, are needed.
2. A consistent thermodynamic treatment of the hydrostatics of liquid water in frozen
porous media, a critical need, has yet to be developed.
25
TO CONTENTS
Previous Page
