pi = p(liquid soil water) p(ice).
(76)
A term similar to matric potential can be defined for the pressure gradient across the ice/
water interface in frozen ground:
p
Ψi = - i .
(77)
ρg
If it is assumed that the volumetric content of soils for a given matric or supercooling poten-
tial is dependent solely on the ratios of pressure gradients to interfacial tensions,
Ψ
Ψ
≈ θ i
θ
(78)
γ wa
γ iw
then moisture-release and soil-freezing curves should be related by
γ
p
θ(Ψ) ≈ θ - wa l i .
(79)
γ iw ρw g
The value of pi as a function of temperature can be estimated by eq 72 and 73 if it is assumed
that pi = dpl+s and t 0 = dT. The necessary data are
γwa (p = 0.1 MPa, t = 0.01C) = 0.07564 N m1 (Haar et al. 1984)
γiw (p = 0.1 MPa, t = 0C) = 0.033 N m1 (Ketcham and Hobbs 1996)
∆ls Hm = 343.2 J mol -1
*
Vml = 18.018 cm 3 mol -1
*
Vms = 19.650 cm3 mol -1.
*
This implies that the pressure gradient across the ice/water interface changes with temper-
ature according to
dpl + s
= 7 699 Pa K -1 ≡ 7 699 Pa C-1.
(80)
dT
Making the proper substitutions into eq 75,
t ,
γ
l *
wa ∆s Hm
θ(Ψ) ≈ θ -
(81)
γ iw T ∆l V * ρl g
fus s m w
the following equation is derived:
θ(Ψ) ≈ θ( ft)
(82)
where f is a constant approximately equal to 1.80 m H2O C1.
Changes in hydraulic conductivity with soil-water content
The relative-hydraulic-conductivity model proposed by van Genuchten (1980) has been
adopted by many investigators. With some changes in notation, van Genuchten's model
represents reduced water content, Θ (dimensionless), as a function of soil-water matric
potential by:
λ -1
Θ=
1
λ
(83)
(Ψα)λ + 1
24
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