(76)

A term similar to matric potential can be defined for the pressure gradient across the ice/

water interface in frozen ground:

Ψi = - i .

(77)

ρ*g*

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

θ(Ψ) ≈ θ - wa l *i * .

(79)

γ iw ρw g

The value of *p*i as a function of temperature can be estimated by eq 72 and 73 if it is assumed

that *p*i = d*p*l+s and *t * 0 = d*T*. 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

*

*

*

This implies that the pressure gradient across the ice/water interface changes with temper-

ature according to

d*p*l + s

= 7 699 Pa K -1 ≡ 7 699 Pa C-1.

(80)

d*T*

Making the proper substitutions into eq 75,

γ

l *

θ(Ψ) ≈ θ -

(81)

γ iw T ∆l V * ρl g

the following equation is derived:

θ(Ψ) ≈ θ( *ft*)

(82)

where *f *is a constant approximately equal to 1.80 m H2O C1.

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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