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138 Cha pte r F o u r
Gori (1983) developed an empirical model for unsaturated frozen
soils that was extended by Tarnawski et al. (2000) and Tarnawski and
Gori (2002). Tarnawski et al. (2000) described the development of the
Kersten function, which is dependent on soil temperature and on the
degree of saturation. The new Kersten function enabled the predic-
tion of the soil thermal conductivity at different moisture contents
and temperatures. The function produced good results for dry soils
(moisture content below PWP) at temperatures ranging from 30 to
90°C, and for wet soils at temperatures ranging from 30 to 50°C.
Tarnawski and Gori (2002) presented a more accurate model to pre-
dict thermal conductivity at high temperatures. The model was appli-
cable between 5 and 90°C, with better results for dry soils.
In further studies, a model for determining soil thermal conduc-
tivity that was valid for dry soils at PWP moisture content was
presented. Such a model improved the estimation of thermal conduc-
tivity, such that it could be incorporated into heat-transfer models
that included latent heat as a component (Tarnawski and Leong 2000).
Later, Tarnawski et al. (2001) developed a software package that
allowed for determining the soil effective thermal conductivity at
high temperatures (50 to 90°C). The relationship between conductiv-
ity and temperature was no longer linear because of the influence of
mass transport, which showed strong dependence on the soil hydraulic
properties.
Balland and Arp (2005) developed a new method, based on the
method by Johansen (1975), to seamlessly calculate thermal conduc-
tivity for various soil conditions, from loose to compact, organic to
mineral, fine to coarse textured, frozen to unfrozen, and dry to wet.
This generalization was fine-tuned empirically with data from soil,
gravel, and peat drawn, for frozen and unfrozen conditions from –30
to 30°C, and for variable moisture and bulk density conditions from
dry to saturated. Usowicz et al. (2006) obtained thermal conductivi-
ties on silt loam in a sloping vineyard from a statistical–physical
model. It was shown that the performance of the equations relating
the thermal conductivity with penetration resistance and air-filled
porosity was greater than it was with penetration resistance and vol-
umetric water content. Zhang et al. (2007) developed a method for
estimating the effective thermal conductivity of the soil from thermal
properties and volume fractions of the components, considering that
the constituent parts of the multiphase medium were all cubic in
shape and randomly mixed. In addition, the difference of the thermal
characteristics between the frozen and unfrozen soils was discussed.
Lu et al. (2007) developed an improved model that described the rela-
tionship between thermal conductivity and volumetric water content
of soils. Soil thermal conductivity could be estimated using soil bulk
density, sand (or quartz) fraction, and water content. Except for the
sand, the precision of their model improved considerably the Johan-
sen (1975) model.