saturation, the thermal conductivity begins leveling off to some
relatively constant value. Another complicating issue in calculating
the thermal conductivity of the soil is that the temperature gradient
in the solid and liquid portion of the soil can be significantly
different from that in the gaseous phase of the soil.
De Vries (1975) presented a method by which the thermal
conductivity could be calculated using a weighted average of the
various soil constituents where the weighting factors were a product of
the individual volume fractions and geometric factors as follows
kqXq + km xmA + k oX 0 + k X + kaxaa (2-36)
Sqxq + kmXm + koXo + kX + kaxa
where
S = thermal conductivity of the soil [W-m-1K-1]
\ = thermal conductivity of soil component [W'm-1.K-I1]
xi = volume fraction of soil component [m3m-3]
ki = geometric weighting factor dimensionlesss]
i = quartz (q), mineral (m), organic (o), water (w), air (a)
The geometric weighting factor depends upon geometric
configuration of the soil particles and the incorporated void space.
It represents the ratio of the spatially averaged temperature gradient
in the i-th soil component to the spatially averaged temperature
gradient of the continuous component of the soil (usually water). For
example, kq represents the space average of the temperature gradient
in the quartz particles in the soil to the space average of the
temperature gradient in the water. The geometric weighting factor can