be determined by
ki (kia + kib + kic) (2-37)
where
kij = the ratio of the temperature gradient in the i-th
component to the temperature gradient in the continuous
component in the direction of the j-th principal axis
i = quartz (q), mineral (m), organic (o), water (w), air (a)
j = a, b, or c for each of the three principal axis of the
particle
The ratio of the temperature gradients in the i-th component can be
determined by the following:
kj = 1 + 1 (2-38)
+ ( x -1
The shape factor for each principal axis (gj) can be approximated by
various empirical relationships depending upon the ratio of the unit
vectors (ua, ub, uc) of the principal axes of the soil components
(Table 2-1). The sum of the three shape factors must be unity.
In most cases, water is considered to be the continuous phase of
the soil in determining soil thermal conductivity. However, as the
soil dries and the film adhering to the surface of the soil particle
begins to break, making air the continuous phase. Equation (2-37) can
be used in these cases replacing the thermal conductivity of water (Aw)
with the thermal conductivity of air (Xa). De Vries (1975) noted that
the values for the thermal conductivity in the case of air being the
continuous phase were consistently low by a factor of approximately