The importance of water migration in the measurement of the thermal conductivity of unsaturated frozen soils

Abstract

The transport of heat in frozen soil may occur by conduction and by the convective transport of sensible and latent heat arising from the flow of water in the vapor, liquid and solid states. Theory describing the coupled flow of heat and of water in the liquid and vapor states is used to derive a definition of apparent thermal conductivity (the convective transport of heat in the movement of ice in unstaturated soils is assumed to be negligible). Calculations suggest that, at temperatures close to 0°C, the transport of latent heat may exceed the contribution of heat flow by conduction. Under these conditions, the apparent thermal conductivity will be much greater than the thermal conductivity calculated from the thermal conductivities and volume fractions of the components. Insufficient published data prevent a rigorous evaluation of the theory. However the functional dependence on temperature of both thermal conductivity and the apparent thermal conductivity are calculated for a Tomakomai soil at different subzero temperatures. These values are compared to the apparent thermal conductivities of this soil which were measured at a water content in the unfrozen state of 0.48 cm 3 cm −3 and at temperatures ranging from −0.7°C to −10°C using the line heat source technique. The dependence of apparent thermal conductivity on subzero temperature, as calculated from theory, compares favourably to the dependence which was observed for this soil.