On: “An analytical study of a two-layer transient thermal conduction problem as applied to soil temperature surveys” by T. H. Larson and A. T. Hsui (February 1992 GEOPHYSICS, p. 306–312)

Abstract

This paper presents a solution to the two‐layer conduction problem, a problem which has already been solved exactly and published (Lachenbruch, 1959; Lunardini, 1981). In fact the three‐layer solution is also available, (Lachenbruch, 1959). Unfortunately the Larson and Hsui paper uses an incorrect boundary condition for the energy flow continuity between the layers; this refers to the last equation after equation (3), or equation (A-20) of their paper. The temperature gradient must be multiplied by the thermal conductivity, not the thermal diffusivity as the paper has done. The results obtained in the paper are only valid if the heat capacities ρc of the two layers are equal. However, few soils have the same heat capacity, as can be seen from the thermal properties of materials often encountered in geotechnical situations, given in Table 1. Thus, a second parameter is required for interpreting ground temperatures: the ratio of the thermal conductivities of the two layers. The interpretation given to the effects of only the thermal diffusivity ratios is then open to question. Calculations of the same ground conditions as used by Larsen and Hsui, with the same diffusivity ratios but with realistic thermal conductivity ratios, give significantly different temperature predictions. Of course, the general conclusions of the paper on the profound effect of layering on the thermal response of soils to periodic surface temperatures are still true.