A MECHANISTIC, MICROPHYSICAL MODEL FOR THE EFFECTIVE THERMAL CONDUCTIVITY OF SOILS

The effective therrmal conductivity (K’) of porous, particulate surface materials – such as soil, sand, dust, or snow – has a wide range of possible values and plays a major role in determining surface and subsurface temperatures and their variation with time and depth. Thermal conductivity is the most variable component of thermal inertia (TI) and thermal diffusivity (TD) – which control, respectively, the amplitude of diurnal and seasonal thermal waves and their penetration depths – and K’ controls the geothermal temperature gradient.

Most existing models for K’ are primarily empirical or semi-empirical and include a number of tuneable parameters with different values for different types of soils and/or degree of saturation. These models can be quite accurate within their intended domain, but have limited usefulness as a general predictive or interpretive tool.

This presentation describes a fully mechanistic model for the effective conductivity of any particulate media that was originally developed for soil/regolith on Mars, the Moon, and other planetary bodies. This model, dubbed “MaxTC”, computes K’ as a function of: bulk porosity; particle characteristics (size and shape); the number and size of interparticle contacts; the intrinsic thermal, mechanical, and cohesive properties of the particle material(s); the conductivity of gas and/or fluid in the pore space,; the volume fraction of water, ice, or cement between particles; and the lithostatic pressure of overlying material.

MaxTC is based on the Maxwell-Eucken expressions for the upper and lower bounds for the conductivity of heterogeneous, isotropic material – equivalent to the Hashin-Shtrikman bounds. The scaling of K’ within this range is proportional to the relative size of the interparticle contacts due to elastic deformation plus any pendular ring of water or cement that is present. The effects of particle shape in the MaxRTC model are parameterized in terms of the sphericity and roundness. MaxRTCM has been validated extensively by comparisons with published laboratory measurements.