A theoretical method to relate the relative permittivity and thermal conductivity of sands

Abstract

A theoretical method to relate the electrical relative permittivity (dielectric constant) and thermal conductivity of sands is presented. Extensive previous work has been done to relate the physical state (void ratio, water content, and saturation percent) of sandy soils to the bulk thermal conductivity and bulk relative permittivity respectively. These parameters have always been observed isolated from each other. However, both the bulk thermal conductivity and bulk relative permittivity are primarily dependent on the same physical characteristics. Therefore, it should be possible to estimate the thermal conductivity of a soil based on the relative permittivity measured (or vice versa). The objective of this research is to show that this estimation is possible based on actual laboratory measurements. Thermal conductivity and relative permittivity measurements were conducted on prepared bench scale specimens of dry Ottawa Sand at varying density. Thermal conductivity was measured using a thermal needle technique and relative permittivity was measured using a Dynamax TH2O probe. Based on the data collected, there appears to be a linear relationship between the two properties. A correlation is proposed based on the data collected that allows for one to calculate thermal conductivity directly from the relative permittivity measurement. Based on the data collected it appears that the theory that these properties could be estimated from each other is valid for dry sand.