Assessing unfrozen water content using capacitance sensors in frozen soils: A new physics‐based conversion curve

Abstract

One of the most widely used techniques to measure the unfrozen water content of cryotic soils is to monitor their apparent dielectric permittivity. Paired with an empirical calibration equation or a dielectric mixing model, this measurement, , gives an estimate of unfrozen water content in soils. The conversion curve selected is crucial to the quality and accuracy of the reported unfrozen water content, or , a failure to appropriately transform into can lead to significant error. The usual methodology for soil specific conversion curves revolves around cost and time‐consuming empirical calibration curve that employ fitting parameters without physical meaning that are not transferable from one system to another. This paper aims to present a new multiphase dielectric mixing model as a conversion curve from to based on soil‐specific parameters, namely, porosity (), surface area , and bulk density . With only a few elementary physical parameters representative of the soil studied, the same conversion curve can be used on widely different soils. The derivation of the conversion curve and its performance on laboratory experiments of fully saturated soil samples are presented. This formulation is based on a dielectric mixing model, including the volume change of water due to freeze/thaw, the change in dielectric properties of water with temperatures, and the characterization of water bound to the soil surfaces. The application of the new multiphase dielectric mixing model rather than the traditional, widely used third‐degree polynomial from Topp, Davis, and Annan considerably alters the final reported: The residual water content is almost three times that reported by Topp, Davis, and Annan, 1980. This difference in residual unfrozen water content dramatically alters a soil's inferred hydrothermal‐mechanical properties such as strength, thermal conductivity, and permeability, which can lead to different behavior in both computer simulation and field conditions. The results provide evidence supporting the reevaluation of the default application of the Topp, Davis, and Annan equation in cryotic soils.