Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR

The soil-freezing characteristic, the relationship between unfrozen water content and temperature, is relevant for any mass transfer processes in frozen porous media. To determine the soil-freezing characteristic, we simultaneously measured liquid water content and relative permittivity of various unsaturated soils at above-zero and subzero temperatures by using pulsed nuclear magnetic resonance (NMR) and time-domain reflectometry (TDR). The dielectric permittivity of frozen soil decreased with a decrease in temperature, which was accompanied by a decrease in liquid (unfrozen) water content. Frozen soils with different total water content had the same amount of unfrozen water at below − 1 °C; however, the permittivity of frozen soil depended on the total water content. A dielectric mixing model without considering reduced dielectric permittivity due to surface forces and ice formation could only describe the data for sandy soils. We expanded the mixing model by including reduced dielectric permittivity due to surface forces and ice formation. The estimations of liquid water content using the expanded mixing model were in agreement with the values measured by NMR at any soil type, total water content, ice content, and temperature.