Physically Based Equation for Phase Composition Curve of Frozen Soils

The relationship between unfrozen water content (or saturation in freezing and thawing) and temperature, which is referred to as the phase composition curve in frozen soils, is a fundamental relationship in cold regions engineering. Because of the lack of a physical basis, there have been only empirical equations for this relationship. This study investigated the mechanisms underlying the phase composition curve. A detailed physical basis was established on the basis of the soil freezing characteristic curve, the Clapeyron equation, and the bundle of cylindrical capillary model. From this physical basis, a closed-form equation was developed for the formulation and prediction of this curve. This physically based equation quantifies the unique correlation between saturation and temperature in frozen soils and takes various factors into account, such as the soil saturation under unfrozen conditions and the lowest temperature used in experiments. The equation was validated with phase composition data measured with a thermal–time domain reflectometry sensor. In addition, the flexibility of the equation and its excellent applicability in various soils with a wide range of properties, in large temperature ranges, and in both freezing and thawing processes (hysteresis) were proved with reported data.