A Fractal Link Between Soil Water Retention and Freezing

Abstract

Soils undergo wetting‐drying and freezing‐thawing cycles, yet their water retention and freezing behaviors are typically described within separate frameworks. This separation raises a fundamental question: do desaturation and freezing share comparable pore‐structure controls? A fractal formulation for the Soil Freezing Characteristic Curve (SFCC) is developed from a fractal pore‐size distribution in which D $D$ characterizes pore‐size scaling. The proposed model provides good fits to 129 experimental SFCC data sets over wide temperature ranges. Combined with an existing fractal description of the Soil Water Characteristic Curve (SWCC), paired SWCC‐SFCC measurements for 14 materials show that the fractal dimensions, D $D$ , inferred from the two curves are generally comparable. These results support a pore‐structure‐based connection between desaturation and freezing and provide a basis for describing water retention and freezing behavior within a common structural framework.