Bayesian inference of hysteretic behavior of unfrozen water content and electrical conductivity in saturated frozen rocks

• A novel model is developed to address hysteresis in temperature-dependent properties of frozen rocks. • Radial and length factors is used to describe pore network constrictivity and irregularity. • This work consider the upscaled single-pore and pore network hysteresis for micro-scale heterogeneities. • This new model accurately reproduces hysteretic behaviors in frozen rocks. Electrical conductivity is a fundamental geophysical parameter of electrical and electromagnetic techniques. It is widely used to non-intrusively assess and monitor physical and chemical properties in cold regions (i.e., liquid water saturation, ice content, salinity, and temperature). However, the significant hysteretic behavior observed in the temperature-dependent physical properties of frozen porous media (i.e., unfrozen water saturation and electrical conductivity) remains difficult to interpret during freezing and thawing processes. Such hysteretic characteristics are mainly associated with the connectivity and irregularity of the pore network. In this study, a physically-based model is developed to consider micro-scale heterogeneities in finite-size percolation during the freezing and thawing processes using an upscaling procedure. We introduce two simple parameters to describe the constrictivity and irregularity of the pore network: the radial factor and length factor of the pore throats within the capillaries. The proposed model accounts for the hysteretic mechanisms, upscaling single-pore hysteresis at the individual pore scale and pore irregularity hysteresis at the pore network scale. Furthermore, we use a series of experimental datasets to test the proposed hysteretic model. Our findings show an excellent agreement between the predicted values and the experimental dataset, indicating that our new physically-based models can effectively predict and interpret hysteretic behaviors in the temperature-dependent physical parameters of frozen rocks during freezing and thawing processes.