Physical Mechanisms of Freeze–Thaw-Induced Rock Weathering and Fragmentation in Cold Regions: A Simple Theoretical Model

Freeze–thaw weathering promotes rock fragmentation and geohazards in cold regions, yet the coupled effects of external loading and temperature on frost-heaving pressure remain insufficiently quantified. This study develops an analytical model integrating elasticity, thermal deformation, pore-water migration, and water–ice phase transition to predict frost-heaving pressure in saturated rock pores. The model is evaluated against published sandstone experiments over approximately −20 to 0 °C and combined with a rock failure criterion to examine pore-wall failure and porosity evolution. The predicted pressure–temperature relationship reproduces the experimental trend, highlighting the influence of rock thermal deformation. Sensitivity analysis indicates that frost-heaving pressure is more sensitive to pore-ice mechanical properties than to rock properties. External loading slightly increases pressure, whereas higher thermal expansion coefficients and water-migration ratios reduce it. Higher elastic moduli of rock and ice and lower temperatures (−22 to 0 °C) favour frost-heave-induced failure, while external loading constrains pore expansion. The model employs idealised pore geometry and elastic material behaviour, providing a simplified representation of the coupled physical processes. The current evaluation is based on published sandstone data, and further assessments across different rock types and freezing conditions would help quantify predictive uncertainty and refine the model’s applicability.