Frost heaving and crack initiation characteristics of tunnel rock mass in cold regions under low-temperature degradation

Water freezing in rock fractures causes volumetric expansion and fracture development through frost heaving. This study introduces a novel analytical model to investigate how uneven freezing force and surrounding rock pressure influence fracture initiation, based on mass conservation, elasticity, and water-ice phase transition principles. A model for rock fracture initiation considering freezing temperature, uneven freezing expansion, in-situ stress, and lateral pressure was proposed based on fracture mechanics. Equations for stress intensity factors were developed and validated using the phase field method. The effects of rock elastic modulus anisotropy and critical fracture energy density on fracture initiation were also discussed. The results show that the values of K_Ⅰ and K_Ⅱ exhibit an upward trend as the freezing temperature, uneven expansion, in-situ stress, and lateral pressure increase. The uneven freezing expansion has the most significant influence on K_Ⅰ and K_Ⅱ values among these parameters. As the uneven freezing expansion coefficient increases to 0.5, the fracture initiation mode shifts from tensile fracture to shear fracture. As the lateral pressure coefficient increases to 1, the fracture initiation mode shifts from tensile fracture to shear fracture. Rock elastic modulus anisotropy causes fractures to propagate in a clockwise direction, forming a 'butterfly' pattern. Critical fracture energy density an isotropy causes counterclockwise deviation in propagation direction, resulting in branching paths and an 'H'-shaped pattern.