A numerical method to consider the interaction between multiple fractures in frozen rocks based on XFEM

The initiation, propagation, and coalescence of fractures in frozen rocks plays an important role in determining the deterioration and stability of the geotechnical engineering structure in cold regions. This study proposes a numerical method to consider the interaction of multiple fractures in frozen rock based on the volumetric expansion theory and extended finite element method (XFEM). The effective expansion coefficient is adopted in this paper to describe the volume change of ice -water mixture. To accurately determine the magnitude of frostheaving pressure during the deformation and propagation of fractures, two iterative methods have been proposed. The correctness of the numerical method is verified by the analytical solution of frost -heaving pressure within a single fracture. In addition, the secant method shows the higher efficiency in solving the problems considering the fracture interaction. The evolution of frost -heaving pressure and cracking behavior under different geometric conditions were studied by the proposed method. The numerical results suggest that stress interference may promote the propagation of fractures and accelerate the deterioration of rock mass when the fractures are located in the favorable zone. After considering the multi -fracture interaction, the configuration of two fractures has a significant influence on the evolution of the frost -heaving pressure.