Phase-field modeling of frost propagation of cracks for rock mass under frost action

As the rock masses in cold regions freeze, water in cracks turns into ice and expands in volume, and the mechanical interaction between ice and rock may lead to the frost propagation of cracks. To study the prediction method for the frost propagation of cracks and further cognize the laws of the frost propagation under different conditions, the phase-field model which represents cracks in a diffusive way with a scalar field is introduced to simulate the frost propagation, and the method for the equivalent thermal expansion coefficient is utilized to simulate the volume expansion of ice in cracks due to phase transition. Moreover, the governing equations for stress field for ice-rock interaction and the governing equations of phase-field evolution for the frost propagation of cracks are solved through the COMSOL Multiphysics software. Numerical simulations with the phase-field model on the frost propagation are conducted based on a series of frost propagation experiments on the rock masses. The numerical results are similar to the experimental ones for both the frost propagation of a single crack under different dip angles and external loads, and the frost propagation of double cracks under different dip angles of rock bridge and different intersection angles. It is indicated that the phase-field model established can accurately simulate the frost propagation of cracks in the rock masses. Furthermore, when subjected to an external load, the frost propagation of a single crack deflects towards the direction of the load. For the double cracks with different dip angles of rock bridge, the frost propagation of inner tips always deflects towards the adjacent crack due to the interaction of two cracks, while the outer tips propagate approximately along the coplanar direction. For double cracks with different intersection angles, two independent new frost cracks in a butterfly shape will form when the two cracks are parallel to each other, while new frost cracks in a radiation shape will form for the double cracks with an inclined intersection angle.