Numerical and theoretical studies on frost heaving pressure in a single fracture of frozen rock mass under low temperature

The frost heaving pressure is induced by water-ice phase transition in water-bearing crack for rock mass at low temperature, which may cause modeⅠcrack propagation. Based on the elastic mechanics, seepage mechanics and phase transition theory, an analytical model for frost heaving pressure in a single fracture is established considering moisture migration. This pressure not only reduces rapidly with the increase of moisture migration flux, but also changes with the mechanical parameters of rock and ice. The crack-tip stress fields under coupled thermal-mechanical condition are simulated by the method of equivalent coefficient of thermal expansion considering water-ice phase transition in crack under low temperature. The numerical solutions of frost heaving pressure and crack-tip stresses are compared with the calculated values from theoretical model. The results show that the analytical solutions are in good agreement with the numerical ones. Then the based on with the fracture mechanics, by using the stress extrapolation method, the numerical solutions of stress intensity factor are obtained, which also coincide well with the analytical and semi-analytical ones. Finally, the numerical simulation method of using the equivalent coefficient of thermal expansion is validated by an example. This study can be a reference for further studies on the damage mechanism and frost propagation of fractured rock mass under freeze-thaw.