Three-dimensional nonlinear model of rock creep under freeze–thaw cycles

In areas with large differences between day and night temperature, the freeze–thaw cycle and frost heaving force in rock mass generate cracks within the rock, which seriously threatens the stability and safety of geotechnical engineering structures and surrounding buildings. This problem can be solved by developing a reasonable model that accurately represents the rock creep behavior. In this study, we developed a nonlinear viscoelastic–plastic creep damage model by introducing material parameters and a damage factor while connecting an elastomer, a viscosity elastomer, a Kelvin element, and a viscoelastic–plastic element in series. One- and three-dimensional creep equations were derived, and triaxial creep data were used to determine the model parameters and to validate the model. The results showed that the nonlinear viscoelastic–plastic creep damage model can accurately describe rock deformation in three creep stages under freeze–thaw cycles. In addition, the model can describe the time-dependent strain in the third stage. Parameters G(1), G(2), and η(20)’ decrease exponentially with the increase in the number of freeze–thaw cycles while parameter λ increases exponentially. These results provide a theoretical basis for studying the deformation behavior and long-term stability of geotechnical engineering structures in areas with large diurnal temperature differences.