Fractional Stress Relaxation Model of Rock Freeze-Thaw Damage

Freeze-thaw cycle is a type of fatigue loading, and rock stress relaxation under freeze-thaw cycles takes into account the influence of the freeze-thaw cycle damage and deterioration. Rock stress relaxation under freeze-thaw cycles is one of the paramount issues in tunnel and slope stability research. To accurately describe the mechanical behaviour of stress relaxation of rocks under freeze-thaw, the software element is constructed based on the theory of fractional calculus to replace the ideal viscous element in the traditional element model. The freeze-thaw damage degradation of viscosity coefficient is considered. A new three-element model is established to better reflect the nonlinear stress relaxation behavior of rocks under freeze-thaw. The freeze-thaw and stress relaxation of rock are simulated by ABAQUS, the relevant model parameters are determined, and the stress relaxation equation of rock under freeze-thaw cycle is obtained based on numerical simulation results. The research shows that the test results are consistent with the calculated results, indicating that the constitutive equation can better describe the stress relaxation characteristics of rocks under freeze-thaw and provide theoretical basis for surrounding rock support in cold region.