Abstract: Numerical simulation technology is crucial in underground engineering for predicting the long-term deformation of rock rheology. A numerical simulation analysis method for rock aging is proposed, utilizing a generalized fractional derivative component based on fractional calculus to capture generalized stress relaxation characteristics, where the parameters are employed to describe the dynamic stress change process of rock. The generalized fractional derivative component is connected in series with the improved Burgers model for strain correction, allowing the model to describe the different rheological directions of rock when stress changes. The established model is further derived into a three-dimensional central difference format for a computational time step, then compiled using C++ and FISH languages, and embedded into the numerical simulation software FLAC3D. Simulation results are compared with the generalized stress relaxation test conducted on tuff. The results show that the secondary development of the generalized stress relaxation rheological model can well simulate the strain change law in different rheological directions of rock, reflecting the generalized stress relaxation characteristics of the rock. This helps to determine a reference range for the rheological deformation of the rock, aiding in more accurate prediction of the long-term deformation of engineering rock masses caused by disturbances such as excavation that leads to changes in the stress field environment.

Key words: generalized stress relaxation, rheological model, fractional calculus, secondary development