A new fractional-order model for time-dependent damage of rock under true triaxial stresses

To reasonably describe the time-dependent characteristics of rock under true triaxial stresses and analyze the long-term stability of deep underground engineering, based on the understanding of time-dependent mechanical properties of rock under true triaxial stresses, a new fractional-order damage element and the method in which the crack initiation stress is taken as the starting point of creep and the crack damage stress as the starting point of creep accelerating stage were established. Then, combined with the Mogi-Coulomb strength criterion, a fractional-order creep damage model of rock under true triaxial stresses was proposed. The proposed model was further verified based on uniaxial, conventional triaxial and true triaxial creep test results. The theoretical curves of the model are highly consistent with the test curves, indicating that the proposed model has wide applicability and rationality. Meanwhile the sensitivity of true triaxial stress states and model parameters to the creep characteristics was further investigated. Finally, based on the proposed creep model, the time-dependent characteristics of rock under untested true triaxial stress levels were predicted. The research provides a theoretical basis for the prediction of time-dependent disasters and the long-term stability analysis of surrounding rock in deep engineering.