Creep-fatigue model of rock salt based on a fractal-order derivative considering thermo-mechanical damage

The increasing global energy demand has propelled compressed air energy storage (CAES) into the spotlight due to its inherent environmental and efficiency advantages. In this study, triaxial creep-fatigue experiments were conducted at various temperatures to investigate how temperature influences the creep-fatigue behavior of rock salt. The results demonstrate that increasing temperature accelerates both the creep rate and overall deformation of the rock salt. Furthermore, elevated temperatures were found to exacerbate strain softening and hysteresis within the rock salt under cyclic loading conditions. Based on these experimental findings, a novel fractal-order derivative creep-fatigue damage (FDCFD) model is developed that incorporates thermo-mechanical coupling effects. This model, comprising the Burgers, Heard, and viscoplastic body, effectively captures the three-stage deformation of rock salt and strongly agrees with the experimental results. The FDCFD model is implemented as a secondary development within FLAC3D 3D and subsequently employed to simulate the deformation of a CAES salt cavern. The Norton model and the FDCFD model predicted displacements of 0.89 m and 1.04 m, respectively, after 10 years of cavern operation at the cavern waist. This difference underscores the enhanced accuracy of the FDCFD model in predicting the time-dependent deformation of salt caverns, effectively addressing the limitations inherent in Norton models, which neglect the initial deformation stages. These findings offer valuable theoretical insights and practical engineering guidance for understanding the creep-fatigue behavior of rock salt under elevated temperature conditions and assessing the stability of CAES salt caverns.