A Three-Dimensional Fractional Calculus-Based Creep Model for Granite Considering Thermal Effects

Understanding the long-term mechanical behavior of rocks, particularly within a moderate temperature range, is crucial for the safe design and operation of high-level radioactive waste (HLRW) disposal systems. This study presents a three-dimensional fractional calculus-based creep constitutive model to accurately analyze the time-dependent deformation behavior of granite subjected to moderate temperatures. Real-time triaxial creep experiments were conducted at 23∘C, 50∘C, and 90∘C to investigate the temperature-dependent mechanical response of Beishan granite. The results indicate that the elastic modulus exhibits minor fluctuations within this temperature range, either slightly increasing or decreasing. Further experimental observations reveal a slight increase in the elastic modulus up to 200∘C, followed by a rapid decline beyond 200∘C, following an exponential trend. Additionally, the strain rate in the steady-state creep stage rises with increasing temperature, suggesting that the viscoplastic modulus decreases according to a negative exponential power-law function. Based on these findings, a novel constitutive creep model incorporating thermal damage evolution was developed using fractional derivatives. By integrating a Perzyna overstress function with a viscoplastic flow rule, the model effectively captures the complete creep process. Validation against experimental data and parameter analysis confirm that the proposed model accurately simulates the nonlinear creep behavior, making it a valuable tool for long-term stability assessments in deep geological disposal.