Creep damage model of rock considering the influence of fractional order and temperature

To address the shortcomings of traditional rock creep models, including neglecting the time-varying cumulative effect of thermal damage, low accuracy in describing accelerated creep, and failing to reflect the thermo-mechanical coupling rheological mechanism of deep high-temperature rock mass, this paper proposes a fractional-order rock creep damage model considering temperature influence, based on continuum damage mechanics and fractional calculus theory. Firstly, a time-varying thermal damage evolution equation dependent on both temperature level and heating duration is developed, and a temperature-coupled stress creep damage equation is established synchronously to realize the synergistic evolution of dual time-varying damage, with damage only acting on the fractional viscosity coefficient to keep the elastic modulus unchanged. Then, combined with the improved fractional-order Kelvin element and optimized Nishihara model, the uniaxial creep damage model is derived via rigorous equation derivation and integration, and the corresponding triaxial model is further deduced for complex engineering stress conditions. Finally, model verification and comparison are conducted based on rock creep tests under 25 °C, 50 °C, 75 °C and 100 °C. The results indicate that the model can accurately characterize the full three-stage creep behavior of rock, with the predicted curves in excellent agreement with test data and all correlation coefficients exceeding 0.95. Compared with the classical Nishihara model and existing models, the proposed model has higher fitting precision and better performance in capturing accelerated creep inflection points, verifying its superiority and reliability, and providing theoretical support for long-term stability analysis of deep high-temperature rock engineering.