A Rock Creep Damage Model Considering the Influence of the Free-Energy Function

Abstract Accurate characterization of the accelerated creep stage in rock is essential for the long-term stability evaluation of deep geotechnical infrastructures, including deep-buried tunnels, high-dam foundations, and nuclear waste repositories. Traditional creep constitutive models, exemplified by the classical Nishihara model, are mostly established through a phenomenological combination of mechanical elements. These models fail to establish an intrinsic coupling relationship between energy dissipation and damage evolution within a unified thermodynamic framework, resulting in pronounced fitting deviations during the accelerated creep stage. In addition, the physical implication of some empirical parameters in these models remains ambiguous. To address the aforementioned limitations, this paper proposes an accelerated creep damage model for rock based on irreversible thermodynamics and free-energy function. Taking free-energy density as the core state variable, the model establishes a quantitative link between elastic strain energy release and internal microcrack propagation via the damage energy release rate and constructs an energy-driven, damage evolution–coupled constitutive relation. The damage-modified viscoelastic and viscoplastic rheological equations are derived, and a damage-weakening coefficient is introduced to describe the attenuation law of the equivalent viscosity coefficient during the accelerated creep stage. All parameters in the proposed model have explicit physical connotations: energy-damage coupling parameters reflect the rate of development of internal microcrack damage, rheological constitutive parameters characterize the rock’s resistance to viscous deformation, and accelerated creep characteristic parameters quantify the evolution intensity of accelerated deformation induced by damage accumulation. The proposed model is validated against triaxial step-loading creep test data of sandstone and quantitatively compared with the classical Nishihara model using multiple evaluation indicators. The results indicate that the model can fully reproduce the three-stage creep deformation law of rock, i.e., decelerating creep, steady-state creep, and accelerated creep. Under different stress levels, the correlation coefficients ( R 2 ) between fitted curves and experimental data are all above 0.90, and the root mean square error (RMSE) of full-stage creep strain is controlled within 2.1 × 10 − 5. Specifically, for the critical accelerated creep stage, the RMSE of the proposed model is 68%–75% lower than that of the Nishihara model, and the relative fitting error is controlled within 7%. The model can also accurately capture the inflection point where the deformation rate shifts from steady growth to rapid increase. This work reveals the internal mechanism of rock creep damage evolution from the perspective of the essence of energy, and provides a more reliable theoretical tool for long-term stability prediction in deep geotechnical engineering.