An improved nishihara model incorporating fractional derivatives for water-induced deterioration and its experimental validation on rock creep

• An improved fractional creep model is proposed to capture water-induced rock deterioration. • The model incorporates wetting–drying effects and time-dependent degradation mechanisms. • Experimental validation confirms accurate reproduction of full rock creep stages. • The model provides a reliable tool for long-term stability assessment of underground rock masses. In deep underground mining, rock creep often leads to time-dependent deformation and progressive failure of surrounding rock masses. This issue is further exacerbated by water-induced deterioration, particularly under repeated wetting–drying cycles, which accelerate creep due to nonlinear rheological behavior. However, conventional Nishihara-type models struggle to capture the complex viscoelastic–plastic responses of rocks under hydro-mechanical coupling and long-term degradation. To address these limitations, this study proposes an improved fractional viscoelastic damage creep model that incorporates environmental deterioration and time-dependent effects. Based on fractional calculus theory, the model replaces the classical dashpot element in the Kelvin body with a nonlinear Abel dashpot and introduces a time-varying degradation function to simulate damage evolution under wetting–drying cycles. This formulation enables full-process modeling of water-induced creep, including the decelerating stage, the steady-state stage, and the accelerating stage. Uniaxial and triaxial creep tests were performed on sandstone specimens subjected to controlled wetting–drying conditions to validate the model. The results show that the proposed model accurately reproduces the entire creep process, with coefficients of determination (R²) exceeding 0.98 across all stages. Compared to the traditional Nishihara model, the improved model demonstrates significantly better fitting performance, greater physical interpretability, and enhanced applicability for long-term stability analysis of water-affected rock masses. This study contributes to performance-based long-term design and risk assessment of critical underground infrastructures.