Fractional Modeling of Deep Coal Rock Creep Considering Strong Time-Dependent Behavior

Deep coal rocks exhibit strong time-dependent behavior, including significant plastic deformation and large tunnel displacements, which complicate tunnel support in deep underground engineering. A fractional creep model considering strong time-dependence was developed based on the classical Nishihara framework to capture this behavior. Additional time-dependent strains induced by stress-state variations were considered, with long-term rock strength adopted as the damage stress threshold. The stress difference between nominal and post-damage stress, σ D ( t ) , defined as the stress gradient, was applied to a viscoelastic–plastic body containing a fractional Abel dashpot, producing conventional creep strain and strong time-dependent strain. The model was extended from one-dimensional to three-dimensional under triaxial stress conditions. The validity of the model was verified using triaxial creep test data for argillaceous sandstone and coal in deep roadways, and the model parameters were determined. The results demonstrate that the model accurately reproduces the full creep process, particularly the nonlinear accelerated stage influenced by strong time-dependence. Through stress-gradient-induced variations in strong time-dependent strain, the proposed creep model elucidates the progression of deformation in the strong time-dependent stage, offering a theoretical framework for the quantitative assessment of deep rock’s strong time-dependence. Sensitivity analysis identified the stress level, fractional order, and strong time-dependence coefficient α as key factors affecting strong time-dependent creep behavior. These findings indicate that tunnel support structures in deep environments are prone to instability, underscoring the necessity of accounting for strong time-dependence to ensure long-term stability.