Creep Characteristics and Fractional-Order Constitutive Modeling of Gangue–Rock Composites: Experimental Validation and Parameter Identification

With the increasing depth of coal resource extraction, the creep characteristics of gangue backfill in deep backfill mining are crucial for the long-term deformation of rock strata. Existing research predominantly focuses on the instantaneous deformation response of either the backfill alone or the strata movement, lacking systematic studies that reflect the long-term time-dependent deformation characteristics of the strata-backfill system. This study addresses gangue–roof composite specimens with varying gangue particle sizes. Utilizing physical similarity ratio theory, graded loading confined compression creep experiments were designed and conducted to investigate the effects of gangue particle size and moisture content on the creep behavior of the gangue–roof composites. A fractional-order creep constitutive model for the gangue–roof composite was established, and its parameters were identified. The results indicate the following: (1) The creep of the gangue–roof composite exhibits two-stage characteristics (initial and steady-state). Instantaneous strain decreases with increasing particle size but increases with higher moisture content. Specimens reached their maximum instantaneous strain under the fourth-level loading, with values of 0.358 at a gangue particle size of 10 mm and 0.492 at a moisture content of 4.51%. (2) The fractional-order creep model demonstrated a goodness-of-fit exceeding 0.98. The elastic modulus and fractional-order coefficient showed nonlinear growth with increasing particle size, revealing the mechanism of viscoplastic attenuation in the gangue–roof composite. The findings provide theoretical support for predicting the time-dependent deformation of roofs in deep backfill mining.