To investigate the influence of aggregate fractal gradation on the time-dependent deformation of cemented coal gangue backfill, four groups of specimens with different aggregate fractal dimensions were prepared based on mass fractal theory. Multi-stage loading creep tests were conducted to examine the effects of aggregate fractal dimension on creep strain, steady-state creep rate, and long-term strength. An improved fractional-order Burgers creep model incorporating a fractional Abel dashpot was then established to describe the creep response and to further interpret the relationship between aggregate gradation and model parameters. The results show that the creep deformation of cemented coal gangue backfill increased with increasing stress level and exhibited instantaneous deformation, decelerating creep, steady-state creep, and accelerating creep stages. With increasing aggregate fractal dimension, the creep deformation, steady-state creep rate, and damage accumulation first decreased and then increased. Among the tested aggregate fractal gradations, the specimen with D = 2.41 exhibited the best creep resistance, with a long-term strength of 8.83 MPa, approximately 33.40% higher than that of the specimen with D = 2.20. This behavior may be attributed to a more favorable coarse–fine particle proportion, which improves particle filling and skeleton continuity under the present material system. The comparison between experimental and fitted results indicates that the improved fractional-order Burgers model can effectively reproduce the creep process of cemented coal gangue backfill, with coefficients of determination greater than 0.97 for all tested specimens. These findings provide a useful reference for aggregate gradation optimization and creep-resistance evaluation of cemented coal gangue backfill under laboratory multi-stage loading conditions.
Zhang et al. (Sun,) studied this question.