Fractional order theory was used to characterize the accelerated creep phase of a nonlinear creep model. To accurately describe each stage of the anthracite creep model, the “gyroscope” unit was introduced by combining the Heaviside function and the creep damage definition. The effect of damage on anthracite creep was determined by designing and completing three-axis graded-separation loading creep tests on anthracite. The test curves were combined to classify anthracite into five stages: transient deformation, pseudo-acceleration, deceleration, isothermal, and acceleration creep. Each stage was combined with suitable components to form a combined fractional-order creep model. The one-dimensional equation of the state of the model was extended to three dimensions. The Levenberg–Marquardt optimization algorithm for fitting origin rheological curves was used to complete the fitting of the basic parameters. Finite differences were performed on the model equation of state, and a secondary development of a combined fractional-order creep model (NEG) was completed based on the built-in Burgers model in FLAC3D. A comparison of the numerical simulation results shows that the combined fractional-order creep model is important for accurately predicting the full creep stage of anthracite.

Fractal derivatives characterize the accelerated creep phase of the creep process. In this study, based on the fractal order theory, the integer-order derivatives are defined from the spatio-temporal self-similarity phenomenon of the dynamic process using the scale change method, and the viscoplastic model is improved to establish a new creep instantonal model with damage to describe the complete creep phase of anthracite. The effects of damage variables on initial and accelerated creep were investigated by performing graded-loading creep tests. Based on the experimental data, inversions of the model-related parameters were performed, and parameter sensitivities were analyzed. The results show that the proposed model can better characterize the complete creep process of anthracite coal, which verifies the correctness and rationality of the model. The damage content affects the initial and accelerated creep strain under different loading levels, and a specific functional relationship exists between them. The study’s findings can provide some reference material for the stability control of anthracite affected by disturbing stresses.