Modeling the creep behavior of coal in a physical fractal framework

Understanding the creep behavior of coal is essential for optimizing gas extraction efficiency and safety, in this paper, it is investigated through a physically meaningful fractal model. Leveraging the fractal characteristics of coal's microscopic structure, the physical fractal space of coal is abstracted and renormalized to propose a fractional creep model with intrinsic physical significance. Analytical solutions to the creep constitutive model are derived using operator algebra methods. Uniaxial creep experiments, conducted on coal samples from the Ningtiaota coal mine in Yulin City, Shaanxi Province, utilized the Geotechnical Consulting & Testing Systems (GCTS) RTR-1000 rock triaxial testing system. Based on these experimental data, a parameter-fitting analysis was conducted to calibrate the physical fractal creep model. Furthermore, sensitivity analysis of the model parameters reveals the role of stress level, elastic modulus, and viscosity coefficient on creep strain. Abstracting coal's physical fractal space based on its microscopic fractal characteristics not only enhances understanding of the macroscopic creep behavior and microscopic structure relationship but also establishes a foundation for developing a fractional model with robust physical relevance.