Fractal Characterization of Surrounding Rock and Coal Matrix Stress Response Enhancing Gas Drainage Efficiency

Multifactorial coupling effects during gas drainage significantly alter coal seam stress, leading to changes in the coal and surrounding matrix structure and inducing nonlinear fracture evolution. To address this complex cross-scale interaction, we propose a novel approach that integrates fractal theory with a multifactorial coupling model applied to the coal matrix (skeleton). Unlike previous studies focusing on void spaces, our model emphasizes the coal-rock matrix's response to external stress fields. By employing fractal dimensions, we quantitatively characterize fracture behavior under stress conditions, providing insights into fracture evolution and its impact on gas drainage efficiency. Simulation results demonstrate that larger fractal dimensions and increased stress reduce permeability by hindering gas migration-a finding consistent with engineering observations. Notably, as the tortuosity fractal dimension <i>D</i> _σT increases from 1.5 to 1.7, the maximum fluid pressure rises by 16.5%, while an equivalent increase in the fractal dimension <i>D</i> _σf produces a 47.1% escalation in fluid pressure. Higher initial coal seam stress leads to increased rock deformation, fracture closure, and reduced permeability, resulting in elevated gas pressure and stress levels. The findings have significant implications for optimizing gas recovery and enhancing mine safety by providing a more accurate predictive model for fracture behavior under varying stress conditions.