A quantitative energy dissipation model for predicting permeability evolution in gas-containing coal under cyclic loading

The dual challenge of ensuring operational safety and enhancing the efficiency of coalbed methane (CBM) extraction is paramount in deep mining. While cyclic disturbances from mining activities are known to affect coal seam integrity and gas seepage, the underlying damage-permeability coupling mechanism remains poorly quantified, lacking a universal predictive model that transcends specific loading conditions. Here, we systematically investigate the mechanical degradation and permeability evolution of gas-containing coal under a range of cyclic loading frequencies, amplitudes, axial stresses, and gas pressures using an advanced dynamic-static triaxial testing system. A pivotal discovery was made: regardless of the external loading path, the evolution of coal permeability is fundamentally governed by a single, unified internal state variable, the cumulative damage factor (D), quantified via energy dissipation. Based on this, we establish for the first time a universal quantitative model that directly links the damage factor (D) to the permeability ratio, unifying the effects of disparate mechanical disturbances on seepage behavior. This work not in a more precise theoretical framework for forecasting gas outburst hazards but, crucially, provides critical scientific guidance and a quantitative tool for emerging energy technologies like Enhanced CBM (ECBM) recovery via controlled mechanical stimulation.