Experimental investigation and theoretical modeling of gas expansion energy during coal and gas outburst based on multi-source emission

Coal and gas outbursts are severe dynamic disasters in underground mining, primarily driven by gas expansion energy. However, accurately quantifying this energy remains challenging due to the complex, instantaneous, and multi-source nature of gas emissions. This study proposes a novel theoretical model to evaluate gas expansion energy by decoupling the participating gas into three sources: free gas in the outburst coal, rapidly desorbed gas from pulverized coal, and gas effused from the outburst cavity wall. An equivalent gas desorption particle size model was derived by integrating fractal size distribution with fractional decay diffusion kinetics, while the cavity wall gas emission was quantified using a fluid–solid coupled numerical approach. The theoretical framework was validated through a self-developed large-scale three-dimensional physical simulation experiment and historical field cases, yielding relative errors of only 6.53% and less than 10%, respectively. Furthermore, an iterative reverse-estimation model based on energy balance was established to back-calculate the actual gas pressure at the moment of outburst. Crucially, energy evolution analysis at varying mining depths (down to 1108 m) revealed a transition in the dominant triggering factors. In deep mining, the contribution of elastic strain energy sharply increases to 35.07%, transitioning the disaster mechanism from a “gas-dominated” to a “stress-gas coupling-dominated” type and dynamically lowering the critical gas pressure required for initiation. These findings demonstrate that traditional static gas thresholds are inadequate for deep mines, highlighting the urgent need for a coupled stress-gas evaluation system and a strategic shift toward active in-seam pressure relief.