Coal and gas outburst prediction: A scale-invariant cascade framework

Coal and gas outbursts represent catastrophic mining hazards characterized by sudden violent ejection within seconds. Although extensive research on outburst mechanisms has effectively characterized the dynamic features of these disaster processes, conventional approaches inadequately explain the rapid evolution from localized instabilities to large-scale disasters. We propose a scale-invariant cascade framework conceptualizing outbursts as progressively intensifying rupture processes governed by energy feedback mechanisms. Through systematic physical simulations coupling acoustic monitoring with morphological analysis, we quantitatively characterized outburst development patterns. Comparative experiments using carbon dioxide (CO 2 ) and helium (He) revealed identical initial rupture signatures (300-350 Pa, <0.2 s), but only CO 2 outbursts maintained sustained oscillatory patterns (20-40 Pa, 0.4-1.0 s), confirming desorption-driven rupture cascades. Cavity morphology analysis revealed consistent expansion ratios (1.8-2.1) across different scales, establishing quantifiable self-similar development patterns. Field validation through the Qiaoziliang outburst case demonstrated the framework's predictive capability under complex geological conditions, confirming that outburst development follows three distinct phases: initial accumulation with baseline growth (0.31 m/sequence), rapid cascade exhibiting approximately 7-fold increased propagation rate with exponential characteristics, and final stabilization phase. The synchronized exponential growth in cumulative outburst radius during the cascade phase provides a mechanistic link between microscopic failures and catastrophic events. This framework establishes that outburst magnitude depends on sustained energy feedback rather than initial conditions, providing quantitative foundation for hazard assessment.