Abstract: The instability and failure of reserved safety rock pillars in tunnels crossing through outburst coal seam faces often lead to coal and gas outbursts. Based on catastrophe theory, we propose an analytical method for assessing the stability of reserved safety rock pillars in such tunnels by using Polynomial distribution functions and dichotomy in a comprehensive manner. By applying the principle of total potential energy, we establish a cusp catastrophe model to represent rock pillar instability, from which a mechanical criterion for rock pillar instability is derived. To further account for the volume catastrophe criterion of the plastic yield zone of surrounding rock, we establish a predictive model for rock pillar stability and obtain a discriminant for assessing rock pillar stability. Engineering examples are employed to verify and analyze the proposed method. Results demonstrate that the stability of reserved safety rock pillars in gas tunnels crossing coal seam is closely correlated with elastic modulus E, thickness L, vertical in-situ stress N, and equivalent height H of tunnel excavation face. The predictive model based on the yield volume catastrophe criterion, as well as the mechanics criterion for stability and instability, exhibits reasonable and feasible outcomes. The discriminant results for rock pillar stability align with the actual on-site conditions, thereby validating the rationality and accuracy of our proposed prediction method and criteria.

Key words: gas tunnel crossing coal seam, rock pillar instability, catastrophe theory, prediction model, catastrophe criterion