Calculation Method and Treatment Scheme for Critical Safety Rock Pillar Thickness Based on Catastrophe Theory

To investigate the safety risks associated with gas tunnel coal uncovering, a physical and mechanical model of the critical safety rock pillar is proposed through a combination of theoretical analysis, numerical simulation, and field testing. Based on the principles of energy conservation and catastrophe theory, an expression for calculating the critical safety for rock pillar thickness is derived. The effects of tunnel radius, burial depth, axial stress, coal seam dip angle, and gas pressure on the critical thickness are systematically analyzed. The results indicate that the critical safety of rock pillar thickness increases with the tunnel radius, burial depth, gas pressure, and axial stress. Moreover, as the tunnel radius increases, the growth rate of the critical thickness also increases. Conversely, as the burial depth increases, the growth rate of the critical thickness decreases. For gas pressure and axial stress, the growth rate remains relatively constant. Using a tunnel project in Hunan as a case study, theoretical analysis yields a critical safety rock pillar thickness of 3.95 m. A corresponding numerical model is developed to simulate this scenario, and the simulation results align well with the theoretical predictions. Based on these findings, a combined treatment scheme of “advanced small-pipe grouting + gas drainage and pressure relief” is proposed for excavation upon reaching the critical rock pillar thickness. This scheme successfully ensures safe tunnel passage through the coal seam.