Analysis of the minimum safe thickness of the outburst prevention layer in double circular karst tunnels

The excavation of double-hole tunnel projects in karst areas poses the risk of water and mud outburst. The outburst prevention layer thickness directly determines the critical capacity of the surrounding rock to resist disasters. However, current research mainly focuses on the safety thickness of the outburst prevention layer for a single tunnel, which lacks the safety thickness for a double tunnel. In this paper, a simplified model for the outburst prevention layer is established, employing elastic theory to analyse the independent safety thickness of double circular karst tunnels. Through geometric approximation methods, the critical safety thickness of double circular karst tunnels is derived for three approximate models: circular, elliptical and rectangular. Considering the mutual influence of tunnel excavation and different failure modes, an asymptotic interpolation calculation model for safe thickness was developed for these three models. Parameter sensitivity analysis demonstrates that the minimum safety thickness is positively correlated with pressure and tunnel section dimensions, but negatively correlated with the tensile and shear strengths of the surrounding rock and the spacing between double circular holes. The rationality of the proposed model was verified through numerical analysis and engineering examples. Meanwhile, it is indicated that the model can serve as an approximate method for evaluating the minimum safe thickness of double hole karst tunnels of other shapes.