Stability analysis of tunnel face in high-pressure karst tunnels based on catastrophe theory

In order to study the bearing capacity and failure mode of the intermediate rock wall in the presence of orthogonal high-pressure caverns in front of horseshoe tunnels, a frustum model for the instability of tunnel face is established considering the influences of the location and size of the cavern on the stability of the intermediate rock wall. Based on the cusp catastrophe theory of the potential energy criterion, the critical pressure can be predicted. At the same time, similar model tests are conducted to reveal the destruction characteristics of the intermediate rock wall when the high-pressure cavern are intersected with the tunnel. The failure model for the tunnel face is additionally verified. The results show that the critical pressure of karst cavern increases with the thickness of the intermediate rock wall and the grade of the surrounding rock and decreases with the increase of the size of karst cavern. The change of the elastic modulus of the rock has a significant effect on the stability of the intermediate rock. When the thickness of the intermediate rock wall exceeds 0.35 times the hole diameter, the cavern is not the main factor causing the failure of the face. The pressure spread angle θ is introduced to describe the destruction pattern of the intermediate rock wall when the cavern and the tunnel are in different orthogonal positions, and founds that the critical pressure of the cave is positively correlated with the curvature of the tunnel boundary near the side of the cavern. The results of the proposed model are basically consistent with the test ones, which can provide reference for the design and construction of high-pressure karst tunnels.