Limit analysis on roof failure mechanism of tunnels subjected to sequential excavations

Compared to traditional full-face excavation methods, sequential excavation methods (SEM), such as central diaphragm (CD) and sidewall drift (SD) methods, can significantly reduce rock disturbance and minimize the extent of roof failure in tunnel crowns. Therefore, they are particularly suitable for tunnel projects in weak rock formations and large cross-sectional underground chambers. This paper presents a kinematic approach to predict the roof failure mechanism of tunnels excavated using the CD method. The collapse blocks at the top are influenced by excavation steps and initial in-situ stresses, and the direction of their failure velocity field is typically non-vertical, posing challenges for limit analysis applications. To address this, a tilted velocity field for the collapse failure of the tunnel crown in the CD method is constructed based on the initial normal stress distribution along the tunnel's top contour, obtaining an upper bound solution for tunnel collapse failure. The proposed method is compared with the full-face excavation method, demonstrating the superiority of the CD method over the full-section method. The rationality of the proposed tilted velocity field mechanism is verified through numerical validation using finite difference methods. Building upon the upper bound solution, safety assessment indicators for tunnels excavated using the CD method, namely allowable rock stress release and safety factor, are proposed. Furthermore, we extend this method to analyze the roof failure mechanism in tunnels constructed using the SD method and confirm its effectiveness through comparison with FDM analysis. Theo-retical analysis and numerical validation both indicate that sequential excavation methods can significantly reduce the potential collapse range at the top and improve the safety of tunnel construction.