Upper Bound Analysis of Passive Instability on the Excavation Face of Shallow-Buried Shield Tunnels with Longitudinal Slope

Due to its insufficient cover thickness, the excavation face of shallow-shield tunnels is susceptible to passive instability. Tunnel longitudinal slope lead to sudden changes in cover thickness, making the passive failure mechanism of tunnel faces more complicated. There is an urgent need to explore analytical methods for excavation face stability in shallow-buried longitudinal slope shield tunnels. Based on upper bound analysis, a two-dimensional rotation-translation mechanism is proposed that simultaneously considers tunnel longitudinal slope and local instability at the excavation face. The mechanism is comprised of two rigid translation blocks and one rigid rotation block. The ultimate support pressure and failure mode of passive instability at the excavation face are obtained. Finally, the effects of longitudinal slope δ and partial failure ratio η on ultimate support pressure and failure mode of tunnel faces are analyzed, and the reasonableness of proposed models is verified by combining with engineering cases. The results indicate that: Partial failure range of excavation faces gradually increases with the increase of longitudinal inclination angle δ. As the cover depth ratio C/D increases, partial failure of the excavation face evolves into global failure. The rotation angle θ of the rigid rotating block decreases with the increase of the longitudinal inclination δ, and the longitudinal inclination δ has a significant effect on the rotation angle θ.