Progressive failure analysis of shield tunnel face considering the soil arching effect

With the widespread application of shield tunneling method in tunnel construction, ensuring the stability of tunnel faces has become increasingly critical. This study develops an innovative three-dimensional failure model for shield tunneling, which integrates an “ellipsoid” and a “logarithmic spiral”. To account for the soil arching effect induced by stress redistribution during tunnel excavation, the model incorporates a curved large principal stress trace. A novel mechanism for the progressive evolution of the failure zone is achieved through the dynamic growth of the ellipsoid, capturing the intricate relationships among excavation-induced soil loss, the height of the loose zone, and the support pressure. Based on the limit equilibrium method and slice discretization technique, a support pressure formula is given to estimate the face stability. Results reveal a three-stage evolution of support pressure: initial decrease, gradual increase, and eventual stabilization as the loose zone expands. Validated through theoretical solutions, model experiments, and sensitivity analysis, this study provides theoretical guidance for tunnel face stability control, reducing risks of excessive deformation or collapse due to over-excavation.