Evaluation on Excavation Face Stability of Shield Tunnel Using 3D Logarithmic Spiral Damage Mechanics in Heavy Rainfall Environments

Most current studies on shield tunnel excavation face stability are conducted under fine weather assumptions, with limited attention to rainfall infiltration and water table variation. However, heavy rainfall can degrade soil conditions and trigger face instability. This paper proposes a novel analytical framework that couples an improved layered Green–Ampt rainfall infiltration model with a three-dimensional (3D) logarithmic spiral failure mechanism, to evaluate shield tunnel face stability under adverse hydrological conditions. Based on shear strength and effective stress theory, a piecewise expression of apparent cohesion is derived as a function of rainfall intensity and duration, incorporating unsaturated soil mechanics. This apparent cohesion is then embedded into the virtual work equation of upper bound limit analysis, forming a new 3D upper bound analytical solution for the required support force at the tunnel face, considering rainfall infiltration and water table depth. The proposed solution is validated against 3D finite-element simulations and centrifuge test data from the literature, showing good agreement. Finally, parametric studies further demonstrate the influence of key factors such as rainfall intensity, water table, and soil type. When rainfall intensity is low, the support force increases rapidly with intensity but is insensitive to duration; under high rainfall or shallow water tables, the support force varies significantly with time or depth, but tends to stabilize under deeper water tables. The developed model provides a theoretically innovative and practically applicable tool for assessing tunnel face stability in rainfall-sensitive environments.