Failure characteristics of semi-circular arch tunnels under variable stress and geometry conditions

The stability of underground excavations is fundamentally governed by the interplay between their geometry and the in-situ stress field. Semi-circular arch tunnels are widely employed, yet their failure mechanisms under coupled geometric and stress variations remain insufficiently understood. This study combined the discrete element method with an elastic theoretical solution based on conformal mapping to systematically analyze the failure characteristics of semi-circular arch tunnels with a constant cross-sectional area. The numerical simulations reproduced the complete failure process from tunnel crack initiation to macroscopic coalescence and showed qualitative agreement in the occurrence of tensile cracking and the principal failure sectors. The theoretical solution provided a predicted stress field. The results show that confining pressure dually suppresses tensile cracking by reducing both the magnitude of boundary tensile stress and the spatial extent of pure tensile zones. The locations of stress extrema predicted by the theoretical solution generally corresponded to the simulated crack-initiation sectors. A sensitivity analysis reveals the dynamic evolution of controlling factors and demonstrates that while tunnel geometric parameters govern the initial compressive stress concentration, the influence of confining pressure strengthens progressively throughout the loading process. Its sensitivity contribution increases markedly from 15.4% at the initial stage to 77.5% at peak strength. This integrated framework decouples geometric and stress effects, with its sensitivity analysis enabling a quantitative contrast between numerical and theoretical results to provide a mechanistic reference for the stability assessment and design optimization of non-circular underground openings.