Three-Dimensional Upper-Bound Analysis of Tunnel Face Stability in Coral Reef Limestone Incorporating New Modified Tensile Strength Cut-off Criteria
摘要
This study develops an upper-bound limit analysis framework to evaluate tunnel face stability in coral reef limestone, accounting for its distinctive geological conditions. Conventional Hoek–Brown (H–B) formulations for terrestrial rocks are shown to overestimate tensile strength; to address this, two modified criteria are introduced: the parabolic truncation model (T-Cpar) and its direct truncation extension (T-Ctru). T-Cpar captures abrupt strength reduction associated with pore collapse and microcrack propagation, while T-Ctru introduces an open-ended tensile boundary, transforming the process from pure shear to a composite tension–shear failure mechanism. A three-dimensional discrete rotational failure mechanism is constructed by combining a multi-tangent linearization of the H–B envelope with kinematically admissible block systems. Critical face pressures are obtained through alternating optimization of stress and geometry. Validation against published solutions and numerical simulations confirms the rationality of the framework and its divergence from conventional approaches. Parametric analyses reveal that strength characteristics and tensile cut-off are the primary controls on stability, while stratification reduces capacity and alters failure mechanisms, and pore pressure significantly exacerbates instability. Results recommend the T-Cpar and T-Ctru criteria for conservative design and synthesize the parametric outcomes into a set of design charts that allow engineers to directly estimate the required face support pressure without repeated numerical calculations, thereby providing a practical tool for stability assessment and preliminary design of tunnels in reef limestone formations.