Three-dimensional upper-bound stability analysis of coral reef limestone cavern roofs under tension-shear failure

This study develops a 3D upper-bound analytical framework for evaluating the stability of cavern roofs in coral reef limestone. A tension–shear composite failure mechanism is formulated by incorporating a tensile strength cut-off into the Hoek–Brown (H–B) criterion to avoid overestimating tensile resistance. In the proposed mechanism, zones under tensile normal stress follow a tensile failure law, whereas compressive zones are governed by the shear branch of the H–B criterion. A hybrid genetic algorithm (GA)–Nelder–Mead optimization scheme is used to determine the critical failure geometry and required support pressure for four representative tension-crack models covering continuous and discontinuous modes. The framework is validated against published analytical solutions and FLAC 3D simulations. Among the examined models, Crack1, defined by a straight tensile fracture aligned with the shear surface, consistently gives the lowest support pressure and is therefore recommended as the conservative configuration for design checks. Parametric analyses show that parameter B has the strongest influence on the required support pressure. Increased pore water pressure reduces roof stability, while the tensile strength cut-off coefficient μ controls the extent of tensile failure. In heterogeneous formations, the position of the stratigraphic boundary strongly affects the tension–shear failure mode. The proposed solutions provide efficient benchmarks for preliminary design and sensitivity analysis of coral reef limestone caverns.