Upper bound limit analysis of coral reef limestone cavern roof stability incorporating a tension‐shear failure mechanism with tensile‐strength cut‐off

Abstract This study proposes an upper‐bound limit analysis framework to evaluate the stability of coral reef limestone cavern roofs. However, existing roof stability analyses are predominantly based on pure‐shear failure mechanisms, which may be inadequate for coral reef limestone with exceptionally low tensile strength; therefore, a tension‐shear composite failure mechanism is required. The framework introduces a composite tension‐shear failure mechanism incorporating a tensile‐strength cut‐off modification to the classical Hoek‐Brown failure criterion. To address the Hoek‐Brown criterion's tendency to overestimate tensile capacity, a tensile‐strength cut‐off coefficient is applied in the tensile regime, remedying this discrepancy while preserving the original formulation for shear‐dominated conditions. In the proposed mechanism, regions under tensile normal stress are governed by a tensile failure law, whereas regions under compressive normal stress follow a shear failure law. This combined tension‐shear failure mechanism accurately captures the progressive collapse behavior of coral reef limestone cavern roofs, which exhibit exceptionally low tensile strength. A hybrid optimization algorithm is employed to compute the required supporting force for four distinct tension crack models, considering both continuous and discontinuous failure modes. The analytical predictions are validated through comparisons with numerical simulations and published results from the literature. A systematic parametric analysis is then conducted to examine the influence of rock mass strength, crack morphology, and the tensile‐strength cut‐off coefficient on the failure mechanism of coral reef limestone cavern roofs. The results indicate that, for coral reef limestone cavern roofs, the proposed tension‐shear composite failure approach yields systematically more conservative outcomes supporting pressure predictions than the pure‐shear failure mechanism typically used for terrestrial rocks. Among the investigated crack models, the “Crack 1” model—characterized by a straight tension crack aligned with the shear failure surface—produces the most conservative support requirements and is recommended for the design of coral reef limestone caverns.