Roof stability for rock cavities and tunnels: Revisiting limit state plastic analysis

Previous observations of the roof stability analyses for deep-depth tunnels in continuum rock mass suggest that the critical roof failure mechanism involves a π/2-rotation of the failure envelope utilized in the analysis. In this study, the results obtained from the kinematic approach of the limit analysis and limit equilibrium method demonstrated that the failure profile of a roof collapse in a physical space is equivalent to the rotated and scaled shear strength envelope in the stress plane. An analytical technique employing parametric expressions is presented to account directly and accurately for the generalized Hoek–Brown criterion without requiring knowledge of its closed-form shear strength envelope or replacing it with approximated functions. The solutions obtained from the two independent methods, that is, the pure and lesser forms of the upper-bound approach, were identical owing to the rigid-block translational mechanism. In addition, several interesting aspects of the mechanics of incipient roof collapse are investigated by inspecting the stress state and failure mechanism in compliance with static force equilibrium and kinematic compatibility. The proposed method overcomes the limitations of conventional studies conducted in this category.