Abstract: To address the stability issues of stope roof in deep metal mines under high-stress conditions, this study establishes a coupled roof deflection model incorporating lateral confining pressure (surrounding rock pressure) based on elastic theory, using a mining area in China as the engineering context. Subsequently, the analytical solutions for roof deflection equations and maximum deflection are derived. Through systematic orthogonal experiments and parametric sensitivity analysis, the deformation behavior of stope roof is unveiled under the coupled effects of multiple factors, including roof span, thickness, elastic modulus, and lateral pressure coefficient. The results indicate that the additional amplification effect of lateral confining pressure on roof deflection via the P- effect (where P denotes the axial pressure on the roof, and  denotes the lateral deflection of roof) is relatively limited (just a 0.74% deflection increase in the case study). However, but its impact escalates with the degradation of roof stiffness. Range analysis reveals that roof span (ranging from 146.6 to 294.8 mm) and thickness (ranging from 129.0 to 260.1 mm) are the dominant control factors, with markedly higher sensitivity than elastic modulus and lateral pressure coefficient. Based on parameter sensitivity, an engineering optimization design criterion is proposed: when the burial depth is between 1 000 and 2 000 m, priority should be given to controlling stope span (B≤32 m) and roof thickness (a ≥ 5 m), and reinforcement support measures should be taken for low elastic modulus rock strata (E <100 GPa). The research outcomes provide theoretical foundation and methodological support for safety design in deep metal mine stopes.

Key words: mine deformation, deeply buried metal mines, roof deformation, elastic theory, high geostress, rock mechanics