The safety factor of roof under deep high stress is a quantitative index for evaluating roof stability. Based on the failure mode of surrounding rock of stope roof, the mechanics model of goaf roof is constructed, and the internal force of roof is deduced by the theory of hingeless arch. The calculation method of roof safety factor (K) under the environment of deep mining is proposed in view of compression failure and shear failure of roof. The calculation formulas of shear safety factor (K₁), compression safety factor (K₂) and comprehensive safety factor (K) of roof are given. The influence of stope span and roof thickness on roof stability is considered in this paper. The results show that when the roof thickness remains constant, the roof safety factor decreases with the increasing of the stope span; when the stope span remains constant, the roof safety factor increases with the increasing of the roof thickness. The deep mining example shows that when the stope span is 30 m and the roof thickness is 10 m, the roof comprehensive safety factor is 1.12, which indicates the roof is in a stable state.

深部高应力下屋面的安全系数是评价屋面稳定性的定量指标。根据采场顶板围岩的破坏模式，建立采空区顶板的力学模型，并根据无铰链拱理论推导了顶板的内力。鉴于顶板的压缩破坏和剪切破坏，提出了深部开采环境下顶板安全系数（K）的计算方法。剪切安全系数（K ₁），压缩安全系数（K ₂）和综合安全系数（K）的计算公式给出屋顶的）。本文考虑了采场跨度和顶板厚度对顶板稳定性的影响。结果表明，当顶板厚度保持不变时，顶板安全系数随采场跨度的增加而减小；当采场跨度保持恒定时，屋顶安全系数随屋顶厚度的增加而增加。深部开采实例表明，当采场跨度为30 m，顶板厚度为10 m时，顶板综合安全系数为1.12，表明顶板处于稳定状态。