基于突变理论的小煤窑采空区失稳判据及应用

小煤窑采空区突发性垮塌灾害是榆神府矿区重大地质灾害问题之一。采用工程地质分析及数理推导的方法，分析了小煤窑采空区成灾条件及致灾机理，构建了顶板–残留煤柱岩石力学系统，推导了基于尖点突变模型的采空区系统失稳力学判据。以枣稍沟小煤窑为例进行分析，结果表明，该方法简便实用，计算结果可靠，为小煤窑采空区稳定性定量评价提供了一种新途径。 

Application of instability criteria of mined-out areas based on catastrophe theory

Sudden collapse in goaf is one of serious geological hazards in Yushenfu mining area. Adopting engineering ecological analysis and mathematical derivation, this paper analyzed disaster-forming conditions and disaster -inducing mechanism in goaf, built rock mechanic system of roof and residual coal pillar, and deduced mechanical instability criterion based on cusp catastrophe model. Taking Zaoshaogou coal mine as an example, the results show that the criterion is simple and practical, the reliable results could be acquired, providing a new approach for quantitative stability evaluation of goaf.