应用突变理论建立了承压水底板关键层在动力扰动下失稳的双尖点突变模型，探讨了动力扰动诱发煤层底板关键层失稳的机制，给出了关键层在动力扰动下失稳的判据，揭示了关键层动力失稳的机理。研究表明，关键层破坏与否，不仅取决于关键层的内因如几何尺寸和岩石的性质等，还取决于外部作用力的大小和方式；承压水等静载荷作用对关键层结构振动频率的变化有一定的影响；对于受承压水等静载荷作用的底板关键层，不同的动压，如扰动的幅度、作用时间和频率的不同组合会对底板关键层结构产生不同的影响，有的是弹性振动，有的是稳定破坏，有的是突然断裂或失稳。

The catastrophe theory is applied to analyze the mechanism of floor water-resisting key stratum instability induced by dynamic disturbance during coal mining;and the double cusp catastrophe model is proposed for instability analysis of floor water-resisting key stratum above confined aquifer under dynamic disturbance in order that the complicated dynamic failure process of floor water-resisting key stratum is described. By using catastrophe theory analysis a new criterion for dynamic instability of floor water-resisting key stratum is given. It is proved that whether failure of the floor water-resisting key stratum being occurred depends not only on the key stratum feature but also on the size and way of exterior loading. And the vibration frequency of floor water-resisting key stratum is affected by static load such as confined aquifer pressure. Moreover, dynamic response of floor water-resisting key stratum loaded by static pressure such as confined aquifer is different when dynamic disturbance including different amplitude, different time and different frequency is loaded to floor water-resisting key stratum.

973计划（No. 2007CB209407）；国家自然科学基金（No. 50874020，No. 50674025，No. 50934006）；辽宁省教育厅高等学校科研项目计划（200802515）湖南省高校科技创新团队支持计划资助。