中文摘要：

针对石膏矿矿柱–护顶层支撑体系的破坏特征,结合非线性力学理论,在建立简化力学模型的基础上,构建石膏矿矿柱–护顶层支撑体系突发破坏的尖点突变模型。利用该突变模型研究石膏矿矿柱–护顶层支撑体系的破坏机制,分析支撑体系的几何参数对采空区稳定性影响。结果表明：石膏矿矿柱–护顶层支撑体系的稳定性是它的内部特性（护顶层弹性模量、护顶层厚度、矿柱之间的宽度、矿柱面积、矿柱高度）与外部荷载共同作用的结果,而位移突跳仅与内部特性有关;在对支撑体系稳定性进行调控时,优化的几何参数顺序依次是：护顶层厚度,矿柱之间的宽度,矿柱面积和矿柱高度。工程应用表明：湖北荆门荆花石膏矿采空区目前的内部几何参数已经达到了失稳的充要条件,这与现场调查具有一定的相符性。

英文摘要：

According to the failure characteristics of pillar-roof system in gypsum mines,and combined with the theory of the nonlinear mechanics,a simplified mechanical model of pillar-roof system was established. Then a cusp catastrophe model of pillar-roof system was build. The failure mechanism of pillar-roof system was analyzed,and the influence of geometric parameters on the stability of the system is analyzed. It is shown that：the stability of pillar-roof system is mainly affected by two factors,namely internal and external factors,and the internal factors indicate that modulus of elasticity of roof,pillar thickness,the width between pillars,pillar area,pillar height and pillar strength. The external factor refers to dead weight of roof and overlying strata. The displacement jump is only related to the internal factor. When regulating the stability of pillar-roof system,the order of these geometrical parameters are：pillar thickness,pillar area,the width between pillars and pillar height. The engineering application shows that the present internal geometric parameters of the mined-out area in Jingmen gypsum mine has reached the sufficient and necessary condition of instability, which consist with field investigation.