承压水底板关键层失稳的尖点突变模型

根据煤矿长壁工作面的布置以及底板突水的可能性分析，提出了底板关键层的力学模型；在此基础上，应用突变理论的方法，对底板关键层的力学模型进行分析，推导出了关键层系统的总势能函数表达式，建立了底板关键层的尖角（ＣＵＳＰ）型突变模型。根据这一模型分析了承压水底板关键层失稳的力学机制，得到的结论符合实际情况，为研究煤矿底板突水机制引入了一种新的理论分析方法。

CUSP CATASTROPHE MODEL FOR INSTABILITY OF KEYSTRATUM IN FLOOR WITH WATER INRUSH

Based on layout of a longwall face and possibility of water inrush from the floor,a mechanical model of a key stratum is proposed,with the help of catastrophic theory,the mechanical model of a key stratum is analyzed,and an expression of total potential energy function is derived.A cusp catastrophe model of a key layer of floor is established.The mechanical mechanism of instability of a unstable key layer in the floor with confined water is studied.The conclusions from the investigation conform with the practical situation.It is a new theoretical approach for studying the mechanism of water inrush from the floor.