中文摘要：

巷道顶部围岩受力系统是高度非线性的复杂大系统,尤其是层状围岩的突变失稳问题更是目前实际工程中的难点和科学研究的重点。在基于层状围岩稳定性地质力学模型和势能函数的基础上,建立了弯折失稳破坏的尖点突变模型,注重研究系统状态发生突变时外界的控制条件,主要阐述非线性系统从连续渐变状态走向系统性质的突变,并据此分析了层状围岩突变失稳破坏过程中的能量转化发生机理。基于定态曲面方程和分支曲线方程,推导得出系统失稳的充要力学条件,建立了符合实际的岩体破坏分析方法和失稳判据,揭示围岩的稳定性主要由外力（P,q）,岩体的弹性模量（E）,容重（γc）,层间极限剪应力（pt）以及几何形态（l,h）控制,并提出了防护建议。结合矿区巷道围岩实例,运用尖点突变失稳判据预测分析结果与实际情况相符合。

英文摘要：

Layered rock mass has some obvious anisotropic mechanical properties and the rock system is of high non- linear and complexity. The cusp catastrophic model of the bending failure of layered rock mass （ rock beam） based on the geological mechanical model and the potential energy function is proposed, that is used in the study on outside con- trol condition when catastrophe happens to system state, and mainly expatiate on how nonlinear system tends towards system character catastrophe from continuous gradual change state. The mechanism of releasing energy in catastrophe process was analyzed by using this theory. According to the function of stationary curved surface and branch curve, the necessary-sufficient mechanical conditions of system instability were derived. The method and the instability criterion were developed to analyze the stability of layered rock mass. The instability criterion of rock beam reveals that the sta- bility of layered rock mass is controlled by the external force （P,q）,the modulus of the elasticity （E）, the severe of rock mass （γc）, the interlayer shear stress （pt） and the geometry （l, h）. Combined with the mine examples, the result of stability analysis of roadway surrounding rock by applying the cusp catastrophe criterion of instability is in accord- ance with the actual situation. It shows that the criterion is scientific, effective and reliable. Meanwhile, the evaluation model provides a reference for the stability evaluation of surrounding rock and production.