基于尖点突变理论的层状围岩失稳判据研究

Study on Instability Criterion of Layered Rock Mass Failure Based on Cusp Mutation Theory

在层状围岩(岩体梁)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,研究系统状态下发生突变时外界的控制条件,主要阐述非线性系统如何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(岩体梁)突变失稳破坏过程中的能量释放的发生机理。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。岩体梁失稳判据揭示,围岩的稳定性主要由外力的p,q,岩体的弹性模量E,重度rc,层间剪应力τ以及几何形态l,h决定。结合矿区巷道围岩实例,运用尖点突变失稳判据分析与实际结果一致性达84%以上。

The cusp mutation 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 control condition when mutation happens to system state, and mainly expatiates on how nonlinear system tends towards system character mutation from continuous gradual change state. The mechanism of releasing energy in mutation 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 in- stability criterion are 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 elasticity E, the severe of rock mass re, the interlayer shear stress T and the geometry l, h. Combined the mine example, the consistency between applying cusp mutation criterion for instabil- ity analysis and the actual results is more than 84%.