非对称开采时矿柱失稳的尖点突变模型

针对非对称开采时矿柱稳定性问题建立了一个简化的力学模型．基于势能原理，应用尖点突变理论对矿柱成为非稳定系统进行了探讨，导出了失稳的充要条件、矿柱变形突跳量和能量释放表达式，为定量研究其失稳问题奠定了基础．结果表明:系统的失稳不仅与其所受载荷有关，而且与其内部刚度分配有关，当相对刚度值越大，所承受的临界载荷也越大，越不容易失稳．反之，越容易失稳，且失稳时所释放的能量越大，危害也越大．给出了算例，其计算结果可为安排开采顺序、合理布置采场等提供依据．

Cusp Catastrophe Model of Instability of Pillar in Asymmetric Mining

A simplified mechanical model of pillar_hang wall was established in asymmetric mining and instability of the system was discussed by means of potential energy principle and cusp catastrophe theory. The necessary_sufficient condition and the jump value of displacement of pillar and the released energy expressions were derived, which established foundation for quantifying of the instability of system. The results show that instability of the system is related to load and its stiffness distribution. The critical load increases with the increasing relative stiffness, and the system is more stable.On the contrary, the instability of system is likely to occur, and the released energy is larger in instability process, and the harm is more tremendous accordingly. Furthermore, an example was calculated,and the estimated results correspond to practical experience, which provide basis for mining order and arranging stope.