基于尖点突变模型的矿柱失稳机理研究

Study of Mechanism of Destabilization of the Mine Pillar Based on a Cusp Catastrophic Model

采用突变理论建立了金矿矿柱失稳的一个尖点突变模型,并据此对矿柱失稳破坏发生机理进行了分析.基于定态曲面方程和分支曲线方程,分别求得矿柱应力强度比Fq和临界破坏宽度rp1.研究表明:当Fq>1或rpz>rp1时,矿柱会发生失稳;当Fq<1或rpz<rp1时,矿柱不会发生失稳;而在控制平面尖点曲线内右分支曲线附近,矿柱破坏宽度rpz微小的增量,就可能导致矿柱由不失稳状态突变为失稳状态.实例分析表明:该模型用于描述矿柱应力强度比的发展规律是恰当的,用其进行矿柱失稳预测也是较准确的.

Based on the catastrophe theory, a cusp catastrophic model of the destabilization of mine pillar was proposed and used in the destabilization mechanism analysis of mine pillar. According to the function of stationary curved surface and branch curve, the stress strength ratio Fq and critical breakage width rp1 can be obtained, respectively. The results show that if Fq〉1 or rpz〉rp1 , mine pillars will be destroyed, while if Fq〈1 or rpz〉rp1 , mine pillars will not be destroyed. And a tiny increment of rpz will result in the instability of mine pillars near the right branch curve in control plane. The application results show that this model is suitable for describing the development rule of the stress strength ratio and is quite exact in predicting destabilization of mine pillar.