深部回采矿柱失稳的尖点突变理论分析及宽度优化

为正确估算矿柱承受载荷，运用普氏理论分析矿柱承载机理，指出矿柱承受载荷为上覆岩层拱形塑性区的重力，计算出矿柱体系中单个矿柱承受的平均载荷。建立矿柱失稳的尖点突变模型，推导出矿柱能量方程，分析矿柱失稳力学机制，根据矿柱失稳的充分条件和必要条件得出矿柱极限宽度值的计算方法，并分析主要因素对矿柱宽度极限值的影响规律。通过工程实例验证矿柱宽度计算方法的有效性和适用性。研究结果表明:影响矿柱宽度的主要因素包括开采深度、采场宽度和矿柱高度；以冬瓜山铜矿为例，矿柱宽度的理论计算值应大于3.63 m，数值分析选取矿柱宽度为4 m时，矿柱处于稳定状态.现场工业试验表明，宽度为4 m的矿柱稳定性较好。

Cusp catastrophe theory analysis and width optimization on instability of pillar in deep mining

In order to estimate the bearing load of the pillar correctly, the Platts theory was used to analyze the load bearing mechanism of pillar, and it was pointed out that the bearing load of the pillar was the gravity of the arched plastic zone of the overlying strata, then the average load of a single pillar in a pillar system was calculated. A cusp catastrophe model of pillar instability was established, then the energy equation of pillar was deduced, and the me-chanical mechanism of pillar instability was analyzed. According to the sufficient conditions and necessary condi-tions of pillar instability, the calculation method on the limit width value of pillar was obtained, and the influence rule of main factors on the limit value of pillar width was also analyzed. Through an engineering example, the va-lidity and applicability of the method for calculating the width of pillar were verified. The results showed that the main factors affecting the pillar width included the mining depth, the stope width and the pillar height. A case study of Dongguashan copper mine showed that the theoretical calculation value of the pillar width should be greater than 3.63 m, and the numerical analysis showed that the pillar was stable when the pillar width was 4 m. The field tests showed that the pillar with a width of 4 m had better stability.