非对称布置人工矿柱失稳的突变理论分析

Catastrophe Theory Analysis on Instability of Asymmetrically Arranged Artificial Pillar

人工矿柱置换矿石矿柱是当前矿柱资源回采的基本模式之一,开展非对称布置人工矿柱突发失稳的力学条件分析具有重要普适意义。根据材料力学理论,建立了"非对称布置人工矿柱-顶板"结构系统力学模型,推导出人工矿柱的压缩量表达式;基于突变理论,在考虑顶板对人工矿柱小偏压作用的基础上,构建了非对称布置人工矿柱突发失稳的尖点突变模型,推导了人工矿柱失稳的充要条件力学判据表达式。分析表明:非对称布置人工矿柱-顶板结构系统失稳与系统刚度比k、介质均匀性系数m相关;改变人工矿柱的参数,可影响人工矿柱对于顶板的调控作用,非对称布置人工矿柱施工应满足最小宽度尺寸。广西某矿实例研究结果表明:在特定人工矿柱非对称布置条件下,该矿应留设21m宽的人工矿柱支撑顶板。研究成果可为矿柱资源回采过程中的人工矿柱设计提供理论依据。

The replacement of ore pillars by artificial pillars is one of the basic recovery modes of pillar resources at present.It is of great universal significance to analyze the mechanical conditions of the sudden instability of asymmetrically arranged artificial pillars.According to the theory of material mechanics,the mechanical model of asymmetrically arranged artificial pillar-roof structure system was established,and the expression of the compression of artificial pillar was deduced.Based on catastrophe theory,the cusp catastrophe model of sudden instability of asymmetrically arranged artificial pillar was constructed considering the small eccentric pressure of roof on artificial pillar.And the mechanical criterion expression of necessary and sufficient condition was deduced for the instability of artificial pillar.The analysis showed that the instability of the asymmetrically arranged artificial pillar-roof structure system was related to the stiffness ratio(k)of the system and the homogeneity coefficient(m)of the medium.Changing the parameters of the artificial pillar could affect the regulation and control of the artificial pillar on the roof,and the construction of the asymmetrically arranged artificial pillar should meet the minimum width size.The results of a case study in a mine of Guangxi showed that under the condition of asymmetrical arrangement of specific artificial pillars,a 21 m wide artificial pillar should be set up to support the roof.The research results could provide a theoretical basis for the design of artificial pillars in the process of pillar recovery.