对称协同开采人工矿柱失稳的突变理论分析

摘要

根据材料力学理论,建立顶板-人工矿柱协同作用力学模型；通过分析组合结构的变形协调机制,推导人工矿柱压缩量关系式；基于突变理论,构建人工矿柱突发失稳的尖点突变模型,导出失稳的充要条件力学判据表达式.研究结果表明:人工矿柱突发失稳与刚度比k、介质均匀性系数m具有密切相关性;改变人工矿柱的力学参数和几何参数,可在一定程度上调控顶板的稳定性,这可为采空区应力环境再造和人工矿柱的科学设计提供基本力学依据.%According to the materials mechanics theory, the synergistic effect mechanical model of roof-artificial pillar was established. By analyzing the deformation coordinated mechanism of the composite structure, the relationship expression of compression amount of the artificial pillar was derived. Based on the catastrophe theory, the cusp catastrophe model of artificial pillar destruction was constructed and the mechanical judgment expression under the necessary and sufficient condition of instability was derived. The results show that the artificial pillar's sudden instability has a close correlation with the rigidity ratio k and medium uniformity coefficient m. Through changing the artificial pillar's mechanics parameter and the geometric parameter, the roofs stability is regulated to a certain extent, which provides the basic mechanics basis for the cavity stress environment reconstructing and the artificial pillar's scientific design.