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充填体下采空区顶板结构普遍存在于利用充填体进行回采的矿山。为了保证矿山的作业安全,合理确定充填体荷载作用下顶板厚度参数具有重要意义。在分析充填体下采空区顶板结构形成及破坏机制的基础上,建立该顶板结构的稳定性力学模型,应用尖点突变理论分析其失稳的力学机制。依据顶板结构尖点突变模型失稳的充分条件和必要条件,推导得到充填体下采空区顶板极限厚度值表达式。结合某铅锌矿工程实例,计算得到矿山安全顶板厚度应大于11.48 m,在数值模拟验证和实际生产中,取顶板厚度值为12 m。验证结果表明:尖点突变理论可以有效阐释充填体下采空区顶板结构失稳的力学机制,而将其运用到顶板或类似结构的稳定性分析和参数设计中是合理可行的。
The roof structure of goaf under the filling body is ubiquitous in the mines where the filling body is used for the mining. In order to ensure the safety of mine operation, it is of great significance to determine the roof thickness parameters reasonably under the condition of filling body load. Based on the analysis of the formation and failure mechanism of roof structure in goaf under backfill, the stability mechanics model of the roof structure is established and the mechanics mechanism of instability is analyzed by using cusp catastrophe theory. According to the sufficient conditions and necessary conditions for the instability of the cusp catastrophe model of roof structure, the expression of the ultimate thickness value of the roof under the gob is deduced. Combined with an example of a lead-zinc mine project, the thickness of mine safety roof should be calculated to be more than 11.48 m. In the numerical simulation and actual production, the roof thickness is 12 m. The results show that the cusp catastrophe theory can effectively explain the mechanics mechanism of roof structural instability in goaf under infill, and it is reasonable and feasible to apply it to the stability analysis and parameter design of roof or similar structures.