基于尖点突变理论的充填体下采空区安全顶板厚度计算模型

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。

A computational model of safe thickness of roof under filling body based on cusp catastrophe theory

The roof structure above goaf is prevalent in mines which use backfill method. Determining the reasonable thickness of the roof under the loads of filling body is important to guarantee the mine safety. The mechanisms of formation and failure of the roof above the goaf under the filling body were analyzed and a mechanical stability model of the roof structure was established to analyze the instability mechanism by applying the cusp catastrophe theory. The expression of the limit thickness of the goaf roof under filling body was deduced according to the sufficient condition and necessary condition of roof structure instability in cusp catastrophe model. The expression was applied to a lead and zinc mine and the safe roof thickness was calculated to be larger than 11.48 m. 12 m was used as the safe thickness and verified in the practical production and numerical simulation.