基于能量法的露天开采下采空区顶板安全厚度研究

为了确定露天开采下采空区顶板安全厚度，基于力学理论，分析了露天开采下采空区顶板受力特性，建立其固支梁力学结构模型。根据能量守恒原理，推导了由顶板弯曲应变能、水平荷载做功和垂直均布荷载做功组成的采空区顶板结构总能量方程，获得了采空区顶板势能函数解析式。采用突变理论，建立了采空区顶板系统的尖点突变模型，获得了采空区顶板失稳判别式，推导出采空区顶板安全厚度计算模型。对某露天矿采空区顶板厚度进行了应用案例分析，理论计算出的最终采空区顶板临界厚度为11.34 m，与现场安全预警经验值12 m基本一致。表明所建立的采空区顶板安全厚度计算模型合理可行，可为露天开采下采空区顶板安全厚度设计提供一定的理论依据和工程指导。

Research on Safety Thickness of Goaf Roof under Open Pit Mining Based on Energy Law

To determine the safety thickness of goaf roof under open pit mining,based on the mechanics theory,the stress characteristics of goaf roof under open pit mining was analyzed,and the mechanical structure model of clamped-clamped beam was established.The equation describing total energy of goaf roof structure was derived from the energy conservation law,noted that the total energy was taken account of roof bending strain energy,horizontal load work and vertical uniform load work,and the potential energy function of the goaf roof was obtained.Based on the catastrophe theory,the cusp catastrophe model for the system of goaf roof was built,the criterion of instability of goaf roof was obtained,and also the computational model of the safety thickness of goaf roof was conducted.According to an application case study on the safety thickness of goaf roof of an open-pit mine,the final critical thickness of goaf roof was 11.34m in theoretical calculation,which is basically the same as the site safety warning of empirical value 12m.The results show that the computational model of the safety thickness of goaf roof is reasonable and feasible,which provides a theoretical basis and engineering guidance for the design of the safety thickness of goaf roof under open pit mining.