基于突变理论的采空区顶板安全厚度多因素预测模型

确定采空区顶板安全厚度对保证矿山作业安全具有重要意义。本文采用有限差分软件FLAC3D，基于尖点突变理论和强度折减法研究西石门铁矿采空区顶板安全系数与其厚度的函数关系，建立了顶板安全厚度判断方法。在此基础上，通过单因素试验研究了采空区纵深、跨度、高度、顶板粘聚力与抗拉强度对采空区顶板安全厚度的影响，结果表明：纵深、跨度、顶板粘聚力、抗拉强度与顶板安全厚度之间分别呈现线性、非线性正相关、非线性负相关、非线性负相关的变化关系；高度对顶板安全厚度的影响非常小。并建立了综合考虑采空区纵深、跨度、顶板粘聚力与抗拉强度4种因素的采空区顶板安全厚度预测模型，为确定采空区顶板安全厚度提供了一种新的研究方法。模型预测结果与某硫铁矿瞬变电磁勘探结果相吻合，验证了预测模型方法的科学性和有效性。

Multi-factor prediction model of roof safety thickness in goaf based on catastrophe theory

It is of great significance to determine the safe thickness of goaf roof to ensure the safety of mine operation. In this paper, based on cusp catastrophe theory and strength reduction method, the functional relationship between roof safety factor and its thickness in Xishimen Iron mine goaf is studied by using finite difference software FLAC3D. On this basis, the influence of goaf depth, span, height, roof cohesion and tensile strength on the safe thickness of goaf roof is studied by single factor test. The results show that: there are linear, nonlinear positive correlation, nonlinear negative correlation and nonlinear negative correlation between depth, span, roof cohesion, tensile strength and roof safety thickness; the influence of height on roof safety thickness is very small. The prediction model of the safe thickness of the goaf roof is established considering the four factors of the depth, span, roof cohesion and tensile strength, which provides a new research method for determining the safe thickness of the goaf roof. The prediction results of the model are consistent with the transient electromagnetic exploration results of a pyrite, which verifies the scientificity and effectiveness of the prediction model method.