采空区复杂顶板的三维分形特性及曲面模拟

摘要

以石人沟铁矿采空区探测为工程背景,首先基于分形理论,对采空区复杂顶板的三维分形特性进行定量研究,得到对应的分维值.针对采空区顶板具有自相似性的特点,应用参数方程分形插值迭代函数系统,对采空区顶板进行模拟分析.在现场有限的已知点的基础上,对采空区顶板曲面进行模拟重构.研究结果表明:采空区顶板具有明显的分形特性,顶板的三维分维值综合反映了边界线的复杂程度、暴露面积及垂直方向上起伏的剧烈程度,定量地表征了顶板的非线性程度;最终模拟重构的精度与参数ci密切相关,ci越小模拟精度越大,越接近实际情况.采空区的分形特性从本质上反映了采空区边界的非线性特征.%Taking gob detection of Shirengou iron mine as the engineering background, based on the fractal theory, the fractal characteristics of the complex roof of gob were quantitatively studied, and the corresponding fractal dimension values were obtained. According to the characteristics of self-similarity of the roof of gob, the parameter equation and iterated function system were applied to the simulation and analysis of the roof. On the basis of the finite known points of the field, the surface of the gob roof was simulated and reconstructed. The results show that the roof of the gob has obvious fractal characteristics. The three-dimensional fractal dimension of the roof reflects the complexity of the boundary line, the exposed area and the degree of fluctuation in the vertical direction, which quantitatively represents the nonlinear degree of the roof. The final precision of the simulation is closely related to the parameters ofci, The smaller theci, the greater the simulation accuracy, and the closer the simulation surface is to the actual situation. The fractal characteristics of the gob reflect the nonlinear characteristics of the gob boundary in essence.