基于分形理论的复杂采空区空间特性定量研究
首发时间:2016-06-17
摘要:综目前分形理论的应用日益增多,逐渐成为了复杂非线性空间物体的定量研究的重要手段。基于分形理论,本文对复杂采空区空间特性进行了定量研究,分别对采空区剖面一维边界线、二维剖面平面及三维顶板的分形特性进行研究,最终得到了对应的分维值,并对分维值的物理意义进行了讨论。研究表明,采空区是矿体空间上的逆反应,因此具有明显的分形特征。分维值与采空区复杂程度有密切的关系,采空区边界线蜿蜒曲折程度越大、所在剖面形状越复杂,顶板起伏越剧烈,对应的分维值也就越大。采空区任意剖面的面积与周长的关系为双对数,通过运算可确定采空区的边界及空间大小。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,并可进行进一步的理论研究,应用前景广阔。
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Quantitative Study on Spatial Characteristics of Complex Gob based on Fractal Theory
Abstract:At present, the application of fractal theory is increasing, and it becomes an important means of the quantitative study of complex nonlinear spatial objects. Based on the fractal theory, the space characteristics of complex gobs are quantitative research. Respectively to study the fractal characteristic of one dimensional boundary line, two-dimensional section plane and three dimensional roof, finally get the corresponding fractal dimension value and the physical meaning of fractal dimension is discussed. The study shows that the gobs are the reverse reaction of the ore body in the space, so it has obvious fractal characteristics. Fractal dimension is closely related to the complexity of gob. Gob boundary line winding degree is bigger, the profile shape more complex, the ups and downs of the roof is fiercer, the corresponding fractal dimension value is bigger also. The relationship between the area and perimeter of the gob is double logarithmic, the boundary and space size of the gob can be determined by calculation. The fractal characteristics of the gob reflect the nonlinear characteristics of the gob and can be further studied, he application prospect is broad.
Keywords: fractal theory complex gob fractal dimension value complex degree quantitative study
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