岩石节理(断裂)表面的多重分形性质

MULTIFRACTAL BEHAVIORS OF FRACTURE SURFACES IN ROCKS 1)

提出了新的投影覆盖法———ＰｒｏｊｅｃｔｉｖｅＣｏｖｅｒｉｎｇＭｅｔｈｏｄ（ＰＣＭ），并结合无接触激光表面测量技术直接测定出断裂表面分维值Ｄ∈［２，３）．建立了表面粗糙性投影覆盖概率函数，分析了节理（断裂）表面的多重分形性质．

Following fractal geometry introduced by B.B. Mandelbrot,many researchers have described quantitatively the roughness of fractured surfaces and also tried to establish the relationship between the fractal dimension and mechanical parameters. Extensive experiments and measurement show that, to some extent, fracture surfaces in rocks exhibit statistical fractal behavior in a certain range of scale. In fact, understanding of fractal behavior of fracture surfaces advances step by step. Initially, people paid attention mainly to the morphology of fracture surface and considered a fracture surface a self similar fractal. The investigation were limited to the measurement of self similar fractal dimension. Recent studies show that fracture surfaces are not simple self similar fractals. It is impossible, therefore, to describe roughness of fracture surfaces by using a single fractal dimension. Fracture surfaces display multifractal behavior. In general, it is very difficult to make a direct measurement for a rough surface. Mostly, some indirect methods had to be employed, such as the slit island analysis (SIA), the divider, and self affine varogram, in measuring of a sectional fracture profile. As a result, fractal dimensions measured by these methods fall in the range 1 <D <2. In other words, these methods simplify two dimensional measurements to one dimensional ones. Since the anisotropy and heterogeneity of fracture surface structure, these measurement do not show a real fractal dimension ( D ∈[ 2, 3)) of the fracture surface. It has been a difficult problem to directly estimate real fractal dimension for a fracture surface. In this paper, a new measurement method—projective covering method is proposed which makes it possible to cover two dimensional fractal object for direct estimation of real fractal dimensions D ∈[ 2, 3) for fracture surfaces. The probability function of surfaces roughness is constructed for the analysis of fracture surface within the framework of〖HJ*4] multifractal theory. Based on the measurements by means of a laser scanner, the fractal dimension D ∈[2, 3) for a set of fracture surfaces in rocks is directly estimated by using this projective covering method. The measuring results agree well with the theory of fractal geometry. The multifractal behavior of natural fracture surfaces in rocks have been investigated. Besides the general relationship between the tensile strength of rocks and fractal dimension of rock fracture surfaces ( σ T is reverse proportional to D ), the multifractal spectrum could pronounce much more information on fracture mechanism. The fracture surfaces induced in rocks under different failure mechanics display distinct multifractal properties.