Complicated geometrical patterns of microcracks are caused by the change in stress field and the heterogeneity in rocks and so on. The geometrical patterns of microcracks are characterized by fractal dimensions, which are related to the physical constants, such as diffusion coefficient and permeability coefficient. The process for characterizing microcracks consists of extraction of microcracks, digitizing the extracted the patterns of microcracks and analysis of digitized data.
In this study, the geometrical patterns of microcracks in granitic rocks are characterized 8 bits (256 levels) gray scale data by using replica method and multifractal analysis which is an expansion of the fractal geometry. The result is summarized as follows:
1) The geometrical patterns of microcracks could be differentiated by width of microcrack.
2) The microcracks of granitic rocks are the multifractal set and have to be characterized by the generalized dimension D (q) which means spectra of the plural fractal dimensions.
3) The generalized dimension D (q) may be an index of a degree of the heterogeneity of the geometrical patterns of microcracks in granitic rocks.
The generalized dimension D (q), which is characterized by the distribution of patterns of microcracks in granitic rocks, could differentiate from its origin such as regional stress, sheeting and weathering.
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