Evaluation of Fracture Characteristics of Random Field with Anisotropic Spatial Correlation

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Soil property varies randomly in a field and there is some correlation between its values at any two points. Especially, in an artificial soil structure like an embankment, it has some anisotropic spatial correlation due to constructive features. In our earlier work, the effect of the standard deviation and the correlation distance of soil permeability on total flow rate in a random field with isotropic spatial correlation has been clarified and spatial spanning of lower or higher permeability that forms "impervious wall" or "flow path" has been reproduced by Percolation theory. This paper attempts to evaluate objectively fracture characteristics of random field with anisotropic spatial correlation by using fractal dimensions. Spatially correlated random fields with anisotropic spatial correlation distance are generated, and fractal dimensions are examined for each of these random fields. As a result, the fractal dimensions are shown to have some close relation to the anisotropic spatial correlation in random fields.

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