| Summary: | The distribution of pore structure inside rock has fractal characteristics in statistical sense, the determination of itsfractal dimension is of great significance to characterize the distribution law of pore structure quantitatively and reveal various mechanical behaviors and physical and mechanical indexes of rock.By combining image processing, fractal theory and mathematical statistics, the spatial distribution model of three-dimensional pore structure was reconstructed based on CT scan slice images, and the distribution box dimension and cluster dimension of pore structure in Hausdorff measure space were calculated. In order to quantitatively characterize the spatial complexity of pore structure distribution, the hypothesis of voxel box dimension and cylinder space bundle dimension was put forward, and the hypothesis was tested by various mathematical statistical methods. Finally, it is pointed out that the pore structure distribution is a multi-scale fractal model, and a single dimension cannot describe all its characteristics.The analysis results show that the voxel box dimension constructed for gray CT images can replace the traditional box dimension, and can quantitatively characterize the pore volume distribution law more reliably, accurately and comprehensively at the meso-scale. In essence, cluster dimension is used to quantitatively characterize the distribution law of pore position. If it is equal to Euclidean dimension, it indicates that pore position distribution has randomness.
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