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<p>The natural fractures in a rock mass may control the hydraulic properties of the rock body, where fracture connectivity serves as a critical indicator for evaluating hydraulic properties between fractures in a network. Utilizing topological theory, this study quantifies the connectivity of two-dimensional (2D) stochastic fracture networks through a dimensionless connectivity index (<i>C</i>) ranging from 1 to 2. Assuming that the fractures are open, the larger the value, the better the connectivity of the fracture network. Fractal geometry principles characterize the relationships between fractal dimension and fracture geometric parameters (length and aperture), enabling the systematic generation of 2D fracture networks with statistically representative structural configurations. These numerically reconstructed networks are subsequently analyzed to investigate the effects of fractal dimension and connectivity index on permeability. A nonlinear regression model is derived through multivariate analysis of computational results, establishing an empirical correlation between 2D fracture permeability and the connectivity index and fractal dimension. The predicted results are compared with those obtained based on the equivalent permeability calculation method to verify the method′s validity.</p>

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Evaluation of two-dimensional fracture permeability based on connectivity and fractal dimension

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Kejing Chen

摘要

The natural fractures in a rock mass may control the hydraulic properties of the rock body, where fracture connectivity serves as a critical indicator for evaluating hydraulic properties between fractures in a network. Utilizing topological theory, this study quantifies the connectivity of two-dimensional (2D) stochastic fracture networks through a dimensionless connectivity index (C) ranging from 1 to 2. Assuming that the fractures are open, the larger the value, the better the connectivity of the fracture network. Fractal geometry principles characterize the relationships between fractal dimension and fracture geometric parameters (length and aperture), enabling the systematic generation of 2D fracture networks with statistically representative structural configurations. These numerically reconstructed networks are subsequently analyzed to investigate the effects of fractal dimension and connectivity index on permeability. A nonlinear regression model is derived through multivariate analysis of computational results, establishing an empirical correlation between 2D fracture permeability and the connectivity index and fractal dimension. The predicted results are compared with those obtained based on the equivalent permeability calculation method to verify the method′s validity.