Characterizing the intrinsic complexity of natural fracture networks: A novel fractal-based approach

Quantitative characterization of the intrinsic complexity of fracture networks in rock mass, which has attracted broad attention for decades, remains challenges because of the featured characteristics of fractal and random distribution. In this study, in view of the fact of the natural porous media being a dual-complexity system, the complex types of fracture networks and their assembly mechanism were firstly identified and elaborated as per fractal topography theory. On this basis, an open mathematical framework with the fractal topography parameters was established to generalize the characterization of complex types of fracture networks and the corresponding modeling algorithm for arbitrary fracture networks was accordingly developed. To realize practical application, an inversion algorithm was then proposed for extracting fractal parameters by defining their relationship with the measurable geometric attributes of fracture networks. Subsequently, CT scanning experiments were conducted, and multiple slices of the sample were analyzed to validate the effectiveness and reliability of the proposed algorithm. Finally, a comparative analysis with existing methods was performed, and the significant advantage of our characterization approach was demonstrated by the good agreement between the generated length sequences and those measured ones in physical experiments, wherein the mean absolute error is in the range of 0.21–0.71 mm across six networks. This study provides an effective framework for analyzing the influence of fracture networks on the mechanical and hydraulic behavior of rock mass, laying a foundation for more accurate assessments and predictive insights.