Complexity analysis of three-dimensional stochastic discrete fracture networks with fractal and multifractal techniques

Systematic analysis of the complexity of fracture systems, especially for three-dimensional (3D) fracture net-works, is largely insufficient. In this work, we generate different fracture networks with various geometries with a stochastic discrete fracture network method. The fractal dimension (D) and the singularity variation in a multifractal spectrum (delta alpha) are utilized to quantify the complexity of fracture networks in different aspects (spatial filling and heterogeneity). Influential factors of complexity, including geometrical fracture properties and system size, are then systematically studied. We generalize the analysis by considering two critical (percolative and over-percolative) stages of fracture networks. At the first stage, kappa (fracture orientation) is the most significant parameter for D, following a (fracture length) and L (system size). F-D (fracture positions) has a weak correlation with D but a strong correlation with delta alpha. At the second stage, the sensitivity results of each geometrical parameter and the system size are the same as in stage one for D. For delta alpha, kappa and F-D become more significant. For both stages, there is a weak finite-size effect for D and no finite-size effect for delta alpha. Therefore, a large fracture system is more suitable for a stable fractal dimension estimation, but no requirement for the estimation of delta alpha. D and A alpha are almost independent. Therefore, they can separately quantify different aspects of complexity.

Automated summary

The systematic analysis of the complexity of fracture systems, especially in three-dimensional (3D) fracture networks, is currently insufficient. In this study, various fracture networks with different geometries were generated using a stochastic discrete fracture network method, and their complexity was quantified using fractal dimension and singularity variation in a multifractal spectrum. The influential factors of complexity, such as geometrical fracture properties and system size, were systematically investigated. The results show that different parameters have varying degrees of significance on the complexity at different stages of fracture network development.