Systematic analysis of the complexity of fracture systems, especially for three-dimensional (3D) fracture networks, 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 (Δα) 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, κ (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 Δα. 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 Δα, κ and F_D become more significant. For both stages, there is a weak finite-size effect for D and no finite-size effect for Δα. Therefore, a large fracture system is more suitable for a stable fractal dimension estimation, but no requirement for the estimation of Δα. D and Δα are almost independent. Therefore, they can separately quantify different aspects of complexity.

对裂缝系统复杂性的系统分析，尤其是对三维 (3D) 裂缝网络的系统分析，在很大程度上是不够的。在这项工作中，我们使用随机离散裂缝网络方法生成具有各种几何形状的不同裂缝网络。利用分形维数（D）和多重分形谱中的奇异性变化（Δα ）来量化裂缝网络在不同方面（空间填充和异质性）的复杂性。然后系统地研究影响复杂性的因素，包括几何裂缝特性和系统大小。我们通过考虑裂缝网络的两个关键（渗透和过度渗透）阶段来概括分析。在第一阶段，κ（裂缝方向）是D的最重要参数，仅次于a（裂缝长度）和L（系统尺寸）。F _D（裂缝位置）与D的相关性较弱，但与 Δ α的相关性强。在第二阶段，每个几何参数的灵敏度结果和系统尺寸与第一阶段的D相同。对于 Δ α，κ和F _D变得更显着。对于这两个阶段，D的有限尺寸效应较弱，而 Δ α没有有限尺寸效应. 因此，大裂缝系统更适合稳定的分形维数估计，但对 Δα 的估计没有要求。D和 Δα几乎是独立的。因此，他们可以分别量化复杂性的不同方面。