Characterization and Quantification of Fracture Roughness for Groundwater Modeling in Fractures Generated with Weierstrass–Mandelbrot Approach

Accurate characterization of fracture roughness is critical for modeling groundwater flow and solute transport in fractured rock aquifers, where subsurface heterogeneity significantly impacts contaminant migration and water resource management. This study investigates fracture roughness characterization by integrating the Weierstrass–Mandelbrot approach with 3D-printed experimental validation and numerical simulation verification. Specifically, all the related parameters including fractal dimensions (D), frequency density (λ), segmentation accuracy (s), and summation number (n), which control the generation of fracture roughness, along with investigation scales (rs), were initially considered, and their corresponding impacts on the fracture roughness characteristics were examined. The results revealed that D is the primary factor controlling fracture roughness characteristics, while λ shows secondary importance when exceeding 1.3. The roughness remains stable when s ≤ 3 mm, n > 200, and rs ≥ 240 × 240 mm2. Two multivariate regression models were established to describe the relationship between fracture roughness and influencing factors. The proposed methodology significantly enhances the precision of groundwater flow and solute transport simulations in fractured media through advanced high-fidelity fracture characterization, offering substantial improvements in groundwater resource management and contaminant remediation strategies.