In subsurface projects where the host rock is of low permeability, fractures play an important role in fluid circulation. Both the geometrical and mechanical properties of the fracture are relevant to the permeability of the fracture. To evaluate this relationship, we numerically generated self-affine fractures reproducing the scaling relationship of the power spectral density (PSD) of the measured fracture surfaces. The fractures were then subjected to a uniform and stepwise increase in normal stress. A fast Fourier transform (FFT)-based elastic contact model was used to simulate the fracture closure. The evolution of fracture contact area, fracture closure, and fracture normal stiffness were determined throughout the whole process. In addition, the fracture permeability at each step was calculated by the local cubic law (LCL). The influences of roughness exponent and correlation length on the fracture hydraulic and mechanical behaviors were investigated. Based on the power law of normal stiffness versus normal stress, the corrected cubic law and the linear relationship between fracture closure and mechanical aperture were obtained from numerical modeling of a set of fractures. Then, we derived a fracture normal stiffness-permeability equation which incorporates fracture geometric parameters such as the root-mean-square (RMS), roughness exponent, and correlation length, which can describe the fracture flow under an effective medium regime and a percolation regime. Finally, we interpreted the flow transition behavior from the effective medium regime to the percolation regime during fracture closure with the established stiffness-permeability function. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

Shallow soils are highly vulnerable to the combined impacts of various factors, including vehicle loading, precipitation, and groundwater. The slope soil at the roadside is inevitably subjected to long-term cyclic loading from traffic. Previous studies have demonstrated that ecological engineering measures can effectively mitigate soil deformation and reduce pore water pressure development, thereby preventing soil erosion and landslides. This study aims to investigate the influence of root distribution patterns on the elastic deformation and pore water pressure development trends in root reinforced soil by simulating cyclic traffic loading through dynamic triaxial tests. The study findings demonstrate that the presence of roots significantly enhances the soil's resistance to deformation. When the vertical root accounts for 25% (while the horizontal root accounts for 75%), experimental results indicate that the soil reinforced by roots exhibits minimal deformation and slower pore water development. Moreover, a parameter D is introduced to enhance the existing pore water pressure models with the increased coefficients of determination, thereby improving the applicability in root-reinforced soils. These findings provide valuable insights for enhancing strength and liquefaction resistance in root reinforced soils while providing guiding research for the mechanical effects of root reinforcement of soil for ecological restoration of highway slopes.