A Study of the Scale Dependency and Anisotropy of the Permeability of Fractured Rock Masses
2025
Honglue Qian | Yanyan Li
Affected by discontinuities, the hydraulic properties of rock masses are characterized by significant scale dependency and anisotropy. Sampling a rock mass at any scale smaller than the representative elementary volume (REV) size may result in incorrect characterization and property upscaling. Here, a three-dimensional discrete fracture network (DFN) model was built using the joint data obtained from a dam site in southwest China. A total of 504 two-dimensional sub-models with sizes ranging from 1 m ×: 1 m to 42 m ×: 42 m were extracted from the DFN model and then used as geometric models for equivalent permeability tensor calculations. A series of steady-state seepage numerical simulations were conducted for these models using the finite element method. We propose a new method for estimating the REV size of fractured rock masses based on permeability. This method provides a reliable estimate of the REV size by analyzing the tensor characteristic of the directional permeability, as well as its constant characteristic beyond the REV size. We find that the hydraulic REV sizes in different directions vary from 6 to 36 m, with the maximum size aligning with the average orientation of joint sets and the minimum along the angle bisector of intersecting joints. Additionally, the REV size is negatively correlated with the average trace length of the two intersecting joint sets. We find that the geometric REV size, determined by the joint connectivity and density, falls into the range of the hydraulic REV size. The findings could provide guidance for determining the threshold values of numerical rock mass models.
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