Is Blockiness an Index of the Existence of Hydraulic Conductivity Representative Elementary Volume in Fractured Rock Masses?
摘要
The hydraulic conductivity representative elementary volume (KREV) is essential for establishing equivalent porous media models in seepage analysis. In fractured rock masses, the existence of KREV is not guaranteed, as it depends on the fracture geometric parameters. This study generated three-dimensional discrete fracture networks (3D DFNs) using Monte Carlo simulation based on the International Society for Rock Mechanics (ISRM) fracture classification, incorporating varying orientation, persistence, spacing, and aperture. Flow simulations were conducted using finite difference methods across 10 domain sizes for each DFN, with equivalent conductivities calculated in 30 directions. KREV existence was assessed through hydraulic ellipsoid fitting errors and principal hydraulic conductivity. KREV is more likely to exist in rock masses with higher fracture persistence, smaller spacing, and larger angles between fracture planes. These geometric effects are quantified through blockiness (B), the ratio of isolated block volume to total rock mass volume, which measures fracture network connectivity and rock integrity. The results show that higher persistence, density, and angle between fracture planes lead to higher blockiness, increase fracture connectivity, and promote KREV formation. The results indicate that blockiness is an effective index for quantifying the existence of KREV in random fracture networks. When B < 0.01%, weak fracture connectivity hinders block formation, and KREV is not present in the fractured rock mass. When B ranges from 0.01% to 0.5%, KREV presence requires evaluation through ellipsoid fitting errors. When B > 0.5%, the fractures intersect better, KREV exists, the rock mass can be approximated as a continuous medium.