Complex Electrical Conductivity of a Single‐Fractured Rock: Fracture‐and‐Matrix Coupling Mechanism and Aperture Size Predictions

Abstract Fractured rocks play a crucial role in myriad natural and engineered systems, including Earth's critical zone, oil/gas/geothermal reservoirs, and geological CO 2 /H 2 /waste storage systems. While complex electrical conductivity is extensively used to estimate the pore and grain sizes of conventional porous rocks and soils, it is rarely used to predict the aperture size of fractured rocks and this remains poorly understood. Here, integrating theory, simulations, and experiments, we show that under external fields, fractured rocks follow the fracture‐and‐matrix coupling to make the bulk complex conductivity non‐linear with respect to water conductivity. We find that the relaxation time and quadrature conductivity for porous media do not apply to fractured rocks, but, instead, reasonably accurate predictions of aperture size can be made based on the true formation factor. This study unravels the fundamental mechanism governing conduction and polarization of fractured rocks and paves the way for the non‐invasive investigation of global fractured rocks.