Fractured-rock aquifers represent an important part of the groundwater that is used for domestic, agricultural, and industrial purposes. In these natural systems, the presence and properties of fractures control both the quantity and quality of water extracted, meaning that knowledge about the fractures is critical for effective water resource management. Here, we explore through numerical modeling whether electrical resistivity (ER) geophysical measurements, acquired from the Earth’s surface, may potentially be used to identify and provide information about shallow bedrock fractures. To this end, we conduct a systematic numerical modeling study whereby we evaluate the effect of a single buried fracture on ER-profiling data, examining how the corresponding anomaly changes as a function of the fracture and domain characteristics. Two standard electrode configurations, the Wenner-Schlumberger (WS) and dipole-dipole (DD) arrays, are considered in our analysis, with three different spacing factors. Depending on the considered electrode array, we find that the fracture dip angle and length will impact the resistivity anomaly curves differently, with the WS array being better adapted for distinguishing between sub-horizontal and sub-vertical fractures, but the DD array leading to larger overall anomaly magnitudes. We also find that, unsurprisingly, the magnitude of the resistivity anomaly, and thus fracture detectability, is strongly affected by the depth of overburden and its electrical resistivity, as well as the fracture aperture and contrast between the fracture and bedrock resistivities. Further research into the electrical properties of fractures, both above and below the water table, is deemed necessary.

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The representative elementary volume (REV) is a critically important concept in fractured rock investigations as it tells us at what scale the fractured domain can be represented by an anisotropic tensor as opposed to requiring the details of each individual fracture for modelling purposes. Whereas the REV size and corresponding tensor characteristics for the hydraulic conductivity (K) in fractured rock have been the subject of numerous previous investigations, no studies to date have focused on the electrical conductivity (σ). This is despite the fact that geoelectrical measurements are arguably the most popular means of geophysically investigating fractured rock, typically via azimuthal resistivity surveying where the observed electrical anisotropy is commonly used to infer hydraulic characteristics. In this paper, we attempt to fill this void and present a systematic numerical study of the impacts of changes in fracturenetwork properties on the REV size and equivalent tensor characteristics for both the electrical and hydraulic conductivities. We employ a combined statistical and numerical approach where the size of the REV is estimated from the conductivity variability observed across multiple stochastic fracture-network realizations for various domain sizes. Two important differences between fluid and electric current flow in fractured media are found to lead to significant differences in the REV size and tensor characteristics for σ and K; these are the greater importance of the matrix in the electrical case and the single power instead of cubic dependence of electric current flow upon aperture. Specifically, the REV for the electrical conductivity will always be smaller than that for the hydraulic conductivity, and the corresponding equivalent tensor will exhibit less anisotropy, often with notably different principal orientations. These findings are of key importance for the eventual interpretation of geoelectrical measurements in fractured rock, where we conclude that extreme caution must be taken when attempting to make the link to hydraulic properties.

Modeling fluid flow in three-dimensional fracture networks is required in a wide variety of applications related to fractured rocks. Numerical approaches developed for this purpose rely on either simplified representations of the physics of the considered problem using mesh-free methods at the fracture scale or complex meshing of the studied systems resulting in considerable computational costs. Here, we derive an alternative approach that does not rely on a full meshing of the fracture network yet maintains an accurate representation of the modeled physical processes. This is done by considering simplified fracture networks in which the fractures are represented as rectangles that are divided into rectangular subfractures such that the fracture intersections are defined on the borders of these subfractures. Two-dimensional analytical solutions for the Darcy-scale flow problem are utilized at the subfracture scale and coupled at the fracture-network scale through discretization nodes located on the subfracture borders. We investigate the impact of parameters related to the location and number of the discretization nodes on the results obtained, and we compare our results with those calculated using reference solutions, which are an analytical solution for simple configurations and a standard finite-element modeling approach for complex configurations. This work represents a first step towards the development of 3D hybrid analytical and numerical approaches where the impact of the surrounding matrix will be eventually considered.