Amongst the numerous existing methods to characterize fractured media, previous work has demonstrated that geoelectrical measurements, acquired either along the Earth's surface or in boreholes, may provide important information regarding fracture network properties. However, the lack of numerical approaches adapted to the strong contrast in geometrical and electrical properties between the fractures and the rock matrix prevents us from systematically exploring the links between geoelectrical measurements and fractured rock properties. To address this issue, we present a highly computationally efficient methodology for the numerical simulation of geoelectrical data in 2.5-D complex fractured domains. Our approach is based upon a discrete-dual-porosity formulation, whereby the fractures and rock matrix are treated separately and coupled through the exchange of electric current between them. Our methodology is validated against standard analytical and finite-element solutions and used to simulate geoelectrical data for a variety of different fracture configurations. This results in demonstrating the sensitivity of these data to important parameters such as the fracture density, depth, and orientation, and in opening new perspectives in terms of the inversion of geoelectrical data in order to characterize fractured rocks.