The electrical conductivity of a porous medium is strongly controlled by the 10 structure of the medium at the microscale as the pore configuration governs 11 the distribution of the conductive fluid. The pore structure thus plays a key 12 role since different geometries translate in variations of the fluid distribution, 13 causing different behaviours measurable at the macroscale. In this study, we 14 present a new physically-based analytical model derived under the assumption 15 that the pore structure can be represented by a bundle of tortuous capillary 16 tubes with periodic variations of their radius and a fractal distribution of pore 17 sizes. By upscaling the microscale properties of the porous medium, we ob-18 tain expressions to estimate the total and relative electrical conductivity. The 19 proposed pore geometry allows us to include the hysteresis phenomenon in the 20 electrical conductivity estimates. The variations on these estimates caused by 21 pore structure changes due to reactive processes are accounted by assuming a 22 uniform dissolution of the pores. Under this hypothesis, we describe the evo-23 lution of the electrical conductivity during reactive processes. The expressions 24 of the proposed model have been tested with published data from different soil 25 textures, showing a satisfactory agreement with the experimental data.