Analysis of the scale-dependence of the hydraulic conductivity in complex fractured media

Fractured geological media are complex systems where hydrodynamic parameters are highly variable as result of their structure. Indeed, measured parameters depend on the scale and the implemented methodologies. with high variability of hydrodynamic parameters. This variableness also depends on the scale of measurement. Most theoretical frameworks assume homogeneous media adding uncertainty to the fractured media hydrogeological characterization. In fractured media, the complexity is even harder to characterize as available theoretical frameworks assume homogeneous media. Nevertheless, the increase of underground engineering projects and their reported impacts on surface and groundwater resources claim efforts to a better understanding of fractured media groundwater hydrodynamics. In this work, we propose a general approach for the scale-dependence of the hydraulic conductivity based on power law concepts. To do so, the hydraulic conductivity field of a highly fractured massif in the Colombian Andes is estimated over scales from 6 cm to 12 km. Laboratory measurements, re-analyzes of hydraulic tests, and calibration of 3D numerical models were performed, using the La Linea tunnels (in Colombia) as real scale laboratory. Hydraulic conductivity values vary up to four orders of magnitude at each characteristic length scale and show an increase until the local scale, followed by a small decrease at regional scale. In this way, field and regional scales display the same orders of magnitude. Finally, the scale-dependence of the hydraulic conductivity values based on power law concepts is proposed. As a consequence, it suggests the possibility to use field data in regional models, once hydrogeological units and structures are properly defined.