Influence of Fracture Orientation and Stress Fields on Hydraulic Conductivity Under Strong Topographic Relief

Fractured crystalline rocks form highly heterogeneous subsurface systems in which fluid flow is controlled by the connectivity and aperture of fracture networks. These hydraulic properties are controlled by in-situ stress fields, which, in the shallow crust, results from the combined effects of regional tectonic stress, gravitational forces, and topographic relief. Although stress-dependent fracture behavior has been extensively studied at the fracture scale, the role of spatially variable stress tensors in controlling hydraulic conductivity at the catchment scale remains poorly constrained.

In this study, we investigate how topography and tectonic stresses interact with fracture network geometry to produce heterogeneity and anisotropy in hydraulic conductivity across a high mountain catchment. A three-dimensional geomechanical model is used to compute spatially variable stress tensors for both synthetic and real topographic surfaces. The resulting stress tensors are extracted cell by cell and applied to discrete fracture networks with different orientation statistics. Subsequently, for each fracture within every cell, the normal stress is calculated and used to determine stress-dependent hydraulic apertures through an exponential closure law. This is followed by the computation of fracture transmissivities using the parallel-plate cubic law. Finally, directional hydraulic conductivities are then obtained by numerical flow simulations in the principal directions (K_x, K_y, K_z).

The results show strong spatial heterogeneity and directional dependence of hydraulic conductivity across the catchment. At first order, the anisotropy of K_x, K_y and K_z is controlled by fracture network geometry, with low conductivities occurring in directions poorly aligned with dominant fracture orientations (e.g., low K_x for predominantly N–S–oriented vertical fractures or low K_z for horizontal fracture sets). Together with this geometric control, the relative orientation between fractures and the local stress tensor exerts a strong mechanical influence, fractures oriented perpendicular to the principal compressive stress experience increased normal stress, reduced aperture, and consequently lower hydraulic conductivity. In addition, spatial variations in topography introduce local perturbations in the stress tensor that produce zones of relatively higher hydraulic conductivity, where fractures remain less compressed. These combined effects lead to pronounced hydraulic anisotropy and preferential pathways at the catchment scale, highlighting the importance of explicitly accounting for spatially variable stress fields when modeling flow in fractured catchments.