Nonlinear Flow Behaviour in Connected Fractures: Experimental and Numerical Investigations

Fluid flow through fractured rock masses is predominantly governed by connected fracture networks, in which intersections may play a critical role in controlling flow redistribution and energy dissipation. However, the emergence of nonlinear flow and its governing mechanisms at the network scale remain insufficiently quantified. This study investigates nonlinear flow behaviour in connected pathways by integrating fracture geometry characterisation, laboratory experiments, and numerical modelling. Borehole-derived fracture statistics are used to constrain representative intersection geometries, apertures, and spacings. Laboratory flow tests reveal a transition from effective mixing at low flow rates to interface-dominated separation at higher flow rates, with the degree of flow redistribution dependent on intersection geometry. Numerical simulations demonstrate that fracture intersections generate a confined nonlinear zone characterised by streamline curvature, vortex formation, and concentrated pressure loss, leading to pronounced deviations from linear Darcy behaviour. Parametric analyses show that cross-sectional geometry has a dominant influence on flow resistance, while a significant scale effect highlights the limitations of directly extrapolating laboratory-scale measurements to field conditions. Based on these findings, a modified cubic law (MCL) is developed by introducing a geometry-dependent exponent into the aperture term to account for interaction-induced nonlinear resistance. Validation against a fracture network model indicates that the classical cubic law overestimates flow rates by approximately 30%, whereas the proposed formulation closely reproduces Navier-Stokes solutions over a wide range of hydraulic gradients. The proposed model provides a computationally efficient and physically reliable approach for incorporating nonlinear fracture flow into network- and field-scale hydraulic analysis.