Analogue Fracture Experiments and Analytical Modeling of Unsaturated Percolation Dynamics in Fracture Cascades

Abstract

Core Ideas Mass redistribution at unsaturated fracture intersections depends on free‐surface flow modes. A Washburn‐type flow regime is recovered via an analytical solution for capillary fracture inflow. A Gaussian transfer function predicts mass partitioning for arbitrary‐sized fracture cascades. Infiltration and recharge dynamics in fractured aquifer systems often strongly deviate from diffuse Darcy–Buckingham type flows due to the existence of a complex gravity‐driven flow component along fractures, fracture networks, and fault zones. The formation of preferential flow paths in the unsaturated or vadose zone can trigger rapid mass fluxes, which are difficult to recover by volume‐effective modeling approaches (e.g., the Richards equation) due to the nonlinear nature of free‐surface flows and mass partitioning processes at unsaturated fracture intersections. In this study, well‐controlled laboratory experiments enabled the isolation of single aspects of the mass redistribution process that ultimately affect travel time distributions across scales. We used custom‐made acrylic cubes (20 by 20 by 20 cm) in analog percolation experiments to create simple wide‐aperture fracture networks intersected by one or multiple horizontal fractures. A high‐precision multichannel dispenser produced gravity‐driven free‐surface flow (droplets or rivulets) at flow rates ranging from 1 to 5 mL min−1. Total inflow rates were kept constant while the fluid was injected via 15 (droplet flow) or three inlets (rivulet flow) to reduce the impact of erratic flow dynamics. Normalized fracture inflow rates were calculated and compared for aperture widths of 1 and 2.5 mm. A higher efficiency in filling an unsaturated fracture by rivulet flow observed in former studies was confirmed. The onset of a capillary‐driven Washburn‐type flow was determined and recovered by an analytical solution. To upscale the dynamics and enable the prediction of mass partitioning for arbitrary‐sized fracture cascades, a Gaussian transfer function was derived that reproduces the repetitive filling of fractures, where rivulet flow is the prevailing regime. Results show good agreement with experimental data for all tested aperture widths.