Time-lapse electrical resistivity monitoring of coupled non-Darcy flow and non-Fickian solute transport in a filled-fracture–matrix sandbox

Abstract Fractured-rock aquifers hold a significant share of the world’s accessible groundwater, yet predicting contaminant migration through them remains difficult: flow in fractures can depart from Darcy’s law, transport across the fracture–matrix interface is rarely Fickian, and direct observation of both domains has typically required invasive sampling. We address these issues with a transparent vertical sandbox in which a coarse-quartz filled fracture (a high-permeability porous-channel analogue) of variable aperture ( b = 0–4 cm) is flanked by fine-quartz matrices of three grain sizes (0.06, 0.12 and 0.27 mm), instrumented with a 64-channel electrical resistivity tomography (ERT) instrument operated in time-lapse monitoring mode (“ERT monitoring” hereafter), whose electrode array recorded point breakthrough curves at six positions. Twelve hydraulic gradients ( J = 0.075–0.9) drove the flow tests, and 1.0 g L⁻¹ NaCl pulses served as conservative tracers; ERT-derived resistivity time series at six monitoring points yielded high-resolution breakthrough curves in both domains. The Darcy regime held when the fracture-to-matrix permeability contrast was ~ 10²; once it reached ~ 10³ and b ≥ 1 cm, the Forchheimer equation provided the better fit. The critical Reynolds number rose nonlinearly with aperture, from 3.4 to 66.5 for K f / K m ≈ 10³ and from 2.9 to 52.4 for K f / K m ≈ 10⁴, scaling approximately as Re c ∝ b (2.0±0.3) . Fracture breakthrough curves displayed early arrival and long tails; matrix curves developed delayed secondary peaks consistent with back-diffusion. Reducing matrix grain size from 0.27 to 0.06 mm tripled the matrix peak time and lowered its peak concentration by 74%. For this sandbox analogue, the dataset establishes quantitative thresholds for the onset of non-Darcy flow in coupled filled-fracture–matrix systems and indicates that back-diffusion is the most likely control on late-time matrix concentrations, providing process-based constraints for dual-domain transport models.