Supplementary data for: Liquid breakthrough time in an unsaturated fracture network

We present an experimental and theoretical study of unsaturated flow in discrete fracture networks. The focus is on the breakthrough time of infiltrating liquid through the fracture networks as well as the spatial distribution of local flow status under a wide range of flow rates. Through visualized experiments, the fluid motion in the fracture network is recorded and analyzed, and gravity-driven preferential pathways are observed. The location of the breakthrough path is found to be insensitive to the flow rate under the single-inlet flow condition. Based on analogy with slug migration in a single fracture and considering liquid accumulation due to the capillary barrier effect at the fracture intersections, we propose a theoretical model of liquid breakthrough time through an initially dry fracture network. The theoretical predictions are found to be in excellent agreement with the experiment results. Using the model, we analyze the relative contribution of times needed for liquid migration and for local liquid accumulation to the breakthrough time. We also find that the spatial distribution of local flow status at the steady-state varies significantly with the flow rate. The improved understanding and the proposed model are of significance for predicting the time required for a fluid/contaminant to reach a certain depth in unsaturated fractured media, and may provide new physical insights on the complex unsaturated flow dynamics.