Steady multiphase flow in two-dimensional (2D) porous media has not been established without the continuous fluctuation in pore occupancy. Cox (2019) proves the ability of liquid to bridge a gas-filled pore throat that is narrow and deeply etched, allowing liquid and gas to flow simultaneously. In this investigation, a pore network study was done to discuss the feasibility of steady two-phase flow given the possibility of liquid bridging. Hypothetical percolating gas networks near the percolation threshold were made using Excel and MATLAB to highlight how each established phase can progress through a 2D square lattice. The percolating network describes the gas phase after it has established continuous flow through a water saturated medium. It was found that flow for both phases is easiest near the percolation threshold, where water progresses through a set of isolated clusters and gas has one major cluster that spans the entire lattice. It is predicted that liquid bridging is most problematic near or in the primary gas backbone due to lamellae mobilization. For a larger lattice, it was found that there is more distance between the primary gas backbone and the main water path. In contrast, the possibility of lamellae division occurring due to pressure differences within the lattice is highlighted.

Under the current climate change projections, droughts and extreme rainfall events are becoming more common and intense. During sustained droughts, soil cracks can develop in the topsoil of a dike. These soil cracks can enhance the infiltration and drainage of the dike, affecting the dike stability. This study’s main objective is to better understand the potential influence of cracks on the hydrology and dike stability of canal dikes. A finite element model (FEM) was built to study the hydrological response and stability of a canal dike due to rainfall infiltration through a uniformly distributed cracked top layer. This model included the fast hydrological response of the fractures and their exchange with the soil. A surrogate model (a simplified data-driven machine learning model) was built using training data generated by the FEM to reduce the computational burden and allow for a sensitivity and stochastic reliability assessment. An evaluation of important model features, such as the connectivity among cracks and soil swelling, revealed that the cracks have a very localized influence on the infiltration and drainage of water through the dike. Water drainage in the toe of the dike is restricted by soil swelling resulting in a larger decline in dike stability. The sensitivity analysis found that the cracks facilitate more infiltration than drainage before the crack parameters, such as the crack aperture and the amount of cracking, reached a threshold. Above this threshold, drainage provided by the cracks is greater than the infiltration. The failure probability was calculated for a variety of different rainfall patterns. A pattern where the rainfall intensity incrementally increases over time results in the highest failure probability. The main conclusion from this study is that soil cracks influence the stability of the dike by enhancing infiltration and drainage under rainfall. Under low-intensity rainfall, the cracks in the toe facilitate more water to drain out of the dike than rainfall to infiltrate, stabilizing the dike. However, in the absence of cracks in the toe, the cracks provide more infiltration than drainage resulting in a lower dike stability. Under high-intensity rainfall, cracks in the crest and the inner slope of a dike advance the wetting front resulting in a larger decline in dike stability than a dike without soil cracks. Rainfall infiltration and drainage in a cracked dike depend on both rainfall characteristics, such as the average rainfall intensity, duration, and pattern, and the crack features, such as the crack width, amount of cracking, and the connectivity of the cracks. Since this study was not validated with observations, it is recommended that further studies aim to validate the observed influence of the cracks by conducting field experiments.