Stochastic modelling of unstable preferential flow in spatially varying water repellent soils

It has been established that material variability can lead to distinct unstable hydraulic behaviour, and is prominent in soils due to their large spatial heterogeneity. This behaviour is amplified when the wettability of the medium is non-uniform, specifically if the soil becomes hydrophobic. When soil is naturally water repellent (WR), there is often spatial variability of wettability, such that a network of preferential flow paths is created. As water infiltrates, the water repellent regions will impede flow, resulting in preferential wetting pathways. This leads to highly preferential fingered flow, and can result in rapid movement of contaminants, or induce localised erosion. The WR properties of soil can be induced artificially through the addition of chemicals, via contamination, and as the consequence of natural processes such as wildfire. In this study, an investigation into the modelling of hydrophobic soil is presented. Local spatial variations in material parameters are accounted for using Gaussian random fields as part of a stochastic finite element model. This is then employed to replicate field scale experiments. A key component of the model is the relationship used to represent the saturation-capillary pressure relationship responsible for defining water entry pressures. For wettable soil, this can be achieved with the standard van Genuchten relation. For hydrophobic soil, this is not applicable; thus, an alternative is employed. Results from numerical simulations are presented, which are based on a set of published experimental data