Stochastic representation of material heterogeneity and its effects on flow: applications in soils of mixed wettabilities

This work presents an investigation into the modelling of the hydraulic behaviour of heterogeneous soils of mixed wettabilities. The model represents moisture transfer of a liquid phase, and can account for the highly non-uniform nature of unsaturated flow in soil due to the presence of strong heterogeneity. This is accounted for with Gaussian random fields to represent an arbitrary number of spatially varying material properties. The theoretical formulations are presented to model this complex behaviour, as well as their numerical solutions which form the foundation of the developed model. The chosen method of random field generation is also investigated in terms of reducing the error in the correlated structures near the domain boundaries, as well as removing the need to solve over an extended domain. Methods to account for water repellency in soil are also given, such that the exaggerated flow behaviour it exhibits in relation to wettable unsaturated soil can be represented. Validation of the model was conducted through representing field tracer experiments to assess the ability of the model to predict suitable vertical profiles of dye coverage. This was conducted for both wettable and water repellent soil, and quantified through confidence intervals such that a very low number of simulations was able to describe the overall model response to a high level of confidence. The following conclusions can be drawn. The inclusion of material heterogeneity is crucial in representing complex unstable flow processes in soil of any wettability. The non-linear constitutive behaviour of the material that was predicted by the model simulations would be difficult to account for without spatial variability of material parameters. Similarly, the applied field generation method is a fast way to introduce this, and the proposed method of error reduction in the correlation structure is suitable for complex domains. The proposed methods to account for hydrophobicity based on the soil water retention curve are sufficient to allow unstable flow to develop. The similarity in finger characteristics of both the wettable and water repellent cases with the experimental observations suggest the model is more than sufficient in representing the complex flow behaviour that both can exhibit