Representation of three-dimensional unsaturated flow in heterogeneous soil through tractable Gaussian random fields

Abstract

The representation of the spatial variability of soil properties is required to model non-uniform hydrological flow processes such as fingering and preferential moisture migration, which are prominent in both unsaturated and hydrophobic soils. This paper presents a new method for simulating three-dimensional hydrological flow processes in soil masses in which random fields of soil properties are conveniently generated through the numerical solution of a set of partial differential equations that have the same structure as those used for computing moisture transport. The method uses the Whittle–Matérn autocorrelation function to generate the required correlated Gaussian random field. A new method for representing statistical boundary effects on the degree of moisture infiltration is also presented. The statistical model component is integrated into a finite-element code for moisture transport and applied to the simulation of moisture infiltration and flow within an in situ layer of sandy loam. The transport properties and associated statistical measures employed to generate the random field are those reported in the experimental study. The results from the numerical simulations show that the model represents fingered flow behaviour with good accuracy, with the numerical and experimental infiltration fronts having similar characteristics and infiltration rates.