A Tensorial Connectivity–Tortuosity Concept to Describe the Unsaturated Hydraulic Properties of Anisotropic Soils

Abstract

The anisotropy in unsaturated hydraulic conductivity is saturation dependent. Yet, there are few options for modeling this phenomenon in natural soils. A tensorial connectivity–tortuosity (TCT) concept is proposed to describe the unsaturated soil hydraulic conductivity. The TCT concept assumes that soil pore connectivity and/or tortuosity are anisotropic and can be described using a tensor. Saturation-dependent anisotropy can be easily invoked in common models of relative permeability by incorporating the connectivity tensor. Synthetic Miller-similar soils having hypothetical anisotropy are defined by allowing the saturated hydraulic conductivity to have different correlation range for different directions of flow. The TCT concept was tested using the synthetic soils with four levels of heterogeneity and four levels of anisotropy. The results show that the soil water retention curves were independent of flow direction but dependent on soil heterogeneity, while the connectivity–tortuosity coefficient is a function of both soil heterogeneity and anisotropy. The TCT model can accurately describe the unsaturated hydraulic functions of anisotropic soils and can be easily combined with commonly used relative permeability functions for use in numerical solutions of the flow equation.