Unsaturated hydraulic conductivity of structured porous media: A review of liquid configuration-based models

Common approaches for modeling hydraulic functions of unsatu- rated structured porous media (SPM) rely on macroscopic continuum representation, where parameterization schemesand constitutive rela- tionships originally developed for homogeneous porous media are extended to represent hydraulic behavior of dual (or multi) continuum SPM. Such models often result in inconsistencies due to lack of consid- erationof structuralporespacegeometry andtheneglect ofunderlying physical processes governing liquid retention and flow under unsatu- rated conditions. We review a new framework that considers equilib- rium liquid configurations in dual continuum pore space as the basis for calculation of liquid saturation and subsequent introduction of hydrodynamic considerations. The SPM pore space is represented by a bimodal distribution of pore sizes, reflecting two disparate popula- tions of matrix and structural pores. Three steady-state and laminar flow regimes are considered to derive unsaturated hydraulic conduc- tivity functions: (i) flow in completely filled pore spaces, (ii) corner flow in partially filled pores and grooves, and (iii) film flow on solid surfaces. Two key assumptions are used in deriving the average cross- sectional flow velocities in these regimes: (i) that equilibrium liquid- vapor interfaces remain stable under slow laminar flows and (ii) that flow pathways are parallel. Liquid-vapor interfacial configurations for different matric potentials are calculated and statistically upscaled to derive sample-scale saturated and unsaturated hydraulic conductivity from velocity expressions weighted by the appropriate liquid-occupied cross-sectional areas, neglecting three-dimensional (3-D) network ef- fects. Similarly, the hydraulic functions for matrix and structural pores are derived separately and later combined by weighting the individual contributions by the porosities of the associated pore spaces. A param- eter estimation scheme was developed to calculate liquid saturation and to predict sample-scale unsaturated hydraulic conductivity. Model evaluation using measured data for homogeneous porous media, frac- tured welded tuff, and macroporous and aggregated soils shows favor- able agreement (within the limitations of model assumptions). Effects of nonequilibrium conditions between matrix and structural pore do- mains on the hydraulic conductivity and approximate consideration of 3-D network effects are discussed.