Unsaturated Hydraulic Conductivity of Structured Porous Media: A Review of Liquid Configuration–Based Models

Abstract

Common approaches for modeling hydraulic functions of unsaturated structured porous media (SPM) rely on macroscopic continuum representation, where parameterization schemes and constitutive relationships 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 consideration of structural pore space geometry and the neglect of underlying physical processes governing liquid retention and flow under unsaturated conditions. We review a new framework that considers equilibrium 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 populations of matrix and structural pores. Three steady‐state and laminar flow regimes are considered to derive unsaturated hydraulic conductivity 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 effects. 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 parameter 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, fractured welded tuff, and macroporous and aggregated soils shows favorable agreement (within the limitations of model assumptions). Effects of nonequilibrium conditions between matrix and structural pore domains on the hydraulic conductivity and approximate consideration of 3‐D network effects are discussed.