Estimating soil water retention curve from particle-size distribution data based on polydisperse sphere systems

Soil hydraulic properties are necessary for understanding water and solute movement in subsurface vadose zone environments. Previous statistical models of soil hydraulic properties have postulated a pore-size distribution from the particle-size distribution by assuming an empirical relationship between pore sizes and particle sizes. This pore-size distribution has been used to develop the soil water retention curve and/or the relative conductivity curve. In this study, we develop soil water retention models from particle-size distribution data based on the results obtained by Torquato and coworkers on polydisperse particle systems. We model soils as systems of randomly placed spheres of random sizes and derive expressions for the soil water retention curve based on the statistical description of the systems. Two special cases of homogeneous systems of polydisperse spheres are considered: fully penetrable spheres (FPS) and totally impenetrable spheres (TIS). A lognormal particle-size distribution is assumed. More than 100 soils are used to corroborate the models. It is found that the TIS model works well for sand and loamy sand soils.