Lognormal Distribution Model for Unsaturated Soil Hydraulic Properties

Abstract

The soil water retention model developed by Kosugi was modified to be compatible with Mualem's model in order to derive an analytical expression for the relative hydraulic conductivity Kr. The modified water retention model is to be derived by applying a lognormal distribution law to the soil pore radius distribution function. Parameters of this retention model have physical significance on the water content (θ)– capillary pressure (ψ) curve and are related directly to the statistics of the pore radius distribution. The accuracy of the resulting combined water‐retention‐hydraulic‐conductivity model is verified for observed data sets for six soils. Results showed that the proposed model produces acceptable matches with observed water retention curves and adequate predictions of hydraulic conductivities in five out of six cases. The θ − ψ and Kr− ψ (or Kr − θ) curves generated by this model are generally similar to those generated by van Genuchten's model.

Column-scale unsaturated hydraulic conductivity estimates in coarse-textured homogeneous and layered soils derived under steady-state evaporation from a water table

“…But in general, there are numerous mathematically more complex expressions for K l (h) for which an analytical solution for Eq. (2) cannot be easily derived (e.g., Kosugi, 1996;Tuller and Or, 2001).…”

Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores

“…The basic geometry of the proposed unit cell is sufficiently simple and tractable for upscaling to represent the liquid retention at sample scale. A statistical framework, similar to the representation of the pore radii distribution in the BCC models [Laroussi and de Backer, 1979;Kosugi, 1994Kosugi, , 1996 …”

Unsaturated hydraulic conductivity from nuclear magnetic resonance measurements

“…P c (S w ) and k rw (S w ) are hysteretic functions describing the dependence of capillary pressure and water relative permeability, respectively, on water saturation. From a theoretical perspective and with particular emphasis on drainage-type displacements, much effort has been directed toward explaining the form of P c (S w ) and k rw (S w ) functions in terms of soil structure and pore-scale fluid distribution [e.g., Tyler and Wheatcraft, 1990;Rieu and Sposito, 1991;Perrier et al, 1995;Kosugi, 1996;Or and Tuller, 1999;Hunt and Gee, 2002;Chan and Govindaraju, 2003], offering physically meaningful alternatives to commonly used empirical expressions [e.g., Brooks and Corey, 1964;Mualem, 1976;van Genuchten, 1980].…”