Lognormal Distribution Model for Unsaturated Soil Hydraulic Properties

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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.

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