Closed-form model for hydraulic properties based on angular pores with lognormal size distribution

We previously presented a mathematical model for hysteretic soil hydraulic properties based on bundles of angular pores. Upscaling to sample-scale hydraulic properties was done analytically, assuming a Gamma density distribution of pore sizes. The required parameter constraint for getting the closed-form solution limited the model's applicability for soils with wide pore-size distributions. The objective of this study was to improve the model by developing a new analytical solution based on a lognormal density function of the pore-size distribution. Closed-form expressions were derived for liquid retention, saturated-unsaturated hydraulic conductivity, liquid-vapor interfacial area, and specific surface area at the sample scale. The new model was applied to retention and conductivity data for three soils with different pore-size distributions. The results show that the previous model is suitable only for sandy materials, whereas the new one describes the soil hydraulic functions of a wider range of soil types quite well.