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.