Van Genuchten’s Empirical Functions: Hypothesis Testing and Comparison with Theoretically Based Analogues

The objective of the work is to theoretically substantiate and functionally represent the hydrophysical properties of a capillary-porous medium (CPM), such as soil or dispersed ground, in a hysteresis scan, as well as to prove the advantages of the proposed hydraulic functions of CPM. This objective is achieved by solving a number of relevant problems: (1) theoretical (physical, physicostatistical) substantiation of the CPM water retention capacity, taking into account the hysteresis phenomenon, and mathematical formulation of the CPM hydraulic functions using a single set of interpreted parameters; (2) comparison of the Van Genuchten’s empirical functions with their theoretically substantiated analogues based on independent data on 38 objects of different texture and genesis from an accessible authoritative source, the Mualem catalogue; and (3) assessing the reliability of differences (according to the Williams–Kloot criterion) between the errors of point approximation of experimental data, as well as between the errors of predicting the values of relative hydraulic conductivity and the scanning branches of the hysteresis of water retention capacity to select the preferred hydraulic functions. We use the concept of the mean radius of the curvature of the surface of moisture meniscus in CPM, which is related to the capillary pressure of moisture by the Young–Laplace law. A number of hydraulic functions proposed earlier are theoretically substantiated. In computational experiments, the original computer programs SoilHydrophysics-v.1.0 and SoilHysteresis-v.1.0 were used. Hypotheses regarding the Van Genuchten’s functions are discussed and recognized as erroneous. The original hydraulic functions presented here are recommended as a replacement for widely known (but less preferred and outdated) analogues.