The ability to calculate soil hydraulic properties from soil physical data has been a dominant objective of soil physics research since the 1950s. The purpose of this study was to develop an approach based on modern physics to deal with an arbitrary porous medium. Some important advances resulted from applying critical path analysis from percolation theory and percolation scaling to a truncated random fractal model (Rieu and Sposito) of a soil. In fact, some of the perceived limitations of the fractal model at high and low saturations were reevaluated as strengths in the previous application. Nevertheless, it is not realistic to expect all media to be characterized accurately in such a simple fashion. We developed an appropriate generalization of the description of the medium to an arbitrary pore size distribution while maintaining the complications related to fluid connectivity at high and low saturations relating to percolation theory. It also maintains the relevance of the pore size distribution to the hydraulic conductivity through the application of critical path analysis. A numerical routine was constructed to apply these concepts to an arbitrary pore size distribution, which in our case was inferred from experimentally determined particle size data. Although more than 50 soils were investigated, our preliminary study does not indicate what the general relevance of fractal models is.

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