Application of critical path analysis to fractal porous media: comparison with examples from the Hanford site

Critical path analysis from percolation theory is used to calculate the unsaturated hydraulic conductivity, K(S), of soils with pore space compatible with a (sometimes complex) fractal description. The fractal descriptions are chosen in accord with particle-size distributions of two soils at the US Department of Energy Hanford Site. One of the two soils exhibits a bimodal particle-size distribution, and is treated as a “dual” fractal. The results are then compared with measured hydraulic properties of these two soils. The analysis yields excellent agreement with experiment over 4–6 orders of magnitude in most investigated properties without use of fitting parameters. It is possible to show that such unusual phenomena as a sudden increase in the spread of K values with reduction of matric potential can be traced to effects of a bimodal distribution of pore sizes. The least certain parameter for calculation of K is the “critical volume fraction”, αc, which describes the minimum water content for which an interconnected network of capillary flow exists. The values deduced for αc, however, allow consistent interpretation in both soils investigated (in contrast to fitted values of a “residual moisture content” obtained by application of the van Genuchten function). Further, values of αc obtained correspond well with threshold moisture contents for solute diffusion reported elsewhere, evidence for the relevance of percolation to dispersion.