For 43 Hanford site soils, we use fractal analysis and assume proportionality of pore radii to particle radii to generate water-retention curves, h(θ), from particle-size distributions. The air-entry head is used as an adjustable parameter to optimize the fit to experimental data for h(θ). At a low moisture content, θd, the predicted and observed water-retention curves deviate. It is shown here that the moisture content at which this deviation occurs is in most cases probably the same value, at which previous experiments found a vanishing of solute diffusion. Where this correlation is indicated, we interpret θd as a critical moisture content for percolation of capillary flow paths, and the relevance of other mechanisms of water transport, such as film flow, to equilibration at lower moisture contents. In other individual cases, however, the deviation is correlated with very low values of the hydraulic conductivity associated with capillary flow. In either case, we infer that the deviation from fractal predictions is due to the lack of equilibration of the medium. Our work thus exploits theoretical and analytical gains from percolation theory and fractal analysis to define the equilibrium limits on water retention curves.