Generalizing the fractal model of soil structure : the pore-solid fractal approach

We reveiw a generalized approach to modeling soil structures, which exhibit scale invariant, or self-similar local structure over a range of scales. Within this approach almost all existing fractal models of soil structure feature as special albeit degenerate cases. A general model is considered which is shown to exhibit either a fractal or nonfractal pore surface depending on the model parameters. With the exception of two special cases corresponding to a solid mass fractal and a pore mass fractal the model displays symmetric power law or fractal pore size and solid size distributions. In this context the model provides an example of a porous structure in which pore sizes can be inferred from associated solid particle sizes through this symmetry. Again with two exceptions the model is shown to exhibit scaling of solid and pore volumes as a function of the resolution of measurement contrary to that of a mass fractal structure and to possess porosity other than zero or unity when local structure is included at arbitrarily small scales contrary to the situation arising in the case of a solid mass fractal and a pore mass fractal model respectively. Consequently the model not only generalizes the fractal approach to modeling soil structure but introduces properties central to the characterization of a soil which are quite distinct from those exhibited by existing fractal models. The model thus offers a wider scope for modeling self-similar multiscale soil structures than that currently operating. (Résumé d'auteur