Delesse principle and statistical fractal sets: 2. Uni®ed Fractal Model for soil porosity

Self-similar fractals are useful models of the soil solid and pore sets along lines, across areas and inside volumes. The scaling properties of these sets, analysed by the divider method within the known scale range over which the fractal extends, were described by three parameters, the solid (Ds) and pore (Dp) linear box or capacity empirical fractal dimensions, and the total number of rulers that covered the line (Nt). The empirical fractal model for soil porosity was developed and compared with the more commonly used theoretical one, and the Uni®ed Fractal Model (UFM) for soil porosity was proposed. This model extracts the soil linear (NL), areal (AP) and volumetric (VP) porosity from the solid and pore distributions along the lines. The accuracy of the empirical model was tested for NL, AP and VP, within the scale range from 0.008 to 3 mm, by using the real macro and micromorphological images of soils and sediments with contrasting genesis, available from ®eld experiments and published by other researchers. It was shown that the proposed model offers a rapid and statistically coherent solution to porosity estimation. The UFM for soil porosity was derived starting from the theoretical and empirical ones. The UFM is useful to solve the relationship between NL, AP and VP, and to estimate the alternative space ®lling ability of solid and pore sets along a line, across an area and inside a volume. # 1999 Elsevier Science B.V. All rights reserved.