The Consequences of Fractal Scaling in Heterogeneous Soils and Porous Media

In light of the subject of the special publication, it is of interest to review traditional concepts of scaling. Scaling works quite well for a large class of problems in which the porous media is homogeneous on a large scale. This chapter begins with a brief overview of fractal scaling and its basic results. It deals with a simple example of fractal scaling as applied to soil water retention. Fractal scaling suggests that soil properties will be a function of the scale of measurement and that traditional concepts of stationarity and averaging may not capture the total nature of the heterogeneity. Based on the successful use of fractals to describe a wide spectrum of physical processes and properties, it appears that it will be a valuable descriptor of the nature of soil spatial variability. The chapter presents a brief description of fractal scaling based on the notion of scale invariant transformations.