The pore–solid fractal model of soil density scaling

We have developed the fractal approach to modelling variations in soil bulk density and porosity with scale of measurement or sample size. A new expression is derived for each quantity based on the pore–solid fractal (PSF) model of soil structure. This new general expression covers a range of fractal media and accommodates existing fractal models as special cases. Model outputs cover a range of scaling behaviour expressed in terms of monotonic functions, from increasing density and decreasing porosity, through constant porosity and density to decreasing density and increasing porosity with increasing scale of measurement. We demonstrate the link between this new model for the scaling of porosity and bulk density and the water retention model for the PSF. The model for scaling bulk density is fitted to data on aggregate bulk density and shown to yield good fits describing bulk density decreasing with increasing aggregate size. Porosity scaling is also inferred from the fitting of water retention data. Inferred porosities from different fittings are shown to follow decreasing, scale‐invariant and increasing values with decreasing size of structural unit, and these theoretical results emphasize the need for further experimental investigation on the basic issue of density scaling in soil science.