Modelling soil fragmentation: the pore solid fractal approach

Models have been developed to explain independently either the powerlaw aggregate size or the powerlaw particle-size distributions observed in many soils. We present a fragmentation model coupled with a recent model of soil structure called the pore solid fractal (PSF). The approach represents a generalisation of existing fragmentation models based on homogeneous and mass fractal soil structures. Scale invariant and incomplete fragmentation is seen to result in the creation of both distributions of aggregates and primary particles of comparable size. These two distributions are powerlaws and combine to yield a single powerlaw expression for the fragment number-size distribution. The powerlaw exponent determines a fragmentation dimension Df which integrates information about both the structure of the parent material and the intensity of the fragmentation process. This can be used to model experimental data which usually comprises a mixture of particles and aggregates. For a PSF model exhibiting scale invariant density, we obtain a powerlaw form for the cumulative distribution of fragment mass versus size that can be fitted easily to available experimental data as shown in an example. We provide a consistent theoretical background for a physically based interpretation of previous powerlaw models.