Fractal modelling, characterization and simulation of particle-size distributions in soil

A modelling of particle-size distribution in soil (PSD) by means of the fractal mass distribution is presented. The model is based on a new interpretation of the invariance of PSD with respect to the scale. It is shown that the modelized PSD can be mathematically determined from soil textural data. Combining some well-founded theoretical results from fractal geometry, the model allows us to simulate the PSD of a given soil and its characterization by means of the entropy dimension. The scaling behaviour of mass-size (or particle-number) distribution empirically shown by different authors, is obtained from the model as a theoretical result. The model allows the testing of the degree of self-similarity of soil PSDs and can be used for predicting soil properties related to the PSD, as well as the characterization of soil textures.