The multi-fractal nature of soil particle size distribution

The particle size distribution of soils is an indicator of their history and it plays a role in their mechanical behaviour, so that characterizing the grading curve of soil and its evolution during loading has been a focus of research in geotechnical engineering and in geology. There is experimental evidence that upon compression to high stress or shearing to high strain, or a combination of both, a soil grading would reach an ultimate fractal distribution. A fractal dimension of 2.5 was found to describe the ultimate grading of several uniform soils, and this dimension has proved to be a useful parameter for constitutive modelling. In its "natural" state however a soil may not have a fractal distribution of particle sizes, especially over the large range of particle sizes that can now be detected using advanced particle imaging technology, and it may never reach an ultimate fractal grading if it is discontinuous e.g. gap-graded soil. This paper investigates the multi-fractal nature of soil grading and its evolution during loading, and its possible relation to the modal nature of the grading. The fractal dimension of the soil is calculated using the two methods of the mass log-log plot particle size distribution and by computing the number of particles.