Soil grains crushing and fractal dimension

The interest of scientists for the behavior of granular materials is justified by the important place they occupy in the implementation of several civil engineering projects such as dams, roads, railways, etc. The structure of these materials is an amalgam of grains from different mineralogical compositions, various sizes and forms, which are infiltrated by a complex system of cracks and fractures. The study of these materials may therefore incorporate a proper identity to each grain through its constitution properties, which sometimes leads to the difficulty of estimating its behavior. Euclidean Geometry is not suitable for representing all complex geometries, because it is established that the grains of the granular materials are never perfect. It becomes essential to study the irregularities of shapes and the fragmentation of grains or granular samples to understand them more and to characterize them with the contribution of the Fractal Dimension. In this study, two bidimensional methods for calculating the fractal dimension were used : the Box Counting "BC" at the scale of a grain and the method of the Masses at the scale of a sample.