Study of the evolution of the fractal dimension of a granular material’s grains during mechanical tests

Granular materials interest scientists because they play an important role in engineering and project achieving like earth-fill or rock-fill dams, pavements and railroads, etc. The structure of these materials is a mixture of different mineralogical grains whose shape and size are also very different and they are separated by a complex cracking process. Therefore, this kind of studies may require the identification of the properties of every single grain composing the material which sometimes leads to the difficulty of estimating its behavior. Euclidean geometry is not suitable to represent all complex geometries because the grains of granular materials are never perfect and, for a better understanding, we need to examine the irregularly shaped grains and to characterize their shapes using fractal dimension which is a parameter that indicates the degree of irregularity and defragmentation of a grain or a sample. In this study, two methods were used to calculate the fractal dimension (box Counting method and the method of masses). These two methods allow the characterization of the surface condition changes with the grains-witnesses’ shapes of each grains samples for the three studied local materials (shale, limestone and sandstone) we got in three forms (sub-rounded, angular and elongated) and three size classes (3.15/8, 3.15/5 and 5/8 mm) after the crushing caused by the mechanical testing performed at laboratory (the direct shear test and oedometer test). The crushing rate is evaluated by comparing the values of the calculated fractal dimension before and after mechanical test and the results show the evolution of the calculated fractal dimension for various samples according to the stress and the constraint paths. These results confirm the existing link between the fractal dimension and various other parameters like the particle size, the nature and the shape of the grains and also the produced fines during the crushing. Consequently, the fractal dimension has an effect on the measurement of mechanical characteristics of granular materials.