Fractal dimension of roughness: Influence of grain size and granular class

Abstract

The soil structure can be described as an assembly of elements of various sizes separated by a complex system of cracks and fractures, since the grains of the soil are differentiated by their shape, size and orientation. They are thus differently associated and related, their masses can form complex and irregular configurations which are in general extremely difficult to characterize in exact geometric terms. To understand the mechanical behavior of granular materials, it is then necessary to characterize the grains using the fractal dimension which is a characteristic that indicates the degree of irregularity and fragmentation of the latter. This experimental work consists in studying the influence of the parameters variation: granular class, grain size and normal stress applied during Casagrande's direct shear tests on the roughness fractal dimension calculated with the method of Box counting. The analysis of the results obtained at the end of a granulometric variation which caused a variation of the fractal dimension of grain roughness. This variation made it possible to analyze the level of fragmentation suffered by the sandstone grains during the various shear tests. This fragmentation produces fines that are the source of variations in the mechanical properties of the sandstone material.