Study of crushing of grains of limestone under the effect of cyclic loading with the fractal dimension

The grains can be of very diverse nature (size, shape, mineralogy, etc), indeed even if each grain is a fairly simple object, the set of grains is a very complex system in which the geometrical and physical properties of the grains, their forces and their orientations play a crucial role in their mechanical behavior. The measurement of their shape in soil mechanics has historically required the use of standards and diagrams to which the different grains can be compared. However, these methods are approaches and remain insufficient and incomplete for the actual measurement of their form and the understanding of their behavior remains a task far from being completed. This work is in this context and proposes to analyze the shape and size of the grains with the fractal theory using the Box Counting method. It also makes it possible to study their influence on the crushing of the grains of the calcareous material under the effect of the cyclic loading-unloading during the oedometer test. The obtained results show that the variation of the fractal dimension, corresponding to the crushing effect of the grains, is strongly influenced by their shape, their size, their particle size distribution and the variation in the number of loading-unloading cycles