Generalization of 3D Mesostructures for a Microstructural Approach of Soil Behavior
In the field of granular materials, a link between microscopic variables (contact force and displacement) and macroscopic variables (stress and strain) requires the use of an intermediate scale called "the mesoscopic scale." At this scale, several mesostructures have been identified and studied as aggregates of attached grains or voids, such as loops, pore spaces, and force chains. From these mesostructures, loops are particularly noteworthy, as they are the only structures not yet defined in 3D conditions. Loops form simple polygons that are capable of partitioning a 2D media into smaller closed spaces, where the sum of the loop surfaces is equal to the total surface of the specimen (known as the pavement property). Therefore, direct application of the definition of loops to 3D conditions leads to the formation of 2D shapes in a 3D media, thereby compromising the pavement property. In this thesis, we propose to extend the loop definition to the 3D case. First, a method to identify loops (2D) based on the merger of cells created through a Delaunay triangulation is analyzed. Then, an extension of this procedure to 3D conditions is proposed. As the newfound structures are no longer representative of the mathematical concept of a loop or cycle, they are named "clusters." These structures are shown to be more complex than their 2D counterpart, necessitating a larger number of metrics to quantify them. For this reason, the concepts of size and order are distinguished as the number of grains and the number of external frontiers, respectively. Furthermore, the concept of deformability is introduced as a way to quantify the interconnectivity of a loop-like structure. A series of 3D discrete element method (DEM) triaxial tests were performed in the software LIGGGHTS. An application was then developed to analyze the properties of clusters during the loading path and in regard to proximity to other coexisting internal granular structures (force chains and shear bands). It is shown that the average void ratio and deformability (capacity to deform) of clusters increase with their size. Furthermore, an increase in the number of denser clusters is observed during the macroscopic strain contraction phase and of looser ones during the dilation. Finally, a relation between force chains, shear bands, and clusters is established. All the aforementioned cluster characteristics are known for 2D loops. Thus, clusters can be seen as extensions of loops in 3D conditions.