A coupled scaled boundary-discrete-finite element method for particle breakage modelling in granular media

The physical behavior of granular media e.g rock-fills and cohesion-less soils are governed, in part, by two mechanisms viz. grain-to-grain interaction; and the particle breakage of the individual grains. Grain interaction is predominantly described by the contact condition of the grains, whereas particle breakage depends on the stress state within each grain. Both the grain interaction and its corresponding stress state have to be appropriately accounted for when modelling the behavior of granular media. To achieve these objectives, this study develops a novel computational framework that combines the use of the scaled boundary finite element method (SBFEM) and the discrete element method (DEM). This approach employs a two-step solution process to resolve the dynamics of the grain interaction and to determine the stress state in individual grains. In the first step, the dynamic interaction between the grains are resolved using the DEM. Once the forces resulting from the interaction between the grains have been determined, a stress analysis is carried out using the SBFEM to determine their corresponding stress states. The stress state in a grain determines the condition for particle breakage according to a predetermined failure criterion. In this way, this method the best use of the salient features of both the DEM and SBFEM. Each grain is a particle within the framework of the DEM. Arbitrary sided polygonal particles are employed to model the morphology of each grain. The contact interaction between the particles is resolved using a potential-based contact model that is applicable to polygonal shaped particles. As the contact condition of a particle is assumed to be restricted to only the other particles adjacent to it, its dynamic response can be determined by solving its corresponding equations of motion, leading to an efficient approach to determine the dynamic response of the granular medium. The use of the polygon shaped particles adapts seamlessly with the SBFEM, which required for the subsequent stress analysis. Each grain can be modelled by the SBFEM using only a single polygon. The stress state in a polygon determines the particle breakage condition, dictated by a failure criterion e.g. Hooke-Brown criterion. Once the breakage condition is detected, the resulting polygon is split into two. The resulting new polygons are directly modelled by the DEM and the SBFEM without any change to the formulations. The flexibility of both approaches therefore, adapts very well to the evolving geometries of the granular medium during the loading process. The feasibility of the developed method is demonstrated through parametric studies to highlight the role of the particle breakage on the behavior of granular media at both the macro- and meso-scales.