It has been observed that the majority of particles in a granular material carries less than the average load and that the number of particles carrying larger than the average load decreases exponentially with increasing contact force. The particles carrying above average load appear to form a strong network of forces while the majority of particles belong to a weak network. The strong network of forces appear to have a spatial characteristic whereby the stronger forces are carried though chainlike particle groups referred to as force chains. There is a strong case for a connection between force chains of the discrete medium and the trajectory of the most compressive principal stress in its continuous idealization. While such properties seem obvious from descriptive analysis of physical and numerical experiments in granular media, progress in quantification of the force chain statistics requires an objective description of what constitutes a force chain. A procedure to quantify the occurrence of force chains is built on a proposed definition having two parts: first, the chain is a quasilinear arrangement of three or more particles, and second, along the chain, stress concentration within each grain is characterized by the vector delineating the most compressive principal stress. The procedure is incorporated into an algorithm that can be applied to large particle assemblies to compile force chain statistics. The procedure is demonstrated on a discrete element simulation of a rigid punch into a half space. It was found that only approximately half of the particles within the group of so-called strong network particles are part of force chains. Throughout deformation, the average length of force chains varied slightly but the number of force chains decreased as the punch advanced. The force chain lengths follow an exponential distribution. The procedure provides a tool for objective analysis of force chains, although future work is required to incorporate branching of force chains into the analysis.

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Interparticle contact friction, packing density and polydispersity are known to be major contributors to the macroscopic strength of particulate assemblies, that is, their bulk resistance to deformation. For example, when a solid object penetrates a particulate material, the penetration resistance (i.e. the force opposing the object) increases concomitantly with an increase in the degree of polydispersity, packing density and interparticle friction. To establish the underlying mechanisms by which these properties govern the macroscopic response, we characterize quantitatively force propagation at length scales beyond that of the interparticle contact region. Using data derived from discrete element simulations of a two-dimensional granular assembly subject to indentation by a rigid flat punch, we examine the properties of force chains and the force chain network as they evolve during the course of the deformation. Findings indicate that increasing interparticle friction, packing density and degree of polydispersity promotes the formation of straighter chains and a greater degree of branching in the force chain network. Although the force chain length appears to be independent of friction and polydispersity, on average, denser systems tend to favour shorter chains. Thus, straighter and shorter force chains, combined with a greater degree of branching in the force chain network, result in a macroscopically stronger granular material.

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