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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Assessing the shear behavior of intact rock & rock fractures is an important issue in the design of a potential nuclear waste repository at Yucca Mountain, Nevada. Cyclic direct shear experiments were conducted on replicas of three natural fractures and a laboratory-developed tensile fracture of welded tuff. The tests were carried out under constant normal loads or constant normal stiffnesses with different initial normal load levels. Each test consisted of five cycles of forward and reverse shear motion. The complete set of experimental results can be found in a data report by Wibowo et al. (1993a). Based on the results of the shear tests conducted under constant normal load, the shear behavior of the joint replicas tested under constant normal stiffness was predicted by using the graphical analysis method of Saeb (1989), and Amadei and Saeb (1990). Comparison between the predictions and the actual constant stiffness direct shear experiment results can be found in a report by Wibowo et al. (1993b). In this report, the results of the constant normal load shear experiments are analyzed using several constitutive models proposed in the rock mechanics literature for joint shear strength, dilatancy, and joint surface damage. It is shown that some of the existing models have limitations. New constitutive models are proposed and are included in a mathematical analysis tool that can _q used to predict joint behavior under various boundary conditions.
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