Fabric and Deformation in Granular Materials

The paper presents results of numerical experiments on a large assembly of smooth circular disks. The assembly was subjected to quasi-static biaxial loading at small to moderate strains by using the Discrete Element Method. Unlike the usual particle-based and coordination number approaches, the fabric was locally measured in relation to the shapes and orientations of voids. Deformation was measured at the smallest possible scale of individual particle clusters. Throughout loading the voids became more elongated in the direction of the major principal compressive stress, even as the average volumetric behavior changed from compressive to dilatant. A direct correlation was observed between local void shape and dilation, which accounts for the transition from compressive to dilatant behavior. The predominant pattern of nonhomogeneous deformation was in the form of thin obliquely trending bands of void cells within which slip deformations were most intense. The fabric in these regions can be characterized by large elongated voids, whose direction of elongation was slightly oblique to the direction of the major principal compressive stress. Introduction Deformation occurs nonuniformly in granular materials, particularly at the microscale of particle groups. We investigated the relationship between local deformation and local fabric by using the Discrete Element Method to track and measure the movements of individual particles within a large assembly of smooth circular disks. The same assembly was used in previous work, in which the author reported that a particular pattern of slip deformation, termed microbands, was the dominant feature of local, nonuniform deformation at low and moderate strains (Kuhn 1998; Kuhn 1999). In this paper, we present an analysis of local fabric and its relation to two forms of local deformation: volume change and slip deformation. We begin with a brief description of the assembly and its loading. The Particle Assembly The assembly contains 4008 smooth circular disks that were initially compacted into a dense and isotropic con guration. Table 1 summarizes essential aspects of the Table 1. Assembly characteristics Number of particles 4008 Particle sizes Multiple Particle size range 0:45D 50 to 1:40D50 Initial void ratio, einit 0:179 Assembly size 54D50 54D50 54D50 D50 represents the median particle diameter assembly, which is illustrated in a previous work (refer to Fig. 1a in Kuhn 1998). The assembly was slowly loaded in biaxial compression by reducing its height at a constant rate L22, while maintaining a constant horizontal stress 11 (Fig. 1a). Local fabric and deformation were studied by constructing the assembly's particle graph (Satake 1992). This graph partitions the entire two-dimensional region A into small subregions A. Each subregion is a void (or void cell) that is surrounded by neighboring particles and bounded by the m branch vectors l of these contacting particles (Fig. 1b). The initial particle graph contained 3950 void cells and is shown in Fig. 2a. We used the void-based loop tensor F of Konishi and Naruse (1988) to characterize the local fabric of ith subregion A,