1 THE DEVELOPMENT OF CIRCULATION CELL STRUCTURES IN GRANULAR MATERIALS UNDERGOING COMPRESSI

1.0 Introduction The macroscopic deformational behavior of a granular material is primarily due to the rearrangement of the individual particles. The particle interactions are governed by the mechanical and geometric properties of the particles, such as shape, size, roughness and contact stiffness. The ultimate goal of studying the micromechanics of granular systems is to provide insight into macroscopic phenomena, such as failure, by relating the microscopic properties to the appropriate macroscopic parameters [1], [2], [3], [4],[5]. Here we use the discrete element technique to characterize granular systems as a collection of rigid particles of different shapes and sizes with specified physical interaction properties and loading configurations [6]. The method provides us with a high degree of control over the simulations and allows access to detailed information about the behavior of each particle in the system.
1. Associate Professor of Civil Engineering Director, Intelligent Engineering Systems Laboratory e-mail: john@ 2. Research Assistant. e-mail: nrege@
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n1=1.0 n2=1.0
n1=0.5 n2=0.5
n1=2.0, n2=2.0
FIGURE 1. Superquadric Shapes
The three specimens generated consist of discs, ellipses and diamonds. Each specimen consists of 845 particles with equal number of particles of three sizes of a particular shape. The size parameters and the superquadric parameters are given in Tables 1 and 2.
ABSTRACT
This paper predicts the formation of microstructures within a granular material undergoing biaxial compression. Using the discrete element method we test ensembles of particles of varying geometric shape and size. The tests predict that the motion of the particles deviates significantly from that predicted by continuum theory. The particles form localized coherent structures (here called circulation cells) in which groups of particles instantaneously behave as a rigid body. These circulation cells migrate and coalesce to form larger structures. Eventually a global shear band forms at the boundary of two or more of the circulation cells.
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In this paper we describe numerical experiments using the discrete element method to study the behavior of an idealized two dimensional particulate system. We are particularly interested in understanding the conditions under which disturbances at the particle level grow to form macroscopic structures, such as shear bands. The experiments performed here focus on the biaxial compression of two dimensional particle ensembles consisting of different particle shapes under a constant confining stress. The experiments track the motion of each individual particle. The results of our numerical models predict the formation of coherent vortex like structures which we call circulation cells. A circulation cell is a group of particles which instantaneously translates and rotates as a rigid body. The presence of these cells is partially masked by the deformation due to the homogeneous strain. The cells become clearly visible when the homogeneous deformation is subtracted and the residual velocity is plotted. The results show that the formation and evolution of these coherent structures influences the global failure of the specimen. The setup used for the numerical simulations is described in Section 2. In Section 3, the observed macroscopic behavior for specimens of different particle shapes is described. In Section 4, particle trajectory plots showing the circulation cells are presented. Finally, the implications of the development of these coherent structures within a granular material are discussed. 2.0 Numerical Test Setup The experiments are performed using MIMES, a Discrete Element based simulation system developed by the authors [7], [8]. Compression tests are conducted on three different granular ensembles, each with a different characteristic particle shape. The shape in each ensemble is characterized by the superquadric function[9], [10] given by;
The particles are initially generated in a regular grid with random orientations as shown in Figure 2 (a). The particles are not touching when the specimen is generated. The particles are consolidated by moving the walls of the container inwards under a constant applied load. For each of the three specimens, we use the same compacting force on the platens. The consolidation process is continued until the specimen is in equilibrium as shown in Figure 2 (b). The different particle shapes offer different resistance to packing, which results in the specimens having different void ratios (discs 0.2, ellipses 0.24, diamonds 0.15) at the same confining preБайду номын сангаасsure. Figure 3 shows close-ups of the specimens after consolidation.