ABSTRACT:

We discuss the use of granular dynamics simulation to simulate elastic properties of loose frictional packs under periodic boundary conditions and study the evolution of elastic and fabric properties with pressure. The granular packs simulated in this case are of glass beads. We use fabric tensor to characterize orientation distributions of contact normals in computational packs. The computed bulk moduli with pressure are compared with laboratory measurements of glass beads and are found to be comparable. We also obtain the eigenvalues of fabric tensor which are used to understand the strength and shape variation in the granular packs.

1. INTRODUCTION

We use granular dynamics to understand the influence of pore-scale rearrangements of grains and compute macroscopic elastic and fabric elastic properties. Porescale effects are important for the study of loose unconsolidated media and are relevant to not only rock physics, but also to several geomechanical stability problems. Microscopic arrangements of fabric and their response to pressure are of crucial interest in a variety of processes undertaken during subsurface exploration and production and well stability. In order to understand pore scale processes and their effect on macroscopic properties, it is essential to characterize the rock microgeometry in a reasonable way. There have been various ways to characterize rock microstructure. Apart from scan images of rocks, stochastic methods and geostatistics have also been used to reconstruct rock pore space. A brief description of the methods and further references are available in Guodong et al. (2005). Loose unconsolidated samples behave differently when they are prepared using different preparation techniques. It has been observed that different behaviors arise from samples with similar porosities but different fabrics. It is difficult to obtain rock fabrics by physical measurements. Moreover, the study of fabric evolution and its response to stress is difficult to be conducted by laboratory measurements. Hence, process - based simulations using granular dynamics, or discrete element method, has demonstrated the ability to study granular materials and soils. Guodong et al [1] and Xavier et al [2] give a fairly good description of the work done in this field. In this work, we have used discrete element method [3, 4], also known as granular dynamics simulation, in order to model the interactions and rearrangements of spherical glass beads. We consider grains which deform through virtual grain overlap; however, we do not explicitly model the deformability of individual grains. The deformability can be modeled by continuum analysis for each individual grain. The simulation is conducted in a computational threedimensional periodic cell so as to mimic infinite space in all three directions, thereby simulating subsurface stratigraphy using a relatively smaller volume. The simulation starts with non-touching spherical grains. The periodic cell is compressed using a constant strain rate. We obtain the initial loose pack at porosity of 37.5%, which is close to the critical porosity reported in literature. We further compare our values with laboratory experiment data on glass beads [5]. The material properties used in this simulation are the same as that reported in the experiments (density - 2650kg/m3, shear modulus -29GPa, Poisson?s ratio - 0.2, friction coefficient - 0.3).

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