Discrete Element Analysis of Granular Materials Preparation and Settlement A. Karrech 1 , D. Duhamel 1 , G. Bonnet 2 , J.N. Roux 3 , F. Chevoir 3 , K. Sab 1 , J. Canou 4 , J.C. Dupla 4 Institut Navier Ecole Nationale des Ponts et Chauss´ ees 77455 Marne La Vall´ ee, France Abstract— Granular materials are discrete solid particles which are large enough to avoid any thermal fluctuations. These materials are widely encountered especially in transportation and pharmaceutical industries. Their behavior is generally out of the scope of the statistical and continuum mechanics approaches. Therefore, their modeling using discrete elements methods is receiving a wide interest. In this communication, we focus on granular materials simulations using the molec- ular dynamics method. First, granular sample preparation is studied, since particles packing are an important starting point for the investigation of mechanical behavior of granular materials. Then, a computational method for the prediction of bed response under cyclic loading is introduced. The suggested approach uses sequentially a molecular dynamics scheme, a time averaging technique, and a relaxation method in order to simulate long term granular materials settlement. I. I NTRODUCTION Unlike dilute granular materials where Boltzman’s kinetic theory can provide useful description, condensed granular materials are difficult to study with statistical approaches [1]. The flow of dense randomly-packed granular materials is characterized with small distances and time scales over which the particle trajectories are generally correlated [2]. Therefore, assuming random collisions of grains seems to be inappropriate. Furthermore, the settlement mechanism cannot be understood unless grains rearrangement and mobility are taken into consideration. Therefore, continuum mechanics seems to be insufficient to study such a behavior. The granular materials under consideration are modeled with discrete spheres. In this study, granular materials are modeled as discrete assemblies, we adopted the Molecular Dynamics (MD) as a numerical method for simulations. Since its introduction for mechanical engineering applications [3], this method has proved its viability and enabled researchers to tackle several complex mechanisms such as granular materials transport [4], mixing [5], segregation [6], compaction [7] etc. Coupled 1 Laboratoire Analyse des Mat ´ eriaux et Identification, ENPC 2 Laboratoire de M´ ecaniques, Universit ´ e de Marne La Vall ´ ee 3 Laboratoire des Mat ´ eriaux et Structures du G´ enie Civil, ENPC 4 Centre d’Enseignement et de Recherche en M´ ecanique des Sols, ENPC with the experimental approaches, the MD is now recognized as a fundamental tool to investigate the behavior of dense granular materials. In their pioneering contribution, Cundall and Strack [3] showed that the MD consists in solving the individual Newton’s equations taking into account the con- tact and gravity forces. In this communication, a predictor- corrector scheme for the integration of the particles equations of motions [8] is used. The particle-particle as well as particle-wall contacts are described with non-linear, path- dependent, dissipative law based on Hertz-Mindlin elastic interactions, Coulomb friction, and viscous damping [9]. In the first section, granular samples preparation is studied. Several parameters such as particle rigidity, internal friction and interaction law as well as mode of preparation can affect the quality of produced granular assemblies. The results which will be presented concern the effects of contact parameters and particles rigidities on the quality of the pro- duced samples in terms of density and coordination number distribution. Moreover, the response of granular samples under quasi-static compression obtained with the numerical simulations will be compared to the experimental results. In the second section, a computational method for discrete granular materials simulation of bed response under cyclic loading will be introduced. The suggested approach is based on the molecular dynamics method which provides learning data in terms of displacements, number of cycles etc. The collected information is then used to estimate trend functions describing the paths of particles and to predict their positions after a given number of loading cycles. A relaxation tech- nique is then used to correct any eventual anomalies that can be encountered. The convergence, accuracy, and efficiency of the suggested method will be discussed in details through specific field cases. II. PREPARATION OF GRANULAR ASSEMBLIES The purpose of this section is to explain the preparation process of amorphous granular samples and to describe the obtained structures. Understanding the mechanism of granular packing is very important as a starting point to