Submit Manuscript | http://medcraveonline.com Abbreviations: DEM, discrete element method; FEM, fnite element method; NIT, Nagoya Institute of Technology Introduction The use of physical models in full or reduced scale in the past was one of the main tools to predict the behavior of civil and mechanical engineering constructions and structures. 1 With the increasing costs of model construction, in part because of the high prices of instrumentation that became increasingly sophisticated and accurate, and also the diffculty to extrapolate quantitative results of reduced analyses, physical models were gradually being less used. Alternatively, computational development provided a greater use of numerical methods for the simulation of these models, with the fnite element method (FEM) having the most practical impact in the last decades. However, it is necessary to evaluate if these models are able to predict the behavior of the problem under study, because when addressing the behavior of the soil as a continuous material, certain constraints are imposed in the analyzes performed. In addition, this approach implies the need to formulate phenomenological constitutive models that study the behavior of materials in a macroscopic or phenomenological way. 2 A macroscopic approach, on the other hand, does not consider the properties of the soil in the grain scale, which may result in an incomplete understanding of its behavior or in an unreasonable approximation for granular soils or highly fractured media. 3 In an attempt to consider the basic phenomena, a new numerical approach that considers the mesoscale aspects in the mechanical model of the soil was developed. This numerical method is known as the discrete element method (DEM) and it is based on the discretization of particles for modeling and problem solving. 4 The application of DEM to simulate small scale problems is an intermediate option to evaluate the mechanisms in a geotechnical analysis. Thus, reduced models properly instrumented and allied to a discrete numerical simulation can be an option with great potential for qualitative and quantitative prediction of geotechnical constructions. The motivation of this research consists in the possibility of improving the understanding of the behavior of shallow foundation, using the DEM associated with reduced model simulations to evaluate the effectiveness of this method to predict shallow foundation (block) behavior. Discrete element method The discrete element method is a numerical technique proposed by Cundall & Strack 5 by which the analyzed medium is constituted by a set of particles with fundamental mechanical properties and defned geometry. In addition, it uses primary physical variables such as contact forces, momentum, displacement and rotation. This method is suitable for the study of particulate medium, since it explicitly considers its discrete nature. Moreover, it is possible to evaluate the physical and mechanical behavior of granular materials by understanding the mechanical properties of particles and their interactions. 2 The DEM consists of a transient analysis that considers the dynamic interactions between a system of particles. 6 Particles in a DEM simulation are considered to be rigid bodies interacting with each other by fctitious springs, dashpots and/or sliding blocks that simulate the contacts. At each time step considered in the transient analysis, particles move and new contacts are created and old contacts cease to exist. Figure 1 shows the development of contact between a pair of particles. The main assumptions considered in this method are: (1) particles are rigid elements and can move or rotate freely from one another; (2) contact occurs only between two particles, over an infnitesimal area; (3) particles may overlap slightly in the contacts, overlaps are considered to be small; (4) compression forces between particles can be calculated from interpenetration and tensile forces from particle separation (if particles are bonded); (5) the time step required to update particle’s velocity and position should be small enough to ensure that, in a single time interval, perturbations will only propagate to the neighboring particles. The time step can be defned as: m dt k = (1) where m is the mass and k is the stiffness of a system of particles. The contact forces developed in the interaction between particles can be calculated according to the contact law employed. The equations of normal and shear contact force vectors, for a linear interaction law, can be calculated respectively by: Material Sci & Eng. 2019;3(4):136 ‒139. 136 © 2019 Rocha et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially. Shallow foundation analysis using the discrete element method Volume 3 Issue 4 - 2019 Jéssica Soares da Rocha, Márcio Muniz de Farias, Bernardo Cascão Pires e Albuquerque, Joaquim Araújo Costa Neto Department of Civil Engineering, University of Brasilia, Brazil Correspondence: Joaquim Araújo Costa Neto, Department of Civil Engineering, University of Brasilia, CLN 411 bloco C, Brasilia, Distrito Federal, Brasil, Email Received: July 20, 2019 | Published: August 08, 2019 Abstract This research presents a numerical evaluation of shallow foundation using the discrete element method and parameters calibrated by means of a reduced laboratory model of an idealized soil. For this evaluation, the Yade software was used to analyze the infuence of grain scale parameters (mesoscale) on the macroscopic behavior of the soil, perceived as an assembly of isolated and interacting particles. It was observed that, despite the need for calibration, the discrete element method showed an appropriate qualitative prediction of failure surfaces and a satisfactory quantitative prediction of ultimate load capacity. Keywords: discrete element method, shallow foundation, reduced model Material Science & Engineering International Journal Research Article Open Access