Damping and Particle Mass in DEM Simulations under Gravity Tang-Tat Ng, F.ASCE 1 ; Wei Zhou 2 ; Gang Ma 3 ; and Xiao-Lin Chang 4 Abstract: This paper presents a study on the input parameters used in the discrete-element simulations with gravity. Input parameters of the discrete-element method (DEM) include particle mass (density), damping, gravity constant, strain rate, and contact relationship. This paper focuses on particle mass and damping. The samples consisted of two kinds of ellipsoidal particles. The unit weight of the particles is constant. Samples are prepared by depositing particles under gravity. The final bulk densities of the samples are different for different damping and par- ticle mass. The effect of the reduction of particle density is similar to that of the reduction of damping in sample preparation. For the samples, static equilibrium can be achieved with a damping ratio greater than 0.24%. When the damping ratio is less than 0.24%, some particles are oscillating. The oscillation cannot be reduced with further relaxation. Undrained simulations are carried out on these samples. Shear strength increases with the increase of damping as expected. Different undrained stress paths are found for simulations of loose samples with different damping. For simulations of loose samples with the same damping ratio, particle density affects the results slightly. However, the effect of damping and particle mass is negligible for dense samples. The ultimate shear strength of the granular material is not affected by either damping or particle mass. DOI: 10.1061/(ASCE)EM.1943-7889.0000889. © 2014 American Society of Civil Engineers. Author keywords: Granular materials; Discrete-element method (DEM). Introduction The discrete-element method (DEM) has been implemented in many engineering fields and in the study of particulate mechanics. Because of the simplicity of the contact model (no requirement of describing the dilatancy behavior of granular materials) and the ease of in- teraction between granular particles and other boundaries (e.g., industrial tools), engineers and scientists have been using the DEM in both fundamental research and industrial applications. Input parameters of the DEM are particle density, damping, time step, loading rate, gravity constant, and boundary conditions and particle-to-particle contact relationship. The input parameters can be determined by particle-level tests or calibrated by physical experi- ments at the system level (Grima and Wypych 2009). The influences of particle density, particle size, and friction on mixing behavior in a two-dimensional (2D) drum have been examined (Xu et al. 2010). The result reveals that particle density and size of the ternary mixture are the dominating factors affecting the mixing behaviors, whereas the effect of the frictional coefficient is less significant. Recent investigations have focused on the friction coefficient between particles and the friction coefficient between particles and bound- aries (Xu et al. 2010; Barreto and O’Sullivan 2012). Studies on other input parameters have been limited. Damping is not considered in these studies. For systems under zero gravitational force, input parameters, including time step, density, damping, and stiffness, have been in- vestigated (Ng 2006). The results indicate that similar results are observed when the parameters are within certain ranges. It is of interest to determine whether the finding is valid when gravity is involved in the simulations. The influence of gravity on material responses of a granular material has been performed (Chung and Ooi 2007). Macroscopic friction angle increases with the reduction of gravity. Another study on sample preparation indicates that the density of a sample slightly increases with gravity (Ng 2013). In that study, the unit weight of particles changes with constant gravity. In this paper, undrained (constant volume) triaxial simulations under gravity were carried out to investigate the effect of damping and particle mass while the unit weight of the particles is constant. The constant volume test was performed by applying vertical compressive strain (ɛ z ) and horizontal tensile strain, which are half the amount of the compressive strain (ɛ x 5 ɛ y 521=2ɛ z ). Simu- lations were carried out under large strains to determine the ultimate shear strength of the granular material. Damping and Particle Mass Nonproportional damping, mass proportional damping, and stiff- ness proportional damping have been used in DEM simulations. Because mass proportional damping is more effective on low fre- quencies and damps out rigid body motion, it is used in the DEM simulations in this study. The dashpot coefficient, c, is c ¼ 2pam (1) where a 5 damping input parameter; and m 5 particle mass. In the DEM simulations, the velocity of the particle, i, at the next time step, V t1Dt i , is 1 Professor, Civil Engineering Dept., Univ. of New Mexico, Albuquer- que, NM 87131; formerly, Professor, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China (corresponding author). E-mail: tang@unm.edu 2 Professor, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. 3 Postdoctoral Researcher, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. 4 Professor, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China. Note. This manuscript was submitted on March 27, 2014; approved on October 2, 2014; published online on October 30, 2014. Discussion period open until March 30, 2015; separate discussions must be sub- mitted for individual papers. This paper is part of the Journal of Engineering Mechanics, © ASCE, ISSN 0733-9399/04014167(9)/ $25.00. © ASCE 04014167-1 J. Eng. Mech. J. Eng. Mech. 2015.141. Downloaded from ascelibrary.org by Wuhan University on 06/11/15. Copyright ASCE. For personal use only; all rights reserved.