Three-dimensional discrete element modeling of asphalt concrete: Size effects of elements Yu Liu a,⇑ , Zhanping You b,1 , Yang Zhao c a School of Highway and Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang’an University, South Erhuan Middle Section, Xi’an City, Shanxi Province 710064, China b Dept. of Civil and Environmental Engineering, Michigan Technological University, Houghton, MI 49931, United States c School of Civil and Architecture Engineering, Xi’an University of Science and Technology, Xi’an City, Shaanxi Province 710054, China highlights " Element size effects were investigated on three-dimensional discrete element modeling of asphalt concrete. " Mineral aggregate particles were simulated with the randomly created ellipsoids. " Element sizes gave insignificant impacts on the predicted creep stiffness. " Element size could affect time-steps, computational time, aggregate shape representations, etc. " The keywords are as follows: 1. Pavement engineering. 2. Asphalt concrete mixture. 3. Discrete element method. 4. Creep stiffness. 5. Discrete element size. article info Article history: Received 5 January 2012 Received in revised form 20 July 2012 Accepted 4 August 2012 Keywords: Asphalt concrete Discrete element method Size effect Creep stiffness abstract This paper investigated effects of element sizes in three-dimensional discrete element modeling of asphalt concrete. Asphalt concrete was considered as a two-phase composite of mineral aggregates larger than 2.36 mm and asphalt mastic. Even though asphalt mastic was a composite of fines, fine aggregates, asphalt, and air voids in the reality, it was considered as a homogenous media to interact with larger-size aggregates. A computer-generated discrete element model was employed to simulate the geometry of asphalt concrete. In the model, mineral aggregate particles larger than 2.36 mm were simulated with ran- domly-created ellipsoids, while asphalt mastic occupied the remaining volume of the asphalt concrete. Each ellipsoid particle in the model was a cluster of discrete elements (balls) which were bonded with a built-in contact-bond model. With the computer-generated model, four digital samples were generated, whose element sizes (radius of balls) were 0.75 mm, 0.65 mm, 0.50 mm, and 0.35 mm. The mechanical interactions within the digital samples were simulated through four contact models, namely the linear contact stiffness model, the Burger’s model, the slip model, and the contact-bond model. The first two models were used to simulate force–displacement relations at contacts, while the last two models were employed to model the strength properties at the contacts. Creep compliance tests were simulated on the four digital samples to investigate size effects of discrete elements on creep stiffness. Through this research, it was found that (1) discrete element sizes gave insignificant effects on creep stiffness (the maximum difference among different samples were within 5%) and (2) discrete element sizes could impact time-steps, computational time, aggregate shape representation, etc. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The discrete element method (DEM), also called the distinct ele- ment method, has been widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials [1–6]. In an asphalt concrete (AC) sample, mineral aggre- gate particles account for 85% of the total volume and play impor- tant roles in determining the overall AC performance. In other words, the majority of an AC volume is occupied by granular par- ticles (aggregates) which result in complex mechanics at disconti- nuities between individual aggregate particles or those between aggregate and asphalt matrix. Meegoda and Chang [7] believed that a discrete element model is an intuitive and direct approach in modeling AC mixture mechanics. 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.08.007 ⇑ Corresponding author. Tel.: +86 18691567519. E-mail addresses: yul@mtu.edu (Y. Liu), zyou@mtu.edu (Z. You), 3612091@qq.com (Y. Zhao). 1 Tel.: +1 906 487 1059. Construction and Building Materials 37 (2012) 775–782 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat