Discrete Element Method (DEM) Contact Models Applied to Pavement Simulation Bo Peng Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Civil Engineering Linbing Wang Montasir Abbas Cristian Druta June 18, 2014 Blacksburg, Virginia Keywords: Discrete element method, contact models, pavement simulation, power-low viscoelasticity Discrete Element Method (DEM) Contact Models Applied to Pavement Simulation Bo Peng ABSTRACT Pavement is usually composed of aggregate, asphalt binder, and air voids; rigid pavement is built with hydraulic cement concrete; reinforced pavement contains steel. With these wide ranges of materials, different mechanical behaviors need to be defined in the pavement simulation. But so far, there is no research providing a comprehensive introduction and comparison between various contact models. This paper will give a detail exploration on the contact models that can be potentially used in DEM pavement simulation; in the analysis, it includes both a theoretical part, simulation results and computational time cost, which can reveal the fundamental mechanical behaviors for the models, and that can be a reference for researchers to choose a proper contact model. A new contact model–the power law viscoelastic contact model is implemented into software PFC 3D and is numerically verified. Unlike existing linear viscoelastic contact models, the approach presented in this thesis provides a detailed exploration of the contact model for thin film power-law creeping materials based on C.Y Chueng’s work. This model is aimed at simulating the thin film asphalt layer between two aggregates, which is a common structure in asphalt mixtures. Experiments with specimens containing a thin film asphalt between two aggregates are employed to validate the new contact model. iii Bo Peng Acknowledgement I cannot express enough thanks to my advisor for his continued support and encouragement: Dr. Linbing Wang, who sometimes is more like a friend rather than an advisor. I offer my sincere appreciation for the learning opportunities provided by him. My completion of this research could not have been accomplished without the support of my colleagues, Wenjuan, Wenjing, Ying, Yingning, Yufeng, and my ACM’s friends. Your technical advice and supports helped and inspired me. Finally, to my caring, loving, and supportive mom and dad: my deepest gratitude. Your encouragement when the times got rough are much appreciated and duly noted. Also, it was a great comfort and relief to know that you are going to pay my bill when I run out of money. My heartfelt thanks. iv Bo Peng Table of Contents Chapter 1 INTRODUCTION .................................................................................................................. 1 1.1 Background ................................................................................................................................... 1 1.2 Research objectives ....................................................................................................................... 2 1.3 Research tasks and organization ................................................................................................... 4 Chapter 2. BACKGROUND ................................................................................................................... 5 2.1 Basic principle of DEM ................................................................................................................ 5 2.1.1 Calculation cycle .................................................................................................................... 5 2.1.2 Law of movement .................................................................................................................. 7 2.1.3 Force-displacement principle ................................................................................................. 8 2.1.4 Boundary and initial conditions ........................................................................................... 11 2.2 Contact model review ................................................................................................................. 11 Chapter 3 Methodology ........................................................................................................................ 13 3.1 Simulation ................................................................................................................................... 13 3.2 Experimental validation .............................................................................................................. 14 3.2.1 X-ray tomography system .................................................................................................... 15 3.2.2 Sample testing ...................................................................................................................... 18 Chapter 4 ELASTIC CONTACT MODEL .......................................................................................... 19 4.1 Literature review ......................................................................................................................... 19 4.2 Simple elastic model ................................................................................................................... 20 4.3 Hertz-Mindlin contact model: ..................................................................................................... 21 Chapter 5 PLASTIC CONTACT MODEL ........................................................................................... 26 5.1 literature review .......................................................................................................................... 26 5.2 Simple ductile contact model ...................................................................................................... 27 5.3 Displacement softening model .................................................................................................... 28 Chapter 6 VISCOUSELASTIC CONTACT MODEL ......................................................................... 33 6.1 literature review .......................................................................................................................... 33 6.2 Simple viscous model ................................................................................................................. 34 6.3 Burger Model .............................................................................................................................. 36 Chapter 7 POWER LAW VISCOELASTIC CONTACT MODEL ..................................................... 42 v Bo Peng 7.1 Theoretical deduction .................................................................................................................. 42 7.2 Model development and verification .......................................................................................... 46 7.3 Experiment validation ................................................................................................................. 48 Chapter 8 CALCULATION TIME FOR EACH CONTACT MODEL ............................................... 53 Chapter 9 CONCLUSIONS .................................................................................................................. 55 REFERENCES ..................................................................................................................................... 57 Appendix A – The key part C++ code for power law contact model ................................................... 60 vi Bo Peng List of Figures and Tables FIGURE 2.1 Flow chart of DEM principle. .......................................................................... 6 FIGURE 2.2 Ball-ball contact and ball-wall contact ............................................................. 9 FIGURE 2.3 Definition of shear overlap ............................................................................. 10 FIGURE 3.1 The model to test contact models. .................................................................. 14 FIGURE 3.2 SKYSCAN 1174 system ................................................................................ 16 FIGURE 3.3 Testing stage of the microscopy system (SKYSCAN, 2006) ......................... 16 FIGURE 3.4 Sample container ............................................................................................ 17 FIGURE 3.5 Loading platform ............................................................................................ 17 FIGURE 3.6 Test sample ..................................................................................................... 18 FIGURE 4.1 Elastic contact model analysis........................................................................ 25 FIGURE 5.1 Ductile contact model analysis. ...................................................................... 32 FIGURE 6.1 Structure for viscoelastic model. .................................................................... 36 FIGURE 6.2 Viscoelastic contact model analysis. .............................................................. 41 FIGURE 7.1 Geometry information of the thin layer [8] .................................................... 43 FIGURE 7.2 Chart flow for power law contact model ....................................................... 47 FIGURE 7.3 Comparison between computed result and analytical result ......................... 48 FIGURE 7.4 Experimental, numerical,