Studies on modeling angular soil particles using the discrete element method

229 Pages·2015·9.93 MB·English

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USF Tampa Graduate Theses and Dissertations USF Graduate Theses and Dissertations
11-12-2004
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Amr M. Sallam
University of South Florida
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Sallam, Amr M., "Studies on Modeling Angular Soil Particles Using the Discrete Element Method" (2004).
USF Tampa Graduate Theses and Dissertations.
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Studies on Modeling Angular Soil Particles Using the Discrete Element Method

by

Amr M. Sallam

A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Civil and Environmental Engineering
College of Engineering
University of South Florida

Major Professor: Alaa Ashmawy, Ph.D.
Manjriker Gunaratne. Ph.D.
Sunil Saigal, Ph.D.
Ashraf Ayoub, Ph.D.
Carlos Santamarina, Ph.D.
Autar Kaw, Ph.D.

Date of Approval:
November 12, 2004

Keywords: numerical modeling, discrete element method, granular soils, dilation,
angularity

© Copyright 2004 , Amr M. Sallam
DEDICATION

This work is dedicated to my wife, Samar, my daughter, Nour, and my son, Seif.
Samar has been a tremendous support. She sacrificed her career to stay at home to take
care of me and our kids. She was always there in the hard days throughout the research
and writing processes. Without her love and support, this work could not be completed.
ACKNOWLEDGMENT

I want to thank my supervisor, Dr Alaa Ashmawy, for his great ideas and support
throughout the research. Dr Ashmawy was always there to suggest solutions for tough
problems, to improve my writing quality, and to expand my academic knowledge in
Geotechnical Engineering. I want to thank my colleagues (Newel, Rory, Naim, Jessica,
Jorge, Nivedita, Brian, and Whitney) for their encouragement. They are really good
friends and I hope our friendship will continue forever.
TABLE OF CONTENT
LIST OF TABLES.............................................................................................................vi
LIST OF FIGURES..........................................................................................................vii
ABSTRACT…. ..............................................................................................................xvii
CHAPTER ONE: INTRODUCTION.................................................................................1
1.1 Modeling of angular particles................................................................................2
1.2 Effect of shape and angularity on dilation of granular soils..................................3
1.3 Organization of the study.......................................................................................4
1.3.1 Chapter one: introduction............................................................................4
1.3.2 Chapter two: literature review.....................................................................4
1.3.3 Chapter three: experimental verification of modeling angular sand
particles using DEM...................................................................................5
1.3.4 Chapter four: the modified overlapping rigid clusters................................5
1.3.5 Chapter five: effect of particle shape and angularity on the
dilation of granular soils.............................................................................6
1.3.6 Chapter six: conclusions and recommendations..........................................7
1.3.7 Appendix A: theory and background of DEM............................................7
CHAPTER TWO: LITERATURE REVIEW.....................................................................8
2.1 Discrete element method for modeling granular media........................................8
2.1.1 DEM versus FEM for modeling granular soils.........................................10
2.1.2 Earlier published work in DEM................................................................10
2.1.2.1 Fundamental investigations: monotonic and cyclic shear
testing...................................................................................................11
2.1.2.2 Contact models is DEM..................................................................16
2.1.2.3 Coupled DEM and FEM.................................................................17
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2.1.2.4 Experimental verification of DEM..................................................18
2.1.2.5 Other applications...........................................................................19
2.1.3 Modeling non-circular particles................................................................19
2.1.3.1 Modeling angular particles as rigid clusters....................................24
2.1.3.2 Overlapping rigid clusters (ORC) technique...................................25
2.2 Dilatancy in granular soils...................................................................................29
2.2.1 Friction angle, dilation angle, and dilatancy.............................................31
2.2.1.1 Relation between friction and dilation angles.................................33
2.2.1.2 True and critical state friction angles..............................................37
2.2.2 Development of the theory of dilatancy....................................................38
2.2.2.1 Rowe’s theory.................................................................................38
2.2.2.2 Bolton’s relative dilatancy index.....................................................40
2.2.3 State-dependent dilatancy..........................................................................43
2.2.3.1 Problems with unique relationship between d and η.......................44
2.2.4 General expression for state dependent dilatancy.....................................46
2.3 Particle shape characterization............................................................................50
2.3.1 Particle shape characterization techniques................................................51
2.3.2 The method introduced by Sukumaran and Ashmawy (2001)..................53
2.3.2.1 The distortion diagram....................................................................54
2.3.2.2 Shape factor.....................................................................................55
2.3.2.3 Angularity factor.............................................................................56
CHAPTER THREE: EXPERIMENTAL VERIFICATION OF MODELING
ANGULAR PARTICLES USING DEM...............................................58
3.1 Introduction..........................................................................................................58
3.2 Background..........................................................................................................59
3.3 Overlapping rigid clusters (ORC)........................................................................60
3.4 Experimental program.........................................................................................62
3.4.1 Material.....................................................................................................63
3.4.2 Test setup...................................................................................................64
3.4.3 Image distortion effect...............................................................................68
3.4.4 Contact normal stiffness............................................................................70
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3.4.5 Experimental testing procedures...............................................................72
3.4.6 Experimental results..................................................................................73
3.4.6.1 Fraser river sand with the rectangular piston..................................73
3.4.6.2 Michigan sand with the trapezoidal piston......................................74
3.5 Numerical simulation...........................................................................................75
3.6 Comparison and discussion.................................................................................83
3.6.1 Fraser river sand........................................................................................84
3.6.2 Michigan sand...........................................................................................88
3.7 Parametric study..................................................................................................92
3.7.1 Effect of interparticle friction....................................................................92
3.7.2 Effect of global damping...........................................................................98
3.7.3 Effect of contact normal stiffness............................................................104
3.8 Conclusion.........................................................................................................104
CHAPTER FOUR: THE MODIFIED OVERLAPPING RIGID CLUSTERS..............109
4.1 Introduction........................................................................................................109
4.2 The modified ORC method...............................................................................109
4.2.1 Operator-independent particle creation procedure..................................109
4.2.2 Kinetic compatibility equations...............................................................112
4.2.3 Procedure.................................................................................................113
4.3 Implementation of the modified ORC method..................................................114
4.3.1 Michigan sand particle # 1......................................................................115
4.3.2 Fraser river sand particle # 4...................................................................115
4.4 Conclusion.........................................................................................................119
CHAPTER FIVE: EFFECT OF PARTICLE SHAPE AND ANGULARITY ON
THE DILATION OF GRANULAR SOILS.........................................122
5.1 Introduction........................................................................................................122
5.2 Background........................................................................................................122
5.2.1 Dilatancy in angular soils........................................................................122
5.2.2 Dilatancy and the discrete element method.............................................123
5.3 Modification to particle shape characterization.................................................126
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5.4 Particle groups with respect to shape and angularity.........................................132
5.5 Numerical simulations.......................................................................................132
5.5.1 Sample preparation..................................................................................134
5.5.2 Sample consolidation to the desired confining pressure.........................134
5.5.3 Pure shear loading...................................................................................136
5.5.4 Simulation program.................................................................................138
5.6 Numerical results...............................................................................................140
5.6.1 Confining pressure (1.0MPa), voids ratio (0.162), and 2574
particles...................................................................................................140
5.6.1.1 Effect of angularity........................................................................140
5.6.1.2 Effect of particle shape..................................................................145
5.6.2 Confining pressure (500 KPa), voids ratio (0.25), and 2394
particles...................................................................................................152
5.6.2.1 Effect of angularity........................................................................152
5.6.2.2 Effect of particle shape..................................................................153
5.6.3 Confining pressure (250 KPa), voids ratio (0.35), and 2215
particles...................................................................................................158
5.6.3.1 Effect of angularity........................................................................158
5.6.3.2 Effect of particle shape..................................................................159
5.7 Critical state line and particle shape characteristics..........................................164
5.8 Effect of interparticle friction............................................................................166
5.8.1 Confining pressure (1.0 MPa), voids ratio (0.162), and 2574
particles...................................................................................................166
5.8.2 Confining pressure (500 KPa), voids ratio (0.25), and 2394
particles...................................................................................................167
5.8.3 Confining pressure (250 KPa), voids ratio (0.35), and 2215
particles...................................................................................................170
5.9 The equivalent interparticle friction coefficient................................................175
5.10 Discussion........................................................................................................180
CHAPTER SIX: SUMMARY AND RECOMMENDATIONS.....................................182
6.1 Summary............................................................................................................182
6.2 Recommendations for future studies.................................................................184
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REFERNCES ..............................................................................................................186
APPENDICES ..............................................................................................................196
Appendix A: theory and background of DEM........................................................197
A.1 Calculation cycle.......................................................................................197
A.2 Force-displacement law.............................................................................197
A.3 Motion.......................................................................................................200
A.4 Damping....................................................................................................201
A.5 Energy dissipation.....................................................................................203
A.6 Time step...................................................................................................203
A.7 Input parameters........................................................................................203
A.8 Contact constitutive models.......................................................................204
ABOUT THE AUTHOR.......................................................................................End page
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LIST OF TABLES

Table 2-1. Literature survey of DEM up to 1992, Dobry and NG (1996)…………….12

Table 3-1. Maple wood properties…………………………………………………….63

Table 3-2. Contact normal stiffness results for Fraser River sand model-grains……..73

Table 4-1. Procedure of enforcing the kinetic compatibility equations for
particle # 1 of Michigan sand…………………………………………….114

Table 4-2. Elements/Discs properties for particle # 1 of Michigan sand……………117

Table 4-3. Results of the ORC and the modified ORC techniques for
Michigan sand particle # 1……………………………………………….117

Table 4-4. Elements/Discs properties for particle # 4 of Fraser River sand…………120

Table 4-5. Results of the ORC and the modified ORC techniques for Fraser
River sand particle # 4……………………………………………………120

Table 5-1. The modified shape factor for some standard geometric shapes………...130

Table 5-2. Shape factors, global shape factors, modified shape factors, and
angularity factors for soils used in the study…………...………………...131

Table 5-3. Shape and angularity factors for different groups………………………..132

Table 5-4. Model dimensions and properties………………………………………..135

Table 5-5. Simulation program………………………………………………………139

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