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Department of Civil and Construction Engineering
Faculty of Science, Engineering, and Technology
Micro-scale Behaviour of Recycled Construction and
Demolition Materials: Discrete Element Method
Simulations and Physical Testing
A thesis submitted for the degree of Doctor of Philosophy
by
Tabassom Afshar
October 2017
Swinburne University of Technology, Melbourne, Australia
iii
To my love
iv
Abstract Granular recycled Construction and Demolition (C&D) materials used in pavements,
roads, and embankments experience static and dynamic loading during their service life.
As a result, particle breakage can cause serious issues such as settlement and reduction in
hydraulic conductivity. Particle breakage depends on different factors such as particle
mineralogy, loading condition, particle size, and particle shape. A new insight into the
importance and effect of particle shape on the degree of crushing is presented. The
particle behaviour of C&D particles, with different mineralogy and microstructure, at
different scales from a single particle to an assembly of particles, is presented and
discussed. The fracture characteristics were found to be highly dependent on the particle
shape factor, and a modified particle tensile strength as a function of particle aspect ratio
is introduced. It has also been found that particle shape plays a more prominent role in
the particle breakage phenomena than the mineralogy and microstructure of C&D
particles. Discrete Element Modelling/Method (DEM) was also used to evaluate the
evolution of cracks through the particles. DEM assisted in measuring breakage energy
more accurately by partitioning and tracking the energy dissipation especially through the
creation of new surfaces during fragmentation. More accurate three-dimensional particle
shapes were generated by a large number of bonded spherical sub-particles and used to
model single particle crushing and particle assembly crushing. The results demonstrated
that brittle C&D granular materials with a higher degree of sphericity and lower flakiness
index would show higher resistance to breakage. Moreover, in order to obtain a better
understanding of C&D particle behaviours in relation to grain-scale damage and post-
breakage changes in grain properties, Synchrotron Radiation-based X-ray Micro-
Computed Tomography (SR-µCT) was used to capture high-resolution 4D images (i.e.
3D monitoring over time) from grain assemblies subjected to compression at different
loading intervals. To conduct CT scanning, a novel loading apparatus, capable of
conducting compression tests at the high stress on an assembly of grains, was designed
and developed. Changes to grain properties, stemming from breakage during compression
of specimens with various particle size distributions, were studied with the aid of three-
dimensional SR-µCT. The fractal distribution of C&D assemblies showed that breakage
becomes dominant in smaller grains rather than larger ones, where an increase in the
amount of newly generated fine fragments leads to a high coordination number
surrounding the larger grains. More importantly, the results of morphological changes in
v
the particulate assemblies revealed that there is a reversal trend in the grain morphology
evolution with increasing stress. The grains tended to create more spherical fragments
with higher aspect ratio whereas, by increasing the stress, this trend completely reversed.
In addition, it was found that the general trend of changes in particle shape obeys
universality. In other words, the same generic evolution by increasing stress was observed
irrespective of material types or sizes.
vi
Acknowledgments I would first like to express my sincere gratitude to Dr. Mahdi Disfani for his untiring
support, guidance, and mentorship during this research. In fact, the work presented in this
thesis would have really been difficult to pursue without his consistent encouragement by
asking questions and providing ideas. Thank you for giving me this opportunity to pursue
the research presented here. I would also like to thank Prof. Arul Arulrajah and Dr.
Guillermo Narsilio for your invaluable support during this project. Whenever a problem
was raised, I could always count on your assistance and scientific guidance.
The CT scanning discussed in the present work was undertaken in the Imaging and
Medical Beam Line at Australian Synchrotron (National Centre for Synchrotron
Science), Victoria, Australia. I wish to give my best thanks to beam scientists at
Australian Synchrotron, technicians in Swinburne workshop, Swinburne advanced
geotechnical engineering laboratory manager, and Swinburne microfabrication and
micro-analytical facility manager for their priceless assistance in conducting
experimental work presented in this dissertation. I wish to acknowledge Alex Fraser
Group for providing samples of recycled concrete, brick, and crushed rock for this
research. The support of Itasca Australia during numerical simulations is also gratefully
acknowledged.
Finally yet importantly, I would like to thank my family, friends, and colleagues at
Swinburne and the University of Melbourne, in particular my parents, Farzaneh and Ali,
and also my sister, Tarannom, for their support and inspiration throughout my studies.
Words could not ever sufficiently show my gratitude for all that you do for me. Special
thanks to my love, Moji, you are a wonderful husband, and I feel so lucky that I have you
on my side. Your love, kindness, patience, and understanding during these years know
no bounds. I love you with all my heart.
vii
Declaration I, Tabassom Afshar, declare that this thesis entitled:
“Micro-scale Behaviour of Recycled Construction and Demolition Materials: Discrete
Element Method Simulations and Physical Testing”
is my own work and has not been submitted previously, in whole or in part, in respect
of any other academic awards.
Tabassom Afshar
Department of Civil and Construction Engineering
Faculty of Science, Engineering, and Technology
Swinburne University of Technology, Melbourne, Australia
viii
List of publications 1. T. Afshar, M. M. Disfani, A. Arulrajah, G. A. Narsilio, & S. Emam, 2017.
“Impact of Particle Shape on Breakage of Recycled Construction and Demolition Aggregates”, Powder Technology, 308:1-12, doi:10.1016/j.powtec.2016.11.043. (IF: 2.825)
2. T. Afshar, M. M. Disfani, G. A. Narsilio, & A. Arulrajah, 2017. “Post-breakage changes in grain properties using synchrotron tomography”, Powder Technology, revised version submitted on 04/10/2017.
3. T. Afshar, M. M. Disfani, G. A. Narsilio, & A. Arulrajah, 2017. “Changes to Grain Properties due to Breakage in a Sand Assembly using Synchrotron Tomography”, European Physical Journal-Web of Conferences, Vol. 140, Article No. 07004, doi:10.1051/epjconf/201714007004.
4. T. Afshar, M. M. Disfani, A. Arulrajah, & G. A. Narsilio, 2017. “Microstructural analysis of particle crushing in Construction and Demolition materials using synchrotron tomography”, Proceedings of the 19th International Conference on Soil Mechanics and Geotechnical Engineering, Seoul, 2017, pp. 1003-1006.
5. T. Afshar, M. M. Disfani, A. Arulrajah, & G. A. Narsilio, 2015. “Discrete Element Modelling of Recycled Waste Rock: Particle Shape Simulations and Effects”, Proceedings of 12th Australia New Zealand Conference on Geomechanics (ANZ 2015), Wellington, New Zealand, 2015, Article No. 186.
6. T. Afshar, M. M. Disfani, A. Arulrajah, & G. A. Narsilio, 2014. “Discrete Element Modelling of Recycled Waste Rock under Monotonic Loading”, Proceedings of the 67th Canadian Geotechnical Conference (GeoRegina), Saskatchewan, Canada, 2014, Article No. 236.
List of grant and award
• M.M. Disfani, T. Afshar, G.A. Narsilio, & A. Arulrajah; “Micro-scale behaviour of recycled construction and demolition materials: focus on particle shape and breakage”; beamtime CT imaging, grant No. AS161/IM/10502, Australian Synchrotron (National Centre for Synchrotron Science), Feb. 2016
• Itasca Educational Partnership Award, Itasca Consulting Group, Feb. 2015
ix
List of abbreviations 2D: two-dimensional
3D: three-dimensional
AR: Aspect Ratio
C&D: Construction and Demolition
CB: Crushed Brick
CCD: Charge-Coupled Device
DEM: Discrete Element Modelling/Method
EDS: Energy-Dispersive X-ray Spectroscopy
FI: Flakiness Index
IDT: Indirect Diametral Tensile strength
IMBL: Imaging and Medical Beam Line
LVDT: Linear Variable Differential Transformer
MASSIVE: Multi-modal Australian ScienceS Imaging and Visualization
Environment
MDD: Maximum Dry Density
OMC: Optimum Moisture Content
PAC: Particle Assembly Crushing
PCM: Portland Cement Mortar
PFC: Particle Flow Code
PIV: Particle Image Velocimetry
PSD: Particle Size Distribution
x
RCA: Recycled Concrete Aggregate
RDF: Relative Distribution Factor
RP: Representative Particle
SEM: Scanning Electron Microscopy
SPC: Single Particle Crushing
SR-µCT: Synchrotron Radiation-based X-ray Micro-Computed Tomography
UCS: Unconfined Compressive Strength
WR: Waste Rock
1
Contents Abstract .................................................................................................................................... iv
Acknowledgments ................................................................................................................... vi
Declaration .............................................................................................................................. vii
List of publications ................................................................................................................ viii
List of grant and award .......................................................................................................... viii
List of abbreviations ................................................................................................................ ix
Contents ................................................................................................................................... 1
List of figures ........................................................................................................................... 6
List of tables .......................................................................................................................... 11
1. INTRODUCTION ...................................................................................................... 12
1.1. Problem statement and research significance ......................................................... 12
1.2. Objective and scope ................................................................................................ 13
1.3. Research method ..................................................................................................... 14
1.4. Thesis outline .......................................................................................................... 16
2. LITERATURE REVIEW ........................................................................................... 18
2.1. Construction and Demolition materials .................................................................. 18
2.2. Necessity of micro-scale studies on C&D materials ............................................... 19
2.3. Micro-scale study of geomaterials .......................................................................... 21
2.3.1. Discrete Element Modelling ........................................................................... 22
2.3.1.1. Laboratory test simulations ......................................................................... 24
2.3.1.2. Different materials ...................................................................................... 24
2.3.2. Experimental methods ..................................................................................... 26
2.3.2.1. X-ray Tomography ...................................................................................... 27
2.3.2.2. Particle Image Velocimetry (PIV) .............................................................. 28
2.4. Particle breakage in granular materials ................................................................... 28
2.4.1. Factors governing particle breakage ............................................................... 29
2
2.4.2. Particle breakage in DEM ............................................................................... 30
2.4.3. Breakage energy .............................................................................................. 32
2.5. Particle shape .......................................................................................................... 33
2.5.1. Shape measurement methods .......................................................................... 33
2.5.2. Shape factors/descriptors ................................................................................ 34
2.5.3. Particle shape in DEM .................................................................................... 35
3. RECYCLED CONSTRUCTION AND DEMOLITION MATERIALS .................... 37
3.1. Geotechnical characteristics .................................................................................... 38
3.1.1. Sample preparation ......................................................................................... 38
3.1.2. Particle size distribution .................................................................................. 39
3.1.3. Specific gravity ............................................................................................... 40
3.1.4. Flakiness Index ............................................................................................... 41
3.1.5. Optimum Moisture Content ............................................................................ 42
3.1.6. Unconfined Compressive Strength ................................................................. 42
3.2. Mineralogy and microstructure ............................................................................... 44
3.3. Particle shape .......................................................................................................... 48
3.3.1. Measurement methods .................................................................................... 48
3.3.1.1. Shape measurement of coarse grains .......................................................... 48
3.3.1.2. Shape measurement of fine grains .............................................................. 49
3.3.2. Analyses .......................................................................................................... 53
3.4. Summary ................................................................................................................. 56
4. EXPERIMENTAL METHODOLOGY AND ANALYSIS TECHNIQUES .............. 58
4.1. Single Particle Crushing .......................................................................................... 58
4.2. Particle Assembly Crushing .................................................................................... 59
4.3. Synchrotron tomography ......................................................................................... 60
4.3.1. Experiment Design .......................................................................................... 60
4.3.2. Synchrotron Radiation-based X-ray Micro-Computed Tomography ............. 62
4.3.2.1. Synchrotron source ..................................................................................... 62
3
4.3.2.2. Synchrotron light ......................................................................................... 63
4.3.2.3. Ruby detector .............................................................................................. 65
4.3.3. Experimental compression set-up ................................................................... 66
4.3.3.1. Sample chamber .......................................................................................... 67
4.3.3.2. Loading and data acquisition system .......................................................... 67
4.3.4. Image processing............................................................................................. 69
4.3.4.1. Density contrast ........................................................................................... 69
4.3.4.2. CT artefacts ................................................................................................. 70
4.3.4.2.1. Ring noise ................................................................................................... 70
4.3.4.2.2. Motion artefact ............................................................................................ 70
4.3.4.3. Segmentation ............................................................................................... 71
4.3.4.4. 3D reconstruction ........................................................................................ 74
4.4. Summary ................................................................................................................. 76
5. PARTICLE BREAKAGE ACROSS THE DIFFERENT SCALES ........................... 77
5.1. Single Particle Crushing .......................................................................................... 77
5.1.1. Qualitative analysis of fragmentation ............................................................. 77
5.1.2. Quantitative analysis of particle breakage ...................................................... 78
5.1.3. Modified particle tensile strength ................................................................... 81
5.2. Particle Assembly Crushing .................................................................................... 83
5.2.1. Post-breakage visual inspection of particles ................................................... 83
5.2.2. Particle shape and cushioning effect ............................................................... 87
5.3. Summary ................................................................................................................. 90
6. DISCRETE ELEMENT MODELLING OF PARTICLE BREAKAGE .................... 91
6.1. Principles of Discrete Element Modelling .............................................................. 91
6.1.1. Updating particle locations ............................................................................. 92
6.1.2. Contact models ................................................................................................ 93
6.1.2.1. Simple linear model .................................................................................... 93
6.1.2.2. Linear contact bond model .......................................................................... 95
4
6.1.2.3. Linear parallel bond model ......................................................................... 96
6.2. 2D modelling of particle breakage and effect of particle shape .............................. 97
6.2.1. Model calibration ............................................................................................ 97
6.2.2. Particle shape modelling ............................................................................... 100
6.2.3. Particle breakage modelling .......................................................................... 101
6.2.4. Simulation of biaxial tests ............................................................................. 102
6.2.5. Effect of particle shape on the macro-scale behaviour of the WR assembly 103
6.3. 3D modelling of particle breakage and effect of particle shape ............................ 103
6.3.1. Precise particle shape modelling ................................................................... 105
6.3.2. Calibration of micro-parameters ................................................................... 106
6.3.3. Internal stress distribution ............................................................................. 108
6.3.4. Breakage energy ............................................................................................ 110
6.4. Summary ............................................................................................................... 113
7. BREAKAGE AND PARTICLE CHARACTERISTICS EVOLUTION THROUGH
SYNCHROTRON TOMOGRAPHY ....................................................................................... 114
7.1. Crack propagation in different C&D granular materials ....................................... 115
7.1.1. Effect of shape .............................................................................................. 115
7.1.2. Effect of internal microstructure on crack patterns ....................................... 118
7.2. Evolution of grain property due to breakage ......................................................... 121
7.2.1. Soil grading and fractal distribution .............................................................. 122
7.2.2. Changes in external morphology .................................................................. 128
7.2.3. Universality of grain property evolution due to breakage............................. 129
7.3. Summary ............................................................................................................... 138
8. CONCLUSIONS AND RECOMMENDATIONS ................................................... 140
8.1. Major conclusions ................................................................................................. 140
8.1.1. Experimental observations and analyses from SPC and PAC tests .............. 140
8.1.2. Discrete Element Modelling ......................................................................... 141
8.1.3. Post-breakage analyses using synchrotron tomography................................ 141
5
8.2. Recommendations for future research .................................................................. 143
References ............................................................................................................................ 145
6
List of figures Figure 1.1. Research methods at a glance ................................................................................... 15
Figure 2.1. Distribution of Melbournian basalt (after Osborne et al. (2010)) ............................. 19
Figure 2.2. Common methods to study geomaterials at micro-scale .......................................... 23
Figure 2.3. Relative number of publications related to DEM simulation of different materials in the last decade ............................................................................................................................. 25
Figure 2.4. Classification of various experimental methods used in micro-scale studies of geomaterials (after Evans (2005)) ............................................................................................... 27
Figure 2.5. Breakage mechanisms (after Pitchumani et al. (2004)) ............................................ 29
Figure 2.6. Particle breakage with a breakage criterion (each particle with a coordination number smaller than 3 is allowed to break if σ > σmax) (Lobo-Guerrero, 2006) ......................... 32
Figure 2.7. 10-balls clump with eight small balls (asperities) bonded as a ballast particle (Lu and McDowell, 2008) ........................................................................................................................ 35
Figure 2.8. Simulation of semi-real-shaped particles with overlapped balls in each clump (Mollanouri Shamsi and Mirghasemi, 2012) .............................................................................. 36
Figure 3.1. C&D stockpiles at Alex Fraser Group Ltd. .............................................................. 37
Figure 3.2. C&D granular materials: a) WR, b) RCA, c) CB ..................................................... 38
Figure 3.3. Riffle splitter as a sample divider ............................................................................. 38
Figure 3.4. Cone and quartering method ..................................................................................... 39
Figure 3.5. Particle size distribution of C&D materials .............................................................. 40
Figure 3.6. Flakiness index sieves and gauge ............................................................................. 42
Figure 3.7. a) Modified compaction machine, b) Compaction curve for unbound WR ............. 43
Figure 3.8. USC results; a) WR sample after failure, b) Stress-strain curve .............................. 43
Figure 3.9. Sample preparation for SEM testing: a) Cold moulding, b) Grinded samples, c) Diamond polishing with Struers Tegramin-25, d) Gold coating by K975X Turbo-Pumped Thermal Evaporator, e) Gold coated specimens ......................................................................... 45
Figure 3.10. Zeiss Supra 40VP Scanning Electron Microscope ................................................. 46
Figure 3.11. SEM images of a) WR, b) RCA, and c) CB ........................................................... 46
Figure 3.12. EDS elemental analysis: (a) WR, (b) RCA, (c) CB ................................................ 47
Figure 3.13. Some example images of WR coarse grains: a) original images, b) binary images 49
Figure 3.14. Some example images of RCA coarse grains: a) original images, b) binary images .................................................................................................................................................... 50
Figure 3.15. Some example images of CB coarse grains: a) original images, b) binary images 51
Figure 3.16. CILAS 1190 Particle Size Analyser: a) schematic view of measurement with particle size analyser, b) Particle Size Analyser setup ................................................................ 51
Figure 3.17. Some example images of C&D fine grains: a) WR, b) RCA, c) CB ...................... 52
Figure 3.18. RCA fine grains: a) microscopic image, b) noise-free and segmented image ........ 53
Figure 3.19. Degree of sphericity distribution of RCA grains: a) coarse grains (>1.18mm), b) fine grains (<1.18mm); N is the number of studied grains ......................................................... 54
Figure 3.20. Degree of sphericity distribution of WR grains: a) coarse grains (>1.18mm), b) fine grains (<1.18mm); N is the number of studied grains ................................................................ 55
Figure 3.21. Degree of sphericity distribution of CB grains: a) coarse grains (>1.18mm), b) fine grains (<1.18mm); N is the number of studied grains ................................................................ 55
7
Figure 3.22. Degree of sphericity of WR grains in different shape categories; particle size fraction: 13.2 to 19 mm, (N: Number of grains. Circles, ‘o’, and asterisks, ‘’, are related to outliers) ....................................................................................................................................... 56
Figure 3.23. WR flaky particle.................................................................................................... 56
Figure 4.1. Single Particle Crushing: a) Schematic view, b) WR grain under loading by Geocomp LoadTrac II ................................................................................................................. 58
Figure 4.2. Particle Assembly Crushing setup ............................................................................ 59
Figure 4.3. Particle Assembly Crushing: (a) Grains before loading, (b) Test setup, (c) Grain crushing after loading ................................................................................................................. 60
Figure 4.4. Experiment design for synchrotron tomography experimets on samples with different particle sizes and under various loading levels ............................................................ 61
Figure 4.5. Maquette of synchrotron light machine in Australian Synchrotron ......................... 62
Figure 4.6. Beamline ................................................................................................................... 63
Figure 4.7. High intensity/brightness of synchrotron light compared to other types of light ..... 64
Figure 4.8. Ruby detector ............................................................................................................ 65
Figure 4.9. Schematic diagram of the experimental layout and the loading setup ..................... 66
Figure 4.10. Schematic view of the loading apparatus and sample chamber .............................. 68
Figure 4.11. Density contrast in a CT image .............................................................................. 69
Figure 4.12. Basaltic WR particle ............................................................................................... 69
Figure 4.13. CT image showing severe ring artefact .................................................................. 70
Figure 4.14. Main steps of image processing in order to obtain quantitative results .................. 72
Figure 4.15. Histogram-based binarization of the sand sample .................................................. 72
Figure 4.16. Image processing illustration: a) Original binary image, b) Image after median filtering, c) Image after Gaussian blur filtering .......................................................................... 73
Figure 4.17. Segmentation: a) Original image, b) Image after filtering, c) Watershed segmentation ............................................................................................................................... 73
Figure 4.18. Watershed segmentation basics: a) Greyscale image as a topographical surface in terms of intensity, b) Watershed transformation ......................................................................... 73
Figure 4.19. Comparison of classical watershed with Watershed Irregular Features ................. 74
Figure 4.20. a) Original and ‘segmented and labelled’ 2D slices, b) 3D reconstructed, segmented, and labelled WR sample at the initial condition (i.e. 0 MPa) .................................. 76
Figure 5.1. Single WR particle crushing: a) Initial state, b) Post-breakage, c) Schematic description of the one-dimensional compression and induced tension ....................................... 77
Figure 5.2. Single RCA particle crushing: a) Initial state, b) Post-breakage .............................. 78
Figure 5.3. Single CB particle crushing: a) Initial state, b) Post-breakage ................................. 78
Figure 5.4. Single Particle Crushing results: Load-displacement comparison of a) WR, b) RCA, and c) CB particles in different shape categories (bulky, solid line; elongated, dashed line; flaky, dotted line) .................................................................................................................................. 79
Figure 5.5. Yielding point range of different types of C&D particles with various shapes (N: Number of particles) ................................................................................................................... 80
Figure 5.6. SEM image of vesicular basaltic WR ....................................................................... 81
Figure 5.7. Particle Assembly Crushing: a) Initial state of bulky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 5 MPa vertical compression .......................................................................... 84
8
Figure 5.8. Particle Assembly Crushing: a) Initial state of bulky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 7.5 MPa vertical compression ....................................................................... 84
Figure 5.9. Particle Assembly Crushing: a) Initial state of bulky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 10 MPa vertical compression ........................................................................ 85
Figure 5.10. Particle Assembly Crushing: a) Initial state of elongated WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 5 MPa vertical compression .......................................................................... 85
Figure 5.11. Particle Assembly Crushing: a) Initial state of elongated WR particles, b) Post-breakage state of particles including Representative Particle (RP) after 7.5 MPa vertical compression ................................................................................................................................ 85
Figure 5.12. Particle Assembly Crushing: a) Initial state of elongated WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 10 MPa vertical compression ........................................................................ 86
Figure 5.13. Particle Assembly Crushing: a) Initial state of flaky WR particles, b) Post-breakage state of particles including Representative Particle (RP) after 2.5 MPa vertical compression ... 86
Figure 5.14. Particle Assembly Crushing: a) Initial state of flaky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 5 MPa vertical compression .......................................................................... 86
Figure 5.15. Particle Assembly Crushing results: a, b, and c) Load-displacement relationship of WR assemblies in different shape categories at different load levels ......................................... 89
Figure 5.16. Comparison of different WR particle shapes in PAC tests in terms of crushing strength and stiffness (K); (solid black line is drawn based on 100 periods moving average) ... 90
Figure 6.1. Simplified linear contact model ................................................................................ 94
Figure 6.2. Linear contact bond model: (a) normal force and (b) shear force versus relative displacement; Fi
c is bond strength, (after Cho et al. (2007)) ....................................................... 95
Figure 6.3. Illustration of parallel bond model provided in PFC; a parallel bond acts like a beam resisting moments as well (after Cundall (2004)) ....................................................................... 96
Figure 6.4. 2D synthetic specimen particle size distribution compared to the real material ....... 98
Figure 6.5. Different clump shapes used for 2D DEM modelling of Crushed Waste Rock, WR Specimen, and its three basic particle shapes............................................................................ 100
Figure 6.6. Cluster modelling; black parallel bonds are three times stronger than red parallel bonds (Ghazvinian, 2010) ......................................................................................................... 101
Figure 6.7. The proposed cluster model; black bonds are parallel bonds and yellow bonds are contact bonds ............................................................................................................................ 102
Figure 6.8. Numerical steps of the biaxial test simulation: a) Isotropic consolidation, b) Shearing phase ......................................................................................................................................... 102
Figure 6.9. Deviator stress versus vertical strain for crushed basaltic Waste Rock from the results of the triaxial test and simulation of biaxial tests with PFC2D ..................................... 104
Figure 6.10. Bond breakage simulation leading to grain crushing (black: parallel bonds, yellow: contact bonds) ........................................................................................................................... 104
Figure 6.11. Examples of different shapes of WR particles: (a) actual particles (top view), (b) 3D scans (side view) ................................................................................................................. 105
9
Figure 6.12. 1D compression on single bulky WR particles: (a) Laboratory and DEM results, (b) Initial state of the particle, (c) Force chain at the failure moment, (d) Total fragmentation at yielding point ............................................................................................................................ 106
Figure 6.13. (a) Laboratory and 3D DEM results of 1D compression on assemblies of bulky WR particles, (b) Contact force network distribution and bond breakage from DEM simulation of PAC test on bulky WR particles ............................................................................................... 109
Figure 6.14. Parallel bond state after loading (i.e. Max load 10kN or 5 MPa). Colours represent tensile (blue) and shear (green) bond breakages and bonded (red) ........................................... 110
Figure 6.15. Input energy versus energy dissipation through breakage based on DEM simulations of different assemblies of WR, (The amount of energy was calculated up to the onset of ‘representative particle’ breakage) .............................................................................. 112
Figure 6.16. Breakage energy per volume change of the WR sample versus applied force in relation to particle shape ........................................................................................................... 112
Figure 7.1. Crack propagation in different grains in a CB assembly: a) Density profile, b) The initial phase, c) After 5 kN compression ................................................................................... 116
Figure 7.2. Bending failure of elongated RCA grains: a) Initial state, b) After 10.2 MPa compression .............................................................................................................................. 117
Figure 7.3. Basaltic Crushed WR under a) 0, b)10, and c)20 MPa compression (asterisks, ‘*’, are highlighting bulky grains not experiencing severe breakage) ............................................. 117
Figure 7.4. SEM image of an agglomerated PCM grain ........................................................... 119
Figure 7.5. Fracture propagation in WR grains: a) Initial ortho-slice, b) After 10 MPa vertical
compression ( : tensile event; : shear event; : crack branching) ........................... 120
Figure 7.6. Porphyritic and vesicular texture of a WR grain .................................................... 120
Figure 7.7. Microstructural effect on grain tensile splitting: a) A close-up of the vesicular WR grains in an assembly, b) After 5 kN (10.2 MPa) compression ................................................ 121
Figure 7.8. Fractures following cleavage in WR grains............................................................ 121
Figure 7.9. Sand particles: a) CT ortho-slice, b) natural sand used in this research ................. 122
Figure 7.10. Changes in WR particle size distribution under different loading levels: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm .................................................................................................................................... 124
Figure 7.11. Changes in RCA particle size distribution under different loading levels: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18, c) 1.18-2.36, and d) 2.36-4.75 mm .................................................................................................................................................. 125
Figure 7.12. Changes in CB particle size distribution under different loading levels: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm .................................................................................................................................................. 125
Figure 7.13. Sand specimen under different loading levels (0, 5, 10, and 20 MPa): a) Changes in grain size distribution, b) The fractal distribution ..................................................................... 126
Figure 7.14. Fractal distribution of WR samples: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm ............................................. 126
Figure 7.15. Fractal distribution of RCA samples: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm ............................................. 127
Figure 7.16. Fractal distribution of CB samples: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm ............................................. 127
10
Figure 7.17. Morphology evolution of WR grains under different loading levels: Aspect Ratio and True sphericity distribution: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm ............................................................................ 130
Figure 7.18. Morphology evolution of RCA grains under different loading levels: Aspect Ratio and True sphericity distribution: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm ............................................................................ 131
Figure 7.19. Morphology evolution of CB grains under different loading levels: Aspect Ratio and True sphericity distribution: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm ............................................................................ 132
Figure 7.20. Morphology evolution of sand grains under different loading levels: a) Aspect Ratio, b) True Sphericity ........................................................................................................... 133
Figure 7.21. Changes in mean values of AR and true sphericity due to breakage: a) WR, b) RCA, and c) CB ........................................................................................................................ 134
Figure 7.22. Relative Distribution Factor of AR and true sphericity distributions: a) WR, b) RCA, and c) CB ........................................................................................................................ 135
Figure 7.23. Skewness of AR distributions: a) WR, b) RCA, and c) CB ................................. 136
Figure 7.24. EDS elemental analysis of sand (insert: SEM image of a sand particle) .............. 137
Figure 7.25. Changes in statistical properties of shape factor distributions of sand fragments due to breakage: a) Mean values of AR and true sphericity, and b) Relative Distribution Factor .. 137
Figure 7.26. Schematic explanation of particle shape evolution due to breakage .................... 138
11
List of tables Table 2.1. A brief list of different topics on granular materials at micro-scale level.................. 23
Table 2.2. Recent DEM simulation of different laboratory tests ................................................ 25
Table 2.3. Recent work on DEM simulation of different materials ............................................ 25
Table 2.4. Factors affecting particle breakage ............................................................................ 31
Table 2.5. Definition of shape factors ......................................................................................... 34
Table 2.6. Representative ballast particles using in the DEM simulation (after Indraratna et al. (2010)) ........................................................................................................................................ 36
Table 3.1. Classification characteristics of C&D materials ....................................................... 40
Table 3.2. Specific gravity of C&D materials and natural sand ................................................. 41
Table 3.3. Flakiness index of C&D materials ............................................................................. 41
Table 3.4. Weight percentage of different elements in different kinds of C&D materials ......... 47
Table 6.1. Calibrated micro-parameters of crushed waste rock used in 2D simulations ............ 99
Table 6.2. Strength and modulus of elasticity of WR resulting from Unconfined Compressive Strength test; DEM simulations and laboratory tests ................................................................ 100
Table 6.3. The clumps’ shape factor used in 2D DEM simulations ......................................... 101
Table 6.4. Micro-parameters used in 3D DEM modelling of WR particles ............................. 107
12
1. INTRODUCTION
1.1. Problem statement and research significance
Recycled Construction and Demolition (C&D) materials are particulate waste
materials usually produced during construction and demolition of buildings and structures
or commercial and industrial activities. C&D materials have been recognised as having
suitable geotechnical properties to be reused as pavement subbase/base materials
commonly used in Victoria, Australia (Arulrajah et al., 2013a). Recycling and reusing of
waste materials leads to decreasing the demand for limited natural resources, and
simultaneously lowers the disposal landfill cost. Among different types of C&D
materials, crushed basaltic Waste Rock (WR), Recycled Concrete Aggregate (RCA), and
Crushed Brick (CB) are of interest in this study. Crushed WR used in this study originates
from surface excavation of Quaternary aged basaltic rock, which normally occurs near
the surface to the west and north of Melbourne, Australia (McAndrew and Marsden,
1973). RCA and CB are by-products of construction and demolition activities of buildings
and structures.
The response of particulate layers under traffic loading is normally characterised by
the resilient modulus test. However, the true nature of the deformation mechanism of
aggregates in pavement layers is still not fully understood (Leiva-Villacorta et al., 2017).
It has been accepted that the deformation of granular materials under loading is the
consequence of three major mechanisms: consolidation, particle rearrangement, and
particle breakage (Luong, 1982). The consolidation mechanism is the alteration in
compressibility of grain assemblies, while the particle rearrangement mechanism includes
sliding and rolling of particles. The breakage mechanism is the crushing that happens
when the applied load exceeds the strength of the particles. Crushing is a progressive
process that can initiate at relatively low stresses, change the soil fabric and packing
gradually, and cause serious issues, such as settlement and reduction in hydraulic
conductivity of the soil (Lekarp et al., 2000a, Lekarp et al., 2000b). In addition, the
engineering characteristics of a granular assemblage, including friction angle, shear
strength, and constitutive behaviour, have been proven to be dependent on properties
altered by breakage (Miao, 2015). In fact, particle breakage is a detrimental phenomenon,
13
particularly in granular pavement layers, and deserves to be fully understood in terms of
its causes, consequences, and the ways to avoid it.
Particle crushing is governed by particle size and shape, the applied stress level, and
mineralogy and microstructure of individual particles (Afshar et al., 2017). Considering
the inherent links between particle size and form/shape, it is reasonable to maintain that
wherever size matters, shape needs to be considered (Jia and Garboczi, 2016).
Nevertheless, a comprehensive review of the most recent literature reveals that studies of
the effect of shape on particle breakage are lagging behind. The most likely reason for
this shortcoming is the fact that particle shape is more difficult to measure compared to
other characteristics, such as particle size or size distribution (Cho et al., 2006).
Due to experimental limitations on measuring force chains, i.e. contact force
distribution, and monitoring crack propagation at particle scale, Discrete Element
Modelling (DEM) has been recently used in a number of studies to explore the
micromechanical breakage behaviour; however, most of them only provide information
on the evolution of the particle size distribution during breakage (Miao and Airey, 2013).
Some studies have utilised agglomerate-based models to study breakage (e.g. Bono et al.
(2014); Cil and Alshibli (2014)), but they failed to quantify the resulting particle shapes
formed.
In the present research, a new insight into the importance and effect of particle shape
on the degree of crushing of C&D materials is presented. Breakage of C&D particles,
individually and in granular assemblies, with different mineralogy and microstructure,
was investigated. A range of advanced laboratory and numerical techniques were applied
and developed to study, not only the breakage phenomenon at particle-scale, but also to
monitor and analyse post-breakage changes in the soil properties.
1.2. Objective and scope
This research contributes to the geotechnical industry and sustainability in
geotechnical engineering, particularly in pavement, road, and embankment applications.
The present research also facilitates a better understanding of particle mechanics and
strength properties of three major C&D materials, namely Waste Rock, Recycled
Concrete Aggregate, and Crushed Brick used in road and pavement constructions. The
14
focus of this study is specifically on the intimate relation between degree of crushing and
particle shape. The main objectives of this research are summarised as follows:
• Quantify the effect of particle-/micro-scale properties, such as
morphology and microstructure, on degree of crushing of different C&D granular
materials (i.e. basaltic crushed Waste Rock, Recycled Concrete Aggregate, and
Crushed Brick);
• Highlight the significant effect of particle shape on crushing strength of
grains by introducing a modified particle tensile strength as a function of particle
shape factor;
• Using three-dimensional Discrete Element Modelling, identify crack
propagation mechanisms by analysing the stress distribution and energy
dissipation in individual grains during single particle and particle assembly
compression; and
• Using three-dimensional Synchrotron Radiation-based Micro-Computed
Tomography (SR-µCT), identify the changes to grain properties of granular
assemblies, with different mineralogy, microstructure, size, and gradation, due to
breakage.
1.3. Research method
As the first step, the particle shape distribution of C&D materials was measured for
coarse and fine particles using image analysis techniques and laser-based microscopy.
The microstructure and mineralogy of each type of C&D materials were also determined
using Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray Spectroscopy
(EDS). Later, to investigate the effect of micro-scale properties, including textural,
microstructural, mineralogical, and morphological properties on the degree of crushing,
Single Particle Crushing (SPC) was conducted. Subsquently, Particle Assembly Crushing
(PAC) was designed and carried out on particle assemblies to take into account the effect
of coordination number. However, in-situ experimental characterisation of the evolution
of grain fracture within a granular system is difficult utilising conventional methods.
Consequently, Discrete Element Modelling was used as an indispensable tool to monitor
force chains developed in the sample, and also to measure energy dissipation due to
breakage.
15
Moreover, due to the experimental difficulty in examining post-breakage changes in
particle-scale properties of the soil, synchrotron tomography was used to conduct 4D
imaging (i.e. 3D monitoring over time). Synchrotron radiation-based tomography was
used in this research owing to its high flux density in contrast to medical or industrial X-
ray CT devices, enabling CT scanning with extremely high spatial resolution. To conduct
scanning during loading, a new loading apparatus capable of conducting compression
tests at the high stress on assemblies of grains was also designed and developed. After
obtaining CT images, post-processing of the images was conducted using a range of
image processing techniques, including local adaptive kriging, in order to visualise and
statistically analyse the changes in particle properties due to breakage in 3D. The research
methods are summarised in Figure 1.1.
Figure 1.1. Research methods at a glance
16
1.4. Thesis outline
This thesis contains eight chapters. A brief description of each chapter is outlined as
follows:
Chapter 1: Introduction
Chapter 1 is composed of an introduction to the present research and highlights the
problem statement and research significance, objective and scope, research method, and
the outline of the study.
Chapter 2: Literature review
In this chapter, after a brief introduction of C&D materials, an extensive review of the
recent research work on micro-scale studies of geomaterials is presented. Common
methods used to study granular materials at particle-scale, including experimental and
numerical methods, are also reviewed. Along the same line, studies on particle breakage
and its governing factors are reviewed. Particle shape measurement techniques and
descriptors used in past research work are also summarised in this chapter.
Chapter 3: Recycled Construction and Demolition materials
In this chapter, a variety of laboratory tests, carried out on C&D materials in order to
determine their geotechnical, mineralogical, microstructural, and morphological
characteristics, are described, and the results presented.
Chapter 4: Experimental methodology and analysis techniques
Different experimental designs conducted and methods used in this research are
explained in this chapter in terms of the design process, procedure, equipment, and
standard followed. After a brief explanation of single particle and particle assembly
crushing, the basics of synchrotron-based radiation tomography are presented. In the
current research, a loading apparatus was developed to perform constraint compression
tests during CT scanning. A number of technical challenges, and the ways of overcoming
these challenges, are discussed in relation to the chamber and loading system design. In
the final sections of this chapter, the image processing techniques applied for segmenting
and 3D reconstructing of CT images are described.
17
Chapter 5: Particle breakage across the different scales
The effect of particle shape on particle breakage at different scales for three different
types of recycled C&D materials was investigated using Single Particle Crushing and
Particle Assembly Crushing tests. The results assisted in proposing a new relationship
between particle tensile strength and particle shape. The results of this chapter have been
published in publication No.1 (see list of publications).
Chapter 6: Discrete Element Modelling of particle breakage
Chapter 6 is dedicated to DEM simulations of particle fracture and shape to study
fragmentation mechanisms and the effect of particle shape. SPC and PAC tests were
simulated using 3D DEM to track the in-situ evolution of force chains and stress
distribution, along with energy dissipation in the system. In this chapter, the principle of
DEM, calibration procedure, and validation results are also presented. The results of this
chapter have been published in publication No. 1, 5, and 6 (see list of publications).
Chapter 7: Breakage and particle characteristics evolution through synchrotron
tomography
The fast scanning and high-resolution 4D imaging were utilised to capture images from
the interior body of the granular assemblies during loading. The changes to grain
properties due to breakage, in particular the evolution of fractal distribution and particle
shape distribution, were investigated. The comprehensive statistical interpretation of
results is discussed in this chapter. The results of this chapter have been accepted for
publication (see publications No. 3 and 4 in the list of publications), and also submitted
as part of publication No. 2.
Chapter 8: Conclusion and recommendation
The findings are summarised in this chapter, along with the recommendations for
potential future research work.
18
2. LITERATURE REVIEW
2.1. Construction and Demolition materials
Construction and Demolition (C&D) materials are solid waste materials normally
collected near curbsides or generated by construction and demolition of buildings and
structures (SustainabilityVIC, 2010). Reusing and recycling of waste materials decrease
the demand for scarce virgin natural resources and simultaneously reduce disposal cost
into the landfills (Disfani et al., 2012). It has been proven that reuse and recycling of C&D
materials in pavement and road constructions are a sustainable option, lowering carbon
footprints in comparison with using traditional quarried materials (Arulrajah et al.,
2013b). In Australia, 3.3 million tons of crushed waste rock, nearly 8.7 million tons of
demolition concrete, and 1.3 million tons of demolition brick are stockpiled per annum
(Arulrajah et al., 2012b, Arulrajah et al., 2014). Recycling and subsequent reuse of C&D
materials provide enormous benefits in terms of waste disposal cost and environmental
impacts (Tam and Tam, 2007).
In this research, three main categories of C&D materials are studied, Waste Rock
(WR), Recycled Concrete Aggregate (RCA), and Crushed Brick (CB). Waste Rock used
in this study originates from surface excavation of basaltic rock, which normally occurs
near the surface to the west and north of Melbourne, Australia (Figure 2.1). Crushed
waste rock is normally produced during excavation for residential development or near
surface and subsurface infrastructure. In terms of mineralogical constituents,
Melbournian basalt primarily consists of pyroxene, olivine, and plagioclase, with rare
apatite, alkali feldspar, and glass. The rock is normally altered to some degree. This
alteration commonly appears in form of filled pores with clay minerals increasing the
density of the rock (Peck et al., 1992). Recycled Concrete Aggregate and Crushed Brick
are by-products of construction and demolition activities of buildings and structures
(Rahman et al., 2014). Concrete chunks from demolition of concrete structures are usually
crushed into aggregates of different sizes, and CB often includes impurities such as dry
mortar paste pieces. WR, RCA, and CB have been recognized as exhibiting geotechnical
properties equivalent or similar to typical quarry pavement subbase materials commonly
used in Victoria, Australia (Arulrajah et al., 2011, Arulrajah et al., 2012a).
19
Figure 2.1. Distribution of Melbournian basalt (after Osborne et al. (2010))
2.2. Necessity of micro-scale studies on C&D materials
To date, there has been some research on the use of C&D materials in pavement
application with the focus mainly on experimental laboratory scale research (Arulrajah et
al., 2014). Despite these efforts, there is still a level of uncertainty and knowledge gap in
the behaviour of C&D material which is one of the main obstacles in further usage of
Port Phillip Bay
Melbournian basalt
20
these waste materials in road infrastructures. Pavements are complicated structures and
normally consist of materials that differ in nature and properties. The concept of design
and methods of analysis of road and pavement structures have been significantly
developed in recent decades, such as material characterization, i.e. the shift from physical
to mechanical tests, and analysis tools, i.e. the development of various models based on
different constitutive models such as elasto-plastic and visco-plastic (Peng, 2014, Lekarp
et al., 2000a). Despite all these advances, the behaviour of granular assemblies in road
performance is still not fully understood. Some pavements and roads designed to a
specified service life demonstrate severe rutting only a few years of being subjected to an
appropriate design (Collop et al., 2006). Earlier, road studies were mostly focused on the
top surface (i.e. asphalt layer) since it exhibited failures such as rutting and cracking and
was easily accessible for maintenance or remediation studies. As a result, a variety of
asphalt mixes are currently available to solve several road problems. Nevertheless, the
persistence and severity of some distress types have led to the new assumption that
considers base, subbase, and subgrade layers as the main reasons for these issues (Lekarp
et al., 2000b). Consequently, some research during the last decade has focused on
improvement of characterization of unbound aggregate materials. The best example of
this progress is shifting from using the California Bearing Ratio test to the resilient
modulus test (Zeghal, 2004).
Geomaterials also show multi-scale behaviours that are associated with the
interactions of individual particles; from the pattern of force chains to the thickness of
shear bands and from laboratory samples to the full geotechnical engineering scope
(Shamy and Zeghal, 2007). It is evident that conventional laboratory tests are unable to
provide all the answers; hence, other methods have to been applied to complement them
(Zeghal and Edil, 2002). Owing to the discrete, heterogeneous, and anisotropic nature of
granular materials, Discrete Element Modelling (DEM) as a numerical approach emerges
for complementing conventional laboratory testing.
Terzaghi (1920) highlighted the importance of micro-scale studies: ‘[Coulomb]
purposely ignored the fact that sand consists of individual grains. Coulomb’s idea proved
very useful as a working hypothesis, but it developed into an obstacle against further
progress as soon as its hypothetical character came to be forgotten by Coulomb’s
successors. [. . .] The way out of the difficulty lies in dropping the old fundamental
21
principles and starting again from the elementary fact that sand consists of individual
grains’. Although discrete element method provide a powerful tool to study geomaterials
at particle-scale, but as Sibille et al. (2007) stated: ‘This has led to the paradox of
micromechanics of granular materials as a science based almost entirely on “virtual
evidence”’.
Recently, non-destructive testing methods have become popular in fields such as
material sciences and geomechanics to observe the interior microstructure of a sample
without penetrating its surface by physical means (Viggiani, 2013). Experimental, along
with numerical, access to particle-scale information facilitates our understanding of
complicated mechanisms as well as helps to explore new mechanisms happening across
the different scales, from micro to macro (Viggiani et al., 2015).
2.3. Micro-scale study of geomaterials
Most of geomaterials, from clays to sands and crushed rocks, have a microstructure
that is sometimes visible to the naked eye, such as sand grains, or is not visible, such as
clay particles. Nevertheless, conventional methods for estimating the mechanical
behaviour of geomaterials generally ignore their microstructure and assume them as a
continuum medium leading to offer a relatively simple framework. It cannot, however,
explain complicated phenomena where microstructure affects the macroscopic behaviour
of a material. As an exemplification, the initiation of a failure zone occurring under
certain conditions cannot be adequately described (Evans, 2005).
Global granular assembly response during loading is a necessary feature of interest for
studying particulate media. It is also essential to relate observed global stress-strain
response of granular materials with local force and displacement at micro-/particle-scale.
For continuum and isotropic materials, the stress-strain relation can be fully explained
macroscopically based on continuum mechanics (Narsilio et al., 2010). Nonetheless, for
a particulate assemblage, it is well-known that the stress-strain relation is complicated,
and is dependent on both the original state of the granular assembly (e.g. local and overall
porosity and particle coordination numbers) and the loading condition. A granular
assembly is an anisotropic, heterogeneous, and non-linear medium, particularly in terms
of the contact forces between particles (Majmudar and Behringer, 2005). The strain
experienced by a granular material stems from two fundamental mechanisms; firstly, the
22
relative motion such as rolling and sliding between grains, and secondly, distortion and
breakage of individual grains (Behringer et al., 1999, Penumadu et al., 2009). A number
of techniques have been developed to interpret the microscopic behaviour of granular
materials in terms of the interaction between particles. Figure 2.2 summarizes different
common methods which have been used to study micro-scale behaviour of geomaterials.
Moreover, various applications of these methods in geoscience are shown in Table 2.1.
2.3.1. Discrete Element Modelling
Discrete Element Modelling/Method (DEM), first introduced by Cundall and Strack
(1979), is a numerical modelling approach that can simulate granular materials taking
into account particle interactions. A “virtual” DEM-simulated test can be calibrated or
validated by comparing the macro-scale response observed in a real physical test with
model’s response. The detailed particle scale information provided in the DEM
simulation can then be utilised to enhance our understanding of the material behaviour
(Cheung and O’Sullivan, 2008).
Itasca PFC2D or PFC3D (Particle Flow Code) are commercial numerical codes based
on DEM used for analysing and testing of granular materials where the interaction of
several discrete objects causes large-strain and/or fracturing (Itasca Consulting Group,
2008). In modelling by PFC, it is necessary to calibrate the micro-parameters to match
the macro-response (Cho et al., 2007). Since this research uses PFC, some fundamental
assumptions and principles of this coding program are presented as follows (Itasca
Consulting Group, 2008, O'Sullivan, 2011):
• Particles are basically presented by rigid circular disks (2D) or rigid
spheres (3D).
• Particles can overlap at their contacts although these overlaps are
extremely small compared to the size of the particles.
• Contacts are characterized by a force-displacement law, and the contact
force is associated with the magnitude of the overlap.
PFC is based on an explicit numerical approach. The calculations made by the program
are based on the numerical integration of the Newton’s second law applied to every
particle and the force-displacement laws applied to every contact. A contact force has two
23
components: the normal and shear component. Thus, two different types of stiffness, the
normal stiffness and the shear stiffness, need to be specified. Broadly speaking, the
constitutive model for each contact includes three different models: the contact-stiffness
model, the slip model, and the bonding model (Kim et al., 2012).
Figure 2.2. Common methods to study geomaterials at micro-scale
Table 2.1. A brief list of different topics on granular materials at micro-scale level
Application Method Example references Level of compaction Numerical/
Experimental Otani et al. (2013)
Shear banding Numerical/ Experimental
Viggiani et al. (2010); Evans (2005)
The time behaviour of materials such as clay
Experimental Yigit and Cinicioglu (2013)
The effect of treatment Experimental Minder and Puzrin (2013) Bonding between grains Numerical Jiang et al. (2013) Shear wave propagation Numerical Ning and Evans (2013);
O’Donovan et al. (2012) Flow of granular
material Numerical Tomac and Gutierrez (2013)
Grain breakage Analytical/ Experimental/
Numerical
Cil and Alshibli (2014); Caicedo et al. (2013); Elghezal et al. (2013);
Hossain et al. (2007); Lobo-Guerrero (2006)
Imaging of stress in samples
Numerical/ Experimental
Lesniewska and Wood (2009); Mitra and Westman (2009)
Ice formation in soils Experimental Viggiani et al. (2015) Soil permeability Experimental/
Numerical Zheng and Tannant (2016); Kress
et al. (2012)
24
• ‘Contact-stiffness model’ is the relationship between force and magnitude
of the overlap at a contact. Linear and simplified Hertz-Mindlin models can be
used in PFC.
• ‘Slip model’ allows particles to slip by defining a maximum shear force at
the contact considering the contact friction coefficient μ.
• ‘Bonding model’ is like a glue between two particles. Two well-known
bonding models are the contact bond model and the parallel bond model.
Maximum allowable normal and shear forces should be specified in advance to
describe the strength of the bond (Lobo-Guerrero, 2006).
2.3.1.1. Laboratory test simulations
Laboratory tests (e.g. triaxial or direct shear tests) on granular specimens have
provided important information about materials’ responses. Discrete Element Modelling
is a powerful numerical tool in the study of granular mechanics, providing details of the
evolution of particle displacements, rotations, and interactions that cannot be readily
measured in the laboratory. The full potential of DEM can only be realised when the
results and findings of DEM simulations are related to the existing (macroscopic)
experimental data. In addition to physical laboratory tests, the particle scale information
from DEM simulations can be used to analyse the distribution of stresses within the
specimen or provide additional insight for experimentalists (Cheung and O’Sullivan,
2008).
Several researchers have tried to simulate different laboratory tests such as triaxial
loading, Unconfined Compressive Strength (UCS), cyclic loading, direct shear, bender
element, plane-strain compression, and Indirect Diametral Tensile strength (IDT). Some
examples of recent DEM simulation of laboratory tests are presented in Table 2.2.
2.3.1.2. Different materials
As shown in Table 2.3 and Figure 2.3, sand and asphalt have recently been of interest
of numerous researchers studying their behaviour using DEM. The most likely reason for
the recent focus on clean uniform sand particles may be the fact that there is less
complexity involved in the simulation of monodisperse sand particles.
25
Table 2.2. Recent DEM simulation of different laboratory tests
Tests Researchers and References Cyclic Loading Phusing and Suzuki (2015); Xin (2013); O’Donovan et al.
(2012); Sazzad and Suzuki (2010); Indraratna et al. (2010); Hossain et al. (2007); Zeghal (2004)
Direct Shear Khalili and Mahboubi (2013), Keppler et al. (2016); Indraratna et al. (2012); Salot et al. (2009); Shafipour and Soroush (2008)
Triaxial Loading Bono et al. (2014), Elghezal et al. (2013); Belheine et al. (2009); Lu and McDowell (2008); Cheung and O'Sullivan (2008)
Plane-Strain Compression Yan et al. (2009); Evans (2005) IDT Khanal et al. (2005); Thornton et al. (2004) UCS McDowell (2002)
Table 2.3. Recent work on DEM simulation of different materials
Materials Example researchers and references Asphalt Liu et al. (2012); Yu and Shen (2012); Kim et al. (2009);
Collop et al. (2006) Ballast Indraratna et al. (2012); Lu and McDowell (2008) Perlite Elghezal et al. (2013) Sand Zhao et al. (2017); Cil and Alshibli (2014); Obermayr et al.
(2013); Yan et al. (2009); Harireche and McDowell (2003) Sugar Particles Lobo-Guerrero (2006)
Steel Balls O'Sullivan and Cui (2009)
Figure 2.3. Relative number of publications related to DEM simulation of different materials in the last decade
26
2.3.2. Experimental methods
Non-destructive testing methods have recently become popular in fields such as
material sciences and geomechanics. Among different methods, wave-based techniques
such as X-ray tomography and contact measurement techniques such as particle image
velocimetry are emerging as powerful tools to study a wide range of materials in terms of
deformation and density. Contact measurement techniques are more conventional
approaches based on the use of transducers located at the specimen boundaries and are
more suitable for studying homogeneous specimens. In contrast, the development of
comprehensive models to explain non-homogeneous processes has historically been
hampered by a lack of access to the core of the material. X-ray Computed Tomography
(CT) is used to observe the interior microstructure of a sample without penetrating its
surface by physical means. 3D CT images offer rich information about the whole
specimen in contrast with point-wise data (Evans, 2005, Viggiani et al., 2004, Viggiani
and Hall, 2004). The recent advances in X-ray Micro-Computed Tomography (µCT),
with synchrotron sources and sensitive detectors, have provided a powerful tool to obtain
much finer spatial resolution of geomaterials, such as particle-scale characterization of
sand undertaken by Zhao et al. (2015) and Cil and Alshibli (2012).
Evans and Frost (2010) classified experimental methods, used for micro-scale studies
of geomaterials, into three main groups: external analysis, wave-based analysis, and
internal analysis (Figure 2.4). They stated that each of these techniques has its own merits
and drawbacks; however, external methods are arguably the most predominant. In
external methods, in other words contact measurement techniques, images are normally
captured at regular intervals during testing from the surface of the specimen, and particle
displacements next to the confining membrane are analysed.
Tomography has been defined as an ‘imaging technique which generates a cross-
sectional picture (a tomogram) of an object by utilizing the object’s response to the non-
destructive, probing energy of an external source’ (Gondrom et al., 1999). This technique
was first introduced by Radon in 1917, who claimed that the interior of a body can be
scanned by analysing energy which has attenuated from one boundary to another
(Herman, 1979). Ultrasonic waves are commonly utilised in laboratory-scale
tomographic studies whereas seismic waves are employed in field studies. Both methods
are commonly used in the analysis of brittle rock samples where micro-cracks are closed
27
during loading. This causes the elastic waves to travel at greater speed through rock. The
main difference between seismic and ultrasonic tomography is in the frequency ranges
utilised. Seismic tomography utilizes low frequency waves whereas in ultrasonic
tomography, the waves have smaller wavelengths. Consequently, seismic tomography in
contrast with ultrasonic tomography is more suitable to measure large-scale anomalies,
like fractures or high stressed zones, since the low frequencies correspond to long
wavelengths which cause greater penetration depth (Mitra and Westman, 2009).
Figure 2.4. Classification of various experimental methods used in micro-scale studies of geomaterials (after Evans (2005))
Among the different experimental methods available, X-ray tomography and Particle
Image Velocimetry (PIV), which can be used to study granular materials, are briefly
explained.
2.3.2.1. X-ray Tomography
CT systems are diverse, from laboratory scanners to synchrotron micro-tomographs.
They are mainly different in X-ray source and energy and detector geometrical
specifications. Full reviews in terms of principles of computed tomography are presented
in the work of Stock (1999), Ketcham and Carlson (2001), and Wildenschild et al. (2002).
X-ray CT is commonly not free of artefacts, which stem from obscuration of a major
feature or misreading of attenuation values. The magnitude of linear attenuation depends
on the chemical composition and density of the material, in addition to the X-ray energy.
These issues can be alleviated through the application of specific filters, precise detector
28
calibration, and sample centring. Moreover, errors can be compounded during CT
reconstruction. This is a common problem with laboratory scanners that use wide cone
beam geometry (Ikeda et al. (2000); (Rebuffel and Dinten, 2007)).
X-ray tomography was first used in the 1960s to measure 2D deformation in sand
samples (Viggiani et al., 2010). Later, X-ray tomography was used by Desrues et al.
(1996) and Alshibli et al. (2000). X-ray micro-Computed Tomography with synchrotron
sources or laboratory scanners has offered fine spatial resolution opening up new
possibilities for understanding and exploring the mechanics of granular materials (in 3D)
at grain-scale. As an example, Takahashi et al. (2004) presented CT images of sand grains
inside a shear band. Viggiani et al. (2010) also provided valuable 3D information on
localization patterns in sand, and showed the potential of X-ray tomography as a
measurement tool, especially for measuring the changes in the global and local void ratio
due to a shear band.
2.3.2.2. Particle Image Velocimetry (PIV)
Particle Image Velocimetry (PIV) is a velocity-measuring technique used for the
analysis of displacements in soil samples during different testing (White et al., 2003). PIV
is based on tracking the spatial changes in brightness within an image, which is divided
into a mesh of different PIV patches, by comparing sequential images. The procedure can
then be automated to extract the displacement data from sequential digital images,
captured during tests in plane-strain conditions (Meinhart et al., 1999).
The fundamental limitations of this method are the need for a transparent boundary;
for example, a glass or Perspex, and that the particulate material should have an adequate
texture that the image analysis software can consistently detect changes from one
photograph to another (Lesniewska and Wood, 2009).
2.4. Particle breakage in granular materials
Granular materials used in pavement structures, embankments, foundations, and even
rail track structures experience static and dynamic loading conditions. Consequently,
particle breakage in the shape of abrasion or asperity breakage and total fragmentation
may occur (Elghezal et al., 2013). Pitchumani et al. (2004) suggested two main
mechanisms for particle breakage: body mechanism and surface mechanism (Figure 2.5).
29
Brittle fracture is owing to the existence of infinitesimal flaws and is controlled by the
critical tensile stresses even if the applied load is compressive (Lawn, 1993). Jaeger
(1967) studied breakage of rock particles between two flat platens and showed that tensile
strength () of rock particles is a function of both the vertical force at failure (F) and the
diameter of the particle (d) when it is compressed diametrically:
2
Fd
Eq. (2.1)
Figure 2.5. Breakage mechanisms (after Pitchumani et al. (2004))
Single particle compression tests, in which a particle is compressed between two rigid
plates, are usually used to measure the strength of particles. Single particle compression
tests have been conducted on sand grains by Nakata et al. (1999), McDowell (2002),
Cavarretta et al. (2010), and Cil and Alshibli (2012). This test can also be used to calibrate
discrete element model of crushable particles. However, there are limited studies on
assemblies of grains where coordination number (i.e. number of neighbouring grains) also
plays a significant role in crushing strength of the grains.
Particle breakage causes various issues such as settlement or reduction in the hydraulic
conductivity of the granular material. Furthermore, the elastic properties and the shear
strength could also be adversely influenced (Lobo-Guerrero and Vallejo, 2005, Bono et
al., 2014). Coop et al. (2004) showed that granular sand samples experience a decrease in
the internal friction angle due to particle breakage before reaching a constant value of
residual strength.
2.4.1. Factors governing particle breakage
Among a number of factors affecting the degree of crushing, the inherent strength of
the particles and effective stress state have been reported as the most important
(Yamamuro and Lade, 1996). This is exemplified in the work undertaken by Indraratna
et al. (2014) who introduced an elastoplastic constitutive model to capture ballast
degradation under monotonic loading. Table 2.4 summarises factors affecting pattern and
the probability of particle breakage. Particle shape is one of the governing factors in the
30
particle breakage phenomena (Afshar et al., 2017). Jia and Garboczi (2016) stated that
particle shape is equally as crucial as particle size distribution in the characterization of
particulate media; however, its importance has been largely overlooked due to difficulties
in obtaining particle shape information. Santamarina and Cho (2004) summarised particle
shape irregularity into three main scales: sphericity, roundness, and smoothness, and
explained how angularity causes difficulty in particle rotation while roughness hinders
slippage.
Le Pen et al. (2013) and Sun et al. (2014) also investigated ballast particle shapes in
relation to particle sizes. To date, several studies have confirmed the notable effect of
particle shape on packing characteristics of granular materials (Cho et al., 2006, Gan et
al., 2004, Williams and Jia, 2003). However, so far studies on the effect of particle shape
on particle breakage are still limited.
2.4.2. Particle breakage in DEM
Particle breakage and fracture is a detrimental phenomenon that can only be fully
understood at the particle scale. Due to experimental limitations on measuring force
chains and monitoring crack propagation at this scale, DEM has been widely used in the
past few years. However, original DEM used circular/spherical balls to simulate particles
(Cundall and Strack, 1979). Later, rolling resistance was added at contact points between
balls to indirectly model angular particles (Iwashita and Oda, 1998). Nevertheless, the
rolling resistance behaves isotropically around the spheres; and cannot accurately
represent the behaviour of elongated particles (Ferellec and McDowell, 2010). Clustering
of balls, first introduced by Thomas and Bray (1999), brought about some improvement
in representing irregular crushable particles. In recent years, crushable and irregular
shaped particles have been simulated by replacing crushed particles with smaller
fragments, and the selection of the failure criterion (Figure 2.6) or the bond strength
between sub-particles has been based on inherent tensile characteristics of the material
(Lobo-Guerrero and Vallejo (2005); Harireche and McDowell (2003); Cheng et al.
(2003); Tsoungui et al. (1999); Åström and Herrmann (1998)).
31
Table 2.4. Factors affecting particle breakage
Factors Example studies Notes Material type/
Mineralogy Lobo-Guerrero and
Vallejo (2005), Bono et al. (2014)
Study of sugar and sand particles, respectively
Loading condition
Thakur (2011), Indraratna et al. (2014)
Ballast breakage under cyclic and monotonic loading was studied.
Particle size Rozenblat et al. (2011); Marsal (1975), Hardin
(1985)
• Breakage probability of different particles with different sizes was investigated.
• Breakage index was introduced with the focus on particle size distribution before and after loading.
Shape Antony et al. (2006); Golchert et al. (2004);
Tavares and King (1998)
• Influence of non-spherical particles during shearing was investigated using DEM.
• Study was conducted on glass ballotini micro-particles with NaCl binder forming a greater agglomerate; totally different from soil particles. The focus was on issues related to chemical and process engineering.
• Particle fracture under impact loading was investigated to understand comminution process in mineral processing field.
Coordination number
Cil and Alshibli (2012); Lobo-Guerrero and
Vallejo (2005); Mishra and Thornton
(2001);
• Studies on three well-rounded sand particles in a compression column, highly affected by boundary conditions
• Breakage criterion only applied to particles having a coordination number smaller than three
• Impact breakage of individual agglomerates
32
Figure 2.6. Particle breakage with a breakage criterion (each particle with a coordination number smaller than 3 is allowed to break if σ > σmax) (Lobo-Guerrero, 2006)
2.4.3. Breakage energy
The vital role of particle breakage in the macro-scale mechanical behaviour of
particulate media has been proven by various researchers such as Nakata et al. (1999), Cil
and Alshibli (2014). However, the quantification of the impact of particle crushing
particularly on stress-strain behaviour of a granular assembly still remains a challenge
(Wang and Yan, 2012, Coop et al., 2004). From the particle-scale point of view, the
difficulty is primarily from two aspects, the role of grain crushing and fragment
rearrangement and accordingly their roles in energy dissipation, which eventually create
a linkage between micro- and macro-scale response of a granular soil (Bolton et al., 2008).
In the well-known Griffith theory, the decrease in strain energy, while a crack is
propagating, is assumed to be equal to the rise in surface energy owing to the increase in
surface area (Griffith, 1921). Thus far, it is accepted that the term ‘breakage energy’ refers
to the energy dissipation due to the creation of new surfaces during fragmentation. Einav
(2007a) proposed a novel constitutive model based on a thermodynamics approach to
estimate energy dissipation due to breakage by considering changes in particle size
distribution.
DEM provides a unique tool to track and ‘quantitatively’ measure energy dissipation
due to breakage which is impossible to measure during conventional experimental tests.
For example, Antonyuk et al. (2006) and Wang et al. (2012) used DEM to monitor energy
distribution and dissipation mechanisms during impact breakage occurring in mills
(during mineral extraction). Khanal et al. (2005) also compared the input energy with new
surface generation and number of broken bonds during a single particle crushing test
using DEM. In this study, DEM was employed to partition energy components precisely,
particularly during breakage, in granular assemblies.
33
2.5. Particle shape
Broadly speaking, the behaviour of a particulate medium is governed by various
factors: stress-dependency and material-dependency. Particle size, degree of cementation,
grading, inherent anisotropy, and particle shape can be categorised as material-dependant
factors (Abbireddy and Clayton, 2015). Even though particle shape has been recognised
as a significant factor by many authors (e.g. Katagiri et al. (2010); Gan et al. (2004);
Nouguier-Lehon et al. (2003); Hansson and Svensson (2001)), due to the lack of practical
methods to measure particle shape, so far its effect, particularly on particle breakage, has
not been properly investigated.
Das (2007) stated that particle shapes are equally as important as the particle size
distribution; “… however, not much attention is paid to particle shape because it is more
difficult to measure”. In addition, it has been accepted that for non-spherical grains, no
definite particle size exists since it is highly affected by the particle form/shape (Jia and
Garboczi, 2016).
2.5.1. Shape measurement methods
Shape measurement can be performed on actual physical objects, photographs, and
micrographs. Further analyses can then be conducted by computers using different image
processing tools. 2D measurements are typically obtained from 2D projections of
particles. Digital images from 2D projections are commonly binarized to measure each
particle’s area or perimeter based on the number of solid pixels (Mora and Kwan, 2000).
2D images can also contain textural information when Scanning Electron Microscopy
(SEM) or Transmission Electron Microscopy is used. The laser diffraction method, first
proposed by Ma et al. (2000) in order to gain particle shape information, is also another
approach to obtain size information and shape factors based on 2D projection areas. In
diffraction methods, the distances between light blobs are normally used to measure
particle dimensions (Blott and Pye, 2006).
3D imaging with the aid of X-ray techniques is essential for characterising hard-to-
describe, i.e. irregular, particle shapes. In fact, a full 3D shape visualisation can be
conducted using CT images; however, extremely sophisticated separation/segmentation
methods are required in order to obtain realistic and accurate results (Cepuritis et al.,
2017b). Cepuritis et al. (2017a) stated that it is very difficult to analyse particles with
34
sizes of less than 10 µm via CT scanning, particularly when they are highly packed. CT
scanning can also be combined with X-ray fluorescence spectroscopy to investigate
materials containing different metallic components (Jia and Garboczi, 2016).
2.5.2. Shape factors/descriptors
Particle shape can be described using quantitative or qualitative factors/descriptors.
The formers are typically dimensionless factors linking particle lengths to particle volume
or surface area (Muszynski and Vitton, 2012). For many years, particle shape has been
characterised by comparing a limited number of particles with a reference chart, such as
visual estimation chart of Krumbein et al. (1949). In recent years, particle shape
information has become more accessible because of the advent of digital cameras and
image analysis techniques. Common shape factors are summarised in Table 2.5.
Table 2.5. Definition of shape factors
Name Formula Reference True sphericity Se/S0 Wadell (1935) Degree of sphericity 2(√𝐴/𝜋)/𝑑𝑐−𝑚𝑖𝑛 Wadell (1933) Circularity 4𝜋𝐴/𝑃2 IOS (2006) Sphericity Ri-max/Rc-min Krumbein et al. (1949), Cho et al.
(2006) Ellipseness Pe/P Le Pen et al. (2013) Aspect ratio D/d IOS (2006) Solidity A/Ac IOS (2006)
Note: Se: Surface area of the sphere with same volume as the particle, S0: Real surface area of the particle, A: Area, P: Perimeter, Ri-max: Radius of the maximum inscribed circle to the section A, Rc-min: Radius of the minimum circumscribed circle to the section A, D and d: the smallest diameter and the intermediate diameter orthogonal to each other, Pe: Perimeter of an ellipse having the same area as the projection of a particle, Ac: Convex area
Although 3D quantification of the bodies’ geometry is more precise and accurate, it
requires application of more advanced techniques. Cavarretta et al. (2009) after
comparing various 2D shape factors with true (3D) sphericity of grains showed that the
two-dimensional shape factor, ‘degree of sphericity’, proposed by Wadell (1933) is
sufficient for 3D characterization of particle sphericity. Nevertheless, the degree of
sphericity is not appropriate to describe platy or flaky shapes. Gantenbein et al. (2011)
suggested Aspect Ratio (AR) for quantifying shape of flaky particles, which is the ratio
of the laminar thickness to intermediate axis length.
35
2.5.3. Particle shape in DEM
A prime feature of particulate DEM is that the particles themselves are idealized. All
numerical models simplify the physical reality. In a particulate DEM simulation, the
particles’ geometries are typically disks (in 2D DEM simulations) or spheres (in 3D DEM
simulations). These particle shape idealisations are popular as it is relatively easy to
recognize whether the particles are in contact or almost touching; besides, the geometry
of the contact point, including the inter-particle contact overlap or separation, can easily
be calculated with a high level of accuracy. At every time increment in a DEM simulation,
every contact is considered individually, and the geometry of that contact point is
calculated. There will be many more contacts than particles in a DEM simulation, and
contact resolution is usually the most computationally expensive part of a DEM algorithm
(O'Sullivan, 2011).
The clump logic introduces another way to generate a group of attached particles that
act as a rigid body to achieve a more realistic particle shape. Clumped particles may have
overlaps to any extent. Contact forces are not created between these particles, so such a
deformable body is not capable of breaking apart regardless of the forces acting upon it.
Therefore, clumped particles are assumed to be a single slaved particle moving as a rigid
body. In this sense, a clump is totally different from a group of particles that are bonded
to one another, i.e. clustered particles (Cho et al., 2007). Lu and McDowell (2008)
compared simulation of ballast particles with different shapes under monotonic loading.
They concluded that the asperity breakage model is an efficient way to study the micro-
scale behaviour of railway ballast (Figure 2.7). Liu et al. (2015) also used four general
geometrically different clumps to model ballast particles, i.e. trapezoidal, triangular,
rectangular, and hexagonal.
Figure 2.7. 10-balls clump with eight small balls (asperities) bonded as a ballast particle
(Lu and McDowell, 2008)
The level of sophistication in the use of overlapping clumps has increased significantly
in recent years. Various researchers have proposed algorithms to create clumped particles
36
from digital images of real particles. For example, the algorithm used by Das et al. (2008)
and Mollanouri Shamsi and Mirghasemi (2012) is shown in Figure 2.8. Their results also
confirmed the fact that an accurate simulation of mechanical behaviour of a granular
assembly relies on the simulation of realistic grain shapes. However, their ‘clump
generation algorithm’ is not capable of simulation of particle breakage or fracture
initiation in a grain.
Indraratna et al. (2010) proposed a slightly different approach for the simulation of
ballast particles. Firstly, the ballast particles were divided into different sieve sizes, then
some representative ballast particles, i.e. three from each size fraction, of different shapes
were selected. The ballast particles’ geometries are finally filled with tangential circles
(Table 2.6).
Figure 2.8. Simulation of semi-real-shaped particles with overlapped balls in each clump
(Mollanouri Shamsi and Mirghasemi, 2012)
Table 2.6. Representative ballast particles using in the DEM simulation (after Indraratna et al. (2010))
Ballast particles
PFC particles
37
3. RECYCLED CONSTRUCTION AND DEMOLITION MATERIALS
The process of recycling Construction and Demolition (C&D) materials involves
initial crushing using jaw and cone crushers. Impurities such as steel, glass, and plaster
are then removed from the crushed materials. Afterwards, the materials are sieved in order
to sort the boulders into different sizes. Recycled materials used in this study were
collected from stockpile storages of various sites in Victoria, Australia, that are owned
and operated by Alex Fraser Group Ltd. (Figure 3.1). The ASTM (2014) standard for
sampling aggregates was adopted to collect representative samples from stockpiles, and
then the collected materials in plastic bags, each of which had a capacity of 20 kg, and
were transported to the Advanced Geotechnical Engineering Laboratory at Swinburne
University of Technology.
Among different kinds of C&D materials, Waste basaltic Rock (WR), Recycled
Concrete Aggregates (RCA), and Crushed Brick (CB) are studied in this project (Figure
3.2). In this chapter, geotechnical, along with microstructural, mineralogical, and
morphological, properties of the C&D materials are presented.
Figure 3.1. C&D stockpiles at Alex Fraser Group Ltd.
38
Figure 3.2. C&D granular materials: a) WR, b) RCA, c) CB
3.1. Geotechnical characteristics
3.1.1. Sample preparation
Riffle splitting and the cone and quartering method were utilized to prepare samples
for further testing. To control for bias in sample preparation, a riffle splitter, which has
an even number of riffles, was used to sub-sample the material (Figure 3.3). Before
splitting, the riffle was levelled and then the material was poured gradually into the
device. In addition, cone and quartering technique was used to reduce the sample size
without any systematic bias (Gerlach and Nocerino, 2003). The split material was piled
in the form of a cone, and after flattening the surface of the cone, it was quartered as
shown in Figure 3.4. Alternate quarters were mixed to make representative sub-samples.
The aforementioned procedure was practiced for the preparation of all WR, RCA, and
CB specimens used in this study.
Figure 3.3. Riffle splitter as a sample divider
39
Figure 3.4. Cone and quartering method
3.1.2. Particle size distribution
The Particle Size Distribution (PSD) of the C&D materials (> 0.075 mm) is determined
by sieve analysis. The sieve analysis tests were performed based on ASTM (2009b). Prior
to the analysis, the test materials were dried in the oven, 105ºC to 110ºC, for 24 hours,
then a minimum of 1.3 kg from each of C&D materials was selected to conduct the sieve
analysis. The analysis was carried out using a sieve shaker apparatus with the standard
shaking period of 10 to 20 minutes.
As demonstrated in Figure 3.5 and Table 3.1, C&D materials are coarse-grained
materials with a maximum particle size of 19 mm. The fine content (< 0.075 mm) is below
5% for all types of material; thus, the hydrometer test was not conducted on the materials.
Based on Table 3.1 and Unified Soil Classification System, the WR, RCA, and CB can
be classified as Well-Graded Gravels (GW).
40
Figure 3.5. Particle size distribution of C&D materials
Table 3.1. Classification characteristics of C&D materials
Characteristic/ Type WR RCA CB
Fine content (< 0.075 mm), (%) 3.19 2.56 1.34
Sand content (0.075-2.36 mm), (%) 23.53 37.46 34.97
Gravel content (> 2.36 mm), (%) 73.28 59.98 63.69
d50 (mm) 6.71 4.75 4.85
Coefficient of uniformity, Cu 18 28 23.33
Coefficient of curvature, Cc 2 0.8 1.9
3.1.3. Specific gravity
Specific gravity (Gs) is the specific gravity of the solids, which is the ratio of the
density of the solid particles relative to the density of water. The specific gravity of the
coarse and fine fractions of the C&D materials was calculated based on ASTM (2004)
and ASTM (2000), respectively. A minimum mass of 3 kg retained on the 4.75 mm sieve
was used to measure the specific gravity of coarse fraction of the C&D materials. Besides,
50 grams passing the 4.75 mm sieve was selected to calculate the particle density of the
fine fraction using a 250 mL pycnometer, along with a suction pump and vibration table,
as specified by ASTM (2000).
41
The average values of specific gravity of C&D materials are presented and compared
with natural sand particles in Table 3.2. The values presented are the average of at least
three test results and are also comparable to the ones reported by Arulrajah et al. (2013a).
Table 3.2. Specific gravity of C&D materials and natural sand
Material/Specific gravity (Gs) Coarse fraction Fine fraction Average
WR 2.85 2.75 2.80
RCA 2.68 2.64 2.66
CB 2.54 2.66 2.60
Sand (Das and Sobhan, 2013) - - 2.64-2.66
3.1.4. Flakiness Index
The existence of flaky/flat particles significantly affects the geotechnical
characteristics of a soil matrix particularly the packing density and internal friction angle
(Hansson and Svensson (2001), Disfani (2011), and Sivakugan et al. (2011)). An
aggregate is classified as flaky when its thickness, smallest dimension, is less than 60%
of its average dimension, where the average dimension is the average sieve size of the
size fraction into which the aggregate falls (BS, 2000). Based on BS 812-105.1(2000),
the Flakiness Index is a dimensionless value representing the percentage of flaky particles
in the material; the FI sieves and gauge are shown in Figure 3.6. As shown in Table 3.3,
the highest Flakiness Index of 26.32 % was recorded for the WR grains, while the
percentage of flaky particles in RCA and CB is much lower. The maximum FI of 35% is
acceptable for the use of crushed recycled materials in pavement construction
(SustainabilityVIC, 2010). Table 3.3 indicates that all kinds of C&D materials of interest
to this study meet the FI requirement for base and subbase applications.
Table 3.3. Flakiness index of C&D materials
Material Flakiness Index (FI), (%)
WR 26.32
RCA 15.20
CB 12.89
42
Figure 3.6. Flakiness index sieves and gauge
3.1.5. Optimum Moisture Content
Broadly speaking, compaction improves soil strength by making the soil fabric denser.
Approximately 95% of the Proctor maximum dry unit weight is a requirement for several
geotechnical infrastructures such as road pavements (Lekarp et al., 2000a). The
Maximum Dry Density (MDD) and Optimum Moisture Content (OMC) were obtained
for unbound WR using the modified dynamic compaction test based on ASTM
D1557(2012) (Figure 3.7a). Later, the measured MDD and OMC (Figure 3.7b) were
used as a basis for determining the degree of compaction of samples, particularly for UCS
testing.
3.1.6. Unconfined Compressive Strength
The static compaction method was initially used to prepare representative samples for
conducting Unconfined Compressive Strength (UCS) tests. A split compaction mould
with dimensions of 100200 mm (diameterheight) was used to compact the soil sample
in 8 layers. A constant pressure of 12.5 MPa was used to compact each layer at OMC,
which was previously measured from the modified compaction curve (Figure 3.7b). Gabr
and Cameron (2011) and Mohammadinia (2016) utilised a similar approach to prepare a
43
more ‘uniform’ sample for UCS tests. To minimise cracking along the layer interfaces
and increase interlocking between the layers, the surface of each layer was scarified
before adding the next layer.
Figure 3.7. a) Modified compaction machine, b) Compaction curve for unbound WR
UCS tests are commonly used to predict the strength and ultimately performance of
materials in different engineering applications. ASTM (2009a) was followed to conduct
UCS tests on WR samples. The axial load with a rate of 1 mm/min was continuously
applied to each sample, with a height-to-diameter ratio of 2.00. Attention was also paid
to ensure a smooth load application, without any sudden impacts to the top of sample.
The failure mechanism of a WR sample in the form of axial splitting is shown in Figure
3.8a. Figure 3.8b also shows that 780 MPa is WR’s strength under an unconfined
compression. The UCS results were later used to calibrate the 2D DEM model as
discussed in Chapter 6.
Figure 3.8. USC results; a) WR sample after failure, b) Stress-strain curve
44
3.2. Mineralogy and microstructure
To observe and identify different minerals and also the microstructure of the C&D
grains, Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray
Spectroscopy (EDS) were utilized. Prior to SEM and EDS testing, a specified sample
preparation procedure was practised. Firstly, a coarse grain, with the mean size of 13.2-
19 mm, from each of WR, RCA, and CB was selected and placed in a mould containing
liquid resin. The soaked grains were cured for 12 to 24 hours until resin set (Figure 3.9a).
Secondly, in order to flatten and smooth the sample surface, the samples were grinded
and polished using different sized SiC abrasive papers from coarse (i.e. 300 grit) to fine
(i.e. 1200 grit) (Figure 3.9b). Following the sawing and grinding operations, further
polishing with diamond paste was conducted in order to remove surface scratches.
Diamond paste is a water-based diamond suspension which enables further efficient
surface polishing and removes contaminants (Stutzman and Clifton, 1999). Diamond
polishing was carried out with Struers Tegramin-25 on polishing cloths with the grit size
ranging from 1 to 3 μm (Figure 3.9c). Once the samples were polished, the ultrasonic
cleaning process using ethanol was performed to clean contaminants which might adhere
to the sample surface. Finally, the samples were coated with a thin layer of gold alloy
(approximately 5 nm) to increase the electrical conductivity of the surface in order to
obtain high resolution images (Solanki and Zaman, 2012). Figure 3.9d shows the K975X
Turbo-Pumped Thermal Evaporator used to spatter gold layer on the specimens and the
coated samples.
After sample preparation, the Zeiss Supra 40VP Scanning Electron Microscope was
used to capture microscopic images from each material (Figure 3.10). A Scanning
Electron Microscope scatters a beam of electrons to scan samples. The electron beam
interacts with atoms in the specimen and produces a variety of signals containing
microstructural information of sample surfaces. Figure 3.11 demonstrates SEM images
of WR, RCA, and CB grains captured at a voltage level of 20 kV and a working distance
of 8 mm, which is the distance from the sample to the beam tip. As shown in Figure 3.11,
among different types of C&D materials, basaltic WR has a vesicular texture with a
relatively large interior void in its microstructure, while CB and RCA have more uniform
microstructures.
45
Figure 3.9. Sample preparation for SEM testing: a) Cold moulding, b) Grinded samples, c) Diamond polishing with Struers Tegramin-25, d) Gold coating by K975X Turbo-Pumped
Thermal Evaporator, e) Gold coated specimens
Energy-Dispersive X-ray Spectroscopy tests were also carried out for elemental
analysis of samples. When the incident beam causes electron migrations at the atomic
level, the energy released in the form of X-rays, is measured by the energy-dispersive
spectrometer. The energy emitted from the specimen reveals the atomic structure of the
specimen elements (Harding, 2002). Figure 3.12 and Table 3.4 show the percentage and
intensity of different elements in C&D grains. Referring to Table 3.4 and Figure 3.12,
clay Crushed Brick is mainly made of silica, alumina, iron dioxide, and lime, and the
chemical composition of Recycled Concrete Aggregate is mostly silica and calcium
alumino- ferrite. As expected, the basaltic Waste Rock consists of albite, olivine, and
pyroxene, and also a low titanium content was observed.
46
Figure 3.10. Zeiss Supra 40VP Scanning Electron Microscope
Figure 3.11. SEM images of a) WR, b) RCA, and c) CB
47
Table 3.4. Weight percentage of different elements in different kinds of C&D materials
Elements/Weight % WR RCA CB
Si 23.1 38.3 30.7
Al 8 8.3 9.1
Fe 6.6 5.4 4.6
Ca 5.2 4.1 4.9
Mg 3.8 0.0 0.0
Na 2.9 2.7 0.0
K 1.1 2.0 2.8
Ti 1.1 0.0 0.0
Figure 3.12. EDS elemental analysis: (a) WR, (b) RCA, (c) CB
48
3.3. Particle shape
As suggested by Cavarretta et al. (2009), the two-dimensional shape factor, ‘degree of
sphericity’, is sufficient for three-dimensional characterization of particle sphericity.
Accordingly, to determine the particle shape distribution of C&D materials, degree of
sphericity was measured for each material. However, the degree of sphericity is not
appropriate to describe the shape of flaky particles. Based on Table 3.3, the highest
Flakiness Index of 26.32 % was recorded for WR grains, while the percentage of flaky
particles in RCA and CB is negligible. Hence, prior to sphericity measurements, flaky
particles were separated from WR grains based on BS (2000) 812-105.1, and the Aspect
Ratio (AR) was measured to quantify the shape of the flaky WR particles.
3.3.1. Measurement methods
3.3.1.1. Shape measurement of coarse grains
In this study, to categorize particle shapes, several images from 1.3 kg of coarse grains
(i.e. >1.18 mm) from each of WR, RCA, and CB were taken. The value of 1.3 kg was
selected based on ASTM (2009b) D6913, the minimum mass requirement of specimens
for sieve analysis. The grains were spread out on white sheets at a reasonable distance
from one another. The most advanced DSLR Nikon camera with a 24.2 megapixel CMOS
sensor and EXPEED 4 image-processing engine was used to capture images from grains
on every sheet (Figure 3.13a, 3.14a, and 3.15a). The images were then imported to an
Image Processing and Analysis software program written in Java (ImageJ) to calculate
the degree of sphericity of particles. Firstly, the images were converted to binary images
using Otsu thresholding. Otsu is a thresholding method used to segment the image into
different homogenous components based on the grey-level histogram of the image
(Jianzhuang et al., 1991) (Figure 3.13b, 3.14b, and 3.15b). Secondly, noise and artefacts
in every image were corrected during image analyses by removing outliers. The number
of removed outliers were 2 to 10 in each dataset containing approximately 300 to 30000
data points. IBM SPSS Statistics 23 (Green and Salkind, 2010) was used for statistical
analyses.
49
Figure 3.13. Some example images of WR coarse grains: a) original images, b) binary images
3.3.1.2. Shape measurement of fine grains
In order to investigate the particle shape distribution of fine C&D grains (i.e. <1.18
mm), the CILAS 1190 Particle Size Analyser was utilized. The particle size analyser is a
laser-based microscope and is suitable to measure particle shapes and sizes ranging from
0.04 μm to 2,000 μm. A flow of moving particles is examined by CILAS 1190, i.e.
dynamic image analysis. Dynamic image analysis enables the investigation of a large
sample size with more randomly oriented particles and causes reduction in overlapping
particles (Altuhafi and Coop, 2011). CILAS dispersing unit brings about a well-dispersed
flow of grains passing through the scanning beam emission. An exposure time of less
than 1 ns is used to ensure that motion blur is negligible. CILAS 1190 also uses laser
diffraction and Charge-Coupled Device (CCD) cameras allowing measurement of
particles between 0.04 and 2,000 μm in different single shots (Cilas, 2008) (Figure 3.16).
The laser diffraction method can be employed to identify particle size and shape from the
light intensity distribution. The CILAS laser diffraction spectrometry is based on the
principle of Fraunhofer diffraction (Weiner, 1984). It should be noted that the
50
measurements of particle properties are more accurate when particles are large enough in
comparison with the wavelength of light. Mie-scattering patterns of single particles can
also be used to extend the method to lower particle size ranges (de Boer et al., 1987). The
Fraunhofer diffraction and Mie scattering theory were utilized to estimate the particle
shape distribution of fine C&D grains. The particle properties were measured using a real-
time Fast Fourier Transform of the images gained with the CCD camera equipped with
an image processing unit (Cilas, 2008) (Figure 3.16).
Figure 3.14. Some example images of RCA coarse grains: a) original images, b) binary images
51
Figure 3.15. Some example images of CB coarse grains: a) original images, b) binary images
Figure 3.16. CILAS 1190 Particle Size Analyser: a) schematic view of measurement with particle size analyser, b) Particle Size Analyser setup
52
A total of 50 grams from each of WR, RCA, and CB were selected, and 3 grams were
poured into the device in each attempt to capture the shape of the fine particle shape
(Figure 3.17). The images were then imported into ImageJ (Abràmoff et al., 2004) to
calculate the degree of sphericity of the particles. Noise in every image was again
corrected during the image analyses. Particles touching each other in an image were also
segmented in order to identify each individual particle in an image. Besides, particles
touching, the image border was removed from further statistical analyses since their full
shapes were not clear in the images. An example is shown in Figure 3.18. More details
on image processing and segmentation methods are provided in Chapter 4.
Figure 3.17. Some example images of C&D fine grains: a) WR, b) RCA, c) CB
53
Figure 3.18. RCA fine grains: a) microscopic image, b) noise-free and segmented image
3.3.2. Analyses
Figure 3.19 illustrates the ‘degree of sphericity’ distribution of 2,879 of RCA coarse
grains and 1,746 of RCA fine grains. The sphericity distribution of coarse RCA grains in
particular, here particle diameter > 1.18 mm, shows mainly two different modes of 0.70
and 0.84 which are related to elongated and bulky particles, respectively (Figure 3.19a).
The bimodal distribution of sphericity of coarse WR and CB grains is also evident in
Figure 3.20a and 3.21a. Figure 3.22 also shows the mean and median of the degree of
sphericity for elongated and bulky WR grains from the largest size fraction of 13.2-19
mm.
As shown in Figure 3.19b, 3.20b, and 3.21b, it is noticeable that the sphericity
distributions of fine C&D grains are slightly skewed to the left. Although a relatively
large number of particles with a sphericity of approximately 0.7 (i.e. elongated grains)
were observed (Figure 3.19b, 3.20b, and 3.21b), the percentage of bulky particles with
a larger value of sphericity is higher in the fine fraction of C&D materials compared to
the coarse fraction. The average degree of sphericity is 0.804, 0.81, and 0.82 for coarse
grains of RCA, WR, and CB, respectively (Figure 3.19a, 3.20a, and 3.21a). On the other
hand, the measured mean value of sphericity is 0.009-0.029 higher for the fine fraction of
each material (Figure 3.19b, 3.20b, and 3.21b). Comparison between the mean value of
sphericity of the coarse and fine fraction of each material confirms that the sphericity
increased slightly as the particle size decreased. Sun et al. (2014) also reported that the
roundness of ballast particles diminished slightly as particle size increased.
54
Moreover, the average Aspect Ratio of 0.13, which is the ratio of laminar thickness to
the intermediate axis length, was measured for WR flaky grains (Figure 3.23). In
summary, based on the average degree of sphericity (i.e. ϕ̅), AR, and FI presented in
Table 3.3, each material was divided into different particle shape categories as follows:
• WR: bulky (ϕ̅ = 0.84 or AR 1), elongated (ϕ ̅= 0.70 or AR 0.33), and
flaky (AR 0.13)
• RCA: bulky (ϕ ̅= 0.84 or AR 1) and elongated (ϕ̅ = 0.70 or AR 0.33)
• CB: bulky (𝜙 ̅= 0.84 or 𝐴𝑅 1) and elongated (�̅� = 0.70 or 𝐴𝑅 0.33)
Figure 3.19. Degree of sphericity distribution of RCA grains: a) coarse grains (>1.18mm), b) fine grains (<1.18mm); N is the number of studied grains
55
Figure 3.20. Degree of sphericity distribution of WR grains: a) coarse grains (>1.18mm), b) fine grains (<1.18mm); N is the number of studied grains
Figure 3.21. Degree of sphericity distribution of CB grains: a) coarse grains (>1.18mm), b) fine grains (<1.18mm); N is the number of studied grains
(a) (b)
Mean=0.819Std. Dev.=0.109
N=1,971
Mean=0.810Std. Dev.=0.090
N=3,075
(a) (b)
Mean=0.820Std. Dev.=0.088
N=3,367
Mean=0.830Std. Dev.=0.084
N=1,458
56
Figure 3.22. Degree of sphericity of WR grains in different shape categories; particle size fraction: 13.2 to 19 mm, (N: Number of grains. Circles, ‘o’, and asterisks, ‘’, are related to
outliers)
Figure 3.23. WR flaky particle
3.4. Summary
Different tests were conducted to determine geotechnical, mineralogical,
microstructural, and morphological characteristics of C&D materials. The results are
summarised as follows:
• C&D materials are coarse-grained granular materials with maximum
particle size of 19 mm.
• Results of SEM and EDS testing show that C&D materials have a variety
of mineralogical and microstructural characteristics, i.e. from basaltic vesicular
waste rock to clayey crushed brick.
57
• Shape measurement of a large number of fine and coarse particles of
different C&D materials was carried out showing a slight increase in degree of
sphericity as particle size decreased.
• Considering the particle shape distribution and Flakiness Index, particle
shape of each type of C&D materials can be classified into two or three main
categories of bulky (ϕ̅ = 0.84 or AR 1), elongated (ϕ ̅= 0.70 or AR 0.33), and
flaky (AR 0.13).
58
4. EXPERIMENTAL METHODOLOGY AND ANALYSIS TECHNIQUES
In order to investigate the effect of particle shape on particle breakage across the
different scales, Single Particle Crushing (SPC) and Particle Assembly Crushing (PAC)
tests were conducted. SPC and PAC tests were carried out on a variety of C&D grains in
the particle size fraction of 13.2-19 mm. Whereas the mean size (i.e. d50 or d30) of C&D
materials, which determines the governing particle-level forces and following macro-
scale behaviour, is between 0.425-4.75 mm. Hence, Synchrotron tomography was
performed on different C&D assemblies to further analyse particle breakage at a smaller
scale, which was impossible to achieve by using conventional laboratory tests.
4.1. Single Particle Crushing
Displacement-controlled single grain compression tests, in which individual particles
are compressed between two rigid plates, are often utilized to measure the strength of
granular materials. The individual C&D grains were subjected to vertical compression
between two flat platens until the induced horizontal tensile stress inside the grain caused
breakage (Figure 4.1a). The Geocomp LoadTrac II with a load/frame capacity of 22 kN
was used to perform the SPC tests (Figure 4.1b). The loading rate was set to 1 mm/min
between the two rigid loading plates.
Figure 4.1. Single Particle Crushing: a) Schematic view, b) WR grain under loading by Geocomp LoadTrac II
59
Single Particle Crushing (SPC) experiments were conducted on 21 single grains of
WR, 14 single grains of RCA, and 14 grains of CB (7 grains from each shape category).
To eliminate the effect of size on particle crushing, grains in the size range of 13.2 to 19
mm were selected. The materials’ largest size fraction was selected since larger particles
have a higher probability of breakage in a particulate assembly. The particles were placed
resting on their longest dimension (lowest potential energy).
4.2. Particle Assembly Crushing
In addition, in order to investigate the effect of particle shape at a larger scale, eight
one-dimensional compression experiments were conducted on assemblies of WR
particles for each shape category (i.e. bulky, elongated, or flaky). The WR particles, with
a size between 13.2 and 19 mm, were placed inside a cylindrical mould and were
vertically compressed at a constant displacement rate of 1 mm/min using Geocomp
LoadTrac II (Figure 4.2). In order to designate one particle as the ‘representative particle’
in the middle of the assembly, a cylindrical mould with a dimension of 50 mm diameter
and height was selected. Particles in the Particle Assembly Crushing (PAC) tests were
coloured prior to testing with spray paint based on their positions in the mould (i.e. close
to the top cap, middle, and close to the base). One particle was deliberately coloured green
in every test specimen (here called the ‘representative particle’) and placed in the middle
of the assembly so that the other particles completely surrounded it to minimize smooth
boundary effects on the representative particle, i.e. simulate in situ conditions (Figure
4.3).
Figure 4.2. Particle Assembly Crushing setup
60
Figure 4.3. Particle Assembly Crushing: (a) Grains before loading, (b) Test setup, (c) Grain crushing after loading
4.3. Synchrotron tomography
4.3.1. Experiment Design
Due to experimental difficulty in examining crack propagation at the particle-scale,
synchrotron tomography was used to conduct 4D imaging (i.e. 3D monitoring over time)
on 12 samples of the C&D materials. Assemblies of C&D grains in the size fractions of
0.425-1.18, 1.18-2.36, and 2.36-4.75 mm were studied under different monotonic loading
conditions, ranging from 5 to 15 kN (i.e. from 10 to 30 MPa). Moreover, to further
investigate the interaction of coarse and fine particles under loading and its consequent
impact on the overall crushing level, three specimens from a spectrum of each of the C&D
materials (i.e. 0.425 mm< particle size< 4.75 mm) were scanned. In addition, one natural
sand sample was scanned under different loading sequences for comparison purposes
(Figure 4.4). Referring to Figure 4.4, a maximum vertical load of 10 kN was applied to
samples in the size fraction of 1.18-2.36 and 2.36-4.75 mm, while assemblies with particle
sizes of 0.425-1.18 and 0.425-4.75 mm were compressed vertically up to 15 kN. Higher
load sequences were selected for assemblies containing smaller particles since smaller
grains normally exhibit higher tensile strength due to the statistical size effect. In total 36
CT scans were performed in this study, which provide a valuable data source for further
statistical and analytical analyses, which are presented in Chapter 7.
61
Figure 4.4. Experiment design for synchrotron tomography experimets on samples with different particle sizes and under various loading levels
62
4.3.2. Synchrotron Radiation-based X-ray Micro-Computed Tomography
In a synchrotron machine, electrons moving at velocities close to the speed of light,
are forced to change their direction under a strong magnetic field causing the electrons to
send out electromagnetic radiation (synchrotron light) (Cowie et al., 2010).
4.3.2.1. Synchrotron source
A synchrotron source consists of a number of main components (Figure 4.5). Firstly,
a barium cathode is heated to nearly 1000C in an electron gun in order to generate
electrons. Secondly, in an accelerator, the electrons are accelerated to 99.99% of the speed
of light. Thirdly, the electrons are transferred to a first ring, i.e. booster ring, where their
energy is increased/boosted using a radio frequency current of 3 GHz. Fourthly, electrons
circulate for about 30-40 hours in a second ring, i.e. storage ring. In this phase, the
synchrotron light is created by bending the path of the electrons using a powerful
magnetic field. Finally, the light is channelled from the ring to the pipelines, i.e.
beamlines, including different types of mirrors, filters, and optical components (Figure
4.6), so that it can ultimately be utilised for different research purposes (Boldeman and
Einfeld, 2004).
Figure 4.5. Maquette of synchrotron light machine in Australian Synchrotron
63
Figure 4.6. Beamline
4.3.2.2. Synchrotron light
Among the unique features of synchrotron light, tuneable, extremely intense, highly
collimated, polarised, pulsed, and non-destructive can be named. The synchrotron light
has a wide spectrum while a certain range of wavelengths can be set to be used for a
specific purpose. The synchrotron light is also highly intense, a million times brighter
than the sun (Figure 4.7). This brightness can reveal highly detailed information that is
impossible to capture by any other method. The synchrotron beam is also very focused
which allows investigating extremely small areas of a specimen. The emitted light is also
pulsed meaning small changes during a very short period of time, such as nanoseconds,
can be observed (Snigirev et al., 1995, Bilderback et al., 2005).
64
Figure 4.7. High intensity/brightness of synchrotron light compared to other types of light
Another benefit of synchrotron light is that it provides CT at much faster frame rates
compared to conventional facilities (Stevenson et al., 2010). All the high-resolution 4D
imaging tests (i.e. 3D monitoring over time) of this research were conducted in the
Australian Synchrotron, the Imaging and Medical Beam Line (IMBL), which provides
high-resolution, phase-contrast X-ray imaging. The cylindrical sample was placed
between the source and the detector to be scanned. The IMBL source is a multi-pole 4 T
wiggler with an optimal energy range of 20 - 120 keV (eV is Electron Volt) (Hausermann
et al., 2010). The optimal energy of 60 keV was used for imaging the granular C&D
materials with an exposure time of 400 msec. The exposure time was chosen based on the
X-ray attenuation of the sample and the power used. The experiment was conducted in
IMBL Hutch 3B whose application is for very high resolution large object 3D CT
scanning. The resolution (i.e. voxel size) depends on the distance between the sample and
the source, and its greatest lower bound was limited to 10 µm. There are always trade-
offs between sample size and resolution, likewise between scan time and process time.
Thus, the scans performed in this study were at the voxel size of 11.6 µm because of the
specimen size and desire to conduct fast scans, giving a scan time of only 10 minutes for
each scan.
65
4.3.2.3. Ruby detector
The vertical beam size Hutch 3B is approximately 25 mm, and scans were conducted
using the Ruby detector. Ruby is a custom designed IMBL detector. Its concept is based
on a photo-sensitive device coupled by a bright lens to a suitable X-ray sensitive
scintillator. The sensor is placed on a vertical motor-driven slide set within a light tight
enclosure. A mirror is utilized to observe a phosphor plate set perpendicular to the
direction of the beam. This permits protection of the sensor from direct and scattered
beam radiation using appropriate high-z materials. For the experiments presented in this
thesis, the sensor was equipped with a Nikon Micro-Nikkor 105 mm/f 2.8 macro lens
allowing the slide to be used as a zoom control (Figure 4.8). The scintillator was a 200
µm thick terbium doped gadolinium oxy-sulphide (Gadox, P43) screen with a thin
aluminium powder layer as an optical block (Hall et al., 2013, Hall, 2015).
Figure 4.8. Ruby detector
66
4.3.3. Experimental compression set-up
A loading apparatus was developed in order to apply one-dimensional compression to
the confined granular samples. The apparatus consists of two major parts: the sample
chamber and the loading and data acquisition system (Figure 4.9).
Wiggler Slits Filters Sample Detector
Load cell
Sample chamber(25 mm diameter)
Data logger
Distance from source to sample > 20 m
Sample to detector ~
0.2 m
X-ray
Figure 4.9. Schematic diagram of the experimental layout and the loading setup
67
4.3.3.1. Sample chamber
The design of the sample chamber involves consideration of a number of items. Firstly,
no barriers should be located between the sample chamber and the radiation path to avoid
blurring of the CT images. Secondly, the chamber must be made of radiolucent materials.
Thirdly, the chamber should resist high compressive stresses during testing. Finally,
efficient and quick removal and replacement of samples between tests are required.
Consequently, the sample chamber was made of a high-strength radiolucent tube of
aluminium with a thickness of 5 mm, 25 mm internal diameter and 25 mm height. The
height was selected based on the limited maximum vertical beam size. The thickness was
dictated by the linear attenuation coefficient of Al 6061 at a radiation energy of 60 keV
in order to be transparent to the beam, and also the required strength to resist up to 61.12
MPa compressive stress on the test samples. The chamber was bolted to the bearing frame
which is capable of resisting a load of 30 kN. Figure 4.10 shows a schematic view of the
loading apparatus and the test chamber. After placing the specimen in the chamber, the
chamber cap was bolted and then fixed onto the rotary base, since full rotation was
required for the sample to be scanned at different angular positions. To be able to place
the sample in the direct path of Synchrotron radiation, the sample chamber was located
in the bottom part of the apparatus.
4.3.3.2. Loading and data acquisition system
In addition to the limitation that radiation path to the sample should be clear, the
maximum mass capacity (70 kg) of the rotary unit was a second factor to be taken into
account. Accordingly, the use of a hydraulic jack or conventional stepping motor was
rejected in the early phase of the design due to their heavy weight and associated cables
causing disruption to the 360 rotation of the base. Hence, a reaction frame was used and
the force was manually exerted to the samples by screwing a threaded rod connected to
the load cell (Model SW, Tovey) (Figure 4.10), which allows sample scanning through
a full rotation without the need to displace or unload the system. A high strength thrust
ball bearing was used between the load cell and the threaded rod to avoid transferring a
moment to the loading piston. At the end of each test and upon completion of imaging,
after removal of the cap, the piston was pushed out to extrude the sample from the
chamber, allowing for post-test sample recovery. During each scan, a Linear Variable
68
Differential Transformer (LVDT) was used to measure deformation while the load cell
continuously recorded the force.
Due to manual application of load using a reaction frame and screw, an average of
0.50 kN load relaxation was observed after each scan, which normally took 15 min to
complete. Although 0.50 kN is negligible compared to the experimental loading
sequences (i.e. 5 kN, 10 kN, and 15 kN), utilization of a mini-actuator/stepping motor to
run load-controlled tests is recommended for future scanning in the situation that the
weight capacity of the rotary base and power supply to the rotary specimen can be
modified.
Figure 4.10. Schematic view of the loading apparatus and sample chamber
69
4.3.4. Image processing
The Multi-modal Australian ScienceS Imaging and Visualization Environment
(MASSIVE), fast data processing computers, were used to reconstruct high resolution
images from 1810 radiograms for each sample. The X-TRACT software was also used to
remove ring noises (which are discussed below) from 2159 reconstructed horizontal slices
of every sample.
4.3.4.1. Density contrast
Contrast within a CT image depends on differences in the density of particles. The
denser the particle, the more X-rays are attenuated. In fact, the greater the difference in
the density of the two phases causes the greater contrast between those phases in a CT
image (Figure 4.11). Low density phases, such as air, appear as black, while denser
materials are represented by brighter shades. Figure 4.12 shows a basaltic WR particle;
the denser pyroxene minerals can easily be distinguished from the lighter minerals such
as olivine and plagioclase.
Figure 4.11. Density contrast in a CT image
Figure 4.12. Basaltic WR particle
70
4.3.4.2. CT artefacts
Image artefacts are a discrepancy between the reconstructed values in an image and
the true attenuation coefficients of the sample. There are various categories of CT
artefacts; however, ring noises and motion artefacts are more likely to occur during each
CT scan.
4.3.4.2.1. Ring noise
Ring noises are commonly encountered in CT images and normally caused by a
miscalibrated detector (Figure 4.13). Calibration or occasionally replacement of the
detector is sufficient to reduce this kind of noise (Boas and Fleischmann, 2012).
4.3.4.2.2. Motion artefact
Motion in the sample during scanning causes blurring, as well as double imaging. A
fixed position sample is a simple means of preventing motion artefacts, which was the
procedure adopted in this research by fixing the test set-up to the rotary base.
Consequently, during a full rotation of the base, the sample did not wobble. Very rapid
scanning is another alternative technique to reduce motion artefacts (Hsieh, 2009).
Although calibrated detector and fixed samples can decrease the level of noise in CT
images, it is practically impossible to achieve perfect, noise-free images. In this research,
several filtering techniques were used to improve the image quality and image
segmentation.
Figure 4.13. CT image showing severe ring artefact
71
4.3.4.3. Segmentation
The main steps involved in image processing in this study are shown in Figure 4.14.
In order to perform statistical analysis on the CT images, each image must be segmented
into particles and the background (i.e. pores in this study). To do so, with the aid of
thresholding segmentation, particles were separated from the background and a binary
image was reproduced. A grey scale value is defined to separate regions based on analysis
of the image histogram (Iassonov et al., 2009). A histogram shape and the basis for
discretising the image are shown in Figure 4.15. However, as shown in Figure 4.14, the
image may still be noisy enough to prevent proper segmentation. In the next step, Median
filtering and Gaussian blur filtering were applied to reduce noise and achieve smooth
images. Median filter runs through every predefined radius of pixels and replaces them
with the median of intensity values of their neighbourhood, while the Gaussian blur filter
smooths the sharp edges using the Gaussian function (Gonzalez, 2009). Figure 4.16
illustrates the outcomes of the Gaussian blur and median filters with a radius of 7 pixels
on a piece of basaltic Waste Rock. In addition, since the basaltic crushed rock studied in
this research has a vesicular texture (Figure 4.17a), the internal grain pores were filled to
improve further segmentation (Figure 4.17b).
Despite denoising, individual fragments cannot be identified as long as they are in
contact with each other (Figure 4.17b); therefore, watershed segmentation technique was
further applied to resolve this issue as shown in Figure 4.17c. Watershed is a
segmentation algorithm that considers the image as a topographic surface (Figure 4.18a).
A watershed transformation segments the regions into catchment basins, while water is
assumed to collect into basins and separate the two basins from each other, as shown in
Figure 4.18b (Beucher and Meyer, 1992, Mangan and Whitaker, 1999). However, the
classical watershed normally leads to over-segmentation in an input image. In fact, the
classical watershed algorithm is more suited to segment connected, near circular
structures. Therefore, the Watershed Irregular Features plugin of Fiji, an image
processing package based on ImageJ, was used to separate, not only circular shaped
grains, but also irregular ones more efficiently by specifying two extra parameters, the
erosion cycle number and separator size.
72
1810 Radiograms
2159 Slices
Reconstruction Binary Images
Thresholding Segmented
Images
Filtering and Watershed Statistical
Files
Measurements
Figure 4.14. Main steps of image processing in order to obtain quantitative results
Figure 4.15. Histogram-based binarization of the sand sample
73
Figure 4.16. Image processing illustration: a) Original binary image, b) Image after median filtering, c) Image after Gaussian blur filtering
Figure 4.17. Segmentation: a) Original image, b) Image after filtering, c) Watershed segmentation
Figure 4.18. Watershed segmentation basics: a) Greyscale image as a topographical surface in terms of intensity, b) Watershed transformation
74
As shown in Figure 4.19, defining the appropriate erosion cycle numbers resolves the
issue of unwanted segmentation. Care should be taken since very high numbers of erosion
cycles will lead to the results being closer to the classical watershed (Schindelin et al., 2012).
The second parameter range (i.e. separator size) describes the length of the line separating
connected grains.
Figure 4.19. Comparison of classical watershed with Watershed Irregular Features
4.3.4.4. 3D reconstruction
As discussed earlier, locally adaptive thresholding was used to segment particles in the
images. This method uses a variable thresholding values based on local image characteristics
rather than using a single global value (Oh and Lindquist, 1999). To increase the accuracy of
the segmentation process, images went through different pre- and post-processing techniques
using erosion or dilation morphological operations (a summary of different techniques can
be found in Soille (2013)) to remove artefacts in the original image. Nevertheless, extensive
pre-processing or post-processing can cause reduction in segmentation quality by either
removing, not only noise, but also actual features, for example blurring of gray scale images,
75
or producing unwanted artefacts when using edge sharpening filters, and thus should be
monitored carefully and applied with care.
In this study, Avizo 9 (Westenberger, 2008), an image processing software package for
3D visualizing of CT images, is used to reconstruct each sample three-dimensionally. Local
adaptive kriging (developed by Oh and Lindquist (1999)) that utilizes both global and local
spatial information and Watershed Irregular Features were used to segment and then
accordingly label each particle or fragment (Figure 4.20). In the initial stage, two global
threshold values (V1 and V2) were chosen, either manually or with a global thresholding
approach. Voxels with grey scale values smaller than V1 and larger than V2 were defined as
the background and foreground, respectively. Later, all uncategorized voxels with grey
values within the range of V1 to V2 were determined as the background or foreground using
a kriging window centred on the unclassified voxel. According to Iassonov et al. (2009),
among available segmentation methods, best overall ‘3D’ segmentation quality can be
obtained with the kriging method; however, still this method requires adequate supervision
by a skilled operator. The segmented and labelled slices were stitched together in order to
visualize the whole 3D sample, where each particle or fragment was identified by a unique
identifier (Figure 4.20b).
Although different image enhancement techniques, such as pre-segmentation and post-
segmentation filtering, can dramatically alleviate noise problems in an image, every filtered
CT image still has some degree of artefacts (Kaestner et al., 2008). In this study, after image
processing, including filtering and segmentation, the resulting data files were processed
statistically using IBM SPSS Statistics 23 to remove outliers in terms of particle size and
shape factors (using ‘if’ commands).
76
Figure 4.20. a) Original and ‘segmented and labelled’ 2D slices, b) 3D reconstructed,
segmented, and labelled WR sample at the initial condition (i.e. 0 MPa)
4.4. Summary
To investigate the effect of particle shape on particle breakage Single Particle Crushing
(SPC) and in a larger scale Particle Assembly Crushing (PAC) tests were designed and
conducted. SPC and PAC tests were carried out on C&D coarse grains while the use of a
non-destructive technique was essential for further investigation of the C&D fine grains. A
novel constraint compression set-up was developed to conduct 4D imaging (i.e. 3D
monitoring over time) using Synchrotron tomography. Synchrotron light is a monochromatic
highly culminated X-ray source that produces a beam with a high flux and a specific energy
level. After CT scanning of the assemblies which were subjected to compression at different
loading intervals, a variety of image processing techniques were applied to reconstruct,
segment, and visualise the C&D samples in 3D. Finally, the data files, including size and
shape factors of each particle, or newly-generated fragment, were obtained for further
analyses.
(a) (b)
25 mm
77
5. PARTICLE BREAKAGE ACROSS THE DIFFERENT SCALES
Despite several efforts to characterize particle breakage (see Chapter 2), the dynamic
propagation and evolution of particle fractures, particularly in an assembly, had not been
studied extensively in the past. In this and subsequent chapters the in-situ evolution of particle
breakage and post-breakage particle characteristics are presented and discussed.
5.1. Single Particle Crushing
5.1.1. Qualitative analysis of fragmentation
Visual inspection of damage in individual particles provides valuable information about
the origin of fracture and the stress state (Quinn, 2007). Figure 5.1-5.3 show the initial and
post-breakage status of the C&D particles. Regardless of the particle shape or type, all
particles split mostly into two equal halves. Several minuscule fragments are also produced
during splitting due to asperity damage. It is evident that the major crack propagated in a
plane along the loading direction, confirming the tensile failure of a particle under diametrical
compression (Figure 5.1c). Visual inspection of single particle breakage under diametrical
compression match those observed in earlier studies on different materials, such as Cil and
Alshibli (2012) and Lobo-Guerrero and Vallejo (2005).
Figure 5.1. Single WR particle crushing: a) Initial state, b) Post-breakage, c) Schematic
description of the one-dimensional compression and induced tension
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Figure 5.2. Single RCA particle crushing: a) Initial state, b) Post-breakage
Figure 5.3. Single CB particle crushing: a) Initial state, b) Post-breakage
5.1.2. Quantitative analysis of particle breakage
SPC tests on C&D particles from different shape categories are compared in Figure 5.4.
The brittle nature of the particles is evident in Figure 5.4. In addition, the highest yield point
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(i.e. when a drastic load drop occurred) was observed in bulky particles of all of the different
kinds of C&D materials (Figure 5.4). Figure 5.5 compares the average yield point of the
different kinds of C&D particles in the different shape categories (i.e. bulky, elongated, and
flaky). The average yield point of bulky WR, RCA, and CB particles are 2.45, 3.32, and 2.90
times higher than the yielding point of the elongated ones, respectively, suggesting that the
bulky particles demonstrated the highest resistance against breakage among the other particle
shapes. This is in agreement with the observation of Tavares and King (1998) who conducted
single particle fracture tests under impact loading and reported that particle strength and
stiffness decreased as particles became more irregular.
Figure 5.4. Single Particle Crushing results: Load-displacement comparison of a) WR, b) RCA,
and c) CB particles in different shape categories (bulky, solid line; elongated, dashed line; flaky, dotted line)
0
1000
2000
3000
4000
5000
0 0.5 1 1.5
Load
: N
Vertical displacement: mm
Bulky Elongated Flaky
WR RCA
0
1000
2000
3000
4000
5000
0 0.5 1
Load
: N
Vertical displacement: mm
Bulky Elongated
0
1000
2000
3000
4000
5000
0 0.5 1 1.5
Load
: N
Vertical displacement: mm
Bulky Elongated
CB
(a) (b)
(c)
80
Figure 5.5. Yielding point range of different types of C&D particles with various shapes (N: Number of particles)
Interestingly, Figure 5.5 demonstrates that particles within the same shape category
fractured at approximately the same load range regardless of the material type (here WR, CB
or RCA). Aggregates with a wide range of mineralogy and microstructure were examined in
this study (see Chapter 3). As an example, basaltic WR particles have a unique microstructure
(i.e. vesicular texture) compared to the other types of C&D materials, which is shown in
Figure 5.6. Referring to results presented in Chapter 3 and Figure 5.6, it is evident that there
is a remarkable difference between the mineralogy and microstructure of WR, CB, and RCA
particles; however, particles falling in similar shape categories showed approximately similar
crushing strength. Hence, Figure 5.5 suggests that the influence of shape on C&D particle
breakage is more dominant than mineralogical or microstructural effects. Rozenblat et al.
(2011) also investigated the crushing strength of various individual particles. Interestingly,
81
even though their focus was entirely on the influence of particle size, their findings suggest
that marble, sugar, and salt particles with the same size range exhibited nearly equal crushing
strength in spite of the remarkable difference in their mineralogy.
Figure 5.6. SEM image of vesicular basaltic WR
5.1.3. Modified particle tensile strength
Despite recent interest in investigating breakage at the particle-scale, due to the versatile
characteristics of particulate media, there are still uncertainties, preventing the development
of a comprehensive description of the mechanical behaviour of particles during
fragmentation. Nonetheless, in general terms, particle breakage has been categorized in two
main forms: abrasion/asperity breakage and particle fracture/fragmentation (Aman et al.,
2010). Most detrimental impacts associated with breakage, such as settlements, are caused
by particle fragmentation. Particle fragmentation normally occurs when a grain is subjected
82
to a tensile stress higher than its tensile strength. To date, different theories, such as well-
known Rumpf’s model proposed for calculating tensile strength of granules. However,
Rumpf’s model is more appropriate for estimating the strength of bridges forming between
parent particles during a granulation process (Salman et al., 2006). Broadly speaking, the
nominal tensile strength of a non-granulated structure is usually defined as follows, when
geometrically similar structures are compared (Bažant, 1999):
NC FbD
Eq. (5.1)
Equation 5.1 is a more comprehensive form of Jaeger (1967)’s equation for measuring the
tensile strength of rock pieces under a quasi-static loading condition. The term D is the
structure thickness, but alternatively, can be defined as the separation between loading plates.
The term b is the dimension normal to D and can be chosen arbitrarily as it is not critical in
comparing geometrically similar structures. CN is an arbitrary coefficient which is typically
equated to unity. Based on the classical hypotheses, the nominal tensile strength is not
variable when geometrically similar structures made of similar substances are compared. In
other words, the ratio of the induced tensile force to the relevant area at yield is identical for
aggregates of the same material (Figure 5.1c). Nevertheless, in practice the tensile strength
of similar structures with different sizes are not identical due to the statistical size effect. The
size effect stems from variability in the tensile strength of the geomaterial due to random
internal flaws and weak zone distributions. This effect is normally expressed by the Weibull
modulus and measured from the particle survival probability versus tensile stress curve
(Jones and Ashby, 2005). However, the statistical size effect study is beyond the scope of
this thesis and is not related to the main discussion herein.
Particles in the same size fraction have a variety of shapes, from bulky to extremely flaky.
Therefore, usage of the mean particle diameter related to a sieve aperture leads to an
imprecise calculation of particle tensile strength. Since particles tend to rest on their longest
dimension (lowest potential energy), a particle thickness can be totally different from its
mean diameter measured from sieve analysis. Referring to Equation 5.1, b also must be
defined appropriately to obtain an accurate estimation of particle tensile strength due to the
83
discrepancy in particle shapes. Hence, to take the effect of particle shape into account,
Equation 5.2 is proposed to calculate the tensile strength of aggregates:
2
Fd AR
Eq. (5.2)
where AR is the Aspect Ratio and is equal to D/d (i.e. the ratio of laminar thickness to the
particle diameter normally measured in a sieve analysis). The Aspect Ratio is closely related
to the degree of sphericity, particularly for bulky and elongated particles. Furthermore, the
degree of sphericity is a 2D shape factor and simpler to measure than the aspect ratio for a
great number of particles (as measured for C&D materials in Chapter 3). Referring to Chapter
3, bulky C&D particles with a mean degree of sphericity from 0.80 to 0.84 had an AR close
to unity, while for elongated ones with a mean degree of sphericity from 0.70 to 0.74, the AR
was measured close to 0.33. Flaky particles usually have low aspect ratios, which were found
to be approximately 0.13 for WR particles in this study. To determine whether the percentage
of flaky particles in a sample is considerable, the Flakiness Index test, based on BS (2000)
812-105.1, can be conducted.
Moreover, one of the disadvantages of the sieve analysis is that it cannot measure the size
of individual particles and it is highly affected by the particle form (Fernlund, 1998). In
Equation 5.2, AR presents particle form with respect to both particle diameter and thickness,
giving a much more accurate particle tensile strength.
5.2. Particle Assembly Crushing
5.2.1. Post-breakage visual inspection of particles
PAC tests were performed to further study the effect of particle shape at a larger scale, in
an assembly, while the cushioning effect of other particles is considered. After compression,
the split mould was opened to examine the crushing level of the Representative Particle (RP),
here the green particle. Figure 5.7-5.14 demonstrate the initial and post-breakage state of
particles of different shapes in the assembly under different compression levels. The post-
breakage state of the particles shows that, regardless of the particle shape, the crushing level
is more dramatic at the upper part of the specimen, close to the piston, particularly at lower
84
loading levels, i.e. 5 and 10 kN or 2.5 and 5 MPa. Nevertheless, under higher loading levels,
fragmentation spread to other parts of the specimen, and severe fragmentation can be
observed even in the bottom half of the specimen (see orange particles in Figure 5.7-5.14).
This post-breakage observation is consistent with recent studies, such as Cil and Alshibli
(2014), indicating that less particle damage occurred in the bottom half of a mould containing
sand particles.
Figure 5.7. Particle Assembly Crushing: a) Initial state of bulky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative
Particle (RP) after 5 MPa vertical compression
Figure 5.8. Particle Assembly Crushing: a) Initial state of bulky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP)
after 7.5 MPa vertical compression
85
Figure 5.9. Particle Assembly Crushing: a) Initial state of bulky WR particles, b) Different
layers of particles in the mould, c) Post-breakage state of particles including Representative Particle (RP) after 10 MPa vertical compression
Figure 5.10. Particle Assembly Crushing: a) Initial state of elongated WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative
Particle (RP) after 5 MPa vertical compression
Figure 5.11. Particle Assembly Crushing: a) Initial state of elongated WR particles, b) Post-breakage state of particles including Representative Particle (RP) after 7.5 MPa vertical
compression
86
Figure 5.12. Particle Assembly Crushing: a) Initial state of elongated WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative
Particle (RP) after 10 MPa vertical compression
Figure 5.13. Particle Assembly Crushing: a) Initial state of flaky WR particles, b) Post-breakage state of particles including Representative Particle (RP) after 2.5 MPa vertical compression
Figure 5.14. Particle Assembly Crushing: a) Initial state of flaky WR particles, b) Different layers of particles in the mould, c) Post-breakage state of particles including Representative
Particle (RP) after 5 MPa vertical compression
87
5.2.2. Particle shape and cushioning effect
While single particle crushing provides valuable information about the crushing strength
of a grain, the cushioning effect of neighbouring particles plays a vital role in crack
propagation in an assembly (Tsoungui et al., 1999). The results from SPC experiments
demonstrate the significant effect of particle shape on breakage. However, normally, grains
are surrounded by other neighbouring particles in a particulate medium. The PAC
experiments were designed and conducted in this study to determine whether the effect of
particle shape remains significant at a larger scale when particle contact points (i.e. its
coordination number) increase in an assembly of particles.
Figure 5.15 shows PAC test results on bulky, elongated, and flaky particles of WR, which
also shows the ultimate state of RP after loading. No drastic drop can be seen in the load-
displacement curves (Figure 5.15), in contrast to the SPC tests (Figure 5.4). This is because
one-dimensional compression was applied to particles confined by the rigid lateral boundary,
and particle breakage progressed continuously until the predefined ultimate loading level was
reached. As compression continues, the number of minuscule particles produced during
fragmentation increased. Comparison between the results of PAC and SPC tests indicates
that single bulky WR particles fractured at a mean load level of 3.6 kN, but in the particle
assembly tests, RP only experienced asperity breakage at a load level of 10 kN. Single
elongated particles also split at an average load level of 1.5 kN, while in PAC, a major
fracture initiated through RP, surrounded by other particles, at a load level of 10 kN. These
results further confirm the cushioning effect of other particles on the Representative Particle
and suggest that when the coordination number surrounding a grain increases, the particle
resistance against breakage increases.
Remarkable differences between PAC test results of different particle shapes in terms of
particle strength and stiffness are shown in Figure 5.16. Based on different stages of particle
damage (Bolton et al., 2008), the representative bulky particle experienced asperity breakage
(Figure 5.16) whereas under a similar loading rate and level, the elongated particle split due
to internal tensile cracking. Interestingly, the flaky particle fractured completely under a
much lower load, i.e. 5 kN, as shown in Figure 5.16. The oscillatory form of the load-
88
displacement curves resulting from the PAC experiments stems from the resistance of newly-
generated fragments to the applied load after a sharp load drop (i.e. yielding). Besides, owing
to rearrangement of fragments during crushing and loading, some relatively low
gradient/plateau parts (i.e. increased displacement without increased force) can be seen in
load-displacement curves. Consequently, the stiffness of the assembly associated with pure
breakage was measured from certain parts of Figure 5.16, shown by the dashed black lines.
The findings indicate that the bulky assembly exhibited the highest stiffness while the
flaky assembly showed the lowest. The results further support the notion of the significant
influence of particle shape on particle breakage. In fact, particle shape played a crucial role
in particle breakage, not only when crushing of a single particle was examined, but also when
the cushioning effect of other particles (here in the same size, shape, and stiffness) in an
assembly was considered.
Moreover, referring to the fact that bulky particles showed higher resistance against
breakage, it can be concluded that less breakage would take place in an assembly containing
a high percentage of bulky particles compared to an assembly with a high Flakiness Index.
Thus, it is expected that the particle size distribution after loading would not be remarkably
different from the particle size distribution before loading in an assembly with a high
percentage of bulky particles. Further investigation into the effect of particle shape on
breakage, particularly in an assembly, is presented in Chapter 6 and 7.
89
Figure 5.15. Particle Assembly Crushing results: a, b, and c) Load-displacement relationship of WR assemblies in different shape categories at different load levels
kN
kN
kN
90
Figure 5.16. Comparison of different WR particle shapes in PAC tests in terms of crushing
strength and stiffness (K); (solid black line is drawn based on 100 periods moving average)
5.3. Summary
The investigation into a variety of Construction & Demolition materials demonstrated
that particle tensile strength is closely dependent on a particle’s shape factor. After studies
on several individual C&D particles, a modified particle tensile strength as a function of
particle Aspect Ratio is introduced, where the effect of particle shape/form is also taken
into account. In addition, it has been found that particle shape plays a more prominent
role in the particle breakage phenomena than mineralogy and the microstructure of C&D
particles. Further studies on particle fracture across the scale also showed that, although
boundary conditions and particle interactions have considerable effects on particle
breakage, the significant influence of particle shape on particle crushing is not diminished
even in an assembly of particles. Taken together, these findings suggest that brittle C&D
granular materials with a higher degree of sphericity (an Aspect Ratio closer to 1) and a
lower Flakiness Index would experience less particle breakage under loading.
kN
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6. DISCRETE ELEMENT MODELLING OF PARTICLE BREAKAGE
Broadly speaking, conventional laboratory experimental tests often measure the
macro-scale behaviours of a specimen, such as the stress-strain behaviour normally
measured at the exterior boundary of a sample. The laboratory tests, designed and
conducted in this study (Chapter 5, SPC and PAC tests), provide valuable information
about the crushing strength of C&D particles. In addition, particle damage information
was obtained through post-breakage analyses of C&D particles by visually inspecting the
fractures in individual particles. However, particle breakage, controlled by
micromechanical properties of a material, needs to be analysed at a particle-scale.
Discrete Element Modelling (DEM) is an indispensable tool for studying granular
materials during loading. It provides a virtual laboratory to track and study not only
particle deformation and crack propagation but also the in-situ evolution of force chains
and stress distribution in a specimen, the latter is impossible to obtain by means of
laboratory tests (Katagiri et al., 2010).
The crushing strength of a particle under quasi-static loading can be estimated by using
Equations 5.1 or 5.2. Although the aforementioned equations are only an approximation
of the tensile strength of a brittle grain, where the plastic effects on breakage can be
neglected, it is one of the feasible ways to estimate the tensile strength of particles. Hence,
it is always helpful to include breakage energy calculations, along with particle tensile
strength, to gain a more accurate estimation of the material breakage, particularly when
an assembly of particles is studied. In this chapter, DEM was used to simulate the SPC
and PAC tests in order to gain a new insight into the internal stress and energy distribution
throughout the entire samples.
6.1. Principles of Discrete Element Modelling
Discrete Element Modelling is a computer simulation approach that can model
particulate media. The distinct advantage of DEM over other numerical modelling
approaches is that it considers the interaction of individual particles in a medium, in
contrast to a continuum model, such as the Finite Element Method, where the relative
displacements and rotations of particles are not taken into account.
92
The key assumptions made in a basic DEM simulation are listed as follows (Iwashita
and Oda (1999), Potyondy and Cundall (2004), and O'Sullivan (2011)):
• The particles are rigid and spherical (i.e. balls).
• The particles can translate and rotate independently.
• A DEM-based software can identify newly generated contacts between
particles.
• A contact occurs over an extremely small area between only two particles.
• Slight overlap is allowed at the contact points between particles, and it is
similar to the deformation occurring between actual particles.
• The compressive inter-particle forces are calculated from the overlap
magnitude.
• Tensile inter-particle forces are calculated by using the separation distance
between two adjacent particles. When the tensile force exceeds the tensile force
threshold, the contact is removed.
• The time step selected in a DEM model has to be adequately small that the
displacement of a particle in one time step is small enough to only affect its
immediate neighbouring particles.
In this study, Particle Flow Code (PFC 5) was utilised to conduct the simulations. PFC
is a DEM-based coding program which can be used to model cemented or unbounded
granular materials (Yoon, 2007).
6.1.1. Updating particle locations
The contact point and interactions are simulated by rigid springs in a particulate DEM
model. When particles move away from each other, the contact, in other words, the
related springs, are removed. Simultaneously new contacts are formed between particles
travelling toward each other and touching each other.
The principal translational and rotational equilibrium of a particle with mass m and the
moment of inertia I are (Zhu et al., 2007):
c ncma F F G Eq. (6.1)
I M Eq. (6.2)
93
where a and α are the acceleration and angular acceleration of the particle,
respectively, Fc are the contact forces, Fnc are the non-contact forces, G is the
gravitational force, and M is the moment. The sources of non-contact forces are often
capillary forces in an unsaturated soil which is outside the scope of the present research.
The acceleration of a particle can be calculated while the resultant forces acting on it are
known. In a DEM code, a time integration method, which is the same as the central-
difference approach, with a time step t is used:
/2 /2
1t t t ta V V
t
Eq. (6.3)
where Vt+t/2 and Vt-t/2 are the velocities of the particle at t+t/2 and t-t/2,
respectively (Rapaport, 2004). Accordingly, the velocity of the particle at time t+t/2 can
be calculated from Equation 6.3. Then, by knowing the velocity at time t+t/2, the
location of the particle x can be updated as (Munjiza, 2004):
/2t t t t tx x t V Eq. (6.4)
Likewise, the angular velocity is also used to update the position of the edges of an
irregular-shaped particle and to calculate the particle’s total rotation.
6.1.2. Contact models
A contact constitutive model typically consists of a combination of springs, sliders,
and dashpots. Generally, the main approach utilised in DEM is a penalty spring approach
which means the force is equated to the magnitude of overlap multiplied by the spring
stiffness, or as another option, the area/volume of the contact overlap is related to the
contact force (Peng, 2014). The following sub-sections describe the contact models used
in the present research.
6.1.2.1. Simple linear model
The simple linear model is the most fundamental contact model, providing elastic (but
no tension) and frictional behaviours along with viscous behaviour with a dashpot
component (Figure 6.1). This model cannot, however, resist relative rotations; thus, the
contact moment is equal to zero (Cundall, 2004). The force-displacement law for a linear
contact is as follows:
94
l dcF F F Eq. (6.5)
where Fl is the linear and Fd is the dashpot component of the contact force. Both forces
are expressed by normal and shear components, Fn and Fs:
ln n nF k and l
s s sF k , l ls nF F Eq. (6.6)
with 1 2
1 2n n
nn n
k kkk k
and 1 2
1 2s s
ss s
k kkk k
2d dn n i n nF m k and 2d d
s s i s sF m k (in the case of full shear) Eq. (6.7)
with 1 2
1 2i
m mmm m
where kn and ks refer to the linear normal and shear stiffness, respectively, µ is the
friction coefficient, and the terms n and s are the relative normal and shear displacement,
respectively. The parameters βn and βs are the normal and shear critical damping ratios,
and mi is the mass of body i. The parameters δnd and δs
d are the relative normal and shear
translational velocity, respectively. If the two balls, with masses m1 and m2, contacting
each other have different stiffness, then the contact normal and shear stiffness is a
combination of each ball’s stiffness, k1 and k2 (Cundall, 2004). The simple linear model
is suitable and efficient to be used where the deformation is elastic and relatively small.
Figure 6.1. Simplified linear contact model
95
6.1.2.2. Linear contact bond model
The linear contact bond model embeds both a linear repulsive part (identical to the
linear model) and a contact bond part, acting like a point of glue between two bonded
balls. The contact bond allows tensile and shear forces to develop at a contact point while
the tensile and shear force is limited by the predefined tensile and shear strength (Figure
6.2). If the normal or shear force, exceed the tensile or shear strength of the bond,
respectively, the bond breaks. In case of tensile bond breakage, the normal and shear
forces are equated to zero. However, in the case of bond failure due to shear, the contact
forces are not changed and if the normal force is compressive, the friction coefficient
multiplied by the normal force is used to update the slip state. If the bond breaks, the
contact is still active as long as the balls are touching, and the linear part is responsible
for the forces acting on the contact. However, if the bond breaks and the two engaged
balls move away enough from each other, the contact is eventually deleted by DEM
coding program, here PFC. Afterwards, if these balls again come close enough to each
other, a new contact is formed, and the contact type is assigned based on the
programmer’s specification (Potyondy et al., 1996).
The linear contact bond model does not resist moment either in bonded or unbonded
conditions. Later in 2004, the linear parallel bond model was introduced by Potyondy and
Cundall (2004) as a model allowing development of force and moment within the bond.
Figure 6.2. Linear contact bond model: (a) normal force and (b) shear force versus relative displacement; Fi
c is bond strength, (after Cho et al. (2007))
96
6.1.2.3. Linear parallel bond model
A parallel bond provides the physical behaviour of a cement-like material acting on
the finite area of a contact. It can also be assumed as a number of elastic springs
distributed over a cross-section centred at the contact point with constant normal and
shear bond stiffness (Figure 6.3).
Figure 6.3. Illustration of parallel bond model provided in PFC; a parallel bond acts like a beam resisting moments as well (after Cundall (2004))
The linear parallel bond model, similar to the linear contact bond model, embeds both
a linear repulsive part and a parallel bond part acting in parallel with the linear part
(Indraratna et al., 2011). A parallel bond also resists moment, and the increment of
twisting and bending moments (Mt and Mb ) are expressed as:
t s tM k J and b n bM k I Eq. (6.8)
where J and I are the polar moment of inertia and the moment of inertia of the parallel
bond cross-section. The parameters t and b are the twist and bend rotation
increments, respectively. The total force associated with the parallel bond is denoted by
Fi :and is given by ׳
n n nF k A and s s sF k A Eq. (6.9)
where kn׳ and ks
,refer to the linear normal and shear stiffness of the parallel bond ׳
respectively, and A is the cross-sectional area of the parallel bond (Cho et al., 2007). The
maximum tensile and shear stresses (max and max) applied to the bond are then calculated
as:
maxnF M R
A I
Eq. (6.10)
97
maxsF
A
Eq. (6.11)
where R׳ is the radius of the bond (Potyondy and Cundall, 2004).
A parallel bond breakage instantly causes stiffness reduction influencing not only the
adjacent balls’ stiffness but also the macro-scale stiffness of an assemblage. Hence, the
linear parallel model is known as a more realistic bond model for materials whereby the
bonds may break in tension or shearing resulting in a reduction in the macro-scale
stiffness of a specimen (Lee, 2007).
6.2. 2D modelling of particle breakage and effect of particle
shape
Two-dimensional DEM modelling, in this study by using PFC, is useful to undertake
initial model development, test ideas and examine phenomena before developing a
comprehensive 3D model. The decrease in computational time is notable in 2D
modelling, and one can obtain significant initial insights into physical processes that are
modelled in 2D. Besides, the interpretation of 3D results can be very time-consuming and
difficult (Cai, 2013). After gaining insights from 2D models, one can more readily
investigate the 3D counterparts. Therefore, in this study, first, 2D models have been
simulated, and then 3D simulations were conducted to thoroughly investigate the effect
of particle shape on the material behaviour, particularly on breakage and the crushing
strength.
6.2.1. Model calibration
PFC micro-parameters, unlike other geotechnical engineering codes or models, need
to be calibrated. The calibration of a PFC model requires adjusting the micro-parameters,
such as contact properties, the choice of the contact model, ball size, and so on (Hanley
et al., 2011).The macro-scale properties of the granular material are determined by
simulating laboratory tests. These macro-scale properties are equivalent to those that are
measured in the laboratory. In this study, the calibration was accomplished by simulating
uniaxial compression tests on rectangular samples (2D model) with the approximate
dimension of 100 × 200 mm, and then the results, in terms of deformability and strength
behaviours, were compared with those obtained from the laboratory test.
98
Due to the limited computing capacity and the large number of particles, the generation
of the synthetic specimen does not include the real particle size distribution. Thus, in
order to optimise the calculation time, a synthetic material with a simplified particle size
distribution (from 1 mm to 10 mm) was simulated (Figure 6.4). A similar approach was
followed by other researchers, such as Camusso and Barla (2009).
Figure 6.4. 2D synthetic specimen particle size distribution compared to the real material
The contact bond and parallel bond models were utilised in the 2D simulations. The
following parameters need to be calibrated for a contact bond model (Cundall, 2004):
• Ec: Particle-particle contact Young’s modulus
• kn/ks: Ratio of particle normal to shear stiffness
• μ: Particle friction coefficient (this applies when the contact bond has
broken)
• σc: Normal strength
• c: Shear strength
For a parallel bond model the following parameters need to be calibrated (Cundall,
2004):
• Ec: Particle-particle contact Young’s modulus
0
20
40
60
80
100
0.0 0.1 1.0 10.0 100.0
Tota
l pas
sin
g (%
)
Particle size (mm)
Crushed Waste Rock
Synthetic material
99
• kn/ks: Ratio of particle normal to shear stiffness
• μ: Particle friction coefficient
• λ׳: Radius multiplier used to set the parallel bond radii
• Ec Parallel bond Young’s modulus :׳
• knks/׳
Ratio of parallel bond normal to shear stiffness :׳
• c The parallel normal bond strength :׳
• c The parallel shear bond strength :׳
These input micro-parameters are normally unknown and can be determined by means
of a calibration process in which the behaviour of the simulated material is compared
with the relevant measured responses of the actual physical material in the laboratory
(Favier et al., 2010). The calibrated micro-parameters of the crushed basaltic Waste Rock
samples are listed in Table 6.1. More information about calibration of PFC micro-
parameters is provided in Section 6.3.2.
Table 6.1. Calibrated micro-parameters of crushed waste rock used in 2D simulations
Micro-parameters Value Ec 6 GPa kn/ks 2 µ 0.3 c 30 MPa c 60 MPa 1 Ec 6 GPa kn/ks 2 c 300 MPa c 300 MPa Rmin 1 mm Rmax 10 mm Sample porosity 0.21-0.22
Using the micro-parameters provided in Table 6.1, DEM simulation of the
Unconfined Compressive Strength (UCS) tests on WR resulted in strength values that
were in a good agreement with the actual laboratory results. Unconfined Compressive
Strength of WR from both numerical and experimental results (see Chapter 3 for the
experimental result) was between 700 to 800 kPa. Moreover, the modulus of elasticity of
the material calculated from UCS test results was also compared with the relevant DEM
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results (Table 6.2). Since E is not constant, usually E50, the secant modulus at 50% of
peak strength, is utilized for numerical analyses (Lambe and Whitman, 2008). The
parameter E50 of the synthetic material is compared directly with the relevant measured
response of the physical material (Table 6.2).
Table 6.2. Strength and modulus of elasticity of WR resulting from Unconfined Compressive Strength test; DEM simulations and laboratory tests
Method UCS (kPa) E50 (kPa) DEM simulation (cluster model) 780 730
Laboratory tests (based on three attempts) 700 - 800 625-769
6.2.2. Particle shape modelling
Based on the true grain shapes of crushed Waste Rock, the particles were simplified
and categorised into three basic types: rectangular, circular, and triangular. Thakur (2011)
also used a slightly different method for simulating particle shapes of railway ballast
rather than using simple circular particles. Figure 6.5 shows the three basic shapes of
WR particles and the primary clump shapes of the proposed model. These primary clump
shapes were later changed to clusters as discussed in the following section. Table 6.3 also
demonstrates the degree of sphericity of the modelled WR particles during the 2D
simulations. The average degree of sphericity of the modelled clumps is 0.79, which is
quite close to the actual average degree of sphericity of WR grains, i.e. 0.81.
Figure 6.5. Different clump shapes used for 2D DEM modelling of Crushed Waste Rock, WR Specimen, and its three basic particle shapes
13 mm
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Table 6.3. The clumps’ shape factor used in 2D DEM simulations
Shape
Degree of sphericity 0.80 0.56 1
6.2.3. Particle breakage modelling
An alternative to clumping is to replace the clumps with clusters that are not rigid and
can allow cracks to propagate through them. As an example, this method was used by
Ghazvinian (2010) who allocated parallel bonds between ball contacts in every clump
that was stronger than the existing parallel bonds between the individual clumps (Figure
6.6). In the current study, a subroutine was developed (using the Fish scripting language)
in PFC2D to replace clumps with clusters. Firstly, the Fish function searches through all
contacts and detects the contacts within and between the clumps. Secondly, the contact
bonds are installed between clumps and parallel bonds are applied between balls, which
form one individual clump. Then, the clumps are released and deleted to represent
breakable clusters (Figure 6.7). Since the adopted crushed Waste Rock was not stabilised
by any cement substances, the contact bond model was assigned between clumps.
Figure 6.6. Cluster modelling; black parallel bonds are three times stronger than red parallel bonds (Ghazvinian, 2010)
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Figure 6.7. The proposed cluster model; black bonds are parallel bonds and yellow bonds are contact bonds
6.2.4. Simulation of biaxial tests
The simulation of biaxial test on WR sample was carried out in two steps (Figure 6.8).
The sample was isotropically consolidated and then sheared under a constant strain rate.
The specimen was confined and loaded by opposing walls during numerical biaxial tests.
While the top and base walls play the role of loading plates, the lateral walls apply a
constant confining stress by means of a numerical servomechanism controlling their
velocities. Since stress is a continuum quantity, it does not exist at each point in a 2D
discrete medium; therefore, an averaging procedure is required to calculate stress from
the contact forces. Hence, stress was computed by dividing the mean force acting on a
wall by the area of the corresponding sample cross section.
Figure 6.8. Numerical steps of the biaxial test simulation: a) Isotropic consolidation, b) Shearing phase
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6.2.5. Effect of particle shape on the macro-scale behaviour of
the WR assembly
Figure 6.9 shows the stress-strain curve obtained using the DEM approach being in a
good agreement with the laboratory results. The experimental data, used to compare with
the DEM models in this section, has been reported previously by Arulrajah et al. (2012b).
Figure 6.9 also indicates the comparison of the clustered particle with the circular particle
assembly, in which the proposed cluster model is more accurate than the unbreakable and
simple shape (circular disks) model. Simulation of particles as disks and spheres clearly
leads to inaccurate results since the internal friction angle and shearing resistance of
spherical particles are less than the real values due to a lower resistance to rotation.
Moreover, the direction of the contact normal forces is always toward the centre in
spherical particles; as a result, no moment can be developed by the normal forces.
Therefore, the rotation is only affected by the contact tangential forces (Mollanouri
Shamsi and Mirghasemi, 2012). Apart from the unrealistic and over-idealised shape of
circular particles, the circular disk model did not represent particle breakage in the
specimen while degradation of particles, by corner breakage or splitting of particles into
two or more parts, was successfully simulated through the clustered particle model.
Figure 6.10 indicates the breakage and rearrangement of clusters in a part of the clustered
particle model. It is evident that the fragments of broken particles moved to the pores of
the assembly and consequently caused further deformation.
6.3. 3D modelling of particle breakage and effect of particle
shape
Initial 2D DEM simulations can help in testing ideas in a reasonable computational
time and also to estimate the approximate range of micro-parameters for a particular
material, accelerating the calibration process. However, it is clear that 3D DEM analyses
provide more realistic results in terms of physical responses of a material under loading.
For example, in a 2D DEM analysis, particles have fewer degrees of freedom, i.e. only
two translational and one rotational, compared to a 3D DEM analysis where a particle
has six degrees of freedom, i.e. three translational and three rotational (O'Sullivan and
Cui, 2009).
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Figure 6.9. Deviator stress versus vertical strain for crushed basaltic Waste Rock from the results of the triaxial test and simulation of biaxial tests with PFC2D
Figure 6.10. Bond breakage simulation leading to grain crushing (black: parallel bonds, yellow: contact bonds)
In this section, DEM simulations of SPC and PAC tests on WR particles are presented
using Particle Flow Code (PFC3D 5.0). In addition, 3D DEM simulations were used to
measure breakage energy more accurately for WR samples. While the input energy can
be calculated from experimental results (the area under the load-displacement curve), it
contains not only breakage energy but also energy dissipation due to friction between the
particles and loading plates and during rearrangement of particle fragments. DEM was
105
used in this study to partition and track the energy dissipated through the creation of new
surfaces during fragmentation.
6.3.1. Precise particle shape modelling
Firstly, to simulate different particle shapes, WR particles (i.e.: bulky, AR=1;
elongated, AR=0.33; and flaky, AR=0.13) were scanned individually using a 3D laser
scanner (Figure 6.11). Subsequently, the particle shape geometries were imported into
PFC3D as a closed wall and filled with bonded smaller sub-particles (Figure 6.12b).
Hence, each WR particle was represented by an agglomerate built by bonding non-
uniformly-sized spherical sub-particles. Lim and McDowell (2007) stated that if the
computer is not able to handle large numbers of sub-particles efficiently and if the number
of sub-particles in the agglomerates falls below 500, the coordination number of the
agglomerates can be tracked and the bond strength scaled appropriately to compensate
for the influence of low coordination number. Accordingly, due to limited computational
capacity, the WR particle was simulated by an agglomerate of 239 bonded sub-particles.
Figure 6.11. Examples of different shapes of WR particles: (a) actual particles (top view), (b) 3D scans (side view)
AR1AR0.33
AR0.13
(a)
(b)
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6.3.2. Calibration of micro-parameters
Cil and Alshibli (2012) showed that yielding of sand is directly controlled by the
crushing strength of individual grains. In the present study, the 3D model micro-
parameters were calibrated based on the single particle compression tests by using an
iterative calibration process.
A linear parallel bond model acting as a cementing material was used to bond sub-
particles at their contact points. Parallel bond normal stiffness is normally estimated using
the following expression:
1 2
cn
EkR R
Eq. (6.12)
where R1 and R2 are the radii of the bonded particles. It is necessary to calibrate and
adjust the micro-parameters, particularly contact model properties, in order to match the
macro-scale properties of the generated specimen with those measured in the laboratory
(Cho et al., 2007, Camusso and Barla, 2009).
Figure 6.12. 1D compression on single bulky WR particles: (a) Laboratory and DEM results, (b) Initial state of the particle, (c) Force chain at the failure moment, (d) Total
fragmentation at yielding point
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In this study, PFC micro-parameters were determined by carrying out numerical SPC
tests on the generated agglomerate and comparing the results in terms of force-
displacement behaviour with those measured by laboratory tests (Figure 6.12a). All
bonds between sub-particles in every agglomerate have the same strength properties,
which were selected randomly from a normal distribution function based on the estimated
mean strength and standard deviation values listed in Table 6.4. To obtain this
distribution parameters, the standard deviation of material strength was initially assumed
to be equal to zero leading to mean bond strength values of approximately 500 and 300
MPa generating the highest and lowest tensile strengths measured in the SPC
experiments. Therefore, the bond strength is defined through a random number generator
using a mean bond strength of 400 MPa with a standard deviation of 100 MPa; the same
approach was also adopted by Cil and Alshibli (2012). Each agglomerate was compressed
between two flat platens at a constant loading rate up to fragmentation. The value of wall
stiffness was set at approximately one order higher than the particle stiffness to simulate
rigid steel walls (Coetzee, 2016).
Table 6.4. Micro-parameters used in 3D DEM modelling of WR particles
Parameter Value Wall stiffness: N/m 1×108 Mean diameter of agglomerates: mm 15 Spherical sub-particle properties Mass density: kg/m3 2800 Young’s modulus, Ec: GPa 8 Minimum radius, Rmin: mm 1 Rmax/Rmin 1.6 Friction coefficient, µ 0.5 Normal stiffness/shear stiffness 1.25 Parallel bond Young’s modulus, Ec
: GPa 8 Normal stiffness/shear stiffness 2 Mean normal strength: MPa 400 Mean shear strength: MPa 400 Normal and shear strength standard deviations:
MPa
100
As shown in Figure 6.12, the results of the DEM simulation of SPC testing on bulky
WR particles were, overall, in good agreement with the laboratory results. Moreover, in
order to simulate the PAC tests, a cluster template was created from the particle geometry,
and accordingly 13 breakable clusters were generated inside a cylindrical wall. A script
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was developed to automate the aforementioned steps using Fish scripting language. The
previously calibrated micro-parameters (Table 6.4) were used to simulate the PAC tests.
To fill the numerical chamber with PAC simulations, clusters were generated at the upper
part of the chamber and then were forced into the chamber by applying only gravity.
Clusters were positioned without friction to optimise the ultimate porosity of the
specimen and the computational time.
6.3.3. Internal stress distribution
SPC and PAC experiments provided valuable information about particle crushing;
however, they do not provide sufficient information about the internal stress distribution
within the particles or the mechanism of cracks and whether they were shear or tensile
cracks. Therefore, DEM was used to estimate particle stress distribution leading to crack
propagation. Fragmentation was monitored by tracking bond breakage in the DEM
agglomerates. Figure 6.12c shows the development of force chains initiating the flaw
zone in an individual particle. Almost all cracks are concentrated in a plane along the
loading direction which is in accord with the tensile failure theory of particles under
compression. Figure 6.13a also provides the DEM result of PAC tests on bulky WR
particles which agrees well with the experimental results in terms of the force-
displacement curve. During compressive loading (Figure 6.13b), the evolution of cracks
and the rapid increase in bond breakages causes the formation of new force chains which
resist the axial load. After a 10 kN compressive loading, comparison of crack distribution
in bulky, elongated, and flaky particle assemblies also revealed that the flaky assembly
had the highest bond breakage percentage (Figure 6.14). Referring to Figure 6.14, the
crack mechanism is comparable to that found in single particle crushing, since tensile
cracks were the dominant type in comparison with shear cracks.
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Figure 6.13. (a) Laboratory and 3D DEM results of 1D compression on assemblies of bulky
WR particles, (b) Contact force network distribution and bond breakage from DEM simulation of PAC test on bulky WR particles
kN
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Figure 6.14. Parallel bond state after loading (i.e. Max load 10kN or 5 MPa). Colours represent tensile (blue) and shear (green) bond breakages and bonded (red)
6.3.4. Breakage energy
During a DEM simulation, the input energies (i.e. boundary forces or body forces)
dissipate in frictional sliding and the rupture of contact bonds. There is also an incessant
conversion of strain energy to kinetic energy and vice versa in the contact springs (Bardet,
1998). Referring to O'Sullivan and Bray (2004), the requirement for energy (E) balance
in a numerical system is:
Kinetic Internal InputE E E Eq. (6.13)
where EInternal consists of the strain energy stored in the contact springs and the
frictional energy dissipated during loading. Thus, to obtain an accurate estimation of
breakage energy, each energy component needs to be known. Research into breakage
energy in particulate media has a long history from the earliest work, such as research by
Rittinger (1867), to the most recent by Russell and Einav (2013). Thus far, it is accepted
that the term breakage energy refers to the energy dissipation due to the creation of new
surfaces during fragmentation. Breakage energy is normally measured based on the input
energy especially in single particle crushing experiments and is assumed to be equal to
the work calculated from a load versus displacement curve, which is exemplified in the
work undertaken by Zhao et al. (2015). Nonetheless, the major drawback of this
assumption is that it dramatically overestimates the breakage energy. The input energy
applied to a particulate medium is dissipated through, not only the fracture process, but
also other mechanisms, particularly frictional/slip dissipation between particles and
loading plates and also between newly generated fragments. The frictional dissipation
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may be neglected in single particle crushing, but it certainly needs to be considered at a
larger scale, particulate assembly, where particles rearrange and rub against each other
during loading. DEM provides a powerful tool to track and partition energy dissipation
and its related mechanisms which are otherwise impossible to measure with experimental
tests. Antonyuk et al. (2006) and Wang et al. (2012) used DEM to monitor energy
distribution and dissipation mechanisms during impact breakage, while Khanal et al.
(2005) compared the input energy with new surface generation and the number of broken
bonds during a single particle crushing test. In this study, DEM was used as a virtual
laboratory to measure slip energy dissipated during PAC tests on WR samples.
Fundamentally, slip energy is updated after each time-step as follows:
12
with
s s so
s s os s
s
E F F
F Fk
Eq. (6.14)
where Eµ is the increment of slip energy, ½((Fs)o+Fs) is the average linear shear force
occurring during the time-step, sµ is the slip component of the adjusted relative shear
displacement increment. In this study, the linear contact bond model and the parallel bond
model were also utilized (more information is given by Cundall and Strack (1979) and
Potyondy and Cundall (2004)). Eventually, slip dissipation was subtracted from the total
work done by the load, to gain an accurate estimation of the breakage energy. Figure
6.15 shows the dramatic difference between total energy and pure breakage energy. The
total energy is 3.45 times higher than the breakage energy. Only 29% of the total energy
was dissipated through the creation of new surfaces during fragmentation, and the rest
was dissipated through other mechanisms, mostly frictional dissipation between particles
and newly generated fragments. The results are consistent with those obtained by Wu et
al. (2005), who reported that frictional energy dissipation forms a major portion of the
total energy dissipation during particle crushing under impact loading. Wang and Yan
(2012) also simulated a triaxial shear test on crushable soil particles using DEM and
pointed out that the major role of particle breakage is to enhance the inter-particle friction
dissipation rather than energy dissipation by itself.
Overall, these results suggest that the total energy dissipated during particle crushing
under quasi-static loading is much higher than the energy required to break inter-particle
bonds. Consequently, neglecting frictional dissipation, especially for an assembly of
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particles, will lead to greatly overestimate breakage energy.
Figure 6.16 presents the breakage energy during loading in different WR samples in
relation to the samples’ Aspect Ratio, indicating a direct link between the breakage
energy and particle shape. The breakage energy per volume change of the sample clearly
rose during loading, and more energy was consumed to break the representative particle
in the bulky assembly compared to those with lower AR. It can thus be suggested that
under the identical compressive stress, less particle fragmentation would ocurr in an
assembly with a higher percentage of bulky particles in comparison with an assembly
consisting of a lower percentage of bulky particles.
Figure 6.15. Input energy versus energy dissipation through breakage based on DEM
simulations of different assemblies of WR, (The amount of energy was calculated up to the onset of ‘representative particle’ breakage)
Figure 6.16. Breakage energy per volume change of the WR sample versus applied force in relation to particle shape
y = 3.45x
y = x
0
30,000
60,000
90,000
0 10000 20000
Inp
ut
Ener
gy: N
.mm
Breakage Energy: N.mm
Bulky
Elongated
Flaky
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6.4. Summary
Subroutines were developed to simulate different particle shapes and also particle
breakage of crushed waste rock during different testing, initially in 2D and ultimately in
3D. It has been confirmed that particle shape and particle breakage have significant
influences on the strength and deformation of a test specimen (using 2D DEM
simulations). The fracture mechanism of brittle WR particles with different shapes was
identified using 3D DEM simulations, indicating that tensile failures on the plane linking
the contact points of the particle with adjacent particles are the dominant type of particle
failure. Precise 3D particle shapes were generated by a large number of bonded spherical
sub-particles and used to model single particle crushing and particle assembly crushing.
The PAC simulations demonstrated that breakage energy is closely dependent on the
particles’ shape factor. Additionally, this study has shown that the energy calculated from
the force-displacement curve is far greater than the energy dissipated through particle
fragmentation. Breakage energy measured accurately by DEM simulations was less than
one-third of the total input energy. The results have indicated that a large portion of input
energy is dissipated through other mechanisms, particularly through frictional dissipation
between particles and fragments, and the input energy cannot be equated to the breakage
energy.
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7. BREAKAGE AND PARTICLE
CHARACTERISTICS EVOLUTION THROUGH
SYNCHROTRON TOMOGRAPHY
Limited studies have been conducted to understand the relationship between particle
fracture and particle morphologies or internal microstructure, due to the experimental
difficulty in examining the evolution of particle microstructure during the fracture process
(Garcia et al., 2009, White et al., 2003). One of the aims of this study is to investigate and
track fracture patterns of granular C&D materials at the particle-scale. To accomplish this
goal, a series of experimental tests and 3D DEM simulations were conducted on WR,
RCA, and CB coarse grains (i.e. size fraction: 13.2-19 mm) across the scale from a single
particle crushing to assemblies of grains. The results demonstrated that particle shape is
one of the main factors governing particle breakage. However, the mean size (i.e. d50 and
d30) of C&D materials, which determines the governing particle-level forces and
associated macro-scale behaviour, is between 0.425 to 4.75 mm. Hence, Synchrotron
Radiation-based X-ray Micro-Computed Tomography was used as a powerful tool for
further analysing particle breakage at a smaller scale, which was impossible to achieve
by using conventional laboratory tests. Rapid advances in high-resolution 4D imaging
techniques have opened up unprecedented access to the grain scale, allowing one to ‘see’
inside the material, which can enhance the understanding of how microscale physics (the
cause) relate to various macroscale phenomena (the effect) (Viggiani et al., 2015).
As mentioned previously, synchrotron light is a monochromatic highly culminated X-
ray source that produces a beam with a high flux and a specific energy level (Boldeman
and Einfeld, 2004). The synchrotron beam, utilised in this study, in contrast with
laboratory scanners, provides much more rapid scanning than other available CT
scanners, and is highly efficient given the sequential loading-imaging cycles required to
characterise progressive deformation and breakage. An in-situ particle assembly
compression apparatus was also designed to carry out crushing tests on different kinds of
C&D particles under confinement during scanning. Crack propagation and particle
deformation, particularly particle morphology changes during loading, were precisely
observed and analysed.
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7.1. Crack propagation in different C&D granular
materials
Grain fracture is common in the form of brittle fracture in geomaterials, causing rapid
propagation of several cracks through a stressed grain. The crack propagation patterns
and branching lead to identification of the point where and when a crack starts, and also
provide valuable information about the root of the crack, crack energy, and stress
condition (Quinn, 2007). CT images are the best available means by which to investigate
and interpret the fracture mechanism and its related theories owing to the remarkable
difference between X-ray attenuation in soil and air phases.
7.1.1. Effect of shape
A central vertical slice tomograph of a Crushed Brick (CB) specimen, in the particle
size fraction of 2.36-4.75 mm, is shown in Figure 7.1 at the initial phase and under 5 kN
(10.2 MPa) constraint compression. Since CB is mostly a by-product of demolition
activities of buildings, it usually consists of a relatively high percentage of other granular
materials, including crushed basaltic Waste Rock (WR), Recycled Concrete Aggregate
(RCA), and Portland Cement Mortar pieces (PCM). The density profile across the sample
helps to differentiate the various grain types, while the lowest density is related to PCM
particles (Figure 7.1a). It should be noted, as mentioned previously, that denser materials
appear in a brighter colour in an X-ray image in contrast to low density materials, such
as the air phases between particles, which are plain black. PCM grains can also be
recognised easily from their internal texture, an agglomeration of smaller particles
bonded together by mortar paste, as shown in Figure 7.1b. The unique microstructure
and low density of PCM result in severe fragmentation of them under 5 kN compression
(Figure 7.1c). Moreover, extensive bending failure occurred to the elongated CB grain,
and tip bending can clearly be observed in the WR-2 particle, where stress concentration
is much higher compared to other regions. Figure 7.2 also shows bending failure of
elongated particles in an RCA sample. However, referring to Figure 7.1b, WR-1 only
experienced asperity breakage since it lost loading contact points with its surrounding
grains. Among grains across the defined line in Figure 7.1b, the bulky RCA grain
remained almost intact under 5 kN compression. An overall view of Figure 7.1 shows
that, apart from low density and agglomerated PCM grains, bulky grains showed higher
116
resistance to breakage. The higher resistance of bulky grains to breakage can also be seen
in Figure 7.3. Central vertical slices of granular basaltic crushed WR, in the particle size
fraction of 2.36-4.75 mm, under 0, 10.2, and 20.4 MPa compression are shown in Figure
7.3. Mostly, bulky grains remained intact or experienced minor asperity breakage while
the rest of the grains crushed dramatically, particularly during the last phase of loading.
Figure 7.1. Crack propagation in different grains in a CB assembly: a) Density profile, b) The initial phase, c) After 5 kN compression
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Figure 7.2. Bending failure of elongated RCA grains: a) Initial state, b) After 10.2 MPa compression
Figure 7.3. Basaltic Crushed WR under a) 0, b)10, and c)20 MPa compression (asterisks, ‘*’, are highlighting bulky grains not experiencing severe breakage)
0 MPa 10 MPa 20 MPa
**
*
*
*
*
(a) (b) (c)
25 mm
118
7.1.2. Effect of internal microstructure on crack patterns
As shown in Figure 7.1, PCM grains experienced severe fragmentation. Apart from
the low density of PCM grains, their microstructure, an agglomeration of small sub-
particles bonded together by mortar paste, influenced the grain’s strength against
breakage. A close-up of a PCM grain resulting from SEM imaging is shown in Figure
7.4. Different deformation response of sub-particles compared to their surrounding matrix
leads to stress concentrations along the sub-particle boundaries and ultimately facilitates
the crack propagation. This is also observed and reported by a number of researchers,
such as Katsaga (2010) testing concrete beams, and Tavares and das Neves (2008) testing
quarry rock samples.
The fractures typically have a complicated spatial distribution. A fast propagation of
numerous cracks through a stressed region is defined as a brittle fracture (Tattersall and
Tappin, 1966). Figure 7.5 presents crack paths in individual WR particles after 10.2 MPa
compression. Although it has been shown that the dominant type of cracks are tensile
cracks (Chapter 5 and 6), some particles experience shear cracking in the assembly, e.g.
No. 2 and 6 in Figure 7.5b. The main cause of the shear fracture could be the orientation
of the particle in relation to its contact points with surrounding particles. Although
particles tend to rest along their longest axis, there are a few cases, such as particle No. 2
and 6, whose longest axis are oblique to the loading direction. On the other hand, tensile
cracking is clear for particle No. 1 and 7, and the crack path is parallel to the loading
direction, being consistent with the theory of tensile fracture (Bažant and Oh, 1983).
Fracture complexities consist of crack deflection, crack branching, and crack arrest
(Katsaga, 2010). Crack branching, stemming from the vesicular texture of WR, is shown
in Figure 7.5, particle No. 3, 4 and 5. Basaltic crushed Waste Rock has a vesicular texture
as depicted in Figure 7.6 obtained using Scanning Electron Microscopy (SEM). When a
crack is arrested by a hole, higher stress is accumulated (Figure 7.7). The release of this
excess energy produces further crack branches (Hutchinson, 1968). In fact, the existence
of voids reduces the stress required for the development of the cracks, similar to the
observation made by Zhao et al. (2015) on single sand particles.
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Figure 7.4. SEM image of an agglomerated PCM grain
Nevertheless, it is difficult to conclude that the cracks initiated from these internal
voids based solely on CT images, especially because a large number of internal voids
remain intact after grain splitting. It can thus be suggested that, although initial
microstructures such as voids can influence crack propagation paths, other factors such
as grain mineralogy and morphology first and foremost play critical roles in the initiation
of a fracture.
The cleavage pattern is also a structural weakness within a soil particle, along with
internal voids. As mentioned previously, Basaltic Waste Rock is mainly composed of
pyroxene, olivine, and plagioclase minerals (Peck et al., 1992). Figure 7.6 shows the
porphyritic texture of a basaltic WR particle; crystals of pyroxene (brighter colour) are
suspended in a groundmass/matrix of fine-grained dark and light (less dense) minerals
(Figure 7.8). Olivine has no cleavage and its fracture type is conchoidal; however,
pyroxene has a perfect cleavage in two directions that intersect at nearly right angles. This
crystallographic structure brings about fractures along the cleavage resulting in the almost
perpendicular fracture planes, as shown in Figure 7.8.
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Figure 7.5. Fracture propagation in WR grains: a) Initial ortho-slice, b) After 10 MPa
vertical compression ( : tensile event; : shear event; : crack branching)
Figure 7.6. Porphyritic and vesicular texture of a WR grain
121
Figure 7.7. Microstructural effect on grain tensile splitting: a) A close-up of the vesicular WR grains in an assembly, b) After 5 kN (10.2 MPa) compression
Figure 7.8. Fractures following cleavage in WR grains
7.2. Evolution of grain property due to breakage
In order to gain a better understanding of soil behaviour in relation to grain-scale
damage, the changes to the grading and grain morphology of specimens were examined.
A uniformly graded and spectrum of C&D materials with grain diameter (d) varying
between 0.425 to 4.75 mm were scanned under 0, 5, 10 and 15 kN compressive loading
(i.e. 0, 10.2, 20.4 and 30.6 MPa). A sand sample, with particle size ranging from 1.18 to
2.36 mm, was also studied for comparison purposes (Figure 7.9). The grain size and
shape distribution after each loading sequence were obtained from precise 3D
reconstruction of 2159 CT horizontal slices using Avizo 9. Image processing techniques,
including image thresholding, filtering, and segmentation as explained in Chapter 4, were
used to separate and label each fragment in the assembly.
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Figure 7.9. Sand particles: a) CT ortho-slice, b) natural sand used in this research
7.2.1. Soil grading and fractal distribution
While initial grain size distribution is one of the main factors governing the mechanical
behaviour of a granular assembly, the way it changes under loading can affect material
behaviour, especially the potential for further breakage. The grain size distribution of the
confined C&D assemblies under different compressive loading is illustrated in Figures
7.10, 7.11, and 7.12. Only fragments with a diameter larger than 0.075 mm were analysed
due to inaccuracy in segmenting and evaluating characteristics of extremely small
fragments. Figure 7.13a shows grain size distributions of a sand assembly under different
loading levels. After scanning under 20 MPa loading, the sand sample was recovered and
sieve analysed. As shown in Figure 7.13a, there is a slight discrepancy between the grain
size distribution measured by 3D reconstruction of the sample and the results from the
sieve analysis, particularly between the fine contents. This discrepancy is related to the
loss of fine grains during extruding the sample from the chamber at the end of the
scanning.
The samples’ grading clearly changed from a uniform to a well-graded distribution as
the stress increased and breakage progressed further (Figures 7.10, 7.11, 7.12, and
7.13a). Altuhafi and Coop (2011) also reported that toward the terminal state, the soil
gradation eventually tends to shift to well-graded, which explains the fact that very well-
123
graded and fractal soil experiences no dramatic breakage. This is evident in the spectrum
of C&D materials experiencing less breakage compared to uniformly-graded C&D
materials (Figures 7.10a, 7.11a, and 7.12a). Fractal theory, first used by Hartmann
(1969) to study crushing processes in meteorites, is widely used to quantify the amount
of breakage occurring under loading or after large displacement. It is widely accepted that
fragmentation is a fractal phenomenon, suggesting that it is also a scale-invariant
mechanism, and the fractal dimension (Df) describes the changes in grain size
distribution. Referring to Equation 7.1, the original fractal dimension can be calculated
based on number of grains, i.e. N(>r) which is the cumulative number of fragments with
a radius larger than r (Zhao et al., 2015). However, due to the difficulty in counting grains,
Einav (2007b) proposed a method based on the mass of grains smaller than a certain size.
3log (r) + log N(> r) (3-Df) log (r) Eq. (7.1)
With the aid of CT scanning, numbers of grains and newly generated fragments were
directly and precisely measured. The radius was calculated by measuring the volume of
each grain and defined as the radius of a sphere having the same volume as the grain. The
fractal condition is clear in Figures 7.14b-d, 7.15b-d, 7.16b-d and 7.13b, which shows
(3-Df) from Equation 7.1. The fractal dimension rises from 0.6 to 1.2 for WR samples, to
1.5 for RCA samples, to 1.3 for CB samples, and 0.3 to 1.4 for sand, with the increase in
compressive stress. It confirms that as further breakage occurs in the sample, the
gradation tends to be more fractal. This is the same trend observed by Turcotte (1986),
Einav (2007c), and Zhao et al. (2015). Nevertheless, it appears that some large grains did
not experience significant fragmentation, and that the fractal region has ended for grains
with diameter above 0.6, 1.4, and 1.6-2.4 mm within the initial size fraction of 0.425-
1.18, 1.18-2.36, and 2.36-4.75 mm, respectively. Interestingly, at all stress levels, the
upper bound of fractality is approximately the same and is close to d50 (i.e. median
diameter). In addition, this limit is also approximately the same for all kind of materials
from the same initial size fraction. This observation contrasts with the notion of size
effects in the strength of material, where breakage survival probability of a grain
decreases as its size increases (Jones and Ashby, 2005). McDowell et al. (1996) also
stated that while crushing strength of a grain depends on its size, high coordination
number (number of neighbouring grains) reduces the probability of grain fractures, and
attempts to model grain breakage based on these two effects (i.e. grain size and
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coordination number) are very limited. Therefore, the termination of fractality in Figure
7.14b-d, 7.15b-d, 7.16b-d and 7.13b is related to the fact that when stress increases, more
fine fragments are generated by breakage, resulting in a denser packing and higher
coordination number around the larger grains. Consequently, breakage becomes more
dominant in smaller grains and less likely for larger ones. It should be noted that no clear
fractal region was observed in the spectrum of C&D materials under crushing (i.e. initial
size fraction of 0.425-4.75 mm, Figure 7.14a, 7.15a, 7.16a) due to the low level of
breakage occurring in the samples.
Figure 7.10. Changes in WR particle size distribution under different loading levels: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-
4.75 mm
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Figure 7.11. Changes in RCA particle size distribution under different loading levels: a)
Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18, c) 1.18-2.36, and d) 2.36-4.75 mm
Figure 7.12. Changes in CB particle size distribution under different loading levels: a)
Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
126
Figure 7.13. Sand specimen under different loading levels (0, 5, 10, and 20 MPa): a) Changes in grain size distribution, b) The fractal distribution
Figure 7.14. Fractal distribution of WR samples: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
5 MPa
10 MPa
20 MPa
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Figure 7.15. Fractal distribution of RCA samples: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
Figure 7.16. Fractal distribution of CB samples: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
128
7.2.2. Changes in external morphology
Statistical and quantitative analyses of 3D labelled images are presented in Figures
7.17, 7.18, and 7.19 in terms of grain shape/morphology evolution. Figures 7.17, 7.18,
and 7.19 show the changes in the Aspect Ratio distribution due to breakage, which is the
ratio of the short axis of the best-fitted ellipsoid to its intermediate axis. Figures 7.17,
7.18, and 7.19 also demonstrate the true sphericity distribution, defined as the ratio of the
surface area of a sphere having the same volume as the fragment to the actual surface area
of the fragment (Wadell, 1933). Figures 7.17, 7.18, and 7.19 indicate that after the first
loading sequence (i.e. 10 MPa or 20 MPa), both AR and true sphericity increased. The
same observation was also seen for the sand sample under the first loading sequence (i.e.
5 MPa) (Figure 7.20). This observation suggests that grains show a tendency to move
away from morphological extremes during crushing. Abbireddy and Clayton (2015) also
reported similar results on changes in grain forms during a triaxial shear test. Nonetheless,
under higher levels of stress, a reverse trend was observed in both true sphericity and
aspect ratio distributions, as both shape factors tend to decrease regardless of the material
types (Figures 7.17, 7.18, 7.19, and 7.20).
Figure 7.21 also illustrates the evolution of mean values of AR and true sphericity
versus Hardin’s relative breakage for different kinds of C&D materials, which is
calculated as the ratio of total breakage to breakage potential (more information is given
by Hardin (1985)). A decrease in the mean value of true sphericity and a notable drop in
average AR were measured at higher stress levels (i.e. 20 MPa or 30 MPa). It is interesting
that newly created fragments under higher stress levels are less spherical and have lower
aspect ratios than the initial grains. Takei et al. (2001) and Zhao et al. (2015) also noted
a slight reduction in sphericity and AR of different individual grains in a single particle
crushing test. Furthermore, to quantify the uniformity of shape distribution, the Relative
Distribution Factor (RDF) was calculated for each shape factor distribution (Equation
7.2):
RDF=AR90 /AR10
RDF=True Sphericity90 / True Sphericity10 Eq. (7.2)
where AR90 and AR10 or True Sphericity90 and True Sphericity10 are the values of the
shape factor at which 90% and 10% of fragments have a smaller value, respectively.
129
Figure 7.22 reveals that initially there has been a slight fall in RDF of true sphericity and
a larger drop in RDF of AR. This implies that the grains during the first phases of splitting
and breakage tend to create fragments with approximately uniform shapes. Then, the RDF
of both shape factors gradually has increased when the sample experienced more severe
fragmentation under the higher stress level. This suggests that, due to the complex
mechanisms of breakage, during severe fragmentation, newly generated fragments
possessed more diverse shapes. It should also be noted that true sphericity at every
loading stage is distributed normally with equal mean, median, and mode values. On the
contrary, considering the skewness of AR distribution, shown in Figure 7.23, the
distribution tends to skew to the right, toward lower values of AR, with increased
crushing in the sample. Skewness is a measure of the asymmetry of a distribution.
Skewness has been measured to determine the extent to which a distribution differs from
a normal distribution. Based on Bulmer (1979), if skewness is between −1 and −½ or
between +½ and +1, the distribution is moderately skewed; thus, the AR distribution is
moderately skewed for all kinds of C&D materials.
A sand sample with an initial particle size of 1.18-2.36 mm was also examined in terms
of morphology/form evolution. Interestingly, although the sand particles have different
mineralogical and microstructural characteristics from C&D materials (Figure 7.24), the
same trend was observed in morphological changes by increasing stress (Figure 7.25).
Overall, morphological changes during breakage showed a reversal trend as stress
increased, with a shift from more spherical and bulky to less spherical and flaky shapes.
7.2.3. Universality of grain property evolution due to breakage
The literature on particle ‘size’ and shape has highlighted that there is a dependency
between size and shape of particles. Domokos et al. (2015) showed that the shape of
fragments generated under (significant) dynamic loading on ‘large’ 15-150 mm particles
obeys universal scaling laws and that the larger crushed particles tend to be elongated.
However, Altuhafi and Coop (2011) and Sun et al. (2014) obtained contrasting results
(increase in sphericity and aspect ratios of sand and ballast particles as particle size
increased), for smaller diameter particle assemblies under different crushing loads than
that of Domokos et al. (2015).
130
Figure 7.17. Morphology evolution of WR grains under different loading levels: Aspect
Ratio and True sphericity distribution: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
131
Figure 7.18. Morphology evolution of RCA grains under different loading levels: Aspect Ratio and True sphericity distribution: a) Sample’s initial particle size: 0.425-4.75 mm, b)
0.425-1.18 mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
132
Figure 7.19. Morphology evolution of CB grains under different loading levels: Aspect Ratio and True sphericity distribution: a) Sample’s initial particle size: 0.425-4.75 mm, b) 0.425-1.18
mm, c) 1.18-2.36 mm, and d) 2.36-4.75 mm
133
Figure 7.20. Morphology evolution of sand grains under different loading levels: a) Aspect Ratio, b) True Sphericity
The main focus of this chapter is on the way grain properties change with increasing
stress (rather than the existing correlation between particle shape and size). Different
C&D materials, along with a sand sample, were investigated in this study. The
composition of the sand sample was found to be mainly SiO2 in the form of quartz being
completely different from C&D materials (Figure 7.24). In the present study, the results
from studies on various grain assemblies of different size ranges, i.e. basaltic crushed
Waste Rock, Recycled Concrete Aggregate, Crushed Brick, and sand particles, show that
the general trend of changes in particle shape obeys an astonishing universality. The same
generic evolution with increasing stress was observed irrespective of material details or
initial size ranges, a reversal shift from more spherical and bulky to less spherical and
flaky shapes by increasing stress (Figures 7.17-7.20). The result can be explained by the
fact that less spherical particles normally fragmented earlier under loading. As discussed
earlier in Chapters 5 and 6, the less spherical particles (i.e. elongated or flaky particles)
showed lower crushing strength; therefore, their total fragmentation is likely at early
phases of loading (Figure 7.26). Tensile splitting in two nearly equal halves was shown
to be the dominant type of fracture in each sample (see Chapters 5 and 6). Therefore, an
increase in true sphericity or Aspect Ratio was observed under lower loading levels.
Asperity breakage or abrasion commonly occurring during early phases of loading also
causes generation of more rounded and spherical fragments.
134
Figure 7.21. Changes in mean values of AR and true sphericity due to breakage: a) WR, b) RCA, and c) CB
135
Figure 7.22. Relative Distribution Factor of AR and true sphericity distributions: a) WR, b) RCA, and c) CB
136
Figure 7.23. Skewness of AR distributions: a) WR, b) RCA, and c) CB
137
Figure 7.24. EDS elemental analysis of sand (insert: SEM image of a sand particle)
Figure 7.25. Changes in statistical properties of shape factor distributions of sand fragments due to breakage: a) Mean values of AR and true sphericity, and b) Relative Distribution Factor
However, by increasing the load, severe fragmentation and catastrophic splitting cause
more irregular fragments and accordingly cause a decrease in true sphericity or Aspect
Ratio. Zheng and Tannant (2016) reported a notable decrease in roundness and the degree
of sphericity of sand particles, with an initial size of 0.3-0.85 mm, under up to 40 MPa
vertical compression. They described the initial shape of their sand particles as rounded
and close to a spherical shape, with a roundness range of 0.8 to 0.9 and a degree of
sphericity between 0.75 to 0.95. In contrast, Abbireddy and Clayton (2015), after studies
on elongated and flaky glass nuggets with particle sizes ranging from 0.6 to 2 mm during
triaxial shear tests, pointed out an increase in aspect ratio of resulting broken particles. In
this study, samples containing particles with a variety of shapes were studied under
sequential loading, revealing the interesting reversal trend in morphology evolution as
138
stress increased. In fact, the findings presented in this study support both previous
aforementioned research studies and suggest that, where the percentage of elongated and
flaky particles is significant, an initial increase is expected in the sphericity and aspect
ratio of the newly generated fragments. However, this initial increase in shape factors is
not likely to occur for granular samples containing only rounded and spherical particles.
Moreover, at all stress levels, the upper bound of fractality was approximately the
same (Figures 7.14-16 and 7.13b). Along the same line, the termination of the fractal
region was dependent on the initial particle size but irrespective of material types or
loading levels (as the fractal region terminated at grains with diameters above 0.6, 1.4,
and 1.6-2.4 mm in samples with initial particle sizes of 0.425-1.18, 1.18-2.36, and 2.36-
4.75 mm, respectively, Figures 7.14-16 and 7.13b).
Figure 7.26. Schematic explanation of particle shape evolution due to breakage
7.3. Summary
Grain breakage brings about changes in characteristics of granular materials,
especially in grain size distribution and grain morphology. These shifts affect the
mechanical behaviour of granular media and, most prominently, the material’s crushing
strength against further breakage.
Various granular materials under different loading levels were studied using
synchrotron tomography. The effect of particle shape was identified as a notable factor
governing grain breakage. Crack formation and its related mechanisms were investigated
for different types of grains. Although the microstructural features such as a vesicular
texture tended to change the crack path, the findings attest to the dominant influence of
grain mineralogy and morphology on crack initiation.
139
Cutting-edge synchrotron tomography was used to study alterations in grain
characteristics of C&D and a sand specimens. The fractal distribution of the particle
assemblies due to crushing demonstrated that breakage becomes dominant in smaller
grains rather than larger ones where an increase in the amount of newly generated fine
fragments causes a high coordination number surrounding the larger grains.
The results of morphological changes also reveal that there is a reversal trend in the
grain shape evolution with increasing stress. The breakage process causes generation of
fragments with a greater isotropic shape, whereas by increasing the stress, this trend
reversed. Owing to severe breakage and splitting under higher stress levels, less spherical
fragments (i.e. anisotropic shape) with a lower aspect ratio compared to the original grains
were created. In addition, the results reported here are from studies on various granular
materials with different particle sizes, i.e. basaltic crushed Waste Rock, Recycled
Concrete Aggregate, Crushed Brick, and sand particles, showing that the general trend of
changes in particle shape obeys an astonishing universality. The same generic evolution
by increasing stress was observed irrespective of material details or sizes, a reversal shift
from more spherical and bulky to less spherical and flaky shapes by increasing stress.
140
8. CONCLUSIONS AND RECOMMENDATIONS
In this research, three different types of granular recycled Construction and Demolition
(C&D) materials (i.e. basaltic crushed Waste Rock, Recycled Concrete Aggregate, and
Crushed Brick) used in roads, pavements, and embankments were studied at particle-
scale. Particle fracture, causing serious issues such as settlements, is the focus of the
present research. In many industrial processes, particle breakage occurs, which may or
may not be desirable. As an example, in mining and ore processing, particle breakage is
desired during grinding and milling processes; however, proppant crushing causes a
dramatic reduction in the recovery rate of hydrocarbons in the oil and gas industry. Hence,
the implications of this research are not limited solely to the geotechnical engineering
industry.
Following geotechnical, mineralogical, microstructural, and morphological
characterisation of the C&D materials, different experimental and numerical tests,
including synchrotron tomography and Discrete Element Modelling (DEM) simulation,
were conducted to improve the understanding of particle fracture and subsequent changes
in grain properties.
8.1. Major conclusions
8.1.1. Experimental observations and analyses from SPC and
PAC tests
The investigation into a variety of C&D materials with various microstructure and
mineralogical aspects demonstrated that:
• Particle tensile strength is profoundly affected by particle shape, and it has
been found that particle shape plays a more prominent role in the particle
breakage phenomena than mineralogy and microstructure of C&D particles.
• Following studies on several individual C&D particles, a modified particle
tensile strength, as a function of particle Aspect Ratio is introduced, where the
impact of particle shape is also considered.
• Further studies on particle fracture using Particle Assembly Crushing (PAC) tests
showed that although boundary conditions and particle coordination number have
141
remarkable effects on particle breakage, the significant influence of particle
shape on particle crushing is not diminished even in an assembly of particles.
• The findings suggest that brittle C&D granular materials with a higher
degree of sphericity (an Aspect Ratio closer to 1) and a lower flakiness index
would experience less particle breakage under loading.
8.1.2. Discrete Element Modelling
Micromechanical analyses, such as contact force measurement, are difficult or
sometimes impossible using conventional laboratory tests. Hence, DEM was employed
to study particle breakage and the associated energy dissipation. Precise three-
dimensional particle shapes were generated using the Fish scripting language, within
PFC2D and PFC3D, and used to model single particle crushing and particle assembly
crushing. The outcomes are summarised as follows:
• 2D DEM simulations confirm the importance of accurate simulation of
particle shape and also the significant influence of particle shape and breakage on
the macro-mechanical behaviour of C&D materials.
• The fragmentation mechanism of brittle WR particles with different
shapes was investigated using 3D DEM simulations. The results imply that tensile
cracks on the plane linking the contact points of the particle with adjacent particles
are the dominant type of particle fracture.
• The PAC simulations proved that energy dissipation due to breakage
depends on the particles’ shape factor.
• Energy components, including strain energy, frictional energy, and
breakage energy, in the particulate system were monitored precisely using DEM.
Energy dissipation measurement showed that less than one-third of the total input
energy was dissipated due to particle breakage. The results indicated that a large
portion of input energy is dissipated through other mechanisms, particularly
through frictional dissipation between particles and newly generated fragments.
8.1.3. Post-breakage analyses using synchrotron tomography
Grain breakage results in changes to the properties of granular materials, particularly
grain size distribution and grain morphology. These alterations affect the macro-
142
mechanical behaviour of particulate systems and most prominently, the material’s
crushing strength against further breakage. Various granular materials, i.e. C&D and sand
specimens, were studied under different loading levels using cutting-edge synchrotron
tomography. Salient observations and findings are summarised as follows:
• The notable effect of particle shape on particle breakage was confirmed
using CT images.
• Crack propagation and associated mechanisms were studied for different
types of grains. The results suggest that, even though microstructural features,
such as the vesicular texture, can facilitate or arrest a propagating crack, other
factors, such as grain mineralogy and morphology, mainly govern crack initiation.
• The evolution of the particle size distribution has shown that some coarse
particles were left relatively unbroken and cushioned by smaller particles. This
contrasts with the concept that larger particles have a higher likelihood of
breakage since they have a higher probability of containing internal flaws. In fact,
the fractal distribution of the particle assemblies due to breakage demonstrated
that there is a competition between cushioning and size effects. Eventually,
breakage becomes dominant in smaller grains rather than larger ones, where an
increase in the amount of newly generated fine fragments causes high
coordination number surrounding the larger grains.
• The results of morphology evolution demonstrated that there is a reversal
trend in the grain shape evolution with increasing stress. The breakage
phenomenon generates fragments with a greater isotropic shape; however, by
increasing the stress, this trend reversed. Due to catastrophic and severe breakage
under higher stress levels, less spherical fragments (i.e. anisotropic shape), with a
lower aspect ratio in comparison to the initial particles, were generated.
• The more significant finding to emerge from this study is that particle
shape evolution due to breakage obeys universality. Studies on various granular
materials with different particle size and gradation, i.e. basaltic crushed WR,
RCA, CB, and sand particles, showed that the generic evolution in particle shape
by increasing stress is the same for each sample irrespective of material details or
sizes.
143
8.2. Recommendations for future research
The investigation carried out in this research has indicated new aspects of particle
mechanics in relation to particle breakage and shape; however, there remains areas where
further research can be undertaken, as follows:
• Investigation of three types of C&D materials during SPC testing showed
that shape plays a more prominent role in particle breakage phenomena than
mineralogy and microstructure of particles. Further investigation is required to
examine this notion for other types of geomaterials.
• All tests and simulations performed in the present research were under
quasi-static compression. A further study could compare the presented results and
observed trends with results obtained under different loading conditions, such as
dynamic, repeated, and cyclic loading.
• In this research, particle shape evolution was investigated for particles in
the size range of 0.425-4.75 mm. The investigation into changes in particle
properties due to breakage is recommended on particles with larger sizes, for
example particle diameters > 20 mm.
• It has been proven that the changes in particle properties, such as the
reduction in particle sizes, due to breakage have a significant effect on the
permeability of the soil (Zheng and Tannant, 2016). It would be useful to examine
the effect of particle morphology evolution during sequential loading on pore
conductivity and void ratio of the soil. The observed reversal trend is likely to
have a noteworthy and interesting effect on pore size or pore conductivity
distribution.
• The development of a model that can predict crushing levels using input
parameters derived from simple tests, such as initial particle size, density, and
particle shape, would be a fruitful area for further work. Although several
breakage indices, based on changes in particle size distribution are currently
available (e.g. Hardin (1985); Indraratna et al. (2014)), the development of a
crushing prediction model has historically been hampered by a lack of access to
particle-scale information of geomaterials. The findings of this study, particularly
the significant effect of particle shape, can facilitate this development.
144
• This research was conducted on unbound granular materials. Further
research to extend the results to stabilised granular materials is also
recommended.
145
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