NUMERICAL MODEL FOR CORROSION OF ROCK BOLTS BY GALVANIC MINERALS IN A HETEROGENEOUS ROCK MASS by  Paul Lee  B.S., Montana Tech, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mining Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2019  © Paul Lee, 2019  ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled:  Numerical model for corrosion of rock bolts by galvanic minerals in a heterogeneous rock mass  submitted by Paul Lee in partial fulfillment of the requirements for the degree of Master of Applied Science in Mining Engineering  Examining Committee: Ilija Miskovic, Mining Engineering Supervisor  Scott Dunbar, Mining Engineering Supervisory Committee Member  Davide Elmo, Mining Engineering Supervisory Committee Member  Additional Examiner   Additional Supervisory Committee Members:  Supervisory Committee Member  Supervisory Committee Member iii  Abstract Corrosion of ground support poses a significant safety risk to underground mines that is difficult to identify and costly to address. The corrosion of embedded ground support elements is undetectable by visual inspection. This leads to unexpected failure typically mitigated by comprehensive rehabilitation that covers any areas suspected of corrosion. Rock bolts are replaced when the visible portion of a rock bolt is judged to be excessively corroded or loss of holding capacity is confirmed by the pull-out test. This thesis investigates the influenced of the mineral electrochemical properties in a heterogeneous rock mass on ground support corrosion. Previous work focused on the uniform corrosion of ground support in wet and dry conditions by empirical experiment in a real or simulated underground mining environment and on the corrosivity classification of environment by various qualitative measures. This thesis approaches the electrochemical influence of rock mass to corrosion of rock bolt by characterization of mineral electrochemical properties, numerical simulation of the galvanic corrosion process, and validation of numerical model by submersion experiment. A procedure for determining the electrochemical properties of minerals was developed with a complementary numerical model for galvanic corrosion of ground support by minerals. Additionally, the simulated numerical corrosion model was validated with a submersion experiment. The numerical model was found to have over-estimated the galvanic corrosion of steel by cathodic mineral, but predicted cathodic protection of steel by anodic mineral. The numerical model did not account for the acid byproducts of oxidized sulphide minerals that resulted in iv  pitting corrosion. These findings allow us to predict galvanic corrosion of steel by minerals and propose a new mechanism for initation of pitting corrosion to by pyrite oxidation. v  Lay Summary Corrosion of ground support poses a significant safety risk to underground mines that is difficult to identify and costly to address. Accelerated ground support corrosion has been connected to the conductivity and electrochemical properties of the rock mass. A procedure for determining the electrochemical properties of minerals was developed with a complementary numerical model for galvanic corrosion of ground support by minerals. The simulated numerical corrosion model was validated with a submersion experiment. The numerical model was found to have over-estimated the galvanic corrosion of steel by cathodic mineral, but predicted cathodic protection of steel by anodic mineral. The numerical model did not account for the acid byproducts of oxidized sulphide minerals that resulted in pitting corrosion. These findings allow us to predict if galvanic corrosion of steel by cathodic minerals is expected and propose a new mechanism for initiation of pitting corrosion by pyrite oxidation. vi  Preface This thesis is original, unpublished, independent work by the author, P. Lee. vii  Table of Contents Abstract .........................................................................................................................................iii  Lay Summary ................................................................................................................................ v Preface ........................................................................................................................................... vi Table of Contents........................................................................................................................ vii List of Tables ............................................................................................................................... xii List of Figures ............................................................................................................................xiii List of Equations ......................................................................................................................... xx List of Abbreviations................................................................................................................. xxi Acknowledgments ................................................................................................................... xxiii Dedication ................................................................................................................................. xxiv Chapter 1: Introduction .............................................................................................................. 1 1.1 Background .................................................................................................................... 1 1.2 Research Objectives....................................................................................................... 2 1.3 Research Outline ............................................................................................................ 2 Chapter 2: Literature Review .................................................................................................... 4 2.1 Introduction .................................................................................................................... 4 2.2 Ground Support Systems ............................................................................................... 5 2.2.1 Continuous Mechanically Coupled (CMC) Rock Bolt ........................................... 6 2.2.2 Continuous Frictionally Coupled (CFC) Rock Bolt ................................................ 7 2.2.3 Discreetly Mechanical or Frictionally Coupled (DMFC) Rock Bolts ................... 8 2.2.4 Surface Support ......................................................................................................... 8 viii  2.3 Corrosion Mechanism Fundamentals ........................................................................... 9 2.3.1 Uniform Corrosion .................................................................................................. 12 2.3.2 Passivation ............................................................................................................... 13 2.3.3 Pitting Corrosion...................................................................................................... 13 2.3.4 Stress Corrosion Cracking ...................................................................................... 14 2.4 Corrosion Inhibiting Measures.................................................................................... 14 2.4.1 Galvanization ........................................................................................................... 15 2.4.2 Plastic Coating ......................................................................................................... 15 2.4.3 Cement Grout ........................................................................................................... 16 2.4.4 Stainless Steel .......................................................................................................... 16 2.4.5 Glass Fibre Reinforced Polymer (GFRP) .............................................................. 17 2.5 Corrosion Monitoring Methods .................................................................................. 17 2.5.1 Destructive Test ....................................................................................................... 18 2.5.2 Non-destructive Test ............................................................................................... 20 2.5.3 Smart Rock Bolt ...................................................................................................... 20 2.6 Corrosion Studies ......................................................................................................... 21 2.6.1 Environmental Classification .................................................................................. 22 2.6.2 In-situ Experiment ................................................................................................... 23 2.6.3 Laboratory Experiment ........................................................................................... 24 2.6.4 Numerical Simulation.............................................................................................. 25 2.7 Galvanic Property of Minerals .................................................................................... 26 2.8 Conclusion .................................................................................................................... 27 Chapter 3: Methodology............................................................................................................ 28 ix  3.1 Introduction .................................................................................................................. 28 3.2 Sample Characterization.............................................................................................. 28 3.2.1 Sample Preparation .................................................................................................. 29 3.2.2 X-ray Fluorescence (XRF) ...................................................................................... 34 3.2.3 Acidity and Conductivity of Electrolytes ............................................................... 35 3.2.4 The resistivity of Rock and Minerals ..................................................................... 37 3.2.5 Linear Sweep Voltammetry (LSV) ........................................................................ 37 3.2.6 Microscopic Photography ....................................................................................... 40 3.2.7 X-ray Powder Diffraction (XRD) ........................................................................... 40 3.3 Numerical Simulation of Corrosion............................................................................ 40 3.3.1 Segmentation............................................................................................................ 41 3.3.2 Geometry .................................................................................................................. 41 3.3.3 Meshing .................................................................................................................... 42 3.3.4 Cell Zone Conditions............................................................................................... 42 3.3.5 Boundary Conditions ............................................................................................... 42 3.3.6 Electric Potential Solver .......................................................................................... 43 3.3.7 User-Defined Function (UDF) ................................................................................ 43 3.3.8 Simulation ................................................................................................................ 44 3.4 Submersion Experiment .............................................................................................. 45 3.4.1 Rock Core Electrode (RCE) Matrix ....................................................................... 45 3.4.2 Steel Sample Preparation ........................................................................................ 45 3.4.3 Confocal Microscopy .............................................................................................. 46 3.5 Conclusion .................................................................................................................... 46 x  Chapter 4: Results ...................................................................................................................... 48 4.1 Introduction .................................................................................................................. 48 4.2 Sample Characterization.............................................................................................. 48 4.2.1 X-ray Fluorescence (XRF) of Rock Samples ........................................................ 49 4.2.2 Mine Water Acidity pH ........................................................................................... 50 4.2.3 Total Dissolved Solids (TDS) ................................................................................. 50 4.2.4 The Resistivity of Rock and Minerals .................................................................... 54 4.2.5 Linear Sweep Voltammetry (LSV) ........................................................................ 55 4.2.6 Mixed Potential ........................................................................................................ 55 4.2.7 X-ray Powdered Diffraction (XRD) ....................................................................... 58 4.3 Numerical Simulation of Corrosion............................................................................ 59 4.3.1 Segmentation............................................................................................................ 59 4.3.2 Mixed Potential Analysis ........................................................................................ 62 4.3.3 Meshing .................................................................................................................... 65 4.3.4 Simulated Corrosion Profile ................................................................................... 67 4.4 Submersion Experiment .............................................................................................. 75 4.4.1 Visual Observation .................................................................................................. 75 4.4.2 Confocal Microscopy .............................................................................................. 81 4.5 Conclusion .................................................................................................................... 93 Chapter 5: Discussion and Recommendation ........................................................................ 94 5.1 Introduction .................................................................................................................. 94 5.2 The Resistivity of Rock and Minerals ........................................................................ 94 5.3 Rock Core Electrode Vs. Single Mineral Electrode .................................................. 94 xi  5.4 Approximating Steel Polarization Curve with Open Circuit Potential (OCP)......... 95 5.5 Choosing the Appropriate Boundary Condition for Corrosion Simulation ............. 96 5.6 Fluid Domain Thickness ............................................................................................. 96 5.7 Validation of Sample 1 Simulated Corrosion ............................................................ 97 5.8 Validation of Sample 3 Simulated Corrosion ............................................................ 98 5.9 Validation of Sample 19 Simulated Corrosion .......................................................... 99 5.10 Validation of RCE Matrix Simulated Corrosion ....................................................... 99 5.11 Secondary Corrosion of Sulphide Minerals ............................................................. 100 5.12 Recommendation ....................................................................................................... 100 Chapter 6: Conclusions ........................................................................................................... 102 6.1 Research Objectives................................................................................................... 102 6.2 Significant Results ..................................................................................................... 102 6.3 Limitations ................................................................................................................. 103 6.4 Future Directions ....................................................................................................... 104 Bibliography .............................................................................................................................. 105 Appendices ................................................................................................................................. 110 Appendix A Greens Creek Sample Catalog ......................................................................... 110 Appendix B Pure Mineral Sample from Ward’s Science .................................................... 114 Appendix C User Defined Function (UDF).......................................................................... 115 Appendix D Numerical Corrosion Simulation Result ......................................................... 116 Appendix E Confocal Profilometry....................................................................................... 124  xii  List of Tables Table 1 List of pure minerals from Ward's Science. .................................................................. 33 Table 2 Greens Creek sample description. ................................................................................. 48 Table 3 Mine water acidity. ......................................................................................................... 50 Table 4 TDS measurement before submersion experiment. ...................................................... 52 Table 5 TDS measurement after submersion experiment. ......................................................... 53 Table 6 Gravimetric TDS measurements. ................................................................................... 54 Table 7 Mixed potential summary............................................................................................... 58 Table 8 Normalized results of quantitative phase analysis by Rietveld refinements. .............. 59 Table 9 Picture of all rock core electrodes labelled with dominant mineralization. ................ 62  xiii  List of Figures Figure 1 Artificial rock vault (L/S=2) modified from (Choquet, 1991). .................................... 5 Figure 2 Fully grouted rock bolt (left) and torque tension bolt (right) (JENNMAR, 2017). .... 6 Figure 3 Friction stabilizer (top) and expansion rock bolt (bottom) (JENNMAR, 2017). ........ 7 Figure 4 Point anchor bolt (left) and expansion shell bolt (right) (JENNMAR, 2017). ............ 8 Figure 5 Iron corroding in water reproduced from (Hack, 2010)................................................ 9 Figure 6 Schematic Evans diagram for corrosion of metal M by an acid showing the application of mixed potential theory (Frankel, 2016)............................................................... 10 Figure 7 Schematic description of atmospheric corrosion reproduced from (Roberge et al., 2002).............................................................................................................................................. 12 Figure 8 Pourbaix diagram for iron at 25°C (McCafferty, 2010). ............................................ 13 Figure 9 Autocatalytic pitting corrosion reproduced from (Bhandari, Khan, Abbassi, Garaniya, & Ojeda, 2015). ........................................................................................................... 13 Figure 10 Typical SCC in service is associated with the initiating at a rock bolt rib, growing to a critical size, followed by fast fracture through the remaining section (Villalba & Atrens, 2008).............................................................................................................................................. 14 Figure 11 Overcored resin grouted rock bolt (R. Hassell et al., 2004). .................................... 18 Figure 12 Pull-out test equipment (JENNMAR, 2017). ............................................................ 18 Figure 13 Pull-out failure modes of fully grouted rock bolt (Choquet, 1991). ........................ 19 Figure 14 RBS™ ultrasonic sensor principle (Quenneville, 2018)........................................... 21 Figure 15 Classification of aqueous corrosion environment, reproduced from (Roy et al., 2016).............................................................................................................................................. 23 xiv  Figure 16 Rock, mine water, and rock bolt sample from Greens Creek mine. ........................ 28 Figure 17 Paired rock slabs (sample 3). ...................................................................................... 29 Figure 18 Collecting rock core with ¾" diamond hole saw. ..................................................... 29 Figure 19 Paired electrode slabs from sample 1 (up), sample 3 (left), and sample 19 (right). 30 Figure 20 Rock core before (left) and after (right) surface grinding. ....................................... 30 Figure 21 Polished rock slab (sample 19). .................................................................................. 31 Figure 22 Rock core electrodes. .................................................................................................. 31 Figure 23 Construction of single mineral (left) and rock core (right) electrodes. .................... 32 Figure 24 Steel electrode in electrochemical cell. ...................................................................... 33 Figure 25 Ring mill used to pulverize XRD samples. ............................................................... 34 Figure 26 Portable XRF in shielded scanning station. ............................................................... 34 Figure 27 Gravimetric TDS analysis of mine water after submersion experiment. ................. 36 Figure 28 Resistivity measurement of rock core saturated in mine water. ............................... 37 Figure 29 3 electrodes electrochemical cell with Rodeostat...................................................... 37 Figure 30 Microscopic photograph of slab sample. ................................................................... 40 Figure 31 Simplified geometry for ground support corrosion. .................................................. 40 Figure 32 Simplified boundary condition. .................................................................................. 42 Figure 33 Submersion test after 70 days. .................................................................................... 45 Figure 34 RCE Matrix. ................................................................................................................. 45 Figure 35 Olympus LEXT OLS3100 laser scanning confocal microscope.............................. 46 Figure 36 Stacked column graph of XRF result. ........................................................................ 49 Figure 37 Triangle plot of XRF result......................................................................................... 50 Figure 38 TDS calibration curve before submersion experiment. ............................................ 52 xv  Figure 39 TDS calibration curve after submersion experiment. ............................................... 53 Figure 40 Resistivity of rock core saturated by various solutions. ........................................... 55 Figure 41 Mixed potential diagram of rock and mineral samples cathode to steel. ................. 56 Figure 42 Mixed potential diagram of rock and mineral samples anode to steel. .................... 57 Figure 43 Sample 1 (left), segmented sample 1 (centre), small segmented sample 1 (right). . 60 Figure 44 Sample 3 (left), segmented sample 3 (centre), small segmented sample 3 (right). . 61 Figure 45 Sample 19 (left), sample 19 (centre), small segmented sample 19 (right). ............. 61 Figure 46 Polarization curves of major minerals in sample 1. .................................................. 63 Figure 47 Polarization curves of major minerals in sample 3. .................................................. 64 Figure 48 Polarization curves of major minerals in sample 19. ................................................ 65 Figure 49 Sample 1 tetrahedral mesh with 1,176,330 cells (left), zoomed in on mineral boundary (right). ........................................................................................................................... 66 Figure 50 Sample 3 cut cell mesh with 1,465,074 cells (left), zoomed in to show adaptive meshing (right). ............................................................................................................................ 66 Figure 51 Sample 19 cut cell mesh with 1,894,146 cells (left), zoomed in to show adaptive meshing (right). ............................................................................................................................ 66 Figure 52 RCE matrix hexahedral mesh with 1,327,645 cells (left), zoomed in (right).......... 67 Figure 53 Sample 1 mesh (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by dolomite edge (a), dolomite centre (b), quartz with pyrite (c), and pyrite (d). .......................................................................................... 68 Figure 54 Sample 3 mesh (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by clinochlore (a), albite (b), quartz (c), and pyrite (d). ....................................................................................................................................... 70 xvi  Figure 55 Sample 19 segmentation (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by calcite (a), biotite (b), quartz (c), and pyrite (d). ......................................................................................................................... 72 Figure 56 RCE matrix photograph (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by M1 bornite (a), 19-6 calcite (b), 19-2 calcite with biotite (c), and 3-4 clinochlore with pyrite(d). .............................................. 74 Figure 57 Steel sample 1 after 100-day submersion (white = quartz, red = pyrite, yellow = zip-tie dry spot, green = zip-tie less corrosion product). ........................................................... 76 Figure 58 Zip-tie induced dry spot on sample 1. ........................................................................ 77 Figure 59 Sample 3 bolt steel after 100-day submersion (white=zip-tie, red=dry spot, yellow=quartz). ............................................................................................................................. 78 Figure 60 Zip-tie induced dry spot on sample 3. ........................................................................ 78 Figure 61 Steel sample 19 after 100-day submersion (red=pyrite, white=quartz, cyan=biotite, yellow=zip-tie).............................................................................................................................. 79 Figure 62 Sample 19 afte submersion test showing zip-tie induced dry spot. ......................... 80 Figure 63 Steel sample zip-tied to the RCE matrix after 100-day submersion (yellow=anodic, red=cathodic). ............................................................................................................................... 81 Figure 64 Sample 1 steel marked with POI and an overlay of transparent and glow edges segmentation. ................................................................................................................................ 82 Figure 65 Sample 3 steel marked with point of interest marked in masking tapes. ................. 86 Figure 66 Sample 19 steel with points of interest marked with masking tapes........................ 89 Figure 67 RCE matrix steel marked with POI and RCE identity. ............................................. 91 Figure 68 Pure mineral sample from Ward's Science. See Table 1 on page 33 for details. .. 114 xvii  Figure 69 Sample 1 electric potential contour. ......................................................................... 116 Figure 70 Sample 1 electric current magnitude contour. ......................................................... 116 Figure 71 Sample 1 corrosion depth contour. ........................................................................... 117 Figure 72 Sample 1 corrosion depth contour with electric current magnitude mesh sections. ..................................................................................................................................................... 117 Figure 73 Sample 3 electric potential contour. ......................................................................... 118 Figure 74 Sample 3 electric current magnitude contour. ......................................................... 118 Figure 75 Sample 3 corrosion depth contour. ........................................................................... 119 Figure 76 Sample 3 corrosion depth contour with electric current magnitude mesh sections. ..................................................................................................................................................... 119 Figure 77 Sample 19 electric potential contour. ....................................................................... 120 Figure 78 Sample 19 electric current magnitude contour. ....................................................... 120 Figure 79 Sample 19 corrosion depth contour.......................................................................... 121 Figure 80 Sample 19 corrosion depth contour with electric current magnitude mesh sections. ..................................................................................................................................................... 121 Figure 81 RCE matrix electric potential contour. .................................................................... 122 Figure 82 RCE matrix electric current magnitude contour...................................................... 122 Figure 83 RCE matrix corrosion depth contour. ...................................................................... 123 Figure 84 RCE matrix corrosion depth contour with electric current magnitude mesh sections. ....................................................................................................................................... 123 Figure 85 Sample 1-1 optical x100 (left), confocal height (right), profile (lower). ............... 124 Figure 86 Sample 1-2 optical x100 (left), confocal height (right), profile (lower). ............... 125 Figure 87 Sample 1-3 optical x100 (upper), confocal height (lower), profile (right). ........... 126 xviii  Figure 88 Sample 1-4 optical x100 (left), confocal height (right), diagonal profile (lower).127 Figure 89 Sample 1-5 optical x100 (left), confocal height (right), profile (lower). ............... 128 Figure 90 Sample 1-6 optical x100 (upper), confocal height (lower), profile (right). ........... 129 Figure 91 Sample 1-7 optical x100 (upper), confocal height (centre), vertical profile (right), horizontal profile (bottom)......................................................................................................... 130 Figure 92 Sample 1-8 optical x100 (upper), confocal height (lower), profile (right). ........... 131 Figure 93 Sample 1-9 optical x100 (upper), confocal height (lower), profile (right). ........... 132 Figure 94 Sample 1-10 optical x100 (left), confocal height (right), profile (lower). ............. 133 Figure 95 Sample 3-1 optical x100 (left), confocal height (right), profile (lower). ............... 133 Figure 96 Sample 3-2 optical x100 (left), confocal height (right), profile (lower). ............... 134 Figure 97 Sample 3-3 optical x100 (left), confocal height (right), profile (lower). ............... 134 Figure 98 Sample 3-4 optical x100 (left), confocal height (right), profile (lower). ............... 135 Figure 99 Sample 3-5 optical x100 (upper), confocal height (lower), profile (right). ........... 136 Figure 100 Sample 3-6 optical x100 (left), confocal height (right), profile (lower). ............. 137 Figure 101 Sample 3-7 optical x100 (left), confocal height (right), profile (lower). ............. 137 Figure 102 Sample 3-8 optical x100 (left), confocal height (right), profile (lower). ............. 138 Figure 103 Sample 19-1 optical x100 (left), confocal height (right), profile (lower). ........... 138 Figure 104 Sample 19-2 optical x100 (left), confocal height (right), profile (lower). ........... 139 Figure 105 Sample 19-3 optical x100 (left), confocal height (right), profile (lower). ........... 139 Figure 106 Sample 19-4 optical x100 (left), confocal height (right), profile (lower). ........... 140 Figure 107 Sample 19-5 optical x100 (left), confocal height (right), profile (lower). ........... 140 Figure 108 Sample 19-6 optical x100 (upper), confocal height (lower), profile (right). ....... 141 Figure 109 Sample 19-7 optical x100 (left), confocal height (right), profile (lower). ........... 142 xix  Figure 110 Sample 19-8 optical x100 (left), confocal height (right), profile (lower). ........... 142 Figure 111 RCE-1 optical x100 (upper), confocal height (lower), vertical profile (right). ... 143 Figure 112 RCE-2 optical x100 (left), confocal height (right), profile (lower). .................... 144 Figure 113 RCE-3 optical x100 (left), confocal height (right), profile (lower). .................... 145 Figure 114 RCE-4 optical x100 (left), confocal height (right), profile (lower). .................... 145 Figure 115 RCE-5 optical x100 (left), confocal height (right), profile (lower). .................... 146 Figure 116 RCE-6 optical x100 (left), confocal height (right), profile (lower). .................... 146 Figure 117 RCE-7 optical x100 (left), confocal height (right), profile (lower). .................... 147 Figure 118 RCE-8 optical x100 (left), confocal height (right), profile (lower). .................... 148  xx  List of Equations Equation 1 Oxidation of iron ......................................................................................................... 9 Equation 2 Oxygen reduction reaction in acids ............................................................................ 9 Equation 3 Oxygen reduction reaction in neutral or basic solutions........................................... 9 Equation 4 Hydrogen evolution in acids ..................................................................................... 10 Equation 5 Hydrogen evolution in neutral or basic solutions.................................................... 10 Equation 6 Typical iron corrosion reaction ................................................................................ 10 Equation 7 Laplace's equation ..................................................................................................... 12 Equation 8 Ohm's law .................................................................................................................. 12 Equation 9 Electrical resistivity ................................................................................................... 37 Equation 10 Peak current function .............................................................................................. 38 Equation 11 Electric potential equation ...................................................................................... 43 Equation 12 Ohm’s law ................................................................................................................ 44 Equation 13 Corrosion rate .......................................................................................................... 44 Equation 14 Electrical conductivity to ppm conversion factor ................................................. 51 Equation 15 Pyrite oxidation ..................................................................................................... 100  xxi  List of Abbreviations AMW artificial mine water BEM boundary element method CA cellular automata CSV comma separated value CFC continuous frictionally coupled CMC continuous mechanically coupled DIW deionized water DMFC discreetly mechanically or frictionally coupled DO dissolved oxygen EC electric conductivity FBR fibre Bragg grating FEM finite element method GFRP glass fibre reinforced polymer GRANIT ground anchorage integrity testing GPR ground penetrating radar HPC high-performance computing LSV linear sweep voltammetry MIC microbe induced corrosion MW mine water OCP open circuit potential PD peridynamic xxii  POI point of interest RFID radio frequency identification RBS rock bolt sensor RCE rock core electrode SME single mineral electrode SE steel electrode SCC stress corrosion cracking SRB sulphate-reducing bacteria TDS total dissolved solids UDF user-defined function XRF X-ray fluorescence XRD X-ray powder diffraction  xxiii  Acknowledgments I thank the faculty, staff and my fellow graduate students in the Mining Department, who have inspired me to continue my work in this field. I offer sincere gratitude to my supervisor Dr. Ilija Miskovic for his guidance and support during this journey. I also thank Ben Beard from Greens Creek mine for supplying rock and water sample, Art Craven from Jennmar for providing steel sample, Libin Tong and Aaron Hope for help in the lab, and Paul Hughes for help preparing rock sample. Special thanks go to my mother, who has supported me through many years of education. xxiv  Dedication This work is dedicated to my father.   1  Chapter 1: Introduction 1.1 Background Ground support corrosion is a significant hazard in underground mining. The purpose of ground support is to keep the excavation safe and open for its intended lifespan, failure to achieve this outcome threatens the safety of persons and equipment and can influence the economic viability of the mining operation. The cost of rehabilitating mine access can run into tens of millions as whole sections of ground support are replaced due to the uncertainty in their condition, resources are taken away from production, and mine access is restricted. The underground mining environment is often favourable to corrosion and highly variable throughout the mine. Existing research on ground support corrosion address the uniform corrosion of ground support in wet and dry conditions by empirical experiment in a real or simulated underground mining environment and has classified the corrosivity of the environment by various qualitative measures. However, localized corrosion influenced by the electrochemical property of minerals in heterogeneous rock mass was not considered. Numerical simulation of the corrosion process has been instrumental in the general study of corrosion. By measuring the electrochemical property of minerals, a numerical model is created in this study to simulate the localized aqueous corrosion of ground support influenced by mineralogy. A submersion experiment was conducted to validate the numerical model. 2  1.2 Research Objectives The purpose of this research is to investigate the influence of galvanic minerals in ground support corrosion. Three measurable goals of this work are: • Develop a procedure for collection of mineral specimens for electrochemical analysis. • Incorporate mineral distribution, the electrochemical property of minerals and steel, and mine water conductivity into a numerical model for rock bolt corrosion. • Validate the numerical model for corrosion with submersion experiment. 1.3 Research Outline The structure of this study is laid out below, connecting the research to stated objectives. Chapter 2 presents an overview of the ground support system and the mechanism of corrosion with common corrosion inhibiting measures and monitoring methods for ground support. The chapter also reviews existing literature on ground-support corrosion, numerical corrosion model, and electrochemical properties of minerals. The significant knowledge gaps in localized corrosion and effects of rock mass are discussed. Chapter 3 presents the research methodology employed to investigate the influence of heterogeneous rock mass on corrosion, from sample characterization and measurement of input parameters for the numerical model; to the setup procedure for the numerical simulation of corrosion; and the submersion experiment that validates the numerical model. Chapter 4 presents the results of sample characterization, the predicted corrosion profile from numerical simulation, and the outcome of the submersion validation experiment. 3  Chapter 5 discuss the results from Chapter 4 in terms of assumptions made during the research, the quality and confidence of the data, and the quality of the simulation. Chapter 6 draws a conclusion over this study, showcases the significant results, determines if research objectives have been achieved, and discusses limitations and future directions of the study. 4  Chapter 2: Literature Review 2.1 Introduction Ground support corrosion is a significant hazard to underground mining. 95 million rock bolts were installed in the US and over 500 million bolts were used globally in 2011 (Song, Li, Wang, & Ho, 2017). Corrosion is partially responsible for 29% of all rock bolt failures during rockfall, which caused 40% of all fatal accidents in Australian underground mines between 1993 and 2001 (Potvin et al. 2001). Visual inspection under-estimates corrosion, an area with 10% visibly broken bolts can have 24% of the remaining bolts damaged to half ultimate capacity (Craig et al., 2016). Due to the difficulty of inspecting corrosion of the embedded rock bolt surface, corrosion is often undetectable until the bolt is weakened by corrosion, resulting in reduced capacity and sometimes unexpected falls of ground that may damage equipment and personel. There are many studies into the corrosion of ground support in the mining industry: Some are empirical research of case studies that correlate rock bolt capacity with corrosion rate and the environmental influence; others are experimental research with controlled variables. In other fields, corrosion studies are more in-depth, from analytical studies of corrosion theories to numerical models of corrosion in general. Their method can be adapted to mining, to provide insight. In these sections, the existing research is organized into six parts: introduction to ground supports; corrosion mechanism fundamentals; corrosion inhibiting measures; corrosion monitoring methods; corrosion studies; and the galvanic properties of minerals. Only studies directly related to mining or research that may be applicable to mining are included. 5  2.2 Ground Support Systems The purpose of the ground support system (Figure 1) is to keep excavations safe and open for their intended lifespan. The use of ground support is growing as mines are being developed deeper underground. About 100 million bolts were consumed in the United State in 1999 (Dolinar & Bhatt, 2000). Choquet (1991) suggest that rock bolts reinforce the ground in the following three ways: 1. Ground suspension; 2. Reinforcing bedded grounds; and 3. Preventing the movement of fissures in jointed grounds. In ground suspension mode, long rock bolts are anchored in competent ground to support the weak ground in place by holding its entire weight. To reinforce bedded grounds, rock bolts stabilize the bedding strata or the schistose ground by friction to form a thicker, self-supporting beam. In heavily fractured rock mass, rock bolts provide clamping pressure on the fissures to prevent cascading failure by restricting the movement of fragmented rock in a “keying effect”. Windsor (1997) generalized that all ground support system has four principal components: the rock; the element, the internal fixture, and the external fixture. Brady & Brown (1999) Figure 1 Artificial rock vault (L/S=2) modified from (Choquet, 1991). 6  stated that “the primary objective of support practice is to mobilize and conserve the inherent strength of the rock mass so that it becomes self-supporting”. The properties of the rock mass have a significant influence on the behaviour of the ground support system, and therefore must be considered an integral part of the system. The element is the actual rock bolt itself, which ranges from solid rebar to thin-walled Split-Set or stranded cable bolt. The internal fixture refers to the mechanism by which the rock bolt is anchored. This can be friction for Split-Set and Swellex, resin or cement grout for rebar and cable, or mechanical anchor. The external fixture includes the nut and plate that provides the confining pressure to the rock mass and the surface support like wire mesh and shotcrete that prevent loosening of rocks. Rock bolts can be categorized into three fundamental types of anchoring mechanisms: continuous mechanically coupled (CMC), continuous frictionally coupled (CFC), and discreetly mechanically or frictionally coupled (DMFC). 2.2.1 Continuous Mechanically Coupled (CMC) Rock Bolt Fully grouted bolts, including fully grouted passive cable bolts, and torque tension bolts fall in this category (Figure 2). Bolt capacity is achieved due to the mechanical bond between the grout and the textured bolt surface and the rough rock surface. The performance (He, An, & Zhao, 2014) and failure mode (Cao, Nemcik, Aziz, & Ren, 2012) of grouted rock bolts are well. Where resin grout offers an advantage in terms of installation time (Gustafson, Schunnesson, Timusk, & Hauta, 2016), cement grout provides Figure 2 Fully grouted rock bolt (left) and torque tension bolt (right) (JENNMAR, 2017). 7  additional protection from corrosion and is preferable for permanent projects (Pells & Bertuzzi, 1999). 2.2.2 Continuous Frictionally Coupled (CFC) Rock Bolt Split-Sets, sometimes known as friction stabilizers, are the most common CFC rock bolt (Figure 3). It relies on the spring action of the C shaped steel tube forced into an undersized hole to provide frictional holding power. Split-Sets are widely adopted as temporary ground support due to shorter installation time and proven holding capacity (Tomory, Grabinsky, Curran, & Carvalho, 1998). Swellex, also known as an expansion rock bolt, is a folded steel tube inflated in-hole via a hydraulic pump to provide superior frictional bond by conforming to the irregular shape of the hole. Swellexs can be made longer than Split-Sets and are also preferred for short term support due to its expedient installation process and validated performance (Skrzypkowski, Korzeniowski, Zagórski, & Dudek, 2017). Due to their tubular section, Split-Sets and Swellexs are very susceptible to corrosion. A grouted variant known as stiff Split-Set offers additional bond strength and corrosion resistance and is gaining popularity in Australia (Davison & Fuller, 2013; E. Villaescusa & Wright, 1997). Other corrosion-inhibiting coatings including galvanization for Split-Sets and polymer coating for Swellexs are available and will be discussed later. Figure 3 Friction stabilizer (top) and expansion rock bolt (bottom) (JENNMAR, 2017). 8  2.2.3 Discreetly Mechanical or Frictionally Coupled (DMFC) Rock Bolts DMFC bolts transfer the load at two discrete points by a nut and plate at the borehole collar and mechanical grout anchor or frictional expansion shell at the end of the bolt (Figure 4). The remaining length of the bolt is decoupled from the rock mass and tensioned to provide clamping pressure that stabilizes the rock mass. This rock bolt is vulnerable to stress corrosion cracking in the exposed length of rock bolt under tension.  Figure 4 Point anchor bolt (left) and expansion shell bolt (right) (JENNMAR, 2017). 2.2.4 Surface Support Rock surface support span across rock bolts to prevent loosening of fragmented rock mass and catch larger loose rock to prevent damage. Wire mesh, shotcrete, and membrane are common rock surface support systems, laboratory performance tests has shown that mesh have the best force and displacement capacity and is suitable for dynamic ground condition; shotcrete is an economic alternative conducive to rapid re-entry but loss effectiveness in high deformation environment due to its limited displacement capacity; and membranes have less force and displacement capacity than both shotcrete and mesh and is not an advisable replacement for shotcrete and mesh (Morton, Thompson, & Villaescusa, 2009). 9  2.3 Corrosion Mechanism Fundamentals Corrosion is a galvanic process where metals spontaneously oxidize to metal oxides, hydroxides, sulphides, or other more chemically stable forms. The corrosion process comprises of two half-cell reactions: an anodic oxidation reaction that liberates electrons, and a cathodic reduction reaction that consumes electrons (Figure 5). The corrosion of steel ground support element involves oxidation of iron (Equation 1). Equation 1 Oxidation of iron  𝐹𝐹𝐹𝐹(𝑠𝑠) → 𝐹𝐹𝐹𝐹2+(𝑎𝑎𝑎𝑎) + 2𝐹𝐹− (1) What cathodic reaction takes place depends on the environment the corrosion takes place. In the presence of dissolved oxygen in aqueous solution, the following oxygen reduction is possible.  Equation 2 is dominant in acidic solution and Equation 3 in neutral or basic solution. Equation 2 Oxygen reduction reaction in acids  𝑂𝑂2(𝑔𝑔) + 4𝐻𝐻+(𝑎𝑎𝑎𝑎) + 4𝐹𝐹− → 2𝐻𝐻2𝑂𝑂(𝑙𝑙) (2) Equation 3 Oxygen reduction reaction in neutral or basic solutions Figure 5 Iron corroding in water reproduced from (Hack, 2010). 10   𝑂𝑂2(𝑔𝑔) + 2𝐻𝐻2𝑂𝑂(𝑙𝑙) + 4𝐹𝐹− → 4𝑂𝑂𝐻𝐻−(𝑎𝑎𝑎𝑎) (3) In the absence of oxygen, hydrogen evolution takes place. In acidic solution, it takes the form of Equation 4 in acids and Equation 5 in neutral or basic solutions. Equation 4 Hydrogen evolution in acids  2𝐻𝐻+(𝑎𝑎𝑎𝑎) + 2𝐹𝐹− → 𝐻𝐻2(𝑔𝑔) (4) Equation 5 Hydrogen evolution in neutral or basic solutions  2𝐻𝐻2𝑂𝑂(𝑙𝑙) + 2𝐹𝐹− → 𝐻𝐻2(𝑔𝑔) + 𝑂𝑂𝐻𝐻−(𝑎𝑎𝑎𝑎) (5) In most mining conditions the groundwater is near neutral and open to the atmosphere so the cathodic reaction in Equation 3 is expected. The complete corrosion reaction for iron in oxygenated water is the sum of oxidation and reduction reactions (Equation 6). Equation 6 Typical iron corrosion reaction  2𝐹𝐹𝐹𝐹(𝑠𝑠) + 𝑂𝑂2(𝑔𝑔) + 2𝐻𝐻2𝑂𝑂(𝑙𝑙) → 2𝐹𝐹𝐹𝐹2+(𝑎𝑎𝑎𝑎) + 4𝑂𝑂𝐻𝐻−(𝑎𝑎𝑎𝑎) (6) Localized conditions in stagnant solution, however, may allow other reactions to take place. Charge conservation dictates that the sum of oxidation current must equal the sum of reduction current, and any electrode has a corrosion potential, also called the open-circuit potential (OCP), free potential, or rest potential, that fulfils this requirement. The corrosion potential is a mixed potential Figure 6 Schematic Evans diagram for corrosion of metal M by an acid showing the application of mixed potential theory (Frankel, 2016). 11  depending on both the anodic and cathodic reaction and is between the reversible potentials of the two half-reactions in the Evans diagram (Figure 6), where the intersection of anodic and cathodic slopes determines the corrosion potential and the corrosion current that predicts the corrosion rate of the system (Frankel, 2016). The anodic and cathodic curve comes from the potentiodynamic polarization curve generated via voltammetry experiment by holding a specimen at a given potential and gradually sweeping the potential while measuring the current required (Hack, 2010). Various material and environmental factors influence galvanic corrosion in addition to the difference of reversible potential of the two electrodes, and the potential distribution on the surface of a galvanic couple can be determined by the Laplace’s equation derived from Ohm’s law (Zhang, 2011):   12  Equation 7 Laplace's equation  ∇2𝐸𝐸 = 0 (7) Equation 8 Ohm's law  𝐼𝐼 = 𝜎𝜎∇𝐸𝐸 (8) 2.3.1 Uniform Corrosion Uniform corrosion can occur in the atmospheric condition in the presence of a thin-film electrolyte (Roberge, Klassen, & Haberecht, 2002) or in an aqueous environment (Figure 7). Localized condition create anodic and cathodic areas on the metal surface that change position continuously, resulting in an even corrosion over the surface (R. Hassell, Villaescusa, Thompson, & Kinsella, 2004). When the exchange of anodic and cathodic position is constrained, localized corrosion occurs. Figure 7 Schematic description of atmospheric corrosion reproduced from (Roberge et al., 2002). 13  2.3.2 Passivation Many metals including iron experience passivity due to the formation of a thin protective film of hydrated oxide (Figure 8). The formation of a passivation oxide film is an important aspect of corrosion protection. Most corrosion-resistant alloys rely on passivation, especially those of chromium ion. Passing of metal ion through this oxide film is slow and the current due to metal dissolution becomes very small when the metal is completely covered with the passive film (Thomas, 1996). This passive film is extremely thin and fragile, and its breakdown can cause localized corrosion (R. C. Hassell, 2008). 2.3.3 Pitting Corrosion Pitting corrosion is the selective attack of passive metals at defects in the passive oxide layer in the form of pits, usually covered by corrosion products or remnants of the passive film and can become autocatalytic by changing the ion concentration within the pit (Figure 9). It is more dangerous than uniform corrosion because it is difficult to detect, predict, and design against (R. Hassell et al., 2004). Frankel (1998) reviews the effects of alloy Figure 8 Pourbaix diagram for iron at 25°C (McCafferty, 2010). Figure 9 Autocatalytic pitting corrosion reproduced from (Bhandari, Khan, Abbassi, Garaniya, & Ojeda, 2015). 14  composition, environment, potential, and temperature on pitting corrosion and the mechanism of pitting from passive film breakdown to metastable pitting and pit growth. Pitting corrosion may be quantified by optical microscopy, 3d optical microscopy, and X-ray radiography by average pit depth, maximum pit depth, remaining wall thickness, and affected area (Gelz, Yasir, Mori, Meyer, & Wieser, 2010). 2.3.4 Stress Corrosion Cracking Current research by Villalba & Atrens (2008) suggests stress corrosion cracking (SCC) is caused by hydrogen embrittlement where hydrogen from the corrosion reaction diffuses into and embrittle the material, allowing crack propagation, and the corrosion at the new crack produce more hydrogen that repeats the cycle until a sudden fracturing of the remaining section (Figure 10). SCC correlates with low pH and negative potential, and cold worked steel appear to be more resistant to SCC. 2.4 Corrosion Inhibiting Measures Common corrosion inhibition measures for ground support elements include surface treatment like zinc galvanization or plastic coating, corrosion-resistant cement grout, and corrosion-resistant material like stainless steel and glass fibre reinforced polymer (GFRP). Figure 10 Typical SCC in service is associated with the initiating at a rock bolt rib, growing to a critical size, followed by fast fracture through the remaining section (Villalba & Atrens, 2008). 15  2.4.1 Galvanization Zinc galvanization is the most common corrosion inhibiting option. A galvanized Split-Set is 30~40% more expensive than uncoated black steel option (A. Craven, personal communication, January 15, 2019). A typical coating is 3 to 4 mils thick and the zinc coating cathodically protects the underlying steel even when the coating is damaged. Wire mesh, frictional stabilizer, expansion shell, thread bar, and cable bolt can all be galvanized to protect against corrosion, but the zinc coating is gradually corroded, especially in aggressive groundwater, and the actual lifespan may vary depending on the environment (JENNMAR, 2017). 2.4.2 Plastic Coating Expandable rock bolt is protected against corrosion by flexible plastic coating because it needs to be inflated during installation. A coated expandable bolt is about 35% more costly than untreated ones (A. Craven, personal communication, January 15, 2019). The plastic coating maybe 7 to 12 mils thick and can also be applied to wire mesh, thread bar, and cable bolt. By design, the plastic coating is impervious to water, abrasion-resistant, and bond tightly to steel to form an excellent corrosion-proof coating (JENNMAR, 2017). However, the plastic coating is often damaged during transportation and installation, and any damage to the plastic coating become vulnerable to localized corrosion. Although patch kits are available, it is rarely used in daily operation. Research is in progress to investigate the use of conductive polymer as a corrosion-inhibiting coating, but the mechanism and superiority of conductive polymer’s corrosion protection are still uncertain (Zarras et al., 2003). Polyurea thin spray-on liner coating for Split-Set and rebar bolt was field-tested in Turkey and found 16  to be an excellent and economical option for corrosion protection (Komurlu, Kesimal, & Colak, 2014). 2.4.3 Cement Grout Resin grout offers no corrosion protection due to microfractures from in-situ stress, even though the resin itself is inert to corrosion. Cement grout, on the other hand, offers excellent corrosion protection because the alkaline portland cement reduces the corrosion rate by neutralizing aggressive mine water and the cement grout self-heal by rehydration when a crack develops. The main downside to cement grout compare to resin grout is the set time, where resin grouted bolt can be installed in 15 minutes, cement grouted bolt take an average of 21 minutes to install (Gustafson et al., 2016). Dual protection is possible when necessary with plastic coated and cement grouted thread bar bolt. 2.4.4 Stainless Steel Stainless steel rock bolt and wire mesh are not immune to corrosion, especially in acidic groundwater. But stainless steel is more resistant to corrosion than carbon steel due to its high chromium content that readily forms a chromium oxide passivation layer inhibiting the underlying steel from corrosion. However, it is about 5 times more expensive than carbon steel depending on the alloy. Stainless steel ground supports are available at a premium in the extremely corrosive environment, although production is often limited due to low demand (A. Craven, personal communication, January 15, 2019). 17  2.4.5 Glass Fibre Reinforced Polymer (GFRP) Commonly known as a fibreglass rock bolt, GFRP rock bolt is gaining popularity in a highly corrosive environment. GFRP thread bar rock bolts are impervious to corrosion, have double the strength of normal steel, but a quarter of the weight, and is cuttable in the field. GFRP rock bolt can be an attractive option for permanent support in corrosive grounds, even with its 65% higher cost than normal thread bar (A. Craven, personal communication, January 15, 2019). 2.5 Corrosion Monitoring Methods Rehabilitation mine access is one of the most expensive practices in a ground support operation. Aside from the cost of rehabilitation itself, it is a risk to the workforce and often hampers production. To minimize the need for rehabilitation, it is best practice to monitor the ground support with geomechanical instrumentation to optimize ground support plan and monitor the deterioration of ground conditions. The cost of instrumentation is minuscule compared to the long term saving of an optimized ground support plan or the cost of an unexpected ground fall (Bawden, Tod, Lausch, & Davison, 2002). Song (2017) reviews the operating principle of current smart bolts and found two technologies: piezoceramic sensor and fibre optic sensor are dominating the field; and the development of smart bolt has matured to the point of replacing conventional sensors in several real-world applications, providing near real-time monitoring of rock bolt critical to the safety of underground mining. Specific to the risk of ground support corrosion, Ahmad, Jibran, Azad, & Maslehuddin (2014) developed a simple setup to measure polarization data of corroding rebar in concrete and calculate corrosion current density to monitor rebar corrosion in-situ. 18  2.5.1 Destructive Test There are two destructive tests that can monitor the performance of ground support elements: overcoring and pull-out test. Hassel & Villaescusa (2005) introduced overcoring techniques, which involves a large 140 mm diameter drill rig aligned to the rock bolt that retrieve the entire ground support system in-situ including the surrounding rock mass (Figure 11). This is the only definitive way to assess the corrosion damage on the rock bolt, allowing evaluation of the rock mass and grouts not typically accessible by conventional pull-out test. The pull-out test is a standardized test method for rock bolt anchor and can be performed in-situ or in a laboratory on rock core via hydraulic ram that stresses the bolt collar to failure (Figure 12) (ASTM, 2014). The failure mode (Figure 13) of pull out test indicates installation quality, overall capacity, and possible damage of the rock bolt (Choquet, 1991). The pull-out test is the most widely adopted method for evaluating rock bolt performance, and the numerous pull-out test result provides an empirical basis for interpretation of results (Kristjánsson, 2014; Nicholson, 2016; Thenevin et al., 2017). However, its result is sometimes inconclusive if the rock bolt damage is not significant. In fact, slightly corroded frictional stabilizer exhibits increased holding Figure 11 Overcored resin grouted rock bolt (R. Hassell et al., 2004). Figure 12 Pull-out test equipment (JENNMAR, 2017). 19  capacity as corrosion product increase confining pressure on the rock bolt until corrosion eventually destroy the rock bolt.  Figure 13 Pull-out failure modes of fully grouted rock bolt (Choquet, 1991). 20  2.5.2 Non-destructive Test The pull-out test can also be performed non-destructively by loading the bolt to 75% of rated capacity. However, such a method passes many bolts that would have failed in standard pull-out test and leaves uncertainty in the integrity of the system. Other non-destructive tests for rock bolt includes Boltometer that measures impedance between the grout and surrounding rock on grouted bolts; JK rock bolt tester that measures the frequency response function of the bolt; the ground anchorage integrity testing (GRANIT) system that uses neural network to analyse vibration response from an impact device; ultrasonic guided wave testing that can detect bolt length and major defects; and modified shock test that identifies bolt length, grout position, and major defects based on mechanical admittance (Hartman, Harvey, Lecinq, Higgs, & Tongue, 2010). Zaki, Chai, Aggelis, & Alver (2015) evaluates other non-destructive test methods for corrosion monitoring of steel-reinforced concrete that are applicable to mining, including open circuit potential (OCP) monitoring used to monitor rock bolt corrosion (Spearing, Mondal, Bylapudi, & Hirschi, 2010), ground-penetrating radar (GPR) that can qualitatively assess the corrosion damage, and optical sensing method like fiber Bragg grating (FBG) that has been adopted as a promising smart rock bolt sensing technology (Song et al., 2017). 2.5.3 Smart Rock Bolt There are two categories of smart rock bolt. The first type is instrumented with strain gauges within the bolt that monitors axial load and strain distribution along the length of the bolt. There are several conventional vibrating wire strain gauges spread out along the bolt (Brahim, Mohamed, & Haixue, 1995) or more recently fibre optic strain gauge that can 21  monitor strain distribution continuously (Grattan et al., 2007; Zou, Sezerman, & Revie, 2008). The increased strain at one point may indicate necking of rock bolt from the reduced cross-sectional area and a distributed strain increase may be caused by the stress of increasing corrosion product layer thickness. The second type is a non-destructive sensor attached to the head of the bolt, National Research Council Canada developed a rock bolt sensor (RBS™) using ultrasonic echo to identify bolt defects (Figure 14) (Quenneville, 2018). Piezoelectric transducers are typically used in this type of rock bolt and require minimal modification to off-the-shelf rock bolt. Smart rock bolts may be tied into a multichannel recorder for real-time monitoring or integrated with radio frequency identification (RFID) tag for manual readout by portable recorders (Song et al., 2017).  Figure 14 RBS™ ultrasonic sensor principle (Quenneville, 2018). 2.6 Corrosion Studies The underground mining condition is commonly corrosive to ground support elements with high humidity, polluted mine air, and aggressive groundwater. Yet the mechanism of corrosion is not adequately studied in the mining industry. Early researches are often 22  qualitative overviews of mine corrosion based on visual inspections and personal interviews (Hoey & Dingley, 1971), others focus on the corrosion of mill equipment and ignore ground support all together (Sastri, Hoey, & Revie, 1994). Current research efforts are mostly empirical, drawing correlations between atmospheric and groundwater quality and corrosion rate by environmental classification, in-situ experiment, and laboratory experiment. And borrowing from the field of corrosion research, numerical simulations that may apply to ground support corrosion are presented. 2.6.1 Environmental Classification Li & Lindblad (1999) proposed two corrosivity classification systems specifically for rock bolt corrosion in the underground environment in wet and dry conditions using parameters like pH, dissolved oxygen (DO), resistivity, and relative humidity. Hassel et al. (2004) validate the applicability of Li & Lindblad (1999) classification system with data from 8 Australian mines. Villaescusa et al. (2007) contradicts that and found previous corrosion classifications, including Li & Lindblad (1999), do not apply to Australian underground mine; rather, atmospheric corrosion is controlled by relative humidity and groundwater corrosion by dissolved oxygen. More recently, Roy, Preston, & Bewick (2016) reviews the corrosion mechanisms in the aqueous environment and purpose a new classification method (Figure 15) for determining aqueous corrosion rate using pH, total dissolved solids (TDS), and dissolved oxygen (DO).  23   Figure 15 Classification of aqueous corrosion environment, reproduced from (Roy et al., 2016). 2.6.2 In-situ Experiment Corrosion is heavily influenced by environmental factors, and every mine is unique. Due to the complex atmosphere, groundwater, and rock mass qualities in underground mines, in-situ experiment like direct exposure of metallic coupon is often used to measure the corrosion rate of steel in mining operation condition. Hassell (2008) conducted overcoring of old bolts, long term corrosion coupon test, and laboratory corrosion chamber test of rock bolt corrosion result in corrosivity classification of groundwater and the atmospheric environment as well as estimated rock bolt service life to corrosion rate for various rock bolts in Australian hard rock mine. Similar corrosion coupon tests conducted in Canadian mines with tensile strength testing quantified the capacity lost due to corrosion and a flow chart method for characterizing the corrosivity of the environment was developed for selecting ground support (J. F. Dorion & Hadjigeorgiou, 2014; Jean Francois Dorion, Hadjigeorgiou, & Ghali, 2009, 2015). A limitation of coupon test for groundwater influenced corrosion is that coupon placed at the excavation boundary experience irregular groundwater flow and underestimates Aqueous corrosionNeutral Conditions4<pH<10Acidic ConditionpH<4Fresh WaterTDS Range:0 to 1000 ppmLow SalinityTDS Range:1000 to 3,500 ppmHigh SalinityTDS Range:3,500 to 200,000 ppmDissolved Oxygen<2.0 mg/LDissolved Oxygen2.0 to 3.0 mg/LDissolved Oxygen>3.5 mg/LDissolved Oxygen3.0 tp 3.5 mg/LHigh/Severe Corrosion>0.3 mm/yearExponential rate increase as pH decreasesHighly influenced by temperatureHigh Corrosion0.3 to 0.4 mm/yearModerate Corrosion0.2 to 0.3 mm/yearLow Corrosion0.1 to 0.2 mm/yearLittle Corrosion0.01 to 0.1 mm/year24  corrosion rate. Craig et al. (2016) developed a non-standard in-hole corrosion coupon test designed to investigate stress corrosion cracking of ground support in an Australian coal mine and found that interaction between groundwater and a claystone band contributes to corrosion. While corrosion coupon is an excellent method to quantify corrosion rate, it does not address the important effect of non-uniform corrosion. Chambers, Sunderman, Benton, Brennan, & Orr (2017) conducted in-situ rock mass conductivity study in an American mine and found that corrosion is primarily influenced by electrochemical properties of the rock with possible microbe induced corrosion (MIC) from sulphate-reducing bacteria (SRB). 2.6.3 Laboratory Experiment To determine the environmental influence of corrosion in a controlled manner, various rock bolts are allowed to corrode in a simulated underground environment with closely maintained temperature, humidity, and continuous artificial groundwater flow to determine their service life (R. C. Hassell, 2008). Spearing, Mondal, & Bylapudi (2010) investigated aqueous corrosion of grouted rebar bolt in artificial mine water tank and found that resin grout does not inhibits corrosion due to development of microfractures, corrosion is localized in threaded part of the rebar, and that uniform corrosion of rebar bolt is not a safety concern in short term support. Aziz, Craig, Nemcik, & Hai (2014) performed a similar corrosion test of threaded rebar bolt in open atmosphere with various load and torque condition accelerated by acidic mine water dripping and found no correlation between loading and corrosion. Electrochemical study of ground support corrosion attempts to predict the corrosion rate using the theoretical mechanism of corrosion. The polarization curve of galvanized and steel Split-Set sample in artificial mine water showed that galvanization is an effective way to 25  prevent pitting corrosion in Split-Set. While calculated corrosion rate from the electrochemical method is questionable after the formation of the surface product, it is useful to compare between materials and mine waters (Tilman, Jolly, & Neumeier, 1984). By measuring the polarization curve of bolt steel, the open circuit potential (OCP) of the rock bolt is compared to the OCP between the rock bolt and the rock mass measured in the field to determine if corrosion will occur (Spearing et al., 2010). 2.6.4 Numerical Simulation Numerical simulation of corrosion was predominantly modelled with the boundary element method (BEM) due to its computational advantage for only calculating the potential distribution on the metal surface. However, BEM cannot model transient progressions of corrosion boundary. Bin (2013) combined cellular automata (CA) and BEM to simulate the growing profiles of pitting corrosion. CA is used to simulate corrosion damage while BEM is used to model the potential gradient. Chen & Bobaru (2015) developed a peridynamic (PD) model for pitting corrosion that bypasses the mathematical discontinuity at the corrosion front by considering corrosion as diffusion of metal ion from solid to metal phase. Their work is later expanded to model lacy covered pitting corrosion (Chen, Zhang, & Bobaru, 2016), stress corrosion cracking (De Meo, Diyaroglu, Zhu, Oterkus, & Siddiq, 2016), and implemented into a commercial finite element platform (COMSOL) capable of creating realistic pit morphology and modeling intermetallic particles in pitting corrosion (De Meo & Oterkus, 2017). Phase-field model use a diffused interface to approximate the evolution of a discontinuous corrosion front, allowing simulation of stress corrosion cracking (SCC) operating under the film rupture-dissolution-re-passivation mechanism by minimizing the 26  free energy in the system and couple the corrosion process with mechanical stress (Mai & Soghrati, 2017). COMSOL is implemented with finite element method (FEM) and models corrosion front as a sharp boundary. The dynamic movement of the corrosion boundary is achieved by conforming mesh between time-steps. Brewick et al. (2017) modelled the effect of crystallographic orientation on pitting corrosion using FEM based COMSOL Multiphysics and showed the effect of microstructure to the geometry of corrosion pit while maintaining the average pit growth rate. 2.7 Galvanic Property of Minerals Galvanic interaction of minerals is a well-known phenomenon. Existing studies are focused mostly on the potential of sulphide minerals to enhance leaching performance by galvanic interaction (Chmielewski, 2010; Liu et al., 2018; Madhuchhanda, Devi, Srinivasa Rao, Rath, & Paramguru, 2000), and the galvanic interaction between sulphide minerals and steel that changes surface properties and impacts the flotation process (Adam, Natarajan, & Iwasaki, 1984; Allahkarami, Zarepoor, & Rezai, 2014; Azizi, Shafaei, Noaparast, & Karamoozian, 2013; Gu, Dai, Wang, & Qiu, 2004; Huai, Plackowski, & Peng, 2018; Nowak, Krauss, & Pomianowski, 1984; Qin et al., 2015; Rao & Finch, 1988). Self-heating between sulphide minerals due to galvanic corrosion was investigated in relation to shipping and handling practice (Payant, Rosenblum, Nesset, & Finch, 2012). Galvanic corrosion of metal by sulphide and oxide minerals in sulfuric acid in terms of mineral processing equipment demonstrate the potential for heterogeneous rock mass to corrode steel ground support (Jones & Paul, 1994). 27  2.8 Conclusion Current knowledge of ground support corrosion in underground mining is presented in this chapter. There is a good grasp of corrosion mechanisms and the uniform corrosion rate can be predicted by classifying corrosivity of the environment. However, state of the art corrosion research only considered localized corrosion due to groundwater contact through rock joints, and current numerical model of corrosion is limited to a single corrosion pit. A gap of knowledge exists in the effects of rock mass on corrosion. Galvanic interaction between steel and minerals need to be investigated for their influence on localized corrosion. And cutting-edge numerical tool can expand the knowledge of corrosion mechanism to the complex geometry and environmental variable in the mining industry. 28  Chapter 3: Methodology 3.1 Introduction To address the knowledge gaps on localized ground support corrosion and the effect of the heterogeneous rock mass, numerical model for generic corrosion research was modified to simulate corrosion damage under the electrochemical influence of various minerals. The research procedures are presented in this chapter from sample characterization and measurement of input parameters for the numerical model; to the setup procedure for the numerical simulation of corrosion; and the submersion experiment that validated the numerical model. 3.2 Sample Characterization An understanding of minerals and steel property, as well as groundwater quality, is required to evaluate the corrosion of rock bolt embedded in a heterogeneous rock mass. Various rock samples, rock bolt samples, and groundwater samples were acquired from the Greens Creek mine in Juneau, Alaska (see Figure 16 and Appendix A  ); pure mineral samples were purchased from Ward’s Science (see Appendix B  ), and steel strip samples used to make frictional stabilizer were obtained from JENNMAR the rock bolt manufacturer. Figure 16 Rock, mine water, and rock bolt sample from Greens Creek mine. 29  3.2.1 Sample Preparation The rock samples from Greens Creek were sawn into slabs of adequate thickness for coring of rock core electrodes, polished to the appropriate surface finish for microscopic imagery, cored to a uniform dimension for conductivity and electrochemical measurements, and pulverized for X-ray powder diffraction (XRD) analysis. Sawing The rock samples were sawn into slabs of 1-inch thickness with a wet tile saw. The thickness of the slab was determined by the length of the diamond hole saw used to collect core samples. Sample 1, 3, and 19 were selected as representative samples and two adjacent slabs sharing the same cut face (Figure 17) were chosen from each sample, one side was photographed under microscope for mineral segmentation and used to perform a submersion test to validate the numeric model; the other side was used to make rock core electrodes (RCE) and single mineral electrodes (SME) for electrochemical measurement used as input parameter for the numerical simulation. Rock Coring To ensure a uniform surface area, a ¾” diamond hole saw was used to collect the rock core samples (Figure 18). It is large enough to collect intact rock core, but not too large to fit into a typical electrochemical reaction cell. A drill press was used to collect the rock core sample with water as Figure 17 Paired rock slabs (sample 3). Figure 18 Collecting rock core with ¾" diamond hole saw. 30  lubrication and coolant from 1-inch thick electrode slabs and bulk samples, but the same can be done with a hand drill and spray bottle in the field. A ¼” diamond hole saw was used to isolate pure mineral samples. Figure 19 shows electrode slabs after coring.  Figure 19 Paired electrode slabs from sample 1 (up), sample 3 (left), and sample 19 (right). Surface Grinding The rock cores collected using a ¾” diamond hole saw had uneven ends that needed to be ground flat perpendicular to the cylinder edge. This was done with a surface grinder (Figure 20). The rock cores were mounted on a jig and the two ends are grounded flat to a perfect cylinder. Figure 20 Rock core before (left) and after (right) surface grinding. 31  Polishing The submersion slab samples were hand polished to a mirror shine with incremental wet sanding paper from 400 to 3,000 Grit on top of a flat glass plate so that rough surface finish from the saw do not diffract light and the true colour of the mineral can be photographed under the microscope without wetting (Figure 21). The rock core electrodes and single mineral electrodes were also hand-polished to 3,000 Grit on the glass plate in a figure-eight pattern to minimize the effect of surface roughness during voltammetry. Rock Core Electrodes (RCE) Procedures for preparing mineral electrodes as described by (Rao & Finch, 1988) and (Jones & Paul, 1994) were adapted to prepare the rock core electrodes (RCE) (Figure 22) for electrochemical measurements. After surface grinding, a 5/32” recessed hole was drilled on the top of the ¾” rock core samples with a carbide bit to facilitated electrical contact to a solid number 10 AWG bare copper wire lead with conductive silver epoxy. The copper wire was encased in 6mm OD x 4mm ID flint glass tubing to insulate against the electrolyte. The glass tube was epoxied to the rock core to form a watertight seal, and the surface of rock Figure 21 Polished rock slab (sample 19). Figure 22 Rock core electrodes. 32  core was masked with dielectric silicone caulking leaving only the bottom circular test area exposed to the electrolyte. Single Mineral Electrodes (SME) The single mineral sample collected with ¼” diamond hole saw was slightly smaller than the inside diameter of the glass tube and will be inserted into to the end of the glass tube butted against a solid number 10 AWG bare copper wire and form an electrical contact using silver epoxy. The core was then sealed with epoxy to insulate silver epoxy and copper wire against electrolyte and polished to reveal the electrode surface (Figure 23). Table 1 below list pure mineral samples from Ward’s Science and if ¾” or ¼” core is collected. Figure 23 Construction of single mineral (left) and rock core (right) electrodes. 33   Table 1 List of pure minerals from Ward's Science.  Steel Electrode (SE) A ¼” strip was cut from stock bolt steel and one end was hand polished to 3000 grit to remove mill scale and surface treatment to establish a uniform surface finish. The exposed length of steel electrode (SE) is calculated using its width and thickness so the exposed surface area is equal to the circular surface area of ¾” rock core electrode (RCE). The rest of the steel surface was covered with dielectric silicone caulk to insulate against electrolyte, leaving only the top exposed to connect by alligator clamp to the potentiostat (Figure 24). ID Name Location Formula MW SG 3/4 core 1/4 core C/A1 Bornite KG Zacatecas, MX Cu₅FeS₄ 501.88 5.07 M1 Cathode2 Calcite KG Minas, Nuevo Leon, MX CaCO3 2.71 M23 Chromite KG Stillwater Montana USA (Fe, Mg)Cr2O4 4.65 M3 Anode4 Graphite-Pure KG Columbo Sri Lanka C 2.15 Graphite-Foliated KG Buckingham Twp, ON, Canada C 2.16 Gypsum-Selenite KG WA Co., Utah, USA CaSO4·2H2O 172.17 2.9 M6 Cathode7 Gypsum-Satin Spar KG Highland, Arkansas, USA CaSO4·2H2O 172.17 2.98 Hematite-Massive/Red KG Hoyt Lake MI USA Fe2O3 5.26 M8 M8 Anode9 Hematite-Red/Oolitic KG Clinton NY USA Fe2O3 5.2610 Hematite KG Red Ochre Custer SD USA Fe2O3 5.26 M10 Anode11 Hematite-Banded KG Hoyt Lake MI USA Fe2O3 5.2612 Ilmenite-Massive KG St. Urbain Quebec Canada FeTiO3 4.74513 Kaolin-Massive KG Twiggs Co. Georgia USA Al2Si2O5(OH)4 2.4214 Limestone-Oolitic KG Bedford, Indiana, USA 2.515 Magnetite KG Isheming, MI, USA Fe2+Fe3+2O4 5.175 M15 M15 Anode16 Malachite KG Arizona, USA Cu2CO3(OH)2 221.1 3.8 M16 M16 Anode17 Phyllite KG Ely, Vermount, USA 2.72518 Pyrite KG Huanzala, Peru FeS2 119.98 5.025 M18 Anode19 Quartz-Chalcedony KG SiO2 60 2.6 M19 Anode20 Quartz-Chert KG Joplin, Missouri, USA SiO2 60.083 2.65 M20 Anode21 Quartz-Flint KG Dover Cliffs, England SiO2 60.08 2.7 M21 Anode22 Sphalerite KG Piedras Verdes, Chihuahua, MX (Zn,Fe)S 4.05 M2223 Talc-Soapstone KG Schuyler, Virginia, USA 2.75 M23 M23 Cathode24 Talc-Foliated KG Van Horn, Texas, USA Mg3Si4O10(OH)2 2.705Figure 24 Steel electrode in electrochemical cell. 34  Pulverization After the submersion experiment was completed, the paired slab samples used for making electrodes were crushed by benchtop jaw and cone crushers before being pulverized in a ring mill to 425 µm particle size by passing a #40 sieve (Figure 25). The pulverized samples were submitted for X-ray powdered diffraction (XRD) analysis for a positive mineral content identification. 3.2.2 X-ray Fluorescence (XRF) X-ray fluorescence (XRF) is a non-destructive analytical technique that can be performed by a portable scanner directly on grab samples with no special preparation (Figure 26). It determines the elemental composition of the sample by displacing electrons from the inner orbital shells of the atom with x-ray beam and measures the fluorescence emitted when electrons from higher orbits fill the vacancy in inner orbits. The energy emitted as fluorescence is proportional to the distance between orbits, which is unique to the atom. Allowing elemental composition of the sample to be determined, but cannot differentiate minerals with the same elemental composition but different crystalline structures. XRF analysis was performed on all rock samples from Greens Creek verify rock classification provided by their Geotechnical engineer. Figure 26 Portable XRF in shielded scanning station. Figure 25 Ring mill used to pulverize XRD samples. 35  3.2.3 Acidity and Conductivity of Electrolytes pH and electrical conductivity of the mine water sample from Greens Creek were measured with a handheld pH meter and total dissolved solids (TDS) meter. The result was used to make up three batches of artificial mine water for the conductivity experiment with the same pH as mine water and conductivity a magnitude greater, same, and smaller than the mine water sample. This was done by adjusting pH of deionized water with diluted 0.1M sodium hydroxide (NaOH) and hydrochloride acid (HCl) to match the pH of mine water, then add pickling salt to reach the desired electrical conductivity (or 10 times greater/lower). Pickling salt was used because it is commonly available and contains no additives like potassium iodide or anti-caking agent.  Acidity The pH of groundwater determines the mechanism of corrosion, and a wide range of pH can be found in the mining environment from alkaline drainage from cemented backfill to acid drainage from the oxidation of sulphide minerals. This research investigates corrosion from an electric potential angle, and a calibrated handheld pH meter is used to measure the pH of the mine water and make up artificial mine water matching the same acidity. Electrical Conductivity Total dissolved solids (TDS) meter is also known as electrical conductivity (EC) meter. It measures the electrical conductivity of the solution and converts the reading to estimates TDS in ppm by a multiplier specific to the ionized solid, usually 500 for NaCl ions. The electrical conductivity of the groundwater has a significant effect on corrosion. A more conductive electrolyte accelerates corrosion by reducing resistance to the galvanic current. 36  However, less conductive electrolyte localizes the corrosion damage to the detriment of ground support capacity. And the electrical conductivity of a porous rock is related to the conductivity of the electrolyte it is saturated with. The handheld TDS meter was calibrated by 6 standard NaCl solutions from 0.08M to 0.0016M and deionized water. It was used to measure the conductivity of the mine water sample and make up artificial mine waters 10 times more conductive, as conductive, and 10 times less conductive as mine water. The conductivity of mine water was used in two places in the simulation: to calculate the potential distribution in the electrolyte, and to calculate the current density from the potential gradient in the user-defined function (UDF).  Total Dissolved Solid (TDS) by Evaporation Total dissolved solids (TDS) of the mine water before and after submersion experiment and the three artificial mine water with varying conductivity was also measured by gravimetric analysis (Figure 27). The mine water was weighted in a clean beaker with known weight and evaporated in the oven until only the solute remains. The solute in the beaker is then weighted and the TDS calculated from the tare weight of solute and solvent. Unlike the conductivity method of measuring TDS, inorganic salt and ionic salt other than NaCl was accurately measured. Figure 27 Gravimetric TDS analysis of mine water after submersion experiment. 37  3.2.4 The resistivity of Rock and Minerals The conductivity of rock and mineral core samples was measured dry and saturated in deionized water, low conductive artificial mine water, medium conductivity artificial mine water, high conductivity artificial mine water, and mine water (Figure 28). The electrical connection was made by copper tape with conductive adhesive backing covering the flat ends of cylindrical core, and the electrical resistance (R) was measured with a multimeter. The cross-sectional area (A) and length (l) of the core samples were measured with a caliper to calculate the electrical resistivity (ρ) of rock and mineral in ohmmeter (Ω⋅m) (Equation 9). Equation 9 Electrical resistivity  𝜌𝜌 = 𝑅𝑅 𝐴𝐴𝑙𝑙 (9) 3.2.5 Linear Sweep Voltammetry (LSV) Formally known as linear potential sweep chronoamperometry, linear sweep voltammetry (LSV) is a voltammetric method that measures the current at the working electrode as the potential between the working electrode and a reference electrode is swept linearly in time (Figure 29). The resulting current (i) and potential (E) can be plotted in a semi-log graph of potential (E) and current Figure 28 Resistivity measurement of rock core saturated in mine water. Figure 29 3 electrodes electrochemical cell with Rodeostat. 38  density (logJ) known also as Tafel plot and polarization curve that relates the rate of the electrochemical reaction to the overpotential. The LSV was conducted on all rock core electrodes (RCE), single mineral electrodes (SME), and the steel electrode (SE) as working electrode using Rodeostat: the open-source potentiostat from IO Rodeo with Ag/AgCl reference electrode and platinum wire counter electrode from CH Instruments. The experiment was conducted in mine water agitated by a magnetic stirrer. And the result was collected in Rodeostat web interface and exported in comma-separated values (CSV) format. Sweep Rate The resultant current-potential (i-E) response curve of LSV was dependent of the sweep rate (ν) in (V/s) such that the peak current (ip) is proportional to the square root of the sweep rate (Bard & Faulkner, 2001). Equation 10 Peak current function  𝑖𝑖𝑝𝑝 = (2.69 × 105)𝑛𝑛3 2⁄ 𝐴𝐴𝐷𝐷𝑂𝑂1 2⁄ 𝐶𝐶𝑂𝑂∗𝜈𝜈1 2⁄  (10) A sweep rate of 0.5V/s was used to keep the response current of rock and mineral electrodes within Rodeostats’ current measurement ranges of ± 1000 uA. Tafel Extrapolation in Python A python script was written in the Jupyter notebook to process the data from linear sweep voltammetry. First, the output files from Rodeostat in CSV format were read and concatenated into a panda data frame, then a Savitzky-Golay filter was applied to the current (i) to reduce noise, and the logarithm of current density (logJ) was calculated. Each response curve was separated into cathodic and anodic curves where current equals zero; and linear 39  regression was performed on each curve on a loop, dropping data points from the heads and tails of the curve until a linear segment is selected where a threshold R-squared value of 0.98 was met signalling a good fit and the intersection of cathodic and anodic extrapolation coincide with the open circuit potential (OCP) where current equals zero. All characterizing parameters are exported in CSV format and the Tafel curve with cathodic and anodic extrapolation and the linear range were plotted in PDF format. Mixed Potential The concatenated response curves exported from Jupyter notebook were further processed in MS Excel. The polarization curve of mineral electrodes was overlaid with that of steel electrode and the intersection of the mineral cathode curve and steel anode curve indicates the mixed corrosion potential (Ecorr) and corrosion current density (Jcorr) and the corrosion rate of the galvanic couple were determined. The corrosion current density (Jcorr) of minerals coupled with steel was later used as a boundary condition in the numerical model for corrosion. 40  3.2.6 Microscopic Photography  Tiled photographs of the polished rock slab samples were taken with an AmScope MU series microscope camera and a stereomicroscope equipped with a ring light (Figure 30). A graphing paper was used beneath the sample to align the sample instead of motorized stages. ImageJ was used to stitch the microscopic image together using both pairwise stitching and big warp plugins. The stitched microscopic image was later segmented at the mineral boundary to create the mesh used in numerical simulation. 3.2.7 X-ray Powder Diffraction (XRD) X-ray powder diffraction (XRD) can positively identify mineral samples of different crystalline phases by comparing peaks of degrees in diffracted X-ray with a Database of known samples. The samples were pulverized after the submersion experiment and submitted for XRD Rietveld quantitative phase analysis to identify the mineral composition of samples in order to assign mineral identities to the segmented sample images. 3.3 Numerical Simulation of Corrosion Numerical simulation has the advantage of applying well-understood corrosion mechanics to a complex system of varying geometric and environmental condition. This makes numerical simulation a promising tool for predicting corrosion Figure 30 Microscopic photograph of slab sample. Figure 31 Simplified geometry for ground support corrosion. 41  damage of ground support element in an underground mining environment. To apply numerical simulation to ground support corrosion, a simplified case is examined. A frictional stabilizer installed in a continuous rock mass with heterogeneous mineral distribution and saturated with groundwater was simplified to a flat steel plate in close contact with a flat rock slab with heterogeneous mineral distributions where the gap between steel and rock was filled with groundwater (Figure 31). 3.3.1 Segmentation The stitched microscopic image of the submersion slab sample was segmented by colour in ImageJ using RGB filters. Some user discretion was required in this step. For example, a pyrite crystal may be photographed as white in the centre with yellow hue in the parameter depending on how light reflects off the surface, so a yellow ring with white core was coloured yellow to represent pyrite crystal. Other imperfections like saw marks on the edge may present as white streaks that need to be differentiated from quartz vein. All samples were segmented to 3 or 4 major mineral components by colour. While trace amounts of other minerals may present in the samples, they were ignored in the corrosion model. Colour segmentation was selected because the samples contain visually distinguishable minerals. If that was not the case, however, other technologies such as ultraviolet microscopy or micro-computed tomography (micro-CT) may be used to the same effects. 3.3.2 Geometry The gap between the frictional stabilizer and the rock mass depends on the roughness of the drill hole. In the submersion validation experiment, the geometry of a rock bolt is simplified 42  to a flat steel plate zip-tied to a rock slab and submerged in mine water. The geometry of the numerical model matches that of the submersion experiment. The fluid domain being modelled is assumed to be 500 microns thick and bounded by steel and rock slab on either side, while exposed to bulk solution everywhere else. 3.3.3 Meshing Hexahedral, tetrahedral, and cut cell mesh methods were used when appropriate to obtain high-quality mesh with minimum cell count. Using adaptive meshing, the mesh was refined to 8 cells across the 500-micron domain in the finest features where preferential corrosion was expected and 2 cells across the domain where uniform corrosion was expected. The results were high definition mesh with one to two million cells depending on the complexity of the model. 3.3.4 Cell Zone Conditions A mine water fluid domain was created for all corrosion models with the same property as liquid water and a custom electrical conductivity σ that was equal to the average of mine water conductivity before and after the submersion experiment (0.68 S/m). 3.3.5 Boundary Conditions At all steel surfaces, the boundary condition was set to the open circuit potential (OCP) of steel at -0.97V as determined in LSV. At each segmented mineral surface, boundary Figure 32 Simplified boundary condition. 43  conditions were set to the corrosion current density of minerals in respect to steel determined in the mixed potential analysis. At the edge where the fluid domain was connected to the bulk solution, the current density was set to zero (Figure 32). 3.3.6 Electric Potential Solver The electric potential solver was enabled in the corrosion simulation, which solved the following electric potential equation. Equation 11 Electric potential equation  𝛻𝛻 ∙ (𝜎𝜎𝛻𝛻𝜎𝜎) + 𝑆𝑆 = 0 (11) Where φ is the electric potential, σ is the electric conductivity, and S is the source term. Note that there is no transient term in the electric potential equation, and the electric potential is solved at steady state with all boundary condition populated. In the transient simulation, the electric potential was solved every time-step after the user-defined function (UDF) has updated the geometry of the boundary surface. 3.3.7 User-Defined Function (UDF) Although Ansys fluent does not support galvanic corrosion simulation natively, it does have an electric potential module and a robust user-defined function. Using the predefined macro DEFINE_GRID_MOTION, A simple UDF was written to model the corrosion damage based on potential gradients (see 0). Looping through all faces, the unit face normal vector wass calculated, and the potential gradient vector stored in the adjacent cell centre were called to the face. Current density J was calculated with Ohm’s law (Equation 12) from electrolyte 44  conductivity σ and the potential gradient 𝛻𝛻𝜎𝜎. Equation 13 was used calculate the corrosion rate, where MW was the equivalent weight of steel calculated from mill certificate (ASTM, 2015), z was the valance number (2, for Fe2+), F was the Faraday’s constant, and ρ was the density of steel (Deshpande, 2010). And all node positions were updated in a loop every time step. Equation 12 Ohm’s law  𝐽𝐽 = 𝜎𝜎(𝛻𝛻𝜎𝜎) (12) Equation 13 Corrosion rate  Corrosion rate = 𝑀𝑀𝑀𝑀𝑧𝑧𝐹𝐹𝜌𝜌𝐽𝐽 (13) The UDF was hooked to the dynamic mesh zones as a user-defined mesh motion on all steel zones, with dynamic mesh enabled, diffusion smoothing, and default remeshing. 3.3.8 Simulation The corrosion simulation was first initiated and ran on steady-state to obtain the potential gradient over the cell zones before running at a fixed time-step of 86,400 seconds (1 day) for 100 time-steps. The duration of 100 days was chosen as a suitable time frame for submersion experiment, and the simulated corrosion profile after 100 days was visually compared with that of the submersion test and the corrosion depth compared by confocal microscopy to the submersion test samples for validation. 45  3.4 Submersion Experiment Designed to reflect the domain simulated in the numerical model, the submersion experiment involves 3 flat pieces of bolt steel each zip-tied to 3 selected rock slab samples with heterogeneous mineral distribution and submerged in mine water for 100 days before being retrieved, cleaned under running tap water, dried in an oven, and observed under a confocal microscope for corrosion profile (Figure 33). 3.4.1 Rock Core Electrode (RCE) Matrix Besides the 3 slab samples chosen for submersion experiment, all rock core electrodes (RCE) are grouped together to construct an RCE matrix by zip-tie and dielectric silicone caulking for submersion corrosion test (Figure 34). 3.4.2 Steel Sample Preparation The bolt steel strips provided by the manufacturer were first flattened and cut to a suitable dimension slightly larger than the rock slab samples. The steel surface is then sanded and polished by hand to 3,000 grits to remove the existing passivation layer and surface defects that may encourage localized corrosion. Figure 33 Submersion test after 70 days. Figure 34 RCE Matrix. 46  3.4.3 Confocal Microscopy Olympus LEXT OLS3100 laser scanning confocal microscope (Figure 35) was used for surface profile characterization of the corroded bolt steel plate from the submersion experiment. It is a non-contact and non-destructive optical profilometry technique that requires no sample preparation. By blocking out of focus light with a spatial pinhole, multiple 2D images at different depth are reconstructed to a 3D structure. It has the maximum of 120 nm lateral and 10 nm axial resolution and a motorized stage capable of image stitching up to a 5x5 array. Features of interest like a corrosion pit, colour change boundary, or known mineral boundary were marked with masking tapes and observed under the confocal microscope. The 2D optical image is recorded, followed by 3D confocal scanning, and the profile step of the feature is measured with some surface roughness measurement when appropriate. The profile of the feature was compared to that of the numerical model for validation. 3.5 Conclusion This chapter describes the research methodology designed to investigate the effect of the electrochemical property of minerals on localized ground support corrosion using numerical simulation. The procedures for sample preparation and an array of tests designed to provide input parameters for the numerical model was described in sample characterization. The Figure 35 Olympus LEXT OLS3100 laser scanning confocal microscope. 47  numerical model employed here combines steady-state electrical potential solver with a UDF for tracking corrosion damage to simulate corrosion damage over time. And a submersion corrosion experiment was designed to validate the numerical model. 48  Chapter 4: Results 4.1 Introduction The results of sample characterization, numerical simulation, and submersion experiment are presented in this chapter. 4.2 Sample Characterization The goal of sample characterization was to obtain the necessary information for the numerical simulation of localized ground support corrosion influenced by mineralogy.  Table 2 Greens Creek sample description. Sample Location Preliminary description1 POA 525/548 bulky corrosive graphitic argillite2 PD2853-368/460 bulky corrosive phyllite3 795 non-corrosive phyllite4 795 non-corrosive phyllite5 795 non-corrosive phyllite6 795 non-corrosive phyllite7 795 non-corrosive phyllite8 795 non-corrosive phyllite9 90XC graphitic argillite10 90XC graphitic argillite11 90XC graphitic argillite12 90XC graphitic argillite13 90XC graphitic argillite14 90XC graphitic argillite15 90XC graphitic argillite16 M540 non-corrosive argillite17 M540 non-corrosive argillite18 M540 non-corrosive argillite19 n/a overcored corrosive argillite20 n/a corroded galvanized split-set with plate in #1921 n/a new black steel split-set22 n/a new galvanized split-set23 n/a corroded swellex bolt with plate24 M480 dripping water from rock not from equipment or paste49  4.2.1 X-ray Fluorescence (XRF) of Rock Samples XRF scanner was used to obtain the elemental composition of rock samples (see Appendix A  ). The rock samples from Greens Creek came with preliminary descriptions from the field (Table 2) that classify the rock as either argillite or phyllite based on visual cues. Note that sample 1, 2, 3, 16 and 19 are too big to fit into the shielded XRF housing and was not scanned.  Figure 36 Stacked column graph of XRF result. The XRF results (Figure 36) showed two groups of samples: sample 4~8 were preliminarily described as non-corrosive phyllites and the elemental analysis was dominated by iron (Fe) and sometimes potassium (K); sample 9~15, 17 & 18 were preliminarily described as graphitic or non-corrosive argillites and the elemental analysis was dominated by Ca. Phyllite is often associated with chlorite, which contains iron, and mica, which contains potassium; 50  with XRF along, it was undetermined what calcium (Ca) bearing minerals were in the argillite samples. But later X-ray powdered diffraction (XRD) of sample 1, which was also described as graphitic argillite, reveals that it was predominately dolomite (CaMg(CO3)2). The triangle plot (Figure 37) of XRF data on three normalized K, Fe, and Ca ratio exhibited two separate groupings of phyllite and argillite samples. 4.2.2 Mine Water Acidity pH Mine water acidity measured with 3 points calibrated handheld pH meter was summarized in Table 3. Artificial mine water (AMW) of different electrical conductivity (EC) was made up to match the pH of mine water (MW) before submersion experiment and the pH of mine water after submersion experiment was measured again showing an acidic shift of 0.5 on the pH scale. 4.2.3 Total Dissolved Solids (TDS) Total dissolved solids (TDS) in the mine water were measured by conductivity method using a handheld TDS meter. Using a calibration curve of standard salt solutions with known concentration, TDS measurements of mine water and artificial mine waters before (Table 4, Figure 37 Triangle plot of XRF result. Table 3 Mine water acidity. 51  Figure 38) and after (Table 5, Figure 39) the submersion experiment is adjusted. The electrical conductivity of the mine waters is then calculated with a conversion factor below. Equation 14 Electrical conductivity to ppm conversion factor  1 𝑠𝑠𝑖𝑖𝐹𝐹𝑠𝑠𝐹𝐹𝑛𝑛𝑠𝑠𝑠𝑠𝐹𝐹𝑚𝑚𝐹𝐹𝑚𝑚= 5,000 𝑝𝑝𝑝𝑝𝑚𝑚𝑚𝑚𝑠𝑠 𝑝𝑝𝐹𝐹𝑚𝑚  𝑠𝑠𝑖𝑖𝑙𝑙𝑙𝑙𝑖𝑖𝑚𝑚𝑛𝑛, 500 𝑠𝑠𝑠𝑠𝑝𝑝𝑙𝑙𝐹𝐹  (14)    52   Table 4 TDS measurement before submersion experiment.  Figure 38 TDS calibration curve before submersion experiment. Unit M ppm ppm ppm ppm ppm ppm ppm ppmSample [NaCl] test 1 test 2 test 3 test 4 test 5 test 6 Avg TDSAdj1M 1.000 OL OL OL OL OL OL OL0.5M 0.5002 OL OL OL OL OL OL OL0.3M 0.3000 OL OL OL OL OL OL OL0.1M 0.1000 OL OL OL OL OL OL OL0.08M 0.0800 6,180 5,090 5,820 6,200 6,200 6,170 5,9430.06M 0.0600 3,800 3,690 3,770 4,010 3,990 3,820 3,8470.05M 0.0500 3,100 2,830 2,970 3,070 3,490 3,110 3,0950.04M 0.0400 2,420 2,200 2,390 2,200 2,280 2,290 2,2970.02M 0.02000 1,180 1,030 1,020 1,050 1,070 1,070 1,0700.0016M 0.00160 104 93 96 96 96 96 97DI Water 0 1 1 1 1 1 1 1AMW LowEC 0.0026 151 136 139 140 137 139 140 155AMW MidEC 0.0590 3,840 3,610 3,820 3,710 3,890 3,860 3,788 3,450AMW HiEC 0.0721 5,000 4,920 5,210 5,010 4,990 5,090 5,037 4,212MW before 0.0536 3,400 3,360 3,120 3,270 3,430 3,430 3,335 3,134MeasurementCalibration53   Table 5 TDS measurement after submersion experiment.  Figure 39 TDS calibration curve after submersion experiment. Unit M ppm ppmSample [NaCl] TDS TDSAdj1M 1.000 4,2900.5M 0.5002 3,9100.3M 0.3000 3,4900.1M 0.1000 2,4500.04M 0.0400 1,4700.02M 0.02000 9020.0016M 0.00160 98DI Water 0 1AMW LowEC 0.0027 164 160AMW MidEC 0.0638 1,960 3,726AMW HiEC 0.0786 2,190 4,592MW after 0.0604 1,900 3,528CalibrationMeasurement54  Gravimetric measurement of total dissolved solids (TDS) for mine water and artificial mine waters before and after submersion experiment is presented in Table 6. This is a more accurate method than estimating TDS by conductivity with a handheld TDS meter and accounted for ionic salts other than NaCl and organic salts.  Table 6 Gravimetric TDS measurements. 4.2.4 The Resistivity of Rock and Minerals The resistivity of rock and mineral cores collected using ¾” diamond hole saw was measured dry and wet after soaking in deionized water (DIW), artificial mine water of low (AMW-L), medium (AMW-M), and high (AMW-H) electrical conductivity, and mine water (MW). The resistivity measurement is shown in Figure 40. Gravimetric TDSSolution MW LowEC MidEC HiEC MWdecant MWmixedSolution+Beaker (g) 205.9401 204.3096 204.2969 203.4320 199.5961 175.8568Solute+Beaker (g) 124.3638 123.7781 120.6461 73.8113 120.7833 73.8845Beaker (g) 123.9652 123.7698 120.3533 73.2545 120.3531 73.2626Solution (g) 81.9749 80.5398 83.9436 130.1775 79.2430 102.5942Solute (g) 0.3986 0.0083 0.2928 0.5568 0.4302 0.6219TDS (ppm) 4862 103 3488 4277 5429 6062[NaCl]equiv (M) 0.08320 0.001763 0.05969 0.07319 0.09290 0.1037   After submersionBefore submersion55   Figure 40 Resistivity of rock core saturated by various solutions. 4.2.5 Linear Sweep Voltammetry (LSV) The electrochemical properties of rock, mineral, and steel electrodes were measured by linear sweep voltammetry (LSV), and the resultant polarization curves were processed by a python code for Tafel analysis. The data was consolidated to a CSV file for mixed potential analysis in Excel. 4.2.6 Mixed Potential The rate of galvanic corrosion was calculated by the intersection of the cathodic curve from the protected material and the anodic curve from the corroded material. Because steel electrode exhibits current density an order of magnitude larger than most other rock and 56  mineral electrodes for a given potential, open circuit potential (OCP) of steel was used to approximate the steel polarization curve where the logarithmic slope of the curve approaches vertical. This simplifies the calculation of any rock and mineral corrosion current density to the current response when potential equal to that of steel OCP. Figure 41 shows the anodic curve of steel electrode in black and steel OCP in red, with cathodic curves of all rock and mineral samples cathode to steel. The intersection of the cathodic curves with the steel anodic curve or steel OCP determined the corrosion potential and corrosion current density of the given galvanic pairs. The results are tabulated in Table 7 below.  Figure 41 Mixed potential diagram of rock and mineral samples cathode to steel. Figure 42 shows the cathodic curve of steel electrode in black and steel OCP in red, with anodic curves of all rock and mineral samples anode to steel. The intersection of the anodic curves with the steel cathodic curve or steel OCP determined the corrosion potential and 57  corrosion current density of the given galvanic pairs. The results are summarized in Table 7 below.  Figure 42 Mixed potential diagram of rock and mineral samples anode to steel. Table 7 summarizes the corrosion potential and current density for all rock and mineral electrodes with respect to steel. For M1 bornite electrode, the corrosion potential and corrosion current density were calculated by the intersection of linear best fit lines of the steel anodic curve and the M1 cathodic curve. For all other electrodes, corrosion potential was approximated with steel OCP and the corrosion current density was simply the current response when the potential equals to steel OCP. 58   Table 7 Mixed potential summary. 4.2.7 X-ray Powdered Diffraction (XRD) X-ray powdered diffraction (XRD) and the Rietveld method were used on 3 representative powdered samples from sample 1, 3, and 19. The relative amounts of crystalline phases normalized to 100% are shown in Table 8. 59   Mineral Ideal Formula Sample 1 Sample 3 Sample 19 Apatite Ca5(PO4)3OH   2.2 Calcite CaCO3 0.4  57.8 Clinochlore  (Mg,Fe2+)5Al(Si3Al)O10(OH)8 0.3 36.5 0.8 Dolomite CaMg(CO3)2 90.1 1.3 2.1 Lizardite Mg3Si2O5(OH)4 0.2   Muscovite 2M1 KAl2(AlSi3O10)(OH)2 4.6 10.1 12.9 Plagioclase (Albite) NaAlSi3O8 – CaAl2Si2O8  15.0  Pyrite FeS2 1.5 6.7 3.7 Quartz  SiO2 2.8 28.0 20.1 Rutile TiO2 0.1 2.4 0.4 Total  100.0 100.0 100.0 Table 8 Normalized results of quantitative phase analysis by Rietveld refinements. 4.3 Numerical Simulation of Corrosion 4.3.1 Segmentation Polished submersion slabs from sample 1, 3, and 19 were tile scanned with a digital stereomicroscope to obtain a high definition image of the samples. The stitched microscopic images were segmented using ImageJ by mineral colours. The full-size segmented images were reduced in size while maintaining geometric likeness before the construction of numerical mesh to optimize the computation load. The mineral composition of the samples was determined by XRD (Table 8) and individually assigned on a case-by-case basis. 60  Sample 1 preliminarily described as bulky corrosive graphitic argillite was composed of 90.1% dolomite, 4.6% muscovite, 2.8% quartz, and 1.5 % pyrite. Visual observation (Figure 43) readily identifies a quartz band on the lower-left corner and disseminated pyrite crystallization throughout the dolomite rock sample. No muscovite crystals were found on the exposed surface, but they may exist within the rock slab. Since mica is a common insulator and most likely does not contribute to the electrochemical process of corrosion in small quantity, it was decided that muscovite can be ignored and the sample was segmented into dolomite, quartz, and pyrite in green, blue, and red.  Figure 43 Sample 1 (left), segmented sample 1 (centre), small segmented sample 1 (right). Sample 3 preliminarily described as non-corrosive phyllite contained 36.5% clinochlore, 28% quartz, 15% albite, 10.1% muscovite, and 6.7% pyrite. Visual observation (Figure 44) readily identifies quartz veins, metallic pyrite crystals, and alternating bands of green clinochlore and yellow albite. No muscovite crystal was visually identified, but it may be disseminated in the clinochlore matrix. Sample 3 was segmented to 4 colours: green for clinochlore, black for albite, blue for quartz, and red for pyrite. 61   Figure 44 Sample 3 (left), segmented sample 3 (centre), small segmented sample 3 (right). Sample 19 preliminarily described as overcored corrosive argillite was found to contain 57.8% calcite, 20.1% quartz, 12.9% muscovite, and 3.7% pyrite. It was determined that muscovite identified in XRD is probably biotite, which is a very similar mineral but black instead of clear. Visual observation (Figure 45) correspond well with the XRD analysis, with greenish calcite matrix segmented in green, white quartz veins segmented in white, black biotite veins segmented in blue, and pyrite segmented in red.   Figure 45 Sample 19 (left), sample 19 (centre), small segmented sample 19 (right). Rock core electrode (RCE) matrix was not segmented. The RCE matrix was constructed from 21 rock core electrodes in Table 9. The mesh for the RCE matrix was created from scratch with 21 circles corresponding to the rock core electrodes.   62  M1 Bornite  M2 Calcite  M3 Chromite M6 Selenite M8 Hematite M15 Magnetite M16 Malachite M23 Talc 1.2 Dolomite 3.1 Clinochlore  3.2 Clinochlore 3.3 Clinochlore  3.4 Clinochlore  4.1 Clinochlore  4.2 Clinochlore  12.1 Argillite 19.1 Calcite  19.2 Calcite  19.5 Calcite  19.6 Calcite  19.7 Calcite Table 9 Picture of all rock core electrodes labelled with dominant mineralization. 4.3.2 Mixed Potential Analysis Polarization curves of the selected representative major minerals composed of sample 1, 3, and 19 were overlaid with the polarization curve and open circuit potential of steel in the following figures: In Figure 46, polarization curves of RCE 12-1 dolomite, SME M20 quartz, SME QM18 pyrite, and steel electrode were plotted with steel OCP in a mixed potential diagram to represent the corrosion process in sample 1. From this diagram, it can be determined that quartz was the most anodic material, followed by pyrite and steel to the most cathodic dolomite. It also showed that pyrite oxidation by steel was the most reactive process, followed by pyrite oxidation by dolomite, steel oxidation by dolomite, and quartz oxidation by dolomite, steel, and pyrite. 63   Figure 46 Polarization curves of major minerals in sample 1. In Figure 47, polarization curves of RCE 3-1 clinochlore, SME Q3-7 albite, SME M20 quartz, SME M18 pyrite, and steel electrode were plotted with steel OCP in a mixed potential diagram to represent the corrosion process in sample 3. From this diagram, it can be determined that clinochlore was the most anodic material, followed by quartz, pyrite, and steel to the most cathodic albite. It also showed that pyrite oxidation by steel was the most reactive process, followed by pyrite oxidation by albite, steel oxidation by albite, quartz oxidation by albite, steel, and pyrite, clinochlore oxidation by albite, steel, pyrite, and quartz. A: pyrite C: steel  A: pyrite C: dolomite  A: quartz C: pyrite  A: quartz C: dolomite  A: steel C: dolomite  A: quartz C: steel  A: anode C: cathode 64   Figure 47 Polarization curves of major minerals in sample 3. In Figure 48, polarization curves of RCE 19-1 calcite, RCE 19-2 biotite, SME M20 quartz, SME M18 pyrite, and steel electrode were plotted with steel OCP in a mixed potential diagram to represent the corrosion process in sample 19. From this diagram, it can be determined that quartz was the most anodic material, followed by pyrite, biotite, and steel to the most cathodic calcite. It also showed that pyrite oxidation by steel was the most reactive process, followed by pyrite oxidation by calcite, steel oxidation by calcite, biotite oxidation by calcite, pyrite oxidation by biotite, biotite oxidation by steel, and quartz oxidation by calcite, steel, biotite, and pyrite. A: pyrite C: steel  A: quartz C: pyrite  A: steel C: albite  A: clinochlore C: albite  A: clinochlore C: quartz  A: clinochlore C: steel  A: clinochlore C: pyrite  A: quartz C: steel  A: quartz C: albite  A: pyrite C: albite  A: anode C: cathode 65   Figure 48 Polarization curves of major minerals in sample 19. 4.3.3 Meshing A high-fidelity mesh is created from the segmented mineral boundaries, cell size was determined by both the thickness of the fluid domain (500 μm) and the level of features detail. The mesh for sample 1 (Figure 49) contained more than 1.1 million tetrahedral cells. Sample 3 (Figure 50) and 19 mesh (Figure 51) was created using the cut cell method and contained 1.4 and 1.8 million cells. For the RCE matrix (Figure 52), the more efficient hexahedral method was used due to its simple geometry. The finished RCE mesh contained 1.3 million cells. Adaptive sizing refined the mesh at mineral boundaries where large potential gradients and localized corrosion was expected. A: quartz C: pyrite  A: quartz C: biotite  A: quartz C: calcite  A: biotite C: calcite  A: biotite C: steel  A: steel C: calcite  A: pyrite C: biotite  A: pyrite C: calcite  A: pyrite C: steel  A: quartz C: steel  A: anode C: cathode 66   Figure 49 Sample 1 tetrahedral mesh with 1,176,330 cells (left), zoomed in on mineral boundary (right).  Figure 50 Sample 3 cut cell mesh with 1,465,074 cells (left), zoomed in to show adaptive meshing (right).  Figure 51 Sample 19 cut cell mesh with 1,894,146 cells (left), zoomed in to show adaptive meshing (right). 67   Figure 52 RCE matrix hexahedral mesh with 1,327,645 cells (left), zoomed in (right). 4.3.4 Simulated Corrosion Profile The corrosion simulation was conducted on a local high-performance computing (HPC) cluster with 128 CPU cores and 252 GB memory. Large memory capacity was required during simulation because temporary memory needed to be stored for the native solver to pass the potential gradient to the UDF for corrosion damage calculation. All 4 numerical models of sample 1, 3, 19, and RCE matrix were simulated for 100 time-steps at 86,400 seconds per step to simulate 100 days of corrosion. See Appendix D   for the complete result of the corrosion simulation. Significant results are highlighted in the following paragraphs. Sample 1 Sample 1 graphitic argillite was comprised of dolomite (sample 1-2, Jcorr = 0.019798 A/m2), quartz (sample QM20, Jcorr = 0.040330 A/m2), and pyrite (sample QM18, Jcorr = 0.466105 A/m2). With all components anodic to steel, no corrosion was expacted. A decision was made to use another more cathodic graphitic argillite (sample 12-1, Jcorr = -0.269046 A/m2), instead 68  of dolomite for the simulation. The significant simulation results are presented in Figure 53 below.  Figure 53 Sample 1 mesh (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by dolomite edge (a), dolomite centre (b), quartz with pyrite (c), and pyrite (d). In Figure 53, significant locations of sample 1 are presented as an array of images with 4 columns of mesh (1), electric potential (2), electric current magnitude (3), and corrosion depth (4) contours with their respective legends. Mesh zones were colour-coded to blue for bulk electrolyte, green for dolomite, red for quartz, and white for pyrite. Electric potential contours showed polarization of steel surface by the mineral it is in contact with, blue for negative potential influenced by cathodic mineral. Electric current magnitude contours represented current flux passing through the steel surface regardless of direction, blue for (2a)     (2b)     (2c)     (2d) (1a)     (1b)     (1c)     (1d) (3a)     (3b)     (3c)     (3d) (4a)     (4b)     (4c)     (4d) 69  zero current. Corrosion depth contour was also the z-coordinate of the steel surface, blue for most heavily corroded spot and red for no corrosion. Row (a) was of steel influenced by dolomite at the edge of the sample, where a maximum corrosion depth of 74 μm was simulated in (3a). Row (b) was of steel influenced by only dolomite at the centre of the sample where a lesser corrosion depth of 56 μm was simulated. Row (c) was of steel influenced by quartz vein with pyrite inclusion in dolomite host rock. Where the anodic quartz cathodically protected steel from corrosion resulting in red uncorroded footprint in the corrosion depth contour, and where pyrite oxidized and released electron, resulting in a distinct cyan-blue-cyan ring around the pyrite footprint in the electric current magnitude contour where the current flux changed direction from out of the steel plate into the steel plate where pyrite act as a sacrificial anode. Row (d) was of steel influenced by a pyrite crystal in the dolomite host rock. The anodic pyrite slightly polarized the steel surface in the electric potential contour and the distinct cyan-blue-cyan ring was found in electric current magnitude contour where pyrite was predicted to act as a sacrificial anode and protect the steel from corrosion. Sample 3 Sample 3 phyllite was comprised of clinochlore (sample 3-1, Jcorr = 0.025311 A/m2), albite (sample Q3-7, Jcorr = -0.097121 A/m2), quartz (sample QM20, Jcorr = 0.040330 A/m2), and pyrite (sample QM18, Jcorr = 0.466105 A/m2). In this configuration, albite was the only cathodic mineral that was expected to corrode steel while pyrite was the most reactive anodic mineral that acted as sacrificial anodes. The significant simulation results are presented in Figure 54 below. 70   Figure 54 Sample 3 mesh (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by clinochlore (a), albite (b), quartz (c), and pyrite (d). In Figure 54, significant locations of sample 3 are presented as an array of images in 4 columns of mesh (1), electric potential (2), electric current magnitude (3), and corrosion depth (4) contours with their respective legends. Mesh zones were colour-coded in green for bulk electrolyte, light blue for clinochlore, dark blue for albite, grey for quartz, and cyan for pyrite. Row (a) was of steel influenced by clinochlore in contact with albite at the top, quartz in the bottom, and pyrite in the left. Since clinochlore was slightly anodic to steel, it cathodically protected steel from corrosion while albite on the top corroded steel (4a). Pyrite inclusions in the clinochlore showed up as warm spots on the electric current magnitude contour (3a) where current spiked because pyrite was more anodic than clinochlore. Quartz inclusion was indistinguishable from clinochlore due to their similar corrosion current density. Row (b) was of steel influenced by albite, which was the only cathodic mineral in (3a)     (3b)     (3c)     (3d) (1a)     (1b)     (1c)     (1d) (2a)     (2b)     (2c)     (2d) (4a)     (4b)     (4c)     (4d) 71  sample 3. It created a spike in the electric current magnitude contour (3b) and galvanically corroded steel to a maximum corrosion depth of 30 μm (4b). Row (c) was of steel influenced by quartz bounded by a distinctive horizontal bar of albite on the top and a triangular pyrite inclusion on the left. Quartz cathodically protected steel from corrosion while albite at the top corroded steel to its distinctive horizontal bar shape in the corrosion depth contour (4c) and pyrite created spikes in electric potential (2c) and electric current magnitude contour (3c) as it was preferentially oxidized. Row (d) was of steel influenced by a large pyrite cluster. Pyrite was the most anodic mineral in sample 3 and a maximum current density of 0.466 A/m2 (3d) was predicted at the centre of the cluster where pyrite was preferentially oxidized and steel cathodically protected under its influence (4d). Sample 19 Sample 19 overcored argillite was comprised of calcite (sample 19-1, Jcorr = -0.273064 A/m2), biotite (sample 19-2, Jcorr = 0.151107A/m2), quartz (sample QM20, Jcorr = 0.040330 A/m2), and pyrite (sample QM18, Jcorr = 0.466105 A/m2). Calcite was the only cathodic mineral expected to galvanically corrode steel, and pyrite was the most reactive anodic mineral expected to be preferentially oxidized. The significant simulation results are presented in Figure 55 below. 72   Figure 55 Sample 19 segmentation (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by calcite (a), biotite (b), quartz (c), and pyrite (d). In Figure 55, significant locations of sample 19 are presented as an array of images in 4 columns of segmentation (1), electric potential (2), electric current magnitude (3), and corrosion depth (4) contours with their respective legends. The segmentation was colour coded to black for bulk electrolyte, green for calcite, blue for biotite, white for quartz, and red for pyrite. Row (a) was of steel influenced by calcite, the only cathodic mineral in sample 19, which was predicted to galvanically corrode steel to a maximum corrosion depth of 87 μm (4a). Row (b) was of steel influenced by a biotite vein in calcite. Biotite was determined to be anodic to steel and was expected to cathodically protect steel from corrosion. In the electric current magnitude contour, Distinctive blue rings (3b) were seen around the biotite mineralization marking the change in direction of the current flux where biotite oxidized instead of steel (4b). Row (c) was of steel influenced by quartz, which was also anodic to (2a)     (2b)     (2c)     (2d) (1a)     (1b)     (1c)     (1d) (3a)     (3b)     (3c)     (3d) (4a)     (4b)     (4c)     (4d) 73  steel and cathodically protected steel from corrosion (4c). However, there was no current flux simulated that oxidizes quartz (3c) due to its corrosion current density that is an order of magnitude smaller than other minerals. Row (d) was of steel influenced by a pyrite vein in calcite where the anodic pyrite created the maximum current flux in the electric current magnitude contour (3d). The distinctive blue ring was seen encircling the pyrite mineralization where current flux changed direction due to the preferential oxidization of pyrite, below which steel was predicted to corrode as normal by calcite to a maximum depth of 87 μm (4d). RCE Matrix RCE matrix was constructed from 21 RCE (see Table 9) each with their corrosion current listed in Table 7. The significant simulation results are presented in Figure 56 below.  74   Figure 56 RCE matrix photograph (1), steel surface electric potential (2), electric current magnitude (3), and corrosion depth (4) contour influenced by M1 bornite (a), 19-6 calcite (b), 19-2 calcite with biotite (c), and 3-4 clinochlore with pyrite(d). In Figure 56, significant locations in the RCE matrix is presented as an array of images in 4 columns of RCE photographs (1), electric potential (2), electric current magnitude (3), corrosion depth (4) contours with their respective legends. Row (a) was of steel influenced by bornite (sample M1, Jcorr = -3.948812 A/m2), which was the most cathodic electrode in the study. The effect of bornite to steel was an order of magnitude greater than all other electrodes, the numerical model predicted a polarization the steel surface by -0.4 mV (2a), a maximum current flux of 3.905 A/m2 at the centre of the electrode (3a), and a maximum corrosion depth of 1,112 μm where steel was exposed to bornite (4a). Row (b) was of steel influenced by calcite from sample 19 (19-6, Jcorr = -0.128208 A/m2), which was also cathodic to steel. A smaller, but visible polarization (2b) and current flux (3b) of steel surface were (1a)     (1b)     (1c)     (1d) (2a)     (2b)     (2c)     (2d) (3a)     (3b)     (3c)     (3d) (4a)     (4b)     (4c)     (4d) 75  observed with a simulated corrosion depth of 42 μm. Row (c) was of steel influenced by calcite and biotite from sample 19 (19-2, Jcorr = 0.151107 A/m2). Electrode 19-2 was determined to be anodic to steel, the numerical model predicted a slight polarization of steel surface in the positive direction (2c) with no corrosion on the steel surface due to cathodic protection (4c). Row (d) was of steel influenced by clinochlore with pyrite from sample 3 (3-4, Jcorr = -0.093773 A/m2), which was again cathodic to steel. Although it was an order of magnitude smaller than those of M1 bornite electrode, a slight polarization of steel surface (2d) and a small current flux (3d) were predicted with a maximum corrosion depth of 27 μm simulated on the steel surface under 3-4 electrode. 4.4 Submersion Experiment 4.4.1 Visual Observation Sample 1 Bolt steel zip-tied to sample 1 after 100-day submersion is presented in Figure 57. Note the two distinct levels of corrosion around the quartz band marked by white arrow. Due to cathodic protection of quartz, steel in contact with quartz was bright and uncorroded after the submersion test. Compare to steel in contact with dolomite, which was slightly cathodic to steel and resulted in minor uniform corrosion seen as a dulling of the steel surface. Although pyrite was the most reactive anodic mineral and was expacted to cathodically protects steel from corrosion, the oxidation of pyrite created a localized concentration of sulphuric acid that developed into pitting corrosion marked in red. 76   Figure 57 Steel sample 1 after 100-day submersion (white = quartz, red = pyrite, yellow = zip-tie dry spot, green = zip-tie less corrosion product). The elongated oval marked in yellow on Figure 57 corresponded to a zip-tie that binded the rock slab to steel. The bond was so tight a dry spot appeared underneath the zip-tie where water could not penetrate (see Figure 58). Strong localized corrosion marked in green showed where the head of a zip-tie prevented deposition of corrosion product and impeded passivation, a less pronounced feature was found on the tail side of zip-tie. 77   Figure 58 Zip-tie induced dry spot on sample 1. Sample 3 Sample 3 steel after 100-day submersion experiment is seen in Figure 59. Clear signs of cathodic protection from quartz veins are marked by yellow arrows. And there were two large areas of bright uncorroded steel circled in red, presumably due to dry spots from over tightened zip-tie, the location of which is shown in dashed white lines. This was confirmed by reviewing the photograph of steel sample 3 right after the submersion test (Figure 60). 78   Figure 59 Sample 3 bolt steel after 100-day submersion (white=zip-tie, red=dry spot, yellow=quartz).  Figure 60 Zip-tie induced dry spot on sample 3. 79  Sample 19 After zip-tied to sample 19 for 100 days in the submersion experiment, steel sample 19 is presented in Figure 61. Some distinctive features were marked for reference. Yellow dash line locates the zip-tie and the dry spot from over-tightening, enclosed in red is corroded steel corresponded to a prominent pyrite vein, cyan arrows mark heavy corrosion where steel was in contact with black biotite veins, enclosed in white are areas of banded quartz and biotite vein showing alternating bands of corrosion by biotite and cathodic protection by quartz vein. And Figure 62 confirmed the existence of dry spots.  Figure 61 Steel sample 19 after 100-day submersion (red=pyrite, white=quartz, cyan=biotite, yellow=zip-tie). 80   Figure 62 Sample 19 afte submersion test showing zip-tie induced dry spot. RCE Matrix Steel sample zip-tied to the RCE matrix after 100 days of submersion experiment is presented in Figure 63. Corresponding rock core electrodes are marked, cathode in red and anode in yellow. Bornite was the most reactive cathodic RCE (M1, Jcorr = -3.948812 A/m2), and it corresponded to the biggest corrosion pit on the submerged sample. The second most reactive cathodic RCE was sample 12-1 (sample 12-1, Jcorr = -0.269046 A/m2), and the steel has shown only slight pitting. The most uniformly corroded steel was under the influence of sample 19-2 (sample 19-2, Jcorr = 0.151107 A/m2), which contains biotite. And as sample 19 submersion test demonstrated, biotite is highly corrosive. The most anodic RCE was sample 19-7 (sample 19-7, Jcorr = 0.168140 A/m2), which was mostly calcite with a little disseminated pyrite and cathodically protected the steel.  81   Figure 63 Steel sample zip-tied to the RCE matrix after 100-day submersion (yellow=anodic, red=cathodic). 4.4.2 Confocal Microscopy Confocal microscopy was used for profilometry measurement of the corroded steel plate because as an optical technique, it does not disturb the corrosion product, does not require special preparation, and has enough resolution to pick up minor corrosion profile after only 100 days of corrosion. 100 times magnification white light microscopic photo, profile height, and cross-sectional profile for all measurements of confocal profilometry are included in Appendix E  .  M6 M2 3.2 1.2  3.1  19.6 M1 19.5 4.2 19.7 19.2  M15 19.1   M16   M23   12.1  4.1 M8 M3 3.3 3.4 82   Sample 1 Ten points of interest (POI) were marked by masking tapes on the sample 1 steel plate in preparation for confocal microscopy shown in Figure 64 and overlaid with sample 1 transparant glow edge segmentation to reference spatial mineral distribution.  Figure 64 Sample 1 steel marked with POI and an overlay of transparent and glow edges segmentation. POI 1 measured in Figure 85 was a corrosion pit corresponded to a pyrite inclusion in the quartz vein. The pit had a stepped edge over 50 μm with the deepest part measuring 82.170 μm deep from the pit edge.  9 10 5 4 6 1 2 3 7 8 83  POI 2 measured (Figure 86) was a boundary of bright and dark steel corresponded to the quartz vein that offered cathodic protection while the dolomite rock mass corroded steel. There were two zones of distinct corrosion, steel on the left side was influenced by quartz, had a corrosion depth of 0.990 μm, and appeared lighter on the optical image. Steel on the right side was influenced by dolomite, had a corrosion depth of 2.700 μm, and appeared darker on the optical image. POI 3 measured (Figure 87) was a corrosion pit corresponded to a pyrite crystal in dolomite. The pit had a near-vertical edge 9.48 μm deep followed by a gradual decline over 77 μm that droped another 22.515 μm at the deepest point, which was 31.995 μm deep from the pit edge. POI 4 measured in Figure 88 was a corrosion boundary corresponded to the edge of the first dry spot. The first dry spot was never wetted, the larger second dry spot was wetted in the first 23 days, but was dry in the later 77 days. Steel generally appeared white above the first dry spot boundary and shown minimal corrosion, preserving the parallel scratch marks from wet sanding (shown in blue on the optical image). A surface deformation on the steel coincided with the first dry spot, showing up as a peak in the diagonal profile 1.729 μm high. The raised peak sealed to the rock surface, forming the first dry spot. POI 5 measured (Figure 89Error! Reference source not found.) was a corrosion boundary corresponded to the edge of the second dry spot. Inside the second dry spot, steel was wetted in the first 23 days, but was dry in the later 77 days. A stair-step of 1.485 μm high could be seen on the profile that coincided with the second dry spot. To the left of the stair-step, the profile was smooth and steel surface appeared brighter on the optical image, to the right of 84  the stair-step, the profile was rougher and steel surface appeared darker on the optical image due to normal corrosion. POI 6 measured in Figure 90 was a corrosion pit that corresponded to a pyrite crystal in dolomite. The pit had a near-vertical edge 31.29 μm deep followed by a gradual decline to 99.085 μm at the deepest point from the pit edge. POI 7 measured (Figure 91) was a corrosion boundary corresponded to a joint in the dolomite rock mass. The joint provided a relatively large volume of electrolyte that buffered the acidification of electrolyte. The less corroded joint area on the top had a corrosion depth of 1.260 μm and appeared brighter in the optical image, the corrosion gradually increases toward the bottom where the corrosion depth was 2.655 μm. And a defect on steel surface was shown on the horizontal profile, where preferential corrosion was evident, and the depth of corrosion reached 2.475 μm in the centre of the defect. POI 8 measured (Figure 92) was a corrosion boundary corresponded to the edge of the dolomite sample. Steel generally appeared brighter and less corroded where covered by the rock sample than the portion exposed to the bulk solution. This boundary presented as a gradual slope of 2.160 μm difference in corrosion depth. This may be caused by oxygen depletion in the stagnant solution trapped between rock sample and steel plate, and the diffusion of oxygen was responsible for the gradual transition in corrosion depth. POI 9 measured (Figure 93) was a group of pitting corrosion caused by the head of a zip-tie blocking corrosion product that would have fallen evenly on the steel plate. The pit had a 85  near-vertical edge 18.880 μm deep followed by a gradual decline to 43.995 μm at the deepest point from the pit edge. POI 10 measured (Figure 94) was a boundary of bright and dark steel correspond to the quartz vein that offered cathodic protection while the dolomite rock mass corroded steel. There were two zones of distinct corrosion, steel on the lower left side was protected from corrosion and appears white on the optical image, steel on the upper right was unprotected and experience 2.565 μm of preferential corrosion. Sample 3 Eight points of interest (POI) were marked by masking tapes on the sample 3 steel plate in preparation for confocal microscopy shown in Figure 65 . 86   Figure 65 Sample 3 steel marked with point of interest marked in masking tapes. POI 1 measured (Figure 95) was a corrosion pit likely corresponded to a pyrite crystal. The pit had a simple sloped edge and measures 5.200 μm deep from one edge, and 4.000 μm deep from another. One can speculate that sulfuric acid produced by the oxidation of pyrite diffused in the upper right direction, resulting in a trailing tail of corrosion damage. POI 2 measured (Figure 96) was a corrosion boundary corresponded to a quartz vein that cathodically protected the steel. Two distinct zones of corrosion were found, yellow on the confocal height image showed the less corroded steel that appeared white in the optical image, and blue on the confocal height image was more corroded and appeared brown in the optical image. The differential corrosion depth was 1.650 μm. 8 3 5 4 6 7 2 1 87  POI 3 measured (Figure 97) was the first corroded bright spot being measured. The bright spot was created when a piece of corrosion product was peeled off the steel when the rock sample was lifted. Its occurrence appeared random and the sharp drop at the boundary showed the thickness of the corrosion product layer, which measured 2.565 μm. And some peak of corrosion product had been deposited at the top of the screen. The peak was 5.415 μm higher than normal corrosion product, which suggests the gap between rock and steel was at least 7.980 μm. POI 4 measured (Figure 98) was the second corroded bright spot being measured. The bright spot was created when a piece of corrosion product was peeled off the steel when the rock sample was lifted. There was a corrosion pit at the centre that measured 2.385 μm deep from the edge and the corrosion product layer was about 0.900 μm thick. POI 5 measured (Figure 99) was a pitting corrosion that appeared as a black spot on bright steel. It was correlated to a cluster of pyrite surrounded by quartz, and the corrosion pit had a shallow slope that reached the corrosion depth of 4.000 μm. POI 6 measured (Figure 100) was the boundary of irregularly shaped (ꝛ) black blob, which was assumed to be the merged diffusion trails of two oxidized pyrite crystals upstream. The area unaffected by pyrite appeared white in the optical image where the corroded surface appeared black and has a gradual sloping profile to the maximum depth of 3.195 μm. POI 7 measured (Figure 101) was a corrosion boundary corresponded to a quartz vein that cathodically protected the steel. Two distinct zones of corrosion were found, orange and blue in the confocal height image represented high and low spots, which appeared white or black 88  in the optical image. The transition was gradual but rough, with the average difference in corrosion depth of 2.088 μm. POI 8 measured (Figure 102) was the third corroded bright spot being measured. The bright spot was created when a piece of corrosion product was peeled off the steel when the rock sample was lifted, which requireed the corrosion product to fill the gap between rock and steel. The average thickness of the corrosion product and the gap between rock and steel was 18.564 μm. Sample 19 Eight points of interest (POI) were marked by masking tapes on the sample 19 steel plate in preparation for confocal microscopy shown in Figure 66. 89   Figure 66 Sample 19 steel with points of interest marked with masking tapes.  POI 1 measured (Figure 103) was the corrosion boundary between dark and bright steel that coincided with the biotite and quartz mineralization. The average corrosion depth difference between protected and unprotected steel was 1.470 μm, and corrosion pits up to 2.565 μm deep may be caused by oxidized pyrite crystal. POI 2 measured (Figure 104) was the corrosion boundary between dark and bright steel in the first dry spot. On the optical image, the uncorroded steel in the first dry spot was white, while outside the dry spot the steel was grey. There was no appreciable corrosion height difference seen on confocal height image or horizontal profile. And a pyrite crystal 3.501 μm 1 2 3 4 5 6 7 8 90  high was found growing out of the wetted side of the first dry spot, which was wetted for 23 days then dried for 77 days. POI 3 measured (Figure 105) was a corrosion boundary corresponded to alternating bands of quartz and biotite. Quartz cathodically protected steel from corrosion and left the steel bright on the optical image. The difference in corrosion depth measured 1.305 μm. POI 4 measured (Figure 106) was a corroded black spot on the steel plate corresponded to a pyrite crystal in a quartz vein. The steel was preferentially corroded to the depth of 2.115 μm. POI 5 measured (Figure 107) was a corrosion boundary corresponded to a quartz vein that cathodically protected the steel. Two distinct zones of corrosion were found, yellow and blue in the confocal height image represented high and low spot, which appeared white or black in the optical image. The transition was gradual but rough, with the average difference in corrosion depth measured 1.530 μm. POI 6 measured (Figure 108) was a corrosion boundary corresponded to a biotite vein very corrosive to steel. The transition was gradual but rough, the corrosion depth was 5.320 μm. POI 7 measured (Figure 109Error! Reference source not found.) was a corrosion boundary corresponded to a quartz vein that cathodically protected the steel. The effect of cathodic protection was gradual to the average corrosion difference of 4.427 μm. POI 8 measured (Figure 110) was a corrosion pit where the corrosion product was removed to reveal fresh steel. The pit had two stepped edges over 50 μm with the deepest part measured 27.440 μm deep from the edge. 91  RCE matrix Eight points of interest were marked by masking tapes on the RCE matrix steel plate in preparation for confocal microscopy shown in Figure 67.  Figure 67 RCE matrix steel marked with POI and RCE identity. POI 1 measured (Figure 111) was a corrosion boundary at the edge of chromite RCE (sample M3, Jcorr = 0.027283 A/m2), which cathodically protected the steel from corrosion. The protected steel appeared white on the optical image while corroded steel appeared black. On the vertical profile, the protected steel appeared smoother from distance 50 to 80 μm marked in black box. The maximum corrosion depth measured was 0.855 μm. M6    M2 3.2 1.2  3.1  19.6 M1 19.5   4.2 19.7 19.2 M15 19.1   M16   M23   12.1    4.1 M8 M3 3.3 3.4 92  POI 2 measured (Figure 112) was a corrosion boundary under the influence of calcite RCE (sample M2, Jcorr = 0.025893 A/m2), which cathodically protected the steel from corrosion. The protected steel appeared white on the optical image while corroded steel appeared black. The corrosion depth measured between black and white steel was 0.840 μm. POI 3 measured (Figure 113) was a corrosion pit corresponded to the bornite RCE (sample M1, Jcorr = -3.948812 A/m2), which was the most anodic electrodes measured. Steel immediately outside the pit edge was smooth and uncorroded, the pit edge was a gradual slope with a drop off at the toe and the maximum depth was 20.735 μm. POI 4 measured (Figure 114) was a corrosion boundary inside the influence of magnetite RCE (sample M15, Jcorr = 0.007904 A/m2), which was only marginally cathodic to steel. The corrosion boundary appeared green and red in the optical image and was variably corroded on confocal height image and in profile. The maximum corrosion depth measured was 2.520 μm. POI 5 measured was a corrosion boundary inside the influence of the Malachite RCE (sample M16, Jcorr = 0.020598 A/m2), which was cathodic to steel. Being a copper carbonate hydroxide mineral, oxidized pyrite from neighbouring electrodes recrystallized in its boundary. Many pyrite crystals were seen in Figure 115, measuring up to 30.225 μm in height. POI 6 measured (Figure 116) was a corrosion boundary inside the influence of 19-2 RCE (sample 19-2, Jcorr = 0.151107 A/m2), which contained biotite and was corrosive to steel. The corrosion edge was a smooth decline to the maximum depth of 34.710 μm. 93  POI 7 measured (Figure 117) was a corrosion pit that lied outside the RCE matrix and exposed to bulk mine water. The pit edge was steep and the bottom uneven. The maximum depth of the pit was 20.280 μm. POI 8 measured (Figure 118) was a corroded bright spot correlated to the silicon caulking matrix. The bright spot was created when the corrosion product builds up across the gap and a piece of corrosion product was peeled off the steel when the RCE matrix was lifted, revelling fresh steel underneath. The maximum thickness of the corrosion product was 6.175 μm. 4.5 Conclusion In this chapter, the results of sample characterization, numerical simulation, and submersion experiment are presented. XRF analysis of rock samples, pH and TDS measurement of mine water and artificial mine water, the resistivity of rock and minerals, LSV of rock and mineral electrodes, mixed potential analysis of electrodes, and XRD of rock samples were all a part of sample characterization and subsequently used to produce the numerical model for corrosion. The segmentation of mineral was achieved with microscopic photograph and mineral composition from the XRD analysis. The meshing of the models is presented to show fidelity to the sample and the result of 100 days of simulated corrosion is presented with the appropriate boundary condition obtained in the mixed potential analysis. The result from the 100-day submersion experiment is first presented visually followed by surface profile measurements at points of interest by confocal microscopy. The significance and implication of the results presented will be discussed in the following chapter. 94  Chapter 5: Discussion and Recommendation 5.1 Introduction In this chapter, the method and the result of the research are discussed in terms of quality and confidence of data, assumptions made, and quality of the simulation.  5.2 The Resistivity of Rock and Minerals The resistivity measurement of rock and minerals were not required for a numerical model of corrosion. However, it was a waste of opportunity not to perform this simple measurement made with a multimeter when we have prepared rock and mineral core with flattened ends. The literature review has connected ground support corrosion rate with electrical conductivity of rock mass (Chambers et al., 2017). Our rock samples have resistivity range from metallic bornite (sample M1, ρMW = 108 Ωm) on the low end, to phyllite rock (sample 4-2, ρMW = 20,200 Ωm) on the high end. All are several orders of magnitude higher than the resistivity of steel, which is on the order of 10-7 Ωm. This is significant for the galvanic corrosion process. Compared to galvanically coupled dissimilar metals, a similarly coupled mineral and steel will corrode at a much lower, although still accelerated rate due to the higher resistivity, which creates smaller current and therefore lower corrosion rate. 5.3 Rock Core Electrode Vs. Single Mineral Electrode Judging by the corrosion current density for both rock core electrodes (RCE) and single mineral electrode (SME) calculated by mixed potential analysis (Table 7), SMEs are preferable to sample only one mineral and getting a repeatable result. There were 4 pure 95  mineral samples (see Appendix B  ) from which both RCEs and SMEs were made: massive hematite (M8, Jcorr = 0.024291 A/m2|QM8, Jcorr = 0.023128 A/m2), magnetite (M15, Jcorr = 0.007904 A/m2|QM15, Jcorr = 1.012696 A/m2), malachite (M16, Jcorr = 0.020598 A/m2|QM16, Jcorr = 0.109920 A/m2), and soapstone (M23, Jcorr = 0.008185 A/m2|QM23, Jcorr = -0.013822 A/m2). Only hematite RCE agrees with its SME out of the four duplicates. Such a wide range of electrochemical property speaks to the purity of the sample and the variability of mineral in general. All 4 RCEs are visibly heterogeneous (Table 9), the ¾” diamond hole saw was not selective enough to collect pure mineral samples even in commercially purchased pure specimen. In the future, it is advisable to collect multiple SMEs from for each mineralization to acquire repeatable results. 5.4 Approximating Steel Polarization Curve with Open Circuit Potential (OCP) An important assumption was made to approximate the steel polarization curve with open circuit potential (OCP) of steel. OCP was determined during voltammetry and represent the potential where no current was passed through the steel electrode. Graphically, in a log-semi graph of logarithmic of current density vs potential (see Figure 41 and Figure 42), it is a vertical line tangent to the polarization curve as current density approaches zero. Because the electrical resistance of steel is several orders of magnitude lower than that of rock and minerals, the current response of steel is greater than that of rock and minerals at a given potential. Any minerals cathode to steel will have a mixed corrosion potential anodically controlled by steel, and minerals anode to steel have a mixed potential cathodically controlled by steel. Both can be approximated by steel OCP. Therefore, steel OCP was used 96  as the boundary condition of fluids contacting steel, while fluid contacting minerals had various corrosion current density determined by the mixed potential analysis. 5.5 Choosing the Appropriate Boundary Condition for Corrosion Simulation The most challenging part of the numerical simulation was the selection of appropriate boundary condition for the segmented mineral boundary. Multiple RCEs and SMEs were collected for each mineralization, but RCE contained heterogeneous minerals and SME of the same mineral have variable results (Table 7). Sample 1 was segmented into dolomite, quartz, and pyrite. For dolomite, the choice was between sample 1-2 (Jcorr = 0.019798 A/m2), Q1-1 (Jcorr = -0.249935 A/m2), Q1-3 (Jcorr = -0.024876 A/m2), and Q1-4 (Jcorr = 0.041448 A/m2), with a choice between RCE and SME, sample 1-2 was the first choice because it was a bigger sample and more representative. That decision did not stand, however, as mentioned in section 4.3.4, all 3 minerals would have been cathodic to steel and sample 12-1 was used instead of sample 1-2 for a more interesting simulation because sample 1 was described as bulky corrosive graphitic argillite from POA525/548 and sample 12 was also described as graphitic argillite but from a different location at 90XC. Similar decisions were made for all samples individually. 5.6 Fluid Domain Thickness The fluid domain of the numerical model was assumed to have a thickness of 500 μm that also represents the gap between rock and steel in an installed frictional stabilizer rock bolt. This number was decided subjectively considering the roughness of the drilled undersize hole and the limited amount steel may conform to the geometry of the hole. For the submersion 97  experiment, both steel and rock samples were flattened and polished before being zip-tied together and would experience a much smaller gap between rock and steel. The gap between rock and steel was measured to be 18.564 μm (Figure 102) in sample 3. The consequence of a larger gap in the numerical model was larger than expected effective distance of cathodic protection, resulting in a more gradual transition between corroded and protected steel in the numerical model compared to the submersion test. 5.7 Validation of Sample 1 Simulated Corrosion Simulated 100-day corrosion of sample 1 (Figure 53) predicted maximum corrosion of 74 μm by dolomite where there was no pyrite and quartz that will cathodically protect the steel, varying degree of corrosion near the influence of pyrite and quartz, and no corrosion under pyrite, quartz, and bulk mine water. 100-day submersion experiment (Figure 57) showed that quartz does cathodically protects steel, measured by confocal microscopy, steel under dolomite was up to 2.565 μm more corroded than steel under quartz. Pyrite encouraged pitting corrosion despite being anodic to steel because the oxidation of pyrite created sulphide ion that reacts with water to form sulphuric acid (a process also known as acid mine drainage) in localized high concentration and caused pitting corrosion. The deepest pit measured 82.170 μm under a pyrite inclusion in quartz, other pits measured 31.995 μm and 31.29 μm deep under pyrite in dolomite. And while the galvanic corrosion of steelby dolomite was evident from the corrosion boundary between quartz vein and dolomite, the fact that there was a very small gap between steel and dolomite inhibited corrosion by depleting dissolved oxygen in the stagnant solution when compared to free corrosion under bulk mine water around the sample. Confocal microscopy measured the reduction in 98  corrosion at the edge of the sample to be 2.160 μm. The inverse effect was found at joints where the larger cavity of solution buffered the acidification of solution by pyrite oxidation and resulted in reduced corrosion of 2.665 μm. Overall, the simulation overestimated the corrosion by dolomite by an order of magnitude, successfully predicted cathodic protection of quartz, but did not account for the acid byproduct of oxidized pyrite. 5.8 Validation of Sample 3 Simulated Corrosion Simulated 100-day corrosion of sample 3 (Figure 54) predicted maximum corrosion of 30 μm under the influence of albite and no corrosion under the influence of clinochlore, quartz, and pyrite due to cathodic protection and no corrosion from mine water outside the sample. 100-day submersion experiment (Figure 59) demonstrated clear cathodic protection by quartz measuring up to 2.088 μm more corrosion in the unprotected areas. The maximum corrosion in sample 3 measured 18.564 μm in a corroded white spot where corrosion products have filled the rock to steel gap and were peeled off with the rock. A corrosion pit (Figure 95) 5.200 μm deep was measured with one side 4.000 μm deep to the edge. The difference of 1.200 μm in corrosion depth was believed to be caused by the diffusion trail of sulfuric acid produced by oxidized pyrite. The same phenomenon was labelled points of interest #6 (Figure 65), where diffusion trails of two oxidizing pyrite clusters appeared as an irregular 99  shaped (ꝛ) black blob with 3.195 μm of corrosion measured inside the influence of diffusion trail (Figure 100). 5.9 Validation of Sample 19 Simulated Corrosion Simulated 100-day corrosion of sample 19 (Figure 55) predicted 87 μm of maximum corrosion under calcite, varying degrees of cathodic protection from quartz, biotite, and pyrite, and no corrosion where cathodically protected. 100-day submersion experiment (Figure 61) showed no corrosion from calcite, cathodic protection from quartz measured at points of interest ranged from 1.305 to 4.427 μm of difference between protected and unprotected steel, and significant corrosion geometrically matched to biotite mineralization was measured in the confocal microscope to have a corrosion depth of 5.320 μm. A corroded white spot was measured (Figure 110) to be the deepest pit at 27.440 μm to the edge. 5.10 Validation of RCE Matrix Simulated Corrosion Simulated 100-day corrosion of RCE Matrix (Figure 56) predicted 1,112 μm of corrosion from M1 bornite electrode and no significant corrosion everywhere else. 100-day submersion experiment (Figure 63) showed many preferential corrosion damages corresponded to the heterogeneous mineralization of RCEs not reflected in the simulation. On the other hand, the largest pitting corrosion corresponded to M1 bornite electrode measuring 20.735 μm deep. The deepest pitting corrosion, however, corresponded to a cluster of pyrite in 19-2 electrode measuring 34.710 μm deep from the edge. The effect of cathodic protection by M3 chromite electrode was seen in Figure 111 where the acidified electrolyte outside M3 corroded the steel to a depth of 0.855 μm but the steel under M3 was protected. Another corrosion pit 100  outside the RCE matrix under bulk mine water with undisturbed corrosion product was measured to be 20.280 μm deep (compared to 43.995 μm from a similar situation in sample 1 but with disturbed corrosion product). 5.11 Secondary Corrosion of Sulphide Minerals Pitting corrosions an order of magnitude deeper (about 30 μm) than uniform corrosion under the influence of cathodic mineral (about 2 μm) in all 4 submerged steel samples were often traced to pyrite mineralizations. This finding was unaccounted for in the galvanic corrosion model, but not unexpected. Mixed potential analysis in section 4.3.2 has shown that pyrite oxidation by steel was the most reactive process in the submersion slab samples. The overall process of pyrite oxidation is known as acid rock drainage (ARD) and summarized as follows: Equation 15 Pyrite oxidation  4𝐹𝐹𝐹𝐹𝑆𝑆2 + 15𝑂𝑂2 + 14𝐻𝐻2𝑂𝑂 → 4𝐹𝐹𝐹𝐹(𝑂𝑂𝐻𝐻)3− + 8𝐻𝐻2𝑆𝑆𝑂𝑂4 (15) In localized stagnant solution, such as the groundwater filled gap between Split-Set and the rock mass, the oxidization of pyrite leads to a localized high concentration of sulfuric acid responsible for the observed pitting corrosion. Similar reactions can be expected from other sulphide minerals. 5.12 Recommendation Future research should employ selective single mineral electrode (SME) rather than the larger rock core electrode (RCE) that may include hetrogeneous minerals. Multiple SME are 101  required for each mineralization to arrive at a consensus that characterizes the electrochemical property of the mineral. Overall, the simulated corrosion model overestimated the galvanic corrosion of steel by cathodic minerals, successfully predicted the cathodic protection of anodic minerals, but failed to address the acid byproduct of oxidized sulphide minerals like pyrite. And carbonate minerals like malachite allowed pyrite to recrystallize (Figure 115), decreasing the concentration of sulphide ion in the electrolyte and indirectly inhibited further corrosion. Future models should track oxygen and ionic species concentration to account for inhibited corrosion in stagnate solution and address acidification of solution by oxidized sulphide minerals. 102  Chapter 6: Conclusions 6.1 Research Objectives This thesis investigates localized corrosion influenced by the electrochemical property of minerals in a heterogeneous rock mass. The investigations have resulted in the development of a procedure for preparation of rock core electrodes (RCE) and single mineral electrodes (SME) for electrochemical analysis of rock and minerals; a numerical model for the galvanic corrosion of steel by minerals using mixed potential analysis; and a submersion experiment that validated the numerical model.  6.2 Significant Results Linear sweep voltammetry (LSV) conducted on prepared RCE and SME samples categorize the rock and minerals as either anodic or cathodic to steel. Cathodic protection of steel from corrosion was expected from anodic mineral such as quartz, which was predicted by the numerical model and verified in submersion experiment. Anodic corrosion of steel was expected from cathodic minerals like dolomite and albite, which was overestimated by the numerical model. Submersion experiment found that steel corrodes about 2 μm over 100 days due to cathodic mineral, which was far from the predicted 30 to 87 μm. Pitting corrosions in the submersion experiment were correlated to the oxidation of pyrite, which was experimentally determined to be anodic to steel and expected to oxidize. However, the numerical model did not account for the acid byproduct of pyrite oxidation and the resultant pitting corrosion. 103  These findings are significant in two ways. Firstly, the galvanic corrosion of cathodic minerals and cathodic protection of anodic minerals are confirmed. The electrochemical properties of the minerals can be determined by linear sweep voltammetry, preferably with single mineral electrodes. Secondly, a novel mechanism for pit initiation was proposed where anodic sulphide minerals were galvanically oxidized by steel and produce a locally high concentration of sulfuric acid to caused pitting corrosion. 6.3 Limitations Due to the complex environment that influences the corrosion mechanism of ground support elements in an underground mine and the variability of natural mineral, there are certain limitations with the findings of this study: • The corrosion model and submersion experiment were designed around the simplified geometry of a frictional stabilizer and other tubular rock bolts like the expansion rock bolt. Adapting the model to other rock bolts, especially grouted rock bolt, requires special consideration regarding fluid paths through microcracks and fluid interaction with grout material. • The electrochemical properties of rock and minerals identified in this study are specific to the sample itself and the mine water it was tested in. 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Retrieved from https://www.ozoptics.com/ALLNEW_PDF/ART0009.pdf  110  Appendices Appendix A  Greens Creek Sample Catalog Sample 1: bulky corrosive graphitic argillite from POA 525/548 Sample 2: bulky corrosive phyllite from PD2853-368/460   Sample 3: non-corrosive phyllite from 795 Sample 4: non-corrosive phyllite from 795   Sample 5: non-corrosive phyllite from 795 Sample 6: non-corrosive phyllite from 795   Sample 7: non-corrosive phyllite from 795 Sample 8: non-corrosive phyllite from 795   111  Sample 9: graphitic argillite from 90XC Sample 10: graphitic argillite from 90XC   Sample 11: graphitic argillite from 90XC Sample 12: graphitic argillite from 90XC   Sample 13: graphitic argillite from 90XC Sample 14: graphitic argillite from 90XC     112  Sample 15: graphitic argillite from 90XC Sample 16: non-corrosive argillite from M540   Sample 17: non-corrosive argillite from M540 Sample 18: non-corrosive argillite from M540   Sample 19: overcored corrosive argillite Sample 20: corroded galvanized Split-Set with a plate in #19        113  Sample 21: new black steel Split-Set Sample 22: new galvanized Split-Set   Sample 23: corroded Swellex bolt with a plate Sample 24: dripping water from rocks, not from equipment or paste    114  Appendix B  Pure Mineral Sample from Ward’s Science   Figure 68 Pure mineral sample from Ward's Science. See Table 1 on page 33 for details.    115  Appendix C  User Defined Function (UDF) /**********************************************************  node motion based on corrosion rate calculated from potential gradient  Remember to change /solve/set/expert> Keep temporary solver memory from being freed? [yes]  **********************************************************/ #include "udf.h"  #include "metric.h" #include "mem.h"  #include "sg_udms.h"  #include "sg.h"  #include "models.h"  #include "dynamesh_tools.h"  DEFINE_GRID_MOTION(corrosion_rate_vector,domain,dt,time,dtime) {  Thread *tf = DT_THREAD(dt);/*dt is the dynamic zone thread, face in this case*/  face_t f;/*face thread*/  Node *v;/*node pointer*/  int n=0;/*initiate node number*/  real Cr=0;/*initiate corrosion rate*/  real d=0.0021082;/*steel plate thickness 0.083i"*/  real F=96485.34;/*Faraday's constant C/mol or A*s/mol*/  real MWT=27.67;/*equivelent weight of steel alloy*/  int z=1;/*unit charge number of equivelent weight*/  real RHO=7900000;/*steel density 7750~8050 kg/m^3*/  real sigma=0.68;/*electrolyte conductivity 5 S/m*/  real d0=0;/*initial steel surface*/  real  A[3];/*declare face area vector*/  real  *E;/*declare potential gradient vector*/  real AMag=0;/*declare face area vector magnitude*/  real EMag=0;/*declare potential gradient magnitude*/   SET_DEFORMING_THREAD_FLAG(THREAD_T0(tf));/*set deforming flag on adjacent cell zone*/  begin_f_loop(f,tf)/*loop all face in face thread*/  {   if PRINCIPAL_FACE_P(f,tf)   {    F_AREA(A,f,tf);/*face normal vector*/    AMag=NV_MAG(A);/*magnitude of face area vector*/    A[0]=A[0]/AMag;    A[1]=A[1]/AMag;    A[2]=A[2]/AMag;    E=C_PHI_1_G(F_C0(f,tf),THREAD_T0(tf));/*call potential gradient vector from adjacent cell of the face*/    EMag=NV_MAG(E);/*magnitude of potential gradient vector*/    if (NV_DOT(E,A)>0)    {     Cr=(sigma*MWT/(z*F*RHO))*EMag;/*Cr=((sigma*(-fvc::grad(phiV)))*mw)/(z*F*rho)*/    } else Cr=0;    f_node_loop(f,tf,n)    {     v=F_NODE(f,tf,n);     if (NODE_POS_NEED_UPDATE (v))     {      NODE_POS_UPDATED(v);/*indicate that node position has been updated*/      if (NODE_Z(v)>(d0-d))      { /*      NODE_X(v)+=Cr*dtime*A[0];/*new x position*/ /*      NODE_Y(v)+=Cr*dtime*A[1];/*new y position*/       NODE_Z(v)+=Cr*dtime*A[2];/*new z position*/      } else      {       NODE_Z(v)=d0-d;/*maximum corrosion depth is reached*/      }     }    }   }  }  end_f_loop(f,tf); }  116  Appendix D  Numerical Corrosion Simulation Result  Figure 69 Sample 1 electric potential contour.  Figure 70 Sample 1 electric current magnitude contour. 117   Figure 71 Sample 1 corrosion depth contour.  Figure 72 Sample 1 corrosion depth contour with electric current magnitude mesh sections. 118   Figure 73 Sample 3 electric potential contour.  Figure 74 Sample 3 electric current magnitude contour.   119   Figure 75 Sample 3 corrosion depth contour.  Figure 76 Sample 3 corrosion depth contour with electric current magnitude mesh sections.  120   Figure 77 Sample 19 electric potential contour.  Figure 78 Sample 19 electric current magnitude contour. 121   Figure 79 Sample 19 corrosion depth contour.  Figure 80 Sample 19 corrosion depth contour with electric current magnitude mesh sections. 122   Figure 81 RCE matrix electric potential contour.  Figure 82 RCE matrix electric current magnitude contour. 123   Figure 83 RCE matrix corrosion depth contour.  Figure 84 RCE matrix corrosion depth contour with electric current magnitude mesh sections. 124  Appendix E  Confocal Profilometry   Figure 85 Sample 1-1 optical x100 (left), confocal height (right), profile (lower).   125    Figure 86 Sample 1-2 optical x100 (left), confocal height (right), profile (lower). 126    Figure 87 Sample 1-3 optical x100 (upper), confocal height (lower), profile (right).  127    Figure 88 Sample 1-4 optical x100 (left), confocal height (right), diagonal profile (lower).  128    Figure 89 Sample 1-5 optical x100 (left), confocal height (right), profile (lower). 129    Figure 90 Sample 1-6 optical x100 (upper), confocal height (lower), profile (right).   130    Figure 91 Sample 1-7 optical x100 (upper), confocal height (centre), vertical profile (right), horizontal profile (bottom).  131    Figure 92 Sample 1-8 optical x100 (upper), confocal height (lower), profile (right). 132    Figure 93 Sample 1-9 optical x100 (upper), confocal height (lower), profile (right). 133   Figure 94 Sample 1-10 optical x100 (left), confocal height (right), profile (lower).   Figure 95 Sample 3-1 optical x100 (left), confocal height (right), profile (lower). 134   Figure 96 Sample 3-2 optical x100 (left), confocal height (right), profile (lower).  Figure 97 Sample 3-3 optical x100 (left), confocal height (right), profile (lower). 135   Figure 98 Sample 3-4 optical x100 (left), confocal height (right), profile (lower). 136   Figure 99 Sample 3-5 optical x100 (upper), confocal height (lower), profile (right). 137   Figure 100 Sample 3-6 optical x100 (left), confocal height (right), profile (lower).  Figure 101 Sample 3-7 optical x100 (left), confocal height (right), profile (lower). 138   Figure 102 Sample 3-8 optical x100 (left), confocal height (right), profile (lower).  Figure 103 Sample 19-1 optical x100 (left), confocal height (right), profile (lower). 139   Figure 104 Sample 19-2 optical x100 (left), confocal height (right), profile (lower).  Figure 105 Sample 19-3 optical x100 (left), confocal height (right), profile (lower). 140   Figure 106 Sample 19-4 optical x100 (left), confocal height (right), profile (lower).  Figure 107 Sample 19-5 optical x100 (left), confocal height (right), profile (lower). 141   Figure 108 Sample 19-6 optical x100 (upper), confocal height (lower), profile (right). 142   Figure 109 Sample 19-7 optical x100 (left), confocal height (right), profile (lower).  Figure 110 Sample 19-8 optical x100 (left), confocal height (right), profile (lower). 143   Figure 111 RCE-1 optical x100 (upper), confocal height (lower), vertical profile (right). 144   Figure 112 RCE-2 optical x100 (left), confocal height (right), profile (lower).  145   Figure 113 RCE-3 optical x100 (left), confocal height (right), profile (lower).  Figure 114 RCE-4 optical x100 (left), confocal height (right), profile (lower).  146   Figure 115 RCE-5 optical x100 (left), confocal height (right), profile (lower).  Figure 116 RCE-6 optical x100 (left), confocal height (right), profile (lower). 147   Figure 117 RCE-7 optical x100 (left), confocal height (right), profile (lower). 148   Figure 118 RCE-8 optical x100 (left), confocal height (right), profile (lower).