School of Mining Engineering O PT I M U M D E PT H F OR T H E I N T R OD U C T I ON OF C R U SH P I L L AR S AT I M P AL A PL AT I N U M M I N E . Tatenda John Maphosa A research dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2022 i DECLARATION I declare that this report is my own, unaided work. I have read the University Policy on Plagiarism and hereby confirm that no plagiarism exists in this report. I also confirm that there is no copying nor is there any copyright infringement. I willingly submit to any investigation in this regard by the School of Mining Engineering and I undertake to abide by the decision of any such investigation. __________________________ __________________ Signature of Candidate Date 25/08/2022 ii ABSTRACT Impala Mine planned to introduce 4 m x 2 m crush pillars on the UG2 Reef, and were interested in finding the depth where such pillars can be safely used. These pillars have the benefit of increasing the extraction ratio whilst reducing the risk of pillar bursting. The mine provided rock samples composed of four rock types namely: anorthosite, chromitite, pegmatoid and pyroxenite for geomechanical testing. In addition, a database of previous tested rock specimens was provided. The rock samples provided for testing were used to determine post-peak behaviour under triaxial loading conditions, as well as Uniaxial Compressive and Brazilian Tensile strengths. During testing it was apparent that the testing machine was showing incorrect deformation readings. Investigations showed the problem to be the axial transducer, and it was replaced. Subsequently, the results of the correct laboratory tests were used as input parameters for a FLAC3D numerical model. Two scenarios for the crush pillar were modelled. Scenario 1 assumes the presence of a 2 m siding and scenario 2 assumes the pillar is right next to the gully. The model assumed repeating geometries of pillars and the results suggested peak strengths of 104 MPa and 79 MPa for scenario 1 and 2, respectively, and a residual strength of about 12 MPa for both scenarios. The investigations showed that the 4 m x 2 m crush pillars can be safely introduced at depths of 663 m and 476 m for pillars with and without a siding, respectively. The pillars can be introduced at shallower depths (from 357 m for pillar with a siding and 272 m for the one without a siding) with caution as the available stress may not be sufficient. iii DEDICATION To the almighty God and my parents Mr and Mrs Maphosa iv ACKNOWLEDGMENTS I would like to express my gratitude to my supervisor Professor Bryan Watson for his contributions, guidance and going the extra mile of assisting me in securing funding for this research. No words are enough to express my gratitude and I am greatly indebted to him. I would like to thank Les Gardner (Group Rock Engineering Manager for Impala Mine) for providing rock samples and data essential for this project. I would also like to thank Mr Andrew Carpede and Mr Andrew Morgan for their assistance with the laboratory work. Thank you to the School of Mining for their incredible support and funding. I would like to thank Mr Alan Kowa and Miss Thelma Mogorosi for providing accommodation and support for the duration of this research. Without their support it would not be possible to conduct this research. I also express my appreciation to Mr Joel Chinyama for his assistance and support during the research. A special thank you to Mr Marlvin Maphosa and Mrs Candice Hendricks for their support during the research. v TABLE OF CONTENTS DECLARATION ........................................................................................... i ABSTRACT ................................................................................................. ii DEDICATION ............................................................................................. iii ACKNOWLEDGMENTS ............................................................................ iv LIST OF FIGURES .................................................................................... ix LIST OF TABLES ...................................................................................... xv APPENDIX LIST OF FIGURES ............................................................... xvi APPENDIX LIST OF TABLES ................................................................. xvii LIST OF SYMBOLS ............................................................................... xviii 1 Introduction ........................................................................................ 1 1.1 Bushveld complex ..................................................................... 1 1.1.1 UG2 geology .................................................................... 2 1.2 Research background ............................................................... 4 1.3 Aims of the research ................................................................. 6 1.4 Research summary ................................................................... 7 2 Literature review ................................................................................. 9 2.1 Sample testing .......................................................................... 9 2.1.1 Calibration........................................................................ 9 2.1.2 Stiffness ........................................................................... 9 2.1.3 Class I post-peak behaviour .......................................... 11 2.1.4 Class II post-peak behaviour ......................................... 12 vi 2.1.5 Servo-controlled testing machine ................................... 14 2.2 Rock Dilatancy ........................................................................ 16 2.3 Defining failure ........................................................................ 18 2.4 Failure modes in pillars ........................................................... 19 2.5 Common pillar types found in the Bushveld complex. ............. 19 2.5.1 Non-yield pillars ............................................................. 19 2.5.2 Barrier pillars .................................................................. 20 2.5.3 Yield pillars .................................................................... 21 2.5.4 Crush pillars ................................................................... 21 2.6 History of crush pillars ............................................................. 22 2.6.1 Design of crush pillars ................................................... 22 2.6.2 Typical crush pillar behaviour and challenges associated with crush pillars. ......................................................................... 25 2.7 Effect of mining depth on crush pillars .................................... 26 2.7.1 Transition zone .............................................................. 27 2.8 Peak strength .......................................................................... 29 2.8.1 Effect of width to height ratio on pillar strength .............. 33 2.8.2 The effects of Foundation draping. ................................ 34 2.9 Pillar Foundation ..................................................................... 35 2.9.1 Pillar system failure ........................................................ 35 2.10 Post-peak behaviour of pillars ................................................. 38 2.10.1 Local mine stiffness stability criterion ......................... 39 2.10.2 Strata stiffness ........................................................... 39 2.10.3 Residual strength ....................................................... 41 vii 2.11 Numerical modelling of pillars ................................................. 42 2.12 Chapter summary.................................................................... 43 3 Laboratory testing ............................................................................. 44 3.1 Calibration ............................................................................... 44 3.2 Challenges faced during rock testing ...................................... 46 3.2.1 Oil contamination ........................................................... 46 3.2.2 Test control procedures ................................................. 47 3.2.3 Problems with the Axial transducer ................................ 48 3.2.4 Investigating transducer issues ...................................... 50 3.2.5 Axial extensometer calibration ....................................... 64 3.2.6 New axial extensometer ................................................ 67 3.3 Sample preparation and test procedure .................................. 70 3.3.1 Rock samples ................................................................ 70 3.3.2 Specimen preparation .................................................... 71 3.3.3 Indirect tensile test (Brazilian test) ................................. 72 3.3.4 Tilt test ........................................................................... 75 3.3.5 Uniaxial Compressive strength test ............................... 77 3.3.6 Triaxial testing using the MTS servo-controlled testing machine. ...................................................................................... 79 3.4 Test results ............................................................................. 88 3.4.1 Post-peak investigations ................................................ 89 3.4.2 Data comparison .......................................................... 104 3.5 Chapter summary.................................................................. 111 4 Numerical modelling ....................................................................... 113 viii 4.1 FLAC3D model input parameters .......................................... 113 4.1.1 The plastic shear strain parameter .............................. 114 4.1.2 Residual cohesion and internal friction angle .............. 118 4.2 Triaxial model ........................................................................ 120 4.3 Crush pillar model ................................................................. 124 4.3.1 Downrating of input parameters ................................... 124 4.3.2 The influence of interfaces ........................................... 126 4.3.3 Model description ......................................................... 138 4.3.4 Scenario 1.................................................................... 142 4.3.5 Scenario 2.................................................................... 145 4.3.6 Safe depth to introduce crush pillars ............................ 149 4.4 Chapter summary.................................................................. 156 5 Conclusions and Recommandations .............................................. 158 5.1 Conclusion ............................................................................ 158 5.2 Recommendations ................................................................ 159 6 Reference List ................................................................................ 160 Appendix A ............................................................................................ 167 Appendix B ............................................................................................ 174 Appendix C ............................................................................................ 177 Appendix D ............................................................................................ 181 ix LIST OF FIGURES Figure 1.1 Map of the Bushveld Complex, showing the different limbs (the eastern, western and northern limbs). Major towns are marked in red and active mines (including mine projects) are marked in green (Cawthorn, 2010). ......................................................................................................... 2 Figure 1.2 UG2 reef stratigraphy ................................................................ 3 Figure 1.3 Location of Impala mine (Implats, 2018) ................................... 4 Figure 1.4 Typical in stope pillar stress-strain behaviour (Jager and Ryder, 1999) .......................................................................................................... 6 Figure 2.1 Typical Class 1 behaviour (Vogler, 2014). .............................. 12 Figure 2.2 Typical class II behaviour (Vogler, 2014) ................................ 14 Figure 2.3 Closed servo-controlled feedback loop (Xu, 2017). ................ 15 Figure 2.4 Idealized bilinear curve for the determination of the dilation angle. Adapted from (Vermeer and De Borst, 1984). ......................................... 17 Figure 2.5 Typical stress-strain behaviour of pillars with different width to height ratio. Points Y and C indicate the operating points of yield pillars and crush pillars, respectively. ........................................................................ 20 Figure 2.6 FLAC model showing effect of width to height ratio for pillars allowed to punch, as well as for pillars surrounded by infinitely strong rock mass (Watson, 2010). .............................................................................. 25 Figure 2.7 Typical barrier-crush pillar layout (Watson et al., 2010). ......... 27 file:///C:/Users/Maphosa/Dropbox/My%20PC%20(LAPTOP-TMFBG062)/Documents/submission/Dissertation%20corrected%20(Tatenda%20Maphosa%20692434).docx%23_Toc111935181 file:///C:/Users/Maphosa/Dropbox/My%20PC%20(LAPTOP-TMFBG062)/Documents/submission/Dissertation%20corrected%20(Tatenda%20Maphosa%20692434).docx%23_Toc111935181 file:///C:/Users/Maphosa/Dropbox/My%20PC%20(LAPTOP-TMFBG062)/Documents/submission/Dissertation%20corrected%20(Tatenda%20Maphosa%20692434).docx%23_Toc111935181 x Figure 2.8 Schematic showing the in-stope pillars appropriate for different mining depths (Jager and Ryder, 1999) ................................................... 29 Figure 2.9 Illustration showing foundation draping (Watson, 2010). ........ 35 Figure 2.10 The Prandtl wedge (Baars, 2015) ......................................... 37 Figure 2.11 Diagram show a typical Prandtl wedge shape (Watson, 2010) ................................................................................................................. 38 Figure 2.12 Illustration showing extreme cases of hangingwall stiffness. At the top shows the case of totally stiff hangingwall and at the bottom shows case of totally soft hangingwall (Kersten, 2016). ...................................... 40 Figure 3.1 The original length of the axial extensometer ......................... 46 Figure 3.2 Stress/strain curve of anorthosite sample at 30MPa confinement. ................................................................................................................. 49 Figure 3.3 Axial (top) and radial extensometer in an empty triaxial cell ... 50 Figure 3.4 Results of pressurized triaxial cell ........................................... 52 Figure 3.5 Specimen with platens and axial extensometer attached. ...... 53 Figure 3.6 Steel sample test setup ........................................................... 54 Figure 3.7 Comparison of extensometer to strain gauges (Aluminium sample) .................................................................................................... 55 Figure 3.8 Comparison of extensometer to strain gauges (Steel sample) 56 Figure 3.9 Adjusted axial extensometer readings. ................................... 57 xi Figure 3.10 Stress/strain curves for no sleeve, with sleeve and with strain gauges ..................................................................................................... 58 Figure 3.11 Influence of the local sleeve under different confinements ... 60 Figure 3.12 Local (left) and American sleeve (right) ................................ 61 Figure 3.13 Effect of confinement on the American sleeve ...................... 62 Figure 3.14 Effect of confinement on the two sleeves .............................. 63 Figure 3.15 Micrometre screw gauge ....................................................... 65 Figure 3.16 Micrometre readings vs MTS reading ................................... 66 Figure 3.17 Existing extensometer vs new extensometer. ....................... 67 Figure 3.18 Comparison of new and old extensometer ............................ 68 Figure 3.19 Comparison of test results from the new and old extensometer on an aluminium sample .......................................................................... 69 Figure 3.20 Strain gauged samples ......................................................... 72 Figure 3.21 Indirect tensile test setup showing the steel jaw cell ............. 73 Figure 3.22 Specimen in the MTS criterion testing machine .................... 74 Figure 3.23 Tilt test setup ........................................................................ 76 Figure 3.24 Amsler compression testing machine ................................... 77 Figure 3.25 Data acquisition unit on the left and on the right the strain gauge amplifier. .................................................................................................. 79 Figure 3.26 The MTS 815 servo-controlled testing machine .................... 80 Figure 3.27 Hydraulic power unit ............................................................. 81 xii Figure 3.28 Servo-valves ......................................................................... 82 Figure 3.29 Confining pressure intensifier ............................................... 84 Figure 3.30 MTS Flex 60 ......................................................................... 85 Figure 3.31 Axial extensometer on the left and the radial extensometer on the right .................................................................................................... 86 Figure 3.32 Specimen ready for testing (American sleeve) ..................... 87 Figure 3.33 MPT procedure used to perform triaxial tests on the MTS machine ................................................................................................... 88 Figure 3.34 Stress-strain curves for pyroxenite........................................ 90 Figure 3.35 Stress-strain curves for pegmatoid ....................................... 91 Figure 3.36 Stress-strain curves for chromitite......................................... 92 Figure 3.37 Stress-strain curves for anorthosite ...................................... 93 Figure 3.38 Effect confinement on residual strength ................................ 94 Figure 3.39 Plot of volumetric strain vs axial strain for a pyroxenite sample at 20 MPa confinement ............................................................................ 95 Figure 3.40 Plot of dilation angles vs confining pressure for pyroxenite .. 96 Figure 3.41 Stress-strain curves for granite (Zhang and Li, 2019) ........... 97 Figure 3.42 Illustration showing the fracture angle (β) (Zhang and Li, 2019) ................................................................................................................. 98 Figure 3.43 The failure angles for each rock type .................................... 99 Figure 3.44 Failure envelopes for pyroxenite ......................................... 100 xiii Figure 3.45 Diagram showing the fracture angles of the two fracture planes ............................................................................................................... 102 Figure 3.46 Fracture angles for samples having two shear planes ........ 103 Figure 3.47 Sample having multiple shear fractures .............................. 104 Figure 3.48 Plot of peak strength vs confining Pressure ........................ 107 Figure 4.1 Stress-strain curve for a chromitite sample with points of crack initiation and crack damage marked ...................................................... 115 Figure 4.2 Estimation of residual cohesion and internal friction angle using Mohr's circles ......................................................................................... 119 Figure 4.3 Model set up for triaxial simulation ........................................ 121 Figure 4.4 Simulated stress-strain curves for pyroxenite at 10 MPa ...... 123 Figure 4.5 Stress-strain curve for pyroxenite at 10 MPa ........................ 123 Figure 4.6 Screen shot of Roclab software used for downrating the input parameters ............................................................................................. 124 Figure 4.7 Boundary conditions applied to model .................................. 127 Figure 4.8 Schematic showing the three interfaces ............................... 128 Figure 4.9 Initial model results ............................................................... 129 Figure 4.10 Progression of failure .......................................................... 130 Figure 4.11 Stress variation as pillar fails .............................................. 131 Figure 4.12 Influence of interface 1 on peak strength ............................ 133 Figure 4.13 Influence of interface 1 on progression of failure ................ 133 xiv Figure 4.14 Influence of interface 2 on peak strength ............................ 134 Figure 4.15 Influence of interface 2 on progression of failure ................ 135 Figure 4.16 Influence of interface 3 on peak strength ............................ 136 Figure 4.17 Influence of interface 3 on progression of failure ................ 137 Figure 4.18 Schematic (plan view) showing the two modelled scenarios ............................................................................................................... 139 Figure 4.19 Shows the strain softening curves ...................................... 140 Figure 4.20 Model showing perfectly plastic behaviour. ......................... 141 Figure 4.21 Strain softening curves used in modelling pillar behaviour . 142 Figure 4.22 3D Model of Scenario 1 ...................................................... 143 Figure 4.23 Model results for Scenario 1 ............................................... 144 Figure 4.24 Progression of failure Scenario 1 ........................................ 144 Figure 4.25 Variation of stress Scenario 1 ............................................. 145 Figure 4.26 Model setup for Scenario 2 ................................................. 145 Figure 4.27 Model results for Scenario 2 ............................................... 146 Figure 4.28 Draping effect ..................................................................... 147 Figure 4.29 Progression of failure Scenario 2 ........................................ 148 Figure 4.30 Stress variation for Scenario 2 ............................................ 148 Figure 4.31 Schematic of the ledging process at Impala Mine (Carollo, 2022) ............................................................................................................... 150 xv Figure 4.32 Full model side view ............................................................ 152 Figure 4.33 Close up view of the ledge and the two stubs ..................... 152 Figure 4.34 Worst-case scenario model results ..................................... 154 Figure 4.35 Side view of the best-case model ....................................... 154 Figure 4.36 Close up view of model ....................................................... 155 Figure 4.37 Best-case scenario model results ....................................... 156 LIST OF TABLES Table 3.1 Summary of rock samples ........................................................ 71 Table 3.2 Tilt test results .......................................................................... 76 Table 3.3 Comparison fracture angles ................................................... 101 Table 3.4 Brazilian test results ............................................................... 105 Table 3.5 Values of cohesion and internal friction angle. ....................... 108 Table 3.6 Comparison of elastic constants ............................................ 110 Table 3.7 Bulk and shear modulus values ............................................. 111 Table 4.1 Numerical model input parameters ........................................ 114 Table 4.2 Shows the shear strain parameters used in the triaxial model 118 Table 4.3 Residual values of cohesion and internal angle of friction...... 119 Table 4.4 Comparison of modelled values and lab test results .............. 122 Table 4.5 Intact rock parameters ........................................................... 125 xvi Table 4.6 Crush pillar model input parameters. C is the cohesion, Φ is the friction angle, Erm is the down rated elastic modulus, δt is the tension, K is the bulk modulus, G is the shear modulus and ψ is the dilation angle. .. 126 Table 4.7 Interface input parameters ..................................................... 129 Table 4.8 Interface input values ............................................................ 138 APPENDIX LIST OF FIGURES Figure A- 1 Stress-strain curves for pyroxenite set 2 ............................. 167 Figure A- 2 Stress-strain curves for pyroxenite set 3 ............................. 168 Figure A- 3 Stress-strain curves for pegmatoid set 2 ............................. 168 Figure A- 4 Stress-strain curves for pegmatoid set 3 ............................. 169 Figure A- 5 Stress-strain curves for pegmatoid set 4 ............................. 169 Figure A- 6 Stress-strain curves for chromitite set 2 .............................. 170 Figure A- 7 Stress-strain curve for chromitite set 3 ................................ 170 Figure A- 8 Stress-strain curve for chromitite set 4 ................................ 171 Figure A- 9 Stress-strain for anorthosite set 2 ....................................... 171 Figure A- 10 Stress-strain for anorthosite set 3 ..................................... 172 Figure C- 1 Failure envelopes for anorthosite ........................................ 177 Figure C- 2 Failure envelopes for pyroxenite ......................................... 178 Figure C- 3 Failure envelopes for chromitite .......................................... 178 Figure C- 4 Estimation of residual cohesion and internal friction angle for anorthosite ............................................................................................. 179 xvii Figure C- 5 Estimation of residual cohesion and internal friction angle for chromitite ............................................................................................... 179 Figure C- 6 Estimation of residual cohesion and internal friction angle for Pegmatoid .............................................................................................. 180 Figure C- 7 Estimation of residual cohesion and internal friction angle for pyroxenite .............................................................................................. 180 Figure D- 1 Simulated stress-strain curves for chromitite ...................... 181 Figure D- 2 Simulated stress-strain curve for anorthosite ...................... 181 Figure D- 3 Simulated stress-strain curve for pegmotoid ....................... 182 APPENDIX LIST OF TABLES Table A- 1 Effect of confinement on the elastic constants ..................... 173 xviii LIST OF SYMBOLS Stress  Shear stress  Strain  Young‘s modulus  Poisson‘s ratio ν Cohesion C Internal friction angle  Plastic shear strain p Dilation angle  Pillar height h Effective pillar height he Pillar width w Pillar effective width we In situ cube strength Ki Pillar width strengthening parameter  Pillar height strengthening parameter  Pillar width-to-height ratio w/h Uniaxial compressive strength δci or UCS Material constant mi 1 1 INTRODUCTION The research in this project investigates the optimum depth at which 4 m x 2 m crush pillars can be introduced in the Upper Group 2 (UG2) reef at Impala Rustenburg mine. To achieve this objective, a series of triaxial tests were done to determine the post-peak behaviour on the supplied samples. The samples were composed of four rock types namely; anorthosite, chromitite, pegmatoid and pyroxenite. For continuity, uniaxial compressive tests and indirect tensile tests were also performed. These tests provided the necessary parameters to calibrate a FLAC3D numerical model. The aim of the model was to determine the stress conditions required for the crush pillar to work effectively. 1.1 Bushveld complex The Bushveld Complex is one of the world’s largest igneous layered intrusions and it hosts most of the platinum group metals on the planet. It also hosts other metals like iron, tin, nickel and gold. Chromium and vanadium seams occur parallel to the platinum orebodies. Chromium seams are normally situated in the footwall and vanadium in the hangingwall (Watson, 2010). The Merensky reef, UG2 and the Platreef are the only three platinum bearing orebodies known to be economically viable in the complex (Labuschagne et al., 2015). The most exploited platinum ore bodies in the complex are the Merensky and UG2. The Bushveld Complex is situated in the northern part of South Africa, north of the city of Pretoria. Figure 1.1 shows a map of the Bushveld Complex. 2 Figure 1.1 Map of the Bushveld Complex, showing the different limbs (the eastern, western and northern limbs). Major towns are marked in red and active mines (including mine projects) are marked in green (Cawthorn, 2010). 1.1.1 UG2 geology The thickness of the UG2 reef varies between 0.4 m -2.5 m (0.5 m – 0.7 m at Impala but rarely reaches thickness over of 1 m). The UG2 reef is generally characterised by a pegmatoidal pyroxenite footwall, a main layer which is a combination of two or more (up to 9) chromitite layers overlain by melanoritic rocks that contain a thin chromitite leader and triplets (very thin chromitite layers). At Impala the immediate hangingwall above the UG2 Chromitite seam is typically comprised of a 6 m – 9 m thick layer of Pyroxenite. This layer is followed by anorthosite linked by a gradational contact. Chromitite layers (Intermediate Chromitite Layer (ICL), the Leader and Triplets) present in the pyroxenite, represent planes of potential parting. These planes occur from a few centimetres into the 3 hangingwall up to 4 m. A general stratigraphy column showing the typical sequence of rock types above and below the UG2 seam is provided in Figure 1.2. The dashed rectangle shows the rock types that were provided by the mine and used for numerical modelling presented in Chapter 4. Figure 1.2 UG2 reef stratigraphy Normal and reverse faults are encountered on the UG2 reef, with reverse faults being the most common (Impala Mine Rock Engineering Department, 2017). The strike of most faults tends towards the reef strike. Geological features like potholes and dykes are prevalent throughout the lease area and these structures contribute to geological losses. Potholes are oval structures where the reef elevation suddenly drops within the confines of the oval. On the UG2 horizon, the presence of potholes is usually indicated by the thinning of the chromitite layer and footwall lithologies and the absence of pegmatoid in the footwall. 4 1.2 Research background The research was conducted at Impala Platinum Mine located in the Western Lobe of the Bushveld Complex. The mining operation is situated 30 km North of Rustenburg in the North West Province of South Africa. Figure 1.3 shows the location of Impala mine in relation to other mines on the Western Bushveld Limb. Figure 1.3 Location of Impala mine (Implats, 2018) Impala mine is the world’s second-largest producer of platinum group metals (PGM). The mine produces approximately 750 thousand ounces of refined platinum plus other PGMs 5 per annum. The Bushveld Complex comprises of alternating pyroxenite, chromitite, norite and several layers of anorthosite rock types. At Impala Platinum Mine, these layers have an average dip of 9 degrees towards the north-east. Two orebodies are currently mined, namely: ➢ Merensky Reef; and ➢ UG2 Reef. The Merensky is almost mined out. In the north, the UG2 layer is 60 m below the Merensky Reef and the distance between the two reefs increases to 130 m in the south. The general strike direction of the layering is north-northwest to south-southeast but local variations can cause the strike direction to change. The average UG2 reef width is 0.91 m (Impala Mine Rock Engineering Department, 2017). The immediate hangingwall and footwall of the UG2 reef stope is pyroxenite and spotted anorthosite, respectively. The depth of the UG2 workings ranges between 30 m and 1400 m. Underground mining operations are conducted from 12 shafts with two new shafts in ramp-up phase. Most of the mining is done using a scattered mining method with selective mining, and geological losses are left unmined. However, a limited amount of stoping is also done using mechanised room and pillar. The regional support strategy comprises barrier pillars together with geological losses. In the stopes, pillar support consists of non- yielding pillars, yield pillars and crush pillars. Figure 1.4 shows typical stress-strain behaviour of in stope pillars for the Merensky reef. Points Y and C marked on Figure 1.4 indicate the operating points of yield and crush pillars, respectively. 6 Figure 1.4 Typical in stope pillar stress-strain behaviour (Jager and Ryder, 1999) 1.3 Aims of the research Currently the mine is using 6 m x 3 m yield pillars but plans to introduce smaller 4 m × 2 m crush pillars on the UG2 reef and are interested in determining at what depth these pillars can be introduced. Crush pillars have the benefit of improving the extraction ratio and do not present a burst risk once they reach the residual strength. However, crush pillars can be prone to violent failure if they do not fail close to the face (Watson, 2010). The available stress at the face must exceed the peak strength of the pillar otherwise crushing will not take place and the pillar becomes a hazard in the back area. Yield pillars Crush Pillars 7 The objective of this research is to determine the depth at which crush pillars can be introduced. However, depth is not the only metric to use when deciding when to introduce pillars. In general, the available stress at the face determines whether the pillar will fail as it is cut. A particular depth does not guarantee that the stresses at the face will be sufficient to initiate failure of the pillar. More focus was therefore placed on determining the peak strength and the minimum available stress required for the 4 m x 2 m pillar failure. This was achieved by conducting laboratory tests and setting up a series of numerical models in FLAC3D to estimate the strength and available stresses. 1.4 Research summary Chapter 2 reviews work done by previous researchers on post-peak behaviour of rocks. This includes triaxial testing using servo-controlled rock testing machines and factors that affect post-peak behaviour. The chapter also reviews previous investigations done on crush pillars. The history of crush pillars and the factors that affect their performance are described in this chapter. Chapter 3 describes the methodology used during rock testing and the challenges that were faced whilst performing the rock tests. The testing procedures for triaxial (involving post-peak), Uniaxial Compressive Strength test (UCS) and indirect tensile test (Brazilian test) are described in this chapter. Procedures used in investigating issues pertaining to the testing as well as the solutions to these issues are also defined. The results from all the rock tests that were performed are presented. Chapter 4 presents the numerical models. FLAC3D was used for numerical simulation of pillar strength and the determination of the available stress. A triaxial numerical model 8 was setup in FLAC3D with the objective of reproducing stress-strain curves obtained in Chapter 3. The calibrated model was subsequently used to simulate crush pillar behaviour. The objective of this model was to estimate the stress requirements of the 4 m x 2 m crush pillar. Two scenarios for the crush pillar were modelled. Scenario 1 assumes the presence of a 2 m siding. Scenario 2 assumes the pillar is right next to the gully. The chapter describes the strength and deformation characteristics of the pillar. 9 2 LITERATURE REVIEW This chapter provides a literature review on post-peak rock testing and crush pillars. The role of machine stiffness and servo control in investigating post-peak investigations is discussed. In addition, the chapter describes the history of crush pillars and factors that affect their performance. 2.1 Sample testing 2.1.1 Calibration Calibration refers to the setting of the origin and choice of scale to be used by a measuring instrument against a traceable reference or standard (Dawkins et al., 2001). This is important as it ensures the collection of accurate data and allows a comparison of collected data with other available data using the same standard. Over time the accuracy of a rock testing machine may change. This can be caused by wear and tear or the equipment standing idle for extended periods. Equipment calibration at recommended intervals is vital to minimise uncertainty and allow the equipment to give reliable, accurate and repeatable measurements. 2.1.2 Stiffness Description Stiffness is the ability of a material (in this case rock) to resist deformation when exposed to a stress (Hudson et al., 1972). 10 Implications of test machine stiffness on rock test According to Hudson et al., (1972) a testing machine is characterised as either soft or stiff with respect to a given rock specimen. During testing, both the specimen and the machine deform as the load increases (Salamon, 1970). Salamon, (1970) observed that the equilibrium between the testing machine and the sample remains stable if the machine is unable to induce further displacement in the specimen without a supply of additional external energy. This is in line with observations made by Cook, (1963) which led him to conclude that the violent, brittle behaviour observed during testing, was due to excess energy stored in the machine (Cook, 1963). This resulted in the design of stiff testing machines. To obtain a complete stress-strain curve, the following condition must be met throughout the test to avoid abrupt violent failure (Hudson et al., 1972). 𝑆𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑐ℎ𝑖𝑛𝑒 > 𝑡ℎ𝑒 𝑝𝑜𝑠𝑡 𝑝𝑒𝑎𝑘 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 (2-1) The post-peak stiffness of the sample depends on factors such as length, loading-area, confinement, presence of discontinuities, etc. This means that the post-peak stiffness of a material is not an intrinsic property of the material (Beruar et al., n.d.). Investigations done by Wawersik and Fairhurst, (1970) showed that the post-peak behaviour exhibited by rock samples can be classified into two distinct classes, Class I and Class II. The investigations also showed that high machine stiffness (which facilitates fracture control) on its own is not always sufficient to obtain a complete stress-strain curve (Wawersik and Fairhurst, 1970). Most rocks exhibit Class I strain softening (post-peak behaviour) where the tangential modulus is negative. The behaviour exhibited by a specimen can be affected by the depth at which the specimen was obtained. Specimens 11 obtained by Watson (2010) at depths greater than 1000 m at Impala Platinum exhibited a different class compared to specimens obtained from the same mine at depths less than 1000 m for the same rock type. 2.1.3 Class I post-peak behaviour Rocks that exhibit class I behaviour require work to be done on them to induce further deformation. Fracture propagation is stable (Wawersik and Fairhurst, 1970) provided that the highest absolute value of post-peak stiffness is less than the machine stiffness (Hudson et al., 1972). Typical Class I behaviour of rock is that both the axial and lateral strain continuously increase during the deformation cycle (Oniyide, 2015). This means either axial or lateral strain can be set as the control to trace out the complete stress-strain curve. When a soft testing machine (machine that accumulates excessive strain energy in its components) is used on a Class I rock, the accumulated strain energy will exceed the energy required by the rock to propagate the fracture, resulting in violent failure (Vogler, 2014). However, if a stiff testing machine is used, the system (machine and rock sample) will remain in equilibrium as the elastic strain energy stored in the machine is less than the energy required by the rock sample for failure propagation. Figure 2.1 shows a typical Class I stress/strain curve with shaded regions indicating energy supplied by the testing machine and energy required to deform the rock specimen (Vogler, 2014). From Figure 2.1, additional energy would have to be supplied to continue testing from A to B. The shaded area (1+2+3) represents the supplied energy by the machine from O to B. The energy supplied by the machine to reach peak at A is represented by area (1+2). Area (1) represents the non-recoverable energy. This includes energy required for crack formation and crack propagation, plastic deformation, heat, extension, etc. Area (2) shows 12 the elastic energy stored in the sample at A. The additional energy required to deform the rock sample from A to B is represented by area (3). If the testing machine has sufficient stiffness it is possible to trace out the complete stress-strain curve for Class I rock samples (Vogler, 2014). Figure 2.1 Typical Class 1 behaviour (Vogler, 2014). 2.1.4 Class II post-peak behaviour Class II behaviour is characterized by unstable and self-sustaining fracture propagation. To obtain a complete stress/strain curve, energy must be extracted from the sample being tested. ‘Even with an infinitely stiff testing machine, it would still not be possible to trace the full stress-strain curves for rocks with Class II behaviour due to the elastic energy stored in the rock specimens’ (Vogler, 2014). In other words, machine stiffness on its own 13 is not adequate to control failure of a Class II rock type. Lateral strain is used as the control (in the post-peak phase) for Class II rock types, as it is the only variable that monotonically increases throughout the rock test (Oniyide, 2015). Figure 2.2 shows a typical Class II stress/strain curve with shaded regions indicating energy supplied by the testing machine and energy required to deform the rock specimen. From Figure 2.2, the axial strain increases from point O to A, then decreases from point A to B after which it starts to increase until point C. Area (1+2+4) represents the total energy supplied by the machine to deform the rock specimen. The energy supplied by the machine to reach peak strength is represented by area (1+2+3). Area (3) represents energy that needs to be extracted from a Class II rock sample. Area (1) shows the non-recoverable energy. Area (2+3) shows the elastic energy present in the sample at point A. The energy required to complete the test from peak strength (from point A to C) is represented by area (2+4) (Vogler, 2014). 14 Figure 2.2 Typical class II behaviour (Vogler, 2014) 2.1.5 Servo-controlled testing machine The main purpose of a servo-controlled testing machine is to trace out the stress-strain curve beyond the peak stress, using the strain in the rock as the controlled variable (Jaeger et al., 2007). In this type of testing machine, deformation is monitored and compared to the desired strain. Any difference between the desired strain and the measured strain creates a correctional signal which adjusts the piston position to bring the strain close to the desired value (Jaeger et al., 2007). Servo-controlled testing machines have very rapid response time (in the range of a few milliseconds). This is quick enough to stop rapid disintegration of the specimen. The machine can trace out the complete stress-strain curve if the lateral strain increases monotonically (Oniyide, 2015). Figure 2.3 shows the closed loop feedback system. 15 Figure 2.3 Closed servo-controlled feedback loop (Xu, 2017). Controlled failure can be achieved if the response time of the controlling transducer is quicker than the initiation of rock failure process (Xu, 2017). This allows rock instability to be detected in advance. A servo-controlled pump can be activated by the onset of instability to reduce the fluid pressure rapidly, which in turn increases the effective unloading stiffness of the test machine. Servo-controlled testing machine are designed to ensure slow contraction rate of the rock which allows servo-pump response to be quick enough (Xu, 2017). This ensures that the effective unloading stiffness of the servo- controlled test machine is greater than the post-peak stiffness of the tested rock (Xu, 2017) and the testing machine does not transfer energy to rock sample (which would result in violent failure) allowing the sample to fail in a controlled manner. A servo-controlled testing 16 machine can be used to trace out the complete stress-strain curve for rock samples exhibiting both Class I and Class II post-peak behaviour. 2.2 Rock Dilatancy The concept of dilatancy was first introduced by Hansen (1958) to soil mechanics. The dilation angle (ψ) is a parameter that defines the degree to which a shear band increases in volume during slip (Walton and Diederichs, 2015). Under triaxial conditions the volumetric strain is equal to the sum of the axial strain and two times the radial strain as shown in Equation (2-2). The volumetric strain (𝜀𝑣) is defined as a measure of the change in volume per unit volume of the material (Vermeer and De Borst, 1984). Vermeer and de Borst (1984) developed an Equation (2-3) to calculate the dilation angle (ψ). This equation holds true for plain strain conditions and triaxial compression. Figure 2.4 shows the idealized bilinear curve. 𝜀𝑣 = 𝜀𝑎 + 2𝜀𝑟 (2-2) Where 𝜀𝑣 is the volumetric strain, 𝜀𝑎 is the axial strain and 𝜀𝑟 is the radial strain. sin(𝜓) = 𝜀�̇� 𝑝 −2𝜀1̇ 𝑝 + 𝜀�̇� 𝑝 (2-3) Where 𝜀�̇� 𝑝 is the volumetric strain and 𝜀1̇ 𝑝 is the principal strain. The superscript p stands for plastic. 17 Figure 2.4 Idealized bilinear curve for the determination of the dilation angle. Adapted from (Vermeer and De Borst, 1984). The initial slope of the idealized curve corresponds to the elastic region (OA). The slope of AB is used in the calculation of ψ and Equation (2-4) is used for this purpose. 𝜓 = sin−1 ( tan 𝛽 −2 + tan 𝛽 ) (2-4) Equation 2-5 can be re-written as follows Ψ = dilation angle Ø = Friction angle ν = poisson’s ratio 18 𝜓 = sin−1 ( 𝑚 −2 + 𝑚 ) (2-5) Where m is the gradient of the idealized post-peak curve in Figure 2.4 (tanβ). Equation 2.5 was used in this research to determine the dilation angle. The dilation angle is sensitive to confinement and tends to decrease with increasing confinement (Walton and Diederichs, 2015). Also, as the confinement increases the onset of dilation is delayed. The angle also varies depending on what stage the rock specimen is at during triaxial testing. The dilation angles in the elastic region are very small or non-existent and are considered insignificant. This is because in the elastic region there is hardly any microcracking taking place in the rock specimen (Vermeer and De Borst, 1984). In the strain hardening regime the rock specimen progressively becomes inelastic because of micro fracturing. The dilation angles in this stage tend to rapidly increase until peak strength. In the strain-softening regime the strain recorded is purely plastic and this is the same when the specimen reaches residual state. At this stage the dilation angles are constant. The dilation angles in the strain -softening regime gradually decrease until the specimen reaches residual state (Walton and Diederichs, 2015). 2.3 Defining failure In geomechanics, several definitions of failure are described. The first definition describes a state where the rock can no longer support the forces applied to it or otherwise fulfil its engineering functions (Galvin, 2014). A second definition is simply a state where the peak strength is exceeded. The latter definition is used in this research. 19 2.4 Failure modes in pillars According to Mathey and Van der Merwe, (2016) there are two failure modes observed in pillars. These are brittle failure and quasi-ductile failure. Brittle failure has been observed in South African mines for pillars with a w/h of less than or equal to 4 (Mathey and van der Merwe, 2016). Brittle pillars exhibit a distinct peak load and if further strain is imposed on the pillar, the strength of the pillar drops to a residual level. The load bearing capacity of brittle pillars is mainly controlled by the cohesive strength of the material. This brittle behaviour is exhibited by crush pillars. In quasi-ductile failure, the pillar may lose its cohesion entirely, but it maintains or even increases its load-bearing capacity with increasing strain (Mathey and van der Merwe, 2016). This failure mode has been observed in pillars with sufficiently high w/h, which allows enough confinement to be generated in the core of the pillar. Ductile pillars get their seemingly unlimited strength from the shear resistance of the fractured material (Mathey and van der Merwe, 2016). 2.5 Common pillar types found in the Bushveld complex. 2.5.1 Non-yield pillars These are pillars that provide support to the overburden. This type of pillar is designed to remain intact and elastic throughout the life of mine (Ozbay et al., 1995). They are commonly used in shallow mines. They usually have a width to height ratio (w/h) of 2-5. The pillar size increases as the depth increases. This makes them less economical to use at deep level. The pillar behaviour is shown in Figure 2.5. 20 2.5.2 Barrier pillars Barrier pillars provide regional support. They have a w/h greater than 5. They are usually oriented towards strike or dip. These pillars are designed to remain intact and elastic throughout the life of mine. They also serve the purpose of compartmentalizing the mine into sections to prevent regional failure of the mine. They also help reduce stope closure and prevent surface subsidence. Barrier pillars also increase the overall strata stiffness Figure 2.5 Typical stress-strain behaviour of pillars with different width to height ratio. Points Y and C indicate the operating points of yield pillars and crush pillars, respectively. 21 which helps prevent large scale failure (Ozbay et al., 1995). Geological losses are also incorporated into barrier pillars. 2.5.3 Yield pillars Yield pillars usually have a safety factor greater than or equal to one. They are designed to operate at stress levels close to their peak strength. Yield pillars can only function provided that the surrounding strata stiffness is higher than the absolute value of the post- peak stiffness of the pillar, otherwise violent failure will occur. This type of pillar is commonly used in the transition zone (300m-600m), where crush pillars cannot readily be used (Ozbay et al., 1995). Yield pillars are prone to bursting. Figure 2.5 shows the operating point of yield pillars. 2.5.4 Crush pillars Crush pillars are designed to support the immediate hangingwall. They are slender pillars with a w/h ratio less than 3 (Watson, 2010). They are usually introduced at depths below 600m. However, they can be used at depths shallower than 600m with caution (Ozbay et al., 1995). At shallow depths, crush pillars become more susceptible to violent failure due to the available stress being lower than the peak strength. This type of pillar is designed to fail close to the face under stiff loading conditions (Ozbay et al., 1995). After failure, the pillar retains some strength which is referred to as the residual strength. The residual strength then provides support of the immediate hangingwall up to the highest active parting plane. The main purpose of crush pillars is to prevent back breaks, for this reason it important to ensure that the crush pillar has sufficient residual strength. The operating point of a crush pillar is shown in Figure 2.5. 22 2.6 History of crush pillars To understand how crush pillars operate it is important to look at how they are designed. Crush pillars were first introduced by Korf at Union Section in 1978 to halt stope collapses (Korf, 1978). These pillars had dimensions of 1.5 m by 3 m and a height of about 1 m. Major challenges of stope collapse were being faced when mining exceeded a span of 30 m. Introduction of these smaller pillars that failed close to the face halted stope collapses in the mining areas where they were used (Watson, 2010). Crush pillars have since been commonly used in the Bushveld as in-stope chain pillars oriented along strike or on dip. The design of crush pillars has, in the past, been based on what has historically worked or on calculations based on the peak strength formulae derived from other hard rock mines (Watson et al., 2010). This resulted in oversized pillars which reduced the extraction ratio, and these oversized pillars were also a potential bursting hazard to personnel working underground. 2.6.1 Design of crush pillars Crush pillars require stiff loading conditions. This loading environment is provided by the face abutments. Fracturing of the pillar should initiate as the pillar is being cut. Observations made by Watson (2010) on the Merensky reef suggest that such loading conditions are present within 5 m to 7 m from the face, and pillars which exceed 10 m without failing would be prone to violent failure. Crush pillars should have reached residual strength by the time loading conditions transition to soft loading in the back area. The residual strength of the pillars provides support to the immediate hangingwall, stabilizing the hangingwall and preventing back breaks (stope collapse) from occurring. The back analysis done by Roberts et al., (2005) at Northam Platinum Mine, showed that a support resistance of about 1 MPa was sufficient to stabilize a stope hangingwall. To meet the 23 requirement of the 1 MPa criterion, crush pillars must have a residual strength of at least 13 MPa to be able to preclude back breaks (assuming 92% extraction ratio) (Watson, 2010). Oversized crush pillars tend to remain intact close to the face and only fail in the back area where loading conditions are soft and loading stresses are higher. In such conditions the pillars are susceptible to uncontrolled failure. Different authors have suggested different ways to approach the design of a crush pillar. The most comprehensive methodology for designing crush pillars was provided by Watson, (2010). His methodology points out the three factors that need to be considered when designing a crush pillar. ● Residual strength requirements – this is how much load the failed pillar must be able to support. If the residual strength provided by the pillar is inadequate, back breaks will occur. ● Loading stiffness of the environment, and how this varies with distance from the face- this describes the available stress and stiffness close to the face. For controlled failure to occur, the loading strata stiffness must be greater than the post- peak stiffness (most negative value) of the pillar. The loading stiffness varies with distance from the face. It has been shown that between 5 m to 7 m from the face on the Merensky reef the conditions are stiff enough. The available stress (stress imposed on the pillar) must exceed the peak strength of the pillar for the pillar to fail. ● The relationship between peak pillar strength and w/h ratio (Watson et al., 2010). FLAC models constructed by Watson, (2010) where fracturing was restricted to the pillar (infinitely strong foundation) and where fracturing was allowed to extend into the foundations. With increasing width to height ratio, the pillar model with infinitely strong foundations deviates from a pillar where foundation failure is allowed. For a comparively ductile pillar, this deviation initiated from a w/h of about 1.2 whilst the more brittle model deviated at about a w/h ratio of 2.5. These points where 24 deviation takes place indicate punching of the pillar core into the foundation. In the models that allow punching of the foundation, at the respective w/h ratio (1.2 and 2.5) where deviation takes place, the centre of the pillar has become stronger than the foundation inducing fracturing in the foundation materials. In the models with infinitely strong foundations, the pillar strength rapidly increases and the pillars quickly become indestructible. Even when failure is allowed into the foundations, pillar strength increases with w/h ratio. This implies that larger pillars are more likely to remain intact close to the face than smaller ones. To avoid intact or partially failed crush pillars in the back area, the available stress must always exceed the peak pillar strength within 5 m of the face (Watson, 2010). It is important to note that the model assumed that the material that makes up the foundations is the same as the pillars, which is approximately true for the Merensky Reef at Impala Platinum. Figure 2.6 shows a series of FLAC models illustrating the effects of w/h for pillars (Watson, 2010). 25 Figure 2.6 FLAC model showing effect of width to height ratio for pillars allowed to punch, as well as for pillars surrounded by infinitely strong rock mass (Watson, 2010). 2.6.2 Typical crush pillar behaviour and challenges associated with crush pillars. Roberts et al. (2005) estimated that a crush pillar reaches its peak strength at 3-10 millistrain. This is then followed by a strain softening regime caused by further compression of about 5 millistrain to reach residual strength. Work done by Watson (2010) shows that the strength drop occurs along an estimated negative post-peak stiffness slope of 12 GN/m. Further compression of the order of 50-90 millistrain would result in footwall heave which is assumed to be caused by the lateral confinement. At this stage, the foundation strength controls the maximum bearing capacity of the pillar (Watson, 2010). Crush pillars like any pillar system have challenges of their own. They require good drilling and blasting practice to ensure they are cut to the correct dimensions otherwise they can 26 become a source of seismic events if they are oversize (Watson et al., 2010). The use of crush pillars results in high stope closure rates, as the pillar continues to deform when it reaches its residual state. 2.7 Effect of mining depth on crush pillars The depth of mining to a greater extent controls the type of in-stope pillars used. It also influences the mining method used. At shallow depth (less than 300 m), non-yield pillars are commonly used as the in-stope pillars that provide support to the overburden up to the surface (Jager and Ryder, 1999). The use of non-yield pillars becomes less economically viable with increasing depth as the extraction ratio reduces because of the heavier loads that need to be supported. At intermediate mining depths (greater than 600 m but less than 1000 m) it is recommended to use barrier pillars to reduce regional spans and the height of the tensile zone (Jager and Ryder, 1999). This reduces the support resistance required between barrier pillars, as only the immediate hangingwall up to the highest potential parting requires support. Crush pillars may therefore be used between the barrier pillars, as the residual strength of the pillar provides the required support. Crush pillars have the benefit of improving extraction and do not have a potential of instability as the pillar has already failed and reached its residual strength. On the downside, crush pillars allow high stope closure rates to occur and this needs to be taken into account when designing the panel support (Jager and Ryder, 1999). Figure 2.7 shows a typical barrier-crush pillar layout (Watson et al., 2010). 27 Figure 2.7 Typical barrier-crush pillar layout (Watson et al., 2010). 2.7.1 Transition zone The transition zone refers to the range of depth (300 m – 600 m) where the pillar stresses are too high for non-yield pillars of reasonable size but too low to initiate fracturing of the crush pillar close to the face (Ozbay et al., 1995). This makes the actual depth to introduce crush pillars difficult to determine. The major challenge with using crush pillars in the transition zone is that failure of the pillar may not occur close to the face, only failing in the 28 back area where loading conditions are soft and the pillar is prone to violent failure (Du Plessis, 2015). Use of crush pillars in the transition zone is possible but caution is advised. Introduction of smaller pillars may be a solution however, they may not have adequate residual strength to arrest back breaks (Watson, 2010). Use of wider spans can help in increasing the available loading capacity. An alternative approach would be to use small pillars close to the barrier pillars when spans are below a certain dimension, and then increase the size of the pillars when the spans are large enough to fail them at the face. The use of yield pillars has been suggested for the transition zone. Yield pillars are not supposed to lose load as they are designed to operate close to their peak strength where they exhibit strain hardening. However, in practice yield pillars are prone to bursting and are associated with footwall punching resulting in excessive footwall heave (Jager and Ryder, 1999). Jager and Ryder (1999) suggested that it is better to use non-yield pillars up to the depth that crush pillars can be safely introduced. Figure 2.8 shows recommended mining depths for different types of in stope support pillars. 29 Figure 2.8 Schematic showing the in-stope pillars appropriate for different mining depths (Jager and Ryder, 1999) 2.8 Peak strength Peak strength is the maximum load that a pillar can support before failing. In the case of a crush pillar, the peak load needs to be exceeded whilst the stiff loading conditions are still present. This makes it important to make precise estimates of the pillar strength. After the tragic events at Coalbrook Colliery in 1960, Salamon and Munro, (1967) developed the pillar strength formula for coal pillars. The formula estimates the strength of coal pillars with w/h in the range of 0.9 to 3.6 (Salamon and Munro, 1967). The formula underestimates the pillar strength when the w/h is greater than 5 or 6. It is important to note that the formula does not estimate the actual pillar strength but rather it predicts the average strength of a specific group of coal pillars, i.e., those that have collapsed (Mathey and van der Merwe, 2016). 300m – 600m 30 𝑃𝑖𝑙𝑙𝑎𝑟 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 𝐾ℎ𝛼𝑤𝛽 (𝑀𝑃𝑎) (2-6) Where: K = 7.2 MPa α = -0.66 (coal) h = Pillar height (m) β = 0.46 (coal) w = Pillar width (m) Hedley and Grant, (1972) adapted the formula for hard rock. A back-analysis of hard rock pillars from the Elliot Lake district in Canada was used to modify the formula (Hedley and Grant, 1972). The pillar strength formula predicted the strength of slender pillars of w/h in the range of 0.7 to 1.5 (Watson, 2010). The modified formula is commonly used by rock engineers in the platinum mines. However, the formula underestimates the pillar strength and does not consider the influence of the foundation. Also, the back analysis was based on only three failed pillars and by Hedley and Grant’s own admission, the measurements taken were not accurate and could vary by as much as 50%. For hard rock, the constants were found to be: K = 0.67 x UCS α = -0.75 β = 0.5 The coal formula was revised by Madden (1991) to account for all w/h ratios. The revised formula is known commonly referred to as the squat pillar formula (Madden, 1991). 31 𝑃𝑆 = 𝐾 𝑅0 𝑐 𝑉𝑑 { 𝑐 𝑒 [( 𝑅 𝑅0 ) 𝑒 − 1] + 1} (2-7) Where K = Rock mass strength e = Rate of strength increase V = Pillar volume c, d = Constants R = Pillar w/h ratio R0 = Critical w/h ratio Ryder and Ozbay, (1990) suggested a methodology for estimating pillar strength that involves the use of correction factors (F1 – F4). These correction factors consider the condition of the pillar, effects of the shape and the effect of w/h ratio. The suggested approach does not consider the effects of the foundation. Pillars with w/h ratio greater than 10 have been observed to withstand any practical load making them essentially indestructible (Mathey and van der Merwe, 2016). However, the pillar system’s ultimate strength can still be affected by foundation failure. According to Watson (2010), Bieniawski and Van Heerden (1975) (cited by Watson) suggested that a linear strengthening law gave more reliable pillar strength estimates than the Salamon-Munro power formula. 𝑃𝑆 = 𝐾𝑖 [𝑏 + (1 − 𝑏) 𝑤 ℎ ] (2-8) Where Ki = In situ cube strength b = constant W = Pillar width h = Pillar height Based on research at Impala Mine, Watson developed a linear formula using the maximum likelihood back analysis to estimate pillar strength on the Merensky reef (Watson et al., 2008). This formula is very similar to Bieniawski and Van Heerden (1975) with the only difference being that Watson’s formula uses the effective width and height. 32 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 𝐾 [𝑏 + (1 − 𝑏) 𝑤𝑒 ℎ𝑒 ] (2-9) Where ℎ𝑒 ≈ [1 + 0.2692( 𝑤 ℎ )0.08] ℎ 𝑤𝑒 ≈ 2𝑤𝐿 𝑤 + 𝐿⁄ K = in situ cube strength b = 𝑤 ℎ𝑒 ⁄ w = pillar width h = pillar height L = pillar length A strength formula was developed for UG2 by Watson (2021). The formula parameters are based on the back analysis done on (failed and unfailed) pillars at three platinum mines on the UG2 reef. The formula is based on the power formula with exponents of α and β and the use of effective height and width. The effective width considers the presence of gullies unprotected by sidings. The adjustment is based on numerical modelling done by Roberts et al. (2002). Equation 2-10 (Watson et al., 2021). Where ℎ𝑒 ≈ [1 + 0.2692( 𝑤 ℎ𝑔 )0.08] 𝑃𝑖𝑙𝑙𝑎𝑟 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 𝐾𝑤𝑒 αℎ𝑒 β (2-10) 33 We = effective width hg = gully vertical height α = 0.67 β = -0.32 K = 67 The modified power formula applicability to the UG2 reef will be tested and compared with the results from modelling. Peak strength of a pillar can be estimated using a numerical model. Numerical models can handle complex geometries. However, the models need to be calibrated using either underground measurements or data from laboratory testing. In this research Numerical modelling is used to estimate the peak strength of a crush pillar. 2.8.1 Effect of width to height ratio on pillar strength Tests done by Bieniawski (1968) on sandstone showed a linear increase in peak strength as the w/h increased, up to a w/h of 5. Samples tested at higher w/h ratios could not be broken even at higher loads (Mathey and van der Merwe, 2016, citing Bieniawski). Results presented by Bieniawski and Van Heerden (1975) showed a similar trend of linear strength increase with increasing w/h ratio up to a w/h ratio of 4. Model pillars with w/h in the range 5-7.5 showed an exponential rise in strength, suggesting the brittle-ductile transition had already occurred (Bieniawski and Van Heerden, 1975). Madden (1991) also performed tests on sandstone pillar models and the results show a linear increase in strength up to a w/h of 6, after which a rapid rise in strength was observed. The results obtained from pillar models suggest that for pillars with w/h of less 6 their peak strength can be predicted by a linear equation (Madden, 1991). Numerical models done by Su and Hasenfus (1999) showed that the ultimate pillar strength of pillars with w/h > 10 was dependent on the 34 competency of the surrounding strata. Weak floor for example could reduce the ultimate pillar strength by as much as 50% (Su and Hasenfus, 1999). 2.8.2 The effects of Foundation draping. Foundation (hangingwall/footwall) draping causes the edges of the pillar to experience high stresses. This causes pillar failure to initiate from the edges and progress towards the centre (Watson, 2010). The interface between the pillar and the foundation controls how much horizontal stress is transferred to the pillar. The frictional resistance at the interface regulates the horizontal stress transferred to the pillar. The higher the frictional resistance the greater the horizontal stresses that are transferred to the pillar. The transferred horizontal stress provides confinement to the core thereby strengthening it (Watson, 2010). The influence of Foundation draping is controlled by the mining spans around the pillar (Watson, 2010). The greater the mining spans around the pillar, the more prevalent the effects of foundation draping become. The effect of foundation draping should be considered when simulating pillar behaviour. Figure 2.9 shows an illustration of foundation draping (Watson, 2010). 35 Figure 2.9 Illustration showing foundation draping (Watson, 2010). 2.9 Pillar Foundation A pillar foundation is a crucial part of the pillar system. It comprises of the hanging- and footwall. Tests conducted by Lougher and Ozbay (1995) showed that pillar stress for 6 m × 3 m pillars (w/h = 3) increased with the extent of mining up to an average pillar stress of 208 MPa. Further mining resulted in the punching of the footwall and the stress level remained approximately the same (Lougher and Ozbay, 1995). This suggests that the foundation may have great influence on pillar failure. 2.9.1 Pillar system failure A pillar system comprises of the pillar, the adjacent footwall and hangingwall. According to Watson, (2010) pillar system failure is a combination of four mechanisms. The mechanisms are listed as follows: 36 ● Fracturing and crushing of the pillar; ● Tensile fracturing into the foundation (Hertzian crack) (Watson et al., 2010); ● Wedge formation in the form of shear fractures (Prandtl, 1921); and ● Horizontal dilation of wedges. (Control the ultimate punch resistance). Fracturing and crushing of the pillar starts in the early stages of pillar failure and continues even when other mechanisms become active. This is usually followed by the fracturing of the foundation. Tensile stresses are induced in the foundation as the load exerted by the pillar to the foundation increases (Watson, 2010). This results in the formation of tensile fractures in the proximity of the pillar. These fractures are called the Hertzian cracks. The development of shear fractures marks the beginning of wedge formation. Modelling done by Watson (2010), showed extensive foundation failure with large solid wedges at the core of the pillar. Watson identified these wedges as the Prandtl wedge (Prandtl, 1921). The Prandtl wedge is a shear failure mechanism in the foundation below a highly stressed stability pillar (Baars, 2015). The unique characteristics of this wedge are that it consists of three zones as shown in figure 2.10. Zone 1 is a triangular zone underneath the pillar which is under elastic equilibrium. The absence of friction (between the strip load and zone 1) implies that the direction of the principal stresses are vertical and horizontal, with the largest principal stress in the vertical direction (Baars, 2015). Zone 2 is in a state of plastic (inelastic) equilibrium and has the shape of logarithmic spirals. The principal stresses are rotated 90° from zone 1 to zone 3. Zone 3 is a passive zone of shear failure. It should be noted that the mentioned zones are applicable to soils (Baars, 2015). No evidence was found in literature that show that these zones are applicable to hard rock. 37 Figure 2.10 The Prandtl wedge (Baars, 2015) Although Watson (2010) did not show if the Prandtl wedge in hard rock is also composed of three zones as in soils, his modelling showed they exhibit similar behaviour. The wedge provides a slip line (shear fracture) which enables the footwall (foundation) to dilate into the stope, creating room for pillar deformation and failure. Foundation failure is the final stage of pillar failure. Figure 2.11 shows a simplified diagram of the Prandtl wedge (Watson, 2010). 38 Figure 2.11 Diagram show a typical Prandtl wedge shape (Watson, 2010) The horizontal resistance against the dilation of wedges controls the ultimate punch resistance. Ryder and Jager, (2002) expressed the ultimate punching resistance as follow: 𝜎𝑝 = 1 + sin 𝜙 1 − sin 𝜙 𝑈𝐶𝑆ℎ (2-11) σp = Punch strength ϕ = Internal friction angle UCSh = In situ horizontal strength 2.10 Post-peak behaviour of pillars When the peak strength of a pillar is exceeded, the pillar enters the post-peak regime. Pillar failure can be either stable or unstable. The stability of the failure process is governed by relative stiffness of the pillar and the loading strata. This is similar to laboratory tests where the machine and sample stiffness determine whether or not violent 39 failure will occur. Salamon (1970), developed the local mine stiffness stability criterion based on observations made on laboratory tests. 2.10.1 Local mine stiffness stability criterion The local mine stiffness stability criterion developed by Salamon (1970) predicts if a pillar would fail in a controlled manner or result in violent failure. For stable failure. For unstable failure |KLMS| > |KP| |KLMS| < |KP| Were KLMS is the local mine stiffness and KP is the pillar stiffness (Salamon, 1970). The criterion does not have a time dependant variable, meaning it cannot predict how quick or slow the failure process would be (Zipf, 1999). Slow yielding pillars allow personnel ample time to evacuate unlike a sudden failure. KLMS is affected by the extraction ratio and tends to decrease with increasing extraction ratio (Zipf, 1999). If a small amount of deformation results for mining a certain distance, the system is stiff. For a soft system, a large deformation would occur for the same distance mined. 2.10.2 Strata stiffness Strata stiffness is defined by Ozbay, (1989) as the force required to cause a unit increment of closure between the hangingwall and footwall at the location of the pillar. It varies with distance between support elements (strata stiffness decreases with increase in span) and is dependent on the surrounding extraction pattern (Ozbay, 1989). The stiffness of the loading strata governs the ability of the hangingwall to redistribute load to surrounding 40 elements providing support. This was illustrated by Kersten, (2016) who looked at the extreme cases of strata stiffness, i.e. a very stiff and soft hangingwall. In his illustration both cases were supported by equally spaced springs with varying moduli. In the case of extreme hangingwall stiffness, each spring had the same convergence but with different resistance force. With a totally soft hangingwall, each spring supports a strip of the total overburden load resulting in varying convergence for each spring. This corresponds to the concept of the tributary area. Figure 2.12 shows an illustration of the extreme cases of hangingwall stiffness. Figure 2.12 Illustration showing extreme cases of hangingwall stiffness. At the top shows the case of totally stiff hangingwall and at the bottom shows case of totally soft hangingwall (Kersten, 2016). Crush pillars are supposed to start failing as soon as they are cut at the face. Part of the energy supplied by the loading strata to deform the crush pillar is used in the creation of 41 new fractures and the rest is stored in the system as strain energy, up until the peak strength of the pillar is exceeded (Galvin, 2014). After exceeding the peak strength, the stored energy is available to drive further deformation of the pillar. The softer the loading strata, the greater the energy stored, and the greater the energy available to cause more deformation. If the stored energy exceeds the energy required to cause further deformation and fracturing, the system becomes unstable resulting in violent failure. It is crucial that a crush pillar fails close to the face where loading conditions are stiff enough allowing controlled failure to occur. 2.10.3 Residual strength The residual strength of a crush pillar serves the fundamental purpose of preventing back breaks. This strength is retained after the pillar fails (Roberts et al., 2005). Some authors attribute this to cohesion between the failed material. Roberts et al. (2005) suggest that crush pillars retain their residual strength from the self-confinement within the failed reef or rock material. A combination of confinement and friction between fragments is a more likely source of residual strength. After yielding, the pillar ends up as an intensely fractured but still well-knit mass of crushed rock (Ozbay et al., 1995). According to Du Plessis, (2015) at depths greater than 600 m, crush pillars reach their residual strength at approximately 9 m from the face. Several attempts have been made to estimate the residual strength of a crush pillar. Ryder and Ozbay (1990) estimated that the residual strength of a crush pillar was 5% to 10% of the peak strength. This translates to a residual strength between 8 MPa and 20 MPa for UG2. Roberts et al. (2005) conducted 2D stress measurements on the Merensky reef and estimated a residual strength of 19 MPa. Underground measurements done by Watson 42 (2010) on the Merensky reef pillars at Impala mine showed the pillars had a peak strength of about 320 MPa and residual strength of 32 MPa. In this research the residual strength for UG2 crush pillar will be estimated using numerical modelling and the model will be calibrated using data from literature and laboratory tests. 2.11 Numerical modelling of pillars All models used in this research were done using FLAC3D. According to Watson et al. (2010), when building a pillar model, the brittleness of the material must be considered. The material brittleness in the model is defined as “the rate of stress decrease after failure” (Watson et al., 2010). Unfortunately, in FLAC3D this parameter is also affected by grid size. The issue is more prevalent in models that involve pillars with large w/h ratios (Watson et al., 2010). In such a case failure progression can reach the core of a pillar before the peak strength is reach. The pillars that were investigated in this research are categorized as slender pillars (having a w/h ratio of less than 2) and the grid size does not have as much influence on the model. As a precaution, the issue was considered in the models used in this research. The friction angle and the dilation angle were kept constant to simplify the model. Only the cohesion was varied. This means the post-peak behaviour (brittleness) was controlled by cohesion loss. This is similar to what was done by Watson et al. (2010). Boundary conditions are important in pillar modelling and can directly affect the results of the model (Itasca, 2019). Two main types of boundaries that can be used in FLAC3D namely: prescribed displacement and prescribed stress. The models used in this research used prescribed displacement boundaries. Roller and velocity boundaries fall under prescribed displacement boundaries. Roller boundaries are recommended to be used on 43 planes where conditions are the same on either side (Itasca, 2019). This is usually along planes of symmetry. Velocity boundaries apply a velocity normal to the specified plane. This boundary was used to load the pillar models used in this research. The models used in this research involve the presence of a gully next to a crush pillar. The estimated strengths from the models and the formula developed by Watson (2021) for UG2 were compared. The formula requires an effective height as an input. The effective height considers the presence of the gully next to the pillar. The equation (2-10) used to calculate the effective height is based on numerical modelling done by Roberts et al. (2002), to account for asymmetric pillars. The presence of a gully next to a pillar changes the effective height of the pillar (Watson, 2010). The models used in this research investigate the effect of a gully on the peak strength of a pillar. 2.12 Chapter summary From the literature survey, it has been established that stress plays a pivotal role in a crush pillar’s performance. The available stress, peak and residual strength must be considered when dealing with crush pillars. The available stress at the face must be greater than the peak strength to ensure pillar failure initiates as the pillar is being cut. It is also important to note that being at depths where crush pillars can be used does not necessarily mean there will be sufficient stress at the face to initiate failure. Pillar and foundation rock properties, presence of weak layers and stiffness (system and pillar) also play a huge role in crush pillar behaviour and design. 44 3 LABORATORY TESTING To accomplish the objectives of the research study, it was necessary to test both pre- and post-failure behaviour of rock samples. During the laboratory testing, some problems were encountered. These include oil spoiling samples during testing and inaccurate reading from the axial transducer. The first part of the chapter deals with the problems encountered and the second part with the laboratory test results. The inaccurate readings from the axial transducer raised questions about the calibration of the instruments used in this research. It is important that all equipment used is correctly calibrated as this affects the results obtained. Without calibration, the results obtained cannot be compared with the works of other researchers as there is no standard on which the results are based. This makes it difficult to draw meaningful conclusions and contribute to the available knowledge. 3.1 Calibration The MTS 815 servo-controlled testing machine that was used in this research was standing idle for 3 years and required calibration. The machine was calibrated before any rock testing was done, however, instead of calibrating the machine for strain (mm/mm), it was set to measure deformation (mm). This meant the recommended values (by ISRM) for control variables (given in strain) for post-peak investigations had to be converted to deformation using Equation 3-1. ∆𝑙 = 𝜀𝑙 (3-1) 45 Where ∆𝑙 = Deformation ε = Strain 𝑙 = original length The original length is the distance between the centres of the mounting points of the transducer as shown in Figure 3.1. The original length for the axial transducer is 50 mm. To calculate the strain from the data collected from the transducers Equations 3-1 and 3- 2 were used. To determine the strain from the axial transducer’s recorded data, Equation 3-1 was rearranged by making strain subject of the formula. Where ∆𝑙 is the deformation reading from the axial transducer and 𝑙 is the original length (50 mm). Equation 3-2 was used to calculate strain from the radial transducer’s data. 𝜀 = ∆𝑙𝑑 𝜋𝐷 (3-2) Where ∆𝑙𝑑 = Deformation D = Diameter of specimen The radial transducer measures circumferential deformation, hence the use of equation 3-2. 46 Figure 3.1 The original length of the axial extensometer 3.2 Challenges faced during rock testing Obtaining a complete stress/strain curve has its own inherent challenges. The challenges discussed in this section are those faced by the author while conducting post-peak rock tests. All rock testing procedures used in this research were based on the ISRM suggested methodologies (Ulusay and Hudson, 2007). 3.2.1 Oil contamination It took many attempts until the first complete stress/strain curve was obtained. The post- peak triaxial test would either fail prematurely or the system would abruptly stop the test. There were a few contributing factors, but the issue of oil contamination of the specimen was the most prevalent. During triaxial tests, the specimen was protected from oil contamination using a shrink sleeve. There are two different products of heat shrinkable Original Length 47 sleeves available in the rock engineering test laboratory. These are the American imported sleeve (referred to as the American sleeve) and the locally sourced sleeve (referred to as the local sleeve). The American sleeve is hard in comparison to the local sleeve and the contact points of the axial transducers are not able to punch through it. However, there is little stock available, and the sleeve is reserved for performing triaxial tests at high confinements. The local sleeve has plenty of stock available, but it has the problem of being punched by the contact points of the axial transducer and allowing oil to infiltrate the specimen. This infiltration usually occurred at failure and therefore did not allow post-failure. The problem was resolved by introducing a second layer of the local sleeve at the points of contact of the axial transducer (Figure 3.1). It was also observed that a 12-hour cooling period after applying the local sleeve greatly improved its performance. 3.2.2 Test control procedures The ISRM procedures for obtaining a complete stress/strain curve of a specimen consist of three stages. The first stage is to use axial strain as the control variable (during pre- failure testing) and at around 70% of the UCS change to the second control variable which is radial strain. The third stage involves changing back to axial strain control when the stress drops to about 50% of the peak strength. The software used to operate the MTS machine does not allow any modification to be made during the test. All instructions are pre-programmed before commencing the test. It proved difficult to determine a changeover point for the third stage and all attempts to predict this point resulted in the machine losing control and the test ending abruptly. It was decided to exclude the third 48 stage as the specimen could still reach residual strength with only radial strain control. However, this made the duration of the triaxial tests very long (between 8 – 10 hours). 3.2.3 Problems with the Axial transducer After resolving the issue of oil contamination and modifying the test procedure, the success rate of obtaining a complete stress/strain curve greatly improved. However, the results from the triaxial tests became illogical and not comparable to previous tests. The problem usually initiated close to the peak strength and the stress/strain curve would deviate from the expected result, producing stress/strain curves that cross the pre-failure region (Figure 3.2). The problem worsened with time. The source of the problematic results seemed to be emanating from the axial transducer (extensometer). The problem started off very sporadically, however, it became a prevalent issue as more rock tests were conducted. An example of this issue is shown in Figure 3.2 which shows a stress- strain curve obtained after performing a triaxial test at 30 MPa on an anorthosite sample. The shape of the curve cannot be classified either class Ⅰ or class Ⅱ as observed by Wawersik and Fairhurst (1970). 49 Figure 3.2 Stress/strain curve of anorthosite sample at 30MPa confinement. The data from the radial extensometer were logical and produced stress/strain curves that were consistent with expectations. The stress/strain curves of specimens of the same rock had similar shapes. This was not the case with the axial transducer. The stress/strain curves produced had unique shapes even for specimens from the same rock type. The problem seemed to initiate as the stress levels approached peak strength or after the peak strength had been exceeded. With no logical explanation for what was causing the axial extensometer to behave in this manner, it was decided to investigate if the transducer was malfunctioning. Tests were conducted to determine the cause. 50 3.2.4 Investigating transducer issues A series of tests was developed to confirm if the problem lay with the axial transducer. The first test was to determine the effect of confining pressure on the transducer, secondly cross talking between the two transducers was investigated. Cross talking occurs when the electrical signals from one transducer are being mixed with the other. The extensometers were placed in an empty triaxial cell as shown Figure 3.3, the axial extensometer was on top with the radial extensometer being beneath. Figure 3.3 Axial (top) and radial extensometer in an empty triaxial cell The triaxial cell was filled with oil and the confining pressure raised at a rate of 10 MPa per minute until 60 MPa. The confining pressure was held constant at 60 MPa for 5 minutes after which the confining pressure was then reduced back to zero at a rate of 10 MPa per minute. The test was again repeated with each transducer separately. The expected results were supposed to show no change in the deformation readings (constant at zero) throughout the test. The results of the two extensometers show decreasing 51 deformation readings as the confining pressure increased. As the confining pressure decreased the axial extensometer showed decreasing deformation readings whilst the radial extensometer showed increasing readings. At constant pressure both extensometers showed a slight drop in deformation readings. The results of the radial extensometer showed a repeatable pattern, suggesting the instrument could have a constant error that can be easily adjusted. However, the axial extensometer’s deformation readings continuously decreased throughout the test, despite the changes in pressure. At the end of the test the axial deformation reading was -0.074 mm and this exceeded the error range of ±0.03. The results suggested that the axial extensometer was malfunctioning. However, this was not conclusive and additional testing was required. There was no evidence of cross talking as the results of the transducers when tested separately produced similar results. The results from the tests are shown in Figure 3.4. The results suggest that these types of extensometers are not suitable to be used in conditions with varying confining pressure. 52 Figure 3.4 Results of pressurized triaxial cell 3.2.4.1 Load test To investigate if the axial extensometer was malfunctioning, a simple load test was developed. Two metal specimens were used, a steel and an aluminium sample. The advantage of metal is that they are homogeneous and reload cycles do not affect the response. The two specimens had the same dimensions. Strain gauges were attached to the specimen together with the extensometers. This provided data than can be directly compared with the extensometers. Properties of these metals like elastic modulus provide additional data to compare with. -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0 10 20 30 40 50 60 70 D ef o rm at io n ( m m ) Confining pressure (MPa) Pressure test Radial extensometer Axial Extensometer 53 3.2.4.2 Sample preparation. The specimens had a diameter of 42 mm and a height of 105 mm. Two pairs of strain gauges were attached to each specimen. The horizontal pair measured lateral strain whilst the vertical pair measured the axial strain. Steel platens and a shrink sleeve (local) were added to the specimens. The shrink sleeve allowed the axial extensometer to attach to the sample, without it the extensometer would just slide off. The final setup of the steel sample before testing is shown in Figure 3.5. Figure 3.5 Specimen with platens and axial extensometer attached. 3.2.4.3 load test procedure The load test was run in the MTS testing machine with the triaxial cell open. The specimens were loaded to the desired load (aluminium to 150kN and steel to 300 kN) at a loading rate of 1 kN/s. Upon reaching the desired load the machine maintained the same 54 load for 5 minutes, after which the load was reduced to zero at a rate of 1 kN/s. Two separate systems were used to capture the data. The MTS testing machine does not have the components that allow the connection of strain gauges. This means an independent data capturing system for the strain gauges had to be introduced. The deck system used by the Amsler soft testing machine was used to collect data from the strain gauges. The setup of the two systems is shown in Figure 3.6. Figure 3.6 Steel sample test setup The deck system recorded strain readings without a corresponding load. This was because the system was not linked to the MTS load cell. This meant data collection had 55 to be recorded manually for there to be a comparison between the strain gauges and the extensometer. The data was captured at 20 kN intervals during the loading and unloading phases of the test. The results comparison is shown in Figures 3.7 and 3.8. Figure 3.7 Comparison of extensometer to strain gauges (Aluminium sample) -1 -0.5 0 0.5 1 1.5 2 0 20 40 60 80 100 120 S tr ai n ( m S tr ) Stress (MPa) Stress strain Aluminium Axial strain (extensometer) Radial strain (extensometer) Axial strain (strain gauge) Radial strain (strain gauge) 56 Figure 3.8 Comparison of extensometer to strain gauges (Steel sample) The difference (in strain readings) between the strain gauge and the axial transducer was more pronounced for the aluminium specimen. The axial strain curve for the extensometer was non-linear. Given that the specimen tested is a metal, obtaining such a curve at low stress is unusual, further suggesting the axial transducer may be malfunctioning. The strain gauges gave an elastic modulus of 73.8 GPa whilst the axial extensometer gave a modulus of 93 GPa. The elastic modulus for aluminium alloy 2024 is 73.1 GPa (Vegas Fastener Manufacturing, 2021). This also suggested that the load cell was operating in the desired manner. Any issues with the load cell would have also affected the stress/strain curves for the strain gauges. -0.5 0 0.5 1 1.5 2 0 50 100 150 200 250 S tr ai n ( M ic ro s tr ai n ) Stress (MPa) Stress - Strain Steel sample Axial Strain (extensometer) Test 1 Radial strain (extensometer) Test 1 Axial Strain (Strain gauge) Radial Strain (strain gauge) Axial Strain (extensometer) Test 2 Radial strain (extensometer) Test 2 Axial Strain (extensometer) Test 3 Radial (extensometer) Test 3 57 From Figure 3.9, the axial extensometer recorded higher strain reading than the axial strain gauges for all three tests and the readings were not linear. The cause of the non- linear curve is unknown. This may suggest an issue with the axial extensometer. Figure 3.9 shows the axial strain extensometer readings multiplied by a factor of 0.48. Attempts were made to use the factor on other materials and a similar trend was obtained. This factor was used to adjust the axial strain for successful triaxial tests performed with this extensometer. The factor was determined by trial and error. The close agreement between the radial extensometer and the radial strain gauges suggests the radial extensometer was functioning correctly and there was no cross talking between the extensometers. Figure 3.9 Adjusted axial extensometer readings. 3.2.4.4 Influence of shrink sleeve. Two shrink sleeves were used in this research (American and the local sleeve), it was important to check if they have any influence on the transducer readings and if they were -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250 S tr ai n ( M ic ro s tr ai n ) Stress (MPa) Stress - Strain Steel sample Axial Strain (extensometer) Test 1 Radial strain (extensometer) Test 1 Axial Strain (Strain gauge) Radial Strain (strain gauge) Axial Strain (extensometer) Test 2 Radial strain (extensometer) Test 2 Axial Strain (extensometer) Test 3 Radial (extensometer) Test 3 58 affecting the performance of the axial transducer. To establish this, simple loading and unloading tests were setup. A chromite sample was loaded up to 97 kN (which is about 50% of the UCS) at 1 kN/s, then held at a constant load for 5 minutes and subsequently dropped back to zero at the same rate. For the first loading cycle the sample had no sleeve attached to it. For the second cycle the local sleeve was attached to the sample. For the final cycle strain gauges were used and the s