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Development of emiprical [sic] and numerical design techniques in burst prone ground at the Red Lake… Kumar, Pravin 2003

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DEVELOPMENT OF EMIPRICAL AND NUMERICAL DESIGN TECHNIQUES IN BURST PRONE GROUND AT THE RED L A K E MINE By Pravin Kumar B.A. Sc., The University of British Columbia, 1994 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE In THE FACULTY OF GRADUATE STUDIES Department of Mining and Mineral Process Engineering We accept this thesis as conforming Xo the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 2003 ©Pravin Kumar, 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of H w i ^ i /VK?J> >™ ,AI<g-KAi_ C\IZJZUB<A e The University of British Columbia Vancouver, Canada Date " J ^ o g i , l o o S DE-6 (2/88) A B S T R A C T This thesis is divided into three sections. It presents the development of empirical and numerical design techniques at Goldcorp Inc's Red Lake Mine. The first section expands upon the understanding of the rockburst mechanism at the mine. Four known rockbursts were analysed to better understand the mechanism. Some variables such as excavation span, dip of orebody, time, location and geology were studied in detail to understand its effect on seismicity and rockbursting. The second section explains the updating of the span graph, which can now be applied to cut and fill stopes in burst prone ground. The third section deals with the development of pillar design techniques. Five failure criteria were calibrated to the Red Lake Mine ground conditions from first principles. A design procedure specific to conditions for entry-type mining within burst prone ground is provided. At the center of the procedure is an "empirical span design chart" and "pillar design methodology" for entry-type excavation. This provides a practical tool for a mining engineer to design a stable entry-type excavation within burst prone ground. ii TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES vii LIST OF FIGURES viii ACKNOWLEDGMENTS x CHAPTER 1. INTRODUCTION 1 1.1 BACKGROUND 1 1.2 RESEARCH METHODOLOGY 2 CHAPTER 2. The RED LAKE MINE 4 2.1 INTRODUCTION 4 2.2 GEOLOGY 5 2.2.1 Regional Geology '. 5 2.2.2 Local Geology 7 2.3 MINING METHODS 8 2.3.1 Primary Development 8 2.3.2 MCF Stope Development 9 2.3.3 Drilling and Blasting 10 2.3.4 Mucking 12 2.3.5 Ground Support 12 2.3.6 Paste Fill 15 2.4 MICRO-SEISMIC SYSTEM 15 CHAPTER 3.0 REVIEW OF ROCKBURSTS AND SEISMICITY 16 3.1 LITERATURE REVIEW 16 3.1.1 Mechanism of Bursting 17 3.1.1.1 Dome Theory 17 3.1.1.2 Cantilever Theory 18 3.1.1.3 Elastic Theory 20 3.1.1.4 Energy Balance 21 3.1.1.5 External Energy Sources 24 3.1.2 Loading System 26 3.1.3 Types of Rockburst 28 3.1.3.1 Strain Bursts 28 iii 3.1.3.2 Pillar Bursts 29 3.1.3.3 Fault-Slip Bursts 30 3.1.4 Rockburst Seismology 30 3.1.4.1 Seismic Wave 30 3.1.4.2 Magnitude 31 3.1.4.3 Location 31 3.1.5 Types of Mine Tremors 32 3.1.5.1 Double Couple Focal Mechanism 34 3.1.5.2 Non-Double Couple Mechanism 35 3.1.6 Summary - Rockburst Mechanism and Seismology 36 CHAPTER 4.0 SEISMICITY AT THE RED LAKE MINE 37 4.1 BACKGROUND 37 4.2 CRITICAL FACTORS AFFECTING BURSTING 37 4.2.1 Excavation Span 39 4.2.2 DipofOrebody 42 4.2.3 Times and Location 43 4.2.3 Location, Magnitude and Seismic Energy 44 4.3 TYPES OF ROCKBURST AT RED LAKE MINE 45 4.3.1 Strain Burst .45 4.3.2 Crush Burst 45 4.4 CASE HISTORIES- RED LAKE MINE 47 4.4.1 Drift 37-816-1 East (1652m Depth) 47 4.4.2 Intersection of 36-756/786Access (Depth 1578m) 49 4.4.3 Stope 34-786-1/2 Cut4 (Depth 1523) 51 4.4.4 Stope 36-746-1 Cut2 (Depth 1585) 53 4.5 CONCLUSION 55 CHAPTER 5 SPAN DESIGN 56 5.1 BACKGROUND 56 5.1.1 Analytical Approximation 56 5.1.2 Numerical Simulation 56 5.1.3 Empirical Methods 56 5.2 DESIGN METHODOLOGY- RED LAKE MINE 59 5.3 SITE CHARACTERIZATION 62 5.3.1 Rock Mass Characterization 62 5.3.2 Intact Rock Strength 63 5.3.2.1 Main Zone 64 5.4 SPAN DAT ABASE 64 iv 5.5 CRITICAL SPAN GRAPH 66 5.5.1 Limits of Span Graph 66 5.5.2 Definition of Stability 67 5.5.2.1 Stable Excavation 68 5.5.2.2 Potentially Unstable Excavation 68 5.5.2.3 Seismicity and Fracturing During Excavation 68 5.5.2.4 Stress -Induced Failure 69 5.5.2.5 Unstable Excavation 69 5.5.3 Modification To Critical Span Graphs : 69 5.6 USE OF NEURAL NETWORKS 71 5.6.1 Neural Network Span Design 72 5.6.2 Training Parameters 73 5.6.2.1 Average Error 75 5.6.2.2 Correlation 75 5.6.3 Results 76 5.6.4 New Critical Span Graph 77 5.7 CONCLUSION 79 CHAPTER 6 PILLAR DESIGN 81 6.1 BACKGROUND 81 6.2 FAILURE CRITERIA - RED LAKE MINE 83 6.2.1 Hoek & Brown Failure Criteria , 83 6.2.2 The Pillar Stability Graph 85 6.2.3 Stored Strain Energy Criteria 87 6.2.4 Deviatoric Stress (ai-03) 90 6.2.5 Induced Stress Level Criteria (<Ji/UCS) 94 6.2.6 Rockwall Condition Factor (RCF) 96 6.2.7 Excess Shear Stress (ESS) 97 6.3 DISCUSSION 98 6.4 PILLAR DESIGN CASE HISTORIES 99 6.4.1 Map 3D Numerical Modeling Program 99 6.4.2 Map 3D Input Parameters ...101 6.4.3 Sill Pillar (32Level, Depth 1450m) 102 6.4.3.1 Hoek-Brown Failure Criteria 104 6.4.3.2 Stored Strain Energy 105 6.4.3.3 Pillar Stability Graph 107 6.4.3.4 Deviatoric Stress (a r a 3 ) 108 6.4.3.5 Induced Stress Level Criteria (rji AJCS) 108 6.4.3.6 Summary of Results 109 6.4.4 Post Pillar/South Access (34Level, Depth 1500m) 111 v 6.4.4.1 Hoek-Brown Failure Criteria 112 6.4.4.2 Stored Strain Energy Criteria 116 6.4.4.3 Pillar Stability Graph 117 6.4.4.4 Deviatoric Stress (G1-O3) 118 6.4.4.5 Induced Stress Level Criteria '(<Ji /UCS) 118 6.4.4.6 Summary of Results 119 6.5 DISCUSSION 120 CHAPTER 7 CONCLUSION 121 7.1 SEISMICITY : 121 7.2 CRITICAL SPAN GRAPH (2003) 122 7.3 PILLAR DESIGN 123 REFERENCE 124 APPENDIX A- UNDERGROUND FAILURE MODES 130 APPENDIX - B SPAN DATABASE 155 APPENDIX - C PILLAR STRENGTH AND STRESS DETERMINATION 165 APPENDIX - D INDUCED PILLAR STRESSES 184 vi L I S T O F T A B L E S Table 1. Drilling and Loading Specifications for Cut and Fill Breasting 11 Table 2. Technical Specifications of Threaded Rebar/Resin Bolts 13 Table 3. Technical Specifications of Swellex Bolts 14 Table 4. Technical Specifications of Chain Link & Wire Mesh 14 Table 5. Classification suggested by Ortlepp (1992) 46 Table 6. Uniaxial Compressive Strength Tests Performed by UBC Geomechanics 63 Table 7. Typical Rock Mass Rating of main zone 64 Table 8. RMR and span data from Red Lake Mine 65 Table 9. Case-History Data Sources 71 Table 10. Results of Deviatoric Stresses at Rockburst Failures 93 Table 11. Modelled Sigmal and 3 Values (From rockburst discussed in Chapter 4) 94 Table 12. Stress Criteria for Tunnel Sidewall (Hoek & Brown, 1980) 94 Table 13. Empirical Instability Criteria for Massive Rock (Stacy & Page, 1986) 95 Table 14. Induced Stress Criteria (Mah, 1995) 95 Table 15. New Induced Stress Criteria > 96 Table 16. Map3D Input Parameters used the Red Lake Mine 101 Table 17. Numerical Assessment- Mining of 32-826-4 from cut6 to Sill of 31-826-4 104 Table 18. Failure Criteria Results 109 Table 19. Numerical Assessment- 34/786/ South Access Induced Stress History 113 Table 20. Numerical Assessment- 34/786/ South Access Induced Stress Options 114 Table 21. Failure Criteria Results 119 vii LIST OF FIGURES Figure 1. Location of Red Lake Mine 4 Figure 2. Geological map of the Campbell-Red Lake gold deposit (Dube et al., 2002) 6 Figure 3 .Primary developments at Red Lake Mine (Rocque, 2001) 9 Figure 4 .Overhand mechanized cut and fill method 10 Figure 5. Location of holes in a typical breast face 11 Figure 6. Concept of doming theory (Morrison, 1942) 17 Figure 7. Concept of cantilever theory (Sinclair, 1936) 18 Figure 8. Stress-Strain curve defining the strain energy resulting from the seismometers deformation of an elastic material (Cook, 1963) 21 Figure 9. Illustration of Elastic Energy Balance (CAMIRO, 1995) 22 Figure 10. (a) Stable and (b) Unstable equilibrium 24 Figure 11. Mechanical model of a fault-slip on a geological weakness 25 Figure 12. Specimen and loading system relationships (Blake, 1972) 27 Figure 13. Stress-displacement characteristics of brittle and soft rock (Hedley 1992) 29 Figure 14. Six models for mine-induced events (Hasegawa 1989) 33 Figure 15. Direction of ground motion for the two types of seismic events (Hedley, 1992) 34 Figure 16. Fault-Slip solution (Hedley, 1992) 35 Figure 17. Common first motions 35 Figure 18. Distribution of Reported Unusual Occurrence from 1990-93 38 Figure 19. Distribution of reported unusual occurrence from 1997-Mar 2002 39 Figure 20. Stress contour above 5.4m (18ft) wide back 40 Figure 21. Stress contours above 6.4m (21ft) wide back : 41 Figure 22. Stress contour above 9.1m (30ft) wide back 41 Figure 23. Change in Stress with change in dip of ore body 43 Figure 24. Position of the face relative to the seismic events (Cook, 65) 43 Figure 25. Number of seismic events versus time, btw Mar and Dec 2001 (Leslie, 2001) 44 Figure 26. Typical strain burst failure mode (Mah, 1995) 46 Figure 27. Location of damage in 37-816-1 East Drift 48 Figure 28. Extent of damage in 37-816-1 East Drift 48 Figure 29. Location of damage in 366-756/876 Intersection 49 Figure 30. Extent of damage in 36-756/786-1 Intersection 50 Figure 31. Location of damage in 34-786-1/2 Stope Cut4 51 Figure 32. Rockburst damage contained in chain-link 52 Figure 33. Location of Damage in 36-746-1 Stope Cut2 53 Figure 34. Slab peeled from back after rockburst in 36-746-1 Stope 54 Figure 35. Stress concentration at the corners of 36-746-1 Stope 55 Figure 36. Underground roof failure mechanisms (Lang, 1994) 58 Figure 37. Span design methodology at Red Lake Mine 61 Figure 38. Definition of span (Lang, 1994) 67 Figure 39. Critical span graph (Lang, 1994) 70 Figure 40. Span design graph with case histories (Wang, 2000) 70 Figure 41. Neural Network process structure 73 Figure 42. Illustration of internal structure of neutral network 74 viii Figure 43. Neural network predicted results 76 Figure 44. Span graph (2003) 78 Figure 45. Comparison of all three span graphs 80 Figure 46. Types of pillars commonly encounters in hard rock mines (Betournay, 1989) 81 Figure 47. Pillar strength curves for the Red Lake Mine. 84 Figure 48. Pillar stability graph using average pillar confinement (Lunder & Pakalnis, 1997)... 86 Figure 49. Pillar stability graph using pillar width-to-height ratio (Lunder &Pakalnis, 1997).... 87 Figure 50. Element subjected to triaxial load (Jeremic, 1987) 88 Figure 51. Mobilization of friction and cohesion as a function of damage (Martin & Read, 1996) ...91 Figure 52. Deviatoric Stress at one-third and one-half UCS 92 Figure 53. Pillar strength and deviatoric stress curves 93 Figure 54. Map3D model of Red Lake Mine 100 Figure 55. Schematic drawing showing the mining of Stope 32-826-4W 103 Figure 56. Induced stress at mining step3 (Cut8) 103 Figure 57. Rock mass strength employing Hoek & Browns failure criteria (fix%) 105 Figure 58. Stored Strain Energy at Observation Point 106 Figure 59. Average Pillar Load/UCS versus W/H ratio 107 Figure 60. Deviatoric Stress per mining cut 108 Figure 61. Back and hangingwall of stope 32-826-4 Cut 7 110 Figure 62. Stope 32-826-4 Cut 7 used as an access 110 Figure 63. Schematic drawing showing the mining of 34-786-4 Cut#4 Stope I l l Figure 64. Induced stress location at mid pillar height 112 Figure 65. Rock Mass Strength Employing m & s Failure Criteria 115 Figure 66. Stored strain energy at mid pillar height 116 Figure 67. Average pillar load/ucs versus W/H 117 Figure 68. Deviatoric stress per mining cut 118 ix A C K N O W L E D G M E N T S The author would like to extend his sincere appreciation to Dr. Rimas Pakalnis for his valuable guidance and comments during the research and preparation of this thesis. Special thanks must be given to the management of Red Lake Mine for co-sponsoring this research and particularly to the chief engineer, Pierre Rocque and the ground control engineer, Grant Corey for their valuable assistance. Finally, thank you to my wife Doreen and my son Adrian for their patience and understanding over the past several years. x CHAPTER 1. INTRODUCTION In 2000, Goldcorp Inc's Red Lake Mine undertook a major research study in developing Design Guidelines for Cut and Fill Stopes in Burst Prone Ground. These guidelines make specific reference: to rockbursting, optimum stope span, and sill pillar dimensions and are the focus of this thesis. This thesis is divided into three sections: The first section focuses on an understanding of the current rockbursting status using the newly installed micro-seismic system at the mine. The second section focuses on span design in burst prone ground while the third section focuses on determining the optimum pillar dimension using several failure criteria. 1.1 BACKGROUND In designing excavation spans and sill pillars for entry-type excavations two limiting constraints exist which influence the design. First, the nature of entry-type mining in burst prone ground is such that workers are exposed to freshly blasted working ground. Secondly, profitable mining often demands the maximum extraction of the ore, which is achieved by maximizing stope spans and by minimizing the size of sill pillars. Although the stope excavations are required to be open for only a short period, stopes in burst prone ground require a higher safety factor as compared to stopes in non-burst prone ground but less than that of permanent underground civil engineering structures. Also, narrow stopes at great depth tend to work violently or even burst. Therefore, by reducing the spans one can reduce dilution, but can increase ground working in the stopes, thus reducing productivity. This thesis will attempt to reconcile these conflicting design objectives by providing for the mining engineer a practical design tool developed specifically for spans and sill pillars for entry-type excavations in burst prone ground. 1 1.2 RESEARCH METHODOLOGY The first phase of the thesis focuses on rockbursting, seismicity and unusual occurrences. In order to understand rockbursting at a particular mine, the study of the causes, conditions and mechanisms for rockbursting has to be understood. The first phase of the thesis describes the effects, causes and mechanism of rockburst and their relation to seismicity as applied to the Red Lake Mine. At the mine, seismic events with significant levels of recorded energy and severe ground workings were visually inspected and studied in detail. The recorded rockburst were analyzed in terms of the three known types - strain, pillar and fault slips. Seismicity and ground workings are analyzed in terms of excavation span, confinement, time and location. All unusual occurrences from bumps to falls-of-ground with significant damage are classified into grouped. The second phase of the thesis focuses on the span graph for the cut and fill mining method. Initially, the critical span graph for cut and fill stopes was developed by Lang (1994). The span graph, used for the initial span design of cut and fill stopes, is based on a graph of rockmass rating (RMR76) against span. However, three major shortcomings exist. First, a statistical method is used to derive the graph, which imparts a major disadvantage as the regression analysis is based on the prediction of mean values only. Mining data is typically very scattered; therefore, use of a statistically derived method may overestimate or underestimate values in some cases. Secondly, the original graph was based solely on 172 cases histories from only one mine. However, the first two shortfalls were solved when Wang, Milne & Pakalnis (2000) after including data from six more operations and with the use of neural nets, the 292 case histories were trained to produce a better outline of the graph. Despite including more data to the span graph, a third shortfall still existed. The previous database did not include cases under high-stress or burst-prone environments. The second phase of the thesis attempts to augment the above by including data from high stress ground on the span graph for cut and fill mining. The final phase of the thesis focuses on sill pillar design in high burst prone ground. The overhand cut and fill mining method at the Red Lake Mine is used to mine 2 the steeply dipping ore bodies. There is always a concern in determining the last possible lift to be mined using the cut and fill mining method, before the remainder of the sill is mined out using the long-hole or other non-entry mining methods. The cut and fill mining method is preferred as it reduces dilution. The intervening sill pillars were numerically modeled and optimum sill pillar heights were determined using five failure criteria -namely Hoek and Brown (1980), Pillar Stability Graph (1994), Stored Strain Energy (Canmet, 1996), Deviatoric Stress (Martin &Read, 1996) and Induced Stress Criteria (Hoek & Brown, 1980). Each of the above criteria were calibrated to the Red Lake Mine ground conditions. The third phase of this thesis is devoted to the "Development of Sill and Post Pillar Design Techniques" within a burst prone environment. 3 CHAPTER 2. THE RED L A K E MINE 2.1 INTRODUCTION The Red Lake gold mine is 100% owned by Goldcorp Inc. and is located in northwestern Ontario, approximately 500 km northeast of Winnipeg, Manitoba, Canada (Figure. 1). Since the start of production in 1948, the mine has produced 3.15 million ounces of gold from underground operations, which has reached the 30 t h level, a depth of 1341 m (4,400 ft) below surface. Figure 1. Location of Red Lake Mine In 1995, diamond drill exploration from the 30 t h level delineated several zones of high-grade ore between the 30 t h and 39 t h levels. In September 1998, results of an independent feasibility study undertaken by Watts, Griffis and McOuat led to a go-ahead decision: to spend 56 million (US$) to expand the mine and mill to 545 tonnes of ore per day. The mine contractor Dynatec Corp. began underground development and construction in May 1999 and completed Phase I of the project by November 2000. This includes four new mining levels in the HGZ: 31-1 sub, 32-1 sub, 34 level and 37 level. This phase also includes a new haulage system on the 37 t h level, and new ventilation and ore and waste handling systems between the 30 t h and 37 t h level. 4 The new orebody has reserves of 2.3 million ounces (71,000 kg) gold. The average cut grade of this deposit, at 47.0 grams/tonne (2.02 oz/ton) gold, makes it one of the highest-grade deposits in the world. 2.2 GEOLOGY 2.2.1 Regional Geology The Campbell-Red Lake gold deposit is hosted by the tholeiitic to komatiitic rocks of the Balmer assemblage as shown in Figure 2. In the vicinity of the deposit, the lithological sequence consists predominantly of basalt and ultramafic rocks with subordinate rhyolite, diorite, and synvolcanic sedimentary rocks. These rocks have been folded by southeast trending F 2 folds, which are transacted by two steeply dipping (70-80°); southeast-trending sub-parallel faults referred to as the Campbell and Dickenson faults. The High Grade Zone is essentially hosted by massive basalt and occurs within an F2 aniform defined by the geometry of the rhyolite to the west and basalt-ultramafic rock contact to the southeast of the High Grade Zone. Quartz-feldspar and feldspar porphyritic rocks cut all these units. The quartz-feldspar porphyry and feldspar porphyry dykes are northwest to southeast trending and the feldspar porphyry cuts the high-grade ore zones (Dube, Williamson & Malo, 2001). 5 L E G E N D V Property boundary B Shaft Figure 2. Geological map of the Campbell-Red Lake gold deposit (Dube et al., 2 0 0 2 ) 6 ^^Cep/FP dyke Larnpraptiyre dyka jDykoitfildtnwui Ixxitoscatej Gabbro iMg-tholellto) Campbell dkxtte Sedimentary Rocks (Bruce CJttniWJ' Huston^ p~J faleie volcanic rocks r r i Basalss toniatiite PeikMc komaliite (PK) Unsubdlvidod ultra malic rocks J Mate volcaric rc>ete \ Mnarallzatlon E S C Ore Zone n 1 Foliation "v. Contacts and ** ore structures 2.2.2 Local Geology The Red Lake Mine is situated on the hangingwall side of a southeast-plunging anticline, within the eastern portion of the Red Lake greenstone belt. The dominant rock type in the mine consists of tholeiitic to komatiitic flows. These rocks are pillowed, often massive, and where unaltered, mafic flows are dark green to black and fine-grained. Mafic volcanics, the main host for ore at the mine, are banded in appearance and moderately to strongly foliated. The mineralogy of these mafic volcanics is plagioclase, quartz,- fibrous amphiboles, biotite, minor chlorite, carbonate, hornblende and talc (Rocque, 2001). Diorite, which occurs as thick flows, is a coarse-grained equivalent of these basalts. Intercalated with the mafic volcanic rocks is a highly carbonatized and altered unit, which is believed to be an altered ultramafic rock of either volcanic or plutonic origin. This unit varies considerably from rhyolite breccia to talc-chlorite schist, to carbonatized andalusite-rich metasomatized rock (Rocque, 2001). Its intense shearing and alteration, in addition to being relatively incompetent characterize this unit. Interbedded interflow sulphide-facies banded iron formation is intercalated with the mafic volcanic rocks. In most locations this unit is folded about a northwest-trending axial plane with the main bedding attitude striking east-west, and dipping vertically. Above this package of mafic rocks one finds felsic flows, pyroclastic, clastic and chemical sedimentary rocks. Rhyolitic flows are mainly seen west of the main workings of the mine, while felsic volcanic breccias found near No. 2 shaft on 35 Level, appear to grade into lapilli-tuff on surface. Greywacke and chert occur inter-bedded. The volcanic and sedimentary rocks and ore zones have been intruded by quartz-feldspar-porphyries (QFP), metadiabase, peridotite/serpentinite and lamprophyres. The lamprophyre dykes exhibit chill margins, show dilatant offset on ore structures, and postdate all ore and most faults. The lamprophyre dykes occur in a 7 conjugate set with a south-southeast trend dipping at 55-65° to the west-southwest, and a south trend dipping 20-40° to the west. The peridotite/serpentinite found in the footwall of the mine appears to postdate all ore zones. Structurally, the unit is massive with minor, shallow, north-trending carbonate veins. The High Grade Zone consists of quartz-carbonate veins and breccia structures and arsenopyrite replacement ore within altered basalts and altered ultramafic rocks. The alteration consists of chlorite, biotite, silica, carbonitization and minor actinolite. The mineralization is characterized by consistent distribution of both coarse and fine flecks of native gold, fine acicular arsenopyrite and pyrrhotite. Accessory mineralization includes chalcopyrite and sphalerite (Rocque, 2001). 2.3 MINING METHODS 2.3.1 Primary Development The mine is accessed from the footwall side of the ore body by a three-compartment shaft (#2). The mine operates two shafts. The #1 shaft extends to just below the 23rd level about 1000m below surface, while the #2 shaft begins at 23rd level, and extends to below the 38th level-loading pocket, at 1700m below surface. The HGZ is accessed from the 30th level, which occurs about 1300m below the surface. The main levels have been driven from the shaft at 45m (150ft) intervals. The five main mining levels have been established, namely: • 31-1 Sub • 32-1 Sub • 34Level • 36-2 Sub • 37Level In addition, a connecting ramp system extends from the 30th level to the 37th level. Between each main level, two sub levels are driven in the hangingwall at 30m intervals as 8 shown in Figure 3. The Main Zone is accessed by means of two crosscuts, referred to as attack ramps, driven off the main ramps. Broken muck is hauled up to a central ore pass system, which passes ore to the 38 t h level-loading pocket. Campbell Mine Red Lake Mine Figure 3. Primary developments at Red Lake Mine (Rocque, 2001) A l l of the mining initially will be accessed by ramp, although there may be a small amount of captive cut and fill in the future. In later stages, the sill pillars will be removed by longhole mining or even man-entry. 2.3.2 M C F Stope Development Mechanized cut and fill (MCF) stopes have been started on the 31-1 Sub, 32-1 Sub, 34 Level, 36-2 Sub and 37 Levels. Typically, a level has three (3) to six (6) stopes. As one of the stopes is being mined, the other is being filled. In this way, a constant mining rate from these stopes can be assured. When a lift has been complete, the attack is back-slashed to provide access to the next lift as shown in Figure 4. This continues until the attack finally reaches an inclination of 20%, at which point another attack ramp is driven at minus 20% from the next level, 30m above. 9 Attack Ramps @ -20% Figure 4. Overhand mechanized cut and fill method 2.3.3 Drilling and Blasting Hydraulic jumbos with twin booms are employed to drill horizontal breasts 3m deep. The face can be up to 8m wide depending on the ore limit and 45mm diameters holes are drilled on a 0.91m by 0.91m (3ft by 3ft) square pattern. The holes are loaded with pneumatically placed ANFO. In areas, where the ore is too narrow for the hydraulic jumbo, jackleg drills are used. The drill hole pattern for jackleg drills are 0.76m by 0.76m (2.5ft by 2.5ft) as shown in Figure 5. A number of ground related problems experienced at the Red Lake Mine have been attributed to either high in-situ stress or poor drilling and blasting practice. For this reason, particular emphasis is placed on drilling flat parallel back holes for ground control purposes. 10 Figure 5. Location of holes in a typical breast face Technical details of the cut and fill breasting at the Red Lake Mine are provided in Table 1. Table 1. Drilling and Loading Specifications for Cut and Fill Breasting Borehole Specification Jumbo Jackleg Hole Diameter 45mm 32mm Length of Hole 3.6m 2.4m Length of Charge 3.4m 2.2m Burden 0.91m (3ft) 0.60-0.76m(2-2.5 ft) Spacing 0.91m (3ft) 0.60-0.76m(2-2.5 ft) Explosives ANFO for production holes Handidet Detonators Number of holes per delay: 3-•5 11 2.3.4 Mucking The ore is mucked with 0.6m to 1.0m wide slusher/scrapers and 0.7m3 to 2.3m3 load-haul-dumpers (LHD). The ore is trammed to the ore passes, which intersect the footwall ramp and pass the ore to the 38th level-loading pocket. Each lift is mucked out to within 0.3 meters of the paste fill in order to maintain a good mucking floor for the equipment to work on. Before a stope is filled, the remaining ^ muck is removed down to the fill level. 2.3.5 Ground Support In accordance with the 1988 Ontario Ministry of Labour's Policy on Ground Support, the freshly blasted area is scaled and ground support is installed immediately after the area is mucked out. Methods of artificial ground support in use at the Red Lake Mine include: • Resin rebar bolts; • Swellex bolts; • Chain-link and welded wire mesh (WWM); The resin rebar bolts are used both in permanent excavations in addition to the cut and fill stopes. Originally, mechanical bolts were used in permanent excavations such as ramps and drifts. Once it was realized that spalling of the drill hole collar, caused by stress fractures rendered mechanical bolts ineffective, they were replaced by resin rebar bolts. The resin rebar bolts offer twice as high yield and breaking strengths than the mechanical bolts, however they have a lower displacement limit than the mechanical bolts. Technical specifications of resin rebar bolts are provided in Table 2. Rock bolting is carried out either with stoppers operated from a scissor-lift vehicle or from the floor of the excavation. Standard 1.2m rock bolt spacing is used which was found through experience to be suitable for most of the Red Lake Mine. In areas where joint spacing is as little as 0.3m, a 1.0m square pattern has been applied. 12 Quality control on the installation of these bolts is maintained through routine torque testing by bolting crews and supervisors and pull testing carried out by the engineering department. Table 2. Technical Specifications of Threaded Rebar/Resin Bolts Type Threaded Rebar-3/4" - 10UNC Yield Load 10.8 tonnes Breaking Strength 18.9 tonnes Bond Strength 18 tonnes/ft* Bolt Length 1.68m (5'6")& 2.13m (7') Resin Cartridge Lengths 300mm, 900mm Cartridge Diameter 28.5mm for both lengths Set Times 30 seconds for 300mm, 2-4 minutes for 900mm * note that bond strength is given in tonnes/ft. The swellex rockbolts are often preferred in wide span excavations such as drift intersections and wider stopes because of their available length. In addition, swellex bolts act as a friction stabilizer, providing anchorage along the entire length of the bolt. This holds the rock together, reduces joint separation, and ultimately helps the rock mass to support itself geometrically. The swellex rockbolt has a higher energy absorption capacity than both rebar and mechanical bolts. Thus the swellex rockbolt is typically used in combination with the resin rebar bolts. The swellex rockbolt is installed in the center of a 1.2m by 1.2m support pattern. Quality control on the installation of swellex rockbolts is maintained by pullout tests conducted by the engineering department. Technical specifications for standard swellex bolt are provided in Table 3. 13 Table 3. Technical Specifications of Swellex Bolts Type Swellex Tube Diameter 26mm Yield Load 12 tonnes Ultimate Load 12 tonnes Bond Strength 2.7-4.6 tonnes/ft Bolt Lengths 1.2m-3.6m The galvanized chain link mesh is used in all stopes up to the stope face and in areas where a probability of bursting exists such as stopes and drifts where faults/dykes intersect across. The welded wire mesh is mainly used in permanent excavations such as ramps and drifts. The main purpose of the chain link and welded wire mesh is to prevent injury to personnel and damage to equipment, by containing the loose rock after a rockburst. In high traffic areas and work station areas where personnel and equipment are often present, the wire mesh is installed as a long term safety measure to contain loose which may fall over an extended time period. The chain-link and the welded wire mesh are generally used in conjunction with swellex and rebar/resin bolts. Technical specifications for standard Chainlink and Welded Wire Mesh are provided in Table 4. Table 4. Technical Specifications of Chain Link & Wire Mesh Type Chain link Welded Wire Mesh Spacing 50mm x 50mm (2"x 2") 100mm x 100mm (4" x 4") Thickness 11/llgauge (3.175mm) 8/8 gauge Width 1.2m (4ft) 1.2m (4ft) Length 2.1m (7ft) 19m (50ft) Bag Strength 1.9 tonnes 3.2 tonnes 14 2.3.6 Paste Fill ; When a lift has been mined out to the ore limits, the remaining 0.4 to 0.6m layer of muck is scraped off the floor down to the paste fill. Paste fill is placed for three to four lifts depending upon the exposed stope span. The lifts filled with waste rock are capped with cemented paste fill to prevent ore from the next lift being mixed with the waste rock. The hydraulically placed paste fill is contained by a fill wall, which is built with rebars and welded wire mesh mattresses and coated with 102mm (4inch) of shotcrete. The fill is normally placed to within 0.6m (two feet) of the back. Paste fill consists of tails from the mill mixed with cement (up to 10% of dry weight) and pumped from surface. This slurry is distributed to the stopes via a series of 12.7cm (5inches) diameter boreholes and pipes. 2.4 MICRO-SEISMIC SYSTEM The Hyperion Micro-seismic System was installed at the Red Lake Mine in June 2000 and consists of an array of 10 sensors (16 Channels), with 7 wall-mounted uniaxial and 3 triaxial accelerometers (geophones), the latter being installed in grout-filled boreholes. The fibre-optic transmission of data between the underground MUX boxes and the surface DE-MUX boxes provides a clean signal with high signal-to noise-characteristics (Leslei, 2001). The approximate volume of ground covered by the array is 532m (north) x 570m (east) x 255m (depth) between the 30th and 34th Levels. The microseismic system not only provides source location but also provides source parameters such as seismic moment, moment magnitude, seismic energy, apparent stress drop and source radius among others. These source parameters can be use to determine the type of a seismic event. In summary, Chapter 1 has explained the methodology utilized to support the three parts of this study. Chapter 2 introduces the geology and mining method of the mine and Chapter 3 reviews the present knowledge with respect to rockbursting at the Red Lake Mine. 15 CHAPTER 3.0 REVIEW OF ROCKBURSTS AND SEISMICITY 3.1 LITERATURE REVIEW A rockburst is defined as a "sudden rock failure characterized by the breaking up and expulsion of rock from its surrounding, accompanied by a violent release of energy" (Blake 72). Hedley (1992) describes this seismic event as a "phenomenon defined as a transient earth motion caused by a sudden release of seismic energy in highly stressed rock masses". Ortlepp (1983) defines rockburst as a "seismic event as one that causes significant damage". No matter how one defines rockburst. it is the most dangerous of the rock stress conditions representing a threat to miners and causing serious interruption in production. The first published information on rockburst was in 1738 from the tin mines of England. During the second half of the 19th century, rockbursts were noted in Western Europe in coal deposits (Turchanov, Iofis, & Kasparyan, 1979), while in the 20th century rockbursts occurred in the gold mines on the Witwaterstrand in South Africa and on the Kolar Gold Field in India. In Canada, rockbursts first became a problem in the mid-1930s in the hardrock mines at Kirkland Lake and Sudbury in Ontario. In the Red Lake Mining district, the first reports of rockbursts was in 1960 at Placer Dome's Campbell Mine (Hedley, 1992) while at Goldcorp Inc's Red Lake Mine the first seismic disturbance was also reported in 1960 (Mah, 1995). The study of the causes, conditions and mechanisms of rockbursting and the development of effective methods of their prediction, prevention and localization represents an important task for the rock mechanics engineer. The importance of this task increases as the mining depth increases and as a result the severity increases. The following section describes the effects, causes and the mechanism of rockburst and its relation to seismicity. 16 3.1.1 Mechanism of Bursting Rockbursts first became a recognized operational problem in the Kolar Gold Fields of India in 1898, while in the early 1900's, at a depth of less than 500m (1500ft), rockbursts became a problem in the mines of the Witwaterstrand of South Africa. By 1915, a committee was formed to investigate the underlying cause of rockbursts. Two theories were suggested to explain the rockburst phenomenon. The first theory attributed rockbursts to the formation of a "Dome", a zone of fractured rocks around the mined openings, while the Cantilever theory suggested layer separation caused by the sagging of seams. 3.1.1.1 Dome Theory Morrison (1942) defined a "dome" as a zone of fractured rock formed around stopes. As the stopes approach each other, the intervening pillar becomes increasingly stressed. If these pillars are removed, the volume of the dome increases. The rupture of the large volume of rock between the two domes, and the release of its accumulated energy were thought to result in rockbursts. The concept of dome theory is illustrated in Figure 6. Figure 6. Concept of doming theory (Morrison, 1942) 17 Although the formation of zones as a rockburst mechanism has been discredited, many of the characteristics associated with domes are still relevant in rockburst control strategies (Hedley, 1992). 3.1.1.2 Cantilever Theory The cantilever theory (Sinclair, 1936) was another early theory used to explain rockbursts. Many mine operators supported the cantilever theory where the veins were flat dipping. As the mining progressed, the timber support bent under the weight of the hangingwall as hangingwall sagged. The larger the areal extent of the opening, the greater the sag. The bedded layers within the sagging area acted as a beams or a cantilever. As the sagging continued, the layers separated and began to fracture within the hangingwall, which caused a small rockburst to occur. As further sagging continued, the beams sheared at the support ends and a large burst occurred. Figure 7 illustrates the cantilever theory. rtomoC}en</c>us fiongtrrg h/a// Formation > ' : ; : . ^ x : : : : x . ' : ; : : : : : ; : o : ; : ; S : ; 1 m^mm i ^ i t ^ l i i s i M f i M ::::V':^'*':' l i l l l l l I I tm i i SB tmm. SI Face Figure 7. Concept of cantilever theory (Sinclair, 1936) This theory was discredited when it was found using seismometers that most of the seismic events occurred in the solid rock ahead of the advancing stope. 18 By the early 1950's it became more and more apparent, that any purely practical attempts to solve the rockburst problem were inadequate. As a result, the Council for Scientific and Industrial research (CSIR) was formed in South Africa to study rockbursts. In Canada, concurrent research was taking place in the Sudbury mines, but there were no published data until late 1950. The Ontario Mining Association formed the first rockburst committee in 1940. It became necessary to obtain both a qualitative and quantitative understanding of the problem. The first phase of this research led to an intensive laboratory investigation of the behavior of rock under high stress conditions. The intent was to determine the deformation characteristics and mechanisms of failure for brittle rock. The second phase of the research included the collection of data through the observation of the occurrence of rockbursts. The analysis of the collected data indicated the significance of a number of variables (Salamon, 1983). Some of the variables that affecting incidents and severity of rockbursts are: Depth of working: The number and violence of rockbursts increase with depth. Structural Features: Hard brittle rocks such as dykes are more susceptible to bursting than softer, weaker rocks. A similar effect exists for joints and faults. Dip of Orebody: Rockbursts were more apt to occur in steeply dipping deposits than in those that gently dip due to a decrease in confinement. This is further elaborated upon in section 4.2.2 Sequence ofStoping Operations: Rockbursting incidence increased with the formation of remnant pillars and decreased until remnants were removed. 19 Rate of Mining: The settlement of ground continues unimpeded regardless of the rate of stoping, resulting in a steadily increasing pressure. Under such conditions, stoping should be as rapid as possible. The first phase of the research gained tremendous impetus when Cook (1965) and Deist (1965) independently put forward the notion that brittle rock under certain loading conditions can maintain an "elastic" behavior. In the late 1950's, Cook embarked on seismic investigations using an underground network of seismometers. The seismic locations of rockburst events showed that the bursts were occurring back from the face in solid rock, an observation that ran counter to the cantilever theory. Perhaps the most striking feature of the investigation was that the number of observed seismic events greatly exceeded that of reported rockbursts. This led to a definition that all rockbursts are seismic events but not all seismic events are rockbursts. 3.1.1.3 Elastic Theory Further work by Cook (1963), which examined the behavior of rock specimens in a conventional stiff testing machine, postulated that rockbursting may pose a stability problem in the same way as a specimen behaves in a laboratory test. Research by Birch (1942) and Jaeger (1962) suggests that the most important mechanical properties of rock are elasticity, plasticity and viscosity. These properties define the relationship between load, deformation and time. Cook (1963) postulated that when a load is applied to an elastic material it deforms instantaneously and recovers to its original shape immediately once the load is removed as shown in Figure 8. In many materials, it is found that the strain is proportional to stress. The work performed in deforming an elastic material is equal to the area underneath the stress-strain curve as shown in Figure 8. 20 <u L •P Strain Figure 8. Stress-Strain curve defining the strain energy resulting from the seismometers deformation of an elastic material (Cook, 1963) Thus, the elastic theory was used as a model for the simulation of the behavior of most of the rock surrounding an excavation. Only the fractured rock immediately around the mining cavity fails to behave in an elastic medium from the analysis. Initial postulations were that only the energy stored within the rock mass was the source of the liberated energy. Later, it was realized that there was a change in potential energy of the surrounding rock mass because of the mining process. This led to development of the concept of energy balance, originally developed by Cook (1967), and later refined by Salamon (1974, 1984). 3.1.1.4 Energy Balance Mining is a progressive activity. Excavations in mines change in shape and grow in size with time. As a consequence of increasing the size, the surrounding rock mass moves towards the excavation, resulting in a change in potential energy (W t). The rock removed during enlargement also contains stored strain energy (U m ) . The sum (W t + U m ) defines the energy quantity that must be expended in some manner as a result of the enlargement. The stress acting on the rock that is removed is transferred to the surrounding rock mass increasing the stored strain energy (U c). 21 If the excavation is supported, which may or may not include backfill, then a certain amount of energy is dissipated in deforming the support (W s). Any excess energy is normally referred to as release energy W r . Using the law of conservation of energy, the energy balance is expressed as in equation 1 and illustrated in Figure 9. W t + U m = U c + W s + W r (1) Figure 9. Illustration of Elastic Energy Balance (CAMIRO, 1995) There are a number of ways the stored strain energy can be released. The stored strain energy U m is released by removing the rock. If the rocks were removed instantaneously, there would be an oscillation in the rock mass. The equilibrium state corresponding to the new mining geometry would be attained through damping. Some kinetic energy would be dissipated in the damping process. As there is no other mode of dissipation, the released energy is expressed as equation 2. W r = W k + U m (2) 22 It is the kinetic energy (also known as seismic energy), which is responsible for the damage caused by a rockburst. Equation (1) thus can be rewritten as: W k =W t - (U c + Ws) (3) Salamon (1974) has shown that the magnitude of Wk approaches zero as the increment in the radius of a cavity becomes infinitesimal. That is AWk =0 thus AWr =AUm and AW t=AUm +AWs (4) where the energy quantities are prefaced by the symbol A to emphasize the effects of infinitesimal changes in geometry is being considered. Some conclusions can be extracted from these energy relationships. i) The work done by the external and body forces during a small change in geometry AWt, is fully expended in straining the rock mass AUC and deforming the support AWS. ii) The energy released in the course of further mining equals the strain energy stored in the rock prior to its removal. iii) The enlargement of mining cavities in small steps is a quasi-static stable process, which does not result in the release of kinetic energy into the rock mass and, therefore, cannot be the source of seismic energy. In some cases, the last conclusion(iii) is contradictory since many mines employ incremental methods but still experience rockbursts. However, this may suggest that 23 some other source of energy is being liberated due to a non-elastic condition, either fracturing or slippage occurring along a fault (see 3.1.1.5). Reference to all the equations in full can be found in the following Canadian authored texts: i) CANMET's Rockburst Handbook For Ontario Hardrock Mines (Hedley, 1992) ii) CAMIRO's Rockburst Research Handbook. Vol. 1-6, 1995 (also discusses ground support design and distress blasting techniques in burst prone ground). 3.1.1.5. External Energy Sources All seismic events radiate kinetic energy. The identification of the source of this energy is an essential pre-requisite to the understanding of the mechanism involved. As mentioned earlier, during the enlargement of cavities in small steps, which is the normal method of mining, the release energy is removed in the excavated rock. Thus, the release energy cannot be the direct cause of seismic activity. Therefore, underground seismic events which cause rockburst can be due to only instabilities which arise from structural weakness and from induced failures in the rock mass. Salamon (1974) discusses the phenomena of stable and unstable equilibrium. Since additional external work is required to move a system in a stable equilibrium, energy is extracted from the system by disturbing a state of unstable equilibrium. This simple example is illustrated in Figures 10a and 10b, which demonstrate this principle. / / / / / . Co) Figure 10. (a) Stable and (b) Unstable equilibrium 24 From the above conclusion, it can be said that a seismic event is the manifestation of a disturbance of a state of unstable equilibrium, thus it follows that the associated seismic energy must be extracted from the rock mass. Thus, the source of this extracted energy is the strain energy stored in the surrounding rock. (The stored strain energy is elaborated upon in section 6.2.3). A simple mechanical model to demonstrate the principle of this type of instability is shown in Figure 11. I6 N- S gM y w W — - T 77'T rr mi uN Figure 11. Mechanical model of a fault-slip on a geological weakness Consider a block, which is placed on a rough surface and which is acted on by a normal force, N, and tangential force, T. This system will be in a stable equilibrium as long as T-u sN>0 (5) where us = static coefficient of friction. When T=usN, an unstable equilibrium and the block will come into motion due to either an infinitesimal increase in T or an infinitesimal decrease in N. When the block starts to move, the small dynamic coefficient of friction Ud becomes the operative and a force of initial value (us-Ud)N will accelerate the block which gains both kinetic and heat energy in the process. The source of the kinetic energy is the stored strain energy, which has been stored in the spring during the gradual increase in T from zero to ua. This simple example resembles the situation when a seismic event is initiated by shear failure in the rock mass or when slips occur along a geological weakness. 25 Two conclusions can be drawn from the above analogy. i) An instability, in the form of a seismic event, can be initiated by the smallest change in stress if any point in the rock mass is close to unstable equilibrium. ii) Kinetic energy, imparted to the rock particle in the course of propagating a seismic event, is drawn from the stored strain energy in the rock around the region where the events are initiated. The above explains how energy is released in the rockbursting process. The next section explains why this energy is released violently. 3.1.2 Loading System The energy approach to explain the mechanism of rockbursting is valid as energy is released as an excavation is slowly created. It was Blake (1972) who showed why the energy is released violently. Cook (1965) initially carried out the work on the loading system. He suggested that rockbursts might be considered a stability problem in the same way as a specimen behaves in a laboratory test. This will depend on the relative stiffness of the specimen versus the loading system. The specimen will fail violently if energy can be extracted from the loading system at failure. Deist (1965) proposed a similar but more complicated mathematical model. For the first time a mechanism was used to account for the two types of failure, violent and non-violent. However, there was no attempt to test the theory in the field. Blake (1972) investigated the violent fracturing of the rock by using a micro-seismic monitoring system developed by the US Bureau of Mines at the Galena Mine in the United States. This study has given an insight into the mechanics of rockbursts in mine pillars. Blake used a finite element model in which he incorporated the results of the micro-seismic results to show that a pillar suffers rockbursting when the average stress exceeds the strength of the pillar and the mine stiffness is lower than the pillar stiffness. 26 He suggested the use of micro-seismic measurements for delineating high stress zones and the potential rockburst hazards. This phenomenon has been confirmed in the laboratory during the testing of rock specimens for uniaxial compressive strength (UCS), where elastic and brittle rocks exhibit sudden failure. According to the concept of mine stiffness, a rock specimen is stiffer than the loading system; all available potential strain energy is transferred to the rock sample varying its properties and behavior. Two principle types of unloading failure are suggested as shown in Figure 12. i) Case (a) where the stiffness of the specimen is greater than the stiffness of the loading system K s > Ki , violent failure occurs when stress in the specimen reaches its strength due to sufficient strain energy available in the loading system to continue to the load the specimen, hence the machine recoil destroys the specimen. Such a case occurred when Galena mine rocks were tested to failure in a conventional or soft testing machine. ii) Case (b) when Ki > K s , a non-violent failure indicates a low stiffness of structure. The stored strain energy in the loading system is not sufficient to deform the rock specimen. Here the loading system is stiffer than the rock, thus the specimen deformation occurs only when more load is applied through the loading system. F Available strain energy^ F FORCE FORCE \ D I S P L A C E M E N T U D I S P L A C E M E N T U C A S E A! Unstable, violent failure CASE B: Stable, nonviolent failure Figure 12. Specimen and loading system relationships (Blake, 1972) 27 3.1.3 Types of Rockburst The previous section described the elastic reaction of the rockmass due to mining. However, in most cases rockbursts are caused by non-elastic rock behavior during the failure process. Salamon (1983) has listed the pre-existing conditions necessary to initiate a rockburst. A region in the rock mass must be on the brink of unstable equilibrium due to a) The presence of an appropriately loaded pre-existing geological weakness such as joints, faults, dykes and bedding plane; or b) where the changing stress are driving a volume of rock towards sudden failure or; c) where a system of pillars is approaching a state of imminent collapse. The three categories of rockbursts can be labeled as strain, pillar and fault-slip burst. The first two usually occur within the mine workings. 3.1.3.1 Strain Bursts Strain bursting, probably the most common type of burst, is caused by high stress concentrations at the edge of the mine openings, which exceeds the strength of the rock. Events can range from small slivers of rock being ejected from the walls to the complete collapse of walls as the excavation tries to achieve a more stable shape. Strain bursting often occurs when a drift is driven through a contact between brittle and relatively soft rock. Damage is normally confirmed to the brittle side of the contact (Hedley 1992). Previously, it was thought that the brittle rock with a higher compressive strength and elastic modulus would contain more stored strain energy. This is not necessary the case as shown in Figure 13. 28 TI CO O KSoft Displacement Figure 13. Stress-displacement characteristics of brittle and soft rock (Hedley 1992) Brittle rocks tend to exhibit a steeper unloading curve than soft rocks. In Figure 13 the area under both the brittle and soft load-displacement curve are roughly the same, hence both rocks consume the same stored strain energy in the fracturing process. Again, the stiffness of the loading system is less than that of the brittle rock and greater than the soft rock, hence, the former fails violently and the latter non-violently. 3.1.3.2 Pillar Bursts Pillar bursting is caused by a sudden change in potential energy as the hangingwall and footwall rapidly converge during the failure process. Whether a pillar fails violently or non-violently depends on the stiffness of the loading system as compared to that of the pillar stiffness. In an underground mine the stiffness of the loading system is influenced by many factors: the areal extent or the span of the mine, the elastic modulus of the rockmass which controls the amount of movement towards the excavation while the size, number and location of pillars also influences the loading system. Pillars cannot be treated in isolation since the presence of one pillar influences the loading stiffness on the other pillars. 29 3.1.3.3 Fault-Slip Bursts Fault-Slip burst accounts for a small number of rockbursts that occur in mines. However, they are responsible for most of the major rockburst of magnitude 3.2 to 4 on the Nuttli scale. Slippage along a fault has long been recognized as the initiation mechanism for an earthquake. The mechanics of a fault-slip burst mechanism has been discussed in section 3.1.1.5 under External Energy Source. Up to this point, different mechanisms have been used to explain rockbursts. Section 3.1.4 explains the rockburst mechanism using seismology. 3.1.4 Rockburst Seismology With the advent of micro-seismic monitoring systems, more researchers are using seismology to understand rockbursts. In the late 1950's, Cook embarked on intensive seismic investigation using an underground network of seismometers. He was the first person to use a three dimensional underground array of seismometers to investigate the problem (Cook 1963). This type of network has proven to be the most effective tool in unraveling the complexities of seismicity associated with mining. The most important result of Cook's study was the realization that only a small fraction of seismic events cause damage to mine working and that very few seismic events manifest themselves as a rockburst. In the next section, some essential features of the mechanisms of seismic events and their relation to mining and underground hazards are discussed. 3.1.4.1 Seismic Wave Most of the source parameters derived in seismology are from seismic wave analysis. When a seismic event occurs underground, strain waves radiate from the source in a spherical pattern. There are two types of waves: P or compressional waves are radial vibration in the same direction of the wave front while the S or shear waves are transverse vibrations perpendicular to the wave front. The velocities of P and S waves in an elastic homogenous isotropic rock mass is as follows: 30 a = ((X + 2u)/p)' (6) P=(H/P)°-5 (7) where: a = P wave velocity P = S wave velocity p. = shear modulus of the rock X = Lame constant p = rock density 3.1.4.2 Magnitude Magnitude is often correlated with damage left by a seismic event or inversely used to establish the energy level required to cause a certain amount of damage. For both mining-induced seismic events and natural earthquakes, the relationship between magnitude and frequency of occurrence is expressed by: LogN = a - b M (8) where: N= number of events greater than or equal to a given magnitude in a given time period, a and b = constants It is important to note that M N is the local magnitude scale introduced by Nuttli for eastern North America whereas M L is the local magnitude scale introduced by Richter and used by seismologist elsewhere. 3.1.4.3 Location The most fundamental piece of information about a seismic event is the coordinates of the location of occurrence. The focus or hypocenter specifies the location from which a seismic wave radiates. Source locations help to delineate zones of highly stressed rock or zones of unusually weak rock mass. It has also led to the identification of 31 commonly occurring rockburst types mention above: 1) strain burst, 2) fault-slip burst and 3) pillar burst. The arrival of the P waves and its time separation to the S wave arrival is used to calculate the distance of sensors from their source allowing the location of an event to be estimated. The distance (Dj) from the source to the ith sensor can be represented by a system of linear algebra. Di = ((x-aO2 + (y-bi)2 + (z-Ci)2)0-5 (9) where: x,y,z = coordinates of the source aj;b;,Cj = coordinates of the ith sensor 3.1.5 Types of Mine Tremors From recent studies of mine-induced seismicity, more researchers agree that: i) Two broad types of tremors are almost universally observed. a. Those directly connected to the mining operation (formation of fractures at the stope face. b. Those that are associated with movement on major geological discontinuities. ii) Mine seismicity is strongly affected by local geology and tectonic stresses. The division of mine tremors into two categories is a general one, and several subsets, six models of induced seismicity in underground mines in Canada have been proposed by Ffasegawa (1989). The models are shown in Figure 14. 32 (o) CAVITY COLLAPSE " _ C a P-«- * - R q £ b _ a (c) TENSIONAL FAULT P l l l l l l l l l l (e) THRUST FAULT ' 1 ' 1 (b) PILLAR BURST -ili2£lJvF3ce (d) NORMAL FAULt SHALLOW ( N E A R H O R I Z O N T A L ) ( f ) THRUST FAULTING Figure 14. Six models for mine-induced events (Hasegawa 1989) While several authors have suggested six types, only two are important: i) the double couple fault or the thrust fault model (d & e) ii) the pillar implosion model (b) as these types of failures are more common in mines. The polarity (wave) of the recorded first motion is used to study focal mechanism. Following polarity calibration, it is possible to deduce if the rock mass at each sensor is in a compression or in a tension mode. The data is then reported on a stereonet and an attempt is subsequently made to determine which principle failure mechanism seems applicable: 1) implosion, 2) tensional or 3) fault-slip. The double couple focal mechanism is used to detect the fault-slip types of rockburst while other rockbursts are detected by the non-double couple focal or isotropic mechanism. 33 3.1.5.1 Double Couple Focal Mechanism The double couple focal mechanism consists of two opposing force couples with no net force or torque. The space around the source is divided into four quadrants according to the sense of the first motion of the P waves. Two quadrants are compressional and two quadrants are dilatational as shown in Figure 15a. a) Doubla-Coupl* Fault Mo4«l b) P i l l a r Implosion Model Figure 15. Direction of ground motion for the two types of seismic events (Hedley, 1992) One of the two nodal planes separating these quadrants coincides with the fault and the other with the auxiliary plane. An equivalent representation involves two orthogonal oriented sets of opposing forces: the pressure, P and tension, T axes as shown in Figure 16. The null motion axis B is useful for relating the focal mechanism to the ambient state of stress. The maximum and minimum principle stresses coincides with the P and T axes respectively while the intermediate principle stress is oriented parallel to the B axes. 34 Figure 16. Fault-Slip solution (Hedley, 1992) 3.1.5.2 Non-Double Couple Mechanism Recent results from focal mechanism studies indicate growing evidence that alternate mechanisms other than shear failure are possible. Sudden collapse of a pillar is considered an "Implosion" in which all first motions would be towards the pillar as shown in Figure 15b. However, a blast would indicate all first motions would be away from the blast. Figure 17 illustrates the common first motions. E o 3 "5 a u at CL ISOTROPIC Mxx 0 0 0 Myy 0 0 0 Mzz -Mxx 0 0 0 -Myy 0 0 0 -Mzz Explosion 7\\ Implosion DOUBLE COUPLE Mxx 0 0 0 -Myy 0 0 0 0 e slip on a fault Figure 17. Common first motions 35 Wong and McGarr (1983) investigated the possible causes of pillar implosion in coal mines. They concluded that in most cases due to poor spherical coverage, the first motion pattern could also be fitted to the double couple focal mechanism. One of the main problems in first motion studies is that data is limited. 3.1.6 Summary - Rockburst Mechanism and Seismology In over a century of research in rockbursting, it has been revealed that there are three main types of bursts: strain, pillar and the fault-slip burst. Strain bursts are the most common type of burst, caused by a high stress concentration at the edge of the mine opening, which exceeds the strength of the rock. Pillar bursts are caused by a sudden change in potential energy as the hangingwall and footwall rapidly converge during the failure process. Whether a pillar fails violently or non-violently depends on the stiffness of the loading system as compared to that of the pillar stiffness. The fault-slip burst is responsible for most major rockbursts of magnitude 3.2 to 4 on the Nuttli scale. Slippage along a fault has long been recognized as a mechanism similar to earthquakes. With the advent of micro-seismic monitoring systems, researchers are now able to delineate rockbursts from seismic events. Seismology is used to understand rockburst mechanisms. Two common mechanisms are the double couple focal mechanism and pillar implosion. Several source parameters such as location magnitude and seismic moment are used to understand the extent of damage. Seismic source parameters described above resulted in a number of trends with potential mining applications. This chapter has reviewed seismicity as it applies to rockbursting as in presently in the literature. The following Chapter will relate the above to the Red Lake Mine in terms of rockburst, seismicity and unusual occurrences reported. 36 CHAPTER 4.0 SEISMICITY AT THE RED L A K E MINE 4.1 BACKGROUND The first seismic disturbance at the Red Lake Mine was reported in 1960 (Mah, 1995). With the introduction of the reporting of all underground "Unusual Occurrences" by the Ministry of Labour, Ontario in 1988, an average of 34 seismic occurrences were reported per year. In June of 2000, a micro-seismic monitoring system was introduced at the mine. By the end of April of 2002, there were an average of 40 seismic events recorded per day while 31 unusual occurrences were reported during 2001. The first half of this section discusses some of the variables that cause seismicity or rockbursting and the latter half discusses the four known rockburst case histories at the Red Lake Mine. 4.2 CRITICAL FACTORS AFFECTING BURSTING Several variables that affected the severity of seismicity at the Red Lake Mine are excavation span, dip of orebody, time, location and geology. These variables are classified into groups, using numerical modeling, micro-seismic monitoring, visual inspections and reported unusual occurrences, Mah (1995) analyzed the unusual occurrences reported from 1990 to 1993 and found the causes of these reported occurrences. He found most of the unusual occurrences were related to sill pillars (57%), double level stopes (20%) and geological structures such as Quartz Feldspar Porphyry (QFP) dyke, Lamprophyre (Lamp) dyke, faults, shears (9 %) and talc zones (5%). Sublevel stopes accounted for 7% and remnant pillars (2%). The above data is graphically illustrated in Figure 18. 37 Unusual Occurence Distribution 5% 2% 20% 9 % 57% • Chicken Feed Contact BReminant Pillars • Double Level Stopes • Structures • Sublevel Stopes • Sill Pillars Figure 18. Distribution of Reported Unusual Occurrence from 1990-93 The author carried out a similar analysis of the reported unusual occurrences from 1997 to the end of March 2002. Because there was a slight change in the original unusual occurrence report form, some variables have changed. The unusual occurrences reported from 1997 to early 2002 were mainly related to seismic activity. Ground working accounted for 44% and "bumps" accounted for 11%, (a total of 55%). Ground working is defined as a seismic disturbance related to an excavation, which may or may not result in a loosening of the rock mass whereas a bump is defined as a brittle fracture inside the rock mass without the failure in the vicinity of mine workings. Bumps are often accompanied by rock mass shaking. Ground working is defined at the mine as follows: Seismicity is defined as events that are recorded by the microseismic system. Events that are not picked up by the microseismic system but can be heard and felt at the face or in the stopes are defined as ground working while high energy seismic events which cause damage to the mine opening are defined as rockbursts. 38 The other variables that caused unusual occurrences were: loosening of rock mass/bulking (9%), support damage (20%), extensive damage (3%) and structurally controlled failures (13%). The above data is graphically illustrated in Figure 19. Unusual Occurance Reported (97 to mar 2002) 11% 9% • No visible Damage (Bump) • Loosening of Rockmass 44% • < 5ton (minimal support damage) 20% • >5ton Extensive Damage • Structurally Controlled Failure • Ground Working - Strain Burst. Figure 19. Distribution of reported unusual occurrence from 1997-Mar 2002 From the above two studies it can be seen that the causes of unusual occurrences are related to: Even though the unusual occurrence variables were slightly different in the two studies, it can be seen from both studies that approximately 90% of occurrences are related to stress and 10% are due to structure. The combination of the two variables are difficult to differentiate. 4.2.1 Excavation Span Higher rockburst frequencies are experienced as the stope span decreased (Mah, 1995). During a 1990-93 study, it was reported that 80% of the reported rockbursts and ground working were attributed to spans less than 9m. The author observed similar results between the 30th-37th levels. i) ii) High horizontal stress or; Geological structures such as dykes, faults and joints or; iii) The combination of i & i i . 39 Numerical modeling was performed to determine the exact span width when the stress concentrations started to change. The starting stope span was 5.4m (15ft), and was increased by an increment of 0.91m (3ft) to a maximum of 9.1 (30ft). The elevation used in the model corresponded to the 34 level mine elevation. The results of the stress distribution are depicted in Figures 20, 21 and 22. From the results it can be seen that, at the 6.4m (21ft) wide stope, very high stresses are concentrated in the upper corners of the stope. Actually, it is at the 6m (20ft) stope width, when the initial migration of stress concentration starts towards the corners. In wider stopes of 9.1m (30ft), the stress concentration seems to move away from the immediate back. In other words, the stress concentration, which is located immediately above the back in the narrow span excavation move higher in the back for wider span excavations. Figure 20. Stress contour above 5.4m (18ft) wide back 40 41 In narrow spanned excavations, the rock mass surrounding the narrow stopes and drifts under high stress acts similar to a non-elastic model, as a result, stress fractures form and strain bursting occurs. Visual inspection of such stopes reveal geological structures and the rockmass is competent and tightly held. The interlocking of the stress fractures is held tightly in place by the horizontal stresses. Wider span excavations tend to allow better stress redistribution. On the other hand, more structural related problems such as wedge failures become common. As the spans of an excavation increases, falls of ground caused by flat dipping joints, dykes or shears may occur in the back. Unsupported stress fractures become unstable as the span of an excavation increases as more structures are exposed. 4.2.2 DipofOrebodv Mah (1995) believed that an increase in ground working was a result of confinement. At the Red Lake Mine, the average dip of the ore body is approximately 60°. From underground observation, it was noticed that as the dip of the ore body increased, so did the ground working and vice versa. Numerical modeling also confirms this observation. A six-meter (20ft) wide stope was modeled at varying degrees of dip. The initial stope had a dip of 30° while the dip of the ore body was increased at an increment of 10° until it was vertical. The results are shown in Figure 23. 42 Stress Vs Dip of Orebody 150 ra Q. 100 9 50 (0 (0 0) CO i m k A 30 40 50 60 70 80 90 Dip of Orebody(Deg) •Sigma 3 Sigma 1 Figure 23. Change in Stress with change in dip of ore body From the results, it can be seen that as the dip of the stope increased, Sigma3 (confinement) decreased. Therefore, ground working is related to confinement. As the ore body becomes steeper, the confinement decreases, and ground working increases and vice versa. 4.2.3 Times and Location. The investigation by Cook (1963) and others have shown that most of the foci of seismic events were confined to the immediate vicinity of mining activity, that is, to regions of high stress and of active mining as shown in Figure 24. 70 CO SO 40 30 20 10 0 V) 20 30 40 SO 60 X> Distance tram fde*(ffl). Figure 24. Position of the face relative to the seismic events (Cook, 65) 43 Similar observations were made at the Red Lake mine that most of the seismic activity were located in close a proximity to an active mining area. The time of occurrences for most seismic events were after blasting, that is, when the immediate stress redistribution takes place. The mine operates on two shifts: (1) 7:00 am to 4:00 pm and (2) 7:00 pm to 4:00 am. The blast time for both night and day shifts is at 5:00 am and 5:00 pm respectively. Figure 25 shows the seismic distribution at the Red Lake Mine within a 24-hour period from March to December 2001. EVENTS ONLY - GOLDCORP HMS Daily Distribution - March2001 to December2001 160 140 «> C 120 > UJ smlc 100 80 <n o >> o c 60 at Freqi 40 20 0 Time of Day Figure 25. Number of seismic events versus time, btw Mar and Dec 2001 (Leslie, 2001) 4.2.3 Location, Magnitude and Seismic Energy The newly installed microseismic system at present is mainly used for source location. By knowing exactly where a major event occurred, this information helps the mine management in taking correct action such as should a crew be sent in a working stope or not. Magnitude is also used to compare the severity of a seismic event. And finally, all seismic events, which have seismic energy above 1000 joules are located and visually inspected by the ground control engineer. In the past, some seismic events above 1000 Joules have caused damage to the excavations. 44 4.3 TYPES OF ROCKBURST AT RED LAKE MINE The phenomena, that constitutes 'rockbursting' is very complex and covers a wide range of magnitude as well as modes of origin (Ortlepp, 1984). However, from underground observations at the Red Lake Mine, it can be concluded that there are two main types of rockburst characteristics found at this stage of mining and depth. These are strain and crush bursts. The new mine is between the 30th and 38th elevation level. At the beginning of the study, a sill pillar was being extracted and by the end of the study the mining had reached Cuts 6 and 7 of the sill pillar elevation. The cut and fill mining method is used where 3.1m (10ft) slices are extracted and later filled with paste. During the two years, from underground observation and with the aid of the micro-seismic monitoring system, two types of rockbursts were observed, that of a strain burst and a crush burst are explained as follows: 4.3.1 Strain Burst Strain bursts are closely related with face mining with its foci located in the direct vicinity of the mine opening. It has been observed to occur in narrow stopes and development headings throughout the mine. Strain bursts are identified by the evidence of superficial spalling in highly stressed corners and stress fractures within the backs. Occasionally there will be a violent ejection of small, angular fragments. Warning signs of highly stressed ground near the bursting point include "snapping and popping". Rock tends to "spit off the face and upper corners in the back. Figure 26 shows a typical strain burst failure mode. 4.3.2 Crush Burst The second type of burst is called the crush burst, which is similar to strain burst but is higher in magnitude and energy. Ortlepp (1992) has classed this type of burst as a buckling burst. Various magnitude ranges have been used in order to differentiate between the two types of burst. 45 Crush bursts have been observed in the sidewalls where geological structures such as lamprophyre dykes and faults are present either parallel to the stope strike or in the backs. These bursts have been observed to occur as a result of an increase in mining induced stress or a sudden decrease in stress as an excavation approaches the burst prone ground. Both strain and crush bursts are outlined in Table 5. Failure zone typically 1.25 m (4 ft) arched and stable Ground above stable arch competent, no stress induced fractures and virgin rockmass rating. Over time, progressive failure occurs and burst may repeat. Faulting and/or induced/ / I tracturing due to HW / . elaxation / / //' Initial burst inducing structural failure along stress induced and pre-existing fractures FW prior to burst solid & tight Figure 26. Typical strain burst failure mode (Mah, 1995) Table 5. Classification suggested by Ortlepp (1992) Seismic Event Postulated Source Mechanism First Motion from Seismic Records Magnitude M L Strain-bursting Superficial spalling with violent ejection of fragments Usually undetected; Could be implosive -0.2 to 0 Crush/Buckling Outward expulsion of pre-existing larger slabs parallel to opening Implosion Oto 1.5 Fault-slip Movement on an existing fault Double-couple 2.5 to 5.0 46 4.4 CASE HISTORIES- RED LAKE MINE During the two-year study period only four rockbursts occurred which caused significant damage. Most of these rockbursts occurred immediately after blasting. These four rockburst cases are associated with significant seismic energy are discussed below. 4.4.1 Drift 37-816-1 East (1652m Depth) Event: On the morning of January 14, 2001, an unusual occurrence report was made regarding unusual ground conditions in the 37-816-1 East Drift situated 1652m (5420ft) below the surface. A fall-of- wedge type ground fall had occurred after the night shift blast. The drift was being excavated for exploration purposes. The ground control engineer at the mine inspected the damaged area. Damage: Uncontrolled fall of ground from the immediate back approximately 4.6m x 3.0m x 0.61m (15ft x 10ft by 2ft) thick in the shape of a wedge. The area with significant damage was 5.0m (15ft) from the face. Figure 27 shows the location in plan and Figure 28 depicts the extent of damage. The weight of the wedge was approximately 12 to 15 tonnes, which was largely formed due to flat dipping joint planes (dip/dip direction), 40-55/195, 25/110, and 45/255. A geological mapping of the area indicated that a carbonate shear and a gouge filled fault ran parallel and to the west of the drift where the fall of ground/burst occurred. Between 4.6m (15ft) and 9.1m (30ft) from the face, broken material from the back was contained in the welded wire mesh. Cause of Event: Few micro-seismic events were recorded prior to the fall of ground on January 13, 2001 at 11.46pm. In this case, the micro-seismic event recording was considered not as reliable as the last row of geophones on the 34th level. The most likely cause of the seismic event or fall of ground was a sudden increase in stress after blasting, in conjunction with the presence of weak geological structures immediate to the excavation. The source mechanism, which caused this rockburst, seemed to be crush burst. 47 Figure 28. Extent of damage in 37-816-1 East Drift 48 4.4.2 Intersection of 36-756/786Access (Depth 1578m) Event: An unusual occurrence was reported on May 18, 2001 by the night shift crew of fallen rock in the travel way of the above intersection, 36-756-2/36-786-1, which is located 1578m (5180ft) below the surface. The event occurred after the blast as no unusual conditions were observed before the blast. The ground control engineer and the author inspected the damaged area. Damage: Wedge failure had occurred covering an approximate area of 3m x 2.1m (10ft x 7ft) with an estimated weight of approximately 2.5-3 tonnes. The extent of failure was confined to joint planes as shown in Figure 29. e r r j u > thy' l i i l W Wi^^^wS^-^*^^^ :f¥^m^:ym:p;::::m :;::k^^:::::-:M-:Y:...v;•/. <k ' «U d Fn 1 j w ft *' ® ^ i f o \ / 1 0 yy to 1 Figure 29. Location of damage in 366-756/876 Intersection Loose slabs were held by local support, however partly day-lighted. Support in the region was 2.1m (7ft) resin/rebar on a 1.2m x 1.2m pattern and welded wire mesh (WWM). Further loose rock was contained in the welded wire mesh as shown in Figure 30. The welded wire mesh was installed with 100cm x 100cm push plates. 49 Figure 30. Extent of damage in 36-756/786-1 Intersection Geology: Predominate rock type at the intersection is basalt with visible joint sets. There were two joint sets; one is flat dipping and the other steep. The wedge came out of the steep and flat joint contacts. Detail mapping of the area has delineated a Lamprophyre dyke dipping 65 degrees in the hangingwall to the east of the ground fall. Cause of Event: Three micro-seismic events were recorded to the south of the intersection, with coordinates of similar Northing and Easting but with a varying elevation of 22.4m (59ft) below and 19-25m (50-65ft) above the back. It is most likely that the seismic events were caused by the lamprophyre dyke. The rockburst activity caused the shake down or loosening of the rock mass along the joint planes. The local support could not withstand the weight of the wedge, causing a wedge to fall to the ground. The source mechanism in this case was a crush burst. 50 4.4.3 Stope 34-786-1/2 Cut4 (Depth 1523) Event - At 5:07 am on June 6, 2001, a rockburst occurred in the hangingwall of 34-86-1/2 stope. The stope is located at depth of 1523m (4940ft) below the surface. The records at Placer Dome's Campbell Mine yielded a magnitude estimate of 2 . 0 M L for the event. Two visits were made by the mine's ground control engineer and the author. Damage - Very intense damage was caused in the stope between the hangingwall and the back along the entire stope. The stope was approximately 10m (30ft) in from the cross cut as shown in Figure 31. Most of the damage was contained by the chain-link mesh as shown in Figure 32. Figure 31. Location of damage in 34-786-1/2 Stope Cut4 The back was bolted with 2.1m (7ft) rebar and 2.4m (8ft) swellex in a varied pattern with spacing ranging from 0.46m to 1.2m (1.5ft to 4ft). The stope on the opposite side of the cross cut was not damaged. 51 Geology - The rock type in the area is basalt. The lamprophyre dyke is located approximately 10m in the hangingwall. Prior to the burst, it was noticed that the hangingwall was heavily fractured, an indication of the high stress concentration. Figure 32. Rockburst damage contained in chain-link Cause of Event: The seismic event associated with in the rockburst was located in the hangingwall of the stope. The event appears to have occurred near the lamprophyre dyke. The seismic event occurred directly after the blast, indicating a change in the local stress state. In addition, the lamprophyre dyke within the hangingwall caused the instability of the rock mass surrounding mainly the hangingwall and the back of the stope. There was a second event at the same time at 5:07:43 am located above 32-786-8 Stope. If the lamprophyre dyke is projected at 60-65 degrees from 34-786-1/2 stope to the 32 n d level, it appears the two events occurred on the same geological feature (Leslie, 2001) The rockburst in the above case can be classed as crush burst. However, Leslie (2001) from the Engineering Seismology Group (ESG) suggests it may be a fault-slip. 52 4.4.4 Stope 36-746-1 Cut2 (Depth 1585) Event: A ground condition report was made on February 11, 2002, of an unusual level of ground working in 36-746-1 stope. The 36-746-1 stope is located 1585m (5200ft) from the surface. The area was inspected by the mines ground control engineer and later visited by Dr. Wilson Blake. The ground was still working during the time of the inspection. Damage: The area most affected was the upper corner of the footwall, with the damaged area 2.4m (8ft) from the current face. The area of the damage is approximately 4.6m x 6m (15ft x 20ft) as shown in Figure 33. Geology - The rock type is predominately basalt with structural discontinuities such as fault and lamprophyre dyke present. The mine face is approaching the lamprophyre dyke. The back had peeled off 2.2-2.4m (6-8ft) above the planned back as shown in Figure 34. 53 Figure 34. Slab peeled from back after rockburst in 36-746-1 Stope The lamprophyre dyke is situated in the north-east direction and the planned stope in the North-South. The footwall side of the stope was most affected because of the presence of the lamprophyre dyke closer to the footwall of the stope. Cause of Event: The sudden increase in seismic activity in the 36-746-1 Cut 2 stope was most likely due to the stope face approaching the lamprophyre dyke, resulting in additional stress concentration. The area was numerically modeled without the presence of the lamprophyre dyke. From the numerical model it can be seen that the stress concentration was mainly in the upper corners of the hangingwall and the footwall of the stope as shown in Figure 35. The stress concentration was predicted as high as 140MPa. Similar to the previously described cases, the source mechanism of this rockburst can be classified as crush burst. 54 Figure 35. Stress concentration at the corners of 36-746-1 Stope. 4.5 CONCLUSION Red Lake Mine's rockburst and seismic parameters such as span, confinement, time and location were discussed. Unusual occurrences during the last five years have been due to high stress and the presence of weak geological structures. The excavation with spans of greater than 6m and ore bodies with shallow dips tends to work less. Most of the seismic events occurred during or immediately after blasting. Few notable rockbursts from the Red Lake Mine were discussed. Historically, it is seen that varying degrees of strain and crush burst mechanisms are the principle causes of the rockburst. Unfavourable geological features such as Lamp dyke were present at every location where a burst had occurred. A possible fault-slip mechanism was suggested for the 34-786-1/2 stope Cut4, however this is inconclusive. 55 CHAPTER 5 SPAN DESIGN 5.1 BACKGROUND Although rnining and tunneling are the oldest engineering activities performed by man underground, the design of underground structures has been a relatively recent practice. The first types of design were simple rule of thumb approaches, which are still practiced even to this day. Requirements for greater mining efficiency and higher safety standards have made necessary a more reliable and effective approach to the design of underground structures. Many design methods have been developed over the years and they can be classified into three categories. • Analytical Approximation • Numerical Simulation • Empirical Methods. 5.1.1 Analytical Approximation Analytical approximation includes closed form solutions, limit equilibrium techniques, photo-elastic modeling and physical modeling (Lang, 1994). Analytical methods usually involve gross simplification of the excavation geometry and rock properties. These simplifications can place severe restrictions on their application to real mining problems. 5.1.2 Numerical Simulation Numerical simulations, based on finite difference, finite element, boundary element or distinct element method, are gaining increased usage due to the availability of software and the low cost for personal computers. Numerical simulations are becoming increasingly sophisticated with 3D modeling packages now commercially available at reasonable costs. 5.1.3 Empirical Methods Empirical design methods, which involve the application of knowledge-based documentation experience which displays similar mining conditions, are gaining increasing acceptance in the mining industry. This approach requires a database of 56 observations relating the stability of the underground structures to geometry, the rock mass characteristic and other factors that influence stability. Empirical methods have been made possible in part by the widespread acceptance of the rock mass classification system. Both empirical and numerical design methods are also discussed in Appendix C as it relates to sill pillar design. Since the numerical method is more applicable to the sill pillar design, it is discussed in detail in Appendix C. The empirical design method is discussed in detail in this chapter as it applies to the six failure modes, which account for the instability of underground openings. These modes of failure are: • Beam failures • Voussoir block failure • Wedge failure • Chimney failure • Rock mass failure • Stress-induced failure The six failure modes are illustrated in Figure 36. Since the above have been explained in detail in (Lang's, 1994) thesis, the six modes of failure are briefly summarized in Appendix A. 57 (a) P)a<e or Beam Failure (b) VouMOir Block Failure (c) Chimney Mm (e) Stress Induced Failure (d) Wedge Failure (0 Rock Mass Failure Figure 36. Underground roof failure mechanisms (Lang, 1994) 58 5.2 DESIGN METHODOLOGY- RED LAKE MINE The best approach to span design is an integrated one that combines elements of analytical solutions, empirical design and numerical modeling. This approach has been successfully applied at the Red Lake Mine for designing safe yet practical spans in cut and fill stopes. The different analysis techniques are considered necessary given the different types of failure mechanics described earlier. Solving a solution from two or more approaches also provides confidence in the design if the two solutions can be made to closely agree. Before any design can be implemented, a detailed fabric analysis of the rock mass must be carried out and the intact rock strength parameters of the rock must be determined. This is required in order to obtain the fundamental parameters, which are required regardless of the design procedure or failure mechanism. The intact rock strength parameters that should be determined prior to carrying out a design are: • Uniaxial Compressive Strength (UCS) • Young's Modulus (E) • Poisson's Ratio (v) and • Unit Weight (y) The fabric analysis must provide sufficient information on the structural characteristics of the rock mass for it to be classified using either the NGI or Geomechanics (RMR) classification systems. At the Red Lake Mine, this information is obtained from drilled core or geotechnical mapping of each lift. Structural data is compiled with stereo nets to determine the dominant joint sets. Faults, dykes and shears are mapped on a daily basis by the geology and the geotechnical staff. As the second step of the design process, the rock mechanics engineer determine the controlling failure mechanism. At the Red Lake Mine, for example, the presence of faults or continuous joints in the back that dip at less than 30° can lead to wedge failure irrespective of span or the overall rock quality. Structural failure, therefore, is the first 59 failure mechanism, which must be accounted for in the design. Prediction of structural failure requires a good database of geotechnical observations for the area under design as well as ongoing visual inspection. A stereonet analysis of the structure defining the wedge is carried out to determine whether failure is kinematically possible. The computer program, UNWEDGE, is used to determine the size of the potential ground fall and to assess the support requirements. In addition to the use of support, the stope spans can be reduced to prevent the formation of the wedges. The next step is to decide which other failure mechanisms and design methods are relevant. At the Red Lake Mine and most underground metal mines, beam failure can be ruled out as a failure mechanism given that discontinuities are generally present and these theories assume horizontally stratified intact rock. Voussoir Block Theory is not applicable to the Red Lake Mine since the jointing pattern does not meet the strict criteria set out above. Chimney failure is unlikely at the Red Lake Mine because there are not any unfavourable structures where the pillar width is low. After structural failure, rock mass failure is the next most common mode of failure. A rock mass failure assessment is made using an empirical approach utilizing a database of observations from stoping case histories at the Red Lake Mine. These observations have been compiled and plotted on a span versus RMR graph to enable future predictions of stable spans given the RMR of the stope. This approach has proven successful in predicting stable spans at the Red Lake Mine. The Red Lake Mine database and empirical design method will be described in greater detail in the next section. Finally, the potential for stress-induced failure is assessed. Here too, prediction of stress-induced failure caused by the presence of geological structures such as a dyke or fault requires? a good database of geo-technical observations for the area under design as well as an ongoing visual inspection. Stress-induced failure caused by the presence of geological structures is analyzed first. The second type of stress-induced failure caused by high in-situ stress is assessed using 3D boundary element modeling. Stope design at the Red Lake Mine is an ongoing process. New structures and changes in the overall rock mass due to stress redistribution can develop from lift to lift, which may warrant design 60 changes. The Red Lake Mine design procedure for cut and fill stopes is outlined in the diagram shown in Figure 37. The development of an empirically based stability graph specifically designed for entry-type stopes in burst prone ground is the focus of the second phase of this thesis. Decision to Mine FABRIC ANALYSIS AND ROCK M A S S CHARACTERIZATION (from core or near by workings) ANALYTICAL DESIGN SOLUTION -wedge analysis -structure induced failure NUMERICAL MODELLING S T R E S S ANALYSIS Engineering Judgement EMPIRICAL DESIGN SOLUTION (Stability Graph for Entry Type Stopes) Limit Span to Prevent Formation of Wedge De-stress Blasting for Structure Induced Failure Support Wedge Excavation And Monitoring Figure 37. Span design methodology at Red Lake Mine 61 . 5.3 SITE CHARACTERIZATION This section discusses the classification system used to collect the rock mass classification data. The Geomechanics Classification (RMR System) (Bieniawski, 1976) was chosen since it is relatively quick to use and understand. In addition to the above, the RMR system has provided a consistent result among those performing the rating and the percentage scale is easier to become acquainted with than the logarithmic NGI-Q system. Geomechanics Classification was also used in the historic parts of the Red Lake Mine. 5.3.1 Rock Mass Characterization As part of this study, detailed geotechnical mapping was carried out in the following areas of the new mine: • 31-1 Sub • 32-2 Sub • 34-Level • 36-2 Sub • 37 Level Detailed geo-technical mapping was carried out and features were recorded on a standard Geomechanical classification-mapping sheet. The variables used were strength, RQD, joint spacing, joint conditions and ground water. Few geo-mechanical mapping data from previous researchers are included in the span design database. The data from previous researchers were mainly mapped on the 25th level (1125m depth) and above and accounts for about 15% of the data used in the span graph. In some areas detailed line mapping was also conducted. Each variable used is briefly described in terms of its use at the Red Lake mine. 62 5.3.2 Intact Rock Strength The uniaxial compressive strength of a rock material constitutes the highest strength limit of the rock mass of which it forms a part. It is determined in accordance with standard laboratory procedures. Laboratory testing on intact sample were conducted previously by University of British Columbia (UBC) Geomechanics Lab and summarized in Table 6. Table 6. Uniaxial Compressive Strength Tests Performed by UBC Geomechanics Rock Type. Uniaxial Compressive Strength (Mpa) Young's Modulus (GPa) Poisson's Ratio Andesite 209 76 0.22 Andesite 140 49 0.18 Pillowed Andesite 178 56 0.20 Chicken feed 107 74 0.28 Lampdyke 262 QFP 217 74 0.245 Talc-chicken feed 23 14 Quartz carbonate 182 37 0.1 Quartz carbonate 53 17 0.11 63 5.3.2.1 Main Zone A typical example of the rock mass rating in the main zone is compiled in Table 7. Note that the joint orientation is set at zero. Table 7. Typical Rock Mass Rating of main zone Category Main Zone Description Rating Strength 160-180 Mpa 13 RQD 90% 17 Joint Spacing 0.4 16 Joint Condition Smooth, hard, tight 17 Ground water None 10 Joint Orientation 0 Total 73 5.4 SPAN DATABASE The span database of the openings of the excavation were measured underground using a construction tape. Occasionally, it was not possible to take measurements as mining equipment was in the middle of the excavation. In these cases, the span lengths were taken from the mine plans. The span lengths were measured in feet and converted to meters. A sample of data collected are summarized in Table 8, which outlines the date the RMR was determined, the location where it was determined and the span of the excavation. The stability of the excavation was determined visually. The complete data set is presented in Appendix B and is comprised of 107 observations. Stability is discussed in more detail in the next section under span design. 64 Table 8. RMR and span data from Red Lake Mine Total Adjusted Visible RMR Span RMR Stability Date Location (%) (m) (%) 21-Jun-92 16-017-1 Cut & Fill near Crib Set 65.0 18.6 55.0 Pot. Unstable 21-Jun-92 24-967-1 LH Stope 60.0 3.7 50.0 Pot. Unstable 21-Jun-92 26-976-1 stope 61.0 11.9 51.0 Pot. Unstable 21-Jun-92 15-2548 Stope 82.0 3.1 82.0 Stable 21-Jun-92 23L 978 E Drift 83.0 3.1 . 75.0 Stable 21-Jun-92 25-957-2 stope 80.0 6.7 80.0 Stable 21-Jun-92 16-017-1 Cut & Fill, North End 60.0 12.2 40.0 Unstable 21-Jun-92 25-957-1 Stope 72.0 8.5 62.0 Pot. Unstable 21-Jun-92 25-957-1 Sub 45.0 3.1 45.0 Unstable 9-Jun-93 13-1764E 74.0 3.7 64.0 Stable 9-Jun-93 15-1573 stp 69.0 7.3 69.0 Stable ll-Jun-93 13-1764 E TDB Stope 74.0 3.7 64.0 Stable ll-Jun-93 17-017-1 LH Stope 66.0 12.2 66.0 Stable ll-Jun-93 26-937-1 stp LH 40.0 6.4 40.0 Unstable ll-Jun-93 26-947-1 Stp 43.0 10.1 43.0 Pot. Unstable ll-Jun-93 26-917-1 Stope (Jumbo) 75.0 6.1 74.0 Stable ll-Jun-93 27-897-1 Stope (Jumbo) 65.0 5.2 65.0 Stable ll-Jun-93 27-907-1 Stope (Jumbo) 70.0 11.9 70.0 Stable ll-Jun-93 28-927-1 Stope (Jumbo) 60.0 13.1 40.0 Unstable ll-Jun-93 28-897-1 Stope 70.0 4.6 70.0 Stable ll-Jun-93 31-846-2 Stope 68.0 2.4 68.0 Stable ll-Jun-93 26-976-1 Stope LH 53.0 12.2 53.0 Unstable 19-Jan-95 27-966-1 Ramp Access 67.0 3.8 67.0 Stable 19-Jan-95 16-017 #1 Access A Sub 66.0 2.4 66.0 Stable 22-Aug-95 22 Sill 75.0 4.9 55.0 Unstable 22-Aug-95 28-897-nth Stope 62.0 7.6 52.0 Pot. Unstable 22-Aug-95 28-887 Stope 67.0 12.2 57.0 Pot. Unstable 22-Aug-95 1-124-1SXC 70.0 2.4 70.0 Stable 22-Aug-95 25-947 Stope 64.0 6.1 54.0 Stable 22-Aug-95 28-897-E Stope 62.0 6.1 52.0 Stable 65 5.5 CRITICAL SPAN GRAPH Brennan Lang developed the critical span graph for cut and fill mining in 1994 at the Detour Lake Mine in Ontario. The span graph has been accepted by many Canadian mining operations for the initial span design of cut and fill stopes. It is based on a graph of RMR against span. However, three major shortcomings existed. First, a statistical method was used to derive the graph. The major disadvantage of a statistical method is the regression analysis because it is based on the prediction of mean values only. Mining data is typically very scattered, therefore, use of a statistically derived method may overestimate or underestimate values in some cases. Secondly, the original graph was based solely on 172 cases histories from only one mine. However, the first two shortfalls were solved when Wang, Milne & Pakalnis ( 2 0 0 0 ) included data from six more operations and with the use of neural nets, the 292 case histories were trained to produce a more accurate and represented outline of the graph. Despite including more data to the span graph, a third shortfall still existed. The previous database did not include cases under high-stress or burst-prone environments. This research augments the above database to extend its use to burst prone environment. 5.5.1 Limits of Span Graph The original span graph was empirically derived and there are some limitations to the application of this method. Some of the constraints for using this design technique are: The span is defined as the diameter of the largest circle that can be drawn between pillars and stope boundaries in the back of the stope as shown in Figure 38. Pillar stability is required for the span design to be reliable. • The back must have local support installed. • The back is horizontal. • The term "stable" refers to short -term stability (approximately 3months). • Discrete wedges must be adequately supported before this design approach can be used reliably. 66 Span Post Pillar Figure 38. Definition of span (Lang, 1994) The span design uses the RMR classification system to assess the rock-mass properties. The joint orientation factor is not applied directly. If joints are present, they dip 0° and 30° from horizontal, or if open joints or shear are present, they dip between 0° and 60°, a score of 10 from the estimated RMR value is subtracted. Reducing, the RMR value, reduces the span, thus eliminating potential wedge failures. Subsequent work has suggested that a score of 20 can be subtracted from the RMR value to account for the high stress environment to the opening back. High stress at Red Lake Mine was defined as seismicity over 1000 Joules of energy or G\/oc ratio in the range of 0.5-0.6. 5.5.2 Definition of Stability Bieniawski (1984) has shown that there is a relationship between span, rock mass rating and stand-up time (Appendix A). Larger spans will result in lower standup times for a given rock mass rating. In this study, most of the data has been obtained from cut and fill stopes where the required stand-up time is approximately three months. Therefore, a stable excavation is one that has remained stable for at least three months. 67 An excavation's stability is classified into three categories: stable, potentially unstable and unstable. 5.5.2.1 Stable Excavation Stable excavations are characterized by the following: • There has been no uncontrolled falls of ground. • If the monitoring is available, no movement of the back has been observed. • No extraordinary support measures implemented other than those required for burst or non burst prone ground. 5.5.2.2 Potentially Unstable Excavation Identifying potentially unstable excavations is usually not difficult for experienced personnel familiar with ground conditions at their operation. The opening may exhibit the following characteristics: • Strong slips or faults with orientations forming potential wedges in the back. • Extra ground support may have been installed to prevent potential falls of ground. • Instrumentation installed in the back indicates continuing back movement. • There may be an increased frequency of seismicity and induced fracturing and ground working. 5.5.2.3 Seismicity and Fracturing During Excavation As mentioned in section 4.2.1, it was observed that seismicity and fracturing was experienced in high stressed ground as the span decreased. During a 1990-93 study, it was reported that 80% of the reported rockbursts and ground working were attributed to spans less than 9m (Mah, 1995). Through numerical modeling of the stopes and in collaboration with visual observations, it was concluded that excavations that were 6.0m 68 (20ft) wide or less had a higher frequency of seismicity and induced fracturing. As the stopes increased in width (>6m), the seismicity and induced fracturing decreased. Since none of the stope spans increased more than 10m (30ft), it is difficult to be certain if seismicity or induced fracturing subsided completely. It is important to note that this increased seismicity and induced fracturing occurs during the excavation. Once the stress around the excavation which is being excavated is redistributed, the excavation returns to a stable state. 5.5.2.4 Stress -Induced Failure There were several occasions where the stopes were sufficiently wide enough for reduced seismicity or ground working, but rockburst occurred in the stope backs and hangingwalls. These rockbursts were, however, caused by increased stored strain energy in geological structure such as dykes. More information on stored strain energy is given under the failure criteria (Chapter 6). 5.5.2.5 Unstable Excavation Unstable openings are those where an uncontrolled fall of ground has occurred. A fall of ground usually involves failure through existing support; or in the case of no support, the extent of the failure would be sufficiently large enough to cause damage to patterned rock bolt support if it were installed. Uncontrolled falls of ground are distinguished from loose incidents, which occur close to the face prior to scaling, and before rock bolts have been installed. These three categories of stability have been used with a neural network analysis for burst prone ground. 5.5.3 Modification To Critical Span Graphs The critical span graph consists of two straight lines that divide the RMR versus span into three zones (stable, potentially unstable and unstable) as shown in Figure 39. 69 o Stable o Potential Unliable a Unstable RMR Figure 39. Critical span graph (Lang, 1994) The design lines for the stable zone fits the data cases well in the RMR range from 60 to 80, but deviate considerably outside this range. To achieve a better and more reliable design, a further study was conducted by (Wang, 2000) using a neural network analysis with the addition of case histories from six more operations as shown in Figure 40. 45 40 f 35 9 3 0 s. <*> 25 20 15 10 5 0 ; . 0 10 20 30 40 50 60 70 80 90 100 . « Stable o Potential Stable A Unstable R M R Figure 40. Span design graph with case histories (Wang, 2000) 70 5.6 USE OF NEURAL NETWORKS Neural networks were used in the design of the new span graph. Neural network technology mimics the brain's own problem solving process (Neuroshell, 1997). Just as humans apply knowledge gained from past experience to new problems or situations, a neural network takes previously solved examples to build a system of "neurons" that makes new decisions, classifications, and forecasts. Neural networks looks for patterns in training sets of data, learns these patterns, and develops the ability to correctly classify new patterns or to make forecasts and predictions. Neural networks excel at problem diagnosis, decision making, prediction, classification, and other problems where pattern recognition is important and precise computational answers are not required (Neuroshell, 1997). The database selected for the study consisted of stope behaviour data from eight operating mines in Canada. Observational data from 399 operational case histories were included in this study. The data case history sources are shown in Table 9. Each case history contains information on rock mass conditions expressed as an RMR 76 value, span, and the opening back stability. Table 9. Case-History Data Sources Mines Number of data cases Total Stable Potentially Unstable Unstable Detour Lake Mine 172 94 37 41 Detour Lake Mine 22 10 0 12 Photo Lake Mine 6 0 6 0 Olympias Mine 13 4 1 8 Brunswick Mining 17 5 3 9 Musslewhite Mine 46 35 10 1 Snip Mine 16 12 2 2 Red Lake Mine 107 81 19 7 Summary 399 241 78 80 71 The RMR ranged from 24 to 87 and the span ranged from 1.8 to 41 m for 399 cases. The RMR values for 57% of the cases were concentrated in the 60 to 80 RMR value range. The span in 94 % of the cases ranged from 3.0 to 26m. The input data was obtained from different mines that had different personnel surveying the stope dimensions and estimating the RMR values. This introduced variability or inaccuracy into the input data. However, the span estimation error should be substantially less than lm, which is within the tolerance of the graphical design approach. The variability in estimating the RMR value can be more significant and will depend on the level of experience of the engineer conducting the rock mass classification work. For experienced practitioners the variability for estimating the RMR value should be within +/-10%. In all cases, a best guess or average value of the RMR was used for the analysis. 5.6.1 Neural Network Span Design A computer simulated neural network called the Neural Shell Predictor system was used in this study. The Neural Shell Predictor requires data in the text file format (sometimes called ASCII file). Application of the Neural Shell Predictor is comprised of the following steps. 1. Select a data file that contains examples of what you are trying to predict. 2. Tell the predictor which columns are input and which columns you are trying to predict. 3. Choose a training strategy. 4. Train the network. 5. Apply the trained network to existing data or new data to test the network's prediction. The inputs from 399 sets of data consisted of the RMR and span. The stability status of the excavation is the output. Figure 41 illustrates the neural network process structure. The stability is assigned a number (one, two, or three), representing stable, potentially unstable and unstable conditions, respectively. 72 J RMR Neural Networks Stability Number Span Figure 41. Neural Network process structure The data were initially split into two parts consisting of a training range and a testing range. For best results, the training range used approximately 60% of the data and testing range used approximately 40%. After training, testing, adjusting and arriving at a satisfactory prediction capacity on the training range, the whole data range was used to train the expert again using the same training settings. The well-trained neural network expert was then used to make predictions on a 19 x 18 grid. The Neural Shell Predictor automatically configures the internal structure of a neural network by assigning weighted adjustment links between the input and output data. Figure 42 illustrates the internal structure of the Neural Shell Predictor. 5.6.2 Training Parameters The Neural Shell Predictor self-monitors most of the training process. The dynamics and internal configuration of the neural networks are controlled and set by the program. However, many parameters can be set manually to assist the Neural Shell Predictor. The two most important ones were average error and correlation. 73 Input Data RMR Span Hidden Neurons Output Data Stability Number Figure 42. Illustration of internal structure of neutral network The network begins by finding linear relationships between the inputs and the output. Weights are assigned to the links between the input and output neurons. After those relationships are found, neurons are added to the hidden layer allowing nonlinear relationships to be found. Input values in the first layer are multiplied by the weights and passed to the second (hidden) layer (Neuroshell, 1997). Neurons in the hidden layer produce outputs that are based upon the sum of weighted values passed to them. The hidden layer passes values to the output layer in the same fashion, and the output layer produces the desired results (predictions). The network "learns" by adjusting the interconnection weights between the layers. The answers the network is producing are repeatedly compared with the correct answers, and each time the connecting weights are adjusted slightly in the direction of the correct answers. Eventually, if the problem can be learned, a stable set of weights evolves and will produce good answers for all of the sample decisions or predictions. The real power of neural networks is evident when the trained network is able to produce good results for data that the network is previously unfamiliar. 74 The training strategy used for this study was Genetic Training. When applying the trained network to new data, the Genetic Training Strategy produces better results when the new data is similar to the training data. It also functions effectively when the training data is sparse. The Genetic method never predicts an output greater than the greatest output with which it was trained and it never predicts an output less than the smallest output with which it was trained. Thus, all the stability numbers predicted were between 1 and 3. 5.6.2.1 Average Error Different problems require different levels of accuracy. The neural network is expected to be accurate, but not accurate to the degree that it has memorized the training data, as this causes poor performance on new cases. Average Error is defined in the equation below: AverageError = ^  ActualValues — Pr edictedValues ^  number.of. pattern (10) The error percentage refers to the average difference scaled to the standard deviation of the output. This error is not necessarily a correct assessment of the expert's accuracy. The accuracy of the expert can only be determined by testing. The input data were very scattered for this study, therefore achieving a small error percentage was difficult. Despite many different approaches, the lowest error obtained was 14%. The performance of the expert on the testing data was, however, deemed adequate for this training error. 5.6.2.2 Correlation Correlation is a measure of how the actual and predicted value correlate to each other in terms of direction, that is, when the actual value increases, the predicted value increases and vice versa. This is not a measure of magnitude. The values for r range from 0 to 1. The closer the correlation value is to 1, the more correlated the actual and predicted values. The highest correlation value obtained for this study was 93%. 75 5.6.3 Results. A well-trained satisfactory neural network was obtained after a series of neural network training and testing sessions were conducted using combinations of different possible settings. The neural shell predictor was used to make predictions on a 19 x 18 grid that covered the RMR range from 5 to 95 and the span range from 2.5 to 45m with an interval of 2.5m. The results were mapped to an RMR versus span chart and the three zones were outlined as shown in Figures 43 and 44. 05 Q_ CO 45-40 35 30-25 20 15 10 5 -0 B.O 3.0 2.8 3.0 3.0 0.0 3.0 D-31T 3.0 3.0 3.0 B.O 3.0 3.0 3.0 B.O 3.0 B.O 3.0 2.9 2.2 2.9 2.5. 3.0 3.0 B.Q/2.8 2.1 1 U^1.0 1.0 h.O 1.0 h.O 1.0 1.0 1.0 1.0 1.0 h.o 1.0 7 1.2/fl.1 1.0 h.o 1.0 h.o 1.0 .9/1.0 h.o 1.0 .0 1.0 h.o 1.0 .0 1.0 h.o 1.0 .0 1.0 h.o 1.0 .0 1.0 h.o 1.0 10 20 30 40 50 60 70 80 90 100 RMR Figure 43. Neural network predicted results Although there were very few case histories in the larger span and the lower RMR sector, the neural networks inferred the results to the overall case history population stability trend. The areas with limited case history data were outlined using the best engineering judgment. 76 The three zones are separated by contour lines using the best visual judgment. Zones with a predicted value of 1 is classed as stable and zones with predicted value of 2 and higher were classed as unstable. Areas in between the two zones are classed as potentially unstable. The three zones are separated as shown in Figure 43. According to the predefined stability categories and the neural network prediction contour outline, the design line should be derived from the transition zone with the predicted values between 1 and 3. Figure 44 shows that there are no unstable cases below the predicted value of one 1 and no stable cases exist above the predicted value of 3. The new underground entry-type excavation span graph was developed on the basis of the neural network contour outline. The design graph uses the contour value of 1 as the boundary between stable and potentially unstable and the contour outline of a value of 2 as the boundary between unstable and potentially unstable conditions. The contour value of 1 was used as the boundary between stable and potentially unstable zones because there were no unstable cases below this contour. Using 81 more stable points from the Red Lake Mine confirms this stable zone. The contour value of 2 was chosen to divide the unstable and potentially unstable zones. Choosing the contour value of 2 causes the potentially unstable zone to become narrower as compared to Wang's (2000) graph. 5.6.4 New Critical Span Graph The new span graph with all the case history data displayed is shown in Figure 44. Since most of the data collected at the Red Lake Mine was less than 10m in span width and in the stable zone, the stable zone is well defined in the lower span ranges. The new span graph also defines the new potentially unstable and unstable (caved)zones. Two new zones were added to the graph. The new zone in the stable size was added to inform design engineers that during excavation under high stress, that this could result in severe ground working and burst prone support may be required. The other zone 77 was added in the potentially unstable-unstable(caved) side. Due to poor rock mass and high stress, closure of the excavation ground can be expected. In addition, under high stress condition, wider spans in higher rock mass (60-80) are stable. However, the presence of geological structures such as dykes and faults near the planned excavation should be analyzed separately. RMR Figure 44. Span graph (2003) 78 The following correction should be made when using the span graph: 1. If open joints and shear are available and dip between 0° and 60°, or if joints are present, the dip 0° and 30° from horizontal in the immediate back, subtract 10 from the RMR value 2. If high stress is present in the immediate back, subtract 20 from the RMR value. (High stress is defined as seismicity over 1000 Joules of energy or o~i/oc ratio in the range of 0.5-0.6). 3. If both are present, then only 20 should be subtracted from the RMR value. 5.7 CONCLUSION A comparison between the new span graph and the previous span graphs is shown in Figure 45. The critical span graph worked well in the RMR region of 50-80, but worked poorly beyond this range owing to limited data. The neural network span designed by Wang (2000) overcame this problem associated with the critical span graph by adding more data from several mines. However, data from burst prone ground was lacking. This research added case study data from burst prone ground and analyzed it using the neural networks. This increased the accuracy of the design, especially in the region with an RMR less than 50 and a span less than 10m. The new neural network derived span design, with data from burst prone ground, shows significant improvement from the previous neural network generated graph. i) By adding more data points greatly increased the confidence level of the graph. ii) The new graph can now also be used in burst prone ground. iii) The most significant difference between the new span graph and the previous one is that the potentially unstable zone has narrowed while the stable zone has basically remained the same. 79 As with any empirical design approach in rock mechanics, its reliability depends on the experience of the practitioner and the complexity of the geological environment. The next section describes the pillar design technique at the Red Lake Mine. 0 10 20 30 40 50 60 70 80 90 100 RMR Figure 45. Comparison of all three span graphs 80 CHAPTER 6 PILLAR DESIGN 6.1 B A C K G R O U N D When the ore body is oriented vertically (or steeply dipping), sill pillars are used to divide the ore body into multiple mining horizons as shown in Figure 46. Post pillars, on the other hand are usually used for local support. At the Red Lake Mine, the overhand cut and fill mining method is used to mine the steeply dipping ore body. Each lift is 3m (10ft) in height. There is always a concern in determining the last possible lift to be mined using the cut and fill mining method, before the rest of the sill pillar is mined using the non-entry mining method. For narrow vein gold deposit at great depths, the cut and fill mining method is preferred as it gives a better control on grade and ground. The third phase of this thesis is devoted to the development of pillar design techniques at the Red Lake Mine's burst prone ground. Crown Pillar Si l l Pillar _ Figure 46. Types of pillars commonly encounters in hard rock mines (Betournay, 1989) There are two general approaches to pillar design: the empirical method and numerical method. The empirical design method is based on observations of case histories and previous experience in similar geo-technical conditions. The numerical design method is largely based on measured parameters and material properties. 81 However, there is no clear division between the two approaches. Some numerical procedures are occasionally used in empirical design and vice versa. In chapter 5 and in (Appendix A), empirical and numerical methods were discussed as it related to span design. This chapter will discuss the two approaches as it relates to pillar design. Using the two methods, five different failure criteria techniques will be calibrated to determine the optimum pillar dimension at the Red Lake Mines burst prone ground. The five different failure criteria are: • Hoek-Brown Failure Criteria (1980) • Pillar Stability Graph Failure Criteria (Lunder, 1997) • Deviatoric Stress Failure Criteria (Martin & Read, 1996) • Store Strain Energy Failure Criteria and (Canmet, 1996) • Induced Stress Failure Criteria (Hoek & Brown, 1980) Other criteria will be mentioned but not discussed in detail. Two case studies will be used to illustrate the use of the above techniques. A wide range of case histories has been studied, ranging from stable to highly burst prone ground conditions, calibrating the failure criteria (Mah, 95). The emphasis is placed on a procedure that can be used by the mine to determine the sill pillar height as it is formed during the mining process. 82 6.2 FAILURE CRITERIA - RED LAKE MINE The boundary element stress analysis technique has been developed to approximate the stress distribution around an opening of irregular shapes oriented in a two or three-dimensional stress field. However, boundary element methods do not directly determine failure. The stress distribution needs to be interpreted to determine the effects on underground stability. Many types of failure criteria have been developed in the analysis of stress distribution. This section will outline the five failure criteria derived using boundary element methods that are used at the Red Lake Mine. 6.2.1 Hoek & Brown Failure Criteria The first failure criterion is the Hoek-Brown (1980) failure criteria. It is simply the ratio of stress over strength. It is sometimes known as the "m" and "s" failure criteria. Hoek and Brown (1983) proposed an empirical failure criteria for estimating the strength of rock mass. It was based on tests on models and observations of jointed rock masses and rockfill. The Hoek and Brown failure criterion does not take the intermediate principle stress ( 0 2 ) , into account. Therefore, it can be used as a first approximation for two-dimensional cases. The failure criteria are given as: 2 I cu = 0-3 + (mac >3 + sac ) (11) where: c?i = major principle stress at failure G3 = minor principle stress at failure G c = the uniaxial compressive strength of rock mass at failure m &s = constants that depend on the properties of the rock mass The constants m and s are dimensionless and are analogous to the friction angle and the cohesion strength. Detailed discussion on the Hoek and Brown Strength Formula can be found in Appendix C. Once the pillar strength is determined, the strength is divided with induced pillar stress, determined using numerical modelling and a factor of safety value is obtained. 83 Hoek and Brown (1980) proposed several of these pillar design curves assuming that the pillar fails when the stress across the center of the pillar exceeds the strength of the rock mass. They stated that the safety factor of 1.0 or less would imply that a pillar is theoretically unstable and that a safety factor greater than 1.5 should be used for permanent pillars. Stage and Page (1986) recommended the use of a safety factor of 2 for man-entry excavations. At the Red Lake mine, the use of safety factor of 2.0 for a given rock mass rating has been used successfully. Figure 47 illustrates typical Red Lake mine pillar strength curves at various rock mass ratings. Red Lake Mine Pillar Strength Curves 350 -, , 1 — , , , 0 10 20 30 40 50 60 70 Confinement (MPa) -»-75%RMR, FS=1 -«-55%RMR, FS=1 —A—55%, FS=2 Figure 47. Pillar strength curves for the Red Lake Mine 84 6.2.2 The Pillar Stability Graph The second failure criteria used at the Red Lake Mine is the Pillar Stability Graph. In 1995, Lunder, after analyzing a comprehensive pillar database produced a pillar stability graph. Lunder and Pakalnis (1997) compiled a database of essential rib pillar histories from a number of hard rock mines. Using the combined rib pillar database, Lunder and Pakalnis proposed "The Confinement Formula" for determining the strength of hard rock mine pillars, given as: Ps = (K x UCS) * (C1+C2 * kappa) (12) where: K = rock mass strength size factor (averaged at 44%) UCS = uniaxial compressive strength of intact pillar material CI, C2 = empirically derived constants which were determined to be 0.68 and 0.52 respectively and; Kappa =the mine pillar friction term In its most basic form, the confinement formula consists of two parts. One part takes into account the size effect and the second term takes into account the shape effect. The mine pillar friction term Kappa is defined as follows: Kappa = tan I-Cpav cos ( ) 1 + Cpav (13) Cpav is the average pillar confinement, which is defined as the ratio of the average minor to the average major principle stress at the mid pillar height. The average pillar confinement can also be calculated using the following equation. 1.4 " 1 -Cpav = 0.46 | log(-^ + 0.75 h (14) 85 Lunder and Pakalnis used the "The Confinement Formula" to generate the pillar stability graphs shown in Figure 48. 0.70 0.60 0.50 0.30 4) > < 0.20 0.10 0.00 * * A " F.S. = 1 1 1 0 0 stable 1 unstable A failed o -1 , lA A i AA A A * A £ A * A ' A ^A"' • w a z A m 1 ,-AJU. m A ' " a a 0 F.S. = 1.4 1 A 9^ / m A¥ A •> m m m o A A O 0 c II i / o f A o O 0 O O 0 0 o ° c o 8 S -k o o J 8 ° ° o § % 8 o o o 0 o O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Cpav Figure 48. Pillar stability graph using average pillar confinement (Lunder & Pakalnis, 1997) The average pillar confinement is presented in the x-axis and the average pillar stress divided by UCS is presented on the y-axis. Lunder and Pakalnis (1997) plotted a similar graph to the above where the y-axis is the same as Figure 48, but the with the pillar width to height ratio on the x-axis as shown in Figure 49. Both the graphs are simplified into a common three-stability classification system as either failed, unstable or stable pillar conditions. The graph showing width to height ratio will be used in the case histories. 86 0.70 T ~ 0.60 0.50 <r> o 3 | 0.40 at 2 K 0.30 3 0.20 0.10 0.00 A F \ i A Unstable AW Zone A * M 1 o stable " unstable A failed • A a A ® * si o F.i 0 !. = 1.4 ° o A, A * |p Ik 1 - ^ A A SB r it ts ( ^ ^ " ^ A i O o St able Zone IN a *»» 9 :^**f?\ 0 1 ; > * 0 i o > o o I o A ° < # g 0 0 < , ° ! % 8 < 0 > i 0 > —' 1 0.5 1 1.5 2 Pillar Wldth/Halaht Ratio 2.5 Figure 49. Pillar stability graph using pillar width-to-height ratio (Lunder &Pakalnis, 1997) By plotting the ratio of pillar load/UCS of intact pillar material against the pillar width/pillar height ratio on the pillar stability graph, one can determine the zone the predicted pillar will fall into, stable, unstable or failed. In Red lake mines ground condition , the zone between average pillar stress/UCS ratio less than 0.6 and Pillar Width/Height ratio greater than 1.5 represents a stable zone and all other zones unstable. 6.2.3 Stored Strain Energy Criteria Stored strain energy is the third failure criteria established at the Red Lake Mine. Initial work on stored strain energy at the Red Lake Mine was done by C A N M E T (1996) who undertook an extensive ground stability study of the sill pillars between levels 19 and 21 on the East-South C Zone. The study was carried out in terms of strategic mine planning to maximize sill pillar extraction while minimizing the risk of potential rockburst damage. 87 Back analysis of rockburst activities around the bay areas between sections 59+75 and 60+00 indicates that induced strain energy levels ranging from 0.60 to 0.65 MJ/m 3 are sufficient to cause rockbursts. On this basis, an induced strain energy level of 0.60 MJ/m 3 was assigned as the design limit when determining the best mining sequence for sill pillar extraction and when identifying potential failure zones. The formulation of the stored strain energy formula is described as follows: Rocks that are more elastic and capable of sustaining high stresses before failure are capable of storing elastic energy, which is denoted as potential energy. Jeremic (1987) explains the formation of stored strain energy. Consider a small cube, loaded as shown in Figure 50. The strains energy are associated with these stresses ai , 02, and 0-3. Suppose that the load is built up incrementally from zero. At any time t, the principle stresses are kc>i, ko"2, and kdj. where 0 < k <1. As k increases from k to k+, the displacement perpendicular to CTI becomes EiAk. Figure 50. Element subjected to triaxial load (Jeremic, 1987) The resulting force on this face is a 2 oi . Since work is equal to force times displacement, the following can be written: 88 vv = a^^kAk (15) Total work (W) is obtained by integration: w'= jw = jo-j^a^Afc = cr,£-,a3 JA:M = —cr,£-,a3 (16) o ^ Because work is energy, the above equation describes the strain energy contained in an unconfined elastic cube. Taking into account the contribution from the principle stresses, the potential energy per unit volume (w) is given by: vv = -^(cr1£l + cr2£2 + o~3e3) (17) By application of the generalized Hooke's law, the above equation could be rewritten as: w = ^ -£'{ erf +o\ +o~l -2v(o-1a2+cr2a3+a3al) } (18) where: E = elastic modulas v = poissons ratio oi = major principle stress o"2 = intermediate principle stress o"3 = minor principle stress 89 6.2.4 Deviatoric Stress (oi-qV) The fourth failure criteria used is the Deviatoric Stress criteria. Martin and Read's (1996) experiment at AECL (Atomic Energy of Canada Limited) best describes the deviatoric stress criteria. Martin and Read (1996) described the progressive failure around a circular tunnel in brittle, unfractured Lac du Bonnet granite. A tunnel was excavated without explosives, and state-of-the-art instrumentation was used to monitor the failure process as described as in-situ cracking. The stress magnitude associated with the onset of cracking is referred to as the crack initiation stress (aci). For Lac du Bonnet granite, this occurred when the compressive stress magnitude reached approximately 0.3 to 0.4 cc\, determined by the laboratory tests, where a c is the uniaxial compressive strength (UCS). During the above range, the damage process is described as stable. Therefore, the rock could carry an additional load. Eventually, when the rock sample contains a sufficient density of these sample cracks, the cracks began to interact and a transition from a stable to an unstable cracking process takes place. For unconfined Lac du Bonnet granite, this transition occurs when the compressive stress reaches about 0.7 rjc. Since a constant load at this stress level cannot be sustained by the rock sample, failure eventually occurs. In brittle rock, the failure process begins with crack initiation. Tests were also performed in the laboratory. It was shown that the rock strength during the progression from intact rock to macroscopic failure could be expressed in terms of a low strength component, intrinsic cohesion strength, and finally frictional strength. In engineering practice, it is generally assumed that cohesion and friction are mobilized at the same displacement. However, tests on samples of Lac du Bonnet granite suggested that friction is mobilized in the sample only as damage accumulates and cohesion is lost, as shown in Figure 51. 90 100 80 60 M 40 I 20 0 T:- '<pr:. >•*%».*..•». - Cohesion '•re t*«*^«^L _ 100 80 | 60 f 40 f 20 0.2 0.4 0.6 0.8 Normalized Damage (oyta^ ,) Figure 51. Mobilization of friction and cohesion as a function of damage (Martin & Read, 1996) Figure 51 also shows that the friction and cohesion components of strength are not mobilized with the same amount of damage. The rock strength is composed exclusively of cohesion, that is, friction has not been mobilized and is therefore O=0 initially. For this condition, the strength of material reduces to equation 19. ai-o"3 = constant (19) Equation 19 can be used to identify the stress level at which damage will begin. In order to understand the failure process in-situ, micro-seismic geophones were used to monitor the formation of the micro-cracks. The micro-seismic activity defines the region where damage accumulates and failure eventually occurs in the tunnel. Because these micro-seismic events represent the initiation of the failure process, the stress level associated with these events is referred to as the in-situ crack initiation stress. The in-situ cracking in Lac du Bonnet granite was found to occur when deviatoric stress is approximately 70MPa or one third of uniaxial compressive strength. Wiles (1998) found at the Creighton mine that the stress prediction can be divided into two zones corresponding to the observable cracked and uncracked rock mass. Over a wide range of confinement, the dividing lines show no dependence on confinement (i.e. a zero fiction angle). 91 The cracking occurred at 0- 1-0-3 = Vi UCS and the seismicity occurred at 01- 0-3 = V% UCS (20) (21) Similar observations have been made at the Red Lake Mine. Using the above analogy, the seismicity at the Red Lake Mine initiate when the deviatoric stress is 60MPa and stress fracturing at 90MPa. The deviatoric stresses can be expressed as shown in Figure 52. Deviatoric Stress co 200 0. 0> (ft o 100 o o u CD U =J "D C 50 0 De i/iatoric J Itress -9 )MPa A i 1 — itress -6 1 * )MPa * 0 ' fiaToTicl 10 20 30 40 Confinement (MPa) 50 60 70 s i g m a 1 - 3 = 1 / 3 u c s - s i g m a 1 - 3 = 1 / 2 u c s Figure 52. Deviatoric Stress at one-third and one-half UCS. When superimposing the deviatoric stress lines on the Hoek-Brown strength curves, it can be seen that the deviatoric stress line 60MPa occurs on the strength line with a safety factor of 2 at 55% RMR, as shown in Figure 53. Thus, the deviatoric stress of 60MPa at which fracturing will occur at the Red Lake Mine can be used with confidence. 92 Deviatoric Stress —•>-75%RMR, FS=1 - » - 5 5 % R M R , FS=1 —A—55%, FS=2 X sigmal -3=1 /3ucs X sigmal -3=1 /2ucs Figure 53. Pillar strength and deviatoric stress curves. A few core samples from the Red Lake Mine were stiff tested in the laboratory to determine at which deviatoric stress failure would occur. The results are presented in Table 10. It is important to note that none of the failure occurred below 90MPa as expected. Table 10. Results of Deviatoric Stresses at Rockburst Failures a3(MPa) ai (Kips) Area (in2) <*j (psi). oi (MPa) O1-O3 Oi/o c 6.89 170.15 2.68 63304 436 429 2.3 10.3 41.77 2.68 15540 107 96.7 0.53 10.3 53.53. 2.68 19915 137 126.7 0.70 13.7 99.13 2.68 36881 254 240 1.3 Similar study was done on the four rockburst cases discussed in Chapter 4. Back analysis was carried out to determine at what deviatoric stress did the rockbursts occur. The results are presented in the Table 11. The readings were taken at approximately 0.6m (2ft) above the back in the stressed corners. The deviatoric stress in four areas of the mine where rockburst had occurred indicated that rockburst is most likely to occur at approximately 90MPa, which is one half of the uniaxial compressive strength being used for design. However, the average 93 deviatoric stress seems higher when compared to the data gathered from triaxial test (Table 16). In the triaxial test the deviatoric stress range is quite wide (96-426MPa). The difference in range is due to core samples being from the host rock and away from the ore zone. The core sample from the ore zone will contain more geological discontinuities. Table 11. Modelled Sigmal and 3 Values (From rockburst discussed in Chapter 4) Rockburst <*3 cfi-<y3 ai/a c 34-786-1/2 Stope Cut4 114 18 96 0.63 36-786/746 Intersection 117 34 83 0.65 36-746-1 Cutl 147 55 92 0.81 37-816-1 Exploration Drift 138 41 97 0.76 For design purposes a deviatoric stress of 60 MPa should be used. This value is when seismicity begins. 6.2.5 Induced Stress Level Criteria (rjj/UCS) During design, it is necessary to know whether the mining block is burst prone or will yield. To help answer this question, an induced stress criteria has been established to assist in determining burst potential and potential failure mechanisms (Mah, 1995). The basis for the criteria is not a new concept. Hoek and Brown (1980) describe tunnel wall failure in highly stressed massive brittle rock using the ratio of vertical applied stress, Pz, to the unconfined compressive strength of intact rock, rjc as shown in Table 12. Table 12. Stress Criteria for Tunnel Sidewall (Hoek & Brown, 1980s) Pz/oc Tunnel Response 0.1 Stable unsupported tunnel 0.2 Minor sidewall spalling 0.3 Severe sidewall spalling 0.4 Heavy support required >0.5 Possible rockburst conditions 94 Stacey and Page (1986) reported an empirical approach to tunnel stability that was developed by Wilson in 1971 for 3m to 4m tunnels in South African, deep level, massive brittle rock. The criteria, similar to Hoek and Brown related the ratio of major principle stress, fJi, to the uniaxial compressive strength of the intact rock, o c to tunnel response as shown in Table 13. Table 13. Empirical Instability Criteria for Massive Rock (Stacy & Page, 1986) Oi/Oc Description of Condition <0.2 No particular problem 0.2-0.4 Spalling from surface parallel to O i , heavier support required 0.4-0.5 Major spalling, heavy support required 0.5r0.67 Very dangerous and difficult to keep open, support heavy, costly >0.67 Impractical or extremely difficult to maintain open To help determine the burst potential and failure mechanisms of a sill pillar or stoping block, an induced stress criteria was developed based on Hoek (1980) and Stacey (1986) using the Red Lake Mine database by Mah (1995). The criteria consists of rating a sill pillar as High, Medium, or Low in terms of burst potential as shown in Table 14. The rating was estimated using visual observation and/or numerical modelling. Table 14. Induced Stress Criteria (Mah, 1995) oyac Description of Condition Burst Potential <0.3 Minor ground working Nil 0.3-0.4 Major ground working, moderate spalling Low 0.4-0.5 Ground working, some bursting, major spalling Medium >0.5 Substantial Bursting High A new Induced Stress criterion was developed at the Red Lake Mine as shown in Table 15. The new Induced Stress Criteria was developed at the 1500m elevations. During sill development, it was noticed that there were no ratio of Induced Stress/UCS 95 below 0.3. The Induced Stress/UCS ratio at the sill (or liftl) was at 0.4. At the end of the project, the mining activity was mainly at lift 5 and 6 and the Induced stress/UCS ratios at these elevations were 0.63. A ratio of 0.7 was never observed, however, it is easy to imagine the difficulty arising in maintaining an excavation open at that ratio. Induced stress per lift was determined at the mine and the results are presented in Appendix IV. Table 15. New Induced Stress Criteria Oi/<yc Description of Condition Burst Potential 0.4-0.5 Major ground working, moderate spalling Low 0.5-0.6 Major Ground working, some bursting, Medium 0.6-0.65 Substantial Bursting, major spalling High >0.65 Very Heavy Bursting Very High Induced stress criteria is more applicable to immediate back and walls as the minor principal stress (CT3) reduces to zero. In this case, the deviatoric stress becomes the induced stress criteria. The ratings were estimated using numerical modelling in collaboration with visual observations. The new Induced stress criteria was developed to help evaluate the severity of potential problems and their impact on mining plans. 6.2.6 Rockwall Condition Factor (RCF) Rock wall condition factor (RCF) is another criterion. However, this criterion is used to determine a suitable location for the tunnel and service excavations. One of the functions of regional design is to control field stress levels as much as possible, that is, to ensure that the absolute stresses in the rock in which service excavations are located never exceed tolerable levels (COMRO, 1988). The rockwall condition factor is defined as: RCF=(3 ai-cj3)/Fac (22) where: 0\= major principle stress 0 3 = minor principle stress oc= uniaxial compressive strength F= empirical rock mass factor 96 Since a sill pillar cannot be moved as compared to a service excavation, the rock wall condition factor criterion is not applicable. 6.2.7 Excess Shear Stress (ESS) The presence of occasional faults or dykes significantly increases the frequency of rockburst. The shear-type seismic event mechanics provides a simple explanation for many of these effects. A plane of weakness in an otherwise strong rock mass can be subjected to shear stresses induced by mining. Once the cohesive strength of such a plane is exceeded, overstressed asperities will shear and slip can occur. The excess shear stress (ESS) is defined as: ESS = T - L i r j n (23) where: x = static shear stress p, = dynamic coefficient of friction an= normal stress Calculations have shown that this mechanism can account for seismic events covering a wide range of high magnitudes (>1). ESS on the other hand requires a precise knowledge of the state of virgin stresses in the area, such as strength properties at rupture, such as cohesion, dynamic friction coefficient and any history of major slip events (COMRO, 1988). Since fault-slip failure is not present at the current stage of mining, this criterion is not applicable either. 97 6.3 DISCUSSION Although there are several failure criteria available that can be calibrated to a mine site, the five failure criteria previously discussed were chosen because they are easy to use. A l l five-failure criteria require the major, the intermediate or minor principle stresses or the combination of the three as in the case for the stored strain energy formula. The principle stresses are derived from numerical models. The uniaxial compressive strength also required is usually obtained from stiff tests. The other parameters required such as, elasticity of modulus and poissons ratio, are readily available. The Rockwall Failure Criteria and the Excess Shear Stress are the other two-failure criterion discussed briefly but will not used, as they cannot be applied to sill pillar design. The input parameters required in the failure criteria formulas and the two case studies to illustrate the use of the five failure criteria are discussed in the next section. 98 6.4 PILLAR DESIGN CASE HISTORIES Two case histories will be used to illustrate the use of the five failure criteria discussed in the previous chapter. Before the case histories are discussed, the input parameters required in the failure criteria formula will be presented. Two main input parameters are the in-situ stresses and rock mass properties. 6.4.1 Map 3D Numerical Modeling Program Map3D is based on the three-dimensional boundary element formulation developed by Terry Wiles of Mine Modelling Ltd. This program was chosen over other numerical modelling programs because of its ease of use and personal computer compatibility. Building a model in Map3D involves a series of blocks, either excavated or planned to be excavated, using conventional numerical modelling techniques or by using a built in CAD interface. Element discretization takes place within the model based upon a number of discretization parameters supplied by the end user. Approximately 800 blocks were used to create the new Red Lake Mine wide model as shown in Figure 54. Using Map3D, stresses are calculated only on grids of field points as specified by the user. This approach to three-dimensional modelling results in reduced computation times over the other modelling programs. The model construction was accomplished by importing AutoCad drawing directly to a Map3D input file. 99 6.4.2 Map 3D Input Parameters The input parameters used for this study are outlined in Table. 16. The data has been organized into the three categories: intact rock properties, in-situ stress and regime and control parameters. There are three general control parameter settings recommended in the Map3D manual: coarse, detailed and high accuracy. The control parameter setting in this study that was used was "coarse to detailed". Table 16. Map3D Input Parameters used the Red Lake Mine Rock Mass Properties Map3D Control Parameters Modulus of Elasticity= 56GPa Max No. of time steps (NLD) = 2000 Poisson's Ratio= 0.2 Max No. of time steps (NIT) = 2000 'm' Hoek-Brown =7.8 Max Relaxation Parameter (RPAR)=0.8 's' Hoek-Brown =0.06 Stress Tolerance (STOL) =100 UCS =180Mpa Allowable Element Side Length (AL) =10 In-Situ Stress Regime D/L Ratio-Grid Discretization (DOL) =1 Datum = 3041m (9978.5ft) D/L Ratio-Element Discretization (DON) =1 C M = 8.18+0.0422 MPa/m D/L Ratio-Coefficient Lumping (DOC) = 1 rj 2 = 8.18+0.0422 MPa/m D/L Ratio-Element Lumping (DOE) = 2 cj3 = 0.029 MPa/m D/L Ratio-Grid Lumping (DOG) = 2 Trend and Plunge of o"i=45/0 Allowable Element Aspect Ratio (DOR) = 5 Trend and Plunge of o"3=315/0 The uniaxial compressive strength used throughout this report is the mean value of 180MPa. All of the above five failure criteria used to determine the optimum pillar dimensions use the uniaxial compressive strength value. Below are two examples to illustrate the use of the five failure criteria are discussed. The first case history is the determination of the 32-826-4 sill pillar dimension 101 and the other is ramp (post) pillar determination at 34-786-4 stope. Since there were no instruments installed to monitor the rise in induced stress in either of the pillars, all five-failure criteria were used to determine the optimum pillar dimensions. The 32-826-4W Sill Pillar will be discussed first. 6.4.3 Sill Pillar (32Level. Depth 1450m) The induced stress levels resulting from the mining of the intervening sill pillar separating the 31-826-4 Stope (above) and the 32-826-4 Stope (below) were determined using the numerical model. This is referred to subsequently as the "31-826-4 Sill". This required the modelling of the subsequent proposed mining lifts above the existing 32-826-4 Cut 6 as it approaches the 31-1 Sub Level. Figure 55 shows the vertical sections of the existing Cut 6 and the simulated mining of Cut 7 through Cut 10, until extraction reaches the floor of the 31-826-4 Sill. At the time of the assessment, Cut 6 was being mined and a vertical sill thickness of 16m (52ft) existed to the floor of the 31-826-4 Sill or 18.5m (60ft) if employing a slope distance of 60° as shown in Figure 55. This represents the dip of the ore as interpolated by the, Red Lake Mine geology. Induced stress measurements were taken at the center of the sill pillar as subsequent cuts were extracted. Individual cuts are 3m (10ft) in height with spans of 7.09m (23ft) and 10.8m(35ft) employed for the 32-826-4 Cuts 7-10 and the 31-826-4 Sill Cut respectively. 102 3 1 - 8 2 6 - 4 SELL CUT H7 CUT tt6 MUNCOTOCLTTM seeeitELEv S C A L E Of t lOf - t 2 D f t VERTICAL SECTION A-A' OF SILL MINING SHOWING 32-826-4 CUTS #6 - #10 AND FLOOR OF OVERLYING 31-826-4 SILL Figure 55. Schematic drawing showing the mining of Stope 32-826-4W Figure 56 shows one of the mining steps. The individual cuts employing a grid are located approximately parallel to the plunge of the ore body and perpendicular to the strike of the ore. Increased induced stress levels are observed at the sill pillar core. As the sill pillar thickness reduces as each lift approaches the 31-lSub Level (floor of 31-826-4). 31-826-4 SILL, Z =5435ft ELEV «"i= ICMMPa.o-j, =46MPa -826-4 COT #8, BACK ELEV=5403 CUT#8 MINED - 32ft VERT. (37ft INCLINED) SILL THICKNESS. STOPE SPAN~23ft. Figure 56. Induced stress at mining step3 (Cut8) 103 The induced stress levels and geometry are summarized in Table 17. Table 17. Numerical Assessment- Mining of 32-826-4 from cut6 to Sill of 31-826-4 Mining Steps Sill(Wp) V ertical Thickness (ft) Induced Pillar Stress O" l / U C S STRENGTH (m&s) Factor of Safety o" 1-0-3 ;S:;:j(fc.1;:;S:::;i (MPa) |(MPa)|r>'IPa) Height Hp (ft) Wp/Hp Ratio 75% RMR (MPa) 55% RMR (MPa) m&s 75% RMR 55%RMR 'lo or 31-826-4** 0.37 281 206 4.2 3.1 27 32-826-4 Cut#6 52(60**) 84 48 44 2.3 0.47 297 219 35 2.6 40 32-826-4 Cutf 7 42(48) 90 52 46 1.8 0.50 302 223 3.4 2.5 44 32-826-4 Cut#8 32(37) 104 54 46 1 4 0.58 305 225 2.9 2.2 58 32-826-4 Cutf 9 22(25) 138 51 42 1.0 0.77 289 212 2.1 1.5 96 32-826-4 CiiWlO 12(14) 198 52 1 •:-.i::23;l 0.5 1.10 57 29 0.3 0.1 197 67 | 42 | 40 | The analysis is used to determine the expected stability of the 31-826-4 Sill using the five failure criteria and to recommend the maximum height to mine the sill pillar from the 32-1 Sub. 6.4.3.1 Hoek-Brown Failure Criteria The average rock mass rating (RMR) value near the 31-826-4W Sill is 75. In high burst prone ground, the RMR is reduced by 20, thus the RMR becomes 55 (see chapter 4 on the correction of RMR values). The uniaxial compressive strength of the ore zone around 31-826-4 Sill is estimated to be 180MPa. Using these values and the confinement ( G 3 ) determined from numerical modeling, the rock strength is determined as shown in Figure 57. The induced core stress has been recorded at the mid-sill pillar height of the intervening sill as the individual cuts have been mined. The factor of safety is determined by dividing the rock strength by the induced stress after each of the individual lifts, as summarized in Table 23. It must be noted that a factor of safety greater than 2.0 exists largely up to Cut 8 for the 55 RMR material. This is due to the high confinement associated with the mining of Cut 6 through Cut 9, which exceeds 40MPa. Thus, the recommended lifts that can be mined using the Hoek-Brown failure criteria is up to Cut 8. 104 31-826-4SMI Pillar Strength CO Q. s co co cu i _ •*-< CO Q> o o •o Q> O 3 •o C 350 300 250 200 150 100 50 0 75%RMRJJ ^ 8=1 55%Rfv IR. FS=J--)<Cut10 c ut9 X i 6 % R M R J S=2 7 10 20 30 40 C o n f i n e m e n t ( M P a ) 50 60 70 Figure 57. Rock mass strength employing Hoek & Browns failure criteria (fix%) 6.4.3.2 Stored Strain Energy Stresses required to determine the stored strain energy were observed 1.5m (5ft or 0.5 x lift height) beneath the floor of the 31-826-4 Sill stope. The stored strain energy increases as individual mining cuts are extracted, as shown in Figure 58. The stored strain energy shows that a major increase in stress (Oi ) occurs only after the mining of Cut 9. However, a gradual increase occurs after Cut 7. By using the stored strain energy criteria, the rockburst will occur if the strain energy gets to 0.6MJ/m 3. Thus, the recommended lifts that can be mined is Cut 7. 105 Stored Strain Energy per Cut 2.4 CO 2.1 £ 1.8 1.5 >. 1.2 © 0.9 LU 0.6 C "<5 0.3 0 <?  (-7 8 9 10 Mining Step (Cuts) 11 Figure 58. Stored Strain Energy at Observation Point 106 6.4.3.3 Pillar Stability Graph By employing the pillar width (sill pillar thickness) to the pillar height (span) to the existing induced core stress to uniaxial compressive strength, it can be seen that pillar mining should not go beyond Cut 7 as shown in Figure 59. At this stage the sill thickness is 12.8m (42ft) vertical and 14.63m (48ft) along the slope distance (60°), resulting in a Wp/Hp of 1.8 and 2.1 respectively for the 7.0m (23ft) stope span (Hp). 0-0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 PILLAR WIDTH/HEIGHT RATIO PILLAR STABILITY CLASSIFICATION - Failed "Unstable A Stable Figure 59. Average Pillar Load/UCS versus W/H ratio 107 6.4.3.4 Deviatoric Stress (Gj^-gj) Deviatoric stress in the core of the sill pillar is plotted against each mining step as shown in Figure 60. At present a value of 60MPa is being used as an initial criterion for failure. However, this value at the Red Lake Mine will be established as more pillars are exposed, although it have been successful as a predictor for the ramp pillar mining of 34-786/Sth Access (discussed next). Generally, mining to Cut 8 is suggested with a jump in deviatoric stress occurring after Cut 8. _ ^ 200 ro 0-160 -co CO CD L _ 120 -+^ (/) o 80 -o ro 40 > CD Q 0 Deviatoric Stress vs Mining Steps Deviatoric Stress @ 60 MPa In 27 •46--44-1 Cut 6 2 Cut 7 Cut 8 Mining Steps Figure 60. Deviatoric Stress per mining cut. 197 6.4.3.5 Induced Stress Level Criteria (c± /UCS) Induced stress level criteria has been employed successfully as a failure criteria at the Red Lake mine in the past. A value in excess of 0.5-0.6 * UCS or 90-1 lOMPa would indicate medium burst potential as shown in Table 24. This value (0.58) is achieved upon the excavation of Cut 8 as shown in Table 28. By employing this criteria, the mining of Cut 8 is possible. 108 6.4.3.6 Summary of Results Results of the all five failure criteria are summarized in Table 18. Table 18. Failure Criteria Results Failure Criteria Results-Mine Lift No. Ffoek-Brown Cut 8 Stored Strain Energy Cut 7 Pillar Stability Graph Cut 7 Deviatoric Stress Cut 8 Induce Stress/UCS Cut 8 According to the results in Table 18 the sill pillar could be mined up to Cut 8. However, taking into consideration the possibility of mining the sill pillar using the top down long-hole mining method where man entry from the top of the sill becomes necessary, the sill pillar extraction should not exceed Cut 7. The Hoek-Brown failure criteria and the deviatoric stress failure criteria do indicate that mining of Cut 8 is possible. In addition, since no instruments were installed in the sill pillar to monitor the rise in induced stress, only mining up to Cut 7 was recommended. The back of Cut 7 should be considered as burst prone and burst prone support should be employed. To date, Cut 7 has been mined successfully without any incident. The evidence of this is clearly shown is Figures 61. The mining personnel from the mine reported stress fractures in the backs and hangingwalls of the stope. Apart from stress fractures, the back is competent and the stope is now being used as an access to a new stope as shown in Figure 62. 109 Figure 61. Back and hangingwall of stope 32-826-4 Cut 7 6.4.4 Post Pillar/South Access (34Level. Depth 1500m) The proposed extent of the 34-786-4 Cut 4 stope in the proximity of the south access (34-1 access) was determined using the numerical model. This will subsequently be the 34-786-4 Ramp (Post) Pillar which required the modelling of the past mining on the 34-786 stopes and the future extraction on Cut 4. The analysis on Cut 4 evaluated a Ramp Pillar separating the 34-786 stope from the south access ranged from 7.62-3.05m (25-10ft). Figure 63 shows the planned sections of extraction of 34-786-4 Cut 4 Stope in the proximity of the South Ramp Access (34-1). During the time of the modeling, Cut 4 was being mined and options of leaving a 7.62m (25ft), 6.1m (20ft) 4.57m (15ft) or 3.48m (10 ft) pillar were being analyzed. Figure 63. Schematic drawing showing the mining of 34-786-4 Cut#4 Stope Figure 64 shows the individual cuts in 3D isometric view. It shows individual cuts and the back slashes taken within the South Ramp Access to access stopes to the south of the ramps. The grids are located approximately perpendicular to the proposed pillars. In total, 5 grids were used as shown in Figure 63. Grid l , Gridl.5, Grid2, Grid3 and Grid4 were used to observe the induced stresses. Increased induced stress levels are observed at the pillar core as the pillar geometry reduces as each cut approaches the 34-1 South Access Ramp. I l l Figure 64. Induced stress location at mid pillar height The induced stress levels and geometry are summarized in Table 18 and in Table 19. The analysis is used to determine the optimum ramp post pillar dimension using the five failure criteria are discussed as follows. 6.4.4.1 Hoek-Brown Failure Criteria. The strength of the 75% R M R near the ore zone having a UCS of 180Mpa is shown as a function of the confinement (03), which is recorded in Table 19 and Table 20. The individual mining cuts have been recorded at the mid-pillar height for the individual cuts. Using the above values and the confinement (03) determined from numerical modeling, the rock strength is determined as shown in Figure 65. The factor of safety is determined by dividing the rock strength by the induced stress after each individual cut, as summarized in Table 19 and Table 20. It must be noted, as shown in Table 20 and in Figure 65, that Cut 3 has a factor of safety under 2.0. This is due to the 2.1m (7ft) ramp pillar thickness, as shown on Grid 1.5, yielding a factor of safety of 1.2 and an individual stress magnitude of 98 MPa. 112 Table 19. Numerical Assessment- 34/786/ South Access Induced Stress History Depth Mining Below. I I I U U U G I i r i u a i h STRENGTH (m&s) a Factor Of Safety cn 0-5 iiisSiiStepssSS;;;: Surface Width (Height Iwp/Hp 75% RMR 55% RMR m&s m&s (ml (MPa) (MPa)|(MPa) Wp(ft)|Hp(ft) Ratio (MPa) (MPa) 75% RMR 55% RMR Back 1511 Sill Cut In-situ 1512 72 i 4 4 i 040 296 21* 41 :<o 28 mMwimM 74 iMmi i:45;:s :::i:40:::::? mwm 40 0.41 221 4.1 30 29 Gnd 1 5 73 mum *:;:45i ''::;::;50:;S Mom: 5 0 0.41 mmmm 221 4.1 28 73 mm 1:441 j;si:57::!;£ 5 7 0.41 296 218 41 30 29 Gnd 3 72 S:47.# 3:45:::: m-fA-m mwm 0.40 300 221 42 3 1 27 Iii fi;: Grid4 i!?S' 72 ::::::44:?;: wmm vSl0.;:K: mzsm 0.40 296 :::s::218:ffiv 41 30 28 SjSiKFlbbrSS;?::. 1514 1508 Cut#l In-situ 1509 72 45 mmi 0.40 296 218 4.1 30 28 iSiSi-sC^dliixiP' 78 miM 4 4 , miom. 1.5 0.43 296 218 38 22 34 S:::S:Gh^ :l::S:H:;S::. 74 i?54S:: 42 m 36::::::: :::;::2oj::::::' 1.8 0 41 289 212 39 2.9 32 :£;£.Giici:2W; 73 5:::54:::i l:42'::.:l:' mx5m: 2.1 0 41 289 212 40 2.9 31 ::::::*:::::::.Gn^:3:V:. 72 :;:;:52i:;: mmf :S:::56s.i;: :«;::20:::::;:; 2.8 0.40 296 218 4.1 30 28 i::S:*sGrid4::S;:.x 72 fiiSO'p mmti i::71;::8! 36 040 296 218 4.1 28 :vS*Flo6f;Sii;.f. 1511 Back 1504 Cut#2 In-situ 1506 72 E45ii m<m 040 296 218 4.1 30 28 Gridl 77 WS3ii 42 ::::::29::::'::: 30 V;-. m. Mm 0.43 289 212 38 2.8 35 Gnd 1.5 94 ::i75?:: 29 :;C:7;::$: 30 0.2 0 52 236 171 :::.:;i:.2:5'::.H:::: 1 8 65 Grid 2 89 :s:;62:;.:. 29 16 30::' 05 0 49 236 171 f S.2.6':;JT:: 1 9 60 Grid 3 74 Wom 43 38 30 : 1.3 0 41 293 215 :m4.0 29 31 Grid 4 73 ::i:53;:;;:' :::;:43::::: 58 yimm- 1.9 0 41 293 215 MMai.m 29 30 • Floor • • 1508 Back 1501 Cut#3 In-situ 1503 <mim i:S45:::S 1441 040 296 218 41 3.0 28 Gndl mwm 28 worn. 03 046 231 167 23 20 54 Grid 15 162'% m1% •:!::?16:::::::i m&m 04 0 54 115 78 1 2 mm&ma 91 Gnd 2 #:;:'9D-S: :|67;::: ::s:i6:;:; m^o'-m 0.5 0 50 172 122 1 9 1 4 74 Gnd 3 62 mm ::*:25:::;::: :m::.y 06 0.46 244 177 29 2.1 52 Gnd 4 •::-;:79:¥:i 40 :;:i::31-s:!:: minm 08 0.44 281 206 36 2.6 39 Floor 1504 Back 1498 Cut*4 In-situ 1500 72 145 :£ 43 0.40 293 215 4 1 3.0 29 Gndl ••••:i:84-i?f i :57i: ; | 3 4 l »::::25 M 50 05 0.47 257 187 3 1 2.2 50 Gridl.5 •S;.9m mism. Il7:& mim. £ 50 0.5 0 51 178 126 2 0 1 4 74 Gnd 2 W94M §56 :# iisll rnism msoU 0.5 :?0:52S: 1S3 130 1 9 1 4 7o Grid 3 i;:l88s8: mm 20 miim msom 05 :::;ffi49.:;:::: 193 138 22 16 6i Grid 4 mom. 28 mm% 0.5 0.45 231 167 29 2.1 mm.5ivM Floor 1501 113 Table 20. Numerical Assessment- 34/786/ South Access Induced Stress Options Depth Mining Below STRENGTH (m&s) *:si F actor Of Safety Steps Surface 0-3 Width lHeight|Wp/Hp °"1AJCS 75% RMR 55% RMR RSiim&siiJii 0"1 °"3 i p l (MP a) (MPa)|(MPa) Wp(ft)|Hp(ft) Ratio (MPal iMPa.i 75% RMR 55% RMR Back 1498 Sill Cut In-situ 1500 72 a:45.;g S:43SS Warn 293 215 4.1 3.0 29 Gnd 1 84 jS57:?i l34i| •mm 0.50 0.47 257 1S7 3.1 2.2 50 Gnd 15 91 mm 0.50 ::;:d;51;:::::: 178 126 20 1 4 74 Gnd 2 94 W56Z s:::18:?:: M25W k S d S ; 0.50 0 52 183 130 1.9 1 4 76 Gnd 3 88 20 M25M 8*501:* 050 0.49 193 138 22 1 6 68 Gnd 4 81 60 28 mm i:ii*50:*ii:: 0.50 0.45 231 167 2.9 wmm 53 1501 Back 1498 Cut#4 (20R) 1500 72 ::;:43:K 0.40 293 215 4.1 30 29 Gndl 86 ami. 'mm iRM**; 040 0.48 222 160 26 1.9 60 Grid 1.5 88 16 mam R.;:50:i:;:;: 0.40 0.49 172 122 20 1.4 72 Grid 2 95 60 i :: :i3l : mail iRiSd**; 0.40 0.53 155 108 1.6 1.1 82 Grid 3 92 62 21 20 :**S0:*'.i: . 0.40 0 51 198 ~m\42:m- 2.2 1 5 71 Grid 4 76 .60 20 S;-?20EV 50 0.40 0.42 193 138 2.5 1.8 56 Floor 1501 Back 1498 Cut#4 (15ft) 1500 :::iS72:,;i •:?:45:;s S:43:*': 0.40 293 215 41 30 29 Gridl :iii:62;:i:i ;:s'25x:i 15 MsaW 0.30 0.49 217 157 • 2.5 1 8 63 Grid 1.5 :4o"9™i S:!W:i':f. 15 sS50 Rs: 0.30 0.52 99 1 1 Co Grid 2 68 10 15 <::50:;% 0.30 0.54 :.:.:i?i36.&i; 94 1.4 1.0 27 Grid 3 66 15 :*;:50:s* 0.30 0.54 . . 167 117 1 7 1 2 Vi Gnd 4 60 20 15 t^OK? 0.30 0.43 "V: 193 138 2.5 1.8 58 Floor 1501 Back 1498 Cu«4 (10ft) 1500 :*i72'::::i> 0.40 293 215 41 3.0 29 Gndl .••:::;92:;::;.; !JV76«- hi24*;i mm. :*i;!i50:*i;: 0.20 0.51 213 153 23 1.7 68 Gndl 5 S.117* :R84:¥ i:i:::4il. mm ilJORT 0.20••: 0.65 91 58 0 3 0.5 113 Grid 2 122 . 76 :-;>7s;::: 50 0.20 0.68 115 78 :-::::'::oi9>:-:i::: 06 115 Grid 3 120,: 70 :S:9:;g 10 50 0.20 0.67 i::-*i30':-:;:i 89 1 1 0.7 111 Gnd 4 78 . 59 12 10 . :'::; 50 •:?:; 0.20 0.43 149 104 1.3 66 Floor 1501 J It must also be noted that these conditions are not duplicated until the ramp pillar is 4.57-3.48m (15-10ft) thick for Cut 4. Mining of the individual cuts from sill cut through to Cut 3 has not shown deterioration within the south ramp access other than a burst that occurred upon opening of Cut 2. This similarity occurred on Cut 4 as the stope was initially being mined. This rockburst is likely due to the proximity of the geological structures such as the Lamp Dyke. (Detailed discussion on this burst can be found in section 3.2 under case histories). Similar to the sill pillar case, a factor of safety of 2.0 existed largely up to the 6.1m (20 ft) pillar dimension for the 75 RMR material. This indicates that ramp pillar of 7.6-114 6.1m (25-20ft) thickness should be employed. Figure 65 also shows the rock mass strength for an RMR of 55 for comparative purposes. 34-786/Sth Access Pillar Strength Figure 65. Rock Mass Strength Employing m & s Failure Criteria 115 6.4.4.2 Stored Strain Energy Criteria Stresses required to determine the stored strain energy similar to the Hoek-Brown failure criteria was observed at mid-pillar height. The individual mining cuts extracted are shown in Figure 66. The stored strain energy shows that a major increase in stress occurs only after leaving 3.05m (10ft) pillar. According to the stored strain energy criteria one can mine until 4.57m (15ft) thick pillar is reached. In general, the stored strain energy increases gradually up to Cut 3. Strain Energy Analysis 34-786-4 Pillar Figure 66. Stored strain energy at mid pillar height 116 6.4.4.3 Pillar Stability Graph By employing the pillar width (sill pillar thickness) to the pillar height (span) and the existing induced core stress to the uniaxial compressive strength, it can be seen that pillar mining should not go beyond the 4.57m (20ft) pillar dimension as shown in Figure 67. According to the stable zone proposed in Figure 67, the pillar dimension should be 6.1m (20ft). This is based upon the pillar height being 3.05m (10ft), which is the exposed pillar. It must also be noted that Cut 3 and Cut 2 have been successfully mined employing Wp/Hp values of less than 2.0. PILLAR STABILITY GRAPH - EMPIRICAL 1.0 0.9 ca 0.7 O.S 0.5 0.4 0.3 0.2 0.1 0.0 f i 1 i if a (J r M 3 i -6 - A I L E D « 4 § a a « J 1 1 S=1.0 . « = l • • m a adP a L •* 1-3 >< . * § a m m » ^ <^ c? a * UNffl A B L f j — A. a n K F M m i s • - A. * a * = § ft & A A t78 obs 0 0. 4 0. B 1. 2 1. S 2 D 2.4 28 SL2 PILLAR WIOTM/HEIGHT RATIO PILLAR STABILITY CLASSIFICATION a Fated » Unstable a Stable X-CUTi REFERS TO WrVM*» WHERE Hp»10R {ONE LIFT HEIGHT) 0-CUT: REFERS TO WpAHp WHERE Hp»TOTAL VERTICAL PILLAR HEIGHT FROM SttJL FLOOR TO BACK OF MINED CUT Figure 67. Average pillar load/ucs versus W / H 117 6.4.4.4 Deviatoric Stress (oyOj) Deviatoric stress in the core of the ramp pillar is plotted against each mining step as shown in Figure 68. Currently value of 60MPa is used as an initial criteria for failure. However, this value was reached at Cut 3. Cut 4 indicates a deviatoric stress of 76MPa. Since 7.6m (25ft) pillar at Cut 4 indicates the lowest deviatoric stress, this width will be used. Thus, according to the deviatoric stress criteria, a 6.1-7.6m (20-25ft) thick pillar is recommended. Deviatoric Stress (s rs 3) Sill Cut Cut#1 Cut#2 Cut#3 Cut#4 Cut#4 Cut#4 Cut#4 (25ft) (20ft) (15ft) (10ft) Mining Steps Figure 68. Deviatoric stress per mining cut. 6.4.4.5 Induced Stress Level Criteria (o± /UCS) The induced Stress Level Criteria has been employed successfully as a failure criterion at Red Lake Mine in the past. A value in excess of 0.5-0.6 * UCS or 90-1 lOMPa would indicate medium burst potential as shown in Table 19 and Table 20. A 6.1m (20ft) thick pillar would yield ratios of (eji /UCS) of 0.53, which has been successfully extracted for Cut 2 and Cut 3 (0.52 to 0.54), as shown in Table 19. By employing this criteria a 6.1-7.6m (15-20ft) pillar is suggested. 118 6.4.4.6 Summary of Results Results of the all five failure criteria are summarized in Table 21. Table 21. Failure Criteria Results Failure Criteria Recommended Pillar Dimension Hoek-Brown 6.1-7.6m(20-25ft) Stored Strain Energy 4.6-6.1m(15-20ft) Pillar Stability Graph 4.6-6. lm(15-20ft) Deviatoric Stress 6.1-7.6m (20-25ft) Induced Stress 4.6-6. lm(15-20ft) According to the results in Table 21, a conservative minimum ramp pillar thickness should be between 6.1-7.6m (20-25ft). The Stored Strain Energy, Pillar Stability Graph and Induced Stress criteria indicate that a 4.6-6. lm (15-20ft) dimension ramp pillar is possible. However, since no instruments were installed in the pillar to monitor the rise in induced stresses, the recommended dimension of the pillar is between 6.1-7.6m (20-25ft). The back and wall near the pillar should be considered as burst prone which would require the employment of burst prone support. A 6.1m (20ft) thick pillar was established in order to mine the remainder of the stopes and the next cut above (Cut 5) was mined successfully. Eventually the established pillar was mined out as it contained high-grade ore. An artificial pillar constructed with paste fill and shotcrete were installed prior to the removal of the established pillar. During the establishing of the pillar, stress fractures were formed in the back and the ground workings around the pillar were low. 119 6.5 DISCUSSION Two case histories have been discussed above. In both cases the lower value was chosen as the acceptable limit as no instruments were installed to monitor the rise in stress or to calibrate the failure criteria. As more and more pillars are designed and established, a better feel for the limits of the failure criteria can be determined. The 32-826-4 Sill Pillar and the 34-786-4 Ramp Pillar, which were designed using the five failure criteria, were successfully established. 120 CHAPTER 7 CONCLUSION The thesis presented the development of empirical and numerical design techniques at Goldcorp Inc's Red Lake Mine. The first phase dealt with the rockburst mechanism, rockburst seismology, unusual occurrences, variables that affected ground working. Four known rockbursts were classified using visual inspection and with the aid of the micro-seismic system. 7.1 SEISMICITY There were several variables that caused ground working, seismicity and even rockbursts to occur. These were excavation span, confinement and time and location of blast and geology. 1) . It was determined through visual inspection and numerical modeling that the excavations that were less than 6m worked violently immediately after the blast as compared to excavations that were wider than 6m. 2) . It was also determined that the dip of the stope had an effect on the ground working. The ground working increased as the dip of the stope increased or as the ore body became steeper. This increase in ground working is due to decrease in the confinement. 3) . Finally, it was determined that most of the ground working and seismic activity occurred immediately after blasting, when stress redistribution was taking place. There were four known rockbursts during the last two years that were studied in detail. The rockbursts occurred on all levels of the mine. All of the rockbursts occurred after blasting. Geological structure such as lamprophyre dykes and faults were present at the location of the rockburst. It was concluded that rockbursts can be classified as crush type burst. It is similar to strain bursts but higher in magnitude. 121 7.2 CRITICAL SPAN GRAPH (2003) The second phase of the thesis dealt with the updating of the span graph, which can be applied to cut and fill stopes in burst prone ground. Over 100 data points were added to the span graph using the neural network "neuroshell predictor". The new underground entry-type excavation span graph was developed on the basis of the neural network contour outline. The outline zones were classified as stable, potentially unstable and unstable as in the previous span graph (Wang, 2000). Since most of the data collected at the Red Lake Mine was less than 10m in span width and in the stable zone, the stable zone is well defined in the lower span ranges. The new span graph also defines the new potentially unstable and unstable zones. 1) . Two new zones were added to the graph. A new zone added to the stable side informs design engineers that during excavation under high stress, severe ground working is expected and burst prone support may be required. 2) . The other zone was added in the potentially unstable-caved side. Due to the poor rock mass and high stress conditions, closure of the excavation ground can be expected. 3) . The presence of geological structure near the planned excavation should be analyzed separately. When high stress and or geological structures are present, the RMR values are to be corrected. The RMR correction should be made as follows: 1. If open joints and shears are present and dip between 0° and 60° or if joints are present the dip 0° and 30° from horizontal in the immediate back, 10 should be subtracted from the RMR value 2. If high stress is present in the immediate back, 20 should be subtracted from the RMR value. (High stress is defined as seismicity over 1000 Joules of energy or G ] / G c ratio in the range of 0.5-0.6). 122 3. If both are present, then only 20 should be subtracted from the RMR value. The new neural network derived span design curve with data from burst prone ground shows significant improvement from the previous neural network generated graph. Adding more data points greatly increased the confidence level of the graph. In addition the new graph can be used in burst prone ground. 7.3 PILLAR DESIGN The third section dealt with the development of pillar design techniques. Five failure criteria were calibrated to the Red Lake Mine ground conditions and two case histories were presented. The five failure criteria were Hoek & Brown failure criteria, the pillar stability graph, stored strain energy, deviatoric stress and induced stress criteria. 1) . A Safety factor of 2, derived using Hoek and Brown criteria, functioned effectively for the Red Lake mines ground conditions. 2) . The pillar stability graph, the zone between average pillar stress/UCS ratio less than 0.6 and Pillar Width/Height ratio greater than 1.5 represents a stable zone and all other zones unstable. 3) . The stored strain energy criterion, the energy above 0.63MJ/m3 indicates that rockbursts can occur. 4) . The deviatoric stress criteria, at one-third uniaxial compressive strength indicates seismic activity will start to occur. Fracturing will occur at one-half uniaxial compressive strength. 5) . The induced stress criterion, which indicates if yielding or bursting, will occur. It was determined through numerical modelling and underground visual observations that major ground working and some bursting may occur between the ratios of 0.5 to 0.6. Future research should be implementing instrumentation to further calibrate the above observation. Stress meters reading during the excavation of the sill pillars would have given a good comparison between the modeled data and the actual in-situ stress. More microseismic data especially the source parameters should be used to determine the types of rockbursts that are being experienced at the mine. 123 REFERENCE 1. Afrouz, A. A., Practical Handbook of Rock Mass Classification System and Modes of Ground Failure. CRC Press , Boca Raton, Florida, 1992. 2. Barton, N. Lien, R., and Lunde, J., Analysis of Rock Mass Quality and Support Practice in Tunneling and a Guide for Estimating Support Requirement, Internal Report- Norwegian Geotechnical Institute, Oslo, 1974. 3. Beer, G. and Meek, J.L., Design Curves for Roofs and Hangingwalls Based on Voussoir Beam and Plate Solution. Trans Inst of Mining and Metallurgy, vol. 91 London, 1992 4. Betournay, M.C., What do we really know about surface crown pillars? In Proc. Int. Conf. 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Hedley, D.G.F. and Grant, F., Stope and Pillar Design for the Elliot Lake Uranium Mines. Can. Inst. Min. Metall., 1972, Bull.65, pp37-44. 27. Hoek, E. and Brown E.T. The Hoek-Brown Failure Criteria - 1988 update. In Proc. 15th Canadian Rock Mechanics Symposium. Toronto (Edited by Curran, J.H.) Dept of civil engineering University of Toronto. Toronto, 1988, pp31-58. 125 28. Hoek, E., A Limit Equilibrium Analysis of Surface Crown Pillar Stability, Proc. Intl. Conf. Surface Crown Pillar Evaluation for Active and Abandoned Metal Mines, Timmins, Ont, 1989. 29. Hoek, E., Kaiser, P., and Bawden, W., Support of underground Excavations in Rocks, AA Balkema Publishers, 1987, pp84-98. 30. Hoek. E, and Brown, E.T., Underground Excavation in Rock, Institution of Mining and Metallurgy, London, 1980. 31. Holland, C.T., Design of Pillars of Overburden Support - Part 1. Min Congr. J3,, 1962, pp24-28. 32. Holland, C.T., Design of Pillars of Overburden Support - Part 2. Min Congr. J3, 1962,pp66-71. 33. Hudyma, M. R., Rib Pillar Design in Open Stope Mining. MASc thesis, University of BC, 1988. 34. Jaeger, J.C., Elasticity, Fracture and Flow, Methuen, 1962. 35. Jeremic, M.L., Ground Mechanics in Hard Rock Mining. AA: Balkema Rotterdam, 1987. 36. Smith, D. J., Inherent Stress Measurements 28 level. Engineering & Associates Limited, Consulting Mining and Geotechnical Engineers by Dr. James F. Archibald, July31, 1989. 37. Lang. B., Span Design for Entry-type Excavation. MASc. Thesis, University of British Columbia, 1994. 38. Leslie, Ian. Data processing from Hyperion Microseismic System-Red Lake Mine. Engineering Seismology Group (ESG) Report, 2001. 39. Lunder, P.J and Pakalnis R.C., Determination of Strength of Hard Rock Mine Pillars. Bull. Can Inst. Min Metall., 90 (103), 1997, pp51-55. 40. Lunder, P.J. Hard Rock Pillar Strength Estimation: An applied empirical approach, M.A.S.c. thesis University of BC, 1994. 41. Mah, P., Development of Empirical Design Techniques in Burst Prone Ground at the A. W. White Mine, CANMET Project No. 1-9180, DSS NO. 02SQ.23440-1-19180, Ottawa, 1995, Vol. 1-3. 42. Martin, CD. , and Read, R.S., AECL's Mine-by Experiment: A test tunnel in brittle rock, Hassani & Mitri (eds), AA Balkema Rotterdam, 1996. 126 43. McGarr, A., Spottiswoode, S.M., and Gay, N.C. Relationships of mine tremors to induced stresses and to rock properties in the focal region, Bull. Seism. Soc. Am., Vol 65, 1975, pp981-993. 44. Morrison, R.G.K. Report on the rockburst situation in Ontario Mines; Trans CIM Vol 45, 1942, pp.225-275. 45. NeuroShell Predictor 2.01, Ward System Group, Frederick, MD, 1997. 46. Obert, L., and Duvall, W.I., Rock Mechanics and the Design of structures in Rock. John Wiley & Sons, New York, 1967. 47. Obert, L., Windes, S.L., and Duvall, W.I., Standardization tests for determining the physical properties of mine rock. U.S. Bureau of Mines Report of Investigation.3891, 1946. 48. Ortlepp, W.D., Considerations in the design of support for deep hard-rock tunnels; 5th Congress Int. Society Rock Mechanics, Melbourne, 1983. 49. Ortlepp, W.D., Rockburst in South African Gold Mines: a phenomenological view. 1st Int Symp on Rockburst and Seismicity in Mines: Johannesburg, 1984. 50. Ortlepp, W.D., The design of support for the containment of rockburst in tunnels-an engineering approach, Rock Support in Mining and Underground Construction, Kaiser & McCreath (eds), Balkema, Rotterdam, 1992. 51. Pakalnis, R., MMPE 551 Course Notes, 2000. 52. Pakalnis and Assosiates, Goldcorp Inc Red Lake Mine internal report, 1997. 53. Pande, G.N., Beer G, William. J.R, Numerical Methods in Rock Mechanics, John Wiley and Sons limited, New York, 1990. 54. Rocque, P., Mine Design Document, Internal Report-Red Lake Mine, 2001 55. Salamon, M.D.G., A method of Design of Board and pillar Working. J.S. Afr. Inst. Min Metall., 1967, pp68-78. 56. Salamon, M.D.G., Rock Mechanics of underground excavations; Proc. 3rd Congr. Int. Soc. Rock Mech., Denver, Colorado, 1974, Vol.1, Part B, pp.951-1099. 57. Salamon, M.D.G., Rockburst Hazard and the fight for its alleviation in South African Gold Mines. Rockbursts: Prediction and Control, IMM, London, 1983. 58. Salamon, M.D.G., Energy considerations in rock mechanics: fundamental results, J.S. Afr. Min, Met., 1984, Vol.84, No.8, pp-233-246. 127 59. Sanborn-Barrie, M„ Skulski, T., and Parker, J., Three hundred million years of tectonic history recorded by the Red Lake Greenstone belt, Ontario; Geological Survey of Canada; Current Research 2001-CI9. 60. Sinclair, W.E., Rockburst-their Cause and Prevention: Chem., Metal. Mining Soc. South African Jour., 1936, Vol.37, p4-l 1. 61. Stacey, T.R., and Page, C.H., Practical Handbook for Underground Rock Mechanics. Clausthal- Zellerfel, West Germany: Trans Tech Publ., 1986. 62. Trifu, C.I and R.P. Young., Analysis of Stroung Ground Motion : An overview and pplication of Rockburst Studies, Engineering Seismology Lab, Internal ' Report to Mining Research Directorate, MRD -SM004, Dec ,1992. 63. Turchanov, I.A., Iofis, M.A., and Kasparyan, E.V., Principle of Rock Mechanics: TERRASPACE INC, 1979. 64. Vongpaisal, S., Yu, Y.S., Boyle, R., and Toew, N., CANMET. Sill Pillar recovery strategies at the East-South c zones, Red Lake Mine, Goldcorp Inc. Phase I. Job No. 514100, 1996. 65. Wang, J., Milne, D., and Pakalnis, R., Application of a Neural Network in the Empirical Design of Underground Excavation Spans. Trans. Instn. Min. Metal., 2002, Vol. m. 66. Wang, J., Empirical Underground Entry-Type Excavation Span Design Modification. In Proc 53rd. Annual Conf. Canadian Geotechnical Society, 2000. 67. Wiles, T.D. Map3D Mining Analysis Program Mine Modeling LTD., Melbourne, Australia, 1991. 68. Wiles, T.D. Correlation Between Local Energy Release Density and Observed Bursting Conditions at Creighton Mine. A report prepared under contract for LNCO Limited Mines Resource Sudbury, Ont Canada, 1998. 69. Wong, I.G., and McGarr, A., Implosinal failure in mining-induced seismicity: a critical review. 2nd Int. Symp. Rockbursts and Seismicity in Mines, Minneapolis, Minnesota, 1988. 70. Zern. E.N., Coal Miners Pocket Book, 11th edition, New York: McGraw Hill, 1926. 128 APPENDIX A FAILURE MODES 129 APPENDIX A- UNDERGROUND FAILURE MODES A. 1 Failure Modes The empirical design method is discussed briefly in this chapter/Section/Appendix as it applies to the six failure modes, which account for the instability of underground openings. These modes of failure are: • Beam failures • Voussoir block failure • Wedge failure • Chimney failure • Rock mass failure • Stress-induced failure These failure mechanisms are illustrated in Figure A l A. 1.1 Beam Failure Beam failure analysis assumes that rock mass behaves as an elastic beam. The analyses method has been adapted from civil engineering solutions for the bending of homogeneous isotropic and linear elastic materials such as concrete (Lang, 1994). Obert (1967) provides a good treatment of beam failure analysis. The following assumptions must be made to apply this type of analysis to the stability of underground structures: • A beam is a straight structural element whose length is longest when compared to its other dimensions. • The rock must be hard, massive and free of joints to a degree that it can reasonably be considered as homogenous, isotropic and linear elastic. • The beam must be continuous with the stope walls so that the beam-ends are considered to be fixed. • In the case of beam bending, no load is applied along the strike plane strain condition. • The beam is considered to have a uniform thickness. 130 (a) Rate or Beam Failure (c) Chimney failure (b) Vou*3oir Block Failure (d) Wedge Failure (e) Sires* Induced Failure (f| Rock Mass Failure Figure A l . Underground roof failure mechanisms (Lang, 1994) 131 For beams (or roofs) with built in ends as shown in Figure A2, the maximum shear stress (x ) at the ends of the beam and the maximum normal stress (a), at the ends of the beams are given as: W - - ^ ( A l ) yS1 ( < 7 ) m a x = ^ (A2) where: y = unit weight t = thickness of beam S= length of beam s F l o o r Figure A2. Beam (or roof) with built-in ends A. 1.1.1 Shear Failure When the ratio of strata thickness to span exceeds approximately 0.2, shear failure begins to dominate over flexural failure (Obert, 1967). Since the shear strength (x ) of a beam is given by: x = C + antan(c^) (A3) where: a n = horizontal compressive stress 132 C = cohesion of the plane of shear acting over the compressive zones (/) = friction angle of the plane of shear By re-arranging these equations, and defining the factor of safety, FOS as the ratio of shear strength to shear stress, the maximum allowable span to resist shear failure of the back in horizontally bedded strata is given by: S = 4(C + ontan(^)) (A4) Where the immediate beam (roof) is composed of more than one bed and the upper beds less rigid are partially supported by the bottom bed as shown in Figure A3, the load on the lowest beam can be calculated by the following equation: Va = iij/j + E2t2 + • • + Ejn n n (A5) where: E„ = Youngs Modulus of the nth layer y n = unit weight of the nth layer tn = thickness of the nth layer Bed separation mm ^^C^rr I I I Figure A3. Horizontal roof with multiple beds (Afrouz, 1992) 133 A. 1.1.2 Tensile Failure Similar to shear failure, maximum span can be determined using the ratios of tensile strength and stress. By setting a m a x = Ro where Ro is the modulus of Rupture (outer fibre tensile strength), and re-arranging, the maximum allowable span to resist tensile failure of the back in horizontally bedded strata can be determined by: A. 1.2 Voussoir Block Failure Stope backs as discrete blocks as in a masonry or Voussoir arch were first analyzed by Evans in 1941. It has been recognized since Roman times that arching can greatly increase the load bearing capacity of a beam. Beer and Meek (1982) later modified the Voussoir beams model as is illustrated in Figure A4. The concept conveyed in this figure is that the line of lateral thrust within such an arch, when traced on the beam span, approximates a parabolic arch. Voussoir Beam theory makes the following assumptions about the rock mass being analyzed. • The rock mass is assumed to be cut by linear discontinuities trending along the strike, such that the back can be assumed to be composed of discrete blocks. • It is assumed that there are no horizontal compressive stresses in the back transferred from the surrounding rock. • No tensile strength develops between individual blocks (c=0). (A6) 134 voussoir controling block central crack • abutments " (•) Voussoir Block Excavation Roof (b) Parabolic Arch Developed In Roof |« sM — 4" «» \ (c) Una of Thrust In Beam to Abutments (after Brady and Brown, 1985) FigureA4. Voussoir block theory (Brady and Brown, 1985) A. 1.2.1 Analytic Procedure Because the solution to the problem is indeterminate, two assumptions are required for the analysis. First the line of thrust is assumed to be parabolic, as mentioned, and secondly the load distribution at the center of the beam and abutment contact is assumed to be triangular as shown in Figure A4b.The triangular end load over a length nt where: 135 n = 1.5 1 - - (A7) V tj where: n= lateral load to depth ratio z= arch height t= beam thickness Applying moment equilibrium around the centroid of the half beam yields: ^ 5 2 = ^ (A8) 8 2 where: fc = the horizontal compressive stress at the center of the beam y = unit weight of beam S = horizontal span of beam Assuming that the'shape of the thrust arch acting in the beam is parabolic, the arc length L can be expressed by: L = S + ^ 1 (A9) 3s where L = arc length of parabolic thrust profile z= height of arch S= horizontal span The resultant force acts through the center of each force distribution, thus the initial moment arm for fc is given by: Int z0=t-— (A10) where: z 0 = initial moment are for fc t= beam thickness 136 As the beam deflects, the arch goes into compression and shortens by a length A L . If the arch height z 0 is shortened in compression due to A L , the new moment arm (z) can be computed by: 3S A L The incremental elastic shortening of the arch, A L is given by (Al l ) A L = favL (A12) where: f a v = the longitudinal stress on the beam E = Young's Modulus of the beam The average longitudinal stress in the beam is now estimated by considering the stresses in only a quarter of the beam, as shown in Figure 40c. At a distance S/4 from the abutment, the stress distribution is uniform over the arch depth. The average longitudinal stress f a v for this quarter of the beam, and hence for the entire beam, is given by: fav = ^fc\ 2 n) / A -i \ 3 + 2 ( A 1 2 ) A n explicit solution for the loading in the beam and beam deformation is not possible. A n iterative procedure is required, which begins with assuming a value for the initial load to depth ratio, n. A n initial value of n=0.5 will normally produce a stable solution. The procedure involves calculating sequentially fc, fav, L , A L , z and n. The process is repeated with the load to depth ratio n, used to calculate fc. Iterations continue until stable load to depth ratios are obtained. A . 1.2.2 Failure Modes Beer and Meek (1982) identified three possible failure modes for Voussoir arches as described below: 137 • Crushing at the hinges formed in the upper portion of the center of the beam and at the lower abutment contacts; • Shear at the abutment when the limiting shear resistance T(tanO) is less than the required abutment vertical reaction force V, (W/2); and, • Buckling of the roof beam with increasing eccentricity of lateral thrust giving rise to a snap through mechanism. For detailed discussion on the Voussoir arch theory refer to Brady and Brown's Rock Mechanics for Underground Mining. A. 1.3 Structurally Control Failure Structurally controlled failure (wedge failure) is a relatively common occurrence in underground metal mines. The intersecting discontinuity planes on the back or wall of an excavation create wedges. The failure occurs either through sliding along a surface or by the wedge's dead weight. The frequency, condition, and the orientation of the jointing, combined with the size of the excavation, determine the size of potential wedges. Wedge failure occurs in both stress states. It occurs when the immediate back is in a relaxed state or under high stress. When the back is under tension, the wedge comes off due to gravity while under compression, the wedge ejects out due to high horizontal stress. A. 1.3.1 Stereonet Analysis Techniques Wedge failure potentially can be analyzed using a stereonet. A good introduction to the use of stereonets for this purpose is provided by Hoek and Brown (1980). A simple example of a wedge of rock falling from the roof of an excavation in jointed rock is shown in Figure A5. The vertical line drawn through the apex of the wedge must fall within the base of the wedge for failure to occur with out sliding on at least one of the joint planes. 138 Figure A5. Conditions for gravity falls of roof wedges (Hoek & Brown, 1980) In a stereographic plot, the three great circles represent the joint planes. The intersection of the three planes represents the formed wedge and the vertical line through the apex of the wedge represents the center point of the net. If the three joints intersect to form a wedge in the roof of an underground excavation, but the vertical line through the apex of the wedge does not fall within the base of wedge, the failure can only occur by sliding on one of the joint surfaces or along one of the lines of intersection. This condition is represented stereographically if the intersection figure formed by the three great circles falls to one side of the center of the net as illustrated in Figure A6. YI V I/I 1 si IS i J h i f\ l/l / Its \ ^ / I If \  N I ft + \ r»*-H \ / v / Figure A6. Conditions for sliding failure of roof wedges (Hoek & Brown, 1980) 139 A . 1.3.2 Computational Techniques An underground wedge stability computer program called U N W E D G E can be used to represent the wedge graphically. This program enables the user to input the excavation geometry, joint patterns, and joint strength properties for use in the analysis. The program can analyze a wedge created by three intersecting joints in the roof or walls of an excavation. The size and shape of the wedge is displayed around the perimeter of the excavation. The program determines if the wedge is stable, falls out under gravity or slides on the plane. An example of an UNWEDGE analysis is given in Figure A7. The useful part of the computational technique is that it enables the design engineer to quickly determine the favourable excavation size and orientation which would take longer if plotted on a stereonet manually. Eg g » £• • u j 15 flu BI rj 3 a IE] i n ] o „ i " . -J? :s|| y js ! if ( / \ +* L 1 0 n O a M V , > *> u 01 -4 0 (4 <\ t 5 a 8 i • > i -M J n i | R ! _ H / \ 1 / N •4 Figure A69. Wedge failure analyzed using unwedge 140 A . 1.4 Chimney Failure Chimney Failure occurs when the entire crown or sill pillar above a stope slides as one block into the stope as shown in Figure A8. This type of failure is not common but has been responsible for some large-scale failures in the past. SurUca Figure A8. Typical chimney failure initiated by a weak dyke or fault (Afrouz, 1992) Chimney failure occurs in very weak rock mass such as schistose or in ore bodies where the hangingwall and footwall are defined by weak discontinuities. Hoek (1989) developed an equation for determining the factor of safety against shear on the sides of the failure block. The factor of safety against downward slide is given by: FS = 2 Txy Tyz X j (A13) Using this approach, chimney failure is defined to occur when the total shear strength along the sliding plane is a function of the cohesion, friction angle, horizontal stress and water pressure along the shear plane, is exceeded by the weight of the pillar. A . 1.5 Rock Mass Failure Rock mass failure or caving is defined as gradual unraveling failure into the stope. Given sufficient time, the failure could continue to cave until the void is filled or stop 141 when a stable shape has been reached by the caving (Lang, 1994). Figure A9 illustrates these two conditions. CAVING MAY CONTINUE UNTIL VOID IS FILLED Figure A9. Progressive rock mass failure (Lang, 1994) Clearly, the susceptibility of a stope to a rock mass failure is dependant upon many factors, the most important of which are: • Rock hardness • Joint spacing • Joint orientation • Joint condition • Ground water • Stress orientation • Excavation geometry 142 Empirical design techniques are the only methods available for analyzing the susceptibility of a rock mass failure. All empirical methods rely on a rock mass classification system that attempts to quantify the rock mass parameter, which contributes to weakness. Classification systems have been used to a limited extent in the past to predict stable spans, standup times and support requirements in underground openings. Unfortunately, however, much of the data has been compiled from civil engineering case histories, which require higher safety factors than mining operations. Two of the most common systems that have been used to develop span design graphs and which have gained broad acceptance in the mining industry are the Norwegian Geotechnical Institute (NGI-Q) rating system and the South African Council for Scientific and Industrial Research (CSIR) geomechanics rock mass rating. A discussion of the two classification systems follows: A. 1.5.1 NGI-0 Rock Mass Classification Barton, Lein and Lunde (1974) developed the Q-rating system at the Norwegian Geotechnical Institute (NGI) from a study of over 200 tunnels. The rating system covers the whole spectrum of the rock mass qualities from heavy squeezing ground to sound unjointed rocks, including 13 igneous, 24 metamorphic, 9 sedimentary rock types, and various types of joint fillings. The NGI-classification, or Q rating system was mainly developed to rate rock mass quality in the vicinity of tunnels. The six parameters chosen to describe the rock mass quality (Q) are combined as follows: RQD v J. J ( i V SRF (A14) where: RQD = rock quality designation J n = Joint set number J r = Joint roughness number Js= Joint alteration number 143 Jw= Joint water reduction number SRF = stress reduction factor The first quotient, RQD/ Jn, is a rough measure of the relative block size. The second quotient, J r / J a , represents the inter block shear strength. Rough, tight, unaltered joints will have higher shear strengths than smooth, open, and altered joints. The third quotient, J w /SRF, is a measure of the active stress in the rock mass. SRF can be a measure of the loosening load in the case of shear zones, a measure of the induced stress around the opening in the case of competent rock, or a measure of the squeezing or swelling load in plastic, incompetent rock. The factor, J w , is a measure of the water pressure that reduces the effective shear strength of the joints. The rating applied to individual parameters for the NGI Q system is provided in Table A l . The rock quality can range from Q=0.001 for exceptionally poor rock masses up to Q= 1000 on the logarithmic scale. Barton (1974) related the Q value with tunnel support requirement by defining the equivalent dimensions (De) of the excavation. This equivalent dimension, which is a function of both the size and the purpose of the excavation, is obtained by dividing the span, the diameter or the wall height of the excavation by a quantity called the excavation support ratio (ESR). Thus, ^ Span, diameter, orheight,m De = — - (A15) ESR where: De = Equivalent Dimension ESR= Excavation Support Ratio 144 Table A l . Classifications Rating for Q-system (Barton, 1976) Parameters Item and Description Value RQD Rock Quality Designation The total length of core pieces over four inches on length in an interval divided by the length of the interval and expressed as a percent Jn Number of Sets of Discontinuities Massive One Set One Set Plus Random Two Set Two Set Plus Random Three Set Three Set Plus Random Four or More Set Crushed Rock 0.5 2.0 3.0 4.0 6.0 9.0 12.0 15.0 20.0 Jr Roughness of Discontinuities Non-continuous joints Rough and wavy Smooth and wavy Rough and planar Smooth and planar Slickenside and planar Filled discontinuities 4.0 3.0 2.0 1.5 1.0 0.5 1.0 Ja Filling and wall Rock Alteration, Essentially Unfilled Healed Joints Staining only, no alteration Slightly altered joint walls Silty or sandy coatings Clay coatings Filling and Wall Rock Alteration, Filled Joint Sand or crushed rock filling Stiff clay filling less than 5mm thick Soft clay filling less than 5mm thick Swelling clay filling less than 5mm thick Stiff clay filling more than 5mm thick Soft clay filling more than 5mm thick Swelling clay filling less than 5mm thick 0.75 1.0 2.0 3.0 4.0 4.0 6.0 8.0 12.0 10.0 15.0 20.0 Jw Water Conditions Dry, or flow < 51itres/ minute locally Medium water flow Large inflow, unfilled joints Large inflow, filled joints with washouts Large inflow, unfilled joints, high transient flow Large inflow, unfilled joints, high continuous inflow 1.0 0.66 0.5 0.33 0.2 to 0.1 0.1 to 0.05 SRF Stress Condition Class Loose rock with clay filled discontinuities Loose rock with open discontinuities Shallow depth (50m or less) rock with clay filled discontinuities Rock with tight unfilled discontinuities, medium stress 10.0 5.0 2.5 1.0 The ESR is related to the use for which the excavation is intended and the degree of safety demanded, as shown in Table A2. 145 Table A22. Excavation Support Ratio for various opening Excavation Category ESR A Temporary mine openings 3-5 B Vertical shafts: Circular section Rectangular/square section 2.5-2.0 C Permanent mine openings, water tunnels for hydropower (Excluding high-pressure penstock), pilot tunnels, drifts and headings for large excavation 1.6 D Storage caverns, water treatment plants, minor highways and railroad tunnels, surge chambers, access tunnels 1.3 E Power stations, major highway or railroad tunnels, civil defense chambers, portals intersections 1.0 F Underground nuclear power stations, railroad stations, factories 0.8 The relation between existing maximum unsupported excavation span (SPAN) and Q around the excavation standing up for more than 10 years, show the following relationship. SPAN= 2Q 0 6 6 = 2(ESR) Q 0 4 (A16) The maximum design of unsupported span for various rock mass quality and excavation support ratio is given in Figure A10. The six parallel lines correspond to various excavation types and support ratios of 0.8 to 5. •: :• e 200 •c .• w,, 100 Z < 0, 50 to a 20 Ul i - 10 cc o 0. 5 a. 3 CO 2 z 3 4 10 40 100 400 1000) ROCK MAS  QUALITY, Q Excavation t; support ratio ESR ' i ) Temporary mine openings. .1 . t • Permanent; mine; openings, water tunnels lor hydro power (exciidTng Wgh pi»»»tire pen-stocks),pilot tunnels, drtfu and headings. ,) • Storage rooms,: water liealntent plants^  minor.:" ^ re cstt: bonnets. .0 • Power houses, major road ami rail tunnels, ctvH defense champers, portals. Intersections. • t-Umterground nuclear power stations, sports and public facilities, factories, etc. Figure A10. Recommended maximum unsupported excavation span for various rock mass quality and excavated support ratios (Barton, 1974) 146 The closeness with which an unsupported opening can be designed to the envelope of maximum design span will depend on the type and shape of the excavation, its use, the Q-value, the degree of safety, and the standup time required. If the maximum design span is exceeded or if some of the above conditions are not satisfied, the stand up time will be less than 10 years. A. 1.5.2 Geomechanics Classification (RMR System) Bieniawski (973) developed the Geomechanics classification or the rock mass rating (RMR) system. The rock mass rating system has also been used to predict stable spans, stand-up time, and support requirements. It was modified over the years as more case histories became available. However, it is important to state that the system has remained essentially the same in principle despite the changes. This engineering classification of rock masses, utilizes the following six parameters, all of which are measurable in the field and can also be obtained from borehole data: RMR= A + B + C+D + E + F (A17) where: A=Uniaxial compressive strength of intact rock material B=Rock quality designation (RQD) C=Spacing of discontinuities D=condition of discontinuities E=Ground water conditions G=Orientation of discontinuities The Geomechanics classification is presented in Table A3. The first five parameters are grouped into five ranges of value. Since the various parameters are not equally important for the overall classification of a rock mass, important ratings are allocated to the different value ranges of the parameters. The rating of each parameter is summed to obtain a value between 0 and 100. A higher rating indicates a better rock condition. Bieniawski (1984) has related the span to stand-up time and the rock mass rating for tunneling and mining case histories as shown in Figure A l 1. The graph illustrates the wide band defining the stable and potentially unstable zone. 147 Table A3 Geomechanics Classification of Rockmass DATE: LOCATION: NAME:. PARAMETER RANGE OF VALUES A Strength of Intact rock Material Point load strength Index >8Mpa 4-8 MPa 2-4 MPa 1-2 Mpa For this low range uniaxial test is preferred Uniaxial Compressive Strength > 200 Mpa 100-200 MPa 50-100 MPa 25-50 Mpa 10-25 MPa 3-10 MPa 1-3 MPa Rating 15 12 7 4 2 2 0 B Drill Core Quality (RQD) 90%-100% 75%-90% 50%-75% 25%-50% <25% Rating 20 17 13 8 3 C Spacing of Joints >3 m 1-3 m 0.3-1 m 50-300 mm < 50 mm Rating 30 25 20 10 5 D Condition of Joints Very rough surface Not continuous No separation Hard joint walls Slightly rough surfaces Separation < 1mm Hard joint walls Slightly rough surfaces Separation < 1mm Soft joint walls Gouge < 5mm thick or Slickenside Surfaces Joints open 1-5 mm Continuous joints Soft Gouge > 5mm thick or Joints open > 5 mm Continuous joints Rating 25 20 12 6 0 E Ground Water Inflow per 10 m Tunnel length None <25 liters/min 25-125 liters/min > 125 liters/min Ratio Joint water pressure Major principle stress 0 0.0-0.02 0.2-0.5 >0.5 General Conditions Completely Dry Moist only Water under moderate pressure Severe water problem Rating 10 7 4 0 F Rating Adjustment for discontinuity Orientation Strike and Dip Orientations of Joints Very Favourable Favourable Fair Unfavorable Very Unfavorable Tunnel 0 -2 -5 -10 -12 Ratings Foundation 0 -2 -7 -15 -25 Slopes 0 -5 -25 -50 -60 148 STAND-UP TIME, hr Figure A l l . Relationship between span, R M R and stand up time (Bieniawski, 1984) A correlation was proposed between R M R and the Q value (Bieniawski, 1976). A total of 117 case histories were analysed involving 68 Scandinavian cases, 28 South African cases, and 21 other cases documented from the United States and Canada. The results are plotted on Figure A12 from which it will be seen that the following relationship is applicable. R M R = 91nQ + 44 (A 18) Caution should be used when relating one to the other due to the different parameters and weightings employed by the respective systems (Pakalnis, 2000). Table A4 relates the rock mass descriptors to the individual classification system. 149 DC 1 • a c 1 o 0.001 0.01 0.1 1 10 Rock Mass Quality - Q 100 1000 Figure A12. Correlations between R M R and Q-Index (Bieniawski, 1984) Table A4. Relating RMR and Q with respect to descriptors (Pakalnis, 2000) Q Equivalent R M R (%) Q Rating Definition R M R (%) Equivalent Q R M R Definition 0.001-0.01 0-3 Exceptionally Poor 0 0.008 Very Poor Rock 0.01-0.1 3-23 Extremely Poor <20 0.07 Very Poor Rock 0.1-1 23-44 Very Poor 21-40 0.08-0.6 Poor Rock 1-4 44-56 Poor 41-60 0.7-6 Fair Rock 4-10 56-65 Fair 10-40 65-77 Good 61-80 7-55 Good Rock 40-100 77-85 Very Good 100-400 85-98 Extremely Good 81-100 61-504 Very Good Rock 400-1000 98-100 Exceptionally Good The Geomechanics classification provides guidelines for the selection of roof support. These guidelines depend on such factors as the depth below surface, excavation 150 size and shape and construction method. Support classifications for the geomechanics classification is given in Table A5. Table A5. Geomechanics Classification Guide for Excavation and Support in Rock Tunnels (Bieniawski, 1984) Rock Mass Excavation Support Class Rockbolts (20mm Dia., fully bonded) Shotcrete Steel Sets Very Good Rock Full Face: 3m advance Generally no support required except for occasional spot bolting RMR.-81-100 Good Rock Full Face Local bolts in 50mm in None RMR:61-80o 1.0-1.5m advance: crown 3m long, crown where Complete support 20m from face spaced 2.5m with occasional wire mesh required Fair Rock Top Heading and Systematic bolts 50-100mm in None RMR:41-60 Bench 4m long, spaced crown and 1.5-3.0m advance in 1.5-2.0min 30mm in sides top heading: crown and walls Commence support with wire mesh after each blast Complete support 10m From face Poor Rock Top Heading and Systematic bolts 100-150mm Light ribs RMR:21-40 Bench 4-5m long, in crown and spaced 1.5m 1.0-1.5m advance in spaced 1-1.5m in 100mm in where top heading: crown and walls sides required Install support with wire mesh concurrently with excavation - 10m from face Very Poor Multiple Drifts: Systematic bolts 150-200mm Medium to Rock 0.5-1.5m advance in 5-6m long, in crown and heavy ribs RMR:<20 top heading; spaced 1-1.5m in 150mm in spaced Install support crown and walls sides and 0.75m with concurrently with with wire mesh 50mm on face steel lagged excavation; shotcrete as Bolt inverted and soon as possible after blasting forepoling if required. Close invert. 151 A.6.6 Stress-induced Failure There are two types of stress-induced failure. The first type failure of is the result of mining induced stresses which exceed the strength of the rock mass. In competent, massive, elastic rock, this type of failure can take the form of spalling or rockbursting. In a jointed rock mass, a gradual yielding failure may take place. In cut and fill stopes, failure caused by high induced stress is most likely to occur in the back of the stopes as the sill pillar widths become smaller with each lift. It may also occur in very stiff post pillars. Figure A13 illustrates the stress-induced failures in sill pillars. Figure A13. High horizontal stresses developing in sill pillars (Lang, 1994) An analysis of the potential for this type of failure must take the form of analyzing the induced mining stresses at the boundaries of an excavation and comparing it to the rock mass strength. The second type of stress-induced failure is often caused by some geological structures. Geological structures such as dykes or faults, when situated near an excavation, can cause very intense ground working and thus result in instability in the 152 immediate back which in some cases may cause rockbursting. The second type of stress-induced failure is shown in Figure A14. Figure A14. Stress-induced failure caused by a dyke close to the roof (Afrouz, 1992) Stress-induced failure caused by geological conditions is discussed under span design. However, Chapters 5 are devoted to the analysis of stress-induced failures in sill and post pillars. 153 APPENDIX - B SPAN DATABASE 154 A P P E N D I X - B S P A N D A T A B A S E Rock mass rating values and its respective spans and stability used to determine the span graph. Number R M R (%) Span(m) Stability 1 55 18.6 2 2 77 12 1 3 40 6.4 3 4 57 13 1 5 47 9.2 2 6 73 8 1 7 79 24 2 8 25 3.5 3 9 79 17 1 10 75 26 2 11 58 12 1 12 77 20 1 13 49 14 3 14 38 5 2 15 68 20 2 16 56 6 1 17 45 7 2 18 28 14 3 19 35 3.5 3 20 61 5.9 1 21 55 3.1 1 22 77 20 1 23 80 12 1 24 52 4.3 2 25 72 5 1 26 42 6 2 27 50 9 2 28 68 21 2 29 56 5.9 1 30 60 10 2 31 78 28 2 32 65 6.5 1 33 55 2 1 34 70 9.2 1 35 70 5 1 36 79 6.7 . 1 37 69 3.7 1 38 75 5 1 39 69 4 1 40 70 4.6 1 155 Number RMR (%) Span(m) Stability 41 77 35 2 42 80 5 1 43 87 25 1 44 45 7 3 45 65 32 3 46 55 6.1 1 47 72 25 2 48 82 3.1 1 49 56 5 1 50 60 8.2 1 51 63 17 2 52 48 15 3 53 46 4.5 2 54 69 25 2 55 52 4.6 2 56 78 35 2 57 61 11 1 58 54 5 1 59 25 3.5 3 60 25 3.5 3 61 25 3.5 3 62 65 7 1 63 63 24 3 64 40 13.1 3 65 73 10 1 66 77 18 1 67 40 4.2 3 68 72 5.5 1 69 58 13 1 70 45 3.1 3 71 64 16 1 72 58 4.9 1 73 79 18 1 74 38 5 2 75 64 8.2 1 76 79 14 1 77 65 18 2 78 55 6.1 1 79 63 20 2 80 51 11.9 2 81 62 3 1 82 65 5.6 1 83 65 12 1 84 50 3.7 1 85 38 5 2 156 Number RMR (%) Span(m) Stability 8 6 8 5 1 5 1 8 7 7 4 1 0 . 7 1 8 8 6 4 2 0 2 8 9 7 4 1 4 1 9 0 4 5 7 2 9 1 7 8 2 0 1 9 2 7 7 2 3 1 9 3 6 3 2 4 3 9 4 7 0 6 1 9 5 6 5 2 . 4 1 9 6 5 0 3 . 7 2 9 7 7 8 1 5 1 9 8 6 8 5 . 2 1 9 9 7 4 9 . 2 1 1 0 0 2 5 1 3 3 1 0 1 2 4 4 . 3 3 1 0 2 6 7 6 . 7 1 1 0 3 6 4 2 5 3 1 0 4 6 9 4 1 1 0 5 5 9 11 1 1 0 6 6 7 9 1 1 0 7 5 4 2 . 7 1 1 0 8 3 3 3 . 5 3 1 0 9 6 8 1 2 1 1 1 0 7 8 2 6 1 1 1 1 7 1 8 1 1 1 2 6 0 1 5 2 1 1 3 8 0 2 1 1 1 4 6 7 2 3 2 1 1 5 6 8 2 1 2 1 1 6 4 5 7 2 1 1 7 6 8 5 . 5 1 1 1 8 6 0 6 1 1 1 9 6 0 5 1 1 2 0 8 5 1 5 1 1 2 1 7 5 3 .1 1 1 2 2 4 0 7 2 1 2 3 6 5 1 5 2 1 2 4 6 2 9 . 5 1 1 2 5 2 5 6 3 1 2 6 6 0 2 . 5 1 1 2 7 6 2 4 . 9 1 1 2 8 7 5 2 6 2 1 2 9 6 0 4 . 6 1 1 3 0 8 1 4 1 3 157 Number R M R (%) Span(m) Stability 131 71 5 1 132 82 2.7 1 133 49 12 2 134 69 3.1 1 135 68 17 2 136 25 3.5 3 137 62 12 1 138 81 9 1 139 67 10 1 140 67 6 1 141 69 20 1 142 87 19 1 143 50 9 2 144 43 7 2 145 64 35 2 146 77 20 1 147 50 5.7 2 148 63 24 3 149 78 39 2 150 78 20 1 151 54 2 1 152 70 14 1 153 38 5 2 154 55 4.6 1 155 45 3.1 3 156 58 8 1 157 67 3.8 1 158 63 10 1 159 80 20 1 160 77 25 2 161 43 10.1 2 162 72 23 2 163 64 3.7 1 164 79 20 1 165 79 25 1 166 50 8.2 2 167 78 18 1 168 78 28 2 169 80 6.1 1 170 74 2.7 1 171 47 2.7 1 172 65 18 2 173 75 15 1 174 44 6 2 175 54 9 3 158 Number RMR (%) Span(m) Stability 176 67 12 1 177 81 5.8 1 178 78 15 1 179 60 9.2 1 180 57 12.2 2 181 73 20 1 182 72 12 1 183 62 5.5 1 184 29 4 3 185 40 4 2 186 52 7.6 2 187 40 4.6 2 188 70 11 1 189 85 14 1 190 55 4.9 2 191 69 4.6 1 192 62 22 3 193 76 24 1 194 69 5 1 195 70 11 1 196 48 20 3 197 79 25 1 198 73 25 2 199 65 6.1 1 200 72 17 1 201 53 10 2 202 76 6 1 203 55 4.9 3 204 66 12.5 1 205 64 25 3 206 55 9.2 2 207 40 12.2 3 208 66 16 1 209 53 12.2 3 210 45 4.8 1 211 57 14 1 212 68 20 2 213 80 6 1 214 64 4.1 1 215 48 15 3 216 70 9.2 1 217 63 24 3 218 72 8 1 219 75 21 2 220 70 6 1 159 Number R M R ( % ) Span(m) Stability 221 70 6.1 1 222 65 8 1 223 55 11 2 224 56 5 1 225 52 6.1 1 226 76 24 1 227 67 25 3 228 68 6 1 229 63 20 2 230 70 12 1 231 67 21 1 232 60 20 3 233 43 7 2 234 78 28 2 235 80 20 1 236 38 5 2 237 58 10 1 238 70 30 3 239 55 5 1 240 67 2 1 241 40 7 2 242 58 7.3 1 243 55 6.1 2 244 79 25 1 245 80 18 1 246 30 3 3 247 73 16 1 248 75 18 1 249 79 31 2 250 62 8.5 2 251 73 20 1 252 67 10.7 1 253 77 25 1 254 28 15 3 255 40 4 2 256 50 3 1 257 57 3.4 1 258 60 1.8 1 259 60 4 1 260 55 7.9 2 261 48 8 2 262 42 5 2 263 67 9 1 264 57 3.1 1 265 70 5 1 160 Number RMR (%). Span(m) Stability 266 66 12.2 1 267 50 5 2 268 65 7.6 1 269 83 15 1 270 45 2.4 1 271 82 14 1 272 48 15 3 273 54 10 3 274 64 3.7 1 275 71 6.2 1 276 80 6.7 1 277 66 17 2 278 66 1.8 1 279 78 35 2 280 55 7.9 2 281 64 2.7 1 282 66 2.4 1 283 62 4 1 284 54 10 2 285 65 5.2 1 286 42 6 2 287 52 7.3 1 288 60 3.8 1 289 77 12 1 290 70 11 1 291 54 6.1 1 292 77 35 3 293 48 7 2 294 78 25 1 295 69 7.3 1 296 63 7 1 297 73 20 1 298 77 16 1 299 60 2.5 1 300 67 18 2 301 50 3.5 1 302 65 13 1 303 63 24 3 304 70 8 1 305 60 8 1 306 52 6 2 307 78 35 2 308 70 4.6 1 309 70 35 3 310 79 32 2 161 Number RMR (%) Span(m) Stability 311 70 7 1 312 68 8.2 1 313 63 24 3 314 63 24 3 315 72 24 2 316 70 20 1 317 60 11 1 318 46 2.7 2 319 80 19 1 320 70 2.4 1 321 79 18 1 322 47 2.7 2 323 66 22 2 324 70 2.4 1 325 72 5 1 326 87 15 1 327 60 22 3 328 74 13 1 329 69 6.7 1 330 67 30 3 331 69 4.9 1 332 78 39 2 333 73 20 1 334 64 17 2 335 45 3.1 1 336 67 9 1 337 69 25 2 338 60 7.3 2 339 70 40 3 340 77 16 1 341 72 16 1 342 45 9.2 2 343 63 5.5 1 344 87 15 1 345 78 15 1 346 55 12 347 80 12 1 348 70 20 1 349 78 18 1 350 51 3.8 1 351 67 25 352 77 22 1 353 70 2 1 354 49 4.4 1 355 65 15 2 162 Number RMR (%) Span(m) Stability 356 54 10 2 357 63 3.7 1 358 79 6.1 1 359 70 11.9 1 360 65 5.2 1 361 57 6.4 1 362 74 6.1 1 363 66 17 364 85 15 1 365 63 8.5 1 366 51 6 367 61 10 1 368 68 16 369 77 20 1 370 78 19 1 371 70 32 372 49 8 373 64 15 1 374 70 11 1 375 72 10.4 1 376 51 13 377 68 2.4 1 378 63 24 379 78 19 1 380 64 11 1 381 71 10 1 382 40 8 383 69 25 384 50 6.1 1 385 67 25 386 58 10 1 387 65 5 1 388 67 20 389 69 5.5 1 390 69 15 1 391 81 23 1 392 69 4 1 393 75 5.4 1 394 63 17 1 395 85 16 1 396 55 7 1 397 61 6.4 1 398 77 25 1 399 43 6 2 163 APPENDIX - C PILLAR STRENGTH & STRESS DETERMINATION 164 APPENDIX - C PILLAR STRENGTH AND STRESS DETERMINATION C.l Pillar Strength The principle of designing any underground structure is simple: >! ( C 1 ) Stress That is, the pillar will remain stable if the load (stress) applied is less than its long-term load bearing capacity. Difficulties often arise in estimating the pillar's ultimate strength in addition to the precise load acting upon it because of the ever-changing stress conditions during the mining process. A rock mass is generally not a homogeneous isotropic medium and as such the determination of pillar strength is highly dependent on the factors that affect the strength of a rock mass including, but not necessarily limited to: • The intact strength of pillar material • The pillar geometry (width to height ratio) • The structural features within the pillar • The material properties of the pillar, such as deformational characteristics • The effects of blasting on the pillar C. l . l Pillar Strength Determination There are many factors, as mentioned above, that may influence the strength of a mine pillar. The number of potentially significant variables makes pillar strength determination using analytical methods very difficult. Some of these variables may not be significant under selected mining conditions. For such situations, pillar strength may be estimated empirically. 165 C.1.2 Empirical Design Methods Various researchers have developed a number of empirical methods for pillar strength determination. These are: • The linear shape effect formula, • The power shape effect formula, • The size effect formula, • The Hoek-Brown (1980) formula These techniques relate to pillar width, pillar height, intact rock strength, and factor of safety to estimate pillar strength. The width of the pillar is measured normal to the major principle stress in the pillar and height is measured parallel to the major principle stress in the pillar. With the exception of Hoek-Brown (1980), these formulae all take the general form of the equation: op =K[A+B(^-)] (C2) n where: op = pillar strength K = uniaxial compressive strength of pillar material w = pillar width h = pillar height A, B, a & b = empirically derived constant The generalized equation has been divided into two well known empirical methods: the "size effect formula" and the "shape effect formula". The shape effect formula uses empirical constants "a" and "b" that are equal, meaning the pillar strength independent of the pillar volume. The size effect formulae uses empirical constants "a" and "b" that are unequal, meaning that for pillars of the same shape. The pillar strength will decrease as pillar volume increases. Various researchers such as Bieniawski (1984), have shown that with increasing sample size, there will be a corresponding decrease in strength, this is thought to result from an increase in the number of structural defects in the sample specimen. 166 C. 1.2.1 The Linear Shape Effect Formula The linear shape effect formula assumes that pillars of equal W/H ratio will have equal strength, independent of the pillar volume, and that the relationship between pillar strength and pillar width/height ratio will be a linear form. The linear shape effect formula is defined as: op =K[A+B(-^)] (C3) h where: oy= pillar strength K = uniaxial compressive strength of pillar material w = pillar width h = pillar height A, B = empirically derived constants The constants "A" and "B", determined by various authors for this formula, are listed in Table CI. J Table CI. Linear Shape Effect empirical constants, "A" and "B", from various authors Source A B w/h Bunting (1911) 0.700 0.300 0.5-1.0 Obert etal. (1960) 0.778 0.222 0.5-2.0 Bieniawski (1968) 0.556 0.444 1.0-3.1 Van Heerden (1973) 0.704 0.296 1.14-3.4 Sorensen and Pariseau (1978) 0.693 0.307 0.5-2.0 Zern (1954) 0.5 0.5 1.0 Hazen and Artier (1976) 0.5 0.5 1.0 Holland (1956) 0.5 0.5 1.0 Morrison et al 0.5 0.5 1.0 167 C. 1.2.2 The Power Shape Effect Formula The Power Shape Effect Formula on the other hand assumes that the strength of a pillar is governed by the square root of the width of the pillar. The formula is defined by equation C4. This relationship has been proposed by authors such as Zern (1926), Holland (1956), and Hazen & Artier (1976). where: a p = pillar strength K = uniaxial compressive strength of pillar material w = pillar width h = pillar height C. 1.2.3 The Size Effect Formula The empirical size effect strength formula have been developed by a number of researchers in the form of Equation 52: A number of researchers have a proposed strength formula in this form and the values of the empirical constants suggested by each author are presented in Table C2. (C4) (C5) where: op = pillar strength MPa w = pillar width h = pillar height a & b = empirical constants 168 Table C23. Size Effect Formula empirical constant, "a" and "b" from various authors Source a b Streat (1954) 0.5 1.0 Holland-Gaddy(1962) 0.5 1.0 Greenwald etal(1939) 0.5 0.833 Hedley and Grant (1972) 0.5 0.75 Salamon and Munro (1967) 0.46 0.66 Bieniawski (1968) 0.16 0.55 The method presented in Table C2 represents the accumulated knowledge with respect to pillar design based upon the "Size Effect Formula". C.1.3 The Hoek and Brown Pillar Strength Formula Hoek and Brown (1980) proposed a series of curves for the estimation of pillar strength as shown in Figure C l . The curves were developed based on numerical modeling and the distribution of failed rock inside pillars of different shapes and for a wide range of rock mass qualities using the empirical rock mass failure criteria: op = o3 + (maco3 + so c 2)1 / 2 (C6) where: a p = average pillar strength 03 = minimum principle stress a c = uniaxial compressive strength of the intact pillar material m&s = empirical constants based on the rockmass quality of the pillar material 169 3.0 -2.5 -Intact samples of fine grained igneous crystalline rock Bl » 17. » - 1 2.0 -Peri / good quality rook mass m - 8.5, s - 0.1 1.5 1.0 Good quality rock mass m - 1.7, s - O.OO'i 0.5 Fair quality rock mass _ i — " - 0.3^, s - 0.0001 . Poor quality rock mass m - 0.09, s - 0.00001 0 ^ 1 1 | _j 0 1 2 3 Pi 1lar w i d t h / h e i g h t Wp/h Figure CI. Strength curves based on the theoretical distribution of rock mass failure in a pillar (Hoek & Brown, 1980) Hoek and Brown (1980) proposed that the influence of structural deficit and pillar volume can be quantified through the use of rock mass classification parameters. This classification results in empirical parameters "m" and "s" for a given rock type and are used in equation C6 to determine the corresponding rockmass strength. Figure C2 illustrates the conceptual transition of a rock mass from an intact condition to a heavily jointed condition. 170 underground excavation intact rock single discontinuity two discontinuities several discontinuities rock mass Figure C2. Idealized illustration of the transition from intact rock to a heavy jointed rock mass with increasing sample size (Hoek & Brown 1980) In 1988, Hoek and Brown proposed a revised set of relations between Bieniawski's rock mass rating and the parameters "m" and "s". For Disturbed rock masses m mi = exp RMR -100 v s = exp 14 , f RMR -100^ v (C7) (C8) For Undisturbed or interlocking rock masses m mi — = exp RMR-IQQ 28 J s = exp RMR -\0ti\ (C9) (C10) where mi values of for different rock are given for the intact rock in Table C3. 171 Table C3. Values of the constant m, (Hoek and Brown, 1997). Rock Class Group Texture Type Course Medium Fine Very Fine Conglomerate Sandstone Siltstone Claystone Clastic (22) Greywacke (18) 19 9 4 Chalk Organic 7 Coal Non-(8-21) :NTARY Clastic Carbonate Breccia (20) Sparitic Limestone (10) Micritic Limestone 8 SEDIME Chemical Gypstone 16 Anhydrire 13 Non Foliated Marble 9 Hornfels (19) Quartzite 24 ORPHIC Slightly foliated Migmatite (30) Amphibolite Mylonites 25-31 (6) METAM Foliated Gneiss 33 Schists 4-8 Phyllites (10) Slate 9 Granite Ryolite Obsidian Light 33 Grandiorite (30) Diorite (28) (16) Dacite (17) Andesite 19 (19) Dark Gabro 27 Norite Dolerite (19) Basalt (17) 22 IGNEOL Extrusive pyroclastic type Agglomerate Breccia (20) (18) Tuff (15) 172 In 1995, Hoek introduced the Generalized Hoek-Brown failure criteria and in 1997 revised the Generalized Hoek-Brown failure criteria slightly. The Geological Strength Index was introduced to overcome the deficiencies in Rock Mass Rating (RMR) for very poor rock quality rock mass. The distinction between disturbed and undisturbed rock masses was eliminated on the basis that disturbance is generally induced by engineering activities and should be allowed for by downgrading the value of the Geological Strength Index. The generalized Hoek Brown equation is given as: Jp - O3 + G c , (73 ^ mo h s (Cll) V ov j where: mb = the value of the constant in for the rock masses s & a = constants that depend upon the characteristic of the rock mass. a c = the uniaxial compressive strength of the intact rock pieces ai & 03 = axial and confining effective principle stresses respectively For GSI > 25 (undisturbed rock masses) mb (GSI-\QO\ — = exp — mi \ 28 J s = exp a =0.5 "G5/-100 , 9 (C12) (C13) For GSI < 25 s= 0 a =0.65 GSI 200 (C14) For higher quality rock masses (GSI > 25), the value of GSI can be estimated directly from the 1976 version of Bieniawski's rock mass rating with ground water set to 10 (dry) and the Adjustment for joint orientation set to 0 (very favorable). 173 For very poor quality rock masses, the value of rock mass rating is very difficult to estimate and balance between the ratings no longer gives a reliable basis for estimating rock mass strength, therefore, Barton's Q value should be used. The Geological Strength Index (GSI) can be obtained from the rock mass quality Q' by the following equations: If the 1989 version of Bieniawski's Rock Mass Rating classification is used then where: RMR ' 89 has the ground water rating set to 15 andthe adjustment for joint orientation set to zero. Hoek and Brown (1997) suggested that when assessing the value of GSI in the field is related to blast damage, some attempt should be made to compensate for the lower value of GSI. Of all strength determination methods discussed above, the Hoek and Brown Strength Formula is widely used as compared to other methods. Possessing an understanding of how to determine the strength of the pillar, discussion on the pillar strength determination follows. C.2 Pillar Stress Design methods are largely based on equating stress to strength so that a stable equilibrium exists. This requires that an estimate of stress be made with levels of accuracy commensurate to strength estimates. The stress acting on a pillar is a function of, but not necessarily limited to: GSI = 91nQ' + 44 (C15) GSI = RMR'89 -5 (C16) • The in-situ stress conditions • The mining induced stress changes 174 • The effects of geological features such as faults and joints • The shape and orientation of pillars • The spatial relationship between pillars and mine openings • The effects of ground water C.2.1 Pillar Stress Determination In an underground pillar design, it is difficult to determine the actual stress that will be acting on a pillar. As mentioned previously, pillar stress depends on number of factors, which include: • The in-situ stress conditions • The mining induced stress changes • The effects of geological features such as faults and joints • The shape and orientation of pillars • The spatial relationship between pillars and mine openings • The effects of ground water The two methods of calculating pillar stress are tributary area theory and numerical modeling. Tributary area theory utilizes a simplified approach to stress redistribution whereas, the numerical modeling technique involves the use of elasticity theory to determine stress redistribution. In contrast to the simplicity of the tributary area theory, numerical modeling requires the use of a computer due to the complexity associated with the calculation process. The importance of valid determination of the in-situ stresses must not be overlooked. It is common to assume that the vertical in-situ component will be equal to the weight of the overlying strata. In horizontally bedded deposits this may be adequate for determining normal stress acting on pillars. In irregular, non tabular deposits, however, the induced pillar stress is a factor of the three principle stresses, not just the vertical component. In-situ stresses in a particular locality may not vary greatly on 175 average but they can vary significantly on a local scale as a result of geological structures and the proximity to the surface. The tributary area theory and numerical modeling techniques used to determine the pillar stress are discussed in the following section. C.2.1.1 Tributary Area Theory The tributary area theory assumes that when stopes are opened there is an equal and symmetric stress redistribution regarding the size and location of the pillars created. It is often described using the analogy of a smooth flowing stream obstructed by bridge piers as shown in Figure C3. In order to accommodate the flow through the gaps between the piers, the stream-lines are crowded together and the flow velocity increases through these gaps. The extent to which the flow of velocity increases depends upon the ratio of the width of the stream to the sum of the distances between piers. Figure C3. Sketch of streamlines in a smoothly flowing stream obstructed by three bridge piers (Hoek and Brown 1980) Tributary area theory has been used with the great success in horizontally bedded deposits that are uniform and cover a large area such as horizontal bedded coal deposits or room and pillar mine layout. 176 Figure C4 illustrates a typical square room and pillar layout used in mining a horizontal bedded deposit. Assuming that the pillars shown are part of a large array of pillars and the stress is uniformly distributed over these pillars, the average pillar stress is given as: wo i op = Yh(l+ — f (C17) ho where: ap = average pillar stress y = unit weight of rock h = depth of overburden wo = width of opening wp = width of pillar Figure C4. Typical square pillar layouts (Hoek &Brown, 1980) 177 Figure C5. shows the application of tributary area theory for different pillar layouts. T i w P rr \ [M|.; J I ... | I L H D D SQUARE PILLARS - « p - Y z ( 1 + w o / W D ) 2 ••••,-,.„•,.•„ i l."^,, _JL n _ L i ( _ . , a — — _ Rock coiu»nn area IRREGULAR PILLARS RECTANGULAR PILLARS - o p - Y z { l *U0/W5)(1 i- L0/Lp) a - Y 7.Rock column area P i I l a r area Figure C5. Typical pillar layouts showing loads carried by various pillars assuming total rock load to be uniformly distributed over all pillars (Hoek & Brown, 1980) C.2.1.2 Numerical Design Methods The other method used to determine pillar stresses are the numerical design methods. In recent years, several numerical methods have been developed specifically for use in underground rock mechanics design. Numerical modeling techniques are able to determine stress redistribution around mine openings with a triaxial stress field either in two dimensions or three dimensions. This alternative to tributary area theory for complex geometry makes pillar stress determination more accurate. In simplistic terms, numerical modeling can be described with Figure C6. A region R is defined in a medium and loading conditions are applied to the region. Excavation (E) is then created in the medium. The principle functions of numerical modeling are to calculate the magnitude and orientation of the stresses and displacements acting in the vicinity of the excavation (Hudyma, 1988). The re-distribution of stresses may be based on elastic and/or plastic behaviour of the medium. 178 Figure C6. An idealized sketch showing the principle of numerical modeling of underground excavations (Hudyma, 1988) C.2.1.3 Types of Modeling Methods Individual computational methods were developed to analyze problems with respect to specific properties of the medium. Brown (1987) divided these properties into three broad groups. • Differential continuum method • Integral method • Differential discontinuum method Pande, Beer and Williams (1990) describe the three numerical methods as follows: C.2.1.3.1 Differential Continuum Methods Differential continuum method is also known as finite element method (FEM). This method essentially involves dividing the body into smaller "elements" of various 179 shapes (triangular or rectangular in two-dimensional cases and tetrahedral or block in three dimensional cases) held together at the nodes, which are corners of the elements. The larger the number of elements used to model the problem, the better the approximation to the solution. Displacements at the nodes are treated as unknowns and are calculated. Stresses are calculated at one or more points inside each of the elements. Each element can have different material properties. Figure C7 illustrates a typical finite element model. Figure Cl. Development of a finite element model of a continuum problem, and specification of element geometry and loading for a constant strain, triangular finite element (Brady & Brown, 1985) A major limitation of the application of finite element methods to exterior problems is that an arbitrary boundary to the problem must be defined. The time requirement for continuum methods for data preparation and solution time can be extremely large if the problem domain is extended sufficiently so that far field stress conditions are satisfied. C.2.1.3.2 Integral Methods Integral methods also known as Boundary Element Methods (BEM) are becoming popular numerical methods. In this method, only the surface of the rock mass to be analyzed needs to be discretized which greatly reduces the amount of data needed to describe the problem and consequently the amount of computer time needed to complete the processing. i ? un i i 180 Whenever there is a change of material properties, the surface defining the separation has to be discretized. Thus, if there are a number of layers of different material, data preparation can still become complex. Boundary element methods are very efficient methods for homogenous linear elastic problems, particularly in three dimensions. C.2.1.3.3 Discontinuum Method The discontinuum method, also known as Distinct Element Method (DEM), is based on treating the rock mass as a discontinuum rather than continuum as is the case in the finite element method and boundary element method. When loads are applied, the changes in contact forces are traced with time. The equation of dynamic equilibrium for each element is repeatedly solved until the laws of contact and boundary are satisfied. Figure C8 illustrates a typical distinct element method. <»> (b) (c) new position • | old position Figure C8. Normal and shear modes of interaction between distinct elements (Brady & Brown, 1985) There are, however several drawbacks. Firstly, the parameters required for the description of material behaviour must be chosen quite carefully in addition to certain additional parameters such as the damping of the system. Secondly, the computation time required to solve even simple problems can be excessive. 181 C.2.3 Discussion Appendic C describes several methods of determining the stress and strength of pillars. For pillar strength determination, the Hoek and Brown strength formula is widely used. The Linear Shape Effect formula, the Power Shapes Effect formula and the Size Effect formula are more applicable to coal and room and pillar mining methods. Lunder and Pakalnis (1997), used the combined shape and size effect formulas, produce the pillar stability curves, which is one of the failure criteria and will be discussed later in the section. Numerical models are widely used for the pillar stress determination. Several types of numerical model are available. The boundary element method and the finite element method are commonly used in the industry. Each of the element methods has their advantages and disadvantages. The boundary element method reduces the amount of data needed to describe the problem and thus reduces the computer time needed to complete the processing. The finite element method on the other hand gives more accurate results, however the time required for the data preparation and solution time can be extremely large.. 182 APPENDIX - D INDUCES PILLAR STRESS 183 APPENDIX - D INDUCED PILLAR STRESSES Deviatoric stress and induce stress ratio per lift. 31-lSub Elevation Lift Name Sigma 1 Sigma 1 Sigma 3 Sigma 3 Deviatoric UCS Induced (psi) (MPa) (psi) (MPa) Stress (Mpa) JMPa) Stress Ratio 31-826-2 Sill 10948 5571 76 38 37 180 0.42 31-826-2 Cut1 11109 3615 77 25 52 180 0.43 31-826-2 Cut2 12617 2280 87 16 71 180 0.48 31-826-2 Cut3 12808 2880 88 20 68 180 0.49 31-826-2 Cut4 13771 2849 95 20 75 180 0.53 31-826-2 Cut5 14830 2937 102 20 82 180 0.57 31-826-1 Sill Access 10432 4041 72 28 44 180 0.40 31-826-1 Sill Cut 10283 3729 71 26 45 180 0.39 31-826-1 Cut1 10702 4653 74 32 42 180 0.41 31-826-1 Cut2 11840 3030 82 21 61 180 0.45 31-826-1 Cut3 12556 2806 87 19 67 180 0.48 31-826-1 Cut4 14066 3455 97 24 73 180 0.54 31-826-1 Cut5 14513 3968 100 27 73 180 0.56 31-826-4 Sill 10798 2440 74 17 58 180 0.41 31-826-4 Cut1 11994 2884 83 20 63 180 0.46 31-826-4 Cut2 13721 3098 95 21 73 180 0.53 31-826-4 Cut3 14517 3904 100 27 73 180 0.56 31-826-4 Cut4 15486 4523 107 31 76 180 0.59 31-826-4 Cut5 15974 4922 110 34 76 180 0.61 31-826-4 Cut6 17487 5771 121 40 81 180 0.67 \ 184 32-1 Sub Elevation Lift Name Sigma 1 Sigma 1 Sigma 3 Sigma 3 Deviatoric UCS Induced (psi) (MPa) (psi) (MPa) Stress (Mpa) (MPa) Stress Ratio 32-826-1OW Sill 11766 3546 81 24 57 180 0.45 32-826-1OW Cut1 13187 4452 • 91 31 60 180 0.51 32-826-1 OW Cut2 13750 4015 95 28 67 180 0.53 32-826-1 OW Cut3 15052 4708 104 32 71 180 0.58 32-826-1 OW Cut4 14655 4801 101 33 68 180 0.56 32-826-1 OW Cut5 14671 4801 101 33 68 180 0.56 32-826-8W Sill 10408 3977 72 27 44 180 0.40 32-826-8W Cut1 10332 3616 71 25 46 180 0.40 32-826-8W Cut2 11290 2620 78 18 60 180 0.43 32-826-8W Cut3 12281 2591 85 18 67 180 0.47 32-826-8W Cut4 12635 2978 87 21 67 180 0.48 32-826-8W Cut5 0 0 0 180 0.00 32-826-1 Sill 11361 2438 78 17 62 180 0.44 32-826-1 Cut1 11960 2554 82 18 65 180 0.46 32-826-1 Cut2 12873 2315 89 16 73 180 0.49 32-826-1 Cut3 14210 2252 98 16 82 180 0.54 32-826-1 Cut4 15135 3133 104 22 83 180 0.58 32-786-1 Sill 10449 3807 72 26 46 180 0.40 32-786-1 Cut1 13121 3480 90 24 66 180 0.50 32-786-1 Cut2 14863 4463 103 31 72 180 0.57 185 34Level Elevation Lift Name Sigma 1 Sigma 1 Sigma 3 Sigma 3 Deviatoric UCS Induced (psi) (MPa) (psi) (MPa) Stress (Mpa) (MPa) Stress Ratio 34-806-4 Sill 11489 2747 79 19 60 180 0.44 34-806-4 Cut1 13273 3133 92 22 70 180 0.51 34-806-4 Cut2 14216 3995 98 28 70 180 0.54 34-806-4 Cut3 14784 4231 102 29 73 180 0.57 34-806-4 Cut4 15465 4846 107 33 73 180 0.59 34-806-4 Cut5 15734 4314 109 30 79 180 0.60 34-806-5 Sill 10872 3114 75 21 54 180 0.42 34-806-5 Cut1 11933 2278 82 16 67 180 0.46 34-806-5 Cut2 13344 3085 92 21 71 180 0.51 34-806-5 Cut3 14034 3352 97 23 74 180 0.54 34-806-5 Cut4 14066 3907 97 27 70 180 0.54 34-806-5Cut5 14957 4323 103 30 73 180 0.57 34-786-1 Sill 11855 3301 82 23 59 180 0.45 34-786-1 Cut1 12351 3085 85 21 64 180 0.47 34-786-1 Cut2 14209 3838 98 26 72 180 0.54 34-786-1 Cut3 15106 4181 104 29 75 180 0.58 34-786-1 Cut4 15353 5039 106 35 71 180 0.59 34-786-1 Cut5 16340 5825 113 40 73 180 0.63 34-786-1 Cut6 19616 4833 135 33 102 180 0.75 34-806-7E Sill 12298 2716 85 19 66 180 0.47 34-806-7E Cut1 12840 2923 89 20 68 180 0.49 34-806-7E Cut2 13786 3323 95 23 72 180 0.53 34-806-7E Cut3 14499 3676 100 25 75 180 0.56 34-806-7E Cut4 14931 3560 103 25 78 180 0.57 34-806-7E Cut5 15639 3495 108 24 84 180 0.60 34-806-3E Sill 10569 2146 73 15 58 180 0.40 34-806-3E Cut1 10800 2657 74 18 56 180 0.41 34-806-3E Cut2 10172 2133 70 15 55 180 0.39 34-806-3E Cut3 10155 2139 70 ' 15 55 180 0.39 34-806-3E Cut4 9814 2257 68 16 52 180 0.38 34-806-3E Cut5 9944 1339 69 9 59 180 0.38 186 36-2 Sub Elevation Lift Name Sigma 1 Sigma 1 Sigma 3 Sigma 3 Deviatoric UCS Induced Stress (psi) (MPa) (psi) (MPa) Stress (Mpa) (MPa) Ratio 36-786-1 Sill 15191 105 3662 25 80 180 0.58 36-786-1 Cut1 15240 105 5954 41 64 180 0.58 36-746-1 Sill 13207 91 2418 17 74 180 0.51 36-746-1 Cut1 14619 101 3437 24 77 180 0.56 36-746-2 Sill 13432 93 5037 35 58 180 0.51 36-746-2 Cut1 15640 108 6037 42 66 180 0.60 37Level Elevation Lift Name Sigma 1 Sigma 1 Sigma 3 Sigma 3 Deviatoric UCS Induced (psi) (MPa) (psi) (MPa) Stress (Mpa) (MPa) Stress Ratio 37-786-1 Sill 12041 83 4906 34 49 180 0.46 37-786-1 Cut1 12373 85 5191 36 50 180 0.47 37-786-1 Cut2 12939 89 5090 35 54 180 0.50 37-786-1 Cut3 13180 91 4041 28 63 180 0.50 37-746-1 Sill 12308 85 3376 23 62 180 0.47 37-746-1 Cut1 13538 93 3699 26 68 180 0.52 37-746-1 Cut2 14900 103 3194 22 81 180 0.57 37-746-1 Cut3 15079 104 3538 24 80 180 0.58 37-746-2 Sill 12491 86 3723 26 60 180 0.48 37-746-2 Cut1 13521 93 3526 24 69 180 0.52 37-746-2 Cut2 14004 97 3600 25 72 180 0.54 37-746-2 Cut3 14276 98 4085 28 70 180 0.55 187 

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