UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Empirical open stope design in Canada Potvin, Yves 1988

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1989_A1 P67.pdf [ 16.49MB ]
Metadata
JSON: 831-1.0081130.json
JSON-LD: 831-1.0081130-ld.json
RDF/XML (Pretty): 831-1.0081130-rdf.xml
RDF/JSON: 831-1.0081130-rdf.json
Turtle: 831-1.0081130-turtle.txt
N-Triples: 831-1.0081130-rdf-ntriples.txt
Original Record: 831-1.0081130-source.json
Full Text
831-1.0081130-fulltext.txt
Citation
831-1.0081130.ris

Full Text

EMPIRICAL OPEN 8TOPE DESIGN IN CANADA By YVES POTVIN B . A . S c , U n i v e r s i t e LAVAL, Quebec 1982 M . A . S c . , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MINING AND MINERAL PROCESS ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA NOVEMBER 1988 @ Yves P o t v i n , 1988 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 KtKtii^C £ hiotfc*) PROCESS E/Q' The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date hft<tctt \C\R<\ n F . f i n / f t - n ABSTRACT This thesis addresses the topic of underground excavation s t a b i l i t y i n open stope mining methods. There are three fundamental aspects to be considered i n an engineering rock mechanics design of open stopes. The f i r s t aspect i s the characterization of the rock mass to i d e n t i f y and quantify the properties and components a f f e c t i n g the rock mass behaviour. The second aspect i s the e f f e c t of the stress f i e l d s on the rock mass that may r e s u l t i n zones of high compressive stress or zones of relaxation i n stope walls. The t h i r d aspect i s the physical condition of the problem and i s defined primarily by the s i z e , geometry and r e l a t i v e o r i e n t a t i o n of openings with regard to the rock mass and the stress f i e l d . The interaction of these three fundamental aspects constitutes the problem to be investigated. The p r i n c i p a l objective of the study i s to develop a r e l i a b l e geomechanical model (based on the above three aspects) that can predict the s t a b i l i t y of open stopes i n t y p i c a l Canadian geological settings. An empirical approach was chosen for the development of the model, because of the complexity of the problem and the d i f f i c u l t y i n estimating the input parameters with pr e c i s i o n . Empirical methods are l i k e l y to be more r e l i a b l e since they make use of past experience. A considerable amount of e f f o r t has been spent i n building a broad data base which includes more than 250 case h i s t o r i e s of i i unsupported and supported stopes from 34 Canadian mines. The application of the model i n the back-analysis of a l a r g e number of r e p r e s e n t a t i v e case h i s t o r i e s allowed c a l i b r a t i o n of each of the factors composing the model. Since the model's predi c t i o n corresponds very well to the actual stope behaviour i n most case h i s t o r i e s , the model i s considered empirically v e r i f i e d . The e f f e c t of external factors (parameters a f f e c t i n g stope s t a b i l i t y t h a t are not r e l a t e d to the geotechnical or geometrical conditions) have also been investigated. The l i m i t of a p p l i c a b i l i t y of cable b o l t i n g has been defined and rough guidelines for the design of cable support systems are proposed based on the systematic compilation of past experience. The e f f e c t of b l a s t i n g , although not quantified, has been observed i n 18 case h i s t o r i e s . More research i s required i n order to include the e f f e c t of b l a s t i n g i n the actual modelwhile the e f f e c t of time i s not of concern in open stope mining, when there are no mining a c t i v i t i e s i n the imediate area of the investigated stope. i i i TABLE OF CONTENTS PAGE ABSTRACT i i LIST OF TABLES. . x i LIST OF FIGURES x i i i ACKNOWLEDGEMENTS xxi CHAPTER 1 INTRODUCTION 1 1.1 DEFINITION OF THE PROBLEM 1 1.2 OBJECTIVE OF THE PROJECT 4 1.3 CONTENTS OF THE THESIS 6 CHAPTER 2 REVIEW OF OPEN STOPE MINING PRACTICES . . . . 8 2.1 INTRODUCTION 8 2.1.1 D e f i n i t i o n of open stope mining . . . . . . . 8 2.1.2 Applications of open stope mining 9 2.2 CLASSIFICATION OF OPEN STOPE MINING METHODS . . . . 14 2.2.1 Mining d i r e c t i o n 14 2.2.2 Use of p i l l a r s and b a c k f i l l 15 2.2.3 D r i l l hole diameter 20 2.2.4 C l a s s i f i c a t i o n of open stope mining . . . . . 21 2.3 DESCRIPTION OF OPEN STOPING PRE-PRODUCTION DEVELOPMENT 21 2.4 DESCRIPTION OF OPEN STOPE MINING AND SEQUENCING . . 24 2.4.1 Open stopirig with no b a c k f i l l 25 2.4.2 Open stoping with b a c k f i l l 25 2.4.3 Stope and f i l l mining 32 iv 2.5 LONGHOLE OPEN STOPING 35 2.5.1 Longhole d r i l l i n g 37 2.5.2 Longhole b l a s t i n g . . . . . . . 39 2.5.3 Longhole retreating methods 39 2.6 BLASTHOLE OPEN STOPING 41 2.6.1 Blasthole d r i l l i n g 43 2.6.2 Blasthole b l a s t i n g 45 2.6.3 Blasthole r e t r e a t i n g methods 4 6 2.7 SUMMARY AND CONCLUSIONS 51 CHAPTER 3 STRESS 56 3.1 INTRODUCTION 56 3 .2 PRE-MINING STRESS 58 3.3 STRESS MEASUREMENT 60 3.3.1 Method 1; F l a t jack 60 3.3.2 Method 2; Hydraulic f r a c t u r i n g 61 3.3.3 Method 3; Overcoring techniques 62 3.3.4 Compilation of stress measurements 64 3.4 INDUCED STRESS AND STRESS DISTRIBUTION 66 3.4.1 Components of stress . 68 3.4.2 Two dimensional state of stress 71 3.4.3 Two dimensional closed form solution of simple excavation shape 72 3.5 NUMERICAL MODELLING 78 3.5.1 Continuum approach 79 3.5.2 Discontinuum approach , 83 v 3.6 SUMMARY AND CONCLUSIONS . . . 84 CHAPTER 4 FAILURE CRITERIA 87 4.1 INTRODUCTION 87 4.2 INTACT ROCK MATERIAL FAILURE CRITERIA 88 4.2.1 Laboratory t e s t i n g 88 4.2.1.1 Uniaxial compressive strength . . . . 89 4.2.1.2 M u l t i a x i a l compressive strength . . . 91 4.2.1.3 Uniaxial t e n s i l e strength 92 4.2.2 A n a l y t i c a l approach 93 4.2.3 Empirical approach 94 4.3 SHEAR FAILURE CRITERION ALONG AN EXISTING DISCONTINUITY 94 4.3.1 Shear strength . 9 6 4.3.2 F r i c t i o n angle 98 4.4 JOINTED ROCK MASS FAILURE CRITERION 101 4.5 SUMMARY AND CONCLUSIONS . 104 CHAPTER 5 REVIEW OF EXISTING DESIGN METHODS FOR UNDERGROUND OPENINGS 108 5.1 INTRODUCTION 108 5.2 ROCK MASS CLASSIFICATION DESIGN CHARTS 109 5.2.1 Bieniawski RMR system 109 5.2.2 Barton et a l . system . I l l 5.2.3 Discussion of the Q and RMR systems 115 5.3 LAUBSCHER1S GEOMECHANICS CLASSIFICATION OF JOINTED ROCK MASSES 120 v i 5.3.1 Description of the model 121 5.3.2 Open stope design application 128 5.3.3 Discussion of the method 130 5.4 MATHEWS' OPEN STOPE DESIGN METHOD 131 5.4.1 Description of the method 131 5.4.2 Discussion of the method 138 5.5 NUMERICAL MODELLING DESIGN 142 5.5.1 Open stope design application 142 5.5.2 Discussion of the method 144 5.6 SUMMARY AND CONCLUSIONS 146 CHAPTER 6 OPEN STOPE FAILURE MECHANISMS 149 6.1 INTRODUCTION 149 6.2 NATURE OF THE ROCK MASS 149 6.3 INTACT ROCK BEHAVIOUR 155 6.4 DISCRETE BLOCK BEHAVIOUR . . . 156 6.5 JOINTED ROCK MASS BEHAVIOUR 158 6.6 SUMMARY AND CLASSIFICATION OF FAILURE MECHANISMS . . 160 CHAPTER 7 DEVELOPMENT OF THE GEOMECHANICAL MODEL . . . . 166 7.1 INTRODUCTION 166 7.2 THE BLOCK SIZE FACTOR 169 7.2.1 Estimation of block si z e 169 7.3 STRESS FACTOR . . . . . 174 7.3.1 E f f e c t of compression 174 7.3.2 Open stope parametric study 17 6 v i i 7.3.2.1 General concept of the parametric study 177 7.3.2.2 Longitudinal open stoping parametric study 179 7.3.2.3 Transverse open stoping parametric study 187 7.4 EFFECT OF JOINT ORIENTATION 195 7.4.1 The c r i t i c a l j o i n t factor 198 7.4.2 E f f e c t of anisotropy 200 7.4.3 Shear strength of the c r i t i c a l j o i n t . . . . 202 7.5 THE GRAVITY FACTOR 2 02 7.6 EFFECT OF STOPE SIZE AND SHAPE 203 7.7 CALCULATION OF THE MODIFIED STABILITY NUMBER AND PRESENTATION OF THE MODIFIED STABILITY GRAPH . . . . 205 7.8 SUMMARY 207 CHAPTER 8 DATA BASE AND MODEL CALIBRATION 210 8.1 INTRODUCTION 210 8.2 DATA COLLECTION 212 8.3 DATA BASE 213 8.3.1 Description of the main data base 214 8.3.2 Description of the complementary data base . 219 8.4 CALIBRATION OF THE FACTORS COMPOSING THE MODIFIED STABILITY NUMBER 219 8.4.1 Block size rating 224 8.4.2 Stress factor rating 225 8.4.3 J o i n t orientation factor rating 229 8.4.4 The gravity factor rating 231 v i i i 8.5 THE MODIFIED STABILITY GRAPH 232 8.6 DESIGN PHILOSOPHY 233 8.7 POSSIBILITY OF USING STASTISTICS 237 8.8 SUMMARY 238 CHAPTER 9 CABLE BOLT SUPPORT IN OPEN STOPE 240 9.1 INTRODUCTION 240 9.2 DESIGN CONCEPT . 242 9.2.1 Prereinforcement 242 9.2.2 S t i f f n e s s of the support system 244 9.3 CABLE BOLT SUPPORT SYSTEMS IN CANADIAN OPEN STOPE MINES 247 9.3.1 Cable bolt patterns for open stope backs . . 247 9.3.2 Cable b o l t patterns for open stope walls . . 251 9.4 DEVELOPMENT OF CABLE BOLT DESIGN GUIDELINES . . . . 257 9.4.1 Design analysis of cable bolt support data . 257 9.4.2 Density of bol t i n g 264 9.4.3 Cable bolt length 266 9.4.4 Bolting factor 2 69 9.4.5 Cable bolt orientation 269 9.5 SUMMARY 271 CHAPTER 10 EXTERNAL FACTORS; BLASTING. BACKFILL AND TIME EFFECT 274 10.1 INTRODUCTION 274 10.2 BLASTING EFFECT 274 10.2.1 Case h i s t o r i e s of bl a s t induced damage . . . 275 ix 10.2.2 Blast monitoring and prediction of bl a s t damage 276 10.2.3 Optimization of bl a s t design for wall s t a b i l i t y 279 10.3 EFFECT OF BACKFILL IN ADJACENT STOPES 283 10.3.1 E f f e c t of b a c k f i l l i n l i m i t i n g walls and back exposure 285 10.3.2 Case h i s t o r i e s analyses 287 10.4 THE TIME EFFECT 292 10.5 SUMMARY AND CONCLUSION 294 CHAPTER 11 SUMMARY AND CONCLUSION 297 11.1 SUMMARY 297 11.2 APPLICABILITY OF THE DESIGN METHOD 301 11.3 INDUSTRY BENEFITS OF THIS STUDY 302 11.4 FUTURE WORK 3 04 11.5 CONCLUDING REMARKS 305 REFERENCES 307 APPENDIX I OREBODY DIAGRAMS AND ROCK MECHANICS DATA . . 311 APPENDIX II DESCRIPTION OF THE BOUNDARY ELEMENT PROGRAMS 2D: BITEM AND 3D: BEAP 333 APPENDIX III PLOT OF INDUCED STRESSES FOR DIFFERENT GEOMETRIES AND K RATIO 339 X LIST OF TABLE PAGE TABLE 2.1 Approximate value of ore for mines using 19 b a c k f i l l , and mines using permanent p i l l a r s . TABLE 2 .2 Comparison of the mining sequence used with 54 the proposed open stope c l a s s i f i c a t i o n system. TABLE 4 .1 Values of the constant A from the Murrell 95 int a c t rock f a i l u r e c r i t e r i o n , and B from the Hoek int a c t rock f a i l u r e c r i t e r i o n , for f i v e rock materials. (After Bieniawski, 1984) TABLE 4.2 Values of Hoek and Brown constants m and s for 105 disturbed and undisturbed rock masses. TABLE 5.1 Bieniawski CSIR geomechanics c l a s s i f i c a t i o n of 112 jointed rock mass. (After Hoek and Brown) TABLE 5 .2 Barton c l a s s i f i c a t i o n of i n d i v i d u a l 116 parameters i n the NGI tunnelling q u a l i t y index, (cont) TABLE 5.3 The excavation support r a t i o (ESR) for 117 d i f f e r e n t underground openings applications. (After Hoek and Brown 198 0) TABLE 5 .4 Assessment of j o i n t conditions for the 122 Laubscher geomechanic c l a s s i f i c a t i o n of jointed rock mass. (After Laubscher, 1976) TABLE 5.5 Summary of the f i v e basic parameters of the 12 5 Laubscher geomechanic c l a s s i f i c a t i o n of jointed rock mass. (After Laubscher, 1976) TABLE 5.6 Adjustment factor for the number of j o i n t s 127 i n c l i n e d away from v e r t i c a l . (After Laubscher, 1976) TABLE 5.7 Adjustment factor for the e f f e c t of b l a s t i n g . 127 After Laubscher, 1976) TABLE 5.8 Summary of the possible adjustment factors. 12 7 (After Laubscher, 1976) TABLE 5.9 Adjustment factor for the i n c l i n a t i o n of the 129 designed stope surface. (After Laubscher, 1976) TABLE 8.1 Background information for the main data base. 215 x i TABLE 8.2 Input parameters from the main data base 218 necessary for open stope design back-analysis. TABLE 8.3 Background information for the complementary 220 data base. TABLE 8.4 Input parameters from the complementary data 222 base necessary for open stope design back-analysis. TABLE 8.5 Relationship between the r e l a t i v e block size 226 factor (RQD/Jn / hydraulic radius), and rock mass behaviour. TABLE 9.1 Background information for the data base of 2 58 case h i s t o r i e s that have used support. TABLE 9.2 Input parameters for the data base of case 260 h i s t o r i e s that have used support. TABLE 10.1 Relationship between the peak p a r t i c l e 280 v e l o c i t y and the r e s u l t i n g condition on rock structure. (After Atlas Powder company, 1987) TABLE 10.2 Relationship between the peak p a r t i c l e 280 v e l o c i t y , the rock mass quality and the r e s u l t i n g s t a b i l i t y of a stope. TABLE 11.1 Importance of d i l u t i o n on the DCF ROR. (After 303 Bawden, 1988) x i i LIST OF FIGURES PAGE FIGURE 1.1 Pie diagram showing the proportion of mines 2 having less than 10% d i l u t i o n , between 10% and 20% d i l u t i o n , between 20% and 35% d i l u t i o n and above 35% d i l u t i o n . (After Pakalnis, 1986) FIGURE 2.1 Range of orebody dips in open stope mining. 11 FIGURE 2.2 Range of rock mass quality (expressed in 12 terms of the Q index) i n open stope backs. FIGURE 2.3 Range of rock mass qual i t y (expressed i n 13 terms of the Q index) i n hanging walls. FIGURE 2.4 Graph of the orebody rock mass qu a l i t y 16 (expressed i n terms of the Q index), versus the orebody width, for longitudinal open stope mines. FIGURE 2.5 Graph of the orebody rock mass qu a l i t y 16 (expressed i n terms of the Q index), versus the orebody width, for transverse open stope mines. FIGURE 2.6 Graph of the stope walls rock mass qual i t y 18 (expressed i n terms of the Q index), versus the stope walls area, for open stope mines, using a " f u l l lens" l o n g i t u d i n a l extraction. FIGURE 2.7 C l a s s i f i c a t i o n system for open stope mining 22 methods applied to Canadian mines. FIGURE 2.8 Idealized isometric drawing of the " f u l l 26 lens" open stope mining method. FIGURE 2.9 Idealized isometric drawing of the sub-level 27 retre a t open stope mining method. FIGURE 2.10 Idealized isometric drawing of the 28 longi t u d i n a l longhole open stope mining method, with permanent p i l l a r s . FIGURE 2.11 Idealized isometric drawing of the trans- 30 verse blasthole open stope mining method, using the "leap frog" sequence of extraction. FIGURE 2.12 Idealized isometric drawing of the 31 longitudinal blasthole open stope mining method, having small primary stopes and large secondary stopes. x i i i FIGURE 2.13 Longitudinal section of a blasthole open 3 3 stope mining method, using the ( 1 - 5 - 9 ) sequence of extraction. FIGURE 2.14 Idealized isometric drawing of the 34 longitudinal open stope mining method, using the "stope and f i l l " sequence of extraction. FIGURE 2.15 Plan view showing the "panel mining" 3 6 sequence of extraction, (after Alexander and Fabjanczyck, 1981) FIGURE 2.16 Typical longhole d r i l l i n g patterns employed 38 in Canadian open stope mines. FIGURE 2.17 Graph of the maximum area of rock to be 4 0 broken by in d i v i d u a l d r i l l hole (burden x spacing), versus hole diameters. FIGURE 2.18 Idealized isometric drawing of the l o n g i t - 42 udinal longhole open stope mining method, using a f u l l face r e t r e a t . FIGURE 2.19 Typical blasthole d r i l l i n g patterns employed 44 in Canadian open stope mines. FIGURE 2.20 I l l u s t r a t i o n of the loading procedure for 47 large diameter blastholes. FIGURE 2.21 Idealized isometric drawing showing the 49 "mass b l a s t " retreat for blasthole open stope mining method. FIGURE 2.22 Cross section of the v e r t i c a l crater retreat 50 method used i n blasthole open stope mining, showing an i n i t i a l b l a s t , and the remnant crown b l a s t . FIGURE 2.23 Cross section of the inverse bench b l a s t i n g 52 method used in narrow blasthole open stope mining. FIGURE 3.1 Analogy of a flowing stream obstructed by 57 three bridge piers, representing stress streamlines around underground openings. (After Hoek and Brown, 1980) FIGURE 3.2 Plot of v e r t i c a l stresses against depth below 65 surface. (After Hoek and Brown, 1980) FIGURE 3.3 Vari a t i o n of r a t i o of average horizontal 65 stress to v e r t i c a l stress with depth below surface. (After Hoek and Brown, 1980) FIGURE 3.4 Variation of r a t i o of average horizontal 67 xiv stress to v e r t i c a l stress with depth below surface, from Canadian s h i e l d measurements. (After Herget, 1987) FIGURE 3.5 Stress components acting on a surface 69 element. (After Hoek and Brown, 1980) FIGURE 3.6 Stress components acting on a cubical 69 element. (After Hoek and Brown, 1980) FIGURE 3.7 Kirsh equations for the stresses i n the 74 material surrounding a c i r c u l a r hole i n a stressed e l a s t i c orebody. (After Hoek and Brown, 1980) FIGURE 3.8 Vari a t i o n i n the r a t i o of tangential stress 76 OQ to the v e r t i c a l applied stress pz with r a d i a l distance r along horizontal axis for K=0. (After Hoek and Brown, 1980) FIGURE 3.9 D e f i n i t i o n of nomenclature for an e l l i p t i c a l 76 excavation with axes p a r a l l e l to the f i e l d stresses. (After Brady and Brown, 1985) FIGURE 3.10 Idealized sketch showing the p r i n c i p l e of 80 numerical modelling. FIGURE 4.1 Typical stress s t r a i n r e l a t i o n s h i p during the 90 t e s t i n g of an unconfined e l a s t i c specimen i n compression. FIGURE 4.2 Idealized sketch showing a rock specimen 97 submitted to t r i a x i a l compression. FIGURE 4.3 Graphical representation of the Mohr c i r c l e 97 and f a i l u r e envelope. (After Hoek and Brown, 198 0) FIGURE 4.4 Idealized sketch showing the shearing along a 99 dis c o n t i n u i t y surface having an exaggerated roughness. (After Brady and Brown, 1985) FIGURE 4.5 Graphical representation of the peak and 99 residual f r i c t i o n angle. (After Brady and Brown, 1985) FIGURE 4.6 Typical d i s c o n t i n u i t y roughness p r o f i l e for 102 the evaluation of the JRC index. (After Barton and Choubey, 1977) FIGURE 5.1 Relationship between the stand-up time of an 113 unsupported underground excavation span and the CSIR Geomechanics C l a s s i f i c a t i o n . (After Bieniawski, 1973) FIGURE 5.2 Relationship between the maximum equivalent 118 dimension (De) of an unsupported underground excavation and the NGI tunnelling quality index Q. (After Barton xv Lien and Lunde, 1974) FIGURE 5.3 Diagram for the evaluation of the j o i n t 123 spacing parameter i n the Laubscher modified geomechanics c l a s s i f i c a t i o n system. (After Laubscher, 1976) FIGURE 5 . 4 Relationship between the adjusted rock mass 129 rat i n g and hydraulic radius of a stope surface. (After Laubscher, 197 6) FIGURE 5.5 Relationship between the s t a b i l i t y number 133 and hydraulic radius of a stope surface. (After Mathews et a l , 1980). FIGURE 5.6 Graph for the estimation of factor A. (After 135 Mathews et a l , 1980). FIGURE 5.7 Graph of the stress induced on the major 13 6 surface of a stope versus the r a t i o of opening dimensions. (After Mathews et a l , 1980). FIGURE 5.8 Graph of the stress induced on the minor 137 surface of a stope versus the r a t i o of opening dimension. (After Mathews et a l , 1980). FIGURE 5.9 Sketch for the estimation of the rock defect 139 orienta t i o n factor B. (After Mathews et al,1980). FIGURE 5.10 Graph for the estimation of the stope 14 0 surface i n c l i n a t i o n factor C (After Mathews et a l , 1980) . FIGURE 6.1 Triangular chart for the estimation of block 152 shape. (After Folk, 1968). FIGURE 6.2 Idealised diagram showing the t r a n s i t i o n 154 from i n t a c t rock to a heavily jointed rock mass with increasing sample s i z e . (After Hoek and Brown, 1980) FIGURE 6.3 Fa i l u r e mechanism of inta c t rock submitted 154 to compressive stress. FIGURE 6 . 4 F a i l u r e mechanism of in t a c t rock i n state of 154 stress relaxation. FIGURE 6.5 Fa i l u r e mechanism of discrete blocks for an 157 i s o t r o p i c rock material submitted to compressive stress. FIGURE 6.6 Fa i l u r e mechanism of discrete blocks for an 157 i s o t r o p i c rock material i n a state of stress relaxation. xv i FIGURE 6.7 Fa i l u r e mechanism of discrete blocks for an 157 anisotropic rock material having elongated blocks oriented p a r a l l e l to the stope surface and submitted to a compressive stress. FIGURE 6.8 F a i l u r e mechanism of discrete blocks for an 157 anisotropic rock material having elongated blocks oriented p a r a l l e l to the stope surface i n a state of stress relaxation. FIGURE 6.9 F a i l u r e mechanism of discrete blocks for an 159 anisotropic rock material having elongated blocks oriented perpendicular to the stope surface and submitted to compressive stress. FIGURE 6.10 Fa i l u r e mechanism of discrete blocks for an 159 anisotropic rock material having elongated blocks oriented perpendicular to the stope surface i n a state of stress relaxation. FIGURE 6.11 Failur e mechanism of jointed rock mass for 159 an i s o t r o p i c material submitted to compressive stress. FIGURE 6.12 Fa i l u r e mechanism of jointed rock mass for 159 an i s o t r o p i c rock material in a state of stress relaxation. FIGURE 6.13 Fa i l u r e mechanism of jointed rock mass for 161 an anisotropic rock material having elongated blocks oriented p a r a l l e l to the stope surface and submitted to a compressive stress. FIGURE 6.14 Fa i l u r e mechanism of a jointed rock mass 161 for an anisotropic rock material having elongated blocks oriented p a r a l l e l to the stope surface i n a state of stress relaxation. FIGURE 6.15 Failur e mechanism of jointed rock mass for 161 an anisotropic rock material having elongated blocks oriented perpendicular to the stope surface and submitted to compressive stress. FIGURE 6.16 Fa i l u r e mechanism of jointed rock mass for 161 an anisotropic rock material having elongated blocks oriented perpendicular to the stope surface i n a state of stress relaxation. FIGURE 6.17 C l a s s i f i c a t i o n of the f a i l u r e mechanisms i n 163 open stope mining. FIGURE 6.18 a) Sketch showing the gravity f a l l mode of 165 f a i l u r e . x v i i FIGURE 6.18 b) Sketch showing the s l i d i n g mode of 165 f a i l u r e . FIGURE 6.18 c) Sketch showing the slabbing and buckling 165 mode of f a i l u r e . FIGURE 7.1 V i s u a l i z a t i o n of the geomechanical model. 168 FIGURE 7.2 Sketch showing the measurement of j o i n t s 17 2 along a scan l i n e . (After P r i e s t and Hudson, 1976) FIGURE 7.3 Relationship between RQD and the average 172 number of d i s c o n t i n u i t i e s per meter. (After P r i e s t and Hudson, 1976) FIGURE 7.4 Graph for the estimation of the compressive 17 5 stress factor. FIGURE 7.5 D e f i n i t i o n of the aspect r a t i o and K r a t i o 178 used i n the estimation of the induced stress acting on a stope surface. FIGURE 7.6 Longitudinal open stope t y p i c a l dimensions. 181 FIGURE 7.7 Longitudinal open stope stress: hanging wall 182 horizontal plane. FIGURE 7.8 Back and HW horizontal stresses: e f f e c t of 183 seam width. FIGURE 7.9 Longitudinal open stope stress: hanging wall 185 v e r t i c a l plane. FIGURE 7.10 Longitudinal open stope stress: back 18 6 stresses. FIGURE 7.11 Longitudinal open stope stress: abutment 188 stress. FIGURE 7.12 Summary of the longitudinal parametric 189 study. FIGURE 7.13 Transverse open stope dimensions expressed 191 in terms of stope length (L). FIGURE 7.14 Transverse stope boundary stresses: 192 abutment wall. FIGURE 7.15 Transverse stope boundary stresses: p i l l a r 194 wall. x v i i i FIGURE end. 7.16 Transversal stope boundary stresses: stope 196 FIGURE 7.17 Summary of the transverse parametric study. 197 FIGURE 7.18 I l l u s t r a t i o n of the c r i t i c a l j o i n t concept. 199 FIGURE 7.19 Influence of j o i n t o rientation. 201 FIGURE 7.20 Influence of gravity for slabbing and gravity f a l l modes of f a i l u r e . 204 FIGURE 7.21 f a i l u r e . Influence of gravity for s l i d i n g mode of 204 FIGURE 7.22 The modified s t a b i l i t y graph. 206 FIGURE 8.1 h i s t o r i e s Modified s t a b i l i t y graph showing the case of high compressive stress. 228 FIGURE 8.2 h i s t o r i e s Modified s t a b i l i t y graph showing the case of stress relaxation. 230 FIGURE 8.3 h i s t o r i e s Modified s t a b i l i t y graph showing the case included i n the main data base. 229 FIGURE 8.4 Modified s t a b i l i t y graph showing the case 234 h i s t o r i e s included i n the t o t a l data base. FIGURE 9.1 a) Uniform cable bolt pattern i n s t a l l e d i n 248 open stope overcuts. FIGURE 9.1 b) Uniform cable bolt pattern i n s t a l l e d i n 248 open stope overcuts and supplemented with short rebar. FIGURE 9.2 Cable bolt support system using i n c l i n e d 250 cables and two phases of overcut development for prereinforcement. FIGURE 9.3 Cable bolt support system using an i n t e r - 250 laced support pattern. FIGURE 9.4 Cable bolt support system designed for 250 overcuts containing a small p i l l a r ( s ) . FIGURE 9.5 Uniform cable bolt pattern i n s t a l l e d i n an 252 open stope wall. FIGURE 9.6 Creation of a rock beam i n the hanging wall 253 by i n s t a l l i n g a l o c a l i z e d high density of cable b o l t s . FIGURE 9.7 Cable b o l t support system for a hanging 255 xix wall, i n s t a l l e d from a p a r a l l e l b o l t i n g d r i f t . FIGURE 9.8 Cable b o l t support system s t a b i l i z i n g p i l l a r 256 walls. FIGURE 9.9 The modified s t a b i l i t y graph for supported 263 case h i s t o r i e s . FIGURE 9.10 Relationship between the density of bo l t i n g 265 versus the r e l a t i v e block si z e factor (RQD/Jn) / hydraulic radius. FIGURE 9.11 Relationship between the cable b o l t length 268 and hydraulic radius of a stope surface. FIGURE 9.12 The modified s t a b i l i t y graph showing the 270 bo l t i n g factor for each of the "supported" case h i s t o r i e s . FIGURE 10.1 The modified s t a b i l i t y graph showing case 277 h i s t o r i e s that had s i g n i f i c a n t b l a s t i n g e f f e c t . FIGURE 10.2 Relationship between the reduction i n rock 281 mass qu a l i t y and the peak p a r t i c l e v e l o c i t y o r i g i n a t i n g from a b l a s t . (After Page, 1987) FIGURE 10.3 The e f f e c t of reducing the burden on a 282 charge of constant energy. (After Atlas powder company, 1987) FIGURE 10.4 The e f f e c t of delaying detonation decks on 284 the r e s u l t i n g wave packets. (After Sprott, 1986) FIGURE 10.5 Idealized isometric view of the mining and 286 b a c k f i l l of a four stope block. FIGURE 10.6 Idealized isometric view of the mining 288 block at Mine #19 of the data base. FIGURE 10.7 The modified s t a b i l i t y graph showing the 290 e f f e c t of b a c k f i l l i n adjacent stopes. FIGURE 10.8 The modified s t a b i l i t y graph showing the 293 time e f f e c t on seventeen case h i s t o r i e s from the data base. FIGURE l l . l The s t a b i l i t y graph method for open stope 299 design. xx ACKNOWLEDGEMENTS The author wishes to thank the p r i n c i p a l sponsors of t h i s project, NSERC, Centre De Technologie Noranda and Falconbridge Ltd as well as the t h i r t y four mining operations that have provided data and expertise. Martin Hudyma and Dr W i l l Bawden are also acknowledged for t h e i r s i g n i f i c a n t contribution i n t h i s research work. The assistance provided by the technical commitee formed by Dr Hamish M i l l e r project supervisor, Ken Mathews, A l l a n Moss, Dr Rimas Pakalnis, Chuck Brawner, Allan Reed and Andy Mular was greatly appreciated. Acknowledgement goes to the following persons for t h e i r continuous support and encouragement during my graduate studies; Wendy Cumming-Potvin, Jacques Potvin, Jeanine Potvin, Audrey Cumming and Antonio de Conceicao Ramos. xx i CHAPTER 1 INTRODUCTION This thesis addresses the topic of underground excavation s t a b i l i t y i n open stope mining methods. The e f f i c i e n c y of open stope mining operations r e l i e s on high productivity r e s u l t i n g from large, non-entry excavations and mechanized equipment. Considering the high cost associated with the development of each stope, the economic incentive to produce a smaller number of large open stopes i s tremendous. On the other hand, the consequences of exceeding the maximum possible stope dimensions can be disastrous. I n s t a b i l i t y around open stopes may cause large remedial costs for ground r e h a b i l i t a t i o n , delay of production, loss of mining equipment, loss of ore reserves and at the extreme, mine worker i n j u r i e s or f a t a l i t i e s . In a Canadian mine survey done by Pakalnis (1986), the actual performance of open stope design was investigated i n terms of d i l u t i o n . I t was found that forty seven percent of the open stope mines had more than 20% d i l u t i o n with twenty one percent s u f f e r i n g more than 35% d i l u t i o n (figure 1.1). This confirmed the need for a r e l i a b l e engineering design technique to optimize open stope dimensions s p e c i f i c a l l y adapted to Canadian geotechnical conditions. 1.1 DEFINITION OF THE PROBLEM There are three fundamental aspects to be considered in an 1 DILUTION - OPEN STOPING METHODS DATA BASE - 15 MINES FIGURE l . l Pie diagram showing the proportion of mines having less than 10% d i l u t i o n , between 10% and 20% d i l u t i o n , between 20% and 35% d i l u t i o n and above 35% d i l u t i o n . (After Pakalnis, 1986) 2 engineering rock mechanics design. The f i r s t aspect i s the characterization of the rock mass to i d e n t i f y and quantify the properties and components a f f e c t i n g the rock mass behaviour. The second aspect i s the e f f e c t of stress f i e l d s on the rock mass. Redistribution of the pre-mining stress f i e l d due to the creation of openings, may r e s u l t i n zones of high compressive stress, or zones of relaxation. Estimation of the magnitude of the (compressive or tensile) stress acting on each stope surface i s very important i n the design procedure. The t h i r d aspect i s the physical condition of the problem defined p r i m a r i l y by the size , geometry and r e l a t i v e orientation of openings with regard to the rock mass and stress f i e l d . The physical condition should also consider (at le a s t i n d i r e c t l y ) the factors inherent to the type of opening environment. For open stoping, these factors include: the e f f e c t of production bl a s t i n g , the influence of cable bolts, the influence of b a c k f i l l i n adjacent stopes and the longevity of the openings (time e f f e c t ) . In t h i s thesis, these factors w i l l be referred to as the external factors. The i n t e r a c t i o n of these three fundamental aspects constitutes the problem to be investigated. Each aspect i s accounted for i n the model by one or more factors empirically c a l i b r a t e d through case h i s t o r i e s . The factors are based on geotechnical parameters that can be estimated with on s i t e data. The p r i n c i p a l hypothesis defended i n t h i s thesis i s stated as follows; 3 " The s t a b i l i t y of open stopes can be predicted by quantifying the e f f e c t of rock mass, stress and the physical condition of the problem." 1.2 OBJECTIVE OF THE PROJECT The o b j e c t i v e of the p r o j e c t i s to develop a geomechanical model for the prediction of open stope s t a b i l i t y . Since one of the major concerns of t h i s study i s to provide a p r a c t i c a l design t o o l for Canadian open stoping mine operators, the f o l l o w i n g g u i d e l i n e s were set regarding the model development: The design method must be capable of predicting the o v e r a l l s t a b i l i t y of a stope i n terms of operating problems. Instead of focussing on precise calculations and the i d e n t i f i c a t i o n of discrete block f a l l s , the method should concentrate on defining conservative stope dimensions, less conservative stope dimensions and c r i t i c a l stope dimensions (beyond which open stoping become impractical). The model must be r e l i a b l e and consequently i t must be s e n s i t i v e to a l l the s i g n i f i c a n t g e o t e c h n i c a l parameters i n underground stope s t a b i l i t y . In addition, i t i s important that the d i f f e r e n t conditions associated with open stope mining, such as t y p i c a l s t o p e geometry, mining sequence, b l a s t i n g and 4 a r t i f i c i a l support ( b a c k f i l l and cable b o l t s ) , be d i r e c t l y or i n d i r e c t l y accounted for. The methodology must be e a s i l y understood by mining or geological engineers on s i t e . The input parameters should r e l y mainly on observational methods rather than expensive tes t i n g , lengthy studies and sophisticated equipment. The design method should be applicable at any stage of mining, including during the f e a s i b i l i t y study and for short term and long term planning. Although the p r e c i s i o n of designs i s l a r g e l y a function of the q u a l i t y of the input parameters, which improves as mining progresses, the method should be capable of p r o v i d i n g at l e a s t approximate answers at the f e a s i b i l i t y study stage. The approach must be representative of rock mass behaviour and be capable of i d e n t i f y i n g underground modes of f a i l u r e . This w i l l provide a better understanding of the ground conditions and help to s e l e c t the proper remedial actions i n case of ground control problems. The model i s based on an empirical approach and i t s r e l i a b i l i t y i s therefore a function of the extent of the data base. A considerable amount of e f f o r t has been spent in bu i l d i n g a broad data base which includes more than 250 case 5 h i s t o r i e s of unsupported and supported stopes from 34 Canadian mines. Each mine has been v i s i t e d (sometimes on several occasions) and case h i s t o r i e s were back-analyzed from discussions with mine personnel, underground observations, rock mass c l a s s i f i c a t i o n and numerical modelling. Empirical r e l a t i o n s h i p s have been d e r i v e d from t h i s systematic compilation of experience acquired i n Canadian open stope operations. 1.3 CONTENTS OF THE THESIS The f i r s t task of t h i s study was to provide a good review of open stope mining methods i n order to define the f i e l d of a p p l i c a b i l i t y of the geomechanical model. D e f i n i t i o n , c l a s s i f i c a t i o n and i d e n t i f i c a t i o n of the p r i n c i p a l variations in open stope mining practices are given i n chapter 2. Chapter 3, 4 and 5 are l i t e r a t u r e reviews covering the three fundamental aspects of stope design (ref. section 1.2). The pre-mining stress and the p r i n c i p a l laws governing the stress d i s t r i b u t i o n for l i n e a r e l a s t i c behaviour are described in chapter 3. Chapter 4 i s a review of rock f a i l u r e c r i t e r i a and the p r i n c i p a l techniques available to estimate the rock mass properties. In chapter 5 the e x i s t i n g models which integrate the rock mass c h a r a c t e r i s t i c s , the e f f e c t of stress and the physical conditions (of tunnels, caving methods and open stoping methods) are reviewed. 6 The study of the f a i l u r e mechanisms associated with open stope mining i s the i n i t i a l step of the model development. From the l i t e r a t u r e review, and more importantly from f i e l d observations of actual f a i l u r e s , a c l a s s i f i c a t i o n of open stope f a i l u r e mechanisms i s proposed i n chapter 6. Chapter 7 provides guidelines for the sel e c t i o n and d e f i n i t i o n of the factors representing the rock mass, stress and physical c o n d i t i o n s . Techniques are recommended for the f i e l d estimation of the geotechnical parameters composing each factor (except for the external f a c t o r s ) . The data base and the empirical c a l i b r a t i o n of the design method are given in chapter 8. Chapter 9 and 10 focus on the e f f e c t s of the external factors. I t should be noted that the investigation of some of the external factors (blasting, b a c k f i l l and time effect) i s very b r i e f because available information, mine s i t e technology and v i s u a l observation were not s u f f i c i e n t to develop guidelines on t h e i r e f f e c t on s t a b i l i t y . . A f u l l chapter (9) i s allocated to cable bolt support because observational methods were more e f f e c t i v e , allowing for a greater data base and more detailed investigation regarding i t s e f f e c t on s t a b i l i t y . The conclusion of the study can be found in chapter 11. 7 CHAPTER 2 REVIEW OF OPEN STOPE MINING PRACTICES 2.1 INTRODUCTION There are a wide v a r i e t y of mining methods that can be used for the extraction of underground orebodies. Open stoping has been practiced i n Canada since the early 1930's. In recent years i t has become the most popular method of underground extraction because i t i s cost e f f i c i e n t and safe. Several modifications of open stoping have evolved as a re s u l t of modern technology such as new mining equipment and improved d r i l l i n g and bl a s t i n g techniques. This chapter w i l l provide a d e f i n i t i o n and a c l a s s i f i c a t i o n of the d i f f e r e n t open stope mining methods. The p r i n c i p a l v a r i a t i o n s in open stope mining practices w i l l also be discussed. This review, based on over 30 Canadian underground mines, w i l l help to c l a r i f y some of the design concepts developed i n t h i s thesis and w i l l define the f i e l d of app l i c a t i o n of the proposed design method. 2.1.1 D e f i n i t i o n of open stope mining There are three c h a r a c t e r i s t i c features that d i s t i n g u i s h open stope mining from the other methods of underground extraction: Open stoping i s a non-entry method. Consequently, a f t e r production has started, the stope does not need to be 8 entered by mine workers, making t h i s one of the safest mining methods. A l l the miner's a c t i v i t i e s are confined to the stope periphery, away from the dangerous production face. Cut and f i l l , longwall, room and p i l l a r and shrinkage stoping are entry mining methods. The stopes are kept open u n t i l the f i n a l dimensions are obtained. The broken ore i s removed as stope extraction progresses. S t a b i l i z i n g b a c k f i l l i s introduced only a f t e r the completion of the stope (delayed b a c k f i l l ) . Since AVOCA uses b a c k f i l l during the extraction sequence, and methods such as shrinkage and sometimes VCR keep the stope f u l l of broken ore, they are not considered open stope methods. The underground excavations are designed to be stable as opposed to caving methods. This implies that there w i l l be no large unstable releases of energy due to a sudden change i n the opening geometry caused by caving. The three c r i t e r i a above have a fundamental influence on the design of openings and on the degree of i n s t a b i l i t y that can be tolerated. 2.1.2 Applications of open stope mining Open stope mining i s more e f f i c i e n t when applied to c e r t a i n types of orebodies and geological conditions. Because open stoping r e l i e s on the gravity flow of the ore 9 to the stope bottom, the stope dip should be above the angle of repose of the broken ore material (greater than 50° to 55°). Figure 2.1 shows the d i s t r i b u t i o n of the stope dips of the mines i n the project data base. Although open stoping i s more suited to a steeply dipping orebody, i t can also be successful i n a shallow dipping orebody (approximately less than 30°). However the stopes must be oriented s u b - v e r t i c a l l y , and the thickness of the orebody, should be at least 15 to 20 meters. The orebody outline should be r e l a t i v e l y regular, because open stoping i s not s e l e c t i v e . In addition, a minimum width of 5 meters i s generally necessary to avoid excessive d i l u t i o n from wall damage created by bl a s t i n g vibra t i o n s and/or d r i l l h o l e deviations. Open s t o p i n g u s u a l l y i n v o l v e s l a r g e opening dimensions. Since there i s no major support system such as b a c k f i l l or p i l l a r s inside the stope during the mining process, at least a " f a i r " to "good" rock mass strength i s required i n the stope back and walls i n order for the excavation to be s e l f supporting. The more competent the country rock, the larger are the stopes that can be created, and the more e f f i c i e n t open stoping w i l l be. Figures 2.2 and 2 . 3 show the d i s t r i b u t i o n of rock mass strength (expressed i n terms of the NGI 'Q' index) for the stope backs and the stope walls of the data base. 10 FIGURE 2.1 OREBODY DIP IN OPEN STOPE MINING S U B - V E R T I C A L MINING O N L Y 35 _. :  0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 O R E B O D Y DIP FIGURE 2.2 ROCK MASS QUALITY IN OPEN STOPE BACKS F R O M 34 C A N A D I A N O P E N S T O P E M I N E S 30 —r — 0.1 - 0.5 0.5 - 1.0 1 - 5 5 - 10 10 - 20 20 - 40 40 - 80 80 + R O C K M A S S Q U A L I T Y ( Q ' ) FIGURE 2 . 3 ROCK MASS QUALITY M HANGING WALLS F R O M 3 4 C A N A D I A N O P E N S T O P E M I N E S 3 0 : 2 8 -2 6 -0.1 - 0 . 5 0 . 5 - 1.0 1 - 5 5 - 1 0 1 0 - 2 0 2 0 - 4 0 4 0 - 8 0 8 0 + R O C K M A S S Q U A L I T Y (Q") 2.2 CLASSIFICATION OF OPEN STOPE MINING METHODS The elements that form open stope mining methods are numerous and variable. Consequently, there are no two open stoping applications that are exactly the same. A proposed c l a s s i f i c a t i o n uses the three following s p e c i f i c a t i o n s to group the open stope mining methods: mining d i r e c t i o n (longitudinal or transverse), use of p i l l a r s , and b a c k f i l l , d r i l l hole diameter (longhole or blasthole). These s p e c i f i c a t i o n s have been chosen to c l a s s i f y open stope mining methods, because they determine the development and stope preparation required, the method of retreat and the sequencing of mining. 2.2.1 Mining d i r e c t i o n The f i r s t c r i t e r i o n for the c l a s s i f i c a t i o n of open stoping methods i s the d i r e c t i o n of mining. In longitudinal mining, the d i r e c t i o n of retreat i s along the orebody s t r i k e , while i n transverse mining, retreat i s i n the d i r e c t i o n perpendicular to the orebody s t r i k e . If the d i r e c t i o n of retreat i s v e r t i c a l ( i e . crater retreat) the orienta t i o n of the longest of the two horizontal axis of the stope u s u a l l y d i s t i n g u i s h the mining d i r e c t i o n . Longitudinal open stopes have t h e i r longest axis p a r a l l e l to the orebody s t r i k e and transverse stopes have t h e i r longest horizontal dimension across orebody. In general longitudinal open stoping requires less development and i s therefore faster and less expensive to b r i n g i n t o p r o d u c t i o n . The l i m i t i n g f a c t o r f o r longitudinal mining i s the a b i l i t y of the stope backs to be self-supporting. In figure 2.4, the width of the stope backs mined l o n g i t u d i n a l l y has been plotted against the NGI rock mass strength index 'Q' for the mines i n the data base. The l i n e s represent orebodies having a variable width, while single points denotes mine with a constant width orebody. The trend shown i n figure 2.4 i s that the better the rock mass i s , the wider i s the orebody that can be mined l o n g i t u d i n a l l y . A s i m i l a r graph has been prepared for orebodies mined transversely (figure 2.5). I t can be seen t h a t t r a n s v e r s e mining i s practiced on wider orebodies, and a minimum width of 15 metres i s needed to make i t e f f i c i e n t . 2.2.2 Use of p i l l a r s and b a c k f i l l Open stope mining methods have four options regarding the use of p i l l a r s and b a c k f i l l : f u l l lens mining can be done without p i l l a r s or b a c k f i l l permanent p i l l a r s can be l e f t unmined, which w i l l l i m i t the orebody recovery, but no b a c k f i l l i s used, 15 0 R E 3 0 D Y S T R E N G T H V S 0 R E 3 0 D Y WIDTH L O N G m j D I N A L MINING 10-0 R E 3 O 0 Y WIOTK (In m. t rma) FIGURE 2.4 Graph of the orebody rock mass quality (expressed in terms of the Q index), versus the orebody width, for longitudinal open stope mines. C R E 3 0 D Y S T R E N G T H V S O R E B O D Y WIDTH TRANSVERSAL. MINING C R E 3 0 0 Y WIDTH (In m . l r o a ) FIGURE 2.5 Graph of the orebody rock mass quality (expressed in terms of the Q index), versus the orebody width, for transverse open stope mines. 16 p i l l a r s can be recovered using cemented b a c k f i l l , avoid the creation of p i l l a r s by sequencing stope and f i l l operations. The ideal open stoping conditions e x i s t i f the rock mass surrounding the orebody i s strong enough that no p i l l a r s or b a c k f i l l are necessary. This method has been termed " f u l l lens open stoping" and i s possible in r e l a t i v e l y small ore lenses. Figure 2.6 i s a graphical presentation of the wall rock competency (NGI, Q index) versus the wall area used i n f u l l lens open stopes. The square shaped points represent stopes that were stable and the diamond shaped points show walls that caved. The dashed l i n e i s a rough c r i t e r i o n for the f e a s i b i l i t y of f u l l lens open stoping, since most cases p l o t t i n g above the l i n e were stable and most cases below the l i n e experienced s t a b i l i t y problems. Often when f u l l lens mining i s not possible, p i l l a r s are l e f t to maintain the o v e r a l l mine s t a b i l i t y . The option of recovering the p i l l a r s at a l a t e r stage of mining, i s a function of the grade and value of the ore. This i s shown i n table 2.1, where the approximate value per ton of ore i s indicated for mines that recovered p i l l a r s and for mines that l e f t permanent p i l l a r s . I f the ore value i s r e l a t i v e l y high, the use of b a c k f i l l and p i l l a r recovery i s j u s t i f i e d . Permanent p i l l a r s are l e f t i f the 17 WALL ROCK MASS STRENGTH VS WALL AREA FULL LENS LONGITUDINAL OPEN STOPING 10O 10-0.1 • > B • H 1 1 • SB tt a _ • • • mm • • • i a  i a • • • • • • r-a  mm mm — — j ^ - . • • • * . « HI m 0 2000 4000 6000 WALL AREA (square metres) • STABLE WALLS • CAVED WALLS FIGURE 2.6 Graph of the stope w a l l s rock mass q u a l i t y (expressed i n terms of the Q ind e x ) , v e r s u s the stope w a l l s area, f o r open stope mines, u s i n g a " f u l l l e n s " l o n g i t u d i n a l e x t r a c t i o n . MINES USING APPROXIMATE VALUE BACKFILL OF ORE ($US/ton) NORITA $ 88 MATTAGAMI LAKE $ 60 MINES GASPE $ 68 WESMIN $ 128 CORBET $ 108 KIDD CREEK $ 125 KIENA $ 69 LOCKERBY $ 123 LAC SHORTT $ 69 GOLDEN GIANT $ 114 LYON LAKE $ 144 GECO $ 70 BRUNSWICK $ 125 CENTENNIAL $ 54 SELBAIE - ZONE B $ 100 FALCONBRIDGE $ 129 MEAN $ 98 MINES USING APPROXIMATE VALUE PERMANENT PILLARS OF ORE • ($US/ton) RUTTAN $ 43 ALGOMA $ 25 HEATH STEELE $ 92 SELBAIE - ZONE A $ 47 MEAN $ 52 Table 2.1 Comparison of the value of ore ($US/ton) for mines using b a c k f i l l against mines using permanent p i l l a r s . (Mine grades from 1987 Canadian Mines Handbook, price of metals from January 1988 Engineering and Mining Journal). 19 ore value i s low. For mines leaving permanent p i l l a r s , the maximum orebody recovery i s about 75% to 80%. In heavily stressed ground, where bursting i s a p o t e n t i a l problem and p i l l a r recovery i s expensive, i t can be advantageous to sequence the extraction and b a c k f i l l operations i n order to avoid the creation of p i l l a r s . This i s done by f i l l i n g a stope immediately a f t e r mining i s finishe d , and mining the stope d i r e c t l y adjacent to the f i l l e d stope as soon as the b a c k f i l l has set. Success of the "stope and f i l l " method i s dependent on the r e l i a b i l i t y of f i l l i n g cycle. In addition i t does not have the i n i t i a l high rate of return associated with primary mining of stope and p i l l a r methods. 2.2.3 D r i l l hole diameter O r i g i n a l l y , a l l open stope mining methods used small diameter d r i l l holes 51 to 64 mm (2 to 2.5 in) for pr o d u c t i o n b l a s t i n g . In the 1970's, large diameter blasthole technology from open p i t mining was introduced i n underground open stope mining. In general, blasthole open stoping i s more highly mechanized and more cost e f f e c t i v e and productive than the small diameter longhole open stoping. However, blasthole open stoping i s less s e l e c t i v e and requires larger and more extensive development p r i o r to mining. The d r i l l i n g , b l a s t i n g and methods of retreat of longhole and blasthole open stope mining w i l l be described 20 i n section 2.5 and 2.6. 2.2.4 C l a s s i f i c a t i o n of open stope mining The c l a s s i f i c a t i o n of open stope mining methods, according to the three s p e c i f i c a t i o n s discussed above i s i l l u s t r a t e d i n a flowchart, figure 2.7. The Canadian mines using each option are also given. I t i s noteworthy that some mines are using more than one open stoping method due to v a r i a t i o n s i n the orebody c h a r a c t e r i s t i c s . There are no rigourous rules for the s e l e c t i o n of the optimum open stoping method. Although some guidelines based on orebody geometry, rock mass strength and ore value have been discussed above, factors such as the type of equipment availa b l e and mine management philosophy often play a major ro l e i n the f i n a l mining method se l e c t i o n . 2.3 DESCRIPTION OF OPEN STOPING PRE-PRODUCTION DEVELOPMENT The t y p i c a l development work necessary for open stope mining (excluding orepasses and v e n t i l a t i o n r a i s e systems) i s comprised of the following four components. Development of i n t e r l e v e l access. Travel between the production l e v e l s can be done v i a ramps, i n the case of a mechanized operation, or manways, for more t r a d i t i o n a l less mechanized mining operations. Ramps are necessary in blasthole open stoping because of the large equipment. 21 FIGURE 2 .7 CANADIAN OPEN STOPE MINES LONGITUDINAL M I N I N G D I R E C T I O N TRANSVERSAL YES YES U S E O F P I L L A R S NO U S E O F F I L L NO YES YES U S E O F F I L L NO YES U S E O F P I L L A R S NO U S E O F F I L L YES I U S E O F F I L L D R I L L H O L E I-i T Y P E CENTENNIAL FALCQNBRIDGE EAST NINE FRASER GECO INCD THOMPSON LAC SHORTT LOCKERBY MINES GASPE MINES SELBAIE STRATHCONA FUN FLON GECO GOLDEN GIANT LYON LAKE VESTHIN LITTLE STOBIE NIDBEC RUTTAN ALGOHA HEATH STEELE RUTTAN flUgrj0" LONOBOLE BLASTHOLE LOBBBOLE BLASTHOLE LOmBOLE BLASTHOLE CHADBOURNE INCO THOMPSON LOCKERBY STRATHCONA GOLDEN GIANT ONAPING CHADBOURNE CORBET DOME NIDBEC ROSS RUTTAN SPRUCE POINT CAMFLO LYON LAKE MATTABI NORITA RUTTAN BRUNSWICK CORBET FRASER KDDD CREEK KIENA LOCKERBY MINES SELBAIE NORITA STOBIE STRATHCONA MATTAGAM LAKE INCO THOMPSON ODD CREEK Development of the d r i l l i n g horizon. An access d r i f t , usually located i n the footwall, i s driven p a r a l l e l to the orebody i n order to maintain access to the d r i l l i n g locations a f t e r the extraction has started. The production d r i l l i n g for longhole mining i s done from one (or several p a r a l l e l ) d r i l l i n g d r i f t s running the length of the stope. The number of d r i l l i n g d r i f t s depends ( v e r t i c a l l y ) on the stope height and the maximum d r i l l hole length, and (horizontally) on the width of the stope. Blasthole open stoping generally requires a f u l l overcut for the production d r i l l i n g equipment. The overcut i s approximately four metres high and covers the entire top surface of the stope. Sometimes, small p i l l a r s are l e f t in the overcut to provide temporary support to large stope backs. Development of the mucking horizon. A haulage d r i f t i s developed p a r a l l e l to the orebody, usually 15 to 30 metres in the footwall. The mucking i s done from drawpoints connected to the haulage d r i f t by cross cuts spaced at 10 to 15 metres. There are three types of drawpoints. C o l l e c t i o n cones which are suited to track or trackless loading equipment as well as chute loading systems. V-cut scram d r i f t s have a role s i m i l a r to the c o l l e c t i o n cones, but i n v o l v e l e s s complicated development work. The more t r a d i t i o n a l slusher mucking i s often used with the V-cut scram d r i f t s . A f u l l y open undercut i s common i n blasthole open stoping. In t h i s case, the d r i l l i n g overcut of the 23 stope below i s used as undercut drawpoint of the l e v e l above, which minimizes the amount of development. Remote control scooptrams are necessary to enter the stopes and remove the l a s t portion of broken ore. Development of the s l o t r a i s e . The s l o t r a i s e i s used to create a free face for the production b l a s t s . Its location i s v a r i a b l e depending on the preferred d i r e c t i o n of retreat. Slot raises can be developed by conventional staging, Alimak r a i s e climber, drop r a i s i n g and i n highly mechanized mines by r a i s e boring machines. 2.4 DESCRIPTION OF OPEN STOPE MINING AND SEQUENCING The most common open stope mining and sequencing procedures can be divided into two groups; methods that do not use b a c k f i l l and methods that use b a c k f i l l . I f b a c k f i l l i s not used, the major concern i s the sequencing of stope extraction in order to avoid an early overstressing of the permanent p i l l a r s . This i s done by mining from the centre of the orebody towards the abutments. When b a c k f i l l i s used, d i f f e r e n t strategies cart be followed to optimize the recovery of p i l l a r s or to simply avoid the creation of p i l l a r s . These options w i l l be discussed i n t h i s section with id e a l i z e d isometric drawings and references to the open stope mining c l a s s i f i c a t i o n (section 2.2) and pre-production development (section 2.3) w i l l be made. 24 2.4.1 Open stoping with no b a c k f i l l The most simple and economic open stope mining method i s f u l l lens extraction because i t has no b a c k f i l l and no p i l l a r s . This method ( i l l u s t r a t e d i n figure 2.8) can be applied i n small orebodies or is o l a t e d lenses providing the rock mass quality i s s u f f i c i e n t for stope surfaces to be self-supporting. A v a r i a t i o n of t h i s approach i s the open stope sub l e v e l retreat method shown i n figure 2.9. Once again, no p i l l a r s or b a c k f i l l are necessary but the method of retreat i s underhand (from top to bottom) instead of overhand (from bottom to top). The methods of retreat for longhole and blasthole mining w i l l be further discussed i n section 2.5.3 and 2.6.3. When the value of the ore does not j u s t i f y the use of b a c k f i l l , but the orebody i s too large to be mined as a single stope, permanent p i l l a r s are l e f t (figure 2.10). The stopes r e t r e a t towards the p i l l a r and permanent stope access development i s located i n the p i l l a r s . In order to maximize the orebody recovery, the p i l l a r s are kept to a minimum width but they need to remain stable to insure o v e r a l l mine s t a b i l i t y and to protect the access to the stope. 2.4.2 Open stoping with b a c k f i l l When b a c k f i l l i s involved, the sequencing of stope extraction becomes part of an ov e r a l l strategy for the optimum recovery of the secondary and t e r t i a r y stopes (temporary p i l l a r s ) . By d e f i n i t i o n , primary stopes are mined against rock 25 FIGURE 2.8 Idealized isometric drawing of the " f u l l lens" ooen stope mining method. Stope Width Distance Haulage— p . . . Orebody Drowpomt 7 Spacing Stope Height FULL LENS VERTICAL CRATER RETREAT April 88 J M H o FIGURE 2.9 I d e a l i z e d i s o m e t r i c drawing of the s u b - l e v e l r e t r e a t open stope mining method. Ul t imate S t o p e H e i g h t Dis tance Between Sub—Levels SUB--LEVEL RETREAT 0A71 MAW «rv. Nov 87 JMH 0 walls, secondary stopes are usually mined against one or more cemented b a c k f i l l wall and t e r t i a r y stopes are usually surrounded by b a c k f i l l e d stopes. Consequently, primary and secondary stopes w i l l often need cemented b a c k f i l l , and t e r t i a r y can be f i l l e d with uncemented f i l l . The most widely used mining sequence i s commonly c a l l e d "leap frog" and alternates between mining a stope and leaving the adjacent stope as a temporary p i l l a r . In figure 2.11, the t r a d i t i o n a l leap frog sequence i s applied to a transverse blasthole open stoping method. The actual order of stope e x t r a c t i o n i s variable and depends on factors such as development and d r i l l scheduling and the a v a i l a b i l i t y of b a c k f i l l . I f there are a s u f f i c i e n t number of stopes, mining can concentrate on one l e v e l (as shown on figure 2.11), thus minimizing d r i l l movement. Otherwise, primary and t e r t i a r y stoping are done simultaneously on multiple l e v e l s . A v a r i a t i o n of the "leap frog" sequence, applied to longitudinal blasthole open stoping i s shown on figure 2.12. F i r s t l y , there i s stope extraction on multiple l e v e l s i n order to increase the production and the f l e x i b i l i t y of mining. It can also be observed that the primary stopes are s i g n i f i c a n t l y smaller than the t e r t i a r i e s . This w i l l reduce the amount of expensive cemented b a c k f i l l but on the other hand, the primary stopes w i l l contribute a much smaller tonnage i n the important f i r s t stage of mining. The 1-5-9 sequence, another v a r i a t i o n of "leap frog" 29 FIGURE 2.11 I d e a l i z e d i s o m e t r i c drawing o f the t r a n s v e r s e b l a s t h o l e open stope mining method, u s i n g the " l e a p f r o g " sequence of e x t r a c t i o n . Primary Secondary Stope Stope Length Length TRANSVERSE BLASTHOLE FIGURE 2.12 Idealized isometric drawing of the longitudinal blasthole open stope mining method, having small primary stopes and large secondary stopes. P r i m a r y S e c o n d a r y S t o p e S t o p e L e n g t h L e n g t h Footwall Access LONGITUDINAL BLASTHOLE " Dec 87 0 sequence i s shown i n longitudinal section i n figure 2.13. The f i r s t , f i f t h and ninth (thirteenth etc.) stopes are extracted for the f i r s t three l e v e l s before the middle stopes ( 3-7-11) are started (see stage 1, 2, 3 of figure 2.13). When mining of stopes 1, 5, 9 reach the f i f t h l e v e l , stopes 3, 7, 11 begin on the t h i r d l e v e l and t e r t i a r y stoping i s i n i t i a t e d at the f i r s t l e v e l (see stage 4, 5, 6 of figure 2.13). The main reasons to follow t h i s order of extraction are to i s o l a t e stopes i n the same mining block from each other, and to keep the l o c a l mining rate low. 2.4.3 Stope and f i l l mining The p r i n c i p l e of "stope and f i l l " i s to mine and b a c k f i l l adjacent stopes consecutively i n a manner such that no p i l l a r s are created. A l l the stopes (except the very f i r s t one) are extracted against one b a c k f i l l wall (secondary mining). This method loses the high rate of return of the primary mining, but i s sometimes necessary to achieve t o t a l orebody recovery in highly stressed ground. A mining sequence using a stope and f i l l method and a longitudinal open stoping i s , shown i n figure 2.14. In t h i s case, the retreat i s done from both ends towards the centre of the mining block, on one l e v e l at a time. This creates two production faces, minimizes the amount of development (only three accesses to the orebody are required), but may cause stress concentration problems i n the central stopes. This s i t u a t i o n can be avoided by re t r e a t i n g from one FIGURE 2.13 1 - 5 - 9 M i n i n g S e q u e n c e • m Mining H Backfilled '•-ry 1 1 1 % i i 1 Stage 1 Stage 2 'n-UJII Stage 3. Stage 4 Stage 5 Stage 6 33 FIGURE 2.14 Idealized isometric drawing of the longitudinal open stope mining method, using the "stope and f i l l " sequence of extraction. Stope Length Ore P a s s oil A c c e s s LONGITUDINAL BLASTHOLE DATE DRAWN H V . 1 Nov 87 JMH o I end of the orebody to the other. However, only one production face w i l l be available. A t h i r d option i s to s t a r t a set of stopes at the centre of the mining block and to retreat towards both of the abutments. This w i l l prevent stress b u i l d up and w i l l keep two production faces but may create access problems and long ore tramming distances. Stope and f i l l has also been applied to wider orebodies and has been rtamed panel mining. The mining block i s divided into a number of small stopes i n a "chess board" manner (see figure 2.15). The sequence of extraction of i n d i v i d u a l stopes varies from mine to mine and i s lar g e l y dependent upon the orebody and geological conditions. It uses small stopes, and thus requires a l o t of pre-mining development. Almost a l l the stopes are b a c k f i l l e d with cemented f i l l which makes panel mining an expensive mining method. I t i s t y p i c a l l y used i n massive orebodies that have bad ground conditions and/or bursting problems. 2.5 LONGHOLE OPEN STOPING Longhole i s the oldest and most conventional open stope mining method. It i s characterized by small diameter holes (51 to 64 millimetre) which influence the d r i l l i n g , b l a s t i n g and retreating practices. Those practices must be adapted to the orebody geometry, geological conditions and the location of the d r i l l i n g d r i f t s . FIGURE 2.15 P l a n v i e w showing t h e " p a n e l m i n i n g " sequence o e x t r a c t i o n , ( a f t e r A l e x a n d e r and F a b j a n c z y c k , 1981) 2.5.1 Longhole d r i l l i n g D r i l l i n g patterns vary from mine to mine, stope to stope and frequently from row to row. However, there are two basic types of longhole d r i l l i n g patterns. In the ring pattern, each row has holes d r i l l e d at 360° from a fixed set-up point (figure 2.16 a and b), while fan patterns have only down holes (figure 2.16 c) . The main advantage of rings i s that the distance between sub-levels can be almost double the maximum hole length. In Canadian s h i e l d rock, i t has been found that longhole deviation becomes excessive at hole lengths over 20 meters. Consequently, the t y p i c a l distance between sub-levels using r i n g patterns i s approximately 30 to 35 meters, while for fan d r i l l i n g , i t i s only 15 to 20 meters. One of the disadvantages of the ring pattern i s that i t may have bad fragmentation o r i g i n a t i n g from the location where the rings meet. Also, i t can be seen on figure 2.16 a) that t h i s pattern has holes ending against the stope walls, which i s not favorable for wall s t a b i l i t y . When the stope i s wider, d r i l l i n g d r i f t s may be located at the hanging wall and footwall l i m i t s . "Contour holes" are d r i l l e d p a r a l l e l to the stope/waste contacts, and generally r e s u l t i n better stope wall s t a b i l i t y (figure 2.16 c ) . In fan d r i l l i n g , contour wall holes are also possible and poor fragmentation i s not a common problem. T y p i c a l l y , the toe spacing between holes i s greater than the row burden to help the blas t break cleaner and reduce 37 FIGURE 2.16 T y p i c a l l o n g h o l e d r i l l i n g p a t t e r n s employed i n Canadian open s tope mines . a) Ring Pattern. b) Ring pattern with p a r a l l e l wall holes. c) Fan pattern with p a r a l l e l wall holes. backbreak. The determination of the burden and spacing of longholes depends upon the d r i l l hole diameter and the hardness of the ore. Figure 2.17 i s based on actual longhole patterns and shows that the amount of ore to be broken by each hole (burden * spacing) increases with the d r i l l hole diameter. 2.5.2 Longhole b l a s t i n g In general, 2 to 4 rings or fans are f i r e d during a longhole production b l a s t . Each hole i s detonated on a single delay and frequently multiple holes are f i r e d on the same delay. Longholes within a ri n g or fan are often loaded a l t e r n a t e l y r i g h t up to the c o l l a r while the next hole i s loaded to a distance of 3 to 5 meters from the c o l l a r . This i s done to avoid overblasting caused by the holes converging near the d r i l l d r i f t . 2.5.3 Longhole ret r e a t i n g methods The conventional method of retreat i n longhole open stoping i s by slashing v e r t i c a l s l i c e s into the s l o t area, giving horizontal retreat. The retreat can be staggered or f u l l face. The staggered retreat method advances the bottom sub-level f i r s t and i s follow by the next sub-level above and then the t h i r d one, etc. (see figure 2.10). This i s done in order to be able to s t a r t production b l a s t i n g , before a l l the development i n the upper subs i s finished. However, a problem associated with staggered retreat i s that the sharp corners 39 FIGURE 2 i 7 BURDEN*SPAOLNG VS HOLE DIAMETER FAN AND RING PATTERNS 8.0 - i o.o H 1 , 1 , 1 1 1 1 1 1 1 1 r r 50 54 58 62 66 70 74 78 HOLE DIAMETER (mm) created are prone to caving, which can lead to oversized muck in the drawpoints and loss of the toe of some d r i l l holes. Another disadvantage i s that p i l l a r s t a b i l i t y problems can s t a r t as soon as the bottom sub i s completed and jeopardize the development and recovery of the rest of the stope. The f u l l face method r e t r e a t s a l l the sub-levels simultaneously ( f i g u r e 2.18). The p i l l a r s created by converging stopes are then diminished progressively and p i l l a r s t a b i l i t y problems are not expected u n t i l the f i n a l stage of the stope extraction. Furthermore, f i l l i n g and resequencing of the extraction i s possible i f stope or p i l l a r problems are encountered. A completely d i f f e r e n t method of retreat i s shown in figure 2.9. This method, often c a l l e d sub-level retreat, mines the top sub-level f i r s t , followed by the ones below. The d r i l l i n g consists exclusively of up holes and the mucking i s done from each sub-level, instead of at the stope bottom. Because the distance between the sublevels i s approximately 10 metres, t h i s method requires a considerable amount of pre-mining development. However, most of i t i s located i n ore which makes the sub-level retreat method, one of the most economic. 2.6 BLASTHOLE OPEN STOPING Blasthole open stoping was derived by modifying longhole 41 FIGURE 2.18 Idealized isometric drawing of the longitudinal longhole open stope mining method, using a f u l l face retreat. P r i m a r y S e c o n d a r y S t o p e S t o p e L e n g t h L e n g t h Manway D i s t a n c e B e t w e e n S u b - L e v e l s LONGITUDINAL LONGHOLE mining to the use of large diameter d r i l l holes. At f i r s t , the vibra t i o n s generated by the b l a s t i n g of big holes caused ground control problems. In recent years, new d r i l l i n g , b l a s t i n g and r e t r e a t i n g techniques have been successfully developed. Since large equipment i s required to d r i l l large diameter holes, most blasthole operations take advantage of mechanization. This makes blasthole open stoping one of the most cost e f f i c i e n t mining methods. 2.6.1 Blasthole d r i l l i n g The p r i n c i p a l c h a r a c t e r i s t i c of blasthole open stoping i s the use of 100 - 200 mm (4 to 8 inch) diameter d r i l l holes for production b l a s t i n g . Because large holes can be d r i l l e d with more pre c i s i o n over a long distance, the stope height can be up to 50 to 60 metres. The spacing between holes and the burden between rows varies from approximately 2.4 metres to 3.6 metres. The most t y p i c a l blasthole d r i l l i n g arrangement has 165 mm (6.5 inch) d r i l l holes and a square pattern with a 3 metre burden and spacing. The holes are d r i l l e d mutually p a r a l l e l , from a f u l l y open overcut to a f u l l y open undercut (figure 2.19 a). The holes' p r e c i s i o n can be surveyed from the undercut. The same p r i n c i p l e can also be apply to i n c l i n e d stopes, except a l l the holes w i l l be i n c l i n e d p a r a l l e l to stope walls (figure 2.19 b). A v a r i a t i o n i s shown on figure 2.19 c), where most of the holes have been kept v e r t i c a l and i n c l i n e d rows are d r i l l e d along the hanging wall. When d r i l l i n g d r i f t s 43 FIGURE 2.19 Typical b lasthole d r i l l i n g patterns employed in Canadian open stope mines. are used instead of a f u l l overcut, a fan pattern such as the one shown i n figure 2.19 d) must be used. This may cause s t a b i l i t y problems since large holes are blasted against the stope walls, and a large quantity of explosive can be concentrated near the d r i l l i n g d r i f t . Blasthole open stoping i s not i d e a l for i r r e g u l a r orebodies, but figure 2.19 e) shows how the d r i l l i n g can be adapted to better s u i t the orebody d e f i n i t i o n . Shorter i n c l i n e d holes sometimes have to be added to a v e r t i c a l p a r a l l e l pattern, i n order to d r i l l under temporary small p i l l a r s which are l e f t for the support of the overcut (see figure 2.19 f) . 2.6.2 Blasthole b l a s t i n g Large diameter holes are blasted using two methods. The f i r s t approach i s s i m i l a r to longhole open stoping and involves the slashing of v e r t i c a l s l i c e s ( f u l l stope height) and r e s u l t i n g i n horizontal retreat from the s l o t area. The holes are loaded with a series of 2 to 4 metre charges separated by 2 or 3 metres of stemming. The f u l l hole i s f i r e d in the same blast, to avoid plugging problems. A t y p i c a l production blast f i r e s one or two rows (of 3 to 5 holes each) at a time. However, mass blasts of several rows are not uncommon. The second approach f o r b i g hole b l a s t i n g breaks horizontal s l i c e s , causing v e r t i c a l retreat, from the bottom of the stope towards the top. This i s known as v e r t i c a l crater retreat or v e r t i c a l block mining. A single charge having a length to width r a t i o less than 6 to 1 i s located i n each hole, at an optimum distance from the free face. During production b l a s t s , the bottom portion of a l l the holes are f i r e d and the horizontal ore s l i c e i s cut. One of the major concerns of many operators, in using large diameter holes, i s the pote n t i a l b l a s t i n g damage to stope walls. Several control b l a s t i n g techniques have been developed to reduce b l a s t vibrations and overbreak i n blasthole open stoping. The amount of explosives in the hole i s reduced by separating the charge into short columns separated by decks of an i n e r t material or wooden a i r spacers (figure 2.20). Diluted AN/Fo i s used to reduce the shattering power of the explosives, and i s e s p e c i a l l y e f f e c t i v e i n perimeter holes for wall control. The weight of explosive f i r e d per delay i s reduced. Preshear holes are used to create a plane of shear along the desired l i n e of break. This i s used to reduce production bl a s t e f f e c t s on nearby development or weak walls. The pressure e f f e c t s of the bulk explosive column are reduced by decoupling the charge i n a smaller diameter cardboard or p l a s t i c tube (figure 2.20). 2.6.3 Blasthole r e t r e a t i n g methods As mentioned i n section 2.6.2, blasthole retreat can be 46 30 FT. ~ TRUNK LINE — E CORD DOWNLINE Primacbrd A*— 6 5 FT. SAND STEMMING AUSTIN PRIMER #5 S.P. DELAY 80 lb. TOVEX 448 AUSTIN PRIMER #3 S.P. DELAY "-4 " C a r d b o a r d t u b e s Drill cuttings or crushed stone K^iU. M i AUSTIN PRIMER #1 S.P. DELAY WOOD PLUG SUSPENDED ON POLY ROPE W o o d p l u g — . •".-IS I— 6.5"—! P r i m e r - A N / F O • P r i m e r Decked Charges Decoupled Charges Detonating Cord A i r Spacer FIGURE 2.20 I l l u s t r a t i o n of the loading procedure for large diameter blastholes. 4 7 horizontal (slashing) or v e r t i c a l (crater r e t r e a t ) . The steps for extraction i n horizontal retreat include: the opening of a s l o t ( f u l l stope height) at the extremity of the stope, e n l a r g i n g the s l o t to f u l l stope width and retreating h o r i z o n t a l l y towards the other extremity of the stope. The retreat can involve slashing of one or two rows at a time, or the use of mass bl a s t s . The p r i n c i p l e of mass b l a s t i n g i s to increase the volume of the blasts, as a greater void i s availa b l e for the swell of the broken ore (figure 2.21). The l a s t h a l f of the stope i s often taken at once i n the l a s t mass bl a s t of the stope. The main advantage of t h i s blasting technique i s i t s high productivity. However, since the overcut i s exposed to the blas t i n horizontal retreat, v i b r a t i o n and f l y rock may cause some damage to the stope backs and the remaining blasthole c o l l a r s may require cleanup. V e r t i c a l crater retreat methods are based on the use of spherical charges and cratering theory (Lang et al.,1977). The bottom horizontal s l i c e of the stope (three to four metre thick) i s blasted successively and mining retreats v e r t i c a l l y u n t i l a s i x to ten metre crown i s l e f t (figure 2.22) . The f i n a l crown i s then mass blasted at once. Some mines have found that i t i s d i f f i c u l t to crater b l a s t i n t h i n stopes. A v a r i a t i o n c a l l e d "inverse bench b l a s t i n g " has been developed to a l l e v i a t e t h i s problem. The central portion of the stope i s brought up a couple of rounds i n advance i n order to create a supplementary free face for the production bla s t , and to avoid 48 Develop s l o t r a i s e . Open s l o t to f u l l stope width. Slash s e v e r a l rows of b l a s t h o l e s i n t o s l o t . i I Mass b l a s t remaining ore. FIGURE 2.21 Idealized isometric drawing showing the "mass blast" retreat for blasthole open stope mining method. 49 3 6-10m FIGURE 2.22 C r o s s s e c t i o n o f the v e r t i c a l c r a t e r r e t r e a t method used i n b l a s t h o l e open s tope m i n i n g , showing an i n i t i a l b l a s t , and the remnant crown b l a s t . 50 b l a s t choking conditions (figure 2.23). The advantages of v e r t i c a l retreat are: i t does not need a f u l l stope height s l o t r a i s e which i s expensive and produces heavy bla s t i n g vibrations, i t uses small blasts with small charges, good fragmentation and low explosives costs are often achieved, - the back of the overcut i s not exposed to production blasts, the option of leaving broken ore i n the stope for temporary wall support i s possible. In t h i s case, the mining method does not meet the open stope s p e c i f i c a t i o n defined in t h i s study. One po t e n t i a l disadvantage of v e r t i c a l retreat occurs i f a weak horizontal structure i s present i n the rock mass. Large blocks may be detached from the face (overbreak), causing mucking problems and secondary bla s t i n g . 2.7 SUMMARY AND CONCLUSIONS Open stoping i s a safe non entry mining method. It i s very cost e f f i c i e n t because i t allows for fast extraction, high mechanization, high p r o d u c t i v i t y and i t i s not labour intensive. However, open stope mining has some l i m i t a t i o n s . It i s not s e l e c t i v e , and consequently i t i s more e f f i c i e n t in regular orebodies. Better r e s u l t s are also obtained in steep orebodies having a minimum thickness of 5 metres. At least a 51 FIGURE 2.23 C r o s s s e c t i o n o f the i n v e r s e bench b l a s t i n g method used i n narrow b l a s t h o l e open s tope m i n i n g . 5 2 f a i r to good rock mass strength for the ore and country rock i s also necessary. There are several major variati o n s of open stope mining methods. They have been c l a s s i f i e d i n t h i s chapter according to: the d i r e c t i o n of mining (longitudinal or transverse), the use of b a c k f i l l and p i l l a r s , and the b l a s t i n g practices (longhole or bl a s t h o l e ) . The pre-mining development required i n open stoping can be r e l a t i v e l y extensive and i s comprised of: i n t e r l e v e l access (ramp or manway), development of the d r i l l i n g horizon (access d r i f t , d r i l l i n g d r i f t or overcut), development of the mucking horizon (haulage d r i f t , drawpoints or undercut, drawpoint cross-cuts), and the s l o t r a i s e ( i f necessary). Four general mining sequences have been observed in a number of Canadian open stope mines. In table 2.2, these sequences are compared ag a i n s t ' the open stope mining c l a s s i f i c a t i o n proposed i n section 2.2.4. There are fundamental differences between longhole and blasthole open stoping. Longhole uses small and conventional equipment which has better s e l e c t i v i t y and lower pre-mining development costs. Blasthole i s the epitome of bulk mining TABLE 2.2 Comparison o f the m i n i n g sequence used w i t h the proposed open s tope c l a s s i f i c a t i o n sys tem. OPEN STOPE CLASSIFICATION SYSTEM .1*. o or w co O LONGITUDINAL TRANSVERSAL PILLARS NO PILLARS PILLARS NO PILLARS FILL NO FILL FILL NO FILL FILL FILL BLAST HOLE LONG HOLE BLAST HOLE LONG HOLE BLAST HOLE LONG HOLE BLAST HOLE LONG HOLE BLAST HOLE LONG HOLE BLAST HOLE LEAP FROG X X X X PERMANENT PILLAR X X DIRECTIONAL STOPE AND FILL X X X X FULL LENS MINING X X PANEL MINING X X X X methods using large development, large equipment, and large stopes. Blasthole open stoping generally has lower production costs than longhole, due to higher d r i l l i n g productivity and more e f f i c i e n t b l a s t i n g practices which r e s u l t i n lower explosives costs. The larger production scale of blasthole gives a very high o v e r a l l productivity. 55 CHAPTER 3 STRESS 3.1 INTRODUCTION The stress acting at any point i n the immediate area of underground openings i s a combination of the pre-mining state of stress and the disturbed stress caused by creating voids i n the medium. The r e s u l t i n g "induced" stress f i e l d i s often represented by stream l i n e s of p r i n c i p a l stress t r a j e c t o r i e s in the d i r e c t i o n of the maximum t r a c t i o n . Figure 3.1 shows that in the v i c i n i t y of excavations the l i n e s concentrate in certain areas and part i n other locations. Heavy concentrations of l i n e s i d e n t i f y zones of high compressive stress. This condition may have various e f f e c t s on opening s t a b i l i t y according to the problem geometry and the nature of the rock. The absence of stress t r a j e c t o r y l i n e s corresponds to a state of relaxation i n the medium. The relaxation w i l l have a s i g n i f i c a n t e f f e c t i n a jointed rock mass because i t provides more freedom of movement to i n d i v i d u a l blocks. This chapter i s a summary of background information on: the o r i g i n of the pre-mining stress, how i t can be measured and the p r i n c i p a l laws governing i t s r e d i s t r i b u t i o n around underground openings. U n d e r s t a n d i n g the magnitude and o r i e n t a t i o n of the (redistributed) p r i n c i p a l stress i s an e s s e n t i a l step i n the 56 FIGURE 3.1 A n a l o g y o f a f l o w i n g stream o b s t r u c t e d by t h r e e b r i d g e p i e r s , r e p r e s e n t i n g s t r e s s s t r e a m l i n e s around underground o p e n i n g s . ( A f t e r Hoek and Brown, 1980) 57 stope design procedure. The following discussion i s a comprehensive review of the subject by Hoek & Brown (1980) , Brady & Brown (1985), Bieniawski (1984), Herget (1987) and Kim and Franklin (1987). 3.2 PRE-MINING STRESS The pre-mining stress i s locked into the earth's crust as a r e s u l t of the geological history. The stress regime i s often represented by p r i n c i p a l stresses confining the rock mass at every point i n three orthogonal d i r e c t i o n s . Pre-mining p r i n c i p a l stress in the Canadian s h i e l d usually acts in the sub-vertical and i n two mutually perpendicular sub-horizontal d i r e c t i o n s . Because of the v a r i a b i l i t y of the rock mass domains, the pre-mining stress w i l l be subject to unpredictable v a r i a t i o n s i n space. The factors influencing the i n - s i t u state of stress are summarized below (after Brady & Brown, 1985). a) Surface Topography: Stress measurements have demonstrated that the v e r t i c a l stress i s approximately equal to the weight of overburden. Consequently, major surface i r r e g u l a r i t i e s such as mountain and v a l l e y w i l l influence the d i s t r i b u t i o n of load i n the underlying rock mass. b) Erosion: Erosion or g l a c i a t i o n may remove part of the rock "crown" in c e r t a i n areas reducing the v e r t i c a l i n - s i t u stress. Because 58 the horizontal stress i s locked i n the medium t h i s s i t u a t i o n i s l i k e l y to show high h o r i z o n t a l - v e r t i c a l stress r a t i o . c) Residual Stress: The residual stress i s att r i b u t a b l e to chemical or physical processes such as thermal expansion during the cooling phase of crust formation. Other phenomena causing residual stresses are l o c a l r e c r y s t a l l i z a t i o n i n a rock mass or changes i n the water content of a mineral aggregation. d) Inclusions, Dikes and Veins: The formation of inclusions i n a rock mass are often extrusive, occurring a f t e r the host rock has s e t t l e d . The orientation of the inclusions i s la r g e l y influenced by the state of stress at the moment of t h e i r formation. They may be composed of very hard or very weak materials. The difference i n s t i f f n e s s between the in c l u s i o n and the host rock may provide a l o c a l rearrangement of the stress f i e l d . Very s t i f f inclusions w i l l a t t r a c t stresses while weak inclusions w i l l be destressed. e) Tectonic Stresses: Tectonic a c t i v i t y may modify the loading conditions on a regional scale and are usually associated with major fa u l t s and fo l d i n g . Their e f f e c t i s to increase both v e r t i c a l and horizontal stresses i n the s t i f f e r components of the host rock. f) Fracture sets and Dis c o n t i n u i t i e s : A t r i a x i a l compressive t e s t on a rock specimen may help to 59 interpret the int e r a c t i o n between fracture formation and the state of stress. The orientation, frequency and continuity of rock mass d i s c o n t i n u i t i e s are a l l indicators of the i n -s i t u stress f i e l d . 3.3 STRESS MEASUREMENT A d i s t i n c t d e f i n i t i o n of stress at every point within the rock mass i s an impossible task. However, representative values can be determined using a number of d i f f e r e n t stress measurement techniques. Kim and F r a n k l i n (1987) i n collaboration with the Commission on Testing Methods have reviewed the p r i n c i p a l methods of stress measurements. This review i s summarized below. 3.3.1 Method 1 - Flatj a c k The method consists of i n s t a l l i n g measuring pins on the surface of an excavation and cutting a s l o t between the pins using a diamond saw, or using a series of boreholes . The creation of t h i s s l o t w i l l relax the material on each side and the r e l a t i v e movement can be recorded by the pins. The stress e x i s t i n g i n the rock can be estimated by measuring the pressure required by a f l a t j a c k to bring the pins back to t h e i r o r i g i n a l locations. This t e s t measures the stress i n only one d i r e c t i o n and a minimum of six measurements w i l l be necessary to obtain the stress tensor. Often, nine tests are ca r r i e d out, three in 60 the roof, three i n the wall and three i n the face. E l a s t i c properties are not necessary for t h i s t e s t . Brady & Brown (1985) have i d e n t i f i e d three prerequisites for a successful i n -s i t u stress determination using f l a t j a c k s : "(a) a r e l a t i v e l y undisturbed surface of the opening constituting the t e s t s i t e ; (b) an opening geometry for which closed form solutions exist, r e l a t i n g the f a r - f i e l d stresses and the boundary stresses; and (c) a rock mass which behaves e l a s t i c a l l y , i n that displacements are recoverable when the stress increments inducing them are reversed." 3 . 3 . 2 Method 2 - Hydraulic f r a c t u r i n g The hydraulic fracturing i s the only e x i s t i n g technique to determine the pre-mining stress when d i r e c t access i s not a v a i l a b l e . The t e s t i s done i n part of a d r i l l h o l e , i s o l a t e d by packers, i n which a f l u i d pressure i s applied. "The f l u i d pressures required to generate, propagate, sustain and re-open fractures i n rock at the test horizon are measured and are related to the e x i s t i n g stress f i e l d . " (Kim & Franklin, 1987). An inspection of the fractures at the t e s t horizon using a borehole camera or an acoustic televiewer w i l l help determining the orientation of the p r i n c i p a l stresses. I t w i l l be assumed that the d r i l l h o l e i s i n the same d i r e c t i o n (± 15°) as one of the p r i n c i p a l stress. The hydraulic f r a c t u r i n g measures the 61 maximum and minimum p r i n c i p a l s t r e s s e s i n the plane perpendicular to the d r i l l h o l e . I t i s found to be more e f f i c i e n t i n rock material which behaves as a b r i t t l e , homogeneous, e l a s t i c , i s o t r o p i c and non-porous media. 3 . 3 . 3 Method 3 - Overcoring techniques The overcoring measurement has become one of the most popular techniques because i t often obtains the f u l l three dimensional state of stress from each measurement. Strain gauges mounted on a c e l l are inserted i n a p i l o t hole (approximately 38mm diameter) and fixed at the location of the stress measurement. To obtain the pre-mining stress a distance of at lea s t one opening diameter from the excavation i s recommended. The rock specimen containing the c e l l i s recovered by overcoring using a core barrel approximately 150mm diameter. During the process of overcoring, the rock specimen i s removed from i t s i n s i t u confining state of stress and w i l l be allowed to expand. This deformation i s measured by s t r a i n gauges and when combined with the e l a s t i c properties of the rock, w i l l be used to calculate the magnitude and d i r e c t i o n of the pre-mining stress. An on-site b i a x i a l t e s t on the specimen determines the e l a s t i c properties. It should be noted that breakage of the overcored sample during the te s t i s l i k e l y to invalida t e the measurement. Three types of c e l l s are widely available commercially. - The USBM d r i l l h o l e deformation gauge i s a re-usable c e l l 62 that measures the rock deformation with s t r a i n gauge cantilevers and adjustable length contact pistons. I t measures the maximum and minimum p r i n c i p a l stress in the plane perpendicular to the borehole. Consequently, at least three non-parallel measurements are necessary to obtain the three dimensional i n s i t u state of stress. Since no glue i s necessary, the c e l l works well i n wet conditions. The maximum horizontal range i s less than 30 metres while measurements up to 70 metres away have been achieved v e r t i c a l l y . Both the South African (CSIR) and Australian (CSIRO) c e l l s are based on s i m i l a r concepts. Three rosettes, each comprising three or four s t r a i n gauges are mounted i n three di r e c t i o n s on a non recoverable c e l l . The c e l l i s glued against the wall of the p i l o t hole several hours p r i o r to overcoring. Because the rosettes are i n s t a l l e d at an orienta t i o n such that s i x independent s t r a i n measurements can be obtained, each t e s t can completely define the stress tensor. Overcore breakage and a i r bubbles i n the glue at the s t r a i n gauges locations are two frequent sources of test f a i l u r e . I t has been generally found that stress measurement techniques are expensive and a l l have experimental problems and inaccuracies. The success of a stress measurement program i s in general dependent on the number of tests done. The rate of success of i n d i v i d u a l t e s t s has been reported to be approximately 50 to 70%. 3.3.4 Compilation of stress measurements When s t r e s s measurement i s not possible, a rough estimation can be obtained from compilation of previous measurements. Hoek and Brown have l i s t e d 116 stress measurements from around the world. This data tends to confirm that the v e r t i c a l stress i s generally equal to the overburden pressure and increases l i n e a r l y with depth (figure 3.2). Horizontal stress i s often presented in the form of a r a t i o K, where K i s the average horizontal stress divided by the v e r t i c a l s t ress. K = Avq aH aV On a pl o t of K versus depth, i t can be seen that the horizontal stress data i s quite scattered (figure 3.3). An envelope drawn by Hoek and Brown defines the minimum and maximum l i m i t s of the r a t i o K at d i f f e r e n t depths and can be described by the following formulas: 100 + 0.3 < K < 1500 + 0.5 depth (m) depth (m) This provides a rough estimation of the horizontal stress. It also shows that K tends to diminish with depth, where more i s o s t a t i c stress conditions are found. Herget (1987) has compiled 54 stress measurements from the Canadian s h i e l d . He concluded that the v e r t i c a l stress i s 64 vtaricM. n u t it «, - <*• ' 8 <0 » » >0 » W TO • 1 • * * • « • — - o. 017 1 4 \ • V • MIITtU IA -• v * UMlTtO * CAMAO* ttt.ni \ 0 10*0 n • tCUTHC IAVIA Ui ATIICA • • 0 O T K H \ sooo FIGURE 3.2 Plot of ver t ica l stresses against depth below surface. (After Hoek and Brown, 1980) V i l T t O L . t T H . i l « x o o.s ' .0 i.; :.o IA [^o J.S s , - • » " « ! • • • » • • T • * • « A A » 0 *• 0 / / 1 • « o • o • i < • • o • • • '/ / • • / / a' [ • 1 - . ' / • AUJTtAllA * IWlTlD ITATTl A CAMAM 0 ICAaOlflAViA • tOU7"(»» AfllU 3 OTxtt i[C(0af 1 • ( / 1 ! ; / • • * • / / . / ! / i FIGURE 3.3 Variation of rat io of average horizontal stress to ver t ica l stress with depth below surface. (After Hoek and Brown, 1980) approximately 0.0260 to 0.0324 MPa per metre of overlying rock. At a depth of 0 to 900 metres, the average horizontal stress can be estimated by the following equation, a H = 9.86 MPa + (0.0371 MPa * depth (m)) and from 900 metres to 2200 metres, the average horizontal stress i s , CTH = 33.41 MPa + (0.0111 MPa * depth (m)). Herget's equations show that at a t y p i c a l Canadian open stoping depth the minimum p r i n c i p a l compressive stress i s v e r t i c a l and the maximum and intermediate p r i n c i p a l stresses are horizontal. P l o t t i n g h i s data i n the form of K (average horizontal s t r e s s / v e r t i c a l s t r e s s ) , versus depth, Herget found trends s i m i l a r to those previously i d e n t i f i e d by Hoek and Brown, but obtained a better "envelope" d e f i n i t i o n for h i s region of focus. The lower and upper bounds for K in the Canadian sh i e l d are shown on figure 3.4. These r e l a t i o n s h i p s are very useful when no stress measurements are available. I t i s important to r e a l i z e that the pre-mining stress regime may deviate s i g n i f i c a n t l y from the estimations proposed by Hoek and Brown or Herget due to the geological h i s t o r y or l o c a l e f f e c t s . 3.4 INDUCED STRESS AND STRESS DISTRIBUTION 66 FIGURE 3.4 V a r i a t i o n of r a t i o of average horizontal stress v e r t i c a l stress with depth below surface, from Canadian s h i e l d measurements. (After Herget, 1987) 67 Stress cannot be transferred through voids, thus the creation of openings w i l l produce a re-arrangement of stress magnitudes and orientations i n the v i c i n i t y of the openings. The new stress d i s t r i b u t i o n w i l l be a function of the o r i g i n a l loading conditions, the opening geometry, and the stress and s t r a i n behaviour of the rock mass as a r e s u l t of loading. The i n t e r a c t i o n of these factors w i l l reach a state of equilibrium that w i l l be v e r i f i a b l e at the excavation boundary and at the far f i e l d . In order to understand how a new d i s t r i b u t i o n i s obtained, i t i s necessary to look at some d e f i n i t i o n s and the concepts of force, t r a c t i o n and stress i n a continuum. 3.4.1 Components of stress Consider a small surface element within the rock mass. The r e s u l t i n g force acting on the element due to the pre-mining and induced stresses can be defined by three components, one acting normal to the surface (a z) and two shear components acting p a r a l l e l ( v z x , r Zy) (Figure 3.5). Now consider a very small cubical element which represents a better model since the pre-mining state of stress i s three dimensional. The three components of stress acting on a surface element are now applied to each of the s i x faces of the cube (figure 3.6). Assuming the cube i s vanishingly small, the components of 68 FIGURE 3 .5 S t r e s s components a c t i n g on a s u r f a c e e l ement . ( A f t e r Hoek and Brown, 1980) FIGURE 3.6 S t r e s s components a c t i n g on a c u b i c a l e l ement . ( A f t e r Hoek and Brown, 1980) 69 stress on p a r a l l e l faces becomes i d e n t i c a l . This s a t i s f i e s the c o n d i t i o n of t r a n s l a t i o n a l e q u i l i b r i u m and a l l o w s s i m p l i f i c a t i o n of the problem by considering only three faces of the cube. In order to s a t i s f y the conditions of r o t a t i o n a l equilibrium, the conjugate shear stresses must cancel each other. Therefore, Txy = ryx Txz = Tzx Tyz = T z y The d e f i n i t i o n of the complete three dimensional state of stress at a point (described by the cubical element) can then be expressed by the following six components of stress: °xi °z' °y T x y Txz' Tyz Since these components of stress are expressed as functions of an a r b i t r a r i l y chosen x, y, z cartesian set of reference axes t h e i r magnitude w i l l be influenced by the r e l a t i v e o r i e n t a t i o n of the cube with the reference axes. A non-a r b i t r a r y system of reference i s required to have a base for comparison and to develop mathematical re l a t i o n s h i p s that w i l l be invariant under any rotations with regard to the reference axes. I f the applied load on a surface element i s i n the same d i r e c t i o n as the normal of the plane, the two shear stress components w i l l disappear. This d i r e c t i o n i s defined as a p r i n c i p a l stress d i r e c t i o n . By convention, the stress d i r e c t i o n having the highest magnitude i s c a l l e d the maximum (or major) p r i n c i p a l stress and i s represented by a^. The lowest stress i s the minimum (or minor) p r i n c i p a l stress and i s represented by a 3 . a 2 i s the intermediate p r i n c i p a l stress and 70 represents the stress acting i n the d i r e c t i o n orthogonal to and o3# The p r i n c i p a l stresses provide a useful non-arbitrary system for which the components of stress can be expressed. Transformation equations w i l l be required i n order to change the components of stress from any a r b i t r a r y system of reference to the p r i n c i p a l s t r e s s system of reference. These transformation equations are b r i e f l y discussed i n Hoek and Brown (1980; p 89) and more d e t a i l s are given i n Brady and Brown (1985; p 19). 3.4.2 Two dimensional state of stress A problem can be considerably s i m p l i f i e d i f i t can be considered i n only two dimensions. In practice, t h i s assumption i s v a l i d only i f the neglected dimension i s very long compared with the two others. For example, a mining raise i s very long i n one d i r e c t i o n compared to i t s cross-section. The stress d i s t r i b u t i o n can be assumed the same for a l l cross-sections of the raise except close to the ends. Three dimensional problems have the lengths of a l l three axes of the opening i n the same order of magnitude. The s i m p l i f i c a t i o n from a three dimensional problem to a two dimensional problem can be made mathematically by assuming plane stress or plane s t r a i n conditions. Plane stress means that a l l forces acting on a body are within the same plane (cross-section). Consequently, a z, v x z , and T y Z are a l l equal to zero and the complete two dimensional state of stress can be 71 expressed by a x, Oy, and r X y (figure 3.5). Photoelastic models where plates of plexiglass are b i a x i a l l y loaded represent a physical example of plane stress conditions. The basic assumption of plane s t r a i n i s that during the process of excavation, displacements can occur only within a plane normal to the long axis of the opening. The forces are a l l assumed to be perpendicular to the long axis and invariable along t h i s axis. In the case of plane s t r a i n , the state of stress can be s i m p l i f i e d to only three components: a x, Oyf Txy. 3.4.3 Two dimensional closed form solu t i o n of simple excavation shape The two dimensional s i m p l i f i c a t i o n s of plane s t r a i n and plane stress permitted the development of two dimensional closed form solutions for excavations having simple geometries. The conditions to be s a t i s f i e d i n the solu t i o n of stress and displacement d i s t r i b u t i o n s for s p e c i f i c problem geometries and loading conditions, have been i d e n t i f i e d by Brady and Brown (1985) as: a) The boundary conditions for the problem. b) The d i f f e r e n t i a l equations of equilibrium. c) The c o n s t i t u t i v e equation for the material. d) The s t r a i n compatibility equations. The two dimensional solution for the simplest possible case, a single c i r c u l a r opening i n a perfect e l a s t i c medium, was proposed by Kirsh (1898). The equations are given on figure 3.7. They are expressed i n terms of: the r a d i a l stress (a r) , tangential stress (OQ), and shear stress (TR&) a s well as i n terms of the major p r i n c i p a l stress (cr^) and the minor p r i n c i p a l stress ( a 3 ) . P r a c t i c a l mining applications of the Kirsh equations are l i m i t e d since few mine have a c i r c u l a r shape. However, t h i s closed form solution i s useful i n examining c e r t a i n e f f e c t s of excavations on stress d i s t r i b u t i o n . a) Boundary stress: In the case of c i r c u l a r openings, the boundary stress can be obtained when " r " (the point of i n t e r e s t measured from the c i r c l e centre) equals "a" (the c i r c l e radius). Substituting t h i s equality in equations 1, 2, and 3, gives r a d i a l stress a r and shear stress r r 0 equal to 0. Thus, the only component of stress acting at the boundary of an opening i s the tangential stress, which i n the case of c i r c u l a r openings i s given by: oQ = P z {(1+K) - 2(1-K)cosineG} b) Zone of influence of an opening: The disturbance e f f e c t on stress due to excavations tends to diminish as the point of i n t e r e s t moves further from the excavation into the medium. The Kirsh equations can be used to determine the zone of influence of a c i r c u l a r opening by 73 V e r t i c a l a p p l i e d s t r e s s p 2 J II I.I I . I IL 1 STRESS COMPONENTS AT POINT ( r , 6 ) R a d i a l O r * i Pz {(1 + k) (1 - a2 / r-) * (1 - k) (1 - ka2/r2 * Uu/r")Zoi 29] T a n g e n t i a l o g • i P j ( ( 1 f k ) (1 +a 2 / r 2) - (1 - k)(1 + 3 a u / r " ) C o s 29 J Shear T - i P z ( - ( l - k ) ( ) - 2 a 2 / r 2 - 3 a V r " ) S i n 26 ) PRINCIPAL STRESSES IN PLANE OF PAPER AT POINT ( r . 6 ) Maximum oj » : (o * a.) + ( i ( o - o „ ) 2 + T D' • 8 r 9 r o Minimum o 2 - H o + c ) - l i f e - o j 2 + T 2 ) 5 r 8 r 6 r 8 I n c l i n a t i o n s to r a d i a l d i r e c t i o n Tan 2a * 2T r g / ( o g - a r) FIGURE 3.7 Kirsh equations for the stresses i n the material surrounding a c i r c u l a r hole i n a stressed e l a s t i c orebody. (After Hoek and Brown, 1980) • i I 11 i 11 r 7 4 c a l c u l a t i n g the tangential stress along the horizontal axes at d i f f e r e n t distances (r=a, r=2a, r=3a e t c . ) , u n t i l the induced tangential stress e f f e c t i v e l y becomes the pre-mining v e r t i c a l stress P z. Figure 3.8 shows that t h i s occurs at a distance of r=3a from the centre of the opening. In the case of multiple openings, the e f f e c t of one excavation on another w i l l be n e g l i g i b l e when t h e i r centers are separated by a distance of at l e a s t r=6a. If the openings are closer, the components of stress due to each excavation w i l l cumulate to produce higher compressive stresses or t e n s i l e stresses inside the medium and at the boundaries of the openings. An increase of tangential stress at the boundary may r e s u l t i n wall or roof i n s t a b i l i t y (due to tension or compression). While inside the medium, an increased stress may a f f e c t p i l l a r s t a b i l i t y . c) E f f e c t of e l a s t i c constants and the size of the excavation: I t can be seen that the e l a s t i c constants (poisson's r a t i o and e l a s t i c modulus) and the opening s i z e do not appear i n the Kirsh equation. This suggests that these factors have no i n f l u e n c e on the d i s t r i b u t i o n of s t r e s s around underground excavations. However, t h i s does not deny t h e i r e f f e c t on the s t a b i l i t y of openings. Bray i n 1977, proposed a set of formulae representing a s i m p l i f i c a t i o n of the closed form solution, for the c a l c u l a t i o n 75 FIGURE 3.8 V a r i a t i o n i n the r a t i o of tangential stress aQ to the v e r t i c a l applied stress pz with r a d i a l distance r along horizontal axis f o r K=0. (After Hoek and Brown, 1980) I ' 1 q = W/H FIGURE 3.9 D e f i n i t i o n of nomenclature f o r an e l l i p t i c a l excavation with axes p a r a l l e l to the f i e l d stresses. (After Brady and Brown, 1985) of the state of stress at a point on the boundary of an e l l i p t i c a l opening. The stresses acting at the sidewall (point A) and i n the roof (point B) shown i n figure 3.9 are given by the following equations: a A = p (1 - K + 2q) = p (1 - K + (2W/PA)^) a B = p (K - 1 + 2K/q) = p (K - 1 + K(2H/P B)^) where: a A = induced stress acting at a point A of the e l l i p s e boundary a B = induced stress acting at a point B of the e l l i p s e boundary, p = minimum pre-mining stress, K = r a t i o of maximum over minimum pre-mining stress, q = r a t i o of the e l l i p s e width and height, W = e l l i p s e width, H = e l l i p s e height, P A = r a d i i of curvature at a point A of the e l l i p s e boundary, P B = r a d i i of curvature at a point B of the e l l i p s e boundary. These equations demonstrate that the smaller the radius of curvature (P A, PB)< t n e larger the stresses at t h i s point w i l l be. Consequently, a high boundary curvature (1/P) w i l l generate high stress concentrations. T h e o r e t i c a l l y , a sharp corner produces i n f i n i t e l y high stresses. The equations also 77 show that the stress d i s t r i b u t i o n i n the case of an e l l i p s e i s a function of the r a t i o of the axes and t h e i r orientation with regard to the p r i n c i p a l stresses. When the long axis of the e l l i p s e i s oriented i n the same d i r e c t i o n as the major p r i n c i p a l stress a more favorable stress d i s t r i b u t i o n i s obtained. These two dimensional e l a s t i c solutions are useful to understand the f a c t o r s i n f l u e n c i n g the d i s t r i b u t i o n of stresses. However, they are r a r e l y suitable to solve t y p i c a l mining problems which involve various arrangements of stopes having i r r e g u l a r shapes. "This may be because the boundary c o n d i t i o n s cannot be d e s c r i b e d by simple mathematical functions, the governing p a r t i a l d i f f e r e n t i a l equations are non-linear, the problem domain i s inhomogeneous, or the c o n s t i t u t i v e r e l a t i o n s for the rock mass are non-linear or otherwise i n s u f f i c i e n t l y simple mathematically." Brown (1987). Consequently, i n most p r a c t i c a l problems, only numerical modelling can provide a r e a l i s t i c solution for the stress d i s t r i b u t i o n . 3.5 NUMERICAL MODELLING There are many types of numerical models having d i f f e r e n t degrees of so p h i s t i c a t i o n . Some models are l i m i t e d to two dimensional problems, assuming plane s t r a i n or plane stress 78 c o n d i t i o n s , while others can handle three dimensional geometries. According to the mathematical concepts used i n the development of numerical models, they are better suited to analyze problems having s p e c i f i c c h a r a c t e r i s t i c s and behaviour. The behaviour of a rock mass can be modelled assuming two d i f f e r e n t approaches. The continuum approach assumes the rock to be a continuous medium with few or no s i g n i f i c a n t geological d i s c o n t i n u i t i e s . The discontinuum approach considers the rock mass to be an assemblage of blocks capable of s l i d i n g and rotati n g . The application of discontinuum models i n mining problems i s s t i l l i n i t s infancy. Consequently, the continuum approach i s by far most popular and best developed method at t h i s time. The emphasis of t h i s review w i l l concentrate on modelling using a continuum approach. 3.5.1 Continuum approach The basic concept used i n the continuum approach i s i l l u s t r a t e d i n figure 3.10. A region "R" i s defined i n a medium subject to loading conditions representing the pre-mining stresses. According to the anticipated response of the medium to load, a var i e t y of rock mass properties may be assigned to the medium by means of c o n s t i t u t i v e equations for the material. Bieniawski (1984), suggested that the properties that can be modelled include the following c o n s t i t u t i v e behaviours; l i n e a r e l a s t i c , non l i n e a r e l a s t i c , l i n e a r v i s c o e l a s t i c , e l a s t o - p l a s t i c , e l a s t o - v i s c o - p l a s t i c , FIGURE 3.10 I d e a l i z e d s k e t c h showing the p r i n c i p l e n u m e r i c a l m o d e l l i n g . 80 anisotropic, d i l a t a n t , thermal-dependant and stochastic. In hard rock mining, l i n e a r and non-linear e l a s t i c media are usually assumed. The e f f e c t on the stress d i s t r i b u t i o n i n the medium of creating excavations w i l l be calculated at discrete points inside the medium or at the excavation boundary, using d i f f e r e n t i a l equations of equilibrium and s t r a i n compatibility equations. Continuum numerical models can be divided into two groups depending on the mathematical method u t i l i z e d . D i f f e r e n t i a l methods approximate the solution for the entire domain while the i n t e g r a l methods require approximation at the problem boundary only. a) D i f f e r e n t i a l methods: The d i f f e r e n t i a l methods divide the entire region into a mesh of elements having various shapes and areas. The f i n i t e element methods tra n s f e r the load o r i g i n a l l y applied to the region along the network of elements. The transmission of the forces from element to element i s completely represented by interactions at the nodes of the elements. The problem i s then analyzed as a set of nodal forces and displacements for a d i s c r e t i z e d region. The f i n e r the mesh, the more accurate the solution w i l l be. When pre c i s i o n i s required i n c e r t a i n areas of the problem, the mesh can be constructed with smaller elements. F i n i t e element i s a powerful and v e r s a t i l e method that i s capable of simulating n o n - l i n e a r e l a s t i c , p l a s t i c and heterogeneous material properties. However, the medium i s not assumed i n f i n i t e and a 81 far f i e l d boundary of the region must be a r b i t r a r i l y defined. The f a r f i e l d stress conditions, i n t h i s case, may not be completely s a t i s f i e d which w i l l introduce inaccuracies i n the solut i o n . The f i n i t e difference models also use a d i f f e r e n t i a l method. Their best application i s i n solving "transient or dynamic problems". They are r a r e l y employed for problems in s t a t i c s (Cundall, 1976). b) Integral methods: Integral methods require only the contour of the excavation inside the region to be d i s c r e t i z e d . This reduces the si z e of the problem by an order of magnitude, and makes them e s p e c i a l l y useful in solving complicated three dimensional problems. In boundary element models, the excavation boundaries are divided into l i n e a r (two dimensional models) or surface elements (three dimensional models). The influence of stresses from one element to another i s calculated using i n t e g r a l equations. Stresses acting anywhere inside the region can be extrapolated from the boundary solution. The boundary element method assumes the medium i n f i n i t e or semi i n f i n i t e and i s usually applicable when the material i s homogeneous and i s o t r o p i c . More sophisticated boundary element models divide the region "R" into piece wise homogeneous sub-regions to which d i f f e r e n t l i n e a r material properties can be assigned. This feature i s useful i n mining applications when hanging wall, ore and footwall have v a s t l y d i f f e r e n t rock mass 82 c h a r a c t e r i s t i c s . The boundary element models are generally simpler to use and i n t r i n s i c a l l y less complicated than f i n i t e element models. Another i n t e g r a l method commonly employed for mining problems i s the pseudo-three dimensional displacement d i s c o n t i n u i t y model. In t h i s method, the orebody i s d i s c r e t i z e d into a g r i d of square two dimensional elements. The t h i r d dimension i s the width of the orebody (seam), which must be small i n r e l a t i o n to the o v e r a l l s i z e of the problem in order for the model to give an accurate solution. For p r a c t i c a l purposes, the reef can be considered two p a r a l l e l planes. Displacement disc o n t i n u i t y components i n three dimensions are associated with each element and represent r e l a t i v e displacements between the two planes. Displacements and stresses at unmined points i n the seam are calculated as a l i n e a r combination of the displacement d i s c o n t i n u i t i e s of a l l the elements i n the seam. 3.5.2 Discontinuum approach " When the rock structure i s large or small compared with the material structure a continuum analysis i s j u s t i f i e d . In intermediate cases the behaviour tends to be that of a discontinuum. This requires the use of a method of analysis that models adequately the load deformation responses of the i n d i v i d u a l d i s c o n t i n u i t i e s and allows for several s p e c i f i c features of discontinuum behaviour." Stewart & Brown (1984). 83 The most important features of discontinuum models are t h e i r d e f o r m a t i o n c h a r a c t e r i s t i c s can be r o t a t i o n a l , extensional or by s l i d i n g , according to the orientation, dip and s t i f f n e s s of d i s c o n t i n u i t i e s . Consequently, the in t e r l o c k i n g of blocks or in d i v i d u a l f a i l u r e of blocks may r e s u l t from the load displacement c h a r a c t e r i s t i c s . Although popular methods such as f i n i t e element, boundary element and f i n i t e difference have been applied in the discontinuum approach, the basic p r i n c i p l e of these methods do not model properly the discontinuum c h a r a c t e r i s t i c s (after Brady & Brown,1985). Brown (1987) described the d i s t i n c t element method as follows: "This method uses a dynamic relaxation technique to solve Newton's laws of motion to determine the forces between, and the displacement of, units d u r i n g the p r o g r e s s i v e , l a r g e - s c a l e d e f o r m a t i o n of discontinua." The t r a n s l a t i o n and rotation at block centers can be determined from the resultant forces and moments acting on each block. The application of d i s t i n c t element method in Canadian mining problems i s currently at the research stage. 3.6 SUMMARY AND CONCLUSIONS The objective of t h i s chapter was to review various .aspects of stress i n the engineering design of underground openings. The design parameter of greatest i n t e r e s t i s the 84 magnitude and orientation of the induced stress acting around excavations. The induced stress i s the r e s u l t of the r e d i s t r i b u t i o n of the pre-mining stress f i e l d caused by the process of mining. In the Canadian s h i e l d , the minimum p r i n c i p a l s t r e s s i s generally sub-vertical, the maximum p r i n c i p a l stress sub-horizontal and perpendicular to the orebody s t r i k e and the intermediate p r i n c i p a l stress i s sub-horizontal and along the orebody s t r i k e . Six factors may have had some influence on the pre-mining stress f i e l d during the geological history: surface topography, erosion, residual stress, inclusion, dykes and veins, tectonic stresses, fracture sets and d i s c o n t i n u i t i e s . The three methods used to determine the pre-mining stress f i e l d at a given location are: the f l a t j a c k , hydro-fracturing and o v e r c o r i n g methods. When stress measurements are not available, relationships based on the compilation of e x i s t i n g measurements can be used for rough estimates. Compilations of stress tests around the world (Hoek & Brown, 1980) are shown in figure 3.2 and 3.3, while a summary of the stress tests done in the Canadian s h i e l d by Herget (1987) i s shown in figure 3.4. The stress d i s t r i b u t i o n around openings may be estimated from the pre-mining stress, using a close form solution for a simple 85 geometry, or using numerical modelling i n more complex and p r a c t i c a l applications. There are many models available having d i f f e r e n t c a p a b i l i t i e s and l i m i t a t i o n s . They can be divided based on the continuum or discontinuum approach of analysis and s u b - d i v i d e d a c c o r d i n g t o the method of c a l c u l a t i o n ( d i f f e r e n t i a l or i n t e g r a l methods). 86 CHAPTER 4 FAILURE CRITERIA 4.1 INTRODUCTION "A c r i t e r i o n of f a i l u r e i s an algebraic expression of the mechanical condition under which a material f a i l s by fracturing or deforming beyond some s p e c i f i e d l i m i t . This s p e c i f i c a t i o n can be i n terms of load, deformation, stress, s t r a i n or other parameters." Z.T. Bieniawski (1984). Because of the variable nature of the rock mass, f a i l u r e may follow several possible mechanisms. I f the rock mass contains very few or no d i s c o n t i n u i t i e s , the f a i l u r e mechanism w i l l be cracking or crushing of inta c t rock. When several, widely spaced d i s c o n t i n u i t i e s are present i n the rock mass, s l i d i n g or shearing of large blocks i s possible. In the case of a heavily jointed rock mass (d i s c o n t i n u i t i e s having close spacing), the mechanism of f a i l u r e w i l l be a r a v e l l i n g of small blocks. Consequently, three types of f a i l u r e c r i t e r i o n w i l l be reviewed i n t h i s chapter: int a c t rock f a i l u r e c r i t e r i o n , a shearing f a i l u r e c r i t e r i o n for geological d i s c o n t i n u i t i e s , and a jointed rock mass f a i l u r e c r i t e r i o n . The variable state of stress to which the rock mass can be submitted also adds to the complexity of the problem. T y p i c a l l y , the rock mass at the boundary of excavations w i l l be submitted to a b i a x i a l stress condition while further into the 87 medium a three dimensional state of stress i s l i k e l y to ex i s t . Different techniques have been used to develop f a i l u r e c r i t e r i a . Laboratory t e s t i n g of rock specimens constitutes a d i r e c t method of observing the behaviour of rock under cont r o l l e d stress conditions. I f the specimen and loading conditions are representative of the i n - s i t u conditions, l a b o r a t o r y t e s t i n g can provide useful f a i l u r e c r i t e r i a . Otherwise, a n a l y t i c a l or empirical relationships have to be used to account for the differences between laboratory and i n -s i t u conditions. The c r i t e r i a reviewed i n t h i s chapter are based on stress and w i l l be expressed i n terms of major and minor p r i n c i p a l stresses (o~]_, 03) or i n terms of shear and normal stresses (r, rj n) . The mathematical equations describing the f a i l u r e of rock are often normalized by d i v i d i n g each member of the equation by the u n i a x i a l compressive strength of the rock material ( C T C ) . This provides a base for the comparison of r e s u l t s from a number of tests made on a vari e t y of specimens under d i f f e r e n t conditions. Also, the most common laboratory tests used in applied rock mechanics w i l l be b r i e f l y discussed i n t h i s chapter. 4.2 INTACT ROCK MATERIAL FAILURE CRITERIA 4.2.1 Laboratory t e s t i n g In the case of i n t a c t rock, small specimens are 8 8 r e p r e s e n t a t i v e of the whole medium, which allows the determination of t h e i r properties i n a laboratory (provided that the scale e f f e c t i s accounted f o r ) . Testing procedures have been developed to determine the un i a x i a l (unconfined) compressive strength or mult i - a x i a l (confined) compressive strength, as well as the t e n s i l e strength of in t a c t rock. 4.2.1.1 Uniaxial compressive strength (o"c, or UCS) The u n i a x i a l (or unconfined) compressive strength provides a simple and useful index to compare the resistance of rock to crushing. I t i s the most widely used c h a r a c t e r i s t i c i n rock mechanics and i t i s included i n most a n a l y t i c a l and empirical f a i l u r e c r i t e r i a . I t can be estimated by submitting a d r i l l core sample (of a standard s i z e and shape) to an increasing a x i a l load. The suggested diameter of the sample i s 54 mm (NX) core or greater. The core length should be 2.5 to 3 times the diameter. The value of un i a x i a l compressive strength can be derived from the plot of the a x i a l deformation of the specimen versus the load applied (figure 4.1). The ultimate compressive strength i s the peak load that the rock specimen can sustain before f a i l u r e . I t i s represented by point B on figure 4.1. Beyond t h i s point, rock may f a i l v i o l e n t l y or simply lose i t s e l a s t i c p r o p e r t i e s , which means g r e a t e r and permanent deformation under a given load. Uniaxial compressive testing also allows the c a l c u l a t i o n of the deformation c h a r a c t e r i s t i c s 89 Strain FIGURE 4.1 Typical stress s t r a i n r e l a t i o n s h i p during the t e s t i n g of an unconfined e l a s t i c specimen i n compression. 90 of the rock: poisson's r a t i o , and e l a s t i c modulus. The e l a s t i c modulus i s the slope of the p r e - f a i l u r e region on the load deformation curve (point A, figure 4.1). Thus i t defines the rock's c a p a b i l i t y to deform a x i a l l y under u n i a x i a l loading before f a i l u r e occurs. The Poisson's Ratio i s defined as the r a t i o of the slope of a x i a l deformation curve divided by the slope of the r a d i a l deformation curve. In order to determine the value of Poisson's Ratio, diametral s t r a i n gauges must be i n s t a l l e d on the sample to record the r a d i a l deformation. These e l a s t i c c h a r a c t e r i s t i c s are often used to numerically model rock deformation or used i n s p e c i f i c f a i l u r e c r i t e r i o n based on rock deformation. The value of i n t a c t rock e l a s t i c modulus and Poisson's r a t i o are not applicable to jointed rock masses unless they are modified to account for the presence of geological d i s c o n t i n u i t i e s . 4.2.1.2 Confined (Multiaxial) Compressive Strength The objective of multi-axial t e s t i n g i s to determine the a x i a l load (o^) necessary to f a i l a rock specimen under a state of confinement ( a 3 ) . The t r i a x i a l compressive t e s t has been designed to represent better the three dimensional stress conditions to which i n s i t u rock i s submitted. The test consists of loading a piece of d r i l l core while o i l pressure applies a constant r a d i a l stress on the specimen. The main inaccuracy of t h i s t e s t i s that i n s i t u horizontal stress i s r a r e l y constant and varies from the normal d i r e c t i o n . According to Brady and Brown (1985;p.102), the major ef f e c t s of increasing confining pressure are: - the peak strength increases, - there i s a t r a n s i t i o n from t y p i c a l l y b r i t t l e to f u l l y d u c t i l e behaviour, with the introduction of p l a s t i c mechanisms of deformation including c a t a c l a s t i c flow and grain s l i d i n g e f f e c t s , - the region incorporating the peak of the a x i a l stress-deformation curve f l a t t e n s and widens, - the post peak drop i n stress (to the residual strength) reduces and disappears at high values of confining stress. A b i a x i a l t e s t also exists where load i s applied to rectangular or cubical specimens i n two orthogonal direc t i o n s , leaving the specimen unconfined i n the t h i r d d i r e c t i o n . This t e s t represents the excavation boundary conditions better than the u n i a x i a l and t r i a x i a l t e s t s . However, among other experimental problems, the end e f f e c t s have a strong influence on the r e s u l t s . 4.2.1.3 Uniaxial t e n s i l e strength Rock materials i n general are known to have a r e l a t i v e l y low t e n s i l e strength. For t h i s reason, t e n s i l e strength tests are often not necessary since low t e n s i l e strength values (approximately 0 to 5 MPa) can be assumed. However, when a 92 greater degree of accuracy i s desirable, a un i a x i a l t e n s i l e strength t e s t can be performed. I t consists of i n s t a l l i n g two gripping devices at each end of the rock sample which allows the a p p l i c a t i o n of a t e n s i l e load on the specimen. The load measured at rupture i s the uni a x i a l t e n s i l e strength of the in t a c t rock material. 4 . 2 . 2 A n a l y t i c a l Approach A n a l y t i c a l approaches attempt to reproduce mathematically the exact mechanism of rock f a i l u r e . The most inter e s t i n g a n a l y t i c a l f a i l u r e c r i t e r i o n for inta c t rock i s probably the one developed by G r i f f i t h i n 1921, and modified by McLintock and Walsh i n 1962. It formed the basis of fracture mechanics which has some application i n the study of rock fracturing. G r i f f i t h based his crack theory on the energy i n s t a b i l i t y concept. "A crack w i l l extend only when the t o t a l p o t e n t i a l energy of the system of applied forces and material decreases or remains constant with an increase i n crack length." Brady and Brown (1985). The extension of cracks w i l l occur i n plane compression i f : (o^ - a 2 ) 2 - 8 To (tf! + a 2) =0 i f a x + 3a 2 > 0 or a 2 + To = 0 i f a-^  + 3a 2 < 0 where, To i s the uni a x i a l t e n s i l e strength of in t a c t material. G r i f f i t h equations can also be written as functions of the shear and normal stresses acting on the plane containing the 93 crack: r 2 = 4 To (cTn + T Q) . 4.2.3 Empirical Approach Bieniawski (1974) studied the application of two empirical f a i l u r e c r i t e r i a (Murrell, 1965; Hoek, 1968), and found them suitable for predicting the t r i a x i a l strength of i n t a c t rock material. The M u r r e l l 1 s r e l a t i o n s h i p can be written: a i / a c = A [a 3 /a c ] ° - 7 5 + 1 where: o-^ = major p r i n c i p a l stress, a2 - minor p r i n c i p a l stress, OQ = un i a x i a l compressive strength, A = an empirical constant. Hoek f a i l u r e c r i t e r i o n for in t a c t rock i s described by: r m / a c = B [a m/a c] °- 9 + 0.1 where: Tm = maximum shear stress; = (a^-a 3)/2 a m = mean normal stress; = {0^+02)/2 As a r e s u l t of 412 tested specimens on f i v e d i f f e r e n t rock types, Bieniawski (1974) proposed the empirical constants A and B l i s t e d i n Table 4.1 for the Murrel and Hoek empirical r e l a t i o n s h i p s . The p r a c t i c a l mining application of a n a l y t i c a l and empirical f a i l u r e c r i t e r i o n for i n t a c t rock are limited because geological d i s c o n t i n u i t i e s are present i n the rock mass and play an important role i n excavation s t a b i l i t y . 4.3 SHEAR FAILURE CRITERION ALONG AN EXISTING DISCONTINUITY 94 Criterion a, <-<»,-> Norile A = 5.0 Error: 3.6°; B = 0 80 Error: 1.8% Quart zite A = 45 9 2% B = 0 78 3.2% Sandstone A = 4.0 5.8% B = 0.75 2.3% Sillstone A = 3.0 5.6% B = 0.70 4.2% Mudstone A = 3.0 6-1% B = 0 70 6.6% Ail Prediction Prediction types A = 3.5 error: 10.4% B = 0.75 error: 8.3% TABLE 4.1 Values of the constant A from the Murrell i n t a c t rock f a i l u r e c r i t e r i o n , and B from the Hoek i n t a c t rock f a i l u r e c r i t e r i o n , for f i v e rock materials. (After Bieniawski, 1984) 95 4 . 3 . 1 Shear strength The shear strength developed along a disc o n t i n u i t y i s usually a c o n t r o l l i n g factor regarding the s t a b i l i t y of large blocks. I t i s dependent on the c h a r a c t e r i s t i c s of the d i s c o n t i n u i t y (roughness, a l t e r a t i o n and i n f i l l i n g ) , as well as the load acting normal to the discon t i n u i t y . The d i r e c t shear tes t has been developed to determine the shear strength of geological d i s c o n t i n u i t i e s i n the laboratory. The major cost of the t e s t comes from the c o l l e c t i o n of jointed specimens, which i n v o l v e s c a r e f u l diamond d r i l l i n g and specimen preparation. A shear box i s used to apply shear and normal s t r e s s e s s i m u l t a n e o u s l y on a specimen c o n t a i n i n g a di s c o n t i n u i t y aligned i n the d i r e c t i o n of the shear stress. It i s then possible to measure the force necessary to induce movement under various normal loading conditions. Coulomb (1776) proposed the following r e l a t i o n s h i p between the shear strength ( r ) , the cohesion of the rock material (C), the stress component normal to the di s c o n t i n u i t y (an) and the f r i c t i o n angle (0) , T - C + a n tan <p. Referring to figure 4.2, r and a n can be expressed in function of the compressive stress (cr^) and the confining s t r e s s (cr 3) a c t i n g on the specimen c o n t a i n i n g the di s c o n t i n u i t y : T = 1/2 (o1 - CT3) s i n 2/3 96 FIGURE 4.2 Idealized sketch showing a rock specimen submitted to t r i a x i a l compression. — Tension I 0 Ccapressisn —— Normal stress o FIGURE 4.3 Graphical representation of the Mohr c i r c l e and f a i l u r e envelope. (After Hoek and Brown, 1980) a n = 1/2 (a-L + a 3) + 1/2 (o1 - a 3) cos 2/3. These rel a t i o n s h i p s can also be displayed on a cartesian system of axes, where on i s represented on the x-axis and T on the z-axis. The c i r c l e defined by the a x i a l stress (a^) and confining stress (a 3) i s c a l l e d the Mohr c i r c l e (figure 4.3). By t e s t i n g a disc o n t i n u i t y under d i f f e r e n t (o± and CT3) loading conditions using a shear box, a series of Mohr c i r c l e s can be determined. This forms the Mohr-Coulomb f a i l u r e envelope (figure 4.3). The unconfined compressive strength i s shown on t h i s graph where the f a i l u r e envelope crosses the shear axis (ie. confining stress i s 0) , while the t e n s i l e strength can be read where the envelope crosses the normal stress axis (figure 4.3). 4.3.2 F r i c t i o n angle The f r i c t i o n angle (cp) i s a useful shear strength c h a r a c t e r i s t i c because i t i s independent of the loading conditions. I t can be obtained from the Mohr-Coulomb f a i l u r e envelope by measuring the angle the envelope makes with the horizo n t a l . Physically, several factors may a f f e c t the f r i c t i o n angle of a material. Among them the roughness of the surface has a major influence. Figure 4.4 shows exaggerated i r r e g u l a r i t i e s on a discontinuity surface. When shear movement i s induced along t h i s plane, depending on the s t i f f n e s s of the i r r e g u l a r i t i e s , they may s l i p on each other and cause dilatancy of the dis c o n t i n u i t y or may simply be crushed. It i s expected 98 1 FIGURE 4.4 Idealized sketch showing the shearing along a di s c o n t i n u i t y surface having an exaggerated roughness. (After Brady and Brown, 1985) FIGURE 4.5 Graphical representation of the peak and residual f r i c t i o n angle. (After Brady and Brown, 1985) 99 that a combination of these phenomenon happen creating the r e s i s t i n g force against shear stress. Another important factor i s the presence of i n f i l l i n g within the disconti n u i t y . Weak i n f i l l i n g material such as c h l o r i t e or graphite has p r a c t i c a l l y no cohesion and a r e l a t i v e l y low f r i c t i o n angle, while hard material such as quartz i n f i l l i n g has a high f r i c t i o n angle and high shear strength. It i s important to d i f f e r e n t i a t e between the peak (0 peak) and the residual (0 res) f r i c t i o n angle. The peak angle of f r i c t i o n i s measured as the i n i t i a l shear displacement occurs. I t corresponds to the maximum shear strength of the material tested. As shearing progresses, the resistance to movement w i l l be diminished u n t i l a residual (minimum) shear strength and f r i c t i o n angle i s obtained. This i s i l l u s t r a t e d on a shear versus normal load diagram i n figure 4.5. Barton and Choubey (1977) proposed an alte r n a t i v e empirical technique to estimate the peak and residual angle of f r i c t i o n . The residual f r i c t i o n angle which generally varies from 15° (weathered discontinuity) to 35°, i s assessed from the r a t i o between the Schmidt hammer rebound (r) measured on the weathered j o i n t wall and the rebound (R) measured on intact rock. The peak angle of f r i c t i o n usually ranges from 30° to 70° and can be calculated using the following r e l a t i o n s h i p : 0 peak = J R C l o 9 l 0 (^-) + <Pr 100 where: JRC i s the j o i n t roughness c o e f f i c i e n t estimated using the roughness p r o f i l e chart, figure 4.6, JCS i s the j o i n t wall compressive strength obtain from a Schmidt hammer measurement, a n i s the normal load, 0 r i s the residual angle of f r i c t i o n , A rough estimation of the residual f r i c t i o n angle can also be obtained experimentally by a simple t i l t t e s t using a rock specimen containing an uncemented discont i n u i t y . When rotating the specimen, the angle which i n i t i a t e s s l i d i n g constitutes the residual f r i c t i o n angle, assuming no cohesion and a low normal force. 4.4 JOINTED ROCK MASS FAILURE CRITERION An exact d e f i n i t i o n of jointed rock mass f a i l u r e i s d i f f i c u l t to obtain because of the complexity of the mechanism involved. Chappell (1979) and (1987), by studying the r e d i s t r i b u t i o n of stress as f a i l u r e propagates proposed an explanation that i s summarized below. The deformations of a blocky rock mass are i n f i n i t e s i m a l at f i r s t . They accumulate to form f i n i t e deformations and i n i t i a t e small rotations of blocks. A r e d i s t r i b u t i o n of stress r e s u l t s from these small rotations and i n t e n s i f i e s the 101 8 10 TYPICAL ROUGHNESS PROFILES for JRC range: 1 o - 2 2 h 5 h 9 \ H 2 4 - 6 . 1 6 - 8 8-10 10 - 12 12-14 14 -16 16 -18 18-20 3 10 l i l t I 1 cm S C A I I FIGURE 4.6 Typical discontinuity roughness p r o f i l e for the evaluation of the JRC index. (After Barton and Choubey, 1977) 102 development of stress gradients. Moments, caused by stress g r a d i e n t s a c t i n g along i n t e r a c t i v e block j o i n t s , are transferred across the j o i n t s from block to block and enhance the tendency of blocks to rotate. Further deformations of s l i p and r o t a t i o n may continue u n t i l a single block i s detached from the excavation boundary, and the rest of the rock mass structure may or may not collapse. The location of the l i n e of thrust between the blocks are defined by the formation of "hinges". A hinge i s a point or small region within the rock mass at which the e f f e c t of a force i s l o c a l i z e d to that small area or region. As each hinge i s formed, the rock mass s t i f f n e s s decreases. Failu r e of the rock mass as a whole w i l l occur when a s u f f i c i e n t number of hinges have been formed. The d i f f i c u l t i e s i n developing a f a i l u r e c r i t e r i o n for a jointed rock mass are extreme because of the numerous possible mechanisms involved and the large number of parameters associated with each mechanism. Although the understanding of rock mass behaviour has evolved considerably in the l a s t decade, there are s t i l l no un i v e r s a l l y accepted f a i l u r e c r i t e r i a f or rock masses to date. The author believes that due to the complexity of the problem, only empirical approaches can approximate rock mass behaviour. The most widely used and advanced f a i l u r e c r i t e r i o n for jointed rock mass i s an empirical r e l a t i o n s h i p proposed by Hoek and Brown (1980): °l/aC = °2/aC + ( m a3/ aC + s) ^  103 where: o-y and a 3 are the major and minor p r i n c i p a l stresses OQ i s the un i a x i a l compressive strength m and s are constants which depend upon the properties of the rock and upon the extent to which i t has been broken before being subjected to the stresses o± and The purpose of t h i s c r i t e r i o n i s to integrate the p r i n c i p a l strength c h a r a c t e r i s t i c s of the rock mass into two empirical factors (m and s) and r e l a t e them to stress conditions (ay and CT3). In the Rankine Lecture (1983), Hoek described the m and s factors as follows: "Constant m and s are both dimensionless and are very approximately analogous to the angle of f r i c t i o n , 0, and the cohesion strength (C), of the conventional Mohr-Coulomb f a i l u r e c r i t e r i o n . " Hoek and Brown have provided c r i t e r i o n to evaluate the m and s factors for d i f f e r e n t rock masses, based on t h e i r q u a l i t y using rock mass c l a s s i f i c a t i o n systems (table 4.2). The l i m i t a t i o n s of rock mass c l a s s i f i c a t i o n as a rock mass strength index w i l l cause some i n s e n s i t i v i t y of m and s to c e r t a i n adverse geological conditions. Consequently, in order to estimate a representative value for m and s, a s i t e c a l i b r a t i o n with back analysis of known f a i l u r e s i s necessary. 4.5 SUMMARY AND CONCLUSIONS Fa i l u r e c r i t e r i a are mathematical expressions that define 104 ac n CI fci * a o j - ~ « r » i » * 1 » ft. p » » «e o rt n ft •» O b o 0 3 M M J f Jj O SS.£ p. ft E M f i e > J K ( A « I ( A ft. 8 2 i » c a a • O r» B M . b Q H O »1 D w M> •» n •» T» ^3 i B. ^ ** * O O O n B •* •* -6 -o -o 0 t ft » M » O • a M P r? ¥*• n n n < n »i I* . * • m 8 IT 2-" 8 • • o o 3 O o a 3 » » • • • • c» o o o § s • 3 a • * • • • o« o o 8 ^  • i • • 0 o . O u» Ot O o t • 4 t> • I • u • 4^ ^- —j • . . • o o o CARBONATE ROCKS WITH WELL DEVELOPED CRYSTAL CLEAVACE dolomita, limaatona and marbla «» O l • • • i o o * • p • C> O O o • o 8 g » a « a « i • i o ^ o o • a • a • • I I O Ot o g o • a <• a • i • • C» N* O U> • • • • Ot C A o • • O O o o LITHIFIED ARCILLACEOUS I0CKS mad*Urns, ailtatona, thai* and »lat* (normal to olaavaga) J " Q • « • • i o o a 8 P § 2 <• a • < C> Ot O O f o 8 " • a > • i * • • O i • . - O l » a O l « _ O t ARENACEOUS ROCKS WITH STRONG CRYSTALS AND POORLY DEVELOPED CRYSTAL CLEAVACE aandatona and quartmiLa C . to • a " a i • • • ? P o » a i ^ . O i o 8 » a • * • a O 0* » a • a ^t N l r- ^4 d d O O FINE CRAINED POLYHINERALLIC ICNEOUS CRYSTALLINE ROCKS ondstit*, dolsri ta, diobaaa and rhyolita I** O O . O r- 8 " O t C4 „ o , Ot *— o » C> d o o COARSE CRAINED POLYHINERALLIC ICNEOUS AND NET AMORPHIC CRYSTALLINE ROCKS Otfhibolita, gobbro, gnaiaa, granita, norite and quarta-diorita the l e v e l at which induced stress exceeds the bearing capacity of the rock mass. The development of f a i l u r e c r i t e r i a can be based on l a b o r a t o r y t e s t i n g , a n a l y t i c a l or e m p i r i c a l techniques. Three types of f a i l u r e c r i t e r i o n suitable for hard rock mining are reviewed i n t h i s chapter: the i n t a c t rock f a i l u r e c r i t e r i o n , the shearing f a i l u r e c r i t e r i o n along geological d i s c o n t i n u i t i e s and the jointed rock mass f a i l u r e c r i t e r i o n . In the case of int a c t rock material, small specimens can be representative of the whole medium which allows the determination of the inta c t properties i n the laboratory. Four d i f f e r e n t tests can be done i n order to reproduce the following induced stress conditions: u n i a x i a l (or unconfined) compressive stress, t r i a x i a l compressive stress, b i a x i a l compressive stress, and u n i a x i a l t e n s i l e stress. The ultimate load at rupture may be d i r e c t l y used as a f a i l u r e c r i t e r i o n , or as a parameter inside an a n a l y t i c a l or empirical f a i l u r e c r i t e r i o n . The shear strength of geological d i s c o n t i n u i t i e s can be estimated using the relat i o n s h i p proposed by Coulomb; r= C + a n tan cj> By t e s t i n g a specimen containing a di s c o n t i n u i t y under varying loading conditions (T and a n ) , the Mohr-Coulomb f a i l u r e envelop and the f r i c t i o n angle can be assessed. 106 The behaviour of a jointed rock mass i s extremely complicated and only empirical relationships can approximate i t s f a i l u r e . The most advanced empirical f a i l u r e c r i t e r i o n for a jointed rock mass was developed by Hoek & Brown (1980) : Oy/o-Q = o 3 / a c + (mo-3/ac +s) % The empirical constants m and s, are estimated using rock mass c l a s s i f i c a t i o n and need to be cal i b r a t e d on s i t e . 107 CHAPTER 5 REVIEW OF EXISTING DESIGN METHODS FOR UNDERGROUND OPENINGS 5.1 INTRODUCTION Design methods for mining excavations are r e l a t i v e l y new and i t i s only i n the 1980's that an engineering approach has been widely used to optimize stope dimensions. In the past, mine operators r e l i e d e s s e n t i a l l y on t h e i r experience in si m i l a r mining conditions and on t r i a l and error for stope design. A turning point i n applied rock mechanics was the development of the two major rock mass c l a s s i f i c a t i o n systems. The Q-system by Barton et a l . (1974) and the RMR-system by Bieniawski (1973), which d i v i d e d the rock mass i n t o q u antifiable parameters characterizing the properties of the rock mass. For the f i r s t time, t h i s provided the necessary "common ground" to systematically compile the geotechnical experience i n a vari e t y of geological conditions, and develop r e l i a b l e empirical models for the predic t i o n of underground excavation s t a b i l i t y . There are several types of underground openings f u l f i l l i n g functions such as: entry mining stopes, non-entry mining stopes, mining d r i f t s , roadway tunnels, hydroelectric chambers, nuclear waste storage caverns etc. Although a l l these cases deal with the problem of creating an excavation i n a rock mass, t h e i r physical conditions and environment are very d i f f e r e n t . 108 Furthermore, since the purpose of the openings are also d i f f e r e n t , the design requirements regarding the excavation longevity and the degree of i n s t a b i l i t y t o l e r a b l e may also be completely d i f f e r e n t . This chapter w i l l review the p r i n c i p a l methods used i n the design of underground openings. E m p i r i c a l models developed for tunnels (Barton and Bieniawski) and caving methods (Laubscher) have been included in t h i s review because some of t h e i r concepts have been adapted to the more relevant open stope model proposed by Mathews. The fourth design method reviewed i s the most widely used, consisting of a combination of numerical modelling and f a i l u r e c r i t e r i o n . The development of the desk-top computer has contributed to make numerical models more accessible, and a s s i s t the designer i n forecasting the e f f e c t of stress re-d i s t r i b u t i o n for d i f f e r e n t mining sequences. 5.2 ROCK MASS CLASSIFICATION DESIGN CHARTS 5.2.1 Bieniawski RMR system Developed by Bieniawski (1974) at the South African Council for S c i e n t i f i c and Ind u s t r i a l Research (CSIR), t h i s rock mass c l a s s i f i c a t i o n system defines an index of rock competency c a l l e d the rock mass ra t i n g (RMR) . The RMR value varies l i n e a r l y from 0 to 100 and relates to the q u a l i t a t i v e assessment of rock as follows: RMR ROCK QUALITY ASSESSMENT 109 0 20 Very Poor Rock 21 40 Poor Rock 41 60 Fa i r Rock 61 80 Good Rock 81 100 Very Good Rock The RMR values are calculated based on f i v e parameters which characterize the rock mass. 1) The rock qu a l i t y designation (RQD) i s a measure of the number of fractures i n the rock mass and w i l l be further discussed i n section 7.2.1. Bieniawski assigns a r e l a t i v e r a t i n g for RQD varying from 0 to 20 . 2) The u n i a x i a l compressive strength of i n t a c t rock accounts for the hardness of the rock material. The ra t i n g for t h i s factor varies 0 to 15 . 3) The r e l a t i v e spacing of j o i n t s i s given a ra t i n g from 5 to 30. This c h a r a c t e r i s t i c of the rock mass i s i n d i r e c t l y taken into account by RQD and consequently gives j o i n t spacing a large r e l a t i v e weighting. 4) The condition of j o i n t s represents the shear strength of the rock mass d i s c o n t i n u i t i e s . A descriptive scale including f i v e d i f f e r e n t j o i n t conditions i s provided to determine a ra t i n g varying from 0 to 25. 5) The groundwater factor varies from 10 for dry conditions to 0 for severe water problems. (In the case of open stope mining i n Canada, water ra r e l y has an e f f e c t on s t a b i l i t y ) . 110 An adjustment for the orientation of j o i n t i n g with respect to openings i s also included. The adjustment w i l l be 0 for a favorable orientation, and up to a maximum of -12 for an unfavourable j o i n t orientation. The f i v e parameters and t h e i r respective adjustment factors are estimated using the charts in Table 5.1 . The rock mass ra t i n g (RMR) i s calculated by adding the ratings described above. Bieniawski proposed a design chart for tunnelling by r e l a t i n g the RMR index to the stand up time of the rock mass i n a number of tunnel spans (figure 5.1). However, the a p p l i c a b i l i t y of t h i s chart to mining should be li m i t e d to d r i f t design. I t has been found extremely conservative for the design of non entry stopes. 5.2.2 Barton et a l . Q system Barton, L i e n and Lunde (1974) of the Norwegian Geotechnical I n s t i t u t e , developed the NGI c l a s s i f i c a t i o n which defines the rock mass qual i t y index Q. The Q value varies from 0.001 to 1000 on a logarithmic scale and i s related to q u a l i t a t i v e rock mass assessments as follows: ROCK QUALITY ASSESSMENT 0. 001 - 0.01 Exceptionally Poor 0.01 - 0.1 Extremely Poor 0.1 - 1 Very Poor 1 - 5 Poor 5 - 10 Fa i r 111 A. C L A S S I F I C A T I O N P A R A M E T E R S A N D T H E I R R A T I N G S P A R A M E T E R RANGES OF VALUES i Strength ot intoct rock mater io( Poml load strength ndex ) 8 MPo 4 - 8 MPo • 2 -4 MPa 1-2 MPo For this low range -untaiial compres-sive test is preferred Uniaxial compressive strength > 200 MPo 100 - 200 MPo 50 -100 MPa 25 - 50 MPo 10- 251 3-10 1-3 MPo | MPo MPo Rating 15 12 7 4 2 1 I I 0 2 Drill core quality R O D 9 0 % -100% 7 5 % - 9 0 % 50"/.-75% 2 5 % - 5 0 % | ( 2 5 % Rating 20 17 13 8 | 3 3 Spacing of joints )3m l -3m 0 .3 - lm 50 - 300 mm < 50 mm Rating 30 25 20 10 j 5 4 Condition erf joints Very rougn surfaces Not continuous No separation Hard joint wall rock Sightly rough surfaces Seporation < 1 mm Herd joint wall rock ISIickensided surfaces Slightly rough s u r f o c e s j * ^ ( 5 r n m t h i c k Seporation (1 mm or Soft joint wall rock open l -5mm j Continuous joints Soft gouge > 5 m m thek or Joints open > 5mm Continuous )Otnts Roung 25 20 12 | . 6 0 5 Ground waier Inflow per lOm tunnel length None <25 litres/min | 25 -125 litres/mm j > 125 litres/mm ,0-nt *ot*r 0 0 0 - 0 2 j 0 . 2 - 0 . 5 ) 0 5 General conditions Completely dry OR "OR Moist only iWaier under moderate (interstitial water) | pressure "OR Severe water problems Rating 10 7 | 4 j 0 B . R A T I N G A D J U S T M E N T F O R J O I N T O R I E N T A T I O N S Strike and dip orientations of joints Very favourable Favourable Fair Unfavourable Very unfavourable Tunnels o -2 - 5 - .0 -12 Ratings Foundations 0 - 2 - 7 -15 - 2 5 Slopes 0 -5 -25 - 5 0 - 6 0 C . R O C K M A S S C L A S S E S D E T E R M I N E D F R O M T O T A L R A T I N G S Rating O C — 8 1 80—61 60—41 4 0 — 2 1 < 20 Class No, 1 II . . . .V V Description Very good rock Good rock Foir rock Poor rock Very poor rock D . M E A N I N G O F R O C K M A S S C L A S S E S ' Cioss No i II III IV V ^Weroge siond-up * , T T * 10 yeors fcr 5m span 6 montns for 4 m soon . week for 3 m span 5 hours for 1.5 m span 10 mm. tor 0.5m spon Cohesion of ihe rock moss >300kPo 2 0 0 - 3 0 0 k P o 150-200 kPo 100 - ISO kPo < .00 kPo Friction angle al the rock mass > 4 5 - 4 0 " - 4 5 * i 5 ° - 4 C 30* - 35" (30* T A B L E 6 - T H E E F F E C T O F J O I N T S T R I K E A N D D I P O R I E N T A T I O N S I N T U N N E L L I N G Strike perpendicular to tunnel axis Strike parallel to tunnel axis Dtp 0 * - 2 0 ° irrespective of strike Drive with dip Drive agoinst dip Dip 4 5 * - 9 0 * Dip 2 0 # - 4 5 * Dip 4 5 " - 9 0 * Dip 2 0 * - 4 5 * Dip 4 5 * - 9 0 " Dip 2 0 * - 4 5 * Very favourable Favourable Fair Unfavourable Very unfavourable Fair Unfavourable TABLE 5.1 Bieniawski CSIR geomechanics classification of jointed rock mass. (After Hoek and Brown, 1980). 112 Stand-up time (h) FIGURE 5.1 R e l a t i o n s h i p between the s t a n d - u p t ime o f an u n s u p p o r t e d underground e x c a v a t i o n span and the CSIR Geomechanics C l a s s i f i c a t i o n . ( A f t e r B i e n i a w s k i , 1973) 113 10 - 50 Good 50 - 100 Very Good 100 - 500 Extremely Good 500 - 1000 Exceptionally Good Q i s calculated using the following equation: Q = ROD * J r * Jw Jn Ja SRF The quotient (RQD/Jn) represents the degree of fracturing and s i z e of the blocks forming the rock mass. The quotient (Jr/Ja) accounts for the shear strength of i n t e r l o c k i n g blocks formed by j o i n t i n g . The quotient (Jw/SRF) accounts for the e f f e c t of stress and ground water i n the rock mass. The in d i v i d u a l factors of the NGI c l a s s i f i c a t i o n are: 1) RQD - the rock quality designation index (see section 7.2.1). The e f f e c t of RQD on Q varies from 1 to 100. 2) Jn - the j o i n t set number quantifies the e f f e c t of the number of j o i n t sets in the rock mass. I t also includes the influence of random j o i n t s . Jn varies from 0.5 to 20. 3) J r - the j o i n t roughness number, characterizes the shape and i r r e g u l a r i t i e s of fracture surfaces. J r may have a value of 0.5 to 4, based on a descriptive scale. 4) Ja - the j o i n t a l t e r a t i o n number, can be related to the f r i c t i o n angle of the j o i n t surface. I t considers the presence of i n f i l l i n g and the condition of the j o i n t surface. Ja varies from 0.75 to 20 defined on a descriptive 114 scale. 5) Jw - the j o i n t water reduction factor, accounts for the presence of water pressure i n the rock mass. This factor varies from 0.05 to 1.0 . 6) SRF - the stress reduction factor i s an attempt to take into account the influence of an underground stress f i e l d on rock masses. However, i t should be noted that the o r i g i n a l factor was proposed for tunnelling and does not represent the stresses conditions induced around open stopes. The six parameters are described on table 5.2. Barton et a l . have proposed a design chart (figure 5.2), in which the maximum unsupported span i s a function of Q and an equivalent opening dimension (De). The equivalent dimension accounts for d i f f e r e n t types of underground excavations and i s calculated as follows: De = opening span ESR where ESR i s given on Table 5.3 and i s analogous to an inverse factor of safety. Nevertheless, t h i s design chart was empirically developed based on tunnelling and c i v i l engineering case h i s t o r i e s and i s not c a l i b r a t e d for non entry stope design. 5.2.3 Discussion of the Q and RMR systems The d e s i g n c h a r t s f o r t h e s e two r o c k mass c l a s s i f i c a t i o n systems have met with approval for tunnel 115 A DC* QUALITY DESIGNATION Very poor I i. tooc n fair SO 0. Cood ?S { • c e d e n t )0 1. JOINT SlT NUHMK festive, no or few Joint* One joint set C. One Joint >et plui random 0. T«4 joint salt C. Two joint ten plus random Three Joint sett Three joint sets plus rendo* Four or more Joint sets, random, heavily jointed 'sugar cube*. etc Crushed rock, eerthlike 1. Where KQO It reported or H i iur«d et • 10 ( Including 0 1, • nomine) value ol 10 It uied to evaluate Q. 2. »Q0 Intervals of 5. 100, 1S, 90 etc are sufficiently accurate. 1. For intersections use ( ) - 0 • J n ) 2. For portels use (2.0 • J ) ). JOINT ftOuCHNi&S NUnOER a. Rook wait oontaot and b . Rock Mil contact btfon 10 c m tKtar. A. 01SCOntInuoul joints 1. Hough or Irregular, undulating C . linooch, undulet ing 0. Sllchenslded, undulating £. Hough o r irregular, planar f. Smooth, planer C. SIickensldad, planar 0 . Ho rock vail contact u n e n ih^artd. H. Zona containing city minerals t h i c k enough to prevent rock M « I I contect. > J . Sandy, grewelly or crushed tone thick enough t o prevent rock » e l I contact. I 5 2 IS l-S 1.0 OS 1. Add 1.0 If the mean spacing of the releaent Joint set it greeter than \m. 2. if * O.S can be used for planar, allck-entldad joints hawing llnettlons, provided the Itneetlons are orientated for minimum tt renaih. JQlHl ALTERATION MUnttH a. Rock, uall oontaat. A. Tightly healed, hard, non-so'ttntng. Impermeable f i l l ing * f (appro*.) Unaliertd Joint walls, Surface staining only Slightly altered joint M a l l s non-»oltcnlng mineral coalings, sandy particles, clay-frte disintegrated rock, etc S i l l y , or sandy-day coatings, S>M11 eley-fract ion (non-tor lining) Soltenlng or low friction clay M i n e r a l coatings, i .e. keolinlta. mice. Also chlorite, t e U , gypiua and graphite t i c , and smell quan-tit ies of swelling clays. (Dis-continuous coatings, I-2mm or less in thickness) b. Rook vail contact torn for* 10 cms enear. Sandy particles, clay-free dis-integrated rock etc Strongly o*er-ton»olidetcd, non-softening clay M inera l f i l l ings (continuous, « £**• thick) Medium or low owtr-r.om.olidatIon, softening, clay M ine ra l f i l l ings , (continuous, * Smm thick) Stalling clay f i l l i n g s . I.e. monimorI Ilonlte (continuous, * S an thick ). Values of depend on percent of Spelling clay-t i le particles, and access to water o. Mo rook uall contact uHen Mktarmd. Zones or bands of disintegrated or crushed rock and clay (see C,H and J for clay conditions) Zones or bands of s i l l y * or sandy clay, small d a y fraction, (non*softening) # f(appro..) (25° • )5°> (25° - J0°) (20° - 2$°) i a° - i6°) (2S« • J0°) (16° • 2*° l (12° - 16°) 1.0 - 12.0 ( 4 ° - 12°) 4 . 0 6.0 8.0 - 12.0 ( 4° - 2k°) Thick, continuous tones or bands or clay ( see C, M end J for clay conditions) 10.0 - M.I n o - 20.0 Values of e f , (he residual friction angle, ere inland ed es en approalaeie guide to the minerelogicel pro-perties of the a Iteration products, 4f present. ( 4 « - 2k<»l S. JOINT WATER A L OUCH OK FACTOR . A. Ory excavations or minor Inflow, I.e. « S H i / - In . locally 1.0 I. Medium Inflow or pressure, occa-sional out-ash of joint f i l l ings 0 . 4 4 C. Large inflow or high pressure In competent rock with unfilled joints 0.$ 0. Large Inflow or high pressure , considerable outwesh of f i l l ings 0.3) t. exceptionally high Inflow or prei* sura at blasting, decaying with lime 0.2 • 0.1 f. Incept tonally high Inflow or pres-sure continuing without decay 0.1 - 0.0$ appro*, water preisure Ug'/cm 3) * 1-0 1.0 • 2.S 2 5 - 10.0 I S - 10.0 > 10 . Factors C to F era crude estimates. Increase J H if drainage measures era installed. Special problem* caused by Ue formation are not considered. TABLE 5.2 Barton c l a s s i f i c a t i o n of individual parameters in the NGI tunnelling quality index. (After Hoek and Brown, 1980). i . I T M S S REDUCTION FACTO* U M b w e * *ot*J intubating *xoa9ation, ttkioh nsy COUMI loomtni^ of rook maM9 vhen t w t a Z it txoauafd. A . M u l t i p l e o c c u r r e n c e s o f weakness t o n e s con ( f i n i n g c l a y o r c h e m i c a l l y d l s I n t e g r a t e d r o c k , v e r y l o o s * S u r r o u n d i n g r o c k (any depth) I. S i n g l e weakness tones c o n t a i n i n g c l a y , o r c h o e r I c e l l y d i s i n t e g r a t e d rock ( e x c a v a t i o n d e p t h < 5QM) C . S i n g l e w e a k n e s s tones c o n t a i n i n g c l a y , o r Chaer-I c a l l y d i s i n t e g r a t e d rock ( e x c a v a t i o n d e p t h • $4*0 ft. M u l t i p l e s h e a r i o n « t In competent rock ( c l a y f r e e ) , l o o * a s u r r o u n d i n g rock ( m y d e p t h ) I . S i n g l e s h e a r t o n e s In c o a p e t e n t rock ( c l a y f r e e ) , ( d e p t h o f e x c a v a t i o n « $0*>) f. S i n g l e s h e e r t o n e s In competent rock ( c l a y t r e a ) , ( d a p t h o f e x c e v e t l o n > SO*) L o o s e o p e n j o i n t s , ( a n T d e p t h ) b. Co*mp*t*nt rook. h e a v i l y J o i n t e d o r ' s u g a r c u b e 1 r ok e t r v e a p r e * La we H. U x s t r e s s , n e a r l o r face > 200 J . H a d l u * fltran 200-10 K. H i g h s t r e s s , v e r y t i g h t s t r u c t u r e ( u i u a l l y f a v o u r a b l e to s t a b i l i t y , | Q _ • a y be u n f a v o u r a b l e for w a l l s t a b i l i t y ) o ( / o , 13-0.w L . N i l d r o c k b u r s t (ewjsslve r o c k ) M. HaavY r o c k b u r s t ( a a s s i v e r o c k ) $ - 1 . 5 <2-5 0 . J ) - 0 . 1 b <0.16 2 -5 1 .0 0.66-0.J3 0 . 5 - 1 5-10 10-20 fteduce t h e s e v a l u e s o f SftF » y 2$ - SOX i f the r e l e v a n t s h e a r t o n e s o n l y i n f l u e n c e but do not I n t e r s e c t the e x c a v a t i o n . 2 . f o r s t r o n g l y a n i s o t r o p i c v i r g i n s t r a t i f i e l d ( I f •Matured) : U*en $ a 4 10 , r e d u c e o c t o Q . S o e and o t t o 0 . & o t . When « l / a j > 10 , r e d u c e o c and o t t o 0 . 6 o c and 0 . o o t , where o c • u n c o n f l n a d c o m p r e s s i v e s t r e n g t h , and 0 , " t e n s l I e s t r e n g t h ( p o i n t l o a d ) and a ( and O) a r e the * e J o r and a i n o r p r i n c i p a l s t r e s s e s . ) . Few c a s e r e c o r d s a v a i l a b l e where d e p t h o f crown below S u r f a c e Is l e s s t h a n span w i d t h . Sugges t SftF In-c r e a s e f r o * 2 . 5 to $ f o r s u c h c a s e s ( l e e H). a. Squstning rock, plastic ,T-*v of incoe>atint rock undtr (na influtnom of high rock prssiurt i(tf A d d SQueeilno, rock pressure 5-10 Heavy squeezing rock pressure 10-20 d. Smiling rock, ohtmizal fuelling aativity (Upending upon pnsmutm of wa te r f l l l d s w e l l i n g r o c k p r e s s u r e Heavy s w e l l i n g rock p r e s s u r e 5-10 10-20 TABLE 5.2 Barton c l a s s i f i c a t i o n of individual parameters in the NGI tunnelling quality index, (cont) Excavation category ESR A. T e m p o r a r y mine o p e n i n g s 3 - 5 B. Permanent mine o p e n i n g s , w a t e r t u n n e l s f o r h y d r o power ( e x -c l u d i n g h i g h p r e s s u r e p e n s t o c k s ) p i l o t t u n n e l s , d r i f t s and h e a d -i n g s f o r l a r g e e x c a v a t i o n s . 1.6 C. S t o r a g e rooms, w a t e r t r e a t m e n t p l a n t s , m i n o r r o a d and r a i l w a y t u n n e l s , s u r g e c h a m b e r s , a c c e s s t u n n e l s . 1.3 p. Power s t a t i o n s , m a j o r r o a d a n d r a i l w a y t u n n e l s , c i v i l d e f e n c e c h a m b e r s , p o r t a I s , i n t e r s e c t i o n s . 1.0 E. U n d e r g r o u n d n u c l e a r power s t a t i o n s , r a i l w a y s t a t i o n s , s p o r t s and p u b l i c f a c i l i t i e s , f a c t o r i e s . 0.8 TABLE 5.3 The excavation support ratio (ESR) for different underground openings applications. (After Hoek and Brown 1980) FIGURE 5.2 R e l a t i o n s h i p between the maximum e q u i v a l e n t d i m e n s i o n (De) o f an u n s u p p o r t e d underground e x c a v a t i o n and the NGI t u n n e l l i n g q u a l i t y index Q. ( A f t e r B a r t o n L i e n and Lunde , 1974) 118 design, but not i n mine design. Factors such as ESR and stand-up time, which were developed to adjust the design charts for other types of openings, are too s i m p l i s t i c to overcome the differences between tunnelling and mining. The differences between mining and tunnelling include: 1) The t y p i c a l shape of tunnel i s long i n one d i r e c t i o n and r e l a t i v e l y small i n the other d i r e c t i o n s . The c r i t i c a l v a r i a b l e to be designed i n tunnelling i s the roof width. In the case of stopes, the shape i s often near cubical and a l l three dimensions (stope height, stope width and stope length) must be designed. 2) Tunnels are usually i s o l a t e d openings. Mining layouts are comprised of panels containing several stopes and p i l l a r s . The e f f e c t of excavating multiple openings i s to produce stress concentrations i n some areas and relaxation i n other areas. 3) Pre-mining stress magnitudes increases with depth. Most tunnels are shallow and stress plays only a minor role in t h e i r s t a b i l i t y . Mine openings are occasionally excavated near surface, but are usually found at depth, where stresses play a c r u c i a l role i n s t a b i l i t y . 4) Tunnels are required to be stable for a long period of time. They are permanent openings. Non-entry mining stopes have no personnel inside them during the extraction process and a c e r t a i n amount of i n s t a b i l i t y i s t o l e r a b l e . Open stopes need to remain open for a comparatively short period of time 119 (approximately 3 to 18 months). They are temporary openings. Consequently, the rock mass c l a s s i f i c a t i o n design charts f i n d t h e i r best application i n tunnel design. They can be used for designing mining d r i f t s , but they w i l l give conservative answers. Both Bieniawski and Barton have supplemented t h e i r design charts with a r t i f i c i a l support design proposals which are also suitable for tunnel and mining d r i f t s . The rock mass c l a s s i f i c a t i o n systems o f f e r a viable method to estimate the competency of a rock mass on a comparative scale. These form the base for other empirical design methods better adapted to mining conditions. 5.3 LAUBSCHER'S GEOMECHANICS CLASSIFICATION OF JOINTED ROCK MASSES Laubscher (1976) was the f i r s t to adapt one of the tunnel c l a s s i f i c a t i o n systems for mining applications, based on his experience with c h r y s o t i l e asbestos caving operations in southern A f r i c a . His modification of the CSIR system i s the r e s u l t of the c l a s s i f i c a t i o n of more than 50,000 metres of mine development and d r i l l core. This research was performed in a wide v a r i e t y of rock conditions and many mining methods including open p i t , cut and f i l l , open stoping, shrinkage stoping and caving methods. 120 5.3.1 Description of the Model Laubscher used the same f i v e basic parameters as Bieniawski, which are: - RQD, - i n t a c t rock strength, - j o i n t spacing, - condition of j o i n t s , - groundwater. In order to improve the a b i l i t y of the CSIR method to c h a r a c t e r i z e rock masses, he proposed the f o l l o w i n g modifications: 1) The r e l a t i v e s i g n i f i c a n c e of intact rock strength, on the t o t a l r a ting was diminished from 15% to 10%, while the e f f e c t of j o i n t conditions has been increased from 25% to 30% of the t o t a l r a t i n g . 2) The j o i n t condition descriptive scale was expanded and improved to provide a more d e t a i l estimate for the e f f e c t of j o i n t roughness, a l t e r a t i o n and i n f i l l i n g . The new guidelines are given i n table 5.4. 3) The factor representing j o i n t spacing has been t o t a l l y changed. Laubscher proposed a chart (figure 5.3) which accounts for multiple j o i n t systems, as well as the spacing of i n d i v i d u a l j o i n t s . This factor i s a much better i n d i r e c t measure of the r e l a t i v e size of the blocks forming the rock mass matrix. The RQD and j o i n t water parameters have not been changed. The 121 ASSESSMENTS OF-JOINT CONDITIONS (Adjustments as combined percentages of t o t a l p o s s i b l e r a t i n g of 30) Parameter D e s c r i p t i o n P e r centage adjustment Wavy u n i - d i r e c t i o n a l 99 90 A. J o i r . t e x p r e s s i o n : ( l a r g e s c a l e ) Curved 89 SO S t r a i g h t 79 70 S t r a i t e d 99 es E. J c i n t e x p r e s s i o n ( s m a l l s c a l e ) Smooth 84 60 P o l i s h e d 59 50 C. A l t e r a t i o n zone S o f t e r than w a l l rock 99 70 Coarse hard-sheared 99 90 F i n e hard-sheared cn o CO CO Coarse s o f t - s h e a r e d 79 70 D.' J o i r . t f i l l i n g F i n e s o f t - s h e a r e d 69 50 Gouge t h i c k n e s s < I r r e g u l a r i t i e s 49 35 Gouge t h i c k n e s s > I r r e g u l a r i t i e s 23 12 F l o w i n g m a t e r i a l > I r r e g u l a r i t i e s 11 0 TABLE 5.4 Assessment o f j o i n t c o n d i t i o n s f o r t h e L a u b s c h e r geomechanics c l a s s i f i c a t i o n o f j o i n t e d r o c k mass. ( A f t e r L a u b s c h e r , 1976) . R A T I N G S F O R M U L T I - J O I N T S Y S T E M S MINIMUM SPACING , m 0 , O J OJ t£ to 0,01 0.1 1,0 ' 0 M A X I M U M S P A C I N G . Tl E X A M P L E : J O I N T S P A C I N G A : 0 , 1 m B r O . S m C = 0 . 6 m D : 1 . 0 m A B ; 1 5 A B C = 6 A B D i l l FIGURE 5.3 Diagram f o r the e v a l u a t i o n o f the j o i n t s p a c i n g parameter i n the L a u b s c h e r m o d i f i e d geomechanics c l a s s i f i c a t i o n system. ( A f t e r L a u b s c h e r , 1976) 123 f i v e parameters used by Laubscher to characterize rock masses are summarized with t h e i r associated ratings on table 5.5. The t o t a l r a t i n g i s c a l l e d the i n - s i t u rock mass rating. In order to extend the a p p l i c a b i l i t y of the c l a s s i f i c a t i o n to mining conditions, f i v e adjustment factors were developed to quantify the sources of i n s t a b i l i t y t y p i c a l l y found in mining operations. 1) Weathering Adjustment. The e f f e c t of weathering i s to decrease the o v e r a l l competency of the rock mass. An adjustment i s made on three of the i n - s i t u parameters. Reductions of up to 5% of the o r i g i n a l RQD value and 4% of the i n t a c t rock strength are suggested. The main influence of weathering i s on the j o i n t condition with a possible decrease of up to 18% of the j o i n t condition rating can be applied. 2) F i e l d and Induced Stresses. Laubscher introduced a factor to account for the e f f e c t of stress which may t r i g g e r i n s t a b i l i t y or contribute to s t a b i l i z i n g p o t e n t i a l shear f a i l u r e due to an increase i n the component of stress acting normal to the discontinuity. Consequently, the adjustment can decrease the t o t a l i n - s i t u rating by 24% for stress relaxation, or increase the rating by 20% i f the j o i n t s are kept i n compression. 3) Change i n Stress. A phenomenon associated with most mining si t u a t i o n s i s l o c a l v a r i a t i o n i n stress. However, for caving mining methods the changes may have very important C l a s s X A B 2 A 3 3 A B 4 A B 5 A B E a t i n g IOO - ei 80 - 61 60 - 41 40 - 21 2 0 - 0 D e s c r i p t i o n Very good Good F a i r P o o r V e r y poor 1 R.Q.D.Jfc ICC- 91 9C-76 75-66 65-56 55-46 45-36 35-26 25-16 15-6 5 - 0 R a t i n g 20 18 15 • 13 11 9 7 5 3 C 2 I . R . S . (MPa) 141-136 135-126 125-111 110-96 95-81 80-66 65-51 50-36 35-21 20-6 5-0 R a t i n g ' .10 9 8 7 6 5 4 3 2 1 0 3 J o i n t s p a c i n g R e f e r T a b l e I I R a t i n g jU ^ ' 1 u 4 C o n d i t i o n o f j o i n t s S t a t i c a n g l e o f f r i c t i o R e f e r T a b l e I I I 4 ? u •> 5° R a t i n g — ^ u 5 Groundwater I n f l o w pe r 10 m l e n g t h = 0 OR J o i n t wa te r p r e s s u r e ^ Major p r i n c i p a l s t r e s s OR C o m p l e t e l y d r y = 25 l i t r e s / ^ n = 0,0 - 0,2 M o i s t o n l y = 25 - 125 l i t r e s / m i n = 0,2 - 0,5 Modera te p r e s s u r e > 125 l i t r e s / n u n > 0,5 S e v e r e problems R a t i n g 10 7 4 . 0 TABLE 5.5 Summary o f t h e f i v e b a s i c parameters o f the Laubscher geomechanics c l a s s i f i c a t i o n o f j o i n t e d r o c k mass. ( A f t e r L a u b s c h e r , 1976) . 125 influence, since large volume rock f a l l s r e s u l t in d r a s t i c changes i n geometry. The adjustment applicable on the t o t a l i n - s i t u r a t i n g varies from minus 40% for the worst possible change i n stress conditions to an increase of 20% when the change i n stress favours, s t a b i l i t y . I t appears that t h i s factor i s more relevant to caving mining methods. 4) Influence of Strike and Dip Orientation. The r e l a t i v e orientation and i n c l i n a t i o n of the opening with regard to geologic structure has an influence on the s t a b i l i t y of rock walls. The adjustment i s proportional to the l i k e l i h o o d of blocks being detached from the walls. Laubscher suggested that, since gravity i s the most s i g n i f i c a n t force in t h i s parameter, the adjustment should be a function of the number of j o i n t s i n c l i n e d away from the v e r t i c a l axis. He provided a guide to estimate the adjustment (table 5.6), which may be as s i g n i f i c a n t as a 30% decrease of the t o t a l i n s i t u r a t i n g . A d i s t i n c t i o n i s also made when the predominant geological structures are shear zones or f a u l t s rather than j o i n t sets. The proposed adjustment for a r e l a t i v e difference in orientation of: 0° - 15° i s minus 24%, 15° - 45° i s minus 16%, 45° - 75" i s minus 8%. 5) Blasting E f f e c t s . In the mining process, i t i s endeavoured to minimize the e f f e c t of b l a s t i n g on stope s t a b i l i t y , however, development of new fractures and a c e r t a i n degree 126 No. o f d e f i n i n g j o i n t s No. o f f a c e s v e r t i c a l and i n c l i n e d away from a d j u s t m e n t p e r c e n t a g e 70% 7 5 % 8 0 % 8 5 % 90% 3 3 2 4 4 3 2 5 5 4 3 2 1 6 6 4 3 2,1 TABLE 5.6 Adjustment f a c t o r f o r t h e number of j o i n t s e t s i n c l i n e d away from v e r t i c a l . ( A f t e r Laubscher, 1976). Technique Adjustment, % Boring 100 Smooth w a l l b l a s t i n g 97 Good c o n v e n t i o n a l b l a s t i n g 94 Poor c o n v e n t i o n a l b l a s t i n g 80 TABLE 5.7 Adjustment f a c t o r f o r t h e e f f e c t o f b l a s t i n g . ( A f t e r L a ubscher, 1976). TOTAL POSSIBLE REDUCTIONS R.Q.D. I.R.S. J o i n t C o n d i t i o n P a r a m e t e r o f j o i n t s T o t a l s p a c i n g W e a t h e r i n g 95% 96% 8 2 % 7 5 % 120% to F i e l d and i n d u c e d 1 2 0 % to s t r e s s e s 7 6 % 76% Changes i n s t r e s s 1 2 0 % to 120% to 7 0 % 6 0 % 6 0 % S t r i k e and d i p 7 0 % o r i e n t a t i o n 8 6 % B l a s t i n g 9 3% 8 0 % TABLE 5.8 Summary of the p o s s i b l e adjustment f a c t o r s . ( A f t e r L aubscher, 1976). 127 of shaking remains in e v i t a b l e . Table 5.7 shows the adjustments proposed by Laubscher for d i f f e r e n t excavating and bla s t i n g procedures. The f i v e mining related adjustments are summarized on Table 5.8. They are expressed i n terms of adjusted ratings. 5 . 3 . 2 Open Stope Design Application In a more recent publication, Diering and Laubscher (1987) proposed one more modification factor to adapt the method for open stope design. Because the i n c l i n a t i o n of stope surfaces influences the action of gravity i n pot e n t i a l block f a i l u r e s , stope i n c l i n a t i o n adjustments were proposed and are reproduced in table 5.9. A r e l a t i o n s h i p between the t o t a l adjusted rating and the hydraulic radius of stope surfaces has been developed and i s shown on figure 5.4. The hydraulic radius of a surface i s defined as the r a t i o of the surface area divided by i t s perimeter: Hydraulic Radius = Stope Surface Area (m) Stope Surface Perimeter (m) The hydraulic radius accounts for the e f f e c t of si z e and shape of stope surfaces. As the r a t i o of spans on surface increases beyond 4:1, the hydraulic radius remains r e l a t i v e l y constant. This corresponds to the most stable shape (long and narrow) for a stope plane of a given area. 128 Dip of surface Adjustment, % 0-30° 80 30-50° 85 50-70° 90 70-30° 95 80-90° 100 TABLE 5.9 Adjustment factor for the incl i n a t i o n of the designed stope surface. (After Laubscher, 1976). O 10 20 30 40 SO SO AREA HYDRAULIC RADIUS = PERIMETER FIGURE 5.4 Relationship between the adjusted rock mass rating and hydraulic radius of a stope surface. (After Laubscher, 1976) 129 The s t a b i l i t y of each open stope plane can be evaluated according to where i t plots on the graph. Stable and caving regions are defined, as well as a t r a n s i t i o n zone where a r t i f i c i a l support i s recommended. 5.3.3 Discussion of the method The modified c l a s s i f i c a t i o n system developed by Laubscher overcomes most of the shortcomings of the CSIR c l a s s i f i c a t i o n , g iving a r e l i a b l e characterization of rock masses. The adjustment factors quantify the e f f e c t of mining induced a l t e r a t i o n s to rock masses surrounding excavations. Although Laubscher has t r i e d to develop a design method applicable to most underground mining methods, i t remains biased towards caving methods of extraction. Consequently, some of the adjustment f a c t o r s and t h e i r r e s p e c t i v e c a l i b r a t i o n s do not n e c e s s a r i l y represent open stoping conditions. Furthermore, the extent of the open stoping c a l i b r a t i o n data base i s not known. In an e a r l i e r paper, Laubscher (1976) stated, "Large open stopes can only be mined i n competent ground and the stope should have a hydraulic radius 20% less than that r e q u i r e d f o r caving a rock mass with t h a t adjusted c l a s s i f i c a t i o n . 11 This i s overly s i m p l i s t i c considering the differences between caving and open stoping mining methods. As well, i t i s 130 not i n agreement with the l i n e s proposed on the design graph (figure 5.4). Another major c r i t i c i s m of t h i s system i s the lack of guidelines for the sele c t i o n of proper adjustment factors. As a re s u l t , t h i s method i s more e f f i c i e n t when employed by s p e c i a l i s t s having a considerable amount of experience i n c l a s s i f y i n g and designing underground openings. As i n the NGI and CSIR systems, Laubscher has developed a r t i f i c i a l support proposals. 5.4 MATHEWS * OPEN STOPE DESIGN METHOD In 1981, K. Mathews, E. Hoek, E. Wyllie, and S.B.V. Stewart of Golder Associates introduced a new empirical approach for predicting the s t a b i l i t y of open stopes i n deep mining environments (below 1000 metres depth). This method i s an extension of the NGI rock mass c l a s s i f i c a t i o n and has the pote n t i a l to recognize: i) stress controlled f a i l u r e in open stopes, i i ) s t r u c t u r a l f a i l u r e i n stopes, i i i ) and a combination of both stress and str u c t u r a l f a i l u r e . 5.4.1 Description of the method Mathews et a l . suggested that the s t a b i l i t y of each plane in a stope should be analyzed separately. This allows for a more det a i l e d investigation of the rock mass, structure orientation 131 and stress conditions at an in d i v i d u a l plane. In the s t a b i l i t y analysis, two parameters are developed. The f i r s t parameter i s defined as the s t a b i l i t y number, "N". The s t a b i l i t y number quantifies the e f f e c t of the geotechnical factors having a major influence on stope s t a b i l i t y . A high s t a b i l i t y number corresponds to stable ground conditions, while a low s t a b i l i t y number corresponds to unstable ground conditions. The second parameter i s the hydraulic radius which accounts for the e f f e c t of s i z e and shape of the stope surface. The hydraulic radius, also used by Laubscher, was b r i e f l y discussed i n section (5.3.2) . A r e l a t i o n s h i p between the s t a b i l i t y number and hydraulic radius was derived by p l o t t i n g them on a semi-log graph (see figure 5.5). The s t a b i l i t y of the plane investigated can be assessed according to where i t plots with respect to the following three zones: - stable, - p o t e n t i a l l y unstable, - and p o t e n t i a l l y caving. These three zones are separated by t r a n s i t i o n areas and were defined based on 26 case studies from three mines (2 Canadian and 1 Australian) and 29 case h i s t o r i e s from l i t e r a t u r e . The s t a b i l i t y number i s calculated with the following formula: N = Q1 * factor A * factor B * factor C where, 132 0.1 L. 1 1 : 1 » 0 5 10 15 20 25 Shape Factor, S = Area/Perimeter (m) FIGURE 5.5 R e l a t i o n s h i p between the s t a b i l i t y number and h y d r a u l i c r a d i u s o f a s tope s u r f a c e . ( A f t e r Mathews e t 1980). Q1 i s a modification of the NGI rock mass c l a s s i f i c a t i o n . It characterizes the rock mass competency by using f i v e of the six o r i g i n a l parameters i n Barton's NGI c l a s s i f i c a t i o n : Q' = RQD * J r * Jw (ref. Chapter 5.2.2) Jn Ja The s t r e s s r e d u c t i o n f a c t o r SRF proposed i n the NGI c l a s s i f i c a t i o n i s not included because i t i s based on tunnelling case h i s t o r i e s and does not e f f e c t i v e l y represent the e f f e c t of stress i n open stoping. Factor A replaces the SRF i n the o r i g i n a l NGI rock mass c l a s s i f i c a t i o n to more accurately quantify the e f f e c t of stresses acting on the exposed surfaces of open stopes. It i s estimated using figure 5.6. This factor i s a function of the r a t i o of inta c t rock strength to induced stress where: the in t a c t rock strength i s represented by the uniaxial compressive strength of the rock and, the induced stress i s defined as the maximum tangential stress acting p a r a l l e l to the exposed surface at the stope boundary. The u n i a x i a l compressive strength can be determined by laboratory t e s t i n g while the induced stress i s best estimated by numerical modelling. When such models are not available, Mathews et a l . have provided two graphs figure 5.7 and 5.8 which describe the stresses induced i n the roof and walls of is o l a t e d openings. These graphs are an approximation of the closed form solution for a two dimensional e l l i p t i c a l opening. 134 1.0 o.e o. Z o n e of potential instability 0 5 10 15 20 ffl/ffl • Uniaxial compressive strength of intact rock (T, • Induced compressive stress FIGURE 5.6 Graph f o r t h e e s t i m a t i o n o f f a c t o r A. ( A f t e r Mathews e t a l , 1980). 135 MAJOR SURFACES c o '35 cn CD a E o O J _ i • c o c 10 o i? 2.0 CO 15 ca ,a ft 6" O ' H , -1.0 Strike <T H l Virgin Streti Oioorom R o t i o of opening d i m e n s i o n s LEGEND Ti • Induced stress <Tv • V e r n c o l v i r g i n s t r e s s cr Hi * Honronto l virgin s t r e s s on st r ike ff H j ' Hor izonta l v i r g i n s t r e s s n o r m o l _ t o str ike Hor izonta l p l a n e , K • <TH 2 / < rH , Verticol p lone , K ' < T H 2 / c r v CTnormal to surface Oparallel to surface Can be shown in plan or section \ \ \ \ \ N \ *• \ \ K - 0 . 5 K . 1 . 2 N \ \ \ — — . K - 1 . 5 K - 2 . 0 1 ( 2:1 3--I A 1 5 1 6 1 7 1 8: FIGURE 5.7 Graph o f t h e s t r e s s i n d u c e d on t h e major s u r f a c e a s t o p e v e r s u s t h e r a t i o o f ope n i n g d i m e n s i o n s . ( A f t e r Mathews e t a l , 1980). 136 MINOR SURFACES Can be seen in section ~ 8.0 3 CO E o ft c o '35 CO CD k_ a E o O 6.0 4.0 2.0 H O T i i o n t o l p l a n t Sin de ^ 1 ' H 2 VifQin Strtst Dip g ro m Can be seen in plan / / / / / / / y . y ^ ^ . — . . — K ; 0 1 5 _ 1:1 2:| 4:| 6 1 Rot io of o p e n i n g dimensions LEG £ NO CTj • Induced stress Cv • Ver t ico l virgin stress C H I • H o r i z o n t o l v i rg in stress on s t r i ke C T M j • Hor i zon ta l v irgin stresi normal to str ike Hor i zon to l p l a n e , K • C V ^ / T H , 1 ° ~ p a r a l l e l to sur tace V e r t i c a l plane , K » <rH^C v J ° " n o r m a l to s u r f a c e 8 1 FIGURE 5.8 Graph of the stress induced on the minor surface of a stope versus the r a t i o of opening dimension. (After Mathews et a l , 1980). 1 3 7 Factor B accounts for the o r i e n t a t i o n of persistent geological structures i n t e r s e c t i n g the stope surface under analysis. Depending upon the r e l a t i v e o r i e n t a t i o n of the structure with respect to the investigated plane, factor B w i l l r e f l e c t favorable or unfavourable cases. The true angle of i n t e r s e c t i o n between the exposed surface and the most predominant structure, i s used i n figure 5.9 to determine factor B. Factor C i s a surface i n c l i n a t i o n factor. Stope backs are inherently less stable than walls because of the influence of gravity. Barton (1974) suggested that the rock q u a l i t y in a tunnel wall i s hypothetically improved f i v e times compared to an horizontal roof. Since some minor i n s t a b i l i t y can be tolerated i n non-entry mining, Mathews et a l . suggested that a v e r t i c a l open stope wall i s eight times as stable as an horizontal roof. Figure 5.10 or the following formula should be used to determine factor C: FACTOR C = 8 - 7 cosine (angle of stope plane i n c l i n a t i o n ) . This factor describes the increased p o t e n t i a l for i n s t a b i l i t y as a surface becomes more horizontal. 5.4.2 Discussion of the method Despite the small data base the Mathews et a l . method of f e r s strong potential for open stope design. S i m i l a r l y to 138 0. 5 R O C K D E F E C T O R I E N T A T I O N F A C T O R (B) FIGURE 5.9 S k e t c h f o r t h e e s t i m a t i o n o f t h e r o c k d e f e c t o r i e n t a t i o n f a c t o r B. ( A f t e r Mathews e t a l , 1 9 8 0 ) . 10 0 I 1 0 20 40 £o SO 90 4ng/e of £>/p fro/77 Mor/zon/a/ (degrees) Factor C » 8-7 Cosine fong/c of cfip) FIGURE 5.10 Graph f o r the e s t i m a t i o n o f the s tope s u r f a c e i n c l i n a t i o n f a c t o r C ( A f t e r Mathews e t a l , 1980) . 140 Laubscher, they based t h e i r method on an e x i s t i n g rock mass c l a s s i f i c a t i o n system, and adjusted the parameters i n order to be more representative of mining conditions. The combination of the four factors ( Q1, A , B , C ) allows for the prediction of i n s t a b i l i t y that may originate from high stress, structure, gravity or an incompetent rock mass, or any combination of these factors. Because each factor i s well developed and presented graphically, the method i s easy to apply i n p r a c t i c a l s i t u a t i o n s and can be used successfully by mine engineers on s i t e . A f t e r extensive application of t h i s method in back analysis of case h i s t o r i e s i n mines across Canada, the author has found the method very promising. I t addresses the most important factors a f f e c t i n g the s t a b i l i t y of open stopes, and has roughly c a l i b r a t e d these factors. The design methodology i s also p r a c t i c a l and e f f i c i e n t . However t h i s method s t i l l has some shortcomings: a) As a r e s u l t of the small data base, the three zones defined on the s t a b i l i t y graph are too vague for adequate design. The t r a n s i t i o n zone between stable and caving i s very large which may lead to uncertain prediction and misinterpretation of the analysis. b) The graphs proposed for the determination of each factor are based on experience, basic rock mechanics concepts and some a n a l y t i c a l work. T h e i r c a l i b r a t i o n appears to be approximately correct for Canadian conditions but should be 141 re-evaluated against a larger data base. c) The o r i g i n a l data base included only seven cases of stope walls which a l l had a steep i n c l i n a t i o n . Consequently, there i s no evidence that the method i s suitable for the design of i n c l i n e d walls. d) The e f f e c t of t e n s i l e stress, b l a s t i n g and a r t i f i c i a l support have not been addressed i n t h i s method. e) The method was o r i g i n a l l y intend for mining at depth below 1000 meters. 5.5 NUMERICAL MODELLING DESIGN Numerical modelling i s the most widely used method for the design of a l l types of underground openings. The method i s f l e x i b l e and capable of modelling a l l kinds of geometries and opening arrangements. Numerical modelling uses t h e o r e t i c a l and empirical c a l c u l a t i o n s to determine the s t a b i l i t y of the rock mass at selected points inside the medium and at the opening boundary. This i s in opposition to the previous empirical methods, which predict the s t a b i l i t y of excavations based on key geotechnical parameters and past experience. D i g i t a l computers are r e q u i r e d to s o l v e the large number of c a l c u l a t i o n s involved i n numerical modelling. 5.5.1 Open stope design application The primary function of numerical modelling i s to 142 c a l c u l a t e the s t r e s s d i s t r i b u t i o n around underground excavations. This t h e o r e t i c a l stress solution may be used in d i f f e r e n t ways to predict excavation s t a b i l i t y . The most simple approach i s to r e l y on rules of thumb to assess the e f f e c t of induced stress around openings. In hard rock mining, i t i s commonly assumed that the rock mass w i l l f a i l i n compression when the induced stress i s more than h a l f the uniaxial compressive strength. A no-tension f a i l u r e c r i t e r i a i s also commonly used i n the analysis of low t e n s i l e strength of rock masses. More sophisticated f a i l u r e c r i t e r i a can be integrated into the numerical model i n t e r a c t i v e l y or as a post processing operation. The advantage of an i n t e r a c t i v e approach i s that as the stress exceeds the rock mass strength (defined by a f a i l u r e c r i t e r i o n ) , the f a i l e d rock i s (mathematically) detached from the opening and the analysis continues assuming a new geometry u n t i l a stable configuration i s obtained. The post p r o c e s s i n g approach compares the f i n a l d i s t r i b u t i o n of stress around a fixed geometry with a f a i l u r e c r i t e r i o n . The s t a b i l i t y at each point i n the medium (where stresses have been calculated) can be estimated. Zones of p o t e n t i a l f a i l u r e around openings due to compressive, shear or t e n s i l e stress can be defined. The p r i n c i p a l f a i l u r e c r i t e r i a applicable to hard rock open stope mining, have been reviewed in chapter 4. Numerical modelling can also be very useful in parametric 143 studies. By keeping a l l input parameters constant except for the one of p a r t i c u l a r int e r e s t , assumptions and inaccuracies regarding the input parameters can be minimized. For instance, d i f f e r e n t opening shapes can be modelled with the one producing the most favorable stress d i s t r i b u t i o n being used for design. The optimization of the mining sequence i s another common appl i c a t i o n of parametric studies. A mining strategy can be developed i n which high stress concentrations have a minimum e f f e c t on s t a b i l i t y . The creation of stress shadows to improve s t a b i l i t y can also be investigated. 5.5.2 Discussion of the method Numerical modelling i s the most sophisticated method for estimating the d i s t r i b u t i o n of stress around underground excavations. In comparison to the empirical models, t h i s technique has the v e r s a t i l i t y to be applicable to underground openings of a l l types. However, i n order to be v e r s a t i l e , i t s formulation must stay general and has to r e l y e n t i r e l y on the input parameters and f a i l u r e c r i t e r i a to account for the s p e c i f i c aspects of each problem's physical conditions. In addition, t h i s method i s mathematically very complex and contains i n t r i n s i c assumptions which are p r a c t i c a l l y impossible to v e r i f y . Consequently, since numerical models have no b u i l t -i n c a l i b r a t i o n , the solutions can be misleading i f the model i s not properly selected, applied and c a l i b r a t e d against case h i s t o r i e s . 144 "Clearly, l i m i t a t i o n s or inadequacies inherent to a method of analysis may cause the r e s u l t s to be r e s t r i c t e d or misleading, i r r e s p e c t i v e of how well the input data are defined." Stewart and Brown (1984). According to Laubscher and Diering (1987), the r e l i a b i l i t y of a stress analysis problem i s dependent on the a p p l i c a b i l i t y of input of four data types. 1) Problem geometry: The contour of actual excavations in hard rock i s usually well defined but too complex to be a c c u r a t e l y modelled. Model l i m i t a t i o n s such as two dimensional plane stress or plane s t r a i n have to be assumed. The size of the models i s also a l i m i t i n g factor on the portion of the mine that can be included in the analysis. P r a c t i c a l experience and engineering judgement i s e s s e n t i a l to define a representative problem geometry. 2) Geology and material strength: Expressing the rock mass behaviour i n the form of mathematical equations i s only an approximation due to the complexity and v a r i a b i l i t y of the medium. In numerical modelling, assumptions and s i m p l i f i c a t i o n s are necessary to model the int e r a c t i o n of calculated stress and rock mass f a i l u r e c r i t e r i o n . As a r e s u l t , most models lack s e n s i t i v i t y to the important factors characterizing the rock mass. Amongst them, the e f f e c t of j o i n t i n g i s s t i l l poorly taken into account by numerical models and f a i l u r e c r i t e r i o n . 145 3) Loading condition: The loading conditions acting on a s p e c i f i c problem geometry originate from two sources. The f i r s t source i s the pre-mining stress f i e l d which can be measured with a cert a i n degree of accuracy (often in proportion to the budget invested i n the t e s t i n g ) . The second source can ari s e from d i f f e r e n t forms of a r t i f i c i a l loading against excavation surfaces, such as hydraulic or rock f i l l , grouted cables and rock anchors and bl a s t i n g . The study of these e f f e c t s i n open stope mining remains r e l a t i v e l y new and has yet to be measured, estimated and c a l i b r a t e d adequately. 4) Choice of numerical model: The numerical models available o f f e r a wide range of c a p a b i l i t i e s and have a wide range of l i m i t a t i o n s . Based on the understanding of the problem to be modelled, a designer must select between a continuum or discontinuum approach according to the r e l a t i v e importance and continuity of blocks compared with the opening s i z e . He w i l l also have to decide whether a two or a three dimensional model i s the most appropriate, based on the geometry of the problem. The f i n a l choice of the model and f a i l u r e c r i t e r i o n w i l l depend on the computer resources avail a b l e (hardware and software), as well as the purpose of the exercise and the degree of pr e c i s i o n required. 5.6 SUMMARY AND CONCLUSIONS 146 Systematic engineering design of underground excavations using empirical schemes, has been made possible with the development of rock mass c l a s s i f i c a t i o n systems. Reliable design charts for the prediction of tunnel s t a b i l i t y have been proposed by the authors of the p r i n c i p a l c l a s s i f i c a t i o n systems (Barton et a l . and Bieniawski). However, because of the fundamental differences between tunnelling and open stoping, these charts are not applicable for open stope design. Modification of the two c l a s s i f i c a t i o n systems, to better represent mining conditions, has been proposed by Laubscher and Mathews et a l . The model developed by Laubscher o f f e r s some i n t e r e s t i n g concepts, but i t lacks guidelines for the estimation of the adjustment factors and more importantly, remains strongly biased towards caving mining methods. The most suitable empirical method for the design of open stopes i s the one proposed by Mathews et a l . I t accounts for the p r i n c i p a l factors a f f e c t i n g the s t a b i l i t y of open stopes and the methodology i s p r a c t i c a l and easy to use i n the f i e l d . It appears to have a f a i r c a l i b r a t i o n for Canadian open stoping conditions. The main c r i t i c i s m of t h i s approach i s i t s small data base. Consequently, i t s r e l i a b i l i t y remains to be proven in conditions such as i n c l i n e d walls and stopes at shallow depth. Also, the t r a n s i t i o n zone between stable and caving needs to be better defined. The fourth design method reviewed i n t h i s chapter i s numerical modelling. Numerical modelling i s a v e r s a t i l e tool 147 that can be adapted to a l l types of underground openings. The p r i n c i p a l function of numerical modelling i s to calculate the stress d i s t r i b u t i o n around underground excavations. When used as a design method, numerical modelling must r e l y on a f a i l u r e c r i t e r i o n to predict ground s t a b i l i t y . Those f a i l u r e c r i t e r i o n can be applied i n t e r a c t i v e l y with the stress c a l c u l a t i o n , or as a post processing step. The inaccuracies of numerical modelling may originate from the: problem geometry, geology and material strength, loading condition, choice of numerical model. One of the major disadvantages of numerical modelling, compared to the empirical approaches i s that i t does not have a b u i l t - i n c a l i b r a t i o n . Consequently, i f the model i s not properly s e l e c t e d , applied, and calibrated, the solution can be misleading. 148 CHAPTER 6 OPEN STOPE FAILURE MECHANISMS 6.1 INTRODUCTION The d i r e c t cause of underground f a i l u r e i s . t h e creation of an opening, which by removing a volume of rock also removes i t s supporting e f f e c t on the rock mass adjacent to the opening. This unsupported rock mass i s submitted to stress o r i g i n a t i n g from the pre-mining stress f i e l d and the induced stress caused by excavation. The e f f e c t of the r e s u l t i n g stresses around openings can be looked at i n terms of zones of compression and zones of relaxation. The response of a medium such as rock mass to compressive 20 stress and relaxation i s extremely complex due to variable nature of that medium. Consequently, the in t e r a c t i o n between the rock mass, opening geometry and stress conditions define the p o t e n t i a l f a i l u r e mechanisms. 6.2 NATURE OF THE ROCK MASS The nature of the rock mass i s i n t r i n s i c a l l y complex and vari a b l e from one point i n the medium to another. I t comprises one or more types of rock material which are c h a r a c t e r i s t i c a l l y d i s c o n t i n u o u s due t o the p r e s e n c e of g e o l o g i c a l d i s c o n t i n u i t i e s . Brady and Brown (1985) proposed the following 149 d e f i n i t i o n for rock material and rock masses: "Rock material i s the term used to describe the i n t a c t rock between d i s c o n t i n u i t i e s ; i t might be represented by a hand specimen or piece of d r i l l core examined i n the laboratory. The rock mass i s the t o t a l i n s i t u medium containing bedding planes, f a u l t s , j o i n t s , folds and other geological features." The most common type of geological d i s c o n t i n u i t y i s the j o i n t . I t i s a regular fracture along which there has been very l i t t l e or no movement. Because of t h e i r formation process, they usually occur i n near p a r a l l e l sets, having a spacing range varying from a few centimeters ( f o l i a t e d rock) to several meters. The combination of in t e r s e c t i n g j o i n t sets and other random d i s c o n t i n u i t i e s divide the rock material into blocks. The orientation and spacing of the j o i n t sets define the s i z e and shape of in d i v i d u a l blocks i n the rock mass matrix. The continuity of geological features determine how well the blocks are defined. Although d i f f i c u l t to assess due to l i m i t e d exposure of underground openings, the e f f e c t of j o i n t continuity may have a major influence on s t a b i l i t y . As a general rule, features less than approximately 1.5 meters (5 feet) long are not considered i n a j o i n t survey. This eliminates most fractures induced by bl a s t i n g . Major d i s c o n t i n u i t i e s such as f a u l t s or shear zones usually have to be dealt with i n d i v i d u a l l y . On the scale of 150 open stopes, they r a r e l y take regular patterns and t h e i r e f f e c t on s t a b i l i t y i s l a r g e l y a function of t h e i r l o c a t i o n and the nature of the f i l l material and the amount of movement that has taken place along the discontinuity. With regard to s t a b i l i t y , two of the most important c h a r a c t e r i s t i c s of the rock mass are the siz e and shape of the blocks forming the rock mass matrix. The importance of block shape determines whether the rock mass w i l l be i s o t r o p i c (in the case of blocky shape) or anisotropic (in the case of elongated or platy shapes). The shape of blocks i s a function of i n d i v i d u a l j o i n t sets. I f a l l the j o i n t sets have sim i l a r spacing, the block w i l l have a cubical shape and the behaviour i s l i k e l y to be i s o t r o p i c . I f the blocks formed by the d i s c o n t i n u i t i e s have one or two long dimensions compared with the t h i r d dimension, the shape w i l l be elongated or platy and the behaviour w i l l be anisotropic. In t h i s case, the r e l a t i v e o r i e n t a t i o n of the blocks with the stope surface w i l l become c r i t i c a l . Generally, the smaller the difference i n dip and s t r i k e (the more p a r a l l e l ) the blocks are to the stope surface, the less stable the condition w i l l be. Blocks oriented perpendicular to a stope surface have l i t t l e e f f e c t on s t a b i l i t y . Folk (1965) developed a triang u l a r chart that may provide assistance i n estimating block shape (figure 6.1). He assumed that blocks are composed of the three most frequent j o i n t sets (closest spacing). If the small side of the blocks have a 151 «0 30 ELONGATE PLATY 3 3 BLADED 67 L-i FIGURE 6.1 Triangular chart for the estimation of block shape. (After Folk, 1968). 152 length "S", the intermediate side length " I " and the larger side length "L", the three axes of the Folk block shape chart are defined by S/L, (L-I)/(L-S) and ( S 2 / L I ) 1 / 3 (figure 6.1). However, underground observation i s usually s u f f i c i e n t to determine the general shape of the block matrix, which in turn adequately defines whether the rock mass i s expected to be i s o t r o p i c or anisotropic. The s i z e of the blocks i s the most important factor with r e g a r d t o e x c a v a t i o n s t a b i l i t y because g e o l o g i c a l d i s c o n t i n u i t i e s are the weakest component of the rock mass. The smaller the blocks are, the more d i s c o n t i n u i t i e s there are exposed per unit surface area and the less stable the rock mass surface w i l l be. Several authors have suggested that the behaviour of a rock mass i s lar g e l y influenced by the r e l a t i v e s i z e of the blocks compared with the surface of rock mass exposed. Figure 6.2 shows that d i f f e r e n t exposures of the same rock mass w i l l produce domains having very d i f f e r e n t c h a r a c t e r i s t i c s and behaviours. In t h i s open stope study, three major trends in the behaviour of rock masses have been i d e n t i f i e d according to the r e l a t i v e s i z e of the blocks composing the rock mass. 1. Intact rock behaviour 2. Discrete block behaviour 3. Jointed rock mass behaviour These three types of behaviour and t h e i r associated f a i l u r e mechanisms w i l l be discussed i n the following sections. 153 FIGURE 6.2 TRANSITION FROM INTACT ROCK TO HEAVILY JOINTED ROCK MASS (After Hoek & Brown, 1980) Intact rock Single discontinuity Two discontinuities Several discontinuities Rock mass FIGURE 6.3 F a i l u r e mechanism of in t a c t rock submitted to compressive s t r e s s , f a i l u r e type l a ; r e f . figure 6.1*7 FIGURE 6 . 4 F a i l u r e mechanism of inta c t rock i n state of stress relaxation, f a i l u r e type l b ; r e f . fig u r e 6.17 154 6.3 INTACT ROCK BEHAVIOUR The rock mass surrounding underground excavations w i l l behave as in t a c t rock when the r e l a t i v e s i z e of the block matrix i s s i m i l a r i n siz e or larger than the opening dimensions. I t usually occurs i n a rock mass containing very few or no d i s c o n t i n u i t i e s which i s not common i n Canadian hard rock mines. For stope design, in t a c t rock i s often assumed to be homogeneous, i s o t r o p i c and show e l a s t i c deformation under stressed but p r e - f a i l u r e conditions. When the compressive stress acting p a r a l l e l to the opening faces exceeds the rock mass strength, t e n s i l e cracks may develop i n the d i r e c t i o n of the compressive forces, i e . p a r a l l e l to the stope walls and back (figure 6 . 3 ) . This phenomenon has been observed and explained by several authors: G r i f f i t h (1924), MacLintock and Walsh (1962), Fairhurst and Cook (1968), Hoek (1965). The compressive f a i l u r e may then occur i n the form of slabbing or buckling along these induced cracks. Several factors such as bl a s t i n g v i b r a t i o n , blast induced fractures, random d i s c o n t i n u i t i e s or changes in stress can also contribute to i n i t i a t e the f a i l u r e . Another commonly observed e f f e c t of high compressive stress occurs i n sharp corners of excavations. This e f f e c t has been demonstrated with a closed form solution in section 3.4 . 3 . The de t e r i o r a t i o n of corners may continue u n t i l a smoother 155 p r o f i l e i s obtained. Intact rock w i l l respond d i f f e r e n t l y i n a zone of relaxation. Rock i s known to have very low strength when submitted to t e n s i l e forces. Tensile cracks may develop perpendicular to the acting t e n s i l e stress and create a zone of relaxation. Because the alignment of cracks i s t y p i c a l l y perpendicular to the stress and the opening boundary (figure 6.4), major rock f a l l s s o l e l y due to t e n s i l e cracks are not common when dealing with open stope mining i n in t a c t rock. 6.4 DISCRETE BLOCK BEHAVIOUR The ground i n which discrete block f a i l u r e occurs i s not extensively fractured and t y p i c a l l y contains three or less j o i n t sets. The spacing of the j o i n t sets are r e l a t i v e l y large which produces blocks of a f a i r s i z e (in the order of several cubic meters). Discrete block f a i l u r e occurs when one or more blocks are detached from the roof or sidewalls. For an i s o t r o p i c medium (blocks having a cubical shape), i f the rock mass i s submitted to a zone o f compressive stress, p o t e n t i a l f a i l u r e may be induced by shearing wedges from the excavation boundaries (figure 6.5). When submitted to a state of relaxation, i s o t r o p i c discrete block f a i l u r e may occur according to two d i f f e r e n t modes: gravity f a l l or s l i d i n g (figure 6.6). The simple gravity f a l l i s the free v e r t i c a l displacement of a block under the t r a c t i o n of i t s own 156 FIGURE 6.5 Failure mechanism of discrete block for an isotropic rock material submitted to compressive stress, fa i lure type 2a; ref. figure 6.17 FIGURE 6.6 Failure mechanism of discrete block for an isotropic rock material in a state of stress relaxation, failure type 2b; ref. figure 6.17 FIGURE 6.7 Failure mechanism of discrete block for an anisotropic rock material having elongated blocks oriented para l le l to the stope surface and submitted to a compressive stress, fa i lure type 2c; ref. figure 6.17 FIGURE 6.8 Failure mechanism of discrete block for an anisotropic rock material having elongated blocks oriented para l l e l to the stope surface in a state of stress relaxation, failure type 2d; ref. figure 6.17 157 g r a v i t a t i o n a l load. Since there are no confining stresses and geological d i s c o n t i n u i t i e s have a n e g l i g i b l e t e n s i l e strength, the determination of block s t a b i l i t y becomes purely kinematic. In s l i d i n g , the d r i v i n g force i s a function of the i n c l i n a t i o n of the " c r i t i c a l " d i s c o n t i n u i t y ( s l i d i n g plane). In the case of anisotropic rock (elongated or platy blocks), the excavation s t a b i l i t y w i l l be greatly influenced by the r e l a t i v e orientation of the blocks with regard to the opening faces. For s i m p l i f i c a t i o n , only the two extreme cases w i l l be discussed here. Figure 6.7 shows elongated blocks sub-p a r a l l e l to a stope face, on which the compressive stress may create a buckling type of f a i l u r e . I f submitted to a zone of relaxation, t h i s condition may produce gravity f a l l , slabbing or s l i d i n g . Figure 6.8, shows the slabbing mode of f a i l u r e . On the other hand, when elongated blocks are sub-per p e n d i c u l a r to the face, the compressive stress w i l l contribute to s t a b i l i z e the surrounding rock mass by clamping the blocks together (figure 6.9). In a zone of relaxation, the s t a b i l i t y of perpendicular blocks becomes purely kinematic because the confining e f f e c t no longer e x i s t s . Figure 6.10 shows the gravity f a l l and s l i d i n g modes of f a i l u r e . 6.5 JOINTED ROCK MASS BEHAVIOUR A jointed rock mass i s a less competent type of ground which i s characterized by a high frequency of j o i n t i n g 158 FIGURE 6.9 F a i l u r e mechanism of d i s c r e t e block f o r an an i s o t r o p i c rock material having elongated blocks oriented perpendicular to the stope surface and submitted to compressive s t r e s s , f a i l u r e type 2e; r e f . f i g u r e 6.17 FIGURE 6.11 F a i l u r e mechanism of jointed.rock mass f o r an i s o t r o p i c rock material submitted to compressive s t r e s s , f a i l u r e type 3a; r e f . figu r e 6.17 FIGURE 6.10 F a i l u r e mechanism of dis c r e t e block f o r an anisotropic rock material having elongated blocks oriented perpendicular to the stope surface i n a state of stress r e l a x a t i o n , f a i l u r e type 2f; r e f . figure 6.17 FIGURE 6.12 F a i l u r e mechanism of jointeo rock mass for an i s o t r o p i c rock material i n a state of str e s s relaxation, f a i l u r e type 3b; r e f . figure 6.17 159 producing a rock mass matrix of small blocks. I t usually includes three or more well defined j o i n t sets having a r e l a t i v e l y close spacing. The f a i l u r e of a jointed rock mass, whether i t occurs under c o n d i t i o n s of compression or relaxation, r e s u l t s i n a r a v e l l i n g of blocks. Rock movement w i l l continue u n t i l the peripheral blocks are interlocked and a stable arch i s formed. The amount of d i l u t i o n contained inside the arch p r i o r to f a i l u r e i s a function of the o r i g i n a l opening span. When the c r i t i c a l span i s exceeded, a stable arch can no longer be formed and r a v e l l i n g w i l l progress as a chimney u n t i l better ground conditions are met or i n the extreme si t u a t i o n , i t w i l l extend to surface. The f a i l u r e mechanisms associated with a jointed rock mass w i l l be s i m i l a r to those previously described for discrete blocks, but on a smaller scale. Figures 6.11 to 6.16 show the six basic cases discussed for discrete block f a i l u r e applied to a jointed rock mass. 6.6 SUMMARY AND CLASSIFICATION OF FAILURE MECHANISMS The open stope f a i l u r e mechanism i s primarily influenced by the nature of the rock mass. Based on the r e l a t i v e size of the rock mass blocks, compared with the opening dimensions, the rock mass w i l l behave as in t a c t rock, discrete blocks or a jointed rock mass. Each of these three types of rock mass behaviour can be submitted to a compressive or t e n s i l e state of 160 FIGURE 6.13 Fai lure mechanism of jointed rock mass for an anisotropic rock material having elongated blocks oriented paral le l to the stope surface and submitted to a compressive stress, fa i lure type 3c ; ref . figure 6.17 FIGURE 6.14 Failure mechanism of jointed rock mass for an anisotropic rock material having elongated blocks oriented para l l e l to the stope surface in a state of stress relaxation, fa i lure type 3d; ref. figure 6.17 FIGURE 6.15 Failure mechanism of jointed rock mass for an anisotropic rock material having elongated blocks oriented perpendicular to the stope surface and submitted to compressive stress. fai lure type 3e; ref. figure 6.17 FIGURE 6.16 Failure mechanism of jointed rock mass for an anisotropic rock material having elongated blocks oriented perpendicular to the stope surface in a state of stress relaxation, fai lure type 3 f ; ref. figure 6.17 stress creating six possible s i t u a t i o n s . I t has been observed that the shape and r e l a t i v e o r i e n t a t i o n of the blocks also play an important role i n the mechanism of f a i l u r e . In the case of compact blocks the rock mass behaviour w i l l l i k e l y be i s o t r o p i c . I f the blocks are elongated, the r e l a t i v e orientation with respect to the stope surface becomes c r i t i c a l . The most favorable orientation, for d i s c o n t i n u i t i e s that delineate blocks, i s perpendicular to stope surface. P a r a l l e l orientation i s more l i k e l y to produce i n s t a b i l i t y . The c r i t e r i a described above to c l a s s i f y open stope f a i l u r e mechanisms are shown on the diagram i n figure 6.17 . Fourteen d i f f e r e n t potential f a i l u r e s ituations may r e s u l t from t h i s c l a s s i f i c a t i o n and are i l l u s t r a t e d in figures 6.3 to 6.16. Although t h i s c l a s s i f i c a t i o n has fourteen d i f f e r e n t f a i l u r e scenarios, only f i v e i n d i v i d u a l modes of f a i l u r e emerge: - gravity f a l l , - slabbing, - buckling, - s l i d i n g , - shearing. A v a r i a t i o n of these modes of f a i l u r e occurs i f the rock mass i s heavily fractured, and the detachment of small blocks occurs in a r a v e l l i n g manner. When looked at from a kinematic point of view (which i s based purely on d i s c o n t i n u i t y orientation and does not account for non-gravitational loads or s t r e s s ) , the 162 Intact Rock 1 a) 1 b) D i s c r e t e Block •Isotropic-Anisotropic-• o n g a t e d Block •Parallel to Stope-Surface • o n g a t e d Block •Perpendicular to Stope Surface compression 2 a) ' relaxation 2 b) — compression 2 c) relaxation 2 d) I compression 2 e) relaxation 2 f) I Isotropic-Jointed Rock Mass ' Anlsotroplc-Elongated Block • Parallel to Stope-Surface • o n g a t e d Block •Perpendicular to Stope Surface compression 3 a) ' relaxation 3 b) I compression 3 c) — relaxation 3 d) compression 3 e) ' relaxation 3 f) FIGURE 6.17 C l a s s i f i c a t i o n of the f a i l u r e mechanisms i n open stope mining. 163 shearing become a sub-case of s l i d i n g or gravity f a l l , and the buckling and slabbing can be approximated by a toppling mode of f a i l u r e . The potential mode of f a i l u r e can be determined by stereographic analysis as described i n chapter 7 of Hoek and Brown (1980), or with the following technique involving simple diagrams. Referring to figure 6.18, the excavation and the " c r i t i c a l j o i n t " are f i r s t sketched. The c r i t i c a l j o i n t represents the persistent j o i n t set oriented at the shallowest angle with the stope surface. If a gravity vector represented by a v e r t i c a l arrow drawn from the approximate centre of gravity of the block (formed by the c r i t i c a l j o i n t ) , f a l l s d i r e c t l y inside the opening, the mode of f a i l u r e w i l l be gravity f a l l (figure 6.18 a). If the gravity vector crosses the c r i t i c a l j o i n t (see figure 6.18 b) , the p o t e n t i a l for s l i d i n g f a i l u r e e x i s t s . I f the gravity vector stays inside the medium without i n t e r s e c t i n g the c r i t i c a l j o i n t , slabbing or buckling f a i l u r e can occur (figure 6 .18 c) . 164 BACK FIGURE 6.18 a) Sketch showing the gravity f a l l mode of fa i lure . jj&jj WALL FIGURE 6.18 b) Sketch showing the s l id ing mode of fa i lure . FIGURE 6.18 c) Sketch showing the slabbing and buckling mode of fa i lure . 165 CHAPTER 7 DEVELOPMENT OF THE GEOMECHANICAL MODEL 7.1 INTRODUCTION The review of e x i s t i n g empirical methods for underground excavation design (chapter 5) has shown an evolution i n t h e i r development. E f f i c i e n t empirical design methods started with r o c k mass c l a s s i f i c a t i o n systems, which allow the characterization of the rock mass competency. Based on the Q and RMR indexes, Mathews and Laubscher have proposed design methods that were better adapted for mining conditions. Because the Mathews et a l . method was s p e c i a l l y developed for open stope mining and i t has been shown to possess a f a i r c a l i b r a t i o n for Canadian conditions (Potvin et a l . , 1987; Bawden et a l . 1988), i t was decided to follow the same methodology for the development of the geomechanical model. Therefore, the factors described i n t h i s chapter w i l l be s i m i l a r to the one used by Mathews et a l . The concept employed i n the proposed geomechanical model i s based on three fundamental aspects of creating an excavation i n a r o c k mass. By d e f i n i n g and c a l i b r a t i n g the c h a r a c t e r i s t i c s of the rock mass (1st aspect) , the induced stress (2nd aspect), and the physical conditions of the problem (3rd aspect) , with a large data base, i t w i l l be possible to predict whether an excavation w i l l be stable or w i l l experience ground control problems. This w i l l constitute the v e r i f i c a t i o n 166 of the main hypothesis (chapter 1.2). The c h a r a c t e r i s t i c s of each aspect can be defined by relevant factors a f f e c t i n g the s t a b i l i t y of excavations. The factors w i l l be defined based on the study of open stope f a i l u r e mechanisms (chapter 6), and the weighting used i n e x i s t i n g models (chapter 5). A rock mass i s characterized by the block size and the c r i t i c a l j o i n t factors. A compressive stress factor, derived from numerical modelling, represents the aspect of induced stress. The physical conditions are divided into a stope size and shape factor and a gravity factor, the l a t t e r being related to the stope surface i n c l i n a t i o n . External factors w i l l be discussed i n chapters 9 and 10. The above f i v e factors can be broken into key geotechnical parameters. The geotechnical parameters can be estimated from: observations and measurements of f i e l d data, laboratory testing of rock specimens and numerical modelling. Figure 7.1 i s a conceptualization of the model showing how the problem i s subdivided into factors and parameters. This chapter w i l l focus on the d e f i n i t i o n of each factor and i t s r o l e i n the potential f a i l u r e mechanisms. The techniques best suited for the estimation of the geotechnical parameters w i l l also be discussed. The c a l i b r a t i o n procedure for the factors w i l l be explained i n chapter 8. An empirical philosophy was chosen to integrate a l l the factors into a design method. It i s believed that an empirical approach i s the most appropriate because of the complexity of the problem 167 FIGURE 7.1 VISUALIZATION OF THE MODEL EXCAVATION IN A ROCK MASS THREE ASPECTS OF THE PROBLEM oo ROCK MASS CHARACTERISITCS BLOCK SIZE FACTOR STRESS EFFECT CRITICAL JOINT FACTOR COMPRESSIVE STRESS FACTOR DIFFERENCE DIFFERENCE IH DIP IN STRIKE SHEAR STRENGTH STOPE INCLINATION FACTOR SLIDING ORAIYY SLABBING OPTICAL S70PE JOINT SURFACE INQ IN ATI OH PHYSICAL CONDITIONS EXTERNAL FACTORS _ BLASTING CABLE STOPE SIZE AND SHAPE FACTORS BOLTING HYDRAULIC • RAWS,. and the d i f f i c u l t y i n e s t i m a t i n g r e p r e s e n t a t i v e input parameters. Empirical methods are l i k e l y to be more r e l i a b l e because they make use of past experience. However, they should be applied i n conditions s i m i l a r to the data base. 7.2 THE BLOCK SIZE FACTOR The most important c h a r a c t e r i s t i c of a rock mass i s i t s degree of fracturing, or the si z e of the blocks forming the matrix. The smaller the blocks the less competent the rock mass w i l l be. Consequently, the parameter representing the block s i z e must have a large influence i n the analysis and have a decreasing value as the rock mass i s more fractured. The parameter selected to quantify the e f f e c t of block size i s the r a t i o of RQD/Jn which was proposed by Barton i n the o r i g i n a l Q-system. The r a t i o RQD/Jn i s e a s i l y estimated on s i t e and provides a useful scale to account for the number of j o i n t exposures. I t has a maximum value of 200 and a minimum of 0.5, and thus a t o t a l possible r e l a t i v e influence of 4 00 on the s t a b i l i t y number. According to the data base for Canadian open stope mines, t h i s influence i n practice ranges from 1 to 90. 7.2.1 Estimation of block s i z e RQD and Jn are the two parameters required to estimate the block si z e factor. The Jn value represents the e f f e c t of having persistent j o i n t sets and random j o i n t sets in the rock 169 mass. I t i s e a s i l y estimated using table 5.2. Kinematically, a rock mass containing several j o i n t sets (of variable dip and orientation) w i l l be less stable than a rock mass having a s i m i l a r degree of fr a c t u r i n g but only one persistent j o i n t set. The Jn parameter allows the d i f f e r e n t i a t i o n between a rock mass that i s heavily fractured by a f o l i a t i o n , which could be r e l a t i v e l y competent when oriented perpendicular to stope surface, and a t o t a l l y incompetent rock mass containing several variable j o i n t sets. The Rock Quality Designation RQD (developed by Deere, 1964) i s a widely used technique measuring the frequency of rock fractures. RQD can be assessed i n d i r e c t l y on diamond d r i l l cores and represents the percentage of i n t a c t pieces of core equal to or longer than 100 mm over the t o t a l length considered. % RQD = 100% * (length of core longer than 100 mm) t o t a l length considered RQD should be measured on core of at least 54 mm diameter (NX), d r i l l e d with double barrel rods. Although RQD i s simple and easy to estimate with l i t t l e supplementary cost, i t may lead to incorrect assessment i f the core i s poorly cared for p r i o r to the RQD estimation. This becomes important when the rock investigated i s weak or b r i t t l e . Another c r i t i c i s m of RQD i s the p o t e n t i a l bias related to the borehole orientation. E f f e c t i v e l y , the d i s c o n t i n u i t i e s 170 p a r a l l e l to the borehole w i l l not be intersected, which w i l l r e s u l t i n an overestimation of RQD. Consequently, the measure of RQD should be v e r i f i e d against other techniques based on d i r e c t underground j o i n t surveys. Hudson & P r i e s t (1976) and Palmstrom (1982) have proposed methods to correlate RQD with underground j o i n t mapping, a) Hudson and Pr i e s t method According to Hudson and P r i e s t , the spacing of d i s c o n t i n u i t i e s i s assumed to have a range of values which follows some form of s t a t i s t i c a l d i s t r i b u t i o n . Based on twenty seven measurements i n three tunnel projects i n the U.K., Hudson and P r i e s t found that the p r o b a b i l i t y density d i s t r i b u t i o n of d i s c o n t i n u i t y spacings can be approximated the negative exponential d i s t r i b u t i o n : v -XX f (x) = Ae where x = ind i v i d u a l d i s c o n t i n u i t y spacing, = discontinuity frequency 1/x, = mean disco n t i n u i t y spacing. Individual d i s c o n t i n u i t y spacing i s measured along a scanline underground as shown in figure 7.2. Hudson and Pr i e s t proposed the following r e l a t i o n s h i p between the discontinuity frequency and RQD: RQD = 100 e -0.1* ( 0 . l \ + 1) When the disco n t i n u i t y spacing frequency (X ) has a value between 6 and 16 per meter, the above r e l a t i o n s h i p i s l i n e a r (figure 7.3) and can be approximated by: 171 Oi&toncs from A to Iht iih dittomrutyifl, Spacing values to given OSl/o^-d,., tor i i ! • « (olD'SContirwly intersection points otong o (b)Sconiins (rneosuring tope^  on exposed straight line CAB) through the rock moss lock tool FIGURE 7.2 S k e t c h showing t h e measurement o f j o i n t s a l o n g a s c a n l i n e . ( A f t e r P r i e s t and Hudson, 1976) Linear approximation ROD** - 3.68* * 110.4 t i i i • i S i i i I ' 0 2 4 6 8 10 12 14 16 18 20 22 21 26 28 30 32 34 36 38 40 Average number ol discontinuities per m, X FIGURE 7.3 R e l a t i o n s h i p between RQD and t h e average number o f d i s c o n t i n u i t i e s p e r meter. ( A f t e r P r i e s t and Hudson, 1976) RQD = -3.68X + 110.4 b) Palmstrom method Palmstrom (1982) proposed an a l t e r n a t i v e technique also based on d i r e c t underground j o i n t surveys. The volumetric j o i n t count (Jv) i s an estimation of the number of j o i n t s per cubic metre i n rock mass. The factor Jv has been related to RQD empirically by the following r e l a t i o n s h i p . RQD = 115 - 3.3 Jv The volumetric j o i n t count (Jv) can be estimated by defining an area of the rock mass where the majority of the persistent d i s c o n t i n u i t i e s are represented. The number of d i s c o n t i n u i t i e s inside the delineated area are counted and the frequency of j o i n t i n g per unit of surface can be calculated (# of j o i n t s per square metre). This value i s transformed into volumetric units (# of j o i n t s per cubic metre) by multiplying by a factor "K": Jv (# of joints/m 2) * K = (# of joints/m 3) Palmstrom provided very few d e t a i l s on how t h i s factor K was derived and did not give a c r i t e r i a on how to choose an appropriate K for a given s i t u a t i o n . He stated: "The factor K w i l l vary with the d i s t r i b u t i o n of the j o i n t s . With an equal d i s t r i b u t i o n i n a l l three d i r e c t i o n s , K w i l l be 1.15 - 1.5 depending upon the orientation of the s u r f a c e with respect to j o i n t planes. For unequal d i s t r i b u t i o n s , the K w i l l have greater v a r i a t i o n . Under normal 173 conditions, however, i t has been found that k = 1.25 - 1.35" Palmstrom (1982). In practice a k factor of 1.0 i s often used assuming that the surface mapped i s representative of the three dimensions. 7 . 3 STRESS FACTOR 7 . 3 . 1 E f f e c t of compression The e f f e c t of a high compressive stress on a rock mass may r e s u l t i n crushing or cracking of int a c t rock, shearing along e x i s t i n g d i s c o n t i n u i t i e s , or rotating of blocks or any combination of the above. The complexity and v a r i a b i l i t y of these phenomena negate any attempt to reproduce them with a high degree of pr e c i s i o n i n the empirical model. The approach chosen was the one proposed by Mathews et a l . , where the t a n g e n t i a l s t r e s s e s induced p a r a l l e l to the excavation boundaries (oy) i s scaled against the u n i a x i a l compressive strength of the rock mass (CT c). This suggests that the e f f e c t of compressive stress i s proportional to the r e l a t i v e magnitude of the tangential stress normalized with i n t a c t rock strength. The adjustment factor for compressive stress i s roughly the same as Mathews1 factor A, and can be estimated using figure 7.4. I t has a t o t a l r e l a t i v e influence of 10 in the s t a b i l i t y number c a l c u l a t i o n . The only modification made was to set a minimum adjustment of 0.1 when the r a t i o of oc/oy i s equal to or less than 2.0 (instead of assuming automatic f a i l u r e as 174 FIGURE 7.4 Graph f o r t h e e s t i m a t i o n o f t h e c o m p r e s s i v e s t r e s s f a c t o r . 175 suggested by Mathews et al.) . This w i l l be further discussed in chapter 8.4.2. The un i a x i a l compressive strength (a c) was discussed i n section 4.2.1. The induced tangential stress (oy) for simple open stope configurations can be determined using numerical modelling or curves developed from a parametric study using two and three dimensional numerical modelling (section 7.3.2) . 7.3.2 Open stope numerical modelling parametric study The determination of induced stress around open stopes can be d i f f i c u l t to estimate at mine s i t e s , because of the lack of numerical modelling hardware and software f a c i l i t i e s . Although most mining operations possess computers and sometimes have access to two dimensional models, three dimensional models are uncommon, d i f f i c u l t to use and time consuming to run. Since "three dimensional" geometries are frequent i n open stope mining, the development of stress induced curves was necessary in order to make the design method applicable at the mine s i t e s . The curves presented below have been developed based on 7 0 runs of the three dimensional boundary element code "BEAP" and a number of runs using the two dimensional boundary element program "BITEM". A b r i e f description of both program i s given in Appendix 2 and the most s i g n i f i c a n t stope design output, plotted i n terms of the stress acting i n the middle of each plane, i s reproduced i n Appendix 3. It should be kept i n mind that a number of assumptions have 176 been made i n t h i s parametric study. The stope geometries used are based on open stopes seen i n more than 3 0 Canadian mines. However, t h e i r shapes have been i d e a l i z e d and v e r t i c a l dip only has been considered. Consequently, the stress curves should serve as a rough guide to determining the stress around simple three dimensional geometries. 7.3.2.1 General concept of the parametric study The p r i n c i p a l stresses induced on each surface of a stope, act i n two perpendicular directions tangential to the stope plane (figure 7.5). The magnitude (and e f f e c t on s t a b i l i t y ) of these induced stresses i s primarily a function of the pre-mining stress r a t i o and the problem geometry. These w i l l constitute the p r i n c i p a l variables of t h i s parametric study. The problem geometries are divided into longitudinal and transverse stope configurations, while the pre-mining stress r a t i o s , "K", are varied from i s o s t a t i c to 1.5, 2.0 and 2.5 in a l l three d i r e c t i o n s . The ef f e c t s of these v a r i a t i o n s on the induced stresses (acting in two dire c t i o n s on each plane) w i l l be analyzed according to the following scheme: 1) No s i g n i f i c a n t e f f e c t , the induced stress can be assumed equal to the pre-mining stress. 2) The induced stress may decrease (from the pre-mining stress value), but never reaches tension, r e s u l t i n g in a low compressive stress condition. In t h i s case, the induced stress w i l l have no negative e f f e c t on s t a b i l i t y and can be 177 PLANE A - ASPECT RATIO = L/H HORIZONTAL PLANE K RATIO = 0<\/$2 VERTICAL PLANE K RATIO = <J-\ FIGURE 7 . 5 D e f i n i t i o n o f t h e a s p e c t r a t i o and K r a t i o used i n t h e e s t i m a t i o n o f t h e i n d u c e d s t r e s s a c t i n g on a s t o p e s u r f a c e . 178 overlooked i n the design analysis. 3) The induced stress may decrease and possibly reach tension. Induced stress curves w i l l be produced i n t h i s s i t u a t i o n , to p r e d i c t which conditions r e s u l t i n a t e n s i l e stress environment. 4) The induced stress may show a s i g n i f i c a n t increase. Once again, induced stress curves w i l l be produced i n order to be able to determine the magnitude of o ± for the design analysis. An important observation, made on most three dimensional problems modelled i n t h i s study, was that the induced stress acting i n a given d i r e c t i o n i s mainly affected by: the dimensions of the stope aspect surface (see figure 7.5), and the K r a t i o , defined by the pre-mining stress acting p a r a l l e l to the induced stress investigated and the pre-mining stress acting perpendicular to the surface of the stope (figure 7.5). I t i s assumed that the pre-mining stress acting i n the t h i r d d i r e c t i o n generally has an i n s i g n i f i c a n t e f f e c t on the induced st r e s s . This s i m p l i f i e s the o v e r a l l problem and s i m p l i f i e s the presentation of the r e s u l t s . In the following sections, guidelines for the estimation of the induced stress w i l l be given for each stope surface (of i n t e r e s t i n longitudinal and transversal open stoping). 7 . 3 . 2 . 2 Longitudinal open stoping parametric study 179 The geometrical shape of longitudinal stopes i s generally-characterized by a stope width that i s small compared to the stope height and length. According to the data base, most Canadian (longitudinal) open stope geometries are between the l i m i t s defined on figure 7.6. A summary of the output of the most important three dimensional models used for the lon g i t u d i n a l study can be found i n Appendix 3. The modelling of the extreme geometries has been done using BITEM. The modelling was performed on iso l a t e d stopes only. The influence of nearby stopes can be considered n e g l i g i b l e for stope wall and stope back analyses. This i s not true for the stope abutments. The three stope surfaces of i n t e r e s t are represented on figure 7.5 by plane A (the stope wall), plane B (the back) and plane C (the stope end). Plane A, stope wall: i) The stress induced i n the horizontal d i r e c t i o n w i l l show a s i g n i f i c a n t decrease and may be t e n s i l e for c e r t a i n geometry (L/H < 1) and stress r a t i o combinations. For longitudinal stope walls, the surface aspect r a t i o i s defined by L/H (stope length/stope height) and K i s given by 0-^/02 (figure 7.7). The horizontal induced stress on plane A can be estimated using the curves i n figure 7.7). The influence of varying the stope width on the stresses i n plane A can be considered n e g l i g i b l e (see figure 7.8). i i ) The stress induced v e r t i c a l l y i s s i m i l a r to the horizontal 180 FIGURE 7.6 LONGITUDINAL O P E N STOPE T Y P I C A L DIMENSIONS EXPRESSED IN TERMS OF STOPE WIDTH (W) L = (1 TO 9)W LP = (1 TO 5)W F I G U R E 7 . 7 LONGITUDINAL OPEN STOPE STRESS HANGING WALL - HORIZONTAL PLANE 0.7 - i 1:INF 1:7 1:5 1:4 1:3 1:2 1:1 2:1 3:1 4 STOPE ASPECT RATIO (LENGTH / HEIGHT) • HW / WIDTH = 5 A BACK / WIDTH a 5 STOPE ASPECT RATIO (LENGTH / HEIGHT) + HW / WIDTH a 1.0 O HW / WIDTH = 20 X BACK / WIDTH = 10 V BACK / WIDTH a 20 induced stress except the problem i s rotated 90°. The stope aspect r a t i o remains L/H, but the s i g n i f i c a n t stress r a t i o K i s defined by a 1 / a 3 . Figure 7.9 can be used to estimate the v e r t i c a l induced stress. Plane B, stope back: i) The induced tangential stress acting i n the d i r e c t i o n perpendicular to the stope s t r i k e (oy direction) may show a s i g n i f i c a n t increase. Because the t y p i c a l stope width does not vary d r a s t i c a l l y compared with stope height and length, the wall aspect r a t i o (L/H) w i l l have a much greater influence on the back induced stress, than a back aspect r a t i o . Consequently, the curves developed for t h i s s i t u a t i o n are a function of the wall aspect r a t i o (L/H) and the K r a t i o of a-y/o3 (see figure 7.10). The stope width assumed for the development of the curves was 1/4 the size of the intermediate dimension. The influence of stope width however i s not necessarily n e g l i g i b l e . When dealing with wider or narrower stopes, the error made can be roughly assessed from figure 7.8. As a general rule , the narrower the stope the higher the back and abutment stresses w i l l be. i i ) The induced stress r a t i o acting along the s t r i k e (a 2 direction) may show a small increase, but i t w i l l not be as s i g n i f i c a n t as the induced stress acting across s t r i k e . Consequently, the a 2 induced stress can be overlooked in the s t a b i l i t y analysis of simple longitudinal stope backs. 184 FIGURE 7.9 LONGTTUDMAL OPEN STOPE STRESS HANGING WALL - VERTICAL PLANE 0.7 -, — 1:INF 1:5 1:4 1:3 1:2 1:1 2:1 3:1 4:1 5:1 7:1 INF:1 STOPE ASPECT RATIO (LENGTH / HEIGHT) FIGURE 7 1 0 LONGITUDINAL OPEN STOPE STRESS BACK STRESSES ASPECT RATIO (LENGTH / HEIGHT) Plane C, stope end or abutment: i) The analysis of induced stress i n an i s o l a t e d abutment wall i s s i m i l a r to the analysis i n the back, but rotated 90". This means that the stope aspect r a t i o used i s L/H again, and the K r a t i o i s a 1 / a 2 for the induced horizontal stress. This induced stress may have a large increase and can be estimated using figure 7.11. The e f f e c t of varying the stope width on the abutment wall induced stress i s sim i l a r to the e f f e c t of varying the width on the back stress (described above). i i ) The induced stress acting v e r t i c a l l y may show some increase, but i t w i l l not be as s i g n i f i c a n t as the increase i n the horizontal d i r e c t i o n . The influence of the induced v e r t i c a l stress can generally be overlooked i n the s t a b i l i t y analysis of longitudinal stope ends. A summary of the p o s s i b l e str e s s conditions acting t a n g e n t i a l l y at longitudinal stope boundaries i s found in figure 7.12. 7.3.2.3 Transverse open stoping parametric study The t y p i c a l geometrical shape of transverse open stopes i s a r e l a t i v e l y small stope length compared with stope width and height. According to the data base, the stope dimensions of 187 FIGURE 7 1 1 LONGITUDINAL OPEN STOPE STRESS ABUTMENT STRESSES 2.5 - i ASPECT RATIO (LENGTH / HEIGHT) FIGURE 7.12 S U M M A R Y O F T H E LONGITUDINAL PARAMETRIC STUDY CASE #1 CASE # 4 . S M figure 7.10 CASE #3. „ B figure 7.7 CASE #3, •ee figure 7.9 L P L A N E A CASE #4 >e figure 7.11 C A S E #1 — no s i g n i f i c a n t i n c r e a s e in t h e i n d u c e d s t r e s s , p r e - m i n i n g s t r e s s is a s s u m e d C A S E #2 — i n d u c e d s t r e s s d e c r e a s e s , low c o m p r e s s i o n is a s s u m e d C A S E #3 — i n d u c e d s t r e s s d e c r e a s e s s i g n i f i c a n t l y , s e e t h e r e f e r e n c e d f i gu re C A S E jfA - i n d u c e d s t r e s s i n c r e a s e s s i g n i f i c a n t l y , s e e t h e r e f e r e n c e d f i gu re 189 most transverse stopes are within the l i m i t s shown oh figure 7.13. A summary of the output for the most important three dimensional models used i n the transverse study can be found in Appendix 3. Since the openings may have a large influence on each other i n transverse mining, at least two stopes were used for the modelling. In figure 7.13, the four stope surfaces of i n t e r e s t have been labelled? plane A (abutment wall), plane B ( p i l l a r wall), plane C (back) and plane D (stope end). Plane A, abutment wall; i) The horizontal induced stress i n the abutment wall may have a s i g n i f i c a n t increase depending on the wall aspect r a t i o (W/H), and the K r a t i o of a 1/a 2 • It can be estimated using the curves shown i n figure 7.14. i i ) The v e r t i c a l induced stress usually shows a s l i g h t decrease but never reaches tension for a t y p i c a l transverse geometry. Stress i n t h i s d i r e c t i o n can be overlooked in the analysis. Plane B, p i l l a r wall; i) The horizontal induced stress i n the p i l l a r wall may show a major increase. The important stope aspect r a t i o i s W/H. Because a 2 i s shadowed by the openings, the stress r a t i o K has only a small influence on the induced stress. However, the opening length to p i l l a r length r a t i o (Lo/Lp) w i l l have a major influence on the concentration of horizontal 190 TRANSVERSE O P E N STOPE DIMENSIONS E X P R E S S E D IN TERMS OF STOPE L E N G T H (L) FIGURE 7.13 F I G U R E 7 . 1 4 TRANSVERSAL STOPE BOUNDARY STRESSES ABUTMENT / SIGMA1 DIRECTION S T O P E W I D T H / S T O P E H E I G H T stress. The curves shown i n figure 7.15 can be used to estimate the horizontal induced stress i n the p i l l a r wall. i i ) The v e r t i c a l induced stress may drop s i g n i f i c a n t l y according to the aspect r a t i o (W/H) but, for t y p i c a l t r a n s v e r s e stope geometries w i l l not reach tension. Consequently, i t does not have to be considered i n the analysis. Plane C, stope back, i) The induced stress acting across s t r i k e remained s i m i l a r to the pre-mining stress (oy) f ° r a H the transverse cases modelled. For the design analysis, v i r g i n stress (a-jj can be assume i n the back. i i ) The induced stress acting along the s t r i k e also stay s i m i l a r to the pre-mining stress magnitude (cr2) • Some inc r e a s e for stopes having a large width i s seen. Generally, the induced stress (a 2) i n t n e back w i l l not be greater than the stress i n the d i r e c t i o n , and can be ignored in the stress analysis. Plane D, stope end. i) The induced stress acting h o r i z o n t a l l y on the stope end may have s i g n i f i c a n t decrease. In the very extreme cases, when 01/02 i s greater than 2 or the length of the stope i s greater than the width (longitudinal geometry), tension i s 193 FIGURE 7 . 1 5 TRANSVERSE STOPE - BOUNDARY STRESSES PILLAR WALL / K = 2.0 2.0 -i — . 0.0 0.25 0.50 0.75 STOPE WIDTH / STOPE HEIGHT possible (see figure 7.16). However for most transverse cases, low compression can be assumed, and the horizontal induced s t r e s s can be disregarded i n the s t a b i l i t y analysis. i i ) In the v e r t i c a l d i r e c t i o n , the induced stress may also decrease, but w i l l stay into low compression. Generally, i t does not need to be considered i n the stress analysis. A summary of the p o s s i b l e s t r e s s conditions acting t a n g e n t i a l l y at transverse stope boundaries i s found in figure 7.17. 7.4 EFFECT OF JOINT ORIENTATION The r e l a t i v e orientation and dip of persistent j o i n t s with respect to each other and with respect to the excavation surfaces, w i l l determine the s t a b i l i t y of blocks and the p o t e n t i a l modes of rock mass f a i l u r e . Kinematic analysis using stereographic projection constitutes the most commonly used method for investigating the e f f e c t of j o i n t orientation. One of the basic assumptions of t h i s type of analysis i s that movement must occur according to e x i s t i n g d i s c o n t i n u i t i e s . Because i t does not account for new fractures created by stress or b l a s t i n g , kinematic analysis alone has been found unreliable in many open stoping s i t u a t i o n s . This was demonstrated by applying stereographic projection i n the back analysis of more 195 FIGURE 7 . i 6 TRANSVERSAL STOPE BOUNDARY STRESSES STOPE END / SIGMA2 DIRECTION 1.2 - i 1.1 -00 2.0 4.0 6.0 STOPE WIDTH / STOPE LENGTH FIGURE 7.17 SUMMARY OF THE T R A N S V E R S E P A R A M E T R I C S T U D Y H CASE #1 — no significant induced stress increase, pre—mining stress is assumed CASE #2 - induced stress decreases, low compression is assumed CASE #3 — significant induced stress decrease, see figure referenced CASE §4 - significant induced stress increase, see figure referenced 1 9 7 than 60 case h i s t o r i e s . The r e s u l t s showed that ten cases of predicted block f a i l u r e s occurred i n stopes that were stable. The s t a b i l i z i n g e f f e c t of a j o i n t clamping compressive stress can explain some of these cases. In addition, the success of non entry mining methods are often not affected by isolated block f a i l u r e when the size of the rock f a l l i s not excessive. Furthermore, nine cases of stopes that experienced caving were predicted stable by stereographic analysis. 7.4.1 The c r i t i c a l j o i n t factor A more general type of analysis that would account i n d i r e c t l y for the possible creation of new fractures, i s more suitable. In the c o l l e c t i o n and analysis of case h i s t o r i e s , i t was observed that most cases of s t r u c t u r a l l y c o n t r o l l e d f a i l u r e occurred along j o i n t s having a shallow angle with respect to the unstable s u r f a c e . The p r i n c i p a l reason for t h i s observation i s that the smaller the difference i n dip (6) between t h i s " c r i t i c a l " shallow j o i n t and excavation face, the greater the p r o b a b i l i t y of having the bridge "B" broken by b l a s t i n g , s t r e s s or other j o i n t s e t s ( f i g u r e 7.18). Furthermore, the component of stress shearing the block or acting p a r a l l e l to the c r i t i c a l j o i n t i s a function of the cosine of the c r i t i c a l j o i n t angle (0). This implies that the shear stress acting along the c r i t i c a l j o i n t increases as (8) diminishes while the normal stress (which has a s t a b i l i z i n g effect) also decreases. Consequently, the angle of the 198 199 c r i t i c a l j o i n t (9), or the shallowest difference i n dip between a persistent j o i n t set and the stope surface, o f f e r s a good in d i c a t i o n of the pr o b a b i l i t y of having s t r u c t u r a l f a i l u r e and i s a via b l e means of accounting for the e f f e c t of j o i n t o r i e n t a t i o n . An adjustment factor for the influence of the c r i t i c a l j o i n t i s shown on figure 7.19. The graph was empirically c a l i b r a t e d giving a adjustment of 0.2 for a small c r i t i c a l j o i n t angle (9), and no adjustment (ie. 1.0) for the influence of a c r i t i c a l j o i n t angle (9) of 90°. This gives a t o t a l influence of 5 on the s t a b i l i t y number. Best r e s u l t s were obtained with the model by setting the adjustment factor to 0.3 for the common case of a j o i n t dipping sub-parallel to stope face, angle (9 equals 0° to 10°). 7.4.2 E f f e c t of anisotropy Because the rock mass may be anisotropic, the r e l a t i v e o r i e n t a t i o n of the c r i t i c a l j o i n t w i l l also have a great e f f e c t on s t a b i l i t y . The c r i t i c a l j o i n t w i l l have a maximum ef f e c t when i t s s t r i k e i s p a r a l l e l to the stope surface. The e f f e c t w i l l diminish as the difference i n s t r i k e increases and w i l l be minimum i n the case of perpendicular c r i t i c a l j o i n t . This e f f e c t of anisotropy i s included i n the adjustment factor for j o i n t orientation by the dashed l i n e s i n figure 7.19, where the difference i n s t r i k e i s shown at increments of 15°. These curves were developed based on the true angle between the 200 FIGURE 7.19 Influence of Joint Orientation Difference In Strike 0.1 -1 1 1 1 r 1 i 1 r 10 20 30 40 50 60 70 80 90 Relative Difference in Dip Between the Critical Joint and Stope Surface 2 0 1 d i s c o n t i n u i t y and stope surface determined by stereographic proj ections. 7.4.3 Shear strength of the c r i t i c a l j o i n t Another important consideration regarding the c r i t i c a l j o i n t i s i t s associated shear strength. The simple shear "index" J r / J a proposed i n the Barton c l a s s i f i c a t i o n (described in table 5.2), has been selected for the model because i t r e l i e s on the observation of d i s c o n t i n u i t y c h a r a c t e r i s t i c s and i s quickly estimated on s i t e . In addition, i t s e f f e c t has already been weighted r e l a t i v e to the block s i z e parameter RQD/Jn. In theory, i t s e f f e c t on the s t a b i l i t y number ranges from 0.02 to 4. However according to the data base, i t s s e n s i t i v i t y for Canadian open stoping conditions i s generally l e s s . 7.5 THE GRAVITY FACTOR Gravity i s the d r i v i n g force acting on removable blocks. Its influence varies according to the p o t e n t i a l mode of f a i l u r e . In section 6.6, the modes of f a i l u r e related to open stope mining were i d e n t i f i e d as: gravity f a l l , slabbing, buckling, s l i d i n g and shearing. In the development of an adjustment factor for gravity, the shearing mode can be treated as a sub-case of s l i d i n g or gravity f a l l with the stress plays a major role in t r i g g e r i n g 202 i n s t a b i l i t y . S i m i l a r l y , buckling can be considered as a sub case of slabbing which reduces the problem to only three modes of f a i l u r e : gravity f a l l , slabbing and s l i d i n g . The potential mode of f a i l u r e can be determined with a simple diagram (described i n section 6.6) or by stereographic analysis. The e f f e c t of gravity, i n the case of gravity f a l l and .slabbing, i s mainly dependent on the i n c l i n a t i o n of the stope plane. For s l i d i n g , the e f f e c t of gravity i s a function of the s l i d i n g plane's ( c r i t i c a l j o i nt's) i n c l i n a t i o n . Consequently, two gravity adjustment factors are proposed. The f i r s t adjustment factor i s shown i n figure 7.20 and i s used for the gravity f a l l and slabbing modes of f a i l u r e . The adjustment according to the stope surface i n c l i n a t i o n has a maximum value of 8.0 for v e r t i c a l walls and a minimum value of 2.0 for horizontal backs (where gravity has the largest e f f e c t ) . The second adjustment factor i s used i n s l i d i n g mode of f a i l u r e and i s shown on figure 7.21. The adjustment has a maximum value of 8.0 when the c r i t i c a l j o i n t i n c l i n a t i o n i s less than 30°. This assumes that the f r i c t i o n angle of the c r i t i c a l j o i n t exceeds the d r i v i n g force. The adjustment w i l l decrease to a minimum of 2.0 as the c r i t i c a l j o i n t i n c l i n a t i o n increases. 7 . 6 EFFECT OF STOPE SIZE AND SHAPE As employed by Laubscher (1976) and Mathews et a l . (1980), 203 > I • I 1 I 10 20 30 40 50 60 70 80 90 Inclination of Stope Plane FIGURE 7 .20 Influence of gravi ty for slabbing and g r a v i t y f a l l modes of f a i l u r e . 8 o 7 -6 -5 -I? % =6 4 < 3 o 1 -10 20 30 40 50 60 70 80 90 Inclination of Critical Joint FIGURE 7 .21 Influence of gravi ty for s l i d i n g mode of f a i l u r e . 204 the hydraulic radius of in d i v i d u a l stope surface appears to be an adequate parameter to account for the e f f e c t of size and shape of the plane under analysis. I t i s calculated by the quotient of the stope plane area and stope plane perimeter. Hydraulic radius favors a long and narrow shape over square shape, allows the analysis of stope surface plane by plane, and i s easy to assess. 7.7 CALCULATION OF THE MODIFIED STABILITY NUMBER AND PRESENTATION OF THE MODIFIED STABILITY GRAPH The c a l c u l a t i o n of the modified s t a b i l i t y number i s done by multiplying the e f f e c t s of the following four factors: block s i z e , stress, j o i n t orientation and gravity. The estimation of each parameter composing the factors has been explained in sections 7.2 to 7.5 and i s shown i n page 207. The range of values t y p i c a l l y seen for each parameter i s given, and the figures required to estimate each parameter are referenced. The application of the design method i n back-analyzing the case h i s t o r i e s c o l l e c t e d i n t h i s study, has led to an improved re l a t i o n s h i p between the modified s t a b i l i t y number and the hydraulic radius. This r e l a t i o n s h i p i s shown on the modified s t a b i l i t y graph (figure 7.22). The c a l i b r a t i o n of the design method and the modified s t a b i l i t y graph w i l l be discussed in chapter 8. 205 FIGURE 7.22 Modified Stabili ty Graph 1000 100 o E ZJ o CO <D 10 =^ 1.0 O 0.1 0 . . . . K i I i n ' ! /»»:*: ::<:°:¥: .^: :: ::V:;:V: ;: :: ::-TJ> 5 10 15 20 Hyd rau l i c R a d i u s ( m ) 25 206 N* = (0.2-720) REFERENCE Block Size RQD/Jn 1-90 Table 5.2 Effect of Stress Effect of Joint Orientation Comp. (0.1-1) Fig 7.4 Relax. Critical Jt. Angle 9 (1.0) (0.2-1) Effect of Gravity Shear Jr/Ja Slabbing (0.05-3) Fig 7.19 Table 5.2 (2-8) Fig 7.20 Sliding (2-8) Fig 7.21 7.8 SUMMARY A geomechanical model for open stope design i s proposed i n t h i s chapter. The methodology adopted i n the model i s based on the modification of e x i s t i n g rock mass c l a s s i f i c a t i o n systems to s p e c i f i c mining conditions, and was i n s p i r e d by preceding models proposed by Barton et a l . (1974), Bieniawski (1973), Laubscher (1976) and Mathews et a l . (1980). The model i s based on the estimation of f i v e key fac t o r s r e l a t e d to the geotechnical conditions and the geometry of open stopes. As shown below, each factor i s composed of parameters easy to estimate on a mine s i t e . 1. Block s i z e f a c t o r : (RQD/Jn) - RQD measures the degree of f r a c t u r i n g i n the rock mass and can be estimated from core logging but preferably from d i r e c t underground mapping using Hudson & P r i e s t or Palmstrom techniques. - Jn i s also estimated from underground mapping and account for the number of j o i n t sets present i n the rock mass. 2. E f f e c t of s t r e s s : (a c/aj_) 207 a c i s usually obtain by laboratory t e s t i n g of d r i l l core. When t h i s i s not possible oc can be roughly estimated using a Schmidt hammer or the point load t e s t . o± i s best estimated by numerical modelling. In section 7.3.2, a series of curves has been constructed from a parametric study based on two and three dimensional numerical modelling, can be read on the curves for common longitudinal and transverse open stoping layouts and a range of pre-mining stress r a t i o s . The adjustment rating for stress can be read from figure 7.4. E f f e c t of j o i n t orientation: The c r i t i c a l j o i n t i s represented by the j o i n t set having the smallest difference i n dip and s t r i k e with the stope surface. The two design parameters required are the difference i n dip and the difference i n s t r i k e between the c r i t i c a l j o i n t and the designed stope surface. The rating for the c r i t i c a l j o i n t i s assessed from figure 7.19. The shear strength of the c r i t i c a l j o i n t i s estimated by the r a t i o of Jr / J a . J r quantifies the roughness of the j o i n t while the Ja represents the degree of a l t e r a t i o n of the j o i n t surface. E f f e c t of gravity In a gravity f a l l or slabbing s i t u a t i o n , the e f f e c t of 208 gravity i s estimated from the i n c l i n a t i o n of the design surface, using figure 7.20. - The e f f e c t of gravity i n a s l i d i n g s i t u a t i o n i s a function of the dip of the j o i n t along which the movement w i l l occur. The rating i s read from figure 7.21. 5. Stope si z e and shape - The hydraulic radius represents the e f f e c t of stope size and shape and i s calculated by the r a t i o of the perimeter/area of the stope surface under analysis. The geotechnical parameters are l a r g e l y based on observational techniques that can be learned quickly, but require a certain amount of pra c t i c e . The input data for the a p p l i c a t i o n of the model can then be c o l l e c t e d at low cost. 209 CHAPTER 8 DATA BASE AND MODEL CALIBRATION 8.1 INTRODUCTION Much importance was given to the construction of a complete data base because of the empirical nature of t h i s study. The majority of the f i e l d work was undertaken during the summers of 198 6 and 1987 by the author assisted by Marty Hudyma, MASc student. More than forty mining operations were v i s i t e d , and data from t h i r t y - f o u r mines using open stoping methods was c o l l e c t e d to form the data base. A p r i n c i p a l objective of the mine v i s i t s was to back analyze case h i s t o r i e s of open stope's s t a b i l i t y and i n s t a b i l i t y . The t o t a l data base now comprises 175 cases of unsupported stopes and 67 cases of cable bolted stopes. The analysis of case h i s t o r i e s has helped to understand f a i l u r e mechanisms found i n open stope mining and formed the basis for the c a l i b r a t i o n of the design method. The c a l i b r a t i o n procedure used the components of a widely accepted rock engineering design methodology (after Brown, 1987). The flowchart concept has been adapted for the empirical development of the design method as shown below: 210 SITE CHARACTERIZATION De f i n i t i o n of geomechanical properties of the host rock mass GEOTECHNICAL MODEL FORMULATION Conceptualization of s i t e characterization data DESIGN ANALYSIS Selection and application of mathematical and computational schemes for study of t r i a l design ROCK MASS PERFORMANCE MONITORING Measurement of the performance of the host rock mass during and a f t e r excavation RETROSPECTIVE ANALYSIS Quantification of i n s i t u rock mass properties and i d e n t i f i c a t i o n of dominant modes of rock mass response (after Brown, 1987) The s i t e characterization (using the geotechnical parameters defined i n chapter 7) for each case hi s t o r y has been performed in the f i e l d with the assistance of mine s t a f f s . The formulation of the geotechnical model consists of grouping the parameters into factors representing the p o t e n t i a l sources of open stope i n s t a b i l i t y (also described i n chapter 7 and figure 7.1). The Mathews empirical method was selected as the most suitable design analysis approach and served as a guideline for the model c a l i b r a t i o n . The rock mass performance for each stope surface was c l a s s i f i e d as stable, unstable or caved. This i s i n accordance with the sub-objective of developing a method that predicts the o v e r a l l s t a b i l i t y of openings (ref. section 1.3). The retrospective analysis investigated the e f f e c t of each factor on the accuracy of the prediction of stope s t a b i l i t y . As a r e s u l t , new parameters have been created, other parameters have been re-calibrated, and modifications to the s t a b i l i t y number and s t a b i l i t y graph have been proposed. 8.2 DATA COLLECTION The c o l l e c t i o n of data had to be done during short mine v i s i t s at the convenience of mine operators. The f i r s t task was to understand the mine history and layouts, the mining practices and the extraction sequence. Areas of the mine were subsequently selected for in-depth study and case h i s t o r i e s were investigated. The use of equipment was reduced to the minimum: a high power spot l i g h t , a Brunton compass and a geological hammer. Direct underground observational methods 212 such as rock mass c l a s s i f i c a t i o n and geological mapping were used to characterize the rock mass. The parameters measured by more sophisticated equipment (pre-mining stress and uniaxial compressive strength) were provided by the mines from exi s t i n g in-house or consultant studies. 8 .3 DATA BASE The t o t a l data base i s comprised of 175 case h i s t o r i e s from Canadian open stope mining operations. The information in the data base includes: the rock mass characterization, the stress condition and physical conditions associated with the case h i s t o r i e s . On some occasions, i t was not possible to estimate a l l the parameters with confidence due to the lack of access for s i t e characterization, or the lack of background information (no stress measurements for instance). For t h i s reason, the t o t a l data base has been divided into a main data base containing the accurate data, and a complementary data base containing information that i s less accurate. Data from l i t e r a t u r e has also been included i n the complementary data base. The geomechanical model described i n chapter 7, w i l l be c a l i b r a t e d with the main data base and confirmed using the complementary data base. Each data base i s presented on two tables: one providing the background information for the c a l c u l a t i o n of the geotechnical parameters, and the second containing the parameter rating and the modified s t a b i l i t y 213 number for each case history. The four factors involved in the c a l c u l a t i o n of the modified s t a b i l i t y number (block size, stress, c r i t i c a l j o i n t and gravity) are shown as headings on a l l the tables, i n order to f a c i l i t a t e the i d e n t i f i c a t i o n of t h e i r relevant parameters and background information. 8.3.1 Description of the main data base The main data base includes 84 case h i s t o r i e s . Table 8.1 shows the background information for the main data base. The f i r s t three columns i d e n t i f y the case h i s t o r i e s by a mine number (at the request of many operations, mine names have been kept anonymous) , a case number and the stope surface investigated. Column 4 i s the block si z e factor (RQD/Jn). The stress condition i s given i n column 5 for compression and column 6 for relaxation. This i s determined using the induced stress graph (figures 7.7 to 7.17) and confirmed where p o s s i b l e with underground v i s u a l observations of stress e f f e c t s . Four types of background data are required for the characterization of the e f f e c t of j o i n t orientation. Column 7 shows the difference i n dip between the c r i t i c a l j o i n t and the designed stope surface and column 8 i s the r e l a t i v e difference in s t r i k e . Column 9 gives an i n d i c a t i o n of the anisotropy of the rock mass (blocky rock tends to be i s o t r o p i c while f o l i a t e d rock tends to be anisotropic). The shear strength of the c r i t i c a l j o i n t , represented by Jr/Ja, i s found i n column 10. The e f f e c t of gravity can be assessed from the dip of the TABLE 8.1 Background i n f o r m a t i o n f o r t h e main d a t a base. JOINT ORIENTATION FACTOR [ EFFECT OF GRAVITY ! ! SIZE ! ; BLOCK ; | STRESS ! ! AND ! ; SIZE i ! FACTOR J J CRITICAL BLOCK i SHEAR ; SLIDING ! FREEFALL/ | ! SHAPE ; j FACTOR I JOINT SHAPE ! STREN. ! ! BUCKLING ! 1 FACTOR 1 JHINE CASK PLANE ! ! RQD ; ! COMP RELAX j J DIP ! STRK BLOCKY/ ! J f ! CRITICAL ; STOPE ! ! HYD. { i ASSESS. TYPE OF FAIL : » 1 ! / J n 1 ! DIFF J DIFF FOLIATED ! / J a ! JNT DIP | PLANE DIP i 1 RADIUS ! BEHAVIOUR MODE 1 ( 1 ) ( 2 ) ( 3 ) ', ! (*) : ', <5) ( 6 ) ', : o ) ', ( 8 ) ( 9 ) ! ( 1 0 ) i ( t i ) : ( 1 2 ) ) ! (13) : ! (14) (15) (16) ! i 1 HW ; ! i 8 ; ! COMP ! 45 ! 35 BLOCKY ; 3 . 0 ! 45 ; 90 ', 1 5 . 0 ; ; STABLE DISC. BLOCK ! ] 2 WALL ; ! 6 ! ; COMP ! 5 ! 0 BLOCKY ; 1.0 ! 85 ; 90 ; .' 8 . 9 ; 1 UNSTABLE JOINTED RM 3a j 3 3 WALL ! ! 6 ! | COMP J 5 : 0 BLOCKY ! 1.0 ; 85 ; 90 ! ! 7 7 ! J CAVE JOINTED RM 3a ! 4 4 HW ; ! 7 ! RELAX ! ! 15 : 0 FOLIATED ! 1-5 ! 30 ; 45 ; ! 7 - i ! ; UNSTABLE JOINTED RM 3d ! 5 5 HW ; ! *o ! RELAX ! ! 0 ! 90 BLOCKY ; 1.0 ! 90 ! 90 ; ! 14 .0 ; 1 STABLE DISC. BLOCK ! 5 6 HW ; ! 40 ; RELAX ! ! 0 ; 90 BLOCKY ; 1.0 1 90 ; 90 | 1 i i - o ! I STABLE DISC. BLOCK : 5 7 HW ; ! 40 ; ! COMP ! 15 J 90 BLOCKY ! 1 0 ! 90 ; 7 5 ! ! 5 . 2 I I STABLE DISC. BLOCK ! 6 8 HW ; ! 6 ! RELAX i ! 30 ! 30 BLOCKY ! 1-5 : 60 1 90 ; ; 8 . 5 ! | STABLE JOINTED RM ! 6 10 END ; ; 4 ; [ COMP ! 15 ! 0 FOLIATED ; 0 . 8 ?5 ! 90 ; ! 4 . 7 ! ; UNSTABLE JOINTED RM 3c ! 7 12 HW ; ! 7 ! RELAX ! ! 0 ! 0 BLOCKY ! 0 . 6 ! 7 5 ! 7 5 ! ! 9 .1 ; ; UNSTABLE JOINTED RH 3b '. 8 13 HW ; ! i s ', RELAX ; ! 0 ! 0 BLOCKY 1 2 . 0 i so ; so ; ! 8 . 3 ! 1 STABLE DISC. BLOCK ! 9 16 BACK ; ! 25 ! ! COMP I 70 ! 0 BLOCKY ; 0 .25 ! 7 0 ! 0 ! ! 5 . 8 ; ! CAVE DISC. BLOCK 2a ! 9 17 BACK ! 1 25 ! ! COMP ! 7<> ! 0 BLOCKY ! 0 .25 ; 70 ; 0 : i 4 . 2 : 1 STABLE DISC. BLOCK ! i i 18 HW ! ! 30 i RELAX ! ! 50 ! 0 BLOCKY ; 1.0 ! 40 ; 90 ; ; 8 . 8 ; ; STABLE DISC. BLOCK ! i i 19 BACK ; 1 30 | ! COMP ! 40 ! 0 BLOCKY ; 1.0 ! 40 ; 0 ! ! 3.5 ; J UNSTABLE DISC. BLOCK l a ! 12 20 BACK ; ! u ! i COMP ! 20 ! 0 BLOCKY ! 1-5 ! 20 ; 0 ! ! 1.8 ; ! STABLE DISC. BLOCK i 12 21 HW ! ! i i : RELAX ! ! 10 ! 0 BLOCKY ! 1-5 ! 65 ! 55 1 ! 4 .7 ! 1 STABLE DISC. BLOCK I 12 22 HW ; ! H I RELAX 1 ! 10 1 0 BLOCKY ! 1-5 65 ; 55 ', ; s.s : ', STABLE JOINTED RM | 12 23 BACK ; 1 i i ! | COMP ! 20 ! 0 BLOCKY ! 1-5 ! 20 | 0 ! ! 2 .1 ; I STABLE DISC. BLOCK ! 13 24 BACK ; ! 1 7 ! J COMP ! 30 ! 0 BLOCKY 1 2 . 0 ! 30 | 0 ! ! 10 .5 i ; CAVE DISC. BLOCK 2a 1 13 25 BACK ; ! 1 7 ! i COMP ; 30 ! 0 BLOCKY | 2 . 0 ! 30 ; 0 ; ! i i - 3 ! ; CAVE DISC. BLOCK 2a ! n 26 BACK ; 1 1 7 i ! COMP ; 30 ! 0 BLOCKY ! 2 . 0 ; 30 ; 0 ; ! 12.2 ! ; CAVE JOINTED RM 2a ! 13 27 BACK ; 1 7 ! ', COMP ! 30 ! 0 BLOCKY I 2 . 0 ', 30 ; 0 ; ; 4 . 1 1 1 STABLE DISC. BLOCK ! 13 28 WALL ; ! 8 ; RELAX ! ! 0 1 10 BLOCKY 1 1.5 ! 90 i 90 : ! 7 - 6 ; ; STABLE JOINTED RM ! 13 29 WALL ; ! 1 7 ! RELAX ; ! 10 ! 10 BLOCKY ! 2 . 0 ! BO ! ' 90 : j 7 .6 ! 1 STABLE DISC. BLOCK ! 13 30 HW ! 1 1 7 ! RELAX J ! 20 ! 10 BLOCKY ! 2 . 0 1 so ; 60 ; ! 9 . 0 ; 1 STABLE DISC. BLOCK ! 1* 31 HW ; ! 90 ! RELAX i ! 90 ! N/A BLOCKY ! 1.0 ! N/A ; 90 ; ! 16 .6 ; ! STABLE DISC. BLOCK I 14 32 BACK i ! 90 ; 1 COMP 1 90 ! N/A BLOCKY ! 1.0 ! N/A | 0 i ! 4 . 0 ! i STABLE INTACT ROCK ! 1* 33 HW ; ! 90 ; RELAX i ! 90 ! N/A BLOCKY ; 1.0 ! N/A I 90 ; | 23.0 ! ! STABLE DISC. BLOCK ! 14 34 BACK ! ! 90 ; ; COMP 1 90 I N/A BLOCKY ! 1.0 ; N/A 1 0 '. ; 10.7 J ', STABLE DISC. BLOCK ! 15 35 BACK ; ! 6 ! ! COMP ! 0 ! 0 BLOCKY ! 1-5 ! 20 ! 20 1 ! 10 .5 | J • CAVE JOINTED RM 3a ! i s 36 HW ; ! 6 ! ! COMP J 20 ! 25 BLOCKY ; 1.5 i 80 ; 60 -| ! 9 . 0 ; ! STABLE JOINTED RM ; 19 53 BACK ; ! 29 ; ! COMP ! 10 ! 0 BLOCKY ! 1.5 ; 10 i 0 ! ! 2 .4 ; I STABLE INTACT ROCK ! 19 54 BACK ; ! 29 J ! COMP ! 10 ! 0 BLOCKY ! 1.5 ! 10 ! 0 ! ! 6 . 8 ! J CAVE DISC. BLOCK 2a ; 19 55 BACK 1 ! 29 | 1 COMP ; 10 ! 0 BLOCKY 1 1.5 ' ! 10 ! 0 i ! 8 . 0 ; 1 CAVE DISC. BLOCK 2a ! 19 56 WALL J ! 4 ! RELAX 1 ! 0 ! 0 FOLIATED J 0 . 5 ! 90 J 90 ! ! 19 .0 : J CAVE JOINTED RM 3d ! i ' 57 BACK ; ! 29 ; ! COMP : 10 ! 0 BLOCKY ! 1-5 ' ! 10 ! 0 ; ! 3 .7 1 STABLE DISC. BLOCK ! 19 58 i WALL ; J 29 ; ; COMP ; so ! 90 BLOCKY ! 1-5 ! 8 ; 90 ; : 8 . 4 i ! STABLE DISC. BLOCK I 19 59 WALL ! ! 4 j ! COMP : 0 ! 0 FOLIATED ! 0 . 5 ! 90 ! 90 ! ! 4 . 5 ! ! STABLE JOINTED RM ; 20 61 ; HW | ! 1 7 ! ; COMP ! 0 ! 0 FOLIATED I 1.5 I 70 ; 70 1 ! 7 - 5 ! 1 STABLE DISC. BLOCK ! 20 62 ! FW ; ! 1 7 ! ! COMP ! 0 ! 0 FOLIATED ! 1-5 ! 7 o ! 70 ! ! 7 - 5 ! ! STABLE DISC. BLOCK t 1 t " I t t 1 1 1 1 1 I I 1 1 1 , 1 1 1 1 TABLE 8.1 Background i n f o r m a t i o n f o r t h e main d a t a base ( c o n t ) . NE CASE I PLANE BLOCK SIZE FACTOR RQD / J n STRESS FACTOR COMP RELAX JOINT ORIENTATION FACTOR CRITICAL JOINT DIP DIFF STRK DIFF BLOCK SHAPE BLOCKY/ FOLIATED SHEAR STREN. / J a (1) (2) (3) ! (4) ! (5) [ (6) | | (7) j (8) (9) | (10) J (11) I (12) | 1 (13) 1 (14) (15) (16) 22 132 ! HW ! 6 ; ; RELAX | i 10 ! 20 FOLIATED i 1.0 | 80 j 90 | i 5.6 I STABLE JOINTED RH 22 133 HW ! 6 ! COMP ! ! 1 io i 20 FOLIATED | 1 .0 ! 80 | 90 I 1 6.7 | STABLE JOINTED RM | 22 134 BACK ! 5 i COMP j !! 30 I 0 BLOCKY J 1 0 l 30 • 0 1 1 1-9 | STABLE DISC. BLOCK | 22 135 BACK ! 13 ; COHP j 1 1 50 | 0 BLOCKY | 2.0 ; 50 | 0 1 ! '2 1 | STABLE DISC. BLOCK | 22 136 BACK ! 13 ! COMP ! !! 50 | 0 BLOCKY | 2.0 | 50 1 0 ', 1 2.4 | STABLE DISC. BLOCK | 22 137 BACK ; 13 ! COMP ! II 50 | 0 BLOCKY | 2.0 1 50 | 0 ! I 2.9 | STABLE DISC. BLOCK 1 22 138 BACK {; 13 I COMP ! 1! 50 | 0 BLOCKY i 2.0 | J 50 ! 0 1 ! 3.1 I STABLE DISC. BLOCK ! 22 139 BACK i 13 ! COMP ! 1 i 50 | 0 BLOCKY j 2.0 1 50 | 0 1 | 3.0 I STABLE DISC. BLOCK | 22 140 HW ;! 8 ; COMP ; II o | 0 FOLIATED ! 1.0 I 70 | 70 I I 7-5 | STABLE JOINTED RM | 22 141 HW ',; 8 i COHP ; i i o | 0 FOLIATED 1 1.0 ; 70 1 70 1 ! 8.1 | UNSTABLE JOINTED RH | 3c 22 142 HW ;; 8 ! COMP ! II 4 | 0 FOLIATED J 1.0 | 70 1 66 | 1 5.3 | STABLE DISC. BLOCK | 22 143 HW !! 8 | COMP ! !! 7 | 0 FOLIATED 1 1 0 | 70 | 63 1 | 5 .7 | STABLE JOINTED RM ] 22 144 BACK ;; 8 ! COMP ! !! io | 0 BLOCKY | 1.0 1! 10 | 0 1 | 1.9 I STABLE DISC. BLOCK { 22 145 BACK' !l 8 ! COMP ! II io I 0 BLOCKY | l . o | ! io ; 0 1 | 1.8 | STABLE DISC. BLOCK | 22 146 BACK ;; 8 ! COHP I !! io 1 0 BLOCKY | 1.0 I 10 | 0 1 | 2.1 1 UNSTABLE DISC. BLOCK I 2a 22 147 BACK ;! 8 ! COMP ! II io 1 0 BLOCKY | 1.0 | i 10 | 0 I 1 2-3 | UNSTABLE DISC. BLOCK 1 2a 23 148 BACK !! 11 ', COHP ! II o ) 0 BLOCKY 1 2.0 l ! 0 1 0 1 1 5.0 1 STABLE DISC. BLOCK 23 149 HW ;| 5 ! ! RELAX ;! o ! 0 FOLIATED 1 0.1 | | 70 | 70 | 1 9.0 1 CAVE JOINTED RH 3d 23 150 HW ; i 5 ; COMP ; II o | 0 FOLIATED | o . i I! 70 | 70 | 1 11.3 1 CAVE JOINTED RM 3c 27 151 BACK ;; 15 ; COMP ; II io I 0 BLOCKY 1 2.0 ! | 10 ; 0 I 1 10.0 1 CAVE DISC. BLOCK 2a 27 152 BACK ;; 15 1 COMP ; II io | 0 BLOCKY | 2.0 | 1 10 | 0 1 | 6.7 I STABLE DISC. BLOCK 27 153 WALL !] 15 ; ; RELAX ]; o ; 45 BLOCKY 1 2.0 | | 90 | 90 | 1 18.0 | STABLE JOINTED RM 28 155 HW. |; 16 ; ! RELAX I; 10 ! 15 BLOCKY 1 2.0 1 | 80 1 90 1 | 9.7 ] STABLE DISC. BLOCK 28 , 156 END ;! 16 1 COHP ; !! io 1 75 BLOCKY 1 2.0 11 80 1 90 | 1 5.6 1 STABLE DISC. BLOCK 28 157 FW ! 9 ; COHP ; II io I 25 BLOCKY 1 1.8 | | 80 | 90 | 1 8.4 | STABLE JOINTED RH 28 158 BACK ]! 10 1 COMP i 11 20 ; 0 BLOCKY 1 2.5 | | 20 | 0 1 | 3.4 1 STABLE DISC. BLOCK 28 159 BACK ;, 8 ! COHP ; II o | 0 BLOCKY | 2.0 | | 0 1 0 1 1 7.6 | CAVE JOINTED RM 3a 29 161 WALL i ; 3 1 COHP ! II 20 1 0 FOLIATED 1 1.0 1 j 70 | 90 | 1 20.0 | CAVE JOINTED RH 3c 30 164 BACK |1 14 1 COHP ! 11 60 1 0 BLOCKY | 1.5 | 60 1 0 1 ! 8.6 I CAVE DISC. BLOCK 2a 30 165 HW I i 14 ! ! RELAX !| 0 I 0 BLOCKY | 1.5 11 90 | 90 J | 9.9 1 STABLE JOINTED RH 30 166 FW | j 9 I J RELAX U 10 1 0 FOLIATED 1 1-5 11 80 1 90 1 1 9.9 1 UNSTABLE JOINTED RM 3d 31 170 BACK ;; 18 | COHP I i ! 35 J 60 BLOCKY I 1.5 II 65 1 30 I | 12.5 | CAVE JOINTED RM 3a 31 171 BACK ;; 18 I COMP 1 II 35 | 60 BLOCKY | 1.5 Jl 65 1 30 ', 1 15.0 1 CAVE JOINTED RM 3a 31 172 BACK !! 18 I COMP I II 35 | 60 BLOCKY | 1.5 !| 65 1 30 | I 15.9 | CAVE JOINTED RM 3a 31 173 BACK I ; 18 | COMP | 1 ! 35 | 60 BLOCKY 1 1 5 | 65 ! 30 1 ! 7-7 I STABLE DISC. BLOCK 31 174 BACK !] 18 1 COHP 1 11 35 | 60 BLOCKY | 1.5 i ; 65 | 30 | I 5.4 | STABLE DISC. BLOCK 31 175 WALL 1! 18 I COHP ; 1 1 20 | 25 BLOCKY 1 1-5 | 70 I 90 1 1 11.6 | UNSTABLE DISC. BLOCK 2a 31 176 BACK ; 18 1 COMP 1 !'. *5 | 60 BLOCKY J 1.5 1J 65 | 20 J 1 7.3 I STABLE DISC. BLOCK 31 177 BACK ! 18 | COHP | 1 ! *5 | 60 BLOCKY | 1.5 | 65 1 20 1 | 9.9 | STABLE DISC. BLOCK | 31 178 BACK ; 18 I COHP j 1 1 *5 | 60 BLOCKY 1 1.5 11 65 1 20 1 1 l t . l 1 UNSTABLE DISC. BLOCK | 2a 32 1 180 ; HW ; 6 | COMP | 1 ! 0 | 0 FOLIATED I .1-0 l 70 | 70 | | 6.9 1 UNSTABLE JOINTED RH | 3c 32 183 ; WALL ; 16 ! COMP | II 0 | 0 BLOCKY 1 1-5 J 90 | 90 1 | 4.9 | STABLE DISC. BLOCK | 32 ; 184 1 HW ;1 6 ', COHP ; 11 0 | 0 FOLIATED 1 1.0 J 80 | 80 1 | 6.7 J STABLE JOINTED RH | EFFECT OF GRAVITY SLIDING CRITICAL JNT DIP FREEFALL/ BUCKLING STOPE PLANE DIP SIZE AND SHAPE FACTOR HYD. RADIUS ASSESS. TYPE OF BEHAVIOUR c r i t i c a l j o i n t (column 11) i n the case of a s l i d i n g mode of f a i l u r e and by the i n c l i n a t i o n of the designed stope surface (column 12) for the other modes of f a i l u r e . Stope size and shape are accounted for by hydraulic radius, column 13. The assessment of the stope plane s t a b i l i t y i s given i n column 14. The mode of f a i l u r e can be determined using figure 6.18 and columns 4 to 12. The second table (8.2) contains the calculated input parameters necessary for the design analysis. It i s based on the background information previously described (table 8.1). Columns 2, 4, 10, 13 and 14 have been kept i d e n t i c a l to table 8.1. Column 17 i s the induced stress factor calculated from figure 7.4. The magnitude of induced stress (ay) can be estimated from figures 7.7 to 7.17 according to the mining d i r e c t i o n (longitudinal/ transverse), stope geometry and pre-mining stress f i e l d . The c r i t i c a l j o i n t factor can be read from figure 7.19. The difference in dip and s t r i k e of the c r i t i c a l j o i n t necessary to read figure 7.19 are found i n columns 7 and 8 of table 8.1. The c r i t i c a l j o i n t shear index (Jr/Ja) i s given i n column 10. Column 19 i s the s l i d i n g g ravity factor and i s evaluated using figure 7.21 and column 11 of table 8.1. Column 20 i s the gravity factor used for other modes of f a i l u r e and i s estimated with figure 7.20 and column 12 of the background information table (8.1). Hydraulic radius (c o l . 13) and stope assessment (co l . 14) are taken d i r e c t l y from table 8.1. F i n a l l y , the s t a b i l i t y number (col . 21) i s 217 TABLE 8.2 Input parameters from the main data base necessary f o r open stope design back-analysis. ; ILOCX S T R E S S J O I N T O R I E N T A T I O N ) : E F F E C T ; : sizz FACTOR FACTOR i OF c u v m C A S E j : IQD ; /Jn (REF. F I C . 7.4) C R I T I C A L J O I N T Jc / J « 1 S L I D I N C F R E E F A L L / 1 SLABBING ; HYD. ; RADIUS N A S S E S S . 1 (2) ' : <*> (17) ( 1 8 ) (10) : <i9) (20) ; : (i3> (21) (i*) : I ; : is 1.0 0.65 3.0 ; : 6.5 : s.o 228 S T A B L E 1 2 : 6 0.2 0.25 i.o : : 2.s ; 8.9 0.7 U N S T A B L E ; 3 ; 6 0.1 0.2 i.o : : 2.5 ! 7.7 0.3 C A V E ; 4 : 7 1.0 0.2 1.5 | 3.7 ! 1 7.1 7.8 U N S T A B L E 1 S ! ! 40 1.0 1.0 i.o ; a.o ; 1 14.0 320 S T A B L E ,' 6 \ 1 40 1.0 1.0 1.0 j 8.0 ! : u.o 320 S T A B L E 1 7 : 40 1.0 1.0 i.o : 6.5 1 ; 5.2 260 S T A B L E 1 8 i ! 6 1.0 0.4 1.5 : i 5.0 : s.s 18 S T A B L E 1 io ; | 4 0.3 0.2 o.i : J 3.5 : 4.7 0.7 U N S T A B L E | 12 ; ', 7 1.0 0.2 o.6 ; 6-5 i ! 9.1 5.5 U N S T A B L E | 13 ; is 1.0 0.2 2.0 ; 7.0 ! ! 8.3 42 S T A B L E 1 it i ! 25 0.1 0.15 0.25 ; 2.0 ! ! 5.8 1.1 C A V E ! 17 i i 25 0.1 0.85 0.25 ; 2.o ; : 4.2 1.1 S T A B L E t is : ! 30 1.0 0.6 i.o ; 8.0 ! : 8 . 8 144 S T A B L E ; 19 : ! 30 0.1 0.4 i.o : 2.0 : ! 3.5 2.4 U N S T A B L E | 20 ; I 1 1 1.0 0.2 1.5 ; 2.0 ! ! l-> 6.6 S T A B L E 1 ii ; i U 1.0 0.2 1.5 i 4-5 i ! 4.7 15 S T A B L E ', 22 ; ! ll 1.0 0.2 l.s : «.s ; : >.8 15 S T A B L E 1 23 1 ! 11 1.0 0.2 1.5 : 2.0 ; : 2.1 6.6 S T A B L E 1 24 ! ; ' t7 1.0 0.2 2.o ; 2.0 : : I O . S 14 C A V E ! 25 ; i 17 1.0 0.2 2.0 J 2.0 i ! 1 1 . 3 14 C A V E ; 26 ; I 17 1.0 0.2 2.0 ; 2.o ; i 12.2 14 C A V E ! 2? ! ! 17 1.0 0.2 2.0 1 2.0 ; ! 4 . 1 14 S T A B L E 1 28 : ! 8 1.0 0.3 i.s ; 2.o : ! 7.6 6.9 S T A B L E ! 25 : ! 17 1 .0 0.2 2.0 1 3.0 ! 7.6 20 S T A B L E ! 30 i ; 17 1.0 0.2 2.0 ; 5.0 i 1 9.0 34 S T A B L E ,' 3i : I 90 1.0 1.0 i.o ; >.o ; : i6.6 720 S T A B L E ! 32 ! : 90 0.1 1.0 i.o ; 2.0 J I 4.0 18 S T A B L E j 33 : : 90 1.0 1.0 i.o j i.o ; i 23.0 720 S T A B L E 1 3* ! ; 90 0.4 1.0 i.o : 2.0 ; : 10.7 72 S T A B L E 1 35 i | 6 0.6 0.3 1.5 : 2.3 ,' ! 10.5 3.9 C A V E : 36 : ; 6 0.9 0.3 i.s ; 5.0 ! : 9.o 13 S T A B L E 1 53 : ! 29 0.5 0.2 i.s ; 2.o : : 2.4 8.a S T A B L E 1 5* : i 29 0.5 0.2 i.s : 2.0 : ; 6.8 8.8 C A V E ! ss : J 29 0.5 0.2 i.s ; 2.0 ! ; a.o 8 . 8 C A V E 1 56 : ; 4 1.0 0.3 o.s ; a.o ; : i9.o 5.2 C A V E J 57 : ! 29 0.2 0.2 i.s ; 2.o ; 1 3.7 3.5 S T A B L E { 58 ; ! 29 1.0 1.0 1.5 : 8.o : : 8.4 352 S T A B L E 1 59 ; ; 4 1.0 0.3 o.s ; 8.0 ! ! 4.5 5.2 S T A B L E ! 6i ; ; 17 1.0 0.3 i.s : 6.o : i 7.5 45 S T A B L E J 62 . : ! 1' 1.0 0.3 1.5 i 4.0 ! : 7-s 30 S T A B L E [ 132 : ! 6 1.0 0.2 i.o ; a.o : ! 5.6 10 S T A B L E 1 133 ; ! 6 1.0 0.2 i.o : a.o ; 1 6.7 9.4 S T A B L E ! 134 ; ; 5 0.1 0.2 i.o : 2.0 ', ', 1.9 0.2 S T A B L E J 135 ! ; 13 0.6 0.6 2.0 ; 2.o : 1 2.1 19 S T A B L E 1 136 : ; 13 0.5 0.6 2.0 : 2.o : ! 2.4 16 S T A B L E | 137 ; ! 13 0.4 0.6 2.0 : 2.0 : 1 2.9 13 S T A B L E : 138 ; ; 13 0.4 0.6 2.0 ; 2.0 J 1 3.1 13 S T A B L E ; 139 : ; 13 0.3 0.6 2.0 : 2.0 | ! 3.0 10 S T A B L E 1 140 ; : 8 1.0 0.3 i.o ; 6.0 ; 1 7.5 15 S T A B L E ! 141 : ! 8 1.0 0.3 i.o ; 6.o ; : 8.1 15 U N S T A B L E ! 142 i : 8 1.0 0.2 i.o ; s.s ; : 5.3 9.2 S T A B L E : 143 : ! 8 1.0 0.2 i.o ; 5.5 i : 5.7 9.2 S T A B L E ; 144 ; ! 8 0.1 0.2 i.o ; 2.o ; | 1.9 0.3 S T A B L E ; 145 ; : 8 0.3 0.2 i.o : 2.0 ! ; i.s 1.0 S T A B L E ! 146 ; : s 0.1 0.2 i.o : 2.0 ; : 2.1 0.3 U N S T A B L E I 147 : : s 0.1 0.2 i.o : 2.0 : : 2.3 0.3 U N S T A B L E 1 148 ; ! 11 0.7 0.2 2.0 ; 2.0 ; : s.o 5.9 S T A B L E 1 149 ; ; s 1.0 0.2 o.i : 6.o ; | 9.0 0.8 C A V E ; 150 ; : s 1.0 0.2 0.1 | 6.o : ! 11.3 0.8 C A V E : 151 ; : 15 0.4 0.2 2 .0 ; 2.0 ; : I O . O 4.8 C A V E ! 152 ; ! 15 1.0 0.2 2.0 : 2.0 : : 6.7 12 S T A B L E ! 153 i ! 15 1.0 0 .5 2.0 : a.o ; ; u.o 120 S T A B L E 1 155 ! : i6 1.0 0.2 2.0 ; i 3.0 : 9.7 19 S T A B L E ; 156 ; ! 16 0.1 1.0 2.0 : : 3.0 : s.6 10 S T A B L E : 157 : ! 9 1.0 0.2 i.8 : 8.0 i : 8.4 26 S T A B L E 1 is8 ; : io 0.1 0.2 2.s : 2.0 ', 3.4 1.0 S T A B L E ', 159 ; ! 8 oa 0.2 2.0 : 2.o ; ; 7.6 0.6 C A V E 1 161 ; ; 3 1.0 0.2 i.o ; s.o : ; 20.0 4 . 8 C A V E : 164 ; : 14 0.1 0 .8 1.5 : 2.0 ! : 8.6 3.3 C A V E : 165 : : u 1.0 0.2 i.s : 8.o : : 9.9 31 S T A B L E ', 166 ; : 9 1.0 0.2 i.s ; i 3.0 : 9.9 8.3 U N S T A B L E I 170 ; ! 18 1.0 0 .8 1.5 ; 2-8 i ; i2.s 60 C A V E | 171 ; : is 1.0 0.8 i.s ; 2.8 ; 1 15.0 60 C A V E ! 172 ; : is 1.0 0 .8 i.s : 2.8 : : is.9 60 C A V E 1 173 ; ; is 1.0 0.8 1.5 ; 2.8 ; ! 7.7 60 S T A B L E 1 174 ; ! 18 1.0 0 .8 1.5 ; 2.8 ; i 5.4 60 S T A B L E ! i7s ; : i< 0.5 0.3 i.s : B . O ; : u.6 32 U N S T A B L E | 176 j ; i> 0 .5 0.85 1.5 ', 2.5 ', 7.3 29 S T A B L E i 177 i : is 0.5 0 .85 1.5 | 2.5 ; ! 9.9 29 S T A B L E ! 178 ; ! 18 0.5 0.85 I . S : 2-5 : : u.i 29 U N S T A B L E i 180 ; : 6 1.0 0.3 i.o ! 6.o : : 6.9 10 U N S T A B L E I 183 ; 16 0.1 0.3 1.5 ! s.o : : 4.9 5.8 S T A B L E I 184 ; ; 6 1.0 0.3 i.o ! 7.0 ; ! 6.7 12 S T A B L E 1 218 calculated by multiplying columns 4,17,18, 10 and (19 or 20). 8.3.2 Description of the complementary data base The complementary data base i s comprised of 91 case h i s t o r i e s . I t was b u i l t using the same p r i n c i p l e s (and parameters) as the main data base. The background information i s displayed on table 8.3 and the design parameters are shown on table 8.4. As mentioned before, i t i s composed of case h i s t o r i e s which have some degree of uncertainty i n the evaluation of one or more parameters, and data from l i t e r a t u r e . The data from l i t e r a t u r e originate from the PhD thesis of R. Pakalnis (1986). A t o t a l of 68 well documented case h i s t o r i e s of open stopes at the Ruttan operation i n northern Manitoba (mine 21 of the data base) have been selected from the Pakalnis study and form the majority of the complementary data base. 8.4 CALIBRATION OF THE FACTORS COMPOSING THE MODIFIED STABILITY NUMBER The c a l i b r a t i o n of the four factors composing the modified s t a b i l i t y number (block si z e , stress, j o i n t orientation and g r a v i t y ) was c a r r i e d out following the design approach described i n section 8.1. Because of the empirical nature of the c a l i b r a t i o n , the value of the ratings associated with the factors i s completely a r b i t r a r y . However, t h e i r r e l a t i v e weighting must be representative of the influence of the 219 TABLE 8 . 3 base. Background i n f o r m a t i o n f o r t h e complementary d a t a BLOCK J O I N T ORIENTATION FACTOR E F F E C T OF GRAVITY STRESS ; S I Z E ; ! FACTOR ! ! C R I T I C A L BLOCK SHEAR j S L I D I N G F R K E F A L L / ! i SHAPE 1 ; FACTOR ; ; ! J O I N T SHAPE S T R E N . i B U C K L I N G i i FACTOR ! | H I N E C A S E P L A N E ; ) RQD !! C0HP ! RELAX \ i D I P i STRK BLOCKY/ Jr 1 C R I T I C A L STOPE i ! H Y D . i ; A S S E S S . T Y P E OF F A I L t II ! /Jn ! ! J | | D I F F | D I F F FOLIATED /Ja | J N T D I P P L A N E D I P i i RADIUS ! BEHAVIOUR MODE (1) (2) (3) ! ! (4) i! (5) j (6) ; ! (7) i (8) (9) (10) i ( ID (12) ! ! (13) ! ! (14) (15) (16) 21 64 HW ; ! 4 ! | i RELAX ! ! o ! o FOLIATED 1.5 i '65 65 i i 6 . 0 ! ; S T A B L E J O I N T E D RM 21 65 HW ; ! 4 !; ; RELAX ; ! o i o FOLIATED 1.5 ! 6 5 65 1 i i 2 . o ; ! CAVE J O I N T E D RH 3d 21 66 HW ; ! 3 i; ; RELAX ; ! o i o FOLIATED 0.8 ! 82 82 ; 1 3.o ; ! S T A B L E J O I N T E D RM 21 67 HW ; ! 3 i! ; RELAX ; ! o ! o FOLIATED 0.8 ! 82 82 i 1 9.o ; 1 UNSTABLE JOINTED RM 3d 21 68 HW ; ! 3 ! | ! RELAX ; ! o i o FOLIATED 0.8 1 82 82 J ! 12.0 | J CAVE J O I N T E D RH 3d 21 69 HW ; 1 18 ! | ! RELAX ; ! o : o FOLIATED 3.0 1 55 55 ; ; i6 .o ; I UNSTABLE J O I N T E D RH 3d 21 70 HW ; ! 6 !! ; RELAX ; t o i 0 FOLIATED 0.8 ; 90 90 ; i 5.o ; 1 UNSTABLE J O I N T E D RH 3d 21 71 HW ; ! 6 ; ; ; RELAX ! 0 i o FOLIATED 0.8 ; 90 90 | i 8.o ; ; CAVE J O I N T E D RH 3d 21 72 HW | 1 i !! ; RELAX ; 0 ! o FOLIATED 0.25 1 25 25 ! ; i6 .o ; i CAVE J O I N T E D RH 3d 21 73 HW ; 1 16 ii ; RELAX ; ! 0 i o FOLIATED 3.0 ! 90 90 i i 7.0 ; J S T A B L E D I S C . BLOCK 21 74 HW ; ! 8 ;! ! RELAX ! 0 i o FOLIATED 1.5 i 55 55 i i 2.0 ; ; S T A B L E D I S C . BLOCK 21 75 HW ; ! 8 !; i RELAX ! 0 ! o FOLIATED 1.5 I 55 55 i ! n o ; ! S T A B L E J O I N T E D RM 21 76 HW I ! i s i i ! RELAX i 0 ! o FOLIATED 3.0 ; 60 60 i I 5.o ; ! S T A B L E D I S C . BLOCK 21 77 HW ; ! 3 11 ; RELAX ! 0 i o FOLIATED 0.25 ; 90 90 i ! 14.0 ; ! CAVE J O I N T E D RM 3d 21 78 HW ; 3 !! i RELAX ; 0 i o FOLIATED 0.25 ; so 80 ; i 6.0 ! ! CAVE J O I N T E D RM 3d 21 79 HW ] 3 ; ; ! RELAX ; 0 1 o FOLIATED 0.25 : so 80 i ; 10.0 ; | CAVE J O I N T E D RH 3d 21 80 HW ; i i i ! RELAX ; 0 o FOLIATED 0.25 : 25 '5 i ! n o ; ; CAVE J O I N T E D RH 3d 21 81 HW ; i is :; ; RELAX l 0 i ° FOLIATED 3.0 ; 60 60 ! ! 9.0 | J S T A B L E D I S C . BLOCK 21 82 HW ; ! 3 ;; i RELAX ; 0 i 0 FOLIATED 0.8 i 65 65 i i 6.0 ; ; UNSTABLE J O I N T E D RH 3d 21 83 HW ; ; l-s ;; ; RELAX ; 0 i o FOLIATED 1.5 i 62 62 ! i i3 .o ; ; CAVE J O I N T E D RH Id 21 84 HW ; i is : i i RELAX 1 0 1 o FOLIATED 3.0 i 55 55 i ; IO .O ; 1 S T A B L E D I S C . BLOCK 21 85 HW i ! ' 1 i ; RELAX ! 0 i o FOLIATED 3.0 1 65 65 ; i 4.0 ; 1 S T A B L E D I S C . BLOCK 21 86 HW ; i 20 :; 1 RELAX ; 0 i o FOLIATED 3.0 i 66 66 ; i i . o ; ! S T A B L E INTACT ROCK ! 21 87 FW i 1 20 ;; ; RELAX ] 0 i o FOLIATED 3.0 ! 66 66 ; i 12.0 | ; UNSTABLE D I S C . BLOCK 2d 1 21 88 HW | 1 20 ;; ; RELAX I 0 i o FOLIATED 0.8 I 90 90 : ! 4.0 ; I S T A B L E D I S C . BLOCK ! 21 89 HW | 1 20 ;; ; RELAX ; 0 i o FOLIATED 0.8 | 90 90 : i n . o i 1 S T A B L E D I S C . BLOCK ! 21 90 HW | 1 3 ; | ; RELAX ; 0 1 o FOLIATED 0.25 ! 52 52 i i 3.0 ; ; S T A B L E J O I N T E D RM ! 21 91 HW ] ! 3 ! | ! RELAX ; 0 ! o FOLIATED 0.25 i 52 52 i i n . o i J C A V E J O I N T E D RM 3d i 21 92 HW j ! 3 ;! ! RELAX ! 0 1 o FOLIATED 0.25 ! 65 65 ! 1 2.0 i ! S T A B L E D I S C . BLOCK ! 21 93 HW ; 3 i i | RELAX ] 0 ! o FOLIATED 0.25 i 65 65 : ! 7.0 ; ! C A V E J O I N T E D RM 3d 21 94 HW ; 3 1! i RELAX 1 0 i o FOLIATED 0.25 1 65 65 ! i 9.0 ! ! CAVE J O I N T E D RM 3d 21 95 HW ; 3 i i ; RELAX ; 0 i o FOLIATED 0.25 1 65 65 ! ! 16.0 i ! CAVE J O I N T E D RM 3d 21 96 HW ; i i ! ; RELAX ; 0 i o FOLIATED 0.25 i 28 78 J i 8.0 ; ! CAVE J O I N T E D RM 3d 21 97 HW ] • ii 1 RELAX ; 0 i o FOLIATED 0.25 i 90 90 ; i 3.0 J ! UNSTABLE J O I N T E D RM 3d 21 98 HW ; i 1! i RELAX ] 0 ! ° FOLIATED 0.25 ! 90 90 | i 5.0 ! ; C A V E J O I N T E D RH 3d 21 99 HW J 8 ; ; i RELAX ! 0 i o FOLIATED 2.0 i 65 65 i ! 3.o ; ! S T A B L E D I S C . BLOCK 21 100 HW | t 3 i; ; RELAX ; 0 i o FOLIATED 1.0 i 60 60 ; I 3.0 ! { S T A B L E J O I N T E D RM 21 101 HW ] 3 i! ; RELAX ; 0 i ° FOLIATED 1.0 i 60 60 i ! 6 .o ; { UNSTABLE J O I N T E D RM 3d 21 102 HW ; 3 i i i RELAX ! 0 i o FOLIATED 1.0 ; 60 60 ; ! i4 .o ; j C A V E J O I N T E D RM 3d 1 21 103 HW ; 1 6 i i ; RELAX ; 0 ! o FOLIATED 0.25 ! 6 3 63 J ! 3.o ! I S T A B L E D I S C . BLOCK ! 21 104 HW ; ! 6 | i ! RELAX ; 0 ! o FOLIATED 0.25 i 63 63 ; ! 8.o ; ! UNSTABLE J O I N T E D RM 3d 1 21 105 HW ; ! 6 ! 1 ! RELAX i 0 ! o FOLIATED 0.25 ! 63 63 ! ! n o ! ; C A V E J O I N T E D RM 3d I 21 106 HW ; ! 15 I i ! RELAX ! 0 i o FOLIATED 2.0 ! 20 70 ! ! io .o ; j S T A B L E D I S C . BLOCK ! 21 107 HW ; ! 2 . ! | ! RELAX ; 0 ! o FOLIATED 0.8 ! 80 80 ; ! 4.0 ; • CAVE J O I N T E D RM 3d ! 21 108 HW ; ! 2 11 1 RELAX i 0 i o FOLIATED 0.8 ! 80 80 ; ! io .o ! ; CAVE J O I N T E D RM 3d ! 21 109 HW ; ! 3 | ! i RELAX i 0 i o FOLIATED 1.0 ! 60 60 ; ! 6 . 0 I i UNSTABLE J O I N T E D RM 3d ! 21 n o HW | ! 3 ; ; i RELAX J 0 i o FOLIATED 1.0 ! 60 60 ; ! n .o ! ! CAVE J O I N T E D RM 3d S I Z E AND O TABLE 8.3 Background i n f o r m a t i o n f o r t h e complementary d a t a base ( c o n t ) . BLOCK S I Z E FACTOR STRESS FACTOR J O I N T ORIENTATION FACTOR C R I T I C A L J O I N T BLOCK SHAPE SHEAR S T R E N . | M I N E C A S E PLANE 1 ; RQD ! COMP RELAX ! ! D I P STRK BLOCKY/ Jr ! C R I T I C A L STOPE ; i HYD. ; ! A S S E S S . T Y P E OF F A I L n II ! /Jn ! | D I F F D I F F FOLIATED /Ja i J N T D I P P L A N E D I P ! ! RADIUS ' BEHAVIOUR MODE (O (2) (3) : ! («) ! (5) (6) ; ! (7) (8) (9) (10) 1 (11) (12) : ! (13) ! ! (14) (15) (16) 21 111 HW ; : 2 j RELAX ! ! o 0 F O L I A T E D 0.5 ! 72 72 ! ! 3.o ; ! S T A B L E J O I N T E D RM ! 21 112 HW j ! 2 j RELAX ; ! o 0 FOLIATED 0.5 ! 72 72 ! ! B . O ! ! UNSTABLE J O I N T E D RM 3d 21 113 HW | ! 2 RELAX ; ! o 0 FOLIATED 0.5 ! 72 72 ! ! 14.0 ] ; CAVE J O I N T E D RM 3d ! 21 114 HW 1 | 3 j RELAX t ! o 0 FOLIATED 0.8 ; 65 65 ; ! 2.0 ] ! S T A B L E D I S C . BLOCK ! 21 U S HW ; 1 3 I RELAX i ! o 0 FOLIATED 0.8 ! 65 65 ! ! s.o ; ; UNSTABLE J O I N T E D RH 3d 21 116 HW J | 3 j RELAX | ! o 0 F O L I A T E D 0.8 1 65 65 i ; I O . O ; 1 UNSTABLE J O I N T E D RM 3d 21 117 HW ; ! 4 RELAX ! ! o 0 FOLIATED 1.5 I 65 65 ; ! io.o ! I S T A B L E J O I N T E D RM 21 118 HW ; [ 1 j RELAX i ! o 0 FOLIATED 0.25 J 76 76 ; | 6.0 ] i UNSTABLE J O I N T E D RH 3d 21 119 HW ! ! i 1 RELAX ! o 0 FOLIATED 0.25 ! 76 76 ! ! 9.0 | J CAVE J O I N T E D RM 3d 21 120 HW J ; I I RELAX ; ! o 0 FOLIATED 0.25 i 60 60 ; ! i.o ; 1 S T A B L E J O I N T E D RM 21 121 HW ; 1 i j RELAX 1 ! o 0 FOLIATED 0.25 i 60 60 ! ! 2 .0 ! ,' UNSTABLE J O I N T E D RH 3d 21 122 HW ! l j. RELAX ! ! o 0 F O L I A T E D 0.25 ! 60 60 ! ; u .o ! i C A V E J O I N T E D RM 3d 21 123 HW ; ; i ; RELAX ; ! o 0 FOLIATED 0.25 ! 65 65 ; ; 6.0 ! ; UNSTABLE J O I N T E D RM 3d 21 124 HW 1 l j RELAX ; ! o 0 FOLIATED 0.25 ! 65 65 ; ; io.o ! ! CAVE J O I N T E D RH 3d 21 125 HW ; | l ] RELAX ! ! o 0 FOLIATED 0.25 ! 71 71 ! ; i.o ! ! S T A B L E J O I N T E D RH 21 126 HW ; l ; RELAX ! o 0 FOLIATED 0.25 ! 71 71 ! | 2.0 | I UNSTABLE J O I N T E D RM 3d 21 127 HW | i 1 RELAX | ! o 0 FOLIATED 0.25 ! 71 71 ! ! i3 .o ; ; CAVE J O I N T E D RH 3d 21 128 HW ; ! 12 j RELAX ; ! o 0 F O L I A T E D 0.8 I 65 65 ! ! 7.0 ; | S T A B L E D I S C . BLOCK 1 21 129 HW 1 RELAX ', ! o 0 FOLIATED 0.25 I 65 65 1 ! 12-0 ; i UNSTABLE J O I N T E D RH 3d ! 21 130 HW ; ! l 1 RELAX ! 1 o 0 FOLIATED 0.25 | 60 60 i ! 4.0 ! 1 UNSTABLE J O I N T E D RH 3d ! 21 131 HW ; [ l j RELAX ', ! o 0 F O L I A T E D 0.25 65 65 ; I 3 .0 ; ; UNSTABLE J O I N T E D RH 3d 1 6 9 WALL | : 12 I RELAX ; ! io 0 BLOCKY 2.0 ; 80 90 | ! 4.7 ; 1 S T A B L E D I S C . BLOCK 7 11 HW ; : 5 j RELAX I ; io 0 BLOCKY 0.6 | 70 80 ; i 7.9 ! ', S T A B L E J O I N T E D RH ! 8 14 HW ; ! 9 RELAX ; ! 6 0 BLOCKY 0.5 | 78 72 ! ! 8.8 ; ! C A V E J O I N T E D RH 3b ! 8 15 HW ; ! 9 | RELAX I ! o 0 BLOCKY 0.5 ! 78 78 J 1 8.8 ; 1 C A V E J O I N T E D RH 3a ! 28 154 BACK ; ! 16 ! COMP ! o 0 BLOCKY 2.0 ! o 0 ! ! 5.2 ! ! UNSTABLE D I S C . BLOCK 2d ! 30 167 HW ; I 9 J RELAX ; ; 20 0 FOLIATED 1.5 ; 70 90 ; I 7.8 1 1 S T A B L E J O I N T E D RM 1 30 168 HW ; 1 15 1 RELAX ! ! 20 0 BLOCKY 1.5 1 70 90 | ! 6.0 ! | S T A B L E D I S C . BLOCK ! 30 169 BACK I ! 15 ! COMP ! o 0 BLOCKY 1.5 ! o 0 ! ! 5.0 ; ! S T A B L E D I S C . BLOCK ! 32 179 BACK ; ! 15 ; COMP ! 70 0 BLOCKY 1.5 ! 70 0 ! ! 4 .1 ; i S T A B L E D I S C . BLOCK I 32 181 BACK ; ! 15 ! COHP ! 70 0 BLOCKY 1.5 ! 70 0 : ! 4.o ! ! S T A B L E D I S C . BLOCK ! 32 182 HW ; ! .15 ; RELAX ! ! o 0 BLOCKY 1.5 I 90 90 ! ! 4.9 | 1 S T A B L E D I S C . BLOCK ! 16 37 BACK ; ! 45 ! COHP | 90 0 BLOCKY 2.7 ; 90 o 1 | 2.7 ! ! S T A B L E I N T A C T ROCK 16 38 BACK ; i 45 I COMP ! 90 0 BLOCKY 2.7 ! 90 o ! ! 6 .1 ! ! UNSTABLE D I S C . BLOCK 2a ! 16 39 BACK ; ! 45 ; COHP ! 90 0 BLOCKY 2.7 ! 90 o ; | 7.6 | ] UNSTABLE D I S C . BLOCK 2a ', 16 40 BACK ; ! 30 ', COMP ; 90 0 BLOCKY 1.3 ; 90 o ! ! s.s ; ! U N S T A B L E D I S C . BLOCK 2a ! 16 41 BACK I ! 15 ] COMP ! 90 0 BLOCKY 2.6 ! 90 o ! ! 13.4 | j UNSTABLE J O I N T E D RH 3a '. 16 42 BACK ; ', 14 ', COMP ! o 0 BLOCKY 1.3 ! o o ! ! 6.1 i 1 UNSTABLE D I S C . BLOCK 2a ! 16 43 BACK ; ! 14 ! COMP ! o 0 BLOCKY 1.3 I 0 o ; ! 15.2 ! ; CAVE J O I N T E D RH 3a ! 16 44 BACK ; ! 14 ! COMP 1 o 0 BLOCKY 1.3 ! o o ', ; 6.4 ; J UNSTABLE D I S C . BLOCK 2a ! 16 46 HW ; ! 30 1 RELAX j ! o 0 BLOCKY 1.3 | 90 90 | ! i 3 . i ! J S T A B L E D I S C . BLOCK ! 17 47 BACK ; ! 9 ; COMP ; 90 0 BLOCKY 2.0 J 90 o ! ! 7.3 ! ; CAVE J O I N T E D RH 3a ! 17 | 48 BACK ! ! 9 ! COMP ! 90 0 BLOCKY 2.0 ! 90 o ! | 5.0 ! ! UNSTABLE D I S C . BLOCK 2a ! 17 49 BACK ; ! 9 ; COMP ! 90 0 BLOCKY 2.0 ; 90 o ', 1 9.9 ] J C A V E J O I N T E D RM 3a ! 17 ! 50 BACK ; ! 9 ! COMP ; 90 0 BLOCKY 2.0 ! 90 o ,' ! 6.8 ] ; CAVE J O I N T E D RH 3a E F F E C T OF GRAVITY S L I D I N G F R E E F A L L / B U C K L I N G S I Z E AND SHAPE FACTOR TABLE 8.4 Input parameters from the complementary d a t a base n e c e s s a r y f o r open s tope d e s i g n b a c k - a n a l y s i s . BLOCK SIZE STRESS FACTOR JOINT ORIENTATION FACTOR EFFECT OF GRAVITY 2 2 2 CASE'! ! RQD |1 (REF. 1 CRITICAL Jr 1 SLIDING FREEFALL/ J 1 HTO. 1 N 1 ASSESS. » ! ', /Jn II FIG. 7 4) i 1 JOINT /J» SLABBING ', 1 RADIUS (2) ! ! (4) !! (17) 1 (18) (10) 1 (19) (20) 1 1 (13) 1 (21) : ( u ) 64 i ! 4 ; ] 1 o ! 1 0.3 1.5 5.5 | ! 6 10 STABLE 65 ! ! 4 | ; 1 o 1 1 0.3 1.5 5.5 ! i 12 : 10 CAVE 66 ; ! 3 :; 1 o 1 1 0.3 0.8 7.0 1 ! 3 1 5.0 STABLE 67 ! : 3 i ; 1 0 1 1 0-3 0.8 7.o ; ! 9 ! 5.0 UNSTABLE 68 ; ! 3 ! | 1 o 1 1 0.3 0.8 7-0 1 ! 12 ! 5.0 CAVE 69 ; ; is ;! 1 o ; 1 0.3 3.0 4.5 1 1 16 ; 73 UNSTABLE 70 ! ! 6 !! 1 o 1 1 0.3 0.8 8.0 1 ! 5 ! 12 UNSTABLE 71 ! 1 6 !', 1 o ', ! 0-3 0.8 8.0 J ', 8 1 12 1 CAVE 72 ! : i 11 1 0 1 1 0.3 0.25 6.5 1 1 16 1 0.5 ! CAVE 73 ! ! i * !! 1 0 1 1 0.3 3.0 8.0 ! ! 7 | 115 ! STABLE 74 ! ! 8 !! 1 o 1 1 0.3 1.5 4.5 ,' ! 2 1 16 ,' STABLE 75 1 ! 8 ; | 1 o ; 1 0.3 1.5 4.5 | i i i : 16 1 STABLE 76 ! 1 18 !! 1 0 1 1 0.3 3.0 5.0 1 ! 5 81 1 STABLE 77 i 1 3 11 1 o ! 1 0.3 0.25 8.0 ! ! 1* 1.8 1 CAVE 78 ; ! 3 1! 1 o 1 1 0.3 0.25 7.0 ; ! 6 1.6 1 CAVE 79 ; ] 3 11 1 0 1 1 0.3 0.25 7.0 1 1 10 1.6 1 CAVE 80 ; ! i l l 1 0 1 1 0.3 0.25 6.5 1 ! i i ! 0.5 1 CAVE si ; ! 18 11 1 0 1 1 0.3 3.0 5.0 ; ! 9 ! 81 ! STABLE 82 ; I 3 i ; 1 o 1 ! 0-3 0.8 5.5 ', ', 6 4.0 1 UNSTABLE 83 ; 1 1-5 11 1 o ! 1 0.3 1.5 5.0 1 1 13 3.4 1 CAVE 84 ; 1 18 1 1 1 o 1 1 0.3 3.0 4.5 1 1 10 73 1 STABLE 85 ; 1 7 1| 1 o 1 1 0.3 3.0 5.5 1 ! 4 ! 35 1 STABLE 86 ; ! 2° !! 1 o I 1 0.3 3.0 1 4.5 ! i 81 1 STABLE 87 ; 1 20 1 | 1 o 1 1 0.3 3.0 1 4.5 ! 12 81 UNSTABLE 88 ; 1 20 1 1 1 0 1 1 0.3 0.8 8.0 1 1 4 ] 38 STABLE 89 ! ! 20 ; i 1 0 1 1 0.3 0.8 8.0 1 ! i i ! 38 1 STABLE 90 ; ! 3 11 1 0 1 1 0.3 0.25 4.0 1 1 3 1 0.9 1 STABLE 91 ! 1 3 11 1 o ! 1 0.3 0.25 4.0 1 ! n 1 0.9 CAVE 92 ; 1 3 11 1 o 1 1 0.3 0.25 5.5 1 1 2 ! 1.2 STABLE 93 ', I 3',1 1 o ', ', 0.3 0.25 5.5 ', 1 7 ] 1.2 1 CAVE 94 ! 1 3 11 1 o 1 1 0.3 0.25 5.5 1 ! 9 | 1.2 1 CAVE 95 | ! 3 1] 1 o 1 1 0.3 0.25 5.5 1 1 16 1 1.2 CAVE 96 ; 1 111 1 o 1 1 0.3 0.25 7.0 1 1 8 ; 0.5 CAVE 97 ; 1 1 1 1 1 o 1 1 0.3 0.25 8.0 1 1 3 1 0.6 UNSTABLE 98 : 1 1 1 1 1 0 1 1 0.3 0.25 8.0 1 1 5 | 0.6 CAVE 99 ! ! 8 11 1 o 1 1 0.3 2.0 ! 5.5 1 1 3 1 26 STABLE 100 ! 1 ' 3 11 1 o 1 1 0.3 1.0 1 5.0 1 ! 3 1 4.5 STABLE 101 i ! 3 11 1 0 1 1 0.3 1.0 5.0 | 6 | 4.5 UNSTABLE 102 ! ! 3 ] 1 1 0 1 1 0.3 1.0 1 5.0 1 1 14 1 4.5 CAVE 103 ! ! 6 11 1 0 1 I 0.3 0.25 1 5.5 1 ! 3 1 2.5 STABLE 104 ; ! 6 i ; 1 0 1 1 0.3 0.25 1 5.5 1 i 8 1 2.5 UNSTABLE 105 : 1 6 11 1 o 1 1 0.3 0.25 1 5.5 1 1 13 1 2.5 CAVE 106 ! ! 15 11 1 0 1 1 0.3 2.0 1 6.0 1 1 10 1 54 STABLE 107 ! i 2 11 1 0 1 1 0.3 0.8 1 7.0 1 1 4 1 3.4 CAVE 108 i 1 2 11 1 0 1 ', 0.3 0.8 1 7.0 1 1 10 1 3.4 CAVE 109 | ! 3 11 1 o 1 1 0.3 1.0 1 5.0 1 ! 6 1 4.5 UNSTABLE n o ! ! 3 1 l 1 0 1 1 0.3 1.0 5.0 1 1 12 1 4.5 CAVE i n ; ! 2 ; l 1 o 1 1 0.3 0.5 1 6.0 1 1 3 1 1.8 STABLE 112 ! ! 2 ' , l 1 o 1 I 0.3 0.5 , 6.0 1 1 8 1 1.8 UNSTABLE 113 1 I 2 11 1 0 1 1 0.3 0.5 1 6.0 1 1 14 1 1.8 CAVE 114 ; 1- 3 11 1 0 1 1 0.3 0.8 1 5.5 1 1 2 1 4.0 STABLE us : ! 3 ' , | 1 o ! 1 0.3 0.8 1 5.5 ', ', 8 1 4.0 UNSTABLE 116 ; 1 3 1 1 1 0 1 1 0.3 0.8 1 5.5 1 1 10 1 4.0 UNSTABLE 117 | ! 4 11 1 0 1 1 0.3 1.5 1 5.5 1 1 10 1 10 STABLE us ; i 111 1 o 1 1 0.3 0.25 1 6.5 1 1 6 1 0.5 UNSTABLE 119 '• 1 1 1 1 0 1 1 0.3 0.25 1 6.5 1 1 9 1 0.5 CAVE 120 ; 1 111 1 0 1 1 0.3 0.25 1 5.0 1 1 1 1 0.4 STABLE 121 ; 1 111 1 0 1 I 0.3 0.25 1 5.0 1 2 1 0.4 UNSTABLE 122 ! ' 111 1 0 1 1 0.3 0.25 1 5.0 1 1 13 1 0.4 CAVE 123 : 1 111 1 0 1 1 0.3 0.25 1 5.5 1 1 6 1 0.4 UNSTABLE 124 i 1 111 1 o 1 1 0.3 0.25 1 5.5 1 1 10 ; 0.4 CAVE 125 ! ] 1 1 1 1 0 1 1 0.3 0.25 1 6.0 1 1 1 ! 0.5 STABLE 126 ; ! 1 1 1 1 o 1 1 0.3 0.25 1 6.0 1 ! 2 l 0.5 UNSTABLE 127 | | 111 1 o 1 1 0.3 0.25 1 6.0 ! ! 13 1 0.5 CAVE 128 ] 1 12 11 1 o 1 1 0.3 0.8 1 i 4.5 1 7 1 13 STABLE 129 ! ! 6 11 1 o 1 ! 0.3 ; 0.25 1 5.5 i I 12 1 2.5 UNSTABLE 130 ', 1 1 1 1 1 0 ', ', 0.3 ' 0.25 1 5.0 1 1 4 ] 0.4 UNSTABLE 131 ; I i 1! 1 0 1 1 0.3 0.25 1 5.5 1 ! 3' l 0.4 UNSTABLE 9 ! ! n i l 0 3 1 1 0.2 ' 2.0 1 8.0 1 1 4.7 1 12 STABLE i i ! 1 5 !; 1 o 1 1 0.2 ' 0.6 1 7.0 1 ! 7.9 1 4.2 STABLE TABLE 8.4 I n p u t p a r a m e t e r s from t h e complementary d a t a base n e c e s s a r y f o r open s t o p e d e s i g n b a c k - a n a l y s i s ( c o n t ) . CASE t (2) BLOCK SIZE RQD / J n (4) STRESS FACTOR (REF. FIG. 7.4) (17) l * ! 9 !', i .o 0.2 i s ! 9 1 1 1.0 l l 0.3 154 ; ie ; ; o . i ; i 0.3 167 | 9 ! ! i .o ! i 0.2 168 ; i s ; : i .o ; ; 0.2 169 ; 15 1! 0.3 l ! 0.3 179 | 15 i ; o . i ! : 0.85 181 ; i s i : o . i ; ! 0.85 182 ; 15 ! 1 i .o i ; 0.3 37 : 45 • ! i o.4 | ! 1.0 38 ; 45 ! ! 0.4 ; ; 1.0 39 ! 45 : i 0.6 | ] 1.0 40 ; 30 i ; 0.6 ; ! 1.0 4 i ; i s ; ; o .6 ; ; 1.0 42 ; 14 ; ; o.s i ; 0.3 43 ! 14 : i o.s ; ; 0.3 44 J 14 ! ; 0.3 ; ; 0.3 46 ; 30 ; ! i .o ; ; 0.3 47 | 9 ; ! 0.3 ; i 1.0 48 ! 9 ; ! o . i ; ; 1.0 49 : 9 ! ! i .o ; | 1.0 50 ; 9 ! ! 0.4 ; ; 1.0 JOINT ORIENTATION FACTOR CRITICAL JOINT (18) J r / J (10 EFFECT OF GRAVITY SLIDING (19) FREEFAU./ SLABBING (20) 6.0 7.0 2.0 8.0 8.0 2.0 2.0 2.0 8.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 8.0 2.0 2.0 2.0 2.0 HYD. RADIUS (13) (21) (14) 8.8 S.4 CAVE 8.8 9.5 , CAVE 5.2 1.9 UNSTABLE 7.8 22 STABLE 6 36 STABLE 5 4.1 STABLE 4.1 3.8 STABLE 4 3.8 STABLE 4.9 54 STABLE 2.7 97 STABLE 6.1 97 UNSTABLE 7.6 146 UNSTABLE 8.8 47 UNSTABLE 13.4 47 UNSTABLE 6.1 5.5 UNSTABLE 15.2 5.5 CAVE 6.4 3.3 UNSTABLE 13.1 94 STABLE 7.3 11 CAVE 5 3.6 UNSTABLE 9.9 36 CAVE 6.8 14 CAVE ASSESS. 223 i n d i v i d u a l factors on open stope s t a b i l i t y . The s t a r t i n g point or p r e - c a l i b r a t i o n of the factors was provided by Q1 and factor A, B and C of the o r i g i n a l Mathews design method. The modification and c a l i b r a t i o n of the factors was an on-going empirical adjustment process as new cases were analyzed and the e f f e c t of d i f f e r e n t parameters on stope s t a b i l i t y were better understood. For t h i s reason, i t i s d i f f i c u l t to provide a d e t a i l e d j u s t i f i c a t i o n for the derivation of each parameter's r a t i n g scheme. However, i n t h i s section, a b r i e f explanation i s given on how the ratings of each parameter presented i n sections 7.2 to 7.5, have been determined. 8.4.1 Block s i z e r a t i n g The rating for the e f f e c t of block si z e (RQD/Jn) has been kept unchanged from the Q-system. There are several advantages in considering block si z e and shear strength separately. The main advantage i s that i t avoids confusion when a rock mass contains j o i n t sets having d i f f e r e n t shear c h a r a c t e r i s t i c s . Instead of assigning the shear c h a r a c t e r i s t i c s of the most prominent j o i n t set i n the rock mass, as suggested by Barton (1974), the shear strength of the c r i t i c a l j o i n t , which has a greater influence on s t a b i l i t y , i s used. The block size factor RQD/Jn can also be used i n the c a l c u l a t i o n of a rough c r i t e r i o n to i d e n t i f y the three types of rock mass behaviour (intact rock, discrete block and jointed rock mass). I t was mentioned i n section 6.2 that the rock mass 224 behaviour i s dependent on the r e l a t i v e s i z e of blocks compared with the surface of the rock mass exposed. Using t h i s concept, the quotient of the block size factor RQD/Jn and the hydraulic radius of the stope surface were calculated for 10 cases of dis c r e t e block f a i l u r e and 19 cases of jointed rock mass f a i l u r e (see table 8.5). Only the cases i n which the size of the f a i l e d blocks could be v i s u a l l y estimated were included. From table 8.5, i t can be seen that most discrete block f a i l u r e s have a (RQD/Jn / hydraulic radius) r a t i o greater than 1.5. For a jointed rock mass t h i s r a t i o i s smaller than 1.5. Since there i s no case of inta c t rock f a i l u r e i n the data base, the only guide to i d e n t i f y t h i s behaviour i s the largest (RQD/Jn / hydraulic radius) r a t i o for discrete block f a i l u r e , which i s 8.6. This can be used as a rough guideline to anticipate the three t y p i c a l open stope rock mass behaviours. F i n a l l y , the block s i z e factor w i l l be useful for the estimation of a suitable density of cable b o l t s . This w i l l be further discussed i n chapter 9.4.2. 8.4.2 Stress factor r a t i n g The r a t i n g for the compressive stress factor i s a function of the r a t i o of the uni a x i a l compressive strength and the induced stress (oc/oy). The rel a t i o n s h i p between the r a t i o (oc/oy) and the compressive stress rating comes from rule of thumb adapted by Mathews et a l . into the o r i g i n a l factor A 225 TABLE 8.5 Relationship between the relative block size factor (RQD/Jn /hydraulic radius), and rock mass behaviour. Discrete Rock Mass Failure R Q D / J n Hyd. Radius R Q D / J n / H y d . Radius 25 5.8 4.3 30 3.5 8.6 17 10.5 1.6 17 11.3 1.5 17 12.2 1.4 29 6.8 4.3 29 8.0 3.6 8 2.1 3.8 8 2.3 3.4 15 10.0 1.5 Mean= 3.4 Jointed Rock Mass Failure R Q D / J n Hyd. Radius R Q D / J n / / H y d . Radius 8 7.6 1.1 6 8.9 0.7 7 7.1 1.0 4 4.7 0.9 7 9.1 0.8 6 10.5 0.6 4 19.0 0.2 8 8.1 1.0 5 9.0 0.6 5 11.3 0.4 3 20.0 0.2 14 8.6 1.6 9 9.9 0.9 18 12.5 1.4 18 15.0 1.2 18 15.9 1.2 18 11.1 1.6 6 6.9 0.9 6 7.7 0.8 Mean=> 0.9 226 curve. This r e l a t i o n s h i p has been kept roughly the same, except for set t i n g a minimum rating of 0.1 (figure 7.4). This was j u s t i f i e d by several cases of highly stressed backs which were stable because of t h e i r small dimensions. These cases have been plotted on the modified s t a b i l i t y graph i n figure 8.1. According to the back-analysis of a l l the case h i s t o r i e s , the factor A c a l i b r a t i o n appears to be adequate for the majority of case h i s t o r i e s . The e f f e c t of stress relaxation on the design analysis has also been investigated. Zones of relaxation are created in walls of longitudinal stopes when the pre-mining stress r a t i o "K" i s approximately greater than 1.5 to 1. Since int a c t rock has a very low t e n s i l e strength and j o i n t s have no strength i n tension, t e n s i l e stress i s not l i k e l y to b u i l d up in a rock mass. Instead, t e n s i l e stress w i l l open e x i s t i n g j o i n t s or induce new cracks through i n t a c t rock creating a zone of relaxation. Inside t h i s zone of relaxation i n d i v i d u a l blocks have more freedom of movement and become more se n s i t i v e to the action of gravity, because they are unconfined. Consequently, i t appears that t e n s i l e stress and i t s associated zone of relaxation have an e f f e c t on stope s t a b i l i t y . This e f f e c t has been investigated using two dimensional and three dimensional numerical modelling (parametric study, section 7.3.2), with the intention of developing an adjustment factor. The case h i s t o r i e s of stope surfaces i n a state of stress relaxation has been plotted on the modified s t a b i l i t y graph, i n figure 8.2. 227 FIGURE 8.1 Modified Stabi l i ty Graph Total Data Base: Cases of High Stress 9 case histor ies «#H:::X* :X;x :x::X:v:x-*-''' yyyyy:^ ^ :»;•;•;•;!;'!'!':':'!!>•' **** ym • —f&i-0 5 10 15 20 25 Hydraul ic Rad ius (m) • Stable Stope Surface • Unstable Stope Surface T Caved Stope Surface 228 I t can be seen that the data does not j u s t i f y ah adjustment factor for stress relaxation, since the assessment of the back-analyzed case h i s t o r i e s are generally i n accordance with the modified s t a b i l i t y graph. Nevertheless, from the parametric study i t has been found that the r e l a t i v e shape of the stope surface i s the most important parameter influencing the " t h e o r e t i c a l " t e n s i l e stress. Since hydraulic radius (which account for the size and shape of the stope surface) and the e f f e c t of gravity are included i n the model, i t seems reasonable to assume that the e f f e c t of relaxation i s i n d i r e c t l y taken into account. Ninety seven case h i s t o r i e s (shown i n figure 8.2) of relaxed walls are in agreement with t h i s hypothesis. 8 . 4 . 3 J o i n t o r i e n t a t i o n factor r a t i n g The j o i n t orientation t o t a l rating depends on the c r i t i c a l j o i n t parameter and the shear strength c h a r a c t e r i s t i c s . The shear strength rating i s Jr/Ja i s taken d i r e c t l y from the Q-system and i s already ca l i b r a t e d with respect to the block size factor. The c r i t i c a l j o i n t rating can be estimated using figure 7.19. The chart was constructed according to the following p r i n c i p l e s : The t o t a l influence of the c r i t i c a l j o i n t on the s t a b i l i t y number c a l c u l a t i o n , should be approximately s i m i l a r to the influence of gravity, because they are two approximately equally important factors. Empirically, i t has been found 229 FIGURE 8.2 Modified Stabi l i ty Graph Total Data Base: Cases of Stress Relaxation 97 case histories 1000 100 _Q E Z3 10 O 00 TD 1.0 "O o 0.1 10 15 20 Hydraul ic Rad ius (m) complementary main data base data base « ^ , , i L O L o • Stable Stope Surface • • Unstable Stope Surface v • Caved Stope Surface 25 230 that an influence of 5 works well. The rating, which i s a function of the difference i n dip between the c r i t i c a l j o i n t and the stope surface, i s a minimum (0.2) when the difference i n dip i s shallow (10° to 30°) . A s l i g h t l y better case (with regard to s t a b i l i t y ) occurs i f the c r i t i c a l j o i n t i s sub-parallel (0° to 10° difference) to the stope surface. A r a t i n g of 0.3 i s assigned i n t h i s s i t u a t i o n . A difference in dip of approximately 60° has a small influence on stope s t a b i l i t y and a rating of 0 .8 i s used. C r i t i c a l j o i n t s perpendicular to the stope surface have no influence on s t a b i l i t y (this i s given a ra t i n g of 1.0). The e f f e c t of anisotropy i s accounted for by considering the tru e d i f f e r e n c e i n dip, which i s influenced by the difference i n s t r i k e between the c r i t i c a l j o i n t and the stope surface. As the difference i n s t r i k e increases, the true difference i n dip increases and the e f f e c t of the c r i t i c a l j o i n t r a ting decreases. 8.4.4 The gravity factor r a t i n g The gravity factor rating i s estimated using figure 7.21 for the s l i d i n g mode of f a i l u r e . The gravity rating w i l l increase the modified s t a b i l i t y number (by up to a factor of 4) as the dip of the s l i d i n g plane ( c r i t i c a l j o i n t ) decreases and s l i d i n g i s less l i k e l y to happen. I f the dip of the 231 d i s c o n t i n u i t y i s smaller than or equal to 30°, the rating i s a maximum, because the f r i c t i o n angle of a t y p i c a l rock j o i n t i s around 30°. When the mode of f a i l u r e i s by gravity f a l l or slabbing, the r a t i n g i s a function of the i n c l i n a t i o n of the designed stope surface. As i n the s l i d i n g analysis, the rating's influence varies from 2 to 8. It i s a maximum for v e r t i c a l walls and a minimum for horizontal backs. The equation used to derive the ra t i n g curve (in figure 7.20) i s given below: rat i n g = 8 - 6 (cosine (angle of i n c l i n a t i o n ) ) . This r e l a t i o n s h i p describes the increasing e f f e c t of gravity on stopes surface dipping closer to the horizo n t a l . 8.5 THE MODIFIED STABILITY GRAPH The modified s t a b i l i t y number and hydraulic radius are related g r aphically on a s t a b i l i t y graph, as i n the methodology proposed by Mathews et a l . This allows the presentation of a l l the key parameters on one graph i n order to determine what combination of s t a b i l i t y number (rock mass quality) and hydraulic radius (stope surface s i z e and shape) leads to stable, unstable or caved conditions. Stable stopes (planes that had low dilution) are represented on the graph by round shaped points. Case h i s t o r i e s that had experienced d i l u t i o n and ground f a l l s causing operational problems are c l a s s i f i e d as unstable. They are shown on the graph by square shaped points. 232 The t r i a n g u l a r points represent case h i s t o r i e s that had severe ground control problems. The s t a b i l i t y graph i n figure 8.3, i s a p l o t of the main data base (84 points) . As expected the graph shows that most points located i n the upper l e f t corner (good rock qu a l i t y and small stope surface) are stable while the cases p l o t t i n g i n the lower r i g h t area (poor rock qu a l i t y and large stope surface) have caved. A t r a n s i t i o n zone between the stable and caved areas i s represented on the graph by a grey band. I t can be noticed that the unstable cases (square points) tend to concentrate around that t r a n s i t i o n zone, which i s also expected. The modified s t a b i l i t y graph i s now comprised of a stable area, a t r a n s i t i o n zone and a caved area. In the next s t a b i l i t y graph ( f i g u r e 8.4), the complementary data base has been added and confirms the r e l a t i o n s h i p previously defined in the modified s t a b i l i t y graph (figure 8.3). This new rel a t i o n s h i p has a reduced t r a n s i t i o n zone between stable and caving areas which makes the modified s t a b i l i t y graph a more precise design t o o l and leaves less room for mis-interpretation of analyses. The large data base i s a warrant of the method 's r e l i a b i l i t y and confirms the a p p l i c a b i l i t y of the design method for stope walls, and stopes at shallow depth. 8 .6 DESIGN PHILOSOPHY 233 FIGURE 8.3 Modified Stabi l i ty Graph 1000 100 CD _ Q E Z3 ^ 10 D -I-' C O " O (D b 1.0 o 0.1 Main Data Base 84 case histories 0 5 10 15 20 Hydraul ic Radius (m) 25 • Stable Stope Surface • Unstable Stope Surface • Caved Stope Surface 234 F I G U R E 8.4 1000 100 E Z3 ^ 10 O 00 "O CD it: 1.0 o 0.1 Modified Stabil i ty Graph Total Data Base 176 case histories 0 10 15 20 complementary Hydraul ic RadlUS (m) data base main data base \ / o • Stable Stope Surface • • Unstable Stope Surface v • Caved Stope Surface 25 235 The modified s t a b i l i t y graph (figure 7.22) can be used as a r e l i a b l e t o o l for predicting open stope dimensions. The f i n a l design must consider the geotechnical parameters involved in the c a l c u l a t i o n of the modified s t a b i l i t y number but also should account for economic, scheduling and mining constraints. Consequently, engineering judgement i s required to determine the most e f f i c i e n t design. As a general rule, the amount of d i l u t i o n i s expected to increase as the design plots deeper into the caving zone. When mining i n the v i c i n i t y of other ore lenses, or when there i s no f l e x i b i l i t y i n the production schedule and no i n s t a b i l i t y can be tolerated, a l l designs should plo t above the grey area, i n the stable zone. Sometimes i t i s not p r a c t i c a l or economical to design in the stable zone. Because of the non entry nature of open stoping, stopes p l o t t i n g i n or below the grey area may s t i l l be v i a b l e . The author's experience with the revised s t a b i l i t y graph has been that when p l o t t i n g inside the t r a n s i t i o n zone (grey area) , the stope w i l l be very s e n s i t i v e to b l a s t i n g and the e f f e c t of time. In t h i s case, i t i s recommended to use control b l a s t i n g techniques and to b a c k f i l l immediately after the stope i s emptied. Designing below the t r a n s i t i o n zone usually requires a r t i f i c i a l support. The p r i n c i p a l action of c a b l e b o l t s i s t o l i m i t movement a l o n g e x i s t i n g d i s c o n t i n u i t i e s . This r e s u l t s i n a hypothetical increase in rock mass qu a l i t y and the s t a b i l i t y number. This w i l l be further discussed in chapter 9 (cable bolt support in open 236 stoping). 8.7 POSSIBILITY OF USING STATISTICS E m p i r i c a l research can be divided into exploratory-research and confirmatory research. In confirmatory research, meaningful hypotheses are developed when the understanding of the empirical r e a l i t y i s well advanced and a sounded theory i s proposed. For t h i s type of research the s t a t i s t i c a l inference allows for the evaluation of the p r o b a b i l i t y of error regarding either the confirmation or infirmation of the hypotheses. In t h i s thesis, the proposed hypothesis i s more relevant to exploratory research because the t h e o r e t i c a l background i s lim i t e d . This i s mainly due to the high complexity of the problem and the r e l a t i v e s c a r c i t y of applied geomechanics research. Therefore, only a l i m i t e d degree of sophi s t i c a t i o n could be achieved i n the model development. S t a t i s t i c a l inference i n exploratory research although less powerful than i n confirmatory research, i s used to estimate the error i n i n f e r r i n g knowledge to a population from observations based on a sample. The qu a l i t y of t h i s type of inference i s highly dependant on the sampling scheme. In order to obtain a s i g n i f i c a n t s t a t i s t i c a l inference i n t h i s study, a random sample of the population of a l l possible stopes would be required. Due to p r a c t i c a l considerations, the sample of stopes (and the assessment of t h e i r s t a b i l i t y ) used i s a convenient sample (in opposition to a random sample). The sampling was based on the t y p i c a l i t y of the stopes and the p o s s i b i l i t y f o r safe measurements of the geotechnical parameters. 8.8 SUMMARY The p r i n c i p a l objective of the proposed design method i s to predict the s t a b i l i t y of open stopes i n terms of operating problems. Because of the economic consequences of a bad design, the r e l i a b i l i t y of the model i s c r u c i a l . For an empirical model, the r e l i a b i l i t y i s l a r g e l y a function of the extent of the data base. In addition, the model i s expected to work better inside the bounds defined by the geotechnical conditions i n the data base. The t o t a l data base of unsupported stopes contains 175 case h i s t o r i e s from t h i r t y - f o u r Canadian mines. The data base has been divided into a main data base (high l e v e l of confidence) and a complementary data base (data from l i t e r a t u r e and data with a lower l e v e l of confidence). The main data base was used for the c a l i b r a t i o n of the design method while the complementary data base was used to confirm the r e l i a b i l i t y of the method. The c a l i b r a t i o n of the geomechanical model was done through the back-analysis of case h i s t o r i e s . For each case, the input data was estimated on s i t e , and the modified 238 s t a b i l i t y number was calculated and plotted on the modified s t a b i l i t y graph. For the cases i n which the s t a b i l i t y graph assessment did not f i t the actual stope behaviour, the causes of the m i s - i n t e r p r e t a t i o n were i n v e s t i g a t e d , and the geomechanical model was modified i n order to become a better predicting t o o l . This procedure resulted i n the creation of new parameters, the r e - c a l i b r a t i o n of e x i s t i n g parameters and a better d e f i n i t i o n of the s t a b i l i t y graph (a smaller t r a n s i t i o n zone between stable and caving). The ratings assigned to each parameter i n the model (ref. chapter 7) are b r i e f l y discussed (in section 8.4) with regard to relevant case h i s t o r i e s . 239 CHAPTER 9 CABLE BOLT SUPPORT IN OPEN STOPING 9.1 INTRODUCTION A r t i f i c i a l support, i n the form of rock anchors, has become an important component of a l l underground mining operations because t h e i r s t a b i l i z i n g e f f e c t contributes to make underground workings safer. There are several types of rock anchors featuring d i f f e r e n t properties and having a var i e t y of functions. This chapter focuses on the application of grouted cable bolts i n open stope mining. Such a support system may improve the competency of a disturbed rock mass to a point approaching the undisturbed rock q u a l i t y by l i m i t i n g j o i n t movement and d i l a t i o n . This r e s u l t s i n more stable, possibly larger and thus more e f f i c i e n t production stopes. The e f f e c t of increasing the rock mass s t a b i l i t y r e s u l t i n g i n larger stope dimensions i s investigated i n t h i s chapter using the modified s t a b i l i t y graph and case h i s t o r i e s of supported open stopes. It i s i n cut and f i l l applications that cable bolts have gained t h e i r greatest popularity. The i n s t a l l a t i o n of long cable bolts i n cut and f i l l backs has the advantage of covering three or four l i f t s , which reduces the r e h a b i l i t a t i o n work necessary a f t e r each b l a s t and reduces the cost of bolting. 240 Furthermore, since the reinforcement i s i n s t a l l e d p r i o r to bla s t i n g , i t considerably l i m i t s the degree of disturbance in the rock mass induced by bl a s t i n g . This concept i s known as pre-reinforcement. In recent years, the Canadian, Australian and Swedish mining industries have been attempting to tra n s f e r the cable b o l t technology from cut and f i l l to open stope mining. In the beginning, because the fundamental differences between the two mining methods (with regard to cable bolting) were not well understood, t h i s technique had l i t t l e success. Fabjanczyk (1982) reported i n a survey of ten Australian mines that 75% of open stopes using cable bolts suffered overbreak. The p r i n c i p a l source of the problems i n open stoping was the lack of access for the i n s t a l l a t i o n of the cable b o l t s . This problem was p a r t i c u l a r l y acute i n hanging walls but also existed i n stope backs, when the d r i l l i n g horizon was not f u l l y open. As a re s u l t , only a low density of cable bolts could be i n s t a l l e d using unfavourable patterns and cable orientations. Another major difference between cut and f i l l and open stoping i s that open stoping usually involves larger stope spans and has rapid changes i n geometry, causing frequent stress r e d i s t r i b u t i o n s . Although the application of cable bolts i n open stope mining i s r e l a t i v e l y new, the popularity of t h i s support technique i s increasing. Among the t h i r t y - f o u r Canadian mines v i s i t e d during t h i s two year study (1986 to 1988), twenty mines 241 used cable bolts to some extent, with a rate of success of approximately 75%. This shows the progress made i n recent years to overcome the problems mentioned above and emphasizes the p o t e n t i a l for cable b o l t a p p l i c a tion i n open stope mining. However, there are s t i l l no accepted guidelines for the design of cable b o l t systems and rules of thumb o r i g i n a l l y developed for conventional rock bolts are sometimes s t i l l applied. This explains the majority of the 25% of the underdesigned case h i s t o r i e s , as well as other cases that seem to be overdesigned. The d i f f e r e n t options available for the design of cable b o l t support systems for open stopes w i l l be presented in t h i s chapter. The complex inte r a c t i o n of the cable bolts with the ground conditions and opening geometry w i l l be looked at in a s i m p l i f i e d empirical manner using the open stope s t a b i l i t y model proposed i n preceding chapters. 9.2 DESIGN CONCEPT 9.2.1 Prereinforcement O r i g i n a l l y the support philosophy was to suspend the loose rock i n the periphery of the excavation to the more competent and undisturbed layers remote from the opening surface. A better understanding of rock mass behaviour and support systems has led to a more e f f i c i e n t technique c a l l e d prereinforcement. The concept of prereinforcement consists of i n s t a l l i n g the support p r i o r to excavating the rock adjacent to the 242 excavation. The p r i n c i p a l e f f e c t i s to l i m i t the displacement of the rock mass to small values. F u l l e r and Cox (1978) suggested that when prereinforced, the rock mass displacement i s l i m i t e d to less than two millimeters. This minimizes the shear and d i l a t i o n along e x i s t i n g geological structures and preserves t h e i r i n - s i t u cohesion and f r i c t i o n angle. The rock mass becomes "self-supporting." Another i n t e r e s t i n g advantage of the prereinforcement technique i s that b l a s t i n g i s done against an already reinforced surface, reducing the amount of damage caused by b l a s t i n g v i b r a t i o n s . In addition, the e f f e c t of the sudden changes i n the surrounding stress f i e l d r e s u l t i n g from the change i n opening geometry (after each blast) can be better con t r o l l e d by a prereinforced rock mass. The p r i n c i p a l l i m i t a t i o n i n applying the prereinforcement technique to open stopes i s the lack of access for cable bolt i n s t a l l a t i o n . T y p i c a l l y , open stope development i s located in the footwall. The mucking horizon (undercut, drawpoints) i s developed f i r s t , followed by the opening of the d r i l l i n g horizon (overcut or d r i l l i n g d r i f t ( s ) ) . The ore between the two horizons can then be retreated v e r t i c a l l y or h o r i z o n t a l l y . As opposed to cut and f i l l mining, at no time during t h i s sequence i s access available to i n s t a l l cable bolts in the overcut and undercut before they are opened. However, the use of prereinforcement may be attempted by i n s t a l l i n g the cable bolts i n the overcut as soon as possible 243 a f t e r i t i s open. A ce r t a i n amount of displacement i s expected to occur, but i f careful b l a s t i n g i s used and the time delay before the support i s i n s t a l l e d i s minimized, the open stope back should be e f f e c t i v e l y supported. The advantage of having the roof reinforced for the heavy production b l a s t i n g remains. This has become the most commonly employed cable bolting procedure and i t has been proven e f f e c t i v e . About the concept of prereinforcement, Hoek & Brown (1980) concluded that: "The p r i n c i p a l objective i n the design of excavation support i s to help the rock mass to support i t s e l f . Pre-placed grouted r e i n f o r c i n g elements are probably the most e f f e c t i v e means of achieving t h i s objective and the authors have no doubt that the future w i l l see a great increase i n t h i s support technique." 9.2.2 S t i f f n e s s of the support system The s t i f f n e s s of a material represents i t s capacity to deform when submitted to stress. S t i f f materials show small deformation before f a i l i n g and are prone to v i o l e n t f a i l u r e . Materials having a low s t i f f n e s s may sustain large deformations before colla p s i n g . In order to obtain the maximum advantage of a cable bolt support system, i t s s t i f f n e s s must be designed according to the rock mass s t i f f n e s s . I f the support i s too s t i f f , the rock mass w i l l be restrained from deforming but the energy usually dissipated through deformation w i l l b u i l d up and could cause the sudden f a i l u r e of the support system. However, i f the s t i f f n e s s of the support i s very low compared with the r o c k mass s t i f f n e s s , the s t a b i l i z i n g e f f e c t may be i n s i g n i f i c a n t . The s t i f f n e s s of a cable bolt system i s dependent on several factors. The density of b o l t i n g and the length of cables are important factors and w i l l be discussed i n sections 9.4.2 and 9.4.3. The bonding strength between the grout and rock and the grout and s t e e l also play a major role because they constitute the weakest points of the system. A f u l l discussion on t h i s subject i s beyond the scope of t h i s thesis and can be found elsewhere (Stheeman, 1982; Jeremic and Delaire, 1983). Although there are c e r t a i n v a r i a t i o n s i n cable b o l t i n g practices i n Canadian mines, i n general 16 mm (5/8 inch) diameter cables are used with a water cement r a t i o less than 0.5. Sometimes additives w i l l be used to reduce the amount of grout slumping i n the hole. When only a low density of cable bolts i s employed, some operators w i l l double the number of cables i n each hole. I t i s important to notice that q u a l i t y control i n the i n s t a l l a t i o n of cables can have a large influence on t h e i r strength. F u l l e r (1983) reported that the grout-steel bond can be damaged by d i r t or debris i f the cables are not properly cleaned before t h e i r i n s t a l l a t i o n . On the other hand, the bond strength w i l l increase when the cables are s l i g h t l y rusted. The "bird cage" type of cable bolts have been s p e c i a l l y designed to improve the grout-cable bond but are not 245 widely used i n Canada at t h i s time. The designer may also adjust the s t i f f n e s s of the cable support system for s p e c i f i c applications, using d i f f e r e n t techniques during the i n s t a l l a t i o n . These adjustments increase or decrease the support s t i f f n e s s . - Increasing the support s t i f f n e s s . A s t i f f e r support system may be more e f f i c i e n t i n zones of stress relaxation where additional reinforcement i s required. This can be achieved by tensioned cable b o l t s . At f i r s t , tensioned cable bolts were applied i n a l l s i t u a t i o n s . It was l a t e r r e a l i z e d that the expansion of the rock mass afte r excavation i n most cases was s u f f i c i e n t to na t u r a l l y tension the cables. Since i t i s a time consuming technique and i n most cases redundant, i t i s now practiced only i n s p e c i f i c applications such as clamping layers of relaxed rock together in a hanging wall. - Decreasing the support s t i f f n e s s . When a large amount of deformation i s expected, i t i s desirable to design a cable bolt system capable of high deformation without losing i t s support capacity. Matthews, Tillmann and Worotnicki (1983) described a debonding procedure to decrease the s t i f f n e s s of cable b o l t s . The procedure includes the i n s t a l l a t i o n of supplementary anchors (swages) and a r t i f i c i a l l y debonding sections of the cable with p l a s t i c 246 tubing or paint. This minimizes the r i s k of premature strand f a i l u r e due to the l o c a l i s e d movement of a j o i n t . Matthews, Tillmann and Worotnicki also reported a successful application of t h i s technique i n the case of a highly stressed crown p i l l a r where l a t e r a l expansion was excessive. However, none of the case h i s t o r i e s c o l l e c t e d for t h i s study used the above debonding technique. 9.3 CABLE BOLT SUPPORT SYSTEMS IN CANADIAN OPEN STOPE MINES Cable b o l t support systems should be i n s t a l l e d according to the nature of the rock mass to be supported, the access avail a b l e and the s p e c i f i c function of the support system. The d i f f e r e n t cable bolt patterns observed i n Canadian open stopes during the data c o l l e c t i o n phase are i l l u s t r a t e d i n figures 9.1 to 9.8 and w i l l be discuss i n t h i s section. Typical cable bolt length and density of cables are also given. However, these values should not be used as design guidelines since cable bolt systems should be designed according to the rock mass conditions and the potential rock mass f a i l u r e mechanism. 9.3.1 Cable b o l t patterns f o r open stope backs The p r i n c i p l e of the system shown i n figure 9.1 a) i s to create a regular p a r a l l e l pattern with a uniform d i s t r i b u t i o n of cables. This constitutes the most commonly used system and i s generally applied when the overcut i s f u l l y open. According 247 FIGURE 9.1 a) U n i f o r m c a b l e b o l t p a t t e r n i n s t a l l e d i n open s t o p e o v e r c u t s . FIGURE 9.1 b) U n i f o r m c a b l e b o l t p a t t e r n i n s t a l l e d i n open s t o p e o v e r c u t s and supplemented w i t h s h o r t r e b a r . to the data base, the length of cable associated with t h i s pattern varies from 10 to 25 metres while the density of b o l t i n g i s designed at 0.1 to 0.4 cable bolts per square metre (cb/ m2) . In some cases, a set of two to three metres grouted r e i n f o r c i n g bar are i n s t a l l e d i n between the cables with a pattern i n t e n s i t y of about 0.7 rebar/ m2. The objective i s to create a reinforced rock beam with a high density of short bo l t s , and t i e that beam into more competent layers with long cable b o l t s . This i s shown in figure 9.1 b). Some mines have also added fan patterns of cable bolts i n the sidewalls in an attempt to provide a l o c a l i z e d wall support as the stopes above are extracted. The second support system t r i e s to take better advantage of the concept of prereinforcement. The overcut i n t h i s case i s driven i n two stages. The central section (C) i s opened f i r s t and cable bolts are i n s t a l l e d v e r t i c a l l y i n the back of the open section (see figure 9.2). Supplementary cable bolts are also i n s t a l l e d at an angle, over the sides (S) that w i l l be "slashed" during the second stage of overcut development. At the only mine using t h i s design, the length of cable bolt used was 9 meters with a density of b o l t i n g of 0.16 cb/ m2. As in the preceding case, 2.7 metre long rebar were u t i l i z e d in between the cables with a density of 0.44 rebar/ m2. Another modification of open stope roof b o l t i n g i s shown on figure 9.3. Cable bolts (in t h i s case s i x metres long) are i n s t a l l e d at an i n c l i n a t i o n of 76° i n one d i r e c t i o n for a given 249 FIGURE 9.2 Cable b o l t s u p p o r t system u s i n g i n c l i n e d c a b l e s and two phases o f o v e r c u t d e v e l o p m e n t f o r p r e r e i n f o r c e m e n t . FIGURE 9 . 4 C a b l e b o l t s u p p o r t system d e s i g n e d f o r o v e r c u t s c o n t a i n i n g a s m a l l p i l l a r ( s ) . row while i n the next row the cables are i n c l i n e d i n the opposite d i r e c t i o n . This alternate i n c l i n a t i o n produces an interlaced pattern which aims at i n t e r s e c t i n g geological d i s c o n t i n u i t i e s at more favorable angles. The density of b o l t i n g achieved i n t h i s type of design varies from 0.2 to 0.25 cb/ m2. When temporary p i l l a r s are l e f t i n the overcut, or p a r a l l e l d r i l l i n g d r i f t s are used as the d r i l l i n g development, cable bolt design has been done as shown in figure 9.4. The o r i g i n a l spans to be supported were very small but w i l l become wider as the stope i s extracted. Once again, t h i s takes advantage of the concept of prereinforcement. The bolt length observed i n these cases were roughly 10 metres with a density of b o l t i n g of 0.2 cb/ m2. 9.3.2 Cable b o l t patterns for open stope walls The f i r s t a p p l i c a t i o n of cable bolts i n stope walls attempted to d i s t r i b u t e the cables as uniformly as possible over the supported wall (figure 9.5). Because of the r e s t r i c t e d access, the d r i l l holes had to be fanned which does not necessarily produce a favourable b o l t i n c l i n a t i o n for support. Only a low b o l t i n g density of approximately 0.06 cb/ m2. was achieved with such design and the bolt lengths were var i a b l e . The approach i l l u s t r a t e d i n figure 9.6 consists of creating a reinforced beam in v e r t i c a l or i n c l i n e d walls. This 251 FIGURE 9.5 U n i f o r m c a b l e b o l t p a t t e r n i n s t a l l e d i n s t o p e w a l l . 252 an open FIGURE 9.6 C r e a t i o n o f a r o c k beam i n t h e h a n g i n g w a l l i n s t a l l i n g a l o c a l i z e d h i g h d e n s i t y o f c a b l e b o l t s . 253 can be done by i n s t a l l i n g cable bolts i n a high density fan pattern at every sublevel. The concept of t h i s form of reinforcement i s to l i m i t the wall spans to e f f e c t i v e l y only one stope height. The length of cable bolts i n t h i s case varies with the stope wall dimensions. The most expensive but c e r t a i n l y the most e f f i c i e n t cable b o l t support system for hanging walls i s when the cables are i n s t a l l e d from a b o l t i n g d r i f t running p a r a l l e l to the s u p p o r t e d w a l l (see f i g u r e 9.7). The concept of prereinforcement can be f u l l y applied and cable i n c l i n a t i o n i s near optimum. Because of the high cost of the b o l t i n g d r i f t development, t h i s approach has been used only occasionally in two mines of the data base. The l a s t example involved the support of p i l l a r walls (or secondary stopes) in transverse blasthole mining. As shown in figure 9.8, cables are i n s t a l l e d from the undercut at such angles that hal f of the p i l l a r i s supported by the stope on i t s l e f t and the second half by the stope on i t s r i g h t . The main purpose of the system i s to prevent the detachment of blocks from the p i l l a r i n order to maintain the i n t e g r i t y of the p i l l a r . In the preceding discussion, the p r i n c i p a l options of cable b o l t support systems and t h e i r applications have been reviewed, as well as the concept of prereinforcement and s t i f f n e s s . A l l these elements must be considered in the optimization process of a support system. The remainder of 254 FIGURE 9.7 Cable b o l t s u p p o r t system f o r a h a n g i n g w a l l , i n s t a l l e d from a p a r a l l e l b o l t i n g d r i f t . 255 FIGURE 9.8 C a b l e b o l t s u p p o r t system s t a b i l i z i n g p i l l a r w a l l s . 256 t h i s paper w i l l focus on the design of three variables characterizing cable bolt support: the density of bolting, the length and the r e l a t i v e orientation of cable b o l t s . 9.4 DEVELOPMENT OF CABLE BOLT DESIGN GUIDELINES During the data gathering program, 66 case h i s t o r i e s of open stopes supported by cable bolts were c a r e f u l l y documented. The c o l l e c t e d data i s presented on tables s i m i l a r to those for the unsupported data. Table 9.1 shows the background information of the case h i s t o r i e s and table 9.2 contains the geotechnical parameters necessary for the design analysis. The three p r i n c i p a l variables of cable b o l t design are the density of bolting, the length of the cables and the o r i e n t a t i o n of the cable b o l t s . 9.4.1 Design analysis of the cable b o l t support data The use of the geomechanical model (and the modified s t a b i l i t y graph) in the design analysis allows for the empirical q u a n t i f i c a t i o n of the supporting e f f e c t of cable b o l t s . Guidelines for the estimation of b o l t density and bolt length w i l l be derived from the analysis. This type of analysis also provides some assistance i n the determination of the most suitable cable bolt orientation by analyzing the possible f a i l u r e mechanisms. The modified s t a b i l i t y numbers and hydraulic radius have 257 TABLE 9.1 Background i n f o r m a t i o n f o r t h e d a t a base o f case h i s t o r i e s t h a t have used s u p p o r t . J O I N T O R I E N T A T I O N F A C T O R ! E F F E C T OF G R A V I T Y i { S I Z E ; 1 BLOCK ! S T R E S S ; ! AND ; ; S I Z E ! ; FACTOR ; J C R I T I C A L BLOCK i SHEAR ; S L I D I N G ! F R E E F A L L / J ; S H A P E ; ! FACTOR ! J O I N T S H A P E 1 S T R E N . i i B U C K L I N G ! ; F A C T O R ! H I H E C A S E P L A N E 1 ! RQD ! ; COMP RELAX ! ! D I P j STRK B L O C K Y / ! Jr i C R I T I C A L J S T O P E ; ! H Y D . | ; A S S E S S . 1 T Y P E O F F A I L I ff ! /Jn ! I D I F F ! D I F F F O L I A T E D ! / J a ! J N T D I P ! P L A N E D I P J ; R A D I U S ; BEHAVIOUR MODE (1) (2) (3) ! : (*) i ! (5) (6) i ! (7) ! (8) (9) ! (10) : ( I D ; (12) i : d 3 ) : ,' (14) (15) (16) 1 251 BACK 1 ! 25 ! i COMP ; 20 ; o BLOCKY ! 0.75 ! 20 ; o ; ! 8 4 ; ! C A V E D I S C . BLOCK 2a 1 252 BACK i ! 25 | J COHP ! 20 ! o BLOCKY J 0.75 ! 20 ; o ; ! 8 4 ; ! C A V E D I S C . BLOCK 2a 1 253 BACK ! ! 25 ] ! COMP ! 20 ! o BLOCKY 1 0 . 7 5 ! 20 ! o ; ; 5 3 | ! S T A B L E D I S C . BLOCK 1 254 BACK ; ', is : ', COMP ! 20 1 0 BLOCKY 1 3 ! 20 l o ; ! 6 4 ! ! S T A B L E D I S C . BLOCK 1 255 HW ; ! 25 ! RELAX ! ! 20 ! o F O L I A T E D ! 0.75 ! 20 ; 90 ; 1 5 o ! j S T A B L E D I S C . BLOCK 1 256 BACK ; ! IB ! j COMP ! 20 ! o BLOCKY ! 3 ! 20 ! o ! ; 5 9 ! ,' S T A B L E D I S C . BLOCK 1 257 BACK ! ! 18 ; ! COMP ! 20 ! o BLOCKY ; 3 ! 20 ; o ! 1 6 7 I ! S T A B L E D I S C . BLOCK 1 258 BACK ! ! 18 ! ! COMP ! 20 ! o BLOCKY ! 3 ! 20 ; o ; ! 7 i ; ! S T A B L E D I S C . BLOCK 1 259 BACK ', ; 18 ! ; COMP i 20 ! o BLOCKY ; 3 ', 20 ', o ; ! 4 6 ; i S T A B L E D I S C . BLOCK 1 260 BACK ! ; is ; ; COMP ; 20 ! o BLOCKY I 3 ! 20 ; o ; ; 5 o ! I S T A B L E D I S C . BLOCK 2 261 BACK ; ! 14 I ; COMP : 40 ! o BLOCKY ! 0.5 ; 66 ; 25 ; ! 13 9 ! | S T A B L E J O I N T E D RM 2 262 BACK ; ; 14 i ! COMP ! 40 ! o BLOCKY ! 0.5 ! 66 ; 25 ; ! 16 o ; ; C A V E J O I N T E D RM 3a 2 263 BACK ! ! 6 ! ! COMP 1 22 ! o BLOCKY ; 0 .7 ! 42 ; 20 ; ] 7 3 ; I S T A B L E J O I N T E D RM 2 264 BACK ; ; 4 ; ; COMP ! 42 ! o BLOCKY ! 0 .2 ! 42 ; o ; ! 6 o ! i S T A B L E J O I N T E D RM ; 2 265 BACK ; ! 6 ; ; COMP ! 22 ! o BLOCKY ! 0.7 ! 42 ; 20 ; : B o ! ! S T A B L E J O I N T E D RH 2 266 BACK ! ! 6 ! ; COMP ! 22 ! o BLOCKY ! 0. 7 ! 42 ! 20 ; 1 14 8 ; ! C A V E J O I N T E D RM 3a 2 267 BACK ; ! 4 ] ! COMP ! 66 ! o BLOCKY ! 0.2 1 66 : o ! | 7 8 ; ; C A V E 1 J O I N T E D RM 3a | 3 268 WALL ! ! 6 ; RELAX ! ! 15 ! o BLOCKY ; i ! 75 ; 9 0 ; ! 8 9 i 1 S T A B L E J O I N T E D RM ! 3 269 BACK ; ! 6 : ; COHP ! 24 1 o BLOCKY ; i 1 24 ; o ! ; 4 4 ; i S T A B L E J O I N T E D RM ', 3 270 BACK ; ! 6 | ; COMP 1 24 ! o BLOCKY ! l ! 24 ; o : | 5 3 ; 1 S T A B L E J O I N T E D RH ! 4 271 BACK ! ! 7 ; ; COMP ! *5 1 o F O L I A T E D ! 1.5 ! 45 | o ; ; 5 3 ; 1 S T A B L E J O I N T E D RM ; s ! 272 BACK ; ! 'o ; ; COMP ; 90 ! o BLOCKY ! i ! 90 ; o ! ! 6 2 ; ! S T A B L E D I S C . BLOCK ! 6 ! 273 BACK ! ! 6 ! ; COMP ! 20 ! o BLOCKY I 1.5 ! 20 ; o ! ! 2 6 : j S T A B L E D I S C . BLOCK : 6 274 BACK ; ! 6 ! 1 COMP i 20 1 o BLOCKY ! 1.5 I 20 ; o i ! 4 2 ! ! S T A B L E J O I N T E D RM ! 6 | 275 END ; ! 6 ; ! COMP ! 30 ! 30 F O L I A T E D ', 1.5 t 60 ; 90 1 S 4 7 ; 1 S T A B L E J O I N T E D RM : 6 1 276 END ; ! 6 ! ! COMP ; 5 ! o F O L I A T E D ! 1-5 ! 60 ; 55 ! t 6 i ! ! S T A B L E J O I N T E D RM : 6 ! 277 BACK ; ! 6 ! ! COMP ! 20 ! o BLOCKY ! 1.5 ; 20 ; 0 i ! 5 2 ! ! S T A B L E J O I N T E D RM I 7 278 BACK ! ! 4 j ! COMP ! 20 ! o BLOCKY ! 0.8 ! 20 ; o i ! 2 5 ! ! S T A B L E D I S C . BLOCK ! 7 279 BACK ! ; 4 | ! COMP ! 20 ! o B L O C K Y ; o.8 : 20 ; o ! I 7 s ; I C A V E J O I N T E D RM 3a : 8 280 BACK ; ! is ! ', COMP ! 20 ! o BLOCKY ! 2 ', 20 ! 0 ', 1 2 7 1 i S T A B L E D I S C . BLOCK 8 281 BACK ; ! 15 ! ; COMP ! 20 1 o BLOCKY ! 2 ! 20 ; o ! I 3 6 ! ! S T A B L E D I S C . BLOCK 1 » 282 BACK ; ! 25 ! ! COMP ! 70 1 o BLOCKY i 0.25 ! 70 ; o ! S 4 l ! I S T A B L E D I S C . BLOCK I 9 284 HW ; ! 9 ; RELAX ! ! Q ! o BLOCKY ! 0.5 ! 70 ! 70 | ! 7. 5 ! ! S T A B L E J O I N T E D RM ! >o 285 BACK ! ! 8 ! J COMP ! 15 1 o B L O C K Y ! 0.75 ! 15 ! o ! ! 6. 3 ! | U N S T A B L E J O I N T E D RM 3a TABLE 9.1 Background i n f o r m a t i o n f o r the d a t a base o f case h i s t o r i e s t h a t have used s u p p o r t , ( c o n t ) . J O I N T O R I E N T A T I O N FACTOR | E F F E C T O F G R A V I T Y i ! S I Z E ; ; BLOCK ! S T R E S S ! J ; AND ; ; S I Z E ! FACTOR ! ! C R I T I C A L BLOCK 1 SHEAR ; S L I D I N G ! F R E E P A L L / | 1 S H A P E | ! FACTOR 1 J O I N T S H A P E ! S T R E N . i i B U C K L I N G ! i FACTOR 1 M I N E C A S E PLANE ! 1 RQD ; J COMP R E L A X ! ! D I P ! STRK B L O C K Y / ! Jr ; C R I T I C A L ; S T O P E ! ; H Y D . ! ! A S S E S S . T Y P E O F F A I L f » ! / J n ! ! D I F F ! D I F F F O L I A T E D ! / J a ! J N T D I P ; P L A N E D I P ! ! RADIUS ; BEHAVIOUR MODE (1) (2) (3) ! ! (4> ; ! (5) (6) J ! (2) ! (8) (9) ! (10) : ( i i ) : (12) : i (13) ! : d 4 ) (15) (16) 10 286 HW ; ! s ! R E L A X I ! o ! o F O L I A T E D ! 0.75 J 70 ! 70 ! 1 io.o ; ; S T A B L E J O I N T E D RM 11 287 HW ; ! 30 ] R E L A X | ! o ! o F O L I A T E D ! 1 ', 90 ! 90 j i 19.7 J ; S T A B L E D I S C . BLOCK 13 289 BACK ! ! i » ! ! COMP ! 20 ! o BLOCKY ; 2 ! 20 i 0 ! : 6.2 i ; S T A B L E D I S C . BLOCK 15 290 BACK ! ! 6 ! ! COMP ! o ! o BLOCKY | 1.5 ! 20 ; 20 ; ! ii .4 ; ! C A V E J O I N T E D RM 3a 15 291 BACK ; ! 6 ; ! COMP ! o ! o BLOCKY | 1.5 ! 20 ; 20 ; ! s.o ; ; S T A B E J O I N T E D RM 15 292 BACK ! ; 6 ; ; COMP ! o ! o BLOCKY ! 1-5 ! 20 ! 20 ; ; 20.8 ; | C A V E J O I N T E D RM 3a 15 293 BACK ! ! 6 ; ; COMP ! o i o BLOCKY ! 1-5 ! 20 ! 20 ; | 9.2 ! j S T A B L E J O I N T E D RM 19 294 WALL ! ! 4 ; R E L A X ! ! o 1 o BLOCKY ! 0.5 ! 90 i 90 ; 1 19 .0 | ; C A V E J O I N T E D RM 3b 19 295 BACK ! ! 29 ! ; COMP ! o ! o BLOCKY ! 1-5 ! o ! o ; ; 3.7 ; ! S T A B L E D I S C . BLOCK 20 296 BACK ! ! I? ! 1 COMP : 20 ! o F O L I A T E D ! 1-5 i 20 : o ! ! 5.3 | ; S T A B L E D I S C . BLOCK 20 297 BACK ; | 25 ! ; COMP ! 20 ! o F O L I A T E D ! 2 i 20 ; o ; ! 9.0 ! ! S T A B L E D I S C . BLOCK 20 298 BACK j ', 25 i ; COMP | 20 ! o F O L I A T E D ! 2 ! 20 J o ! ! 3.9 ; ; S T A B L E D I S C . BLOCK 20 299 BACK ! ! > 7 ! ; COMP | 70 ! o F O L I A T E D ! 1-5 ! 70 ! o ! | 8.0 ! ! S T A B L E D I S C . BLOCK 22 300 BACK ; ! 9 ; 1 COMP ! 10 ! o F O L I A T E D ; i.s ! io ! o ; ! 4 . 7 ! ! S T A B L E D I S C . BLOCK 22 301 BACK ; ! 9 j ; COMP 1 10 ! o F O L I A T E D ; i.s ! io ! o 1 ! 7 . 7 i | C A V E J O I N T E D RM 3c 26 302 BACK ; ! 2 | ! COMP ; 20 ! o BLOCKY ; I .o ! 20 J o ! : 5.6 i ! S T A B L E J O I N T E D RM 26 303 BACK ! ! io ; ! COMP ! 20 ! o BLOCKY i 1.0 ; 20 ! o ! I 4.3 | ! S T A B L E D I S C . BLOCK 26 304 BACK ! ! 5 ; ! COMP ! ?o ! o BLOCKY ! i o ! 7 o ! o ! ! 2.7 ; ; S T A B L E D I S C . BLOCK 26 305 BACK | ; 2 ; ! COMP ! 20 ! o BLOCKY ; i.o ! 20 ; o ! ! 14 ! ; C A V E J O I N T E D RM 3a 26 306 BACK ; ! 5 ; ; COMP ! 20 ! o BLOCKY ; i.o 1 20 i o ; 1 9.3 ; i U N S T A B L E J O I N T E D RM 3 a 26 307 BACK ! ! i ! ; COMP ! 20 ! o BLOCKY ! i o 1 20 ; o 1 1 12.7 ; ; C A V E J O I N T E D RM 3a , 26 308 BACK ; ! 8 i 1 COMP 1 20 ! o BLOCKY ; I .o ; 20 ! o ! ! 146 j 1 S T A B L E J O I N T E D RM 1 26 309 BACK ; ; 15 : ; COMP I 20 ! o BLOCKY ! i.o ! 20 ; o ! ! 7.1 ; ! S T A B L E D I S C . BLOCK ! 26 310 BACK ; ! 25 ; ; COMP ! 20 ! o BLOCKY ; i.o ! 20 ; o I : s.o ; 1 S T A B L E D I S C . BLOCK ! 26 , 311 BACK ; ! 20 | ; COMP i 20 ! o BLOCKY ; i.o ', 20 ', o ; ', 7 . 4 | ', S T A B L E D I S C . BLOCK ! 26 312 BACK ; ! 5 | | COMP ! 20 ! o BLOCKY ; i.o ! 20 ! o ! 1 13.7 ; ! C A V E J O I N T E D RM 3a ! 26 313 BACK ; ! io i ; COMP | 20 ! o BLOCKY ; 1.0 ; 20 ; o ! ! io ! 1 S T A B L E J O I N T E D RM 26 314 BACK ; ! 20 ; ! COMP 1 20 ! o BLOCKY ; 1.0 1 20 ; o 1 ! 5.3 ; ! S T A B L E D I S C . BLOCK I 26 315 BACK ! ! 20 ; ; COMP ! 20 ! o BLOCKY ; i.o 1 20 ! o i ! 6.9 ; ! S T A B L E D I S C . BLOCK 28 316 HW ; ! 9 ! R E L A X J ! >5 ! o BLOCKY ; i.s i so ; 65 ; ! 8.4 ; i S T A B L E J O I N T E D RM 30 317 BACK ; I 14 ! ; COMP ! 60 ! o BLOCKY ! 1-5 ! 60 ; o ! ! 8.6 ; ! U N S T A B L E D I S C . BLOCK 3a 32 318 BACK | ! n ! ; COMP ! 70 ! o BLOCKY ; i.s ! 70 ! o ! ! 5.9 ; 1 S T A B L E D I S C . BLOCK I I I I I I I I i i i i i I I i I I I I i i TABLE 9.2 In p u t parameters f o r t h e d a t a base o f c a s e h i s t o r i e s t h a t have used s u p p o r t . ; BLOCK ; : SIZE i ; STRESS ; ! FACTOR | 1 JOINT ORIENTATION \ | FACTOR ! ! EFFECT ! OF GRAVITY •j CABLE BOLT DATA |CASE ! RQD ! ! oc/ ! ! CRITICAL Jr | 1 SLIDING ! FREEFALL/ ! ! HYD. ; N ASSESS. 1 !! SUPPORT BOLT BOLT BOLTING i; ; i ! / Jn ! 1 01 ; ! JOINT /J« ! ; ; SLABBINC ; ; RADIUS ! J ;; TYPE DENSITY LENGTH FACTOR ;; : (2) : (4) i : ( i2 ) i ! (18) do) : I (19) ! (20) ; ! (i j) ; (21) (14) j i! (22) (23) (24) (25) i i ! 251 ! 25 ! 1 0.25 ! ! 0.2 0.75 ; ! ! 2 o ! ! 8 4 ; 1 9 CAVE J ;; REBAR 0.7 2.2 5.1 i i J J 1 1 ! ;; CABLE 0.17 21 | j 1 252 ! 25 [ ! o.s i ! 0.2 0.75 J ! ! 2 o i : 8 4 ; 3 8 CAVE 1 I; REBAR 0.7 2.2 5. i ;; 1 j 1 1 ;; CABLE 0.17 21 ;; ! 253 ! 25 | i 0.25 ! ! 0.2 0.75 i ; i 2 0 i ; 5 3 1 9 STABLE 1 ;; REBAR 0.7 2.2 5.1 ; | ] | ! ! ! !; CABLE 0.17 21 ;; ! 254 ! is ; ! o . i ! i 0.2 3.0 i ! ; 2 o i : 6 4 2 2 STABLE 1 ;1 REBAR 0.7 2.2 5.1 ;; ! ! ! i | I! CABLE 0.17 21 j [ ! 255 ! 25 ! ! i.o ; i 0.2 0.75 i ! ! 8 o i i 5 o 30 STABLE ; 1| CABLE i.o ;; i 256 ! 18 ; i o. I i ! 0.2 3.0 ; 1 ! 2 o i i 5 9 2 2 STABLE 1 ;; CABLE 0.16 9 • i .7 ;! ] ] ; i j ;; REBAR 0.44 2.7 ;; J 257 ! is : ; o.i ; 1 0.2 3.0 ; ! ! 2 o ! ! 6 7 j 2 2 STABLE i ;; CABLE 0.16 9 1.7 | ; ! ; ! ; ; ;; REBAR 0.44 2.7 ;; 1 258 ! is : ! o. I | | 0.2 3.0 i ! ! 2 o I | 7 1 ] 2 2 STABLE | ;; CABLE 0. 16 9 1.7 ;; ] | ] ; J ;: REBAR 0.44 2.7 I j i 259 ', 18 1 i o. i ; ! 0.2 3.0 J ', ', 2 o ; J 4 6 i 2 2 STABLE ', i', CABLE 0.16 9 I .• 7 ; i ! [ I ; | 1; REBAR 0.44 2.7 1 1 1 260 ; is ; 1 o. I ! ; o.2 3.0 ; : ; 2 o ! ; 5 o ; 2 2 STABLE ! ;; CABLE 0.16 9 1.7 ;; ; ] ! | ; 1! REBAR 0.44 2.7 ;; ! 261 ! 14 ; i o.i ; ! 0.4 o.s ; I ! 2 6 ; i 13 9 ; 0 7 STABLE j ;; REBAR 0.7 2.4 6.8 ; j ; ; | [ | ;] CABLE 0.17 6 ;; ; ; ; ] ] ;; CABLE 0.17 24 j | | 262 : 14 ; ! o . i ; ; 0.4 0.5 i ! ! 2 6 : 1 16 o ! 0 7 CAVE ; ;; REBAR 0.7 2.4 6.8 ;; 1 ] j | - ; ;; CABLE 0.17 6 ; [ ; | ; ] 1 ;; CABLE 0.17 24 ; j ! 263 ! 6 ; i 0.36 j ; 0.2 0.7 i ! 1 2 4 ] ; 7 3 ! 0 7 STABLE 1 ;; CABLE 0.17 3 3.6 !| I | j j | ;; CABLE 0. 17 18 ] | ! 264 ! 4 ; 1 0.1 | ! 0.4 0.2 i 1 ! 2 o ; ! 6 o ; 0 1 STABLE ! ;; CABLE 0.17 3 3.6 : i ] | I I | ;; CABLE 0.17 18 ! | | 265 ! 6 ! i 0.35 '; ! 0.2 0.7 ; ] ! 2 4 ; i 8 o ; 0 7 STABLE ! ;; CABLE 0.17 3 5.1 || j | ; | ; ;; CABLE 0.17 18 ! | | | ! ] 1 !; CABLE 0.05 30 11 i 266 i 6 ; | 0.77 J ! 0.2 0.7 j ! ! 2 4 ! ! 14 8 ! 1 6 CAVE ! !; CABLE 0.17 3 3.6 | | i i | ] 1 ;; CABLE 0.17 18 ! | ! 267 ! 4 ; ! o.i ; ! 0.85 0.2 | ! ! 2 o ! ! 7 8 i 0 1 CAVE | ! ; CABLE 0.23 18 4.2 | | 1 268 ! 6 ; ! i.o j | 0.2 1.0 ! ! 3.5 J ! 8 9 ! 4 2 STABLE ! ;; CABLE 0.04 10 0.4 11 ! 269 : 6 ; ! 0.2 ; ; 0.2 i.o : ! ! 2 o i ; 4 4 ! 0 5 STABLE i ;! CABLE 0.2 3 0.6 | | J 270 ! 6 : ! o.i ; ! 0.2 1.0 | ! ! 2 o ! ! 5 3 ; 0 2 STABLE ! ;1 CABLE 0.2 6 1.1 | | ! 271 ! 2 ! ! o.i ; ! 0.5 1.5 ; ! ! 2 o ; | 5 3 ; 1 1 STABLE ! ;; CABLE 0.3 9 2.8 | | ! 272 ! 40 ! ! o.i ; ! i.o i.o ; ! ! 2 o ! : 6 2 | 8 0 STABLE 1 ;; CABLE 0.7 3 2.1 II ! 273 ! 6 ; 1 0.1 | ! 0.2 1.5 ! ! ! 2 o ! ; 2 6 ! 0 4 STABLE ! ;: REBAR 0.7 2 .4 3.0 | | j j j i [ ;; CABLE 0.24 6 I | » t i I I (i i I I i I I i i I I I i i i I I O TABLE 9.2 I n p u t parameters f o r t h e d a t a base o f c a s e h i s t o r i e s t h a t have used s u p p o r t , ( c o n t ) . BLOCK S I Z E S T R E S S F A C T O R J O I N T O R I E N T A T I O N FACTOR EFFECT OF GRAVITY iCASE ; RQD ! ! 0c/1 ! C R I T I C A L Jr ! S L I D I N G ! F R E E F A L L / | ; H Y D . ; N A S S E S S . ! ; ! SUPPORT BOLT BOLT B O L T I N G « I / Jn i ! oi ; J O I N T / Ja ; ; S L A B B I N G ; ; R A D I U S ; j | | T Y P E DENSITY LENGTH FACTOR (2) ! (*) ! : d 7 ) ! (18) (10) ! (19) ! (20) ; ! d 3 ) ! (21) (u) ; !! (22) (23) (24) (25) 274 ! « ! ! o . i ! 0.2 1.5 ! ! 2.0 | ! 4 2 1 0.4 S T A B L E ; ; ; REBAR | ! C A B L E 0.7 0.24 2.4 6 3.0 275 ! 6 I i 0.1 j 0.4 1.5 ! 5.0 ! j ! 4 7 ; 1.8 S T A B L E 1 ; ; C A B L E 0.06 9 0.5 276 ! 6 i j 0 .23 ! 0.25 1.5 ! ! 4.6 ! ! 6 i ; 2.4 S T A B L E ! ; | C A B L E 0.06 9 0.5 277 ! 6 i ; o . i ! 0.2 1.5 ! 1 2 . 0 ! ; 5 2 ! 0.4 S T A B L E ! ! ; C A B L E 0.23 9 2.1 278 ! 4 | ! o.i | 0.2 0.8 ! ! 2 . 0 ; ! 2 s ; 0.1 S T A B L E ! ; ; REBAR 0.4 2.4 1.1 279 ! 4 ! ! 0.2 ! 0.2 0.8 ; ! 2 . 0 ; ; 7 5 ; 0.3 C A V E ! ! ! REBAR 0.4 2.4 1.1 280 ! 15 ! ! 0.6 ! 0.2 2.0 ! ! 2 . 0 { ! 2 7 ! 7.2 S T A B L E ! ; ; REBAR 0.7 2.1 1.5 281 ! is ! ; o.s ; o.2 2.0 ! ! 2 . 0 ! ! 3 6 ! 9.6 S T A B L E ; ; ; REBAR 0.7 2.1 1.5 282 ! 25 ; ! o.i | 0.9 0.25 ! l 2 . 0 ; ! 4 i ; 1.1 S T A B L E ; ] ; C A B L E 0.1 15 1.7 284 ! 9 ! ! 0.45 : o.3 0.5 ! ; 6.o ; ! 7 5 ! 3 .6 S T A B L E ! 1! C A B L E 0.03 15 0.4 285 ! s ; ! 0.5 i 0.2 0.75 ! ! 2 . 0 ! ! 6 3 ] 1.2 U N S T A B L E I ; ; REBAR 0.7 2.4 0.7 286 ! 8 ; I 1.0 ! 0.3 0.75 ! ! 6 . 0 ; ! io o ! 11 S T A B L E ; ; ; REBAR 0.04 2.4 0.1 287 ! 30 ; ! l .o ! 0.3 1.0 ! [ s.o ! ! 19 7 ! 72 S T A B L E ; ; ! C A B L E 0.07 21 1.5 289 ! 1? ! ! i.o ! 0.2 2.0 ! ! 2 . 0 ! ! 6 2 ! 14 S T A B L E ; ; ! C A B L E 0.07 11 0.8 290 ! 6 ! ! 0.6 ; o.3 1.5 ! ! 2.4 ; ! l l 4 ; 3.9 C A V E J ; ; C A B L E 0.1 20 1.9 291 ! 6 ; ! l .o ! 0.3 1.5 ! ! 2.4 i : 8 o 1 6.5 S T A B E ; ; ; C A B L E 0. 1 20 1.9 292 ! 6 ! i 1 .0 J 0.3 1.5 ', ! 2.4 ; ; 20 8 1 6.5 C A V E i ; ; C A B L E 0.1 20 1.9 293 ! 6 ! ; l .o ; 0 . 3 1.5 ! | 2.4 ; ! 9 2 ! 6.5 S T A B L E ; ; ; C A B L E 0.1 20 1.9 294 ; 4 ; i 1.0 i 0.3 0.5 ! i 8.0 | ! 19 o ! 4.8 C A V E ; ! i C A B L E 0.02 6 0.1 295 ! 29 ! ; 0 . 2 ; o.3 1.5 ! | 2 . 0 ; ; 3 7 ; 5.2 S T A B L E ! ; ; C A B L E 0.15 6 0.9 296 ! i ' ! ! o.i ; 0 . 2 1.5 ; ! 2 . 0 ; ; 5 3 ! 1.0 S T A B L E 1 ; ; C A B L E 0.23 9 2.1 I 297 ! 25 ! ! 0.3 | 0.2 2.0 ! ! 2 . 0 | 1 9 o ! 6.0 S T A B L E ,' ; ; C A B L E 0.27 10 2.7 ! 298 ! 25 ; ! o. I ! 0.2 2.0 ! ; 2 . 0 ; : 3 9 ! 2.0 S T A B L E J ; ; C A B L E 0.2 5 1.0 ! 299 1 17 1 ; 0 . 3 ! 0.9 1.5 ! ! 2 . 0 ; : 8 o ! 11 S T A B L E i ; ; C A B L E 0.21 10 2.1 ! 300 ! 9 ! ; 0.1 I 0.2 1.8 1 ! 2 . 0 ; ; 4 7 ; 0.6 S T A B L E I ; ; C A B L E 0.22 12 2.7 ! 301 ! ' ; ! o.i ! . 0 . 2 1.8 1 ! 2 . 0 ; | 7 7 ! 0.6 C A V E ! ! ! C A B L E 0.22 12 2.7 ! 302 ! 2 ; ; l .o ; 0 . 2 1.0 ! i 2.0 | ; s 6 ] 0.8 S T A B L E ; ! ; C A B L E 0.33 10 3.3 ! 303 ! io ; | 1.0 ! 0.2 1.0 I ; 2.0 | ! 4 3 ; 4.0 S T A B L E J ; ; C A B L E 0.33 7.5 2.5 ! 304 ! 5 [ ! i.o ! 0.9 1.0 ! ! 2 . 0 | ! 2 7 ! 9.0 S T A B L E ! ; i C A B L E 0.37 7.5 2.8 ! 305 ! 2 ; ; i.o ; o.2 1.0 | ! 2.0 i ! 14 ! 0.8 C A V E ! ; l C A B L E 0 .22 10 2.2 ! 306 ! 5 ! ! i.o ! 0.2 1.0 ! ! 2 . 0 I ! 9 3 ; 2.0 U N S T A B L E | ; ; C A B L E 0.19 10 1.9 307 ! i ! ! i -0 ; o.2 1.0 ! ! 2 . 0 ! ! 12 7 ! 0.4 C A V E ; ! i C A B L E 0.28 10 2.8 308 ! 8 ; ! i.o i 0.2 1.0 ! ! 2 . 0 ; ! 14 6 ! 3.2 S T A B L E ! ! ! C A B L E 0 . 2 10 2 . 0 309 ! 15 ! ! 0.7 ! 0.2 1.0 ! ! 2 . 0 ; ; 7 i ! 4 .2 S T A B L E ; ; ; C A B L E 0 .16 15 2 .4 310 | 25 ! ! 0.7 ; o.2 1 .0 ! ! 2-0 ! ! 8 o | 7.0 S T A B L E ! ! ; C A B L E 0 .16 10 1.6 311 ! 20 | ! 0 . 7 ! 0.2 1.0 ! ! 2 . 0 ! ! 7 4 ; 5.6 S T A B L E J ;1 C A B L E 0.16 25 4.0 312 ! 5 ! ! 0.7 ! 0.2 1.0 ! ; 2 . 0 ; ! 13 7 ! 1.4 C A V E ! ; ; C A B L E 0.25 10 2.5 313 ! io ! ! 0.7 ! 0.2 1.0 ! ! 2 . 0 ; ! 10 ! 2.8 S T A B L E | ; ; C A B L E 0.16 18 2 . 9 314 ! 20 ; ! 0.5 ! 0.2 1.0 ! ! 2 . 0 ! J 5 3 ! 4.0 S T A B L E ; ; i C A B L E 0 .16 15 2.4 | 315 ! 20 ; ! 0.5 i 0.2 1.0 ! ! 2 . 0 | ; 6 9 ! 4.0 S T A B L E ! ; ; C A B L E 0.13 25 3.3 ! 316 ! 9 ! ! l .o ; 0 . 2 1.8 ! ! 5.5 ; ! 8 4 ; 18 S T A B L E j ; ; C A B L E 0.07 12 0.9 1 317 ! >4 ! ! o.i ! 0.8 1.5 ! ! 2 . 0 ; ! 8 6 : 3.4 U N S T A B L E ! ; ; C A B L E 0.11 15 1.7 ; sis ! 13 ! ; o.i : o.9 1.8 ! ! 2 . 0 ; ; 5 9 ! 4.2 S T A B L E ! ; ; C A B L E 0.31 6 1.9 C A B L E B O L T DATA been calculated for a l l s i x t y - s i x case h i s t o r i e s (table 9.2). They have been plotted on the revised s t a b i l i t y graph i n figure 9.9. The assessment of the cable bolted stope planes was d i v i d e d into three groups. Stable stope surfaces are represented by round shaped points. Cases where the support system f a i l e d are shown on the graph by t r i a n g l e s . The empty tr i a n g l e s represent f a i l e d cases where the cause was attributed to bad grouting. The square shaped points are the unstable cases where r a v e l l i n g of rock occurred between the cables. A couple of in t e r e s t i n g conclusions can be derived from figure 9.9. Most case h i s t o r i e s p l o t i n or below the t r a n s i t i o n zone between stable and caving. Assuming that the revised s t a b i l i t y graph i s accurate t h i s means that cable bolts in general have been used by open stope mine operators only when i t was necessary. Only one cable bolt support system had success when p l o t t i n g below the dashed l i n e drawn on figure 9.9, while twelve other attempts have been reported unsuccessful. This suggests that cable bolts are an impractical means of support when p l o t t i n g below the dashed l i n e because of the combination of bad ground condition and large openings. The only stable case was heavily bolted with three d i f f e r e n t sets of cables. The grey area of the support s t a b i l i t y graph (figure 9.9) 262 Modified Stability Graph Main Data Base 66 case histories 1000 CD _ Q 100 ^ 10 D CO -a T5 o 1.0 0.1 0 *^-*-* V.'.'.v.vvv'VC** 5 10 15 20 Hydraul ic Rad ius (m) 25 • Stable Stope Surface • Unstable Stope Surface T Caved Stope Surface FIGURE 9.9 The m o d i f i e d s t a b i l i t y graph f o r s u p p o r t e d case h i s t o r i e s . 263 shows the maximum unsupported stope surface dimensions that can be opened for d i f f e r e n t geotechnical conditions. The maximum cable bolted stope surface dimensions are defined by the dashed l i n e . The increase in possible stope dimensions can be roughly estimated for a given s t a b i l i t y number by subtracting the hydraulic radius corresponding to the grey area and the hydraulic radius at the dashed l i n e . The economical benefit of cable b o l t i n g can then be estimated. 9.4.2 Density of b o l t i n g The purpose of cable bolts i s to prevent the movement along e x i s t i n g d i s c o n t i n u i t i e s . Consequently the density of bo l t i n g should be related to the frequency of j o i n t i n g . The r a t i o of the block s i z e parameter (RQD/Jn) and the hydraulic r a d i u s of the stope surface are useful parameters in representing the r e l a t i v e size of blocks. I t i s expected that a higher density of bolting (closer spacing) should be used when the block s i z e i s r e l a t i v e l y small. Figure 9.10 shows a plot of the r a t i o of (RQD/Jn) and hydraulic radius, versus the density of b o l t i n g used in the case h i s t o r i e s . Only the cases involving stope backs are included in t h i s analysis. The convention regarding the shape of the points i s the same as the one i n the s t a b i l i t y graph in figure 9.9. Once again, several i n t e r e s t i n g observations can be made from t h i s data. The f i r s t observation i s the scatter of the data. This 264 FIGURE 9.10 Design Chart for Cable Bolt Density 0.40 0.35 0.30 H 0.25 H 0.20 H 0.15 0.10 0.05 0.00 1 2 3 4 5 6 (RQD/Jn) / Hydraulic Radius O Stable Stope Surface • Unstable Stope Surface v Caved Stope Surface implies that for s i m i l a r rock mass conditions the intensity of b o l t i n g used at d i f f e r e n t mines varied greatly. Some cases must have been designed conservatively while others have been nearly underdesigned. This also r e f l e c t s well the t r i a l and error approach used i n most cases. The horizontal dashed l i n e indicates that with only one exception, the minimum bo l t i n g density used i n open stope backs i s 0.1 cb/ m2. In the zone between the v e r t i c a l dashed l i n e and the y-axis only two cases have been reported stable out of a t o t a l of ten attempts. This suggest that cable bolts are not l i k e l y to be e f f e c t i v e when the r e l a t i v e block s i z e factor (RQD/Jn / hydraulic radius) i s smaller than 0.75. The band shown on figure 9.10 indicates the trend of using a higher density of b o l t i n g for smaller block s i z e (and smaller (RQD/Jn / hydraulic radius). I t can be noted that most cases p l o t t i n g i n s i d e t h i s zone are s t a b l e . Consequently, i t appears that a conservative design guideline for the density of b o l t i n g i s to use the centre of that zone. This corresponds to the average density of b o l t i n g used with success i n s i m i l a r rock mass conditions. 9 . 4 . 3 Cable b o l t length The length of cable bolts should reach far enough into undisturbed ground to insure a proper anchor. According to numerical modelling analysis, the disturbance e f f e c t of stress 266 i n the rock mass surrounding underground openings i s a function of the r e l a t i v e size and shape of i n d i v i d u a l stope surface. Consequently, a rough r e l a t i o n s h i p i s expected to e x i s t between the hydraulic radius of stope surfaces and the length of cable b o l t used. These two parameters have been plotted on figure 9.11, for the cases of supported backs i n the data base, and the following observations can be made. As i n the bo l t density plo t , figure 9.11 shows that the data i s quite scattered. Once again i t i s believed that t h i s can be attributed to the lack of guidelines for support design and a t r i a l and error process. The use of cable bolts i n very large open stope surfaces has had l i t t l e success. I t can be seen on figure 9.11 that for hydraulic radius exceeding ten, seven support systems out of nine have collapsed. The minimum stope plane dimension i n which cable bolts have been i n s t a l l e d has an hydraulic radius of approximately three. The minimum cable bolt length included i n the data base i s three meters. This was a r b i t r a r i l y decided p r i o r to the data c o l l e c t i o n i n order to d i f f e r e n t i a t e cable b o l t action and other kinds of shorter rock anchors. A rough and conservative guideline can be derived from the p l o t of cable bolt length and hydraulic radius. This i s shown on figure 9.11 by the l i n e "L" which correspond to a cable design approximately equal to the span of opening. It 267 FIGURE 9.11 Design Chart for Cable Bolt Length 30 - i 1 Hydraulic Radius (m) o Stable Stope Surface v Caved Stope Surface also constitutes an approximate average of what Canadian open stope operators have been using with success. 9 . 4 .4 Bolting factor The conditions i n which cable b o l t systems are capable of s t a b i l i z i n g open stopes have been defined i n figure 9.9, 9.10, and 9.11. In the s t a b i l i t y graph analysis i t seems reasonable to assume that the in t e n s i t y of bo l t i n g (density and length) should increase as a stope surface plots towards the dashed l i n e of figure 9.9. A p r a c t i c a l factor to account for the int e n s i t y of bo l t i n g has been developed and i s c a l l e d the bo l t i n g factor. The bol t i n g factor i s simply calculated by multiplying the density of bol t i n g (bolts/ square meter) and bolt length (meter). When used on the support s t a b i l i t y graph, the b o l t i n g factor i s expected to increase as a case i s located further below the grey area. Figure 9.12 i s a pl o t of the bol t i n g factors from the support data base and roughly shows the trend expected. However, the scatter of the data makes i t impossible to draw recommended design b o l t i n g factor l i n e s on the graph. 9.4.5 Cable b o l t o r i e n t a t i o n The design of cable b o l t orientation i s a three dimensional problem i n which the optimum s t r i k e and i n c l i n a t i o n must be defined. At the optimum orientation, the cable bolt system should develop a maximum strength against the forces 269 FIGURE 9.12 Modified Stabi l i ty Graph Bolting Factor 66 case histories 1000 Hyd rau l i c R a d i u s ( m ) • Stable Stope Surface • Unstable Stope Surface • Caved Stope Surface 270 acting on the cables. These forces are dependant on the pote n t i a l mode of f a i l u r e of the stope surface. For instance, in the case of gravity f a l l the p r i n c i p a l forces generated on the cables are t e n s i l e . The cable bo l t s should then be oriented v e r t i c a l l y i n order to maximise the t e n s i l e strength acting against gravity. For a s l i d i n g mode of f a i l u r e , the shear force acting along the pot e n t i a l s l i d i n g plane i s the one that may induce s t a b i l i t y problems. M i l l e r (1984) based on a three dimensional a n a l y t i c a l model suggested that cable bolts develop a maximum shear strength when i n s t a l l e d i n the same d i r e c t i o n as the shear plane but having an i n c l i n a t i o n of 17° to 27°. The optimum orientation of bol t i n g when dealing with slabbing or buckling mode of f a i l u r e i s perpendicular to the f o l i a t i o n because i t i s the d i r e c t i o n of pot e n t i a l movement. The intention i n t h i s case i s to clamp the layers of rock together. The mode of f a i l u r e can be e a s i l y determined using stereographic projection techniques or a simple "sketching" method described i n section 6.6. 9 . 5 SUMMARY The use of cable bolt support systems i n open stope mining has become increasingly popular and e f f i c i e n t . The o r i g i n a l problem of a lack of proper access for cable bolt i n s t a l l a t i o n 271 can be p a r t l y solved by using the support patterns described i n section 9.3.1 i n the case of stope backs and 9.3.2 for stope walls. Two important design concepts for the optimization of a support system have also been discussed. The concept of prereinforcement contributes to make the rock mass s e l f -supporting and helps to minimize the disturbance of the rock surrounding the opening during the excavation process. Consequently, when designing support systems, prereinforcement should be used whenever i t i s possible. The concept of s t i f f n e s s can have a large influence on the performance of a support system. In most applications i t i s desirable to match the s t i f f n e s s of the support system with the s t i f f n e s s of the rock mass. However, for s p e c i f i c applications i t might be useful to increase or decrease the s t i f f n e s s of the cable b o l t s . This can be done using special cable bolting i n s t a l l a t i o n techniques such as pretensioning or debonding. The three p r i n c i p a l variables to be designed i n a cable b o l t system are the density of bolting, the length of cable bolts and t h e i r r e l a t i v e orientations. The orientation of cable bolts should be designed according to the possible mode of f a i l u r e . When gravity f a l l or slabbing are anticipated, the cable should be i n s t a l l e d v e r t i c a l l y . In the case of s l i d i n g , the most e f f i c i e n t design i s when the cables are i n s t a l l e d at an angle between 17° and 27° to the shear d i r e c t i o n . Based on the compilation of actual Canadian experience, 272 some rough design guidelines have been proposed for the determination of density and length of cable b o l t s . I t has been found that a rough re l a t i o n s h i p exists between the density of b o l t i n g and the r e l a t i v e size of blocks formed by j o i n t i n g . Figure 9.10 can be used to estimate an appropriate density of bo l t i n g according to the block si z e factor (RQD/JN / hydraulic radius). S i m i l a r l y , the length of cable bolts has been related to the siz e and shape of the supported stope surface and figure 9.11 can a s s i s t i n the determination of adequate cable bolt length. It i s important to mention that these guidelines have not been used i n actual design at t h i s time and s t i l l need to be proven. Nevertheless, the guidelines appear to be conservative when compared with some past experience and o f f e r an int e r e s t i n g a l t e r n a t i v e to the t r i a l and error process. 273 CHAPTER 10 EXTERNAL FACTORS: BLASTING, BACKFILL AND TIME EFFECT 10.1 INTRODUCTION The e f f e c t of external factors on the s t a b i l i t y of open stopes i s well recognized by rock mechanics engineers, although the factors are hardly ever measured, monitored or accounted for i n a design procedure. The p r i n c i p a l reason for t h i s over-s i m p l i f i c a t i o n i s the lack of accessible monitoring technology and the fact that mining practices have evolved rapidly. In t h i s chapter, the e f f e c t of blast i n g , time, and b a c k f i l l in adjacent stopes w i l l be discussed q u a l i t a t i v e l y , based on observations of these external factors i n case h i s t o r i e s . The number of relevant case h i s t o r i e s i s s u f f i c i e n t to formulate hypotheses, but further work and a larger data base would be required to confirm some of them. 10.2 BLASTING EFFECT The p r i n c i p a l objective of a b l a s t design i s to obtain good fragmentation at the lowest possible cost, to avoid miss-f i r i n g and to minimize the v i b r a t i o n related damage done to the rock walls exposed to the bl a s t . The explosive energy released has the desirable e f f e c t s of fr a c t u r i n g the rock mass around the charge and r e l i e v i n g the hole burden. In a non optimum 274 b l a s t , t h i s energy may also create flyrock, temperature increases, a i r blasts and excessive ground vi b r a t i o n s . These w i l l r e s u l t i n a decrease of the rock mass qual i t y i n the stope walls and may cause potential s t a b i l i t y problems. Ideally, the e f f e c t of b l a s t damage i n a case history design analysis should be accounted for by c l a s s i f y i n g the rock mass a f t e r the b l a s t . However, i n practice, there i s no access to enter the stopes and map the walls a f t e r production has begun. In general, the rock mass i s c l a s s i f i e d i n the d r i l l i n g or mucking horizon, p r i o r to production. I t i s then assumed, that the error made i n (over) estimating the rock mass quality (due to over-looking the e f f e c t of b l a s t damage) i s included within the pr e c i s i o n and s e n s i t i v i t y of the design method. This w i l l be true only i f the b l a s t i n g practices are not excessive and are s i m i l a r to the majority of the data base conditions. This assumption i s confirmed for the majority of the cases shown on the modified s t a b i l i t y graph, figure 8.4. However, i n s p e c i f i c cases, the e f f e c t of b l a s t i n g on s t a b i l i t y was i s o l a t e d by the s t a b i l i t y analysis. 10.2.1 Case h i s t o r i e s of b l a s t induced damage The e f f e c t s of bl a s t induced damage was observed in several case h i s t o r i e s at d i f f e r e n t mines. For instance at Ruttan, Pakalnis (1986) documented the percent d i l u t i o n a t t r i b u t e d to b l a s t i n g for his entire data base (which i s included i n t h i s study's complementary data base). On the 275 s t a b i l i t y graph (figure 10.1), the s t a b i l i t y p r e d i c t i o n of case numbers 70, 107, 121 and 12 6 i s stable, which i s not i n accordance with the actual assessment. For a l l these cases, the d i l u t i o n induced by bl a s t i n g was between 3% and 7%. The e f f e c t of bl a s t i n g was also observed i n four other case h i s t o r i e s (170, 171, 172, 175, see figure 10.1) from mine number 31 of the data base. Once again, stopes that should have been at lea s t marginally stable, have suffered large ground f a l l s . Blasting induced damage i s suspected as being part of the problem since t h i s mine uses the mass blast technique described i n section 2.6.3. The amount of explosive f i r e d simultaneously i n the mass bl a s t i s several times greater than that of regular practices. I t can surmised that other cases of b l a s t i n g induced damage have occurred but could not be is o l a t e d by the s t a b i l i t y graph analysis because b l a s t i n g was not the predominant cause of caving. Cases 71, 78, 79, 82, 83, 109, 118, 119, 123, 124 (figure 10.1) from the Ruttan study have a l l experienced more than 5% d i l u t i o n related to blas t damage. 10.2.2 Blast monitoring and pre d i c t i o n of b l a s t damage S i g n i f i c a n t progress has been made in recent years, in using monitoring systems to quantify b l a s t induced damage and to optimize b l a s t design. A bl a s t can be monitored by measuring the vi b r a t i o n waves created by the explosion. Some of the energy released by the blast , t r a v e l s at the speed of 276 FIGURE 10.1 Modified Stabi l i ty Graph BLASTING DATA BASE 18 case histories 1000 0.1 5 10 15 Hydraul ic Rad ius (m) 20 25 complementary data base ""^^ J main data base Stable Stope Surface • • Unstable Stope Surface v • Caved Stope Surface 277 sound into the unbroken rock i n the form of a pressure wave. There are three types of wave motion: compressional, shear, and r a l e i g h . The pressure wave causes ground p a r t i c l e s to move. This movement, can be compared to a cork bobbing on water. The displacement of a p a r t i c l e i s the distance t r a v e l l e d from i t s s t a t i c p o s i t i o n . I f movements are within the e l a s t i c l i m i t s of rock, no breakage occurs and the material w i l l recover to i t s o r i g i n a l shape and volume. If movements exceed the e l a s t i c l i m i t s , breakage occurs as the rock mass i s pulled apart in tension. The p a r t i c l e v e l o c i t y i s the speed at which the ground p a r t i c l e s have moved. By measuring the v e l o c i t y of rock p a r t i c l e vibrations, the size and strength of a pressure wave can be determined and related to damage c r i t e r i a . The p a r t i c l e v e l o c i t y can be measured by recording audio frequency signals from the bla s t . The dynamic range necessary to capture the peak amplitude i s i n the order of 50 inches per second at frequencies over 1000 Hz. The peak p a r t i c l e v e l o c i t y i s the highest v e l o c i t y value attained at a given point and time, by a passing wave. The analysis of the v i b r a t i o n trace allows the determination the peak p a r t i c l e v e l o c i t y . Rock fracture i s associated with peak p a r t i c l e v e l o c i t y l e v e l s of approximately 25 to 40 inches per second or higher, 278 depending on the rock quality and geological conditions. Table 10.1. shows how peak p a r t i c l e v e l o c i t y i s related to the amount of rock damage. Page (1987) proposed a s l i g h t l y refined r e l a t i o n s h i p by accounting for three types of rock mass quality ( t a b l e 10.2). Page has also empirically developed a r e l a t i o n s h i p between the peak p a r t i c l e v e l o c i t y and the percentage reduction i n the rock mass qual i t y i n terms of Q (Barton et al) and MRMR (Laubscher) (see figure 10.2). This technology, when b e t t e r understood and documented, may ultimately generate enough accurate data to develop a r e l i a b l e b l a s t correction factor c a l i b r a t e d i n function of the s t a b i l i t y graph design method. 10.2.3 Optimization of b l a s t design f o r wall s t a b i l i t y The amount of damage caused by b l a s t i n g w i l l be minimized i f the ground vibrations and peak p a r t i c l e v e l o c i t y are kept low. This can be achieved by optimising: the bl a s t pattern and geometry, the charge weight per delay, and the b l a s t sequencing. The amount of burden, as shown i n figure 10.3, i s c r i t i c a l for the r e l i e f and fragmentation of the rock mass. In open stope mining, t h i s burden i s l a r g e l y a function of the d r i l l h o l e s i z e . Large diameter blastholes, t y p i c a l l y have a burden of approximately 3 metres, while a burden of 1.2 to 1.8 metres i s often used for small hole diameters. The most common longhole 279 PPV Resulting condition on rock in/s structure 10-12 falls of rock in unlined tunnels: no fracturing of intact rock 12-25 minor tensile slabbing will occur 25-100 strong tensile and some radial cracking will occur >100 complete break-up of rock mass TABLE 10.1 R e l a t i o n s h i p between the peak p a r t i c l e v e l o c i t y and the r e s u l t i n g c o n d i t i o n on rock s t r u c t u r e . ( A f t e r A t l a s Powder company, 1987) ROCK MASS QUALITY STABILITY THRESHOLD DAMAGE LIMITS PPV mm/s in/s POOR MARGINAL HIGH 200 8 600 25 GOOD MARGINAL HIGH 600 25 2000 80 UNFAVOURABLE JOINTING (Unstable Key Blocks) MARGINAL HIGH 100 4 600 25 TABLE 10.2 R e l a t i o n s h i p between the peak p a r t i c l e v e l o c i t y , the rock mass q u a l i t y and the r e s u l t i n g s t a b i l i t y o f a stope. 280 1000 2000 3000 4000 P t i k P a r t k l e V e l o c i t y m m / i FIGURE 10.2 R e l a t i o n s h i p between the r e d u c t i o n i n r o c k mass q u a l i t y and the peak p a r t i c l e v e l o c i t y o r i g i n a t i n g from a b l a s t . ( A f t e r Page, 1987) 281 FIGURE 10.3 co CO to THE EFFECT OF REDUCBNG THE BURDEN ON A CHARGE OF CONSTANT ENERGY TOP VIEW Confined (few cracks, charge ejection) Cracks on face (no relief) Optimum crater (ful relief, good fragmentation) Overblast (flyrock, noise) and blasthole d r i l l i n g patterns have been discussed i n chapters 2.5.1 and 2.6.1. The amount of explosive detonated at one time also has a large influence on the b l a s t vibrations generated (peak p a r t i c l e v e l o c i t y ) . The cube root s c a l i n g equation i s an empirical, s i t e c a l i b r a t e d r e l a t i o n s h i p which can be used to estimate the peak p a r t i c l e v e l o c i t y at a distance "D", associated with the charge detonated "W". VELOCITY = K( D / ( W ° ' 3 3 ) ) ~ m The cube root scaling equation i s useful to estimate the maximum amount of explosive per delay that can be used without damaging the stope walls. In blasthole mining, i t w i l l be found that the decking and decoupling of charges i s a p r a c t i c a l means of lowering the bl a s t vibrations. F i n a l l y , the sequencing of the b l a s t i n g and the delay i n t e r v a l between in d i v i d u a l detonations must be long enough to eliminate of p o s s i b i l i t y of v i b r a t i o n wave superposition. Figure 10.4 shows an i d e a l i z e d wave packet from an iso l a t e d detonation, a two wave packet of a properly delayed p a i r of detonations and a wave packet from two improperly delayed detonations. In the t h i r d s i t u a t i o n , the wave amplitude and peak p a r t i c l e v e l o c i t y from the packet are superimposed because the delay was too short. This could r e s u l t i n bl a s t induced damage. 10.3 EFFECT OF BACKFILL IN ADJACENT STOPES 283 FIGURE 10 .4 The e f f e c t of d e l a y i n g d e t o n a t i o n decks on the r e s u l t i n g wave packets. ( A f t e r S p r o t t , 1986) to CO wave packet from one deck detonation *\]— /^jM/vw— J - -I a t wave packets from two properly delayed decks ^ll^f^ V^Arw- * > A t |: -id, A t resulting wave packet from two improperly delayed decks A X 2 A X 2 » Xj d t < A t The present trend i n open stoping i s towards t o t a l l y recover the orebody, which in most case means mining against cemented b a c k f i l l walls. Although i t i s not intended to review thoroughly the subject of b a c k f i l l i n open stope mining, the e f f e c t of b a c k f i l l (in adjacent stopes) on the s t a b i l i t y analysis w i l l be investigated. B a c k f i l l provides passive support counter acting the displacement of the walls towards the opening and gives some confinement i n the d i r e c t i o n of movement. I f t h i s confinement i s s u f f i c i e n t , i t can be assumed that the t o t a l e f f e c t i v e opening span i s limi t e d by the b a c k f i l l . 10.3.1 E f f e c t of b a c k f i l l i n l i m i t i n g walls and back exposure Figure 10.5 i l l u s t r a t e s a common s i t u a t i o n when mining with b a c k f i l l . The mining block has four stopes; stopes 1 and 3 are b a c k f i l l e d , stope 2 i s empty and mining i n stope 4 has not started yet. For the s t a b i l i t y analysis of the roof (plane B) and the wall (plane E) of stope 2, two hypotheses w i l l be formulated: 1) The surface to be designed for the wall of stope 2 i s the surface of plane E, which implies that b a c k f i l l e f f e c t i v e l y l i m i t s the exposure of the b a c k f i l l e d walls (plane D and F). 2) The designed surface of the stope back i s the summation of a l l the backs of consecutive b a c k f i l l e d and empty stopes 285 286 (plane A + plane B + plane C) . I t i s assumed that the b a c k f i l l i s not t i g h t enough against the back to have a s i g n i f i c a n t e f f e c t on confinement, and therefore does not e f f e c t i v e l y l i m i t the t o t a l stope back exposure. However, i f a back caving occurs, part of the f a i l e d rock may s i t on b a c k f i l l r e s t r i c t i n g most of the emptied stope back (plane B) . It should be noted that a common assumption made i n numerical modelling i s to ignore the b a c k f i l l meaning stress i s not transmitted through that medium. In the determination of the induced stress oy for each stope surface, the b a c k f i l l e d stopes w i l l be considered empty. 10.3.2 Case h i s t o r y analyses The implications of the above hypothesis w i l l be described with respect to case h i s t o r i e s from mine #19, which uses a transverse blasthole mining method (ref. section 2.6). An ide a l i z e d isometric view of the mining block i s shown on figure 10.6. The stope dimensions are i d e n t i c a l on each l e v e l : 11m long, 23m wide and 60m high for the bottom l e v e l , and 11m x 23m x 45m for the top l e v e l . The sequence of extraction i s indicated on the stopes by c i r c l e d numbers. I t i s a v a r i a t i o n of the leap frog sequence described i n section 2.4.2. The mining of a l l primary stopes (stopes 1 to 18) was completed with no s t a b i l i t y problems i n the roof or walls. As shown 287 FIGURE 10.6 I d e a l i z e d i s o m e t r i c v iew o f t h e m i n i n g b l o c k a t Mine #19 o f the d a t a b a s e . T R A N S V E R S E B L A S T H O L E O P E N S T O P I N G below, the back analysis of case h i s t o r i e s 59 (hanging wall) and 57 (roof) are i n accordance with t h i s assessment (see Figure 10.7) . RQD/Jn STRESS CRITICAL Jr / J a GRAVITY N S ASSESS FACTOR JOINT FACTOR MENT WALL 4 1 0.3 0.5 8.0 4 . 8 4 . 5 Stable #59 BACK 29 0.2 0.2 1.5 2.0 3.5 3.7 Stable #57 In the mining of the t e r t i a r y stopes (between two b a c k f i l l e d walls), the hanging walls of stope 19 to 34 remained stable but the backs experienced considerable de t e r i o r a t i o n and systematic cable bolt support had to be i n s t a l l e d i n a l l the t e r t i a r y backs. This w i l l allow the t e s t i n g of the hypothesis regarding b a c k f i l l (mentioned above). a) T e r t i a r y hanging walls: Supposing that hypothesis 1) i s true and b a c k f i l l e f f e c t i v e l y l i m i t s the stope wall dimensions to the exposure of the empty stope, the s t a b i l i t y number and hydraulic radius of t e r t i a r y walls w i l l remain i d e n t i c a l to the ones calculated for primary walls, case #59 (see figure 10.7, case #59). This i s i n accordance with the stable t e r t i a r y wall assessment. I f hypothesis 1) i s false and the b a c k f i l l does not e f f e c t i v e l y l i m i t the wall exposure, then the hydraulic radius of the t e r t i a r y walls would be calculated based on a hanging wall exposure of at least three stope lengths (stope 19, 2 and 8 i n figure 289 FIGURE 10.7 Modified Stabili ty Graph cases of backfilled stopes 1000 0.1 5 10 15 20 Hydraul ic Radius (m) 25 o Stable Stope Surface • Unstable Stope Surface • Caved Stope Surface 290 10.6). The new hydraulic radius would be 10.6 and the s t a b i l i t y number i s s t i l l 4.8. This plots i n the caving zone (see figure 10.7, case 59-) which i s not i n accordance with the actual assessment. Both of the above analyses support hypothesis 1) regarding the e f f e c t of b a c k f i l l i n adjacent walls. b) T e r t i a r y backs: The hypothesis 2) for t e r t i a r y backs i s th a t b a c k f i l l does not e f f e c t i v e l y l i m i t the back dimensions, and b a c k f i l l e d stopes should be considered empty in the analysis. The hydraulic radius of the t e r t i a r y back w i l l be calculated for an exposure of three times the stope lengths and the stope width. The s t a b i l i t y number remains 3.5 but the hydraulic radius increases to 6.8 which plots in the caving zone of the s t a b i l i t y graph (figure 10.7 case 57 + ) . This i s in accordance with the s t a b i l i t y problems reported, and the need for cable bolt support of the back. Supposing the hypothesis 2) was incorrect and the b a c k f i l l e f f e c t i v e l y l i m i t s the stope backs, then the analysis of the t e r t i a r y backs would be s i m i l a r to that of primary backs (case 57) . A stable "prediction" for the t e r t i a r y backs does not f i t the actual assessment. These hypotheses have been v e r i f i e d for a number of other cases. However, monitoring, instrumentation and more case h i s t o r i e s would be required to prove them systematically. 291 10.4 THE TIME EFFECT The time e f f e c t i n hard rock mining can be considered i n two d i f f e r e n t perspectives. The f i r s t perspective i s when there i s no mining a c t i v i t y i n the stope area to create dynamic loads (such as changes i n stress or b l a s t i n g v i b r a t i o n ) . In t h i s case, the time e f f e c t w i l l be d i r e c t l y associated with the sources of rock mass a l t e r a t i o n (mainly ground water). Since open stope extraction i s usually rapid (less than one year) and open stope mines i n the Canadian Shield are usually dry, the time e f f e c t w i l l not be s i g n i f i c a n t i n dormant mining conditions. I t was possible to observed t h i s absence of the e f f e c t of time i n some case h i s t o r i e s where open stope mining (with no b a c k f i l l ) was used and the stopes remained open for a long period of time. These cases are plotted i n figure 10.8. At the time of the back-analysis, the stopes had been open for more than one year (sometimes several years) and no signs of i n s t a b i l i t y had been reported, even though t h e i r s t a b i l i t y analysis plotted close to the grey area (see figure 10.8). The second perspective of the time e f f e c t can be considered when there are mining a c t i v i t i e s i n the area. The dynamic loads induced by mining may cause premature f a i l u r e during the stope extraction. Most of the case h i s t o r i e s of i n s t a b i l i t y and caving included i n the database can be 292 F I G U R E 1 0 . 8 Modified Stabi l i ty Graph TIME EFFECT DATA BASE 17 case histor ies 1000 • • i . I — Hydraul ic Rad ius (m) • Stable Stope Surface • Unstable Stope Surface T Caved Stope Surface 293 c l a s s i f i e d i n t h i s group. Although the s t a b i l i t y of stope surfaces has shown rapid deterioration with time, the possible sources of i n s t a b i l i t y are numerous and varied which make an exact q u a n t i f i c a t i o n of the (short term) time e f f e c t nearly impossible. However, when the design analysis predicts s t a b i l i t y problems, caving i s expected to occur within a short period of time and l i k e l y during the extraction process. 10.5 SUMMARY AND CONCLUSION The e f f e c t s of blasti n g , b a c k f i l l and time in the s t a b i l i t y analysis are discussed i n t h i s chapter and are based on the observation of these external factors i n s p e c i f i c case h i s t o r i e s . For the blas t i n g e f f e c t , i t w i l l be assumed that the reduction i n s t a b i l i t y i s within the s e n s i t i v i t y and accuracy of the design method, unless excessive bl a s t i n g techniques are used. The amount of b l a s t induced damage can be minimized by optimising the d r i l l i n g patterns, the charge weight per delay and the sequence of the b l a s t i n g . The development of b l a s t monitoring techniques allows the measurement of the peak p a r t i c l e v e l o c i t y associated with each detonation, which can be related to b l a s t induced damage. Ultimately, t h i s may o f f e r a means for the development of a bl a s t correction factor for the s t a b i l i t y graph design method. The presence of b a c k f i l l i n adjacent stopes i s a very common s i t u a t i o n i n open stope mining. I t i s suggested that the three following assumptions can be used to account for t h i s e f f e c t i n the s t a b i l i t y analysis; 1) Stope walls are supported by b a c k f i l l and only the surface are a c t u a l l y exposed to empty openings should be considered i n the c a l c u l a t i o n of the hydraulic radius. 2) Stope backs are not generally supported by b a c k f i l l and the t o t a l surface exposed by a l l the consecutive empty and b a c k f i l l e d stopes should be considered i n the c a l c u l a t i o n of the hydraulic radius. The e f f e c t of time on stope s t a b i l i t y can be assumed n e g l i g i b l e when dealing with stopes that are remote from mining a c t i v i t i e s , because the t y p i c a l l y dry conditions of Canadian open stope mines r e s u l t only i n a slow det e r i o r a t i o n of exposed rock mass. When stopes show a rapid d e t e r i o r a t i o n of s t a b i l i t y with time, i t i s generally due to mining a c t i v i t i e s in the v i c i n i t y of the stopes. In these conditions the time e f f e c t i s nearly impossible to d i f f e r e n t i a t e from the e f f e c t s of dynamic loading due to mining. The e f f e c t of external factors i n the s t a b i l i t y analysis can make the difference between a stable and a caving prediction. Consequently, i t i s ess e n t i a l to understand these e f f e c t s and attempt to take them into account i n the design analysis. Although the assumptions regarding the e f f e c t s of external factors have not been confirmed by a large number of case h i s t o r i e s , the explanations are i n accordance with the 295 case h i s t o r i e s of the data base. Future work should be undertaken to improve the confidence i n the above assumptions, which w i l l contribute to the accuracy of the s t a b i l i t y p redictions. 296 CHAPTER 11 SUMMARY AND CONCLUSION 11.1 SUMMARY The problem investigated i n t h i s thesis i s the design of open stopes i n t y p i c a l Canadian geological settings. The geomechanics investigation focus on the e f f e c t of creating a s p e c i f i c type of opening i n a var i e t y of rock mass media and submitting them to mining related dynamic loads. For s i m p l i f i c a t i o n , the problem was subdivided into three aspects: the c h a r a c t e r i s t i c s of the rock mass, the r e d i s t r i b u t i o n of i n s i t u stress, or the stress induced on the stope surfaces, the physical condition of the problem including stope geometry and i n c l i n a t i o n , cable bolt, b l a s t i n g , b a c k f i l l and the e f f e c t of time. Each of the above aspects i s divided into factors i n order to qu a n t i f y and c a l i b r a t e the possible sources of ground i n s t a b i l i t y . The rock mass c h a r a c t e r i s t i c s are represented by the block si z e and the c r i t i c a l j o i n t factors. The e f f e c t of stress i s accounted for by the stress induced factor, which i s based on three dimensional numerical modelling. The physical condition of the problem includes the stope si z e and shape factor (hydraulic radius), the gravity factor and the external factors. Each factor i s quantified by a combination of parameters (geotechnical or geometrical) . Most of the parameters are estimated from f i e l d i nvestigation, r e l y i n g on observational methods such as rock mass c l a s s i f i c a t i o n , j o i n t mapping and the study of mine layouts. The methodology of design and the organization of the input data i s s i m i l a r to the one proposed by Mathews et a l . (1980). Figure 11.1 i s a graphical presentation of the open stope design method. It shows how the parameters combine into factors and how the s t a b i l i t y analysis i s developed. The main hypothesis of the study i s : "The s t a b i l i t y of open stopes can be predicted by quantifying the e f f e c t of the rock mass c h a r a c t e r i s t i c s , the stress induced at the stope surfaces and the physical conditions of the problem". The v e r i f i c a t i o n of the hypothesis involves the a p p l i c a t i o n of the model described i n figure 11.1 i n the back-analysis of a large number of representative case h i s t o r i e s . I f the actual stope behaviour corresponds to the model's prediction on the modified s t a b i l i t y graph, the hypothesis w i l l be v e r i f i e d . Figure 8.4 shows a plot of the t o t a l data base of unsupported stopes. The cle a r separation between stable and caving cases confirm the design method (and the hypothesis) for stopes not using cable bolt reinforcement. The e f f e c t of external factors on the design analysis i s summarized as follows: The s t a b i l i z i n g action of cable bolts allows the design of stope dimensions, below the t r a n s i t i o n area of the modified s t a b i l i t y graph (see figure 9.9). However, a minimum in t e n s i t y of b o l t i n g i s necessary to maintain 298 663 CRITICAL JOINT FACTOR B L O C K SIZE F A C T O R •4h > 2 . O i t o S FFEREN IP ic S 0.2 -JOIN NUMB 0.5 -ICE 1 TRIKI 1.0 m -H _ ° s l i s s 5 > COMPRESSIVE S T R E S S FACTOR P c — o > > CD O > Tl GRAVITY FACTOR m — =•3 z: o 2 -n C ""I > m - u i O =d -H POTENTIAL EXTERNAL F A C T O R S POTENTIAL EXTERNAL FACTOR O -O S z o ? > c O m * z 3 n 1 I II •••• -CO to to SI " i t o CO •-3 > i — i t—i Q > -3. O a o o CO o w o CO I—I Q STOPE P L A N E SIZE AND S H A P E FACTOR s t a b i l i t y , and the necessary i n t e n s i t y i s expected to increase as a case plots further into the caving zone (figure 9.12). A p r a c t i c a l l i m i t to the a p p l i c a b i l i t y of cable b o l t i n g i n open stope mining i s indicated by the dashed l i n e i n figure 9.9. The e f f e c t of b l a s t i n g i s to decrease the q u a l i t y of the rock mass i n walls exposed to the e f f e c t of the b l a s t . I t w i l l be assumed that, for normal b l a s t i n g practices, t h i s e f f e c t i s b u i l t into the model's c a l i b r a t i o n , and i s within the precision of the design method. This i s supported by the good c o r r e l a t i o n obtained between stope predictions and actual stope assessments for the t o t a l data base (see figure 8.4), and the fact that cases of excessive b l a s t i n g practices were i s o l a t e d i n the analysis graph (figure 10.1). The e f f e c t of b a c k f i l l i n adjacent stopes i s taken into account by two assumptions: b a c k f i l l e f f e c t i v e l y l i m i t s wall exposure, and the b a c k f i l l does not e f f e c t i v e l y l i m i t back exposure. The e f f e c t of time, when there are no mining a c t i v i t i e s i n the investigated stope area, can be considered n e g l i g i b l e . No signs of i n s t a b i l i t y have been noticed in the case h i s t o r i e s shown i n figure 10.8, which have been open for a period of time exceeding one year. When a stope i s not i s o l a t e d from mining a c t i v i t i e s , the dynamic loads a s s o c i a t e d with mining may induce 300 premature f a i l u r e . The stope stand-up time i n these conditions was evaluated only i n function of the entire stope l i f e . Figure 8.4 shows the case h i s t o r i e s that have been stable for t h e i r f u l l stope l i v e s , and the stopes that have caved at one time during t h e i r l i f e . 11.2 APPLICABILITY OF THE DESIGN METHOD The design method proposed i n t h i s t h e s i s was developed for open stope mining methods i n geological conditions si m i l a r to those encountered i n the Canadian s h i e l d . Open stope mining i s better suited to steep dipping orebodies (dip greater than 50°), having a r e l a t i v e l y regular d e f i n i t i o n , and a minimum width of approximately 5 meters. Because the stope roof and walls must be s e l f supporting, a f a i r to good rock mass quality i s desirable for the ore zone and the country rock. In appendix 1, the orebody shape of the open stope mine included in the data base has been drawn, along with the mining method used and the geotechnical c h a r a c t e r i s t i c s of the ore, hanging wall and footwall. Open stope mining i s a non entry mining method which means mine workers are not exposed to the production face. Consequently, a cert a i n degree of i n s t a b i l i t y can be tolerated, as long as adjacent mine workings are not affected and the d i l u t i o n does not become excessive. The c a l i b r a t i o n of the proposed design method w i l l be non conservative i f used with 301 entry mining methods. Open stope mining also involves fas t extraction r e s u l t i n g , in s i g n i f i c a n t mining related dynamic loading. The e f f e c t of frequent changes i n stope dimensions, stope geometry and large production blasts may play an important role i n the s t a b i l i t y of open stopes. 11.3 INDUSTRY BENEFITS FROM THIS STUDY There are several potential benefits i n using the systematic open stope design method proposed here. The most important one i s the reduction i n stope d i l u t i o n . Bawden (1988) described the economical impact of d i l u t i o n as follows: " I f we assume basic costs of $5.00/ton for m i l l i n g and crushing, $2.00/ton for mucking and haulage and $1.00/ton for h o i s t i n g then, for a " t y p i c a l " open stope hanging wall of say 100m x 30m, each meter of wall d i l u t i o n which i s hoisted and m i l l e d reduces the p r o f i t a b i l i t y of the stope by over $100,000.00. A l t e r n a t i v e l y , i f the d i l u t i o n r e s u l t s in plugging of the drawpoints, serious production delays and secondary b l a s t i n g costs may be incurred. In the worst case, the stope may be l o s t . " Bawden (1988) also provided a table showing the large influence of d i l u t i o n on the ROR of a zinc orebody (see table 11.1). Another benefit of t h i s design approach i s i n providing a c l e a r understanding of the rock mass medium behaviour and 302 TABLE 11.1 Importance o f d i l u t i o n on t h e DCF ROR. ( A f t e r Bawden, 1988) Zinc Tomagt Grade Mining Rata : 2,500.000 torn 20X Zn 360,000 tpy DILUTION % OK MK 20X JOK 40X Tomaae 2.500.000 2.780,000 3.130.000 3.570.000 4.170.000 Grade 20.OX 18.0X 16.0X 14.0X 12.0X Mining Rat* 360,000 360,000 360.000 360.000 360.000 Nina Lift, yr». 6.9 7.7 8.7 9.9 11.5 o U ) Natal Recovery 85X BSX 85X 85X 85X *7n/ton 340 304 272 238 204 •Zn/yr 1.22*10® 1.OtalO8 0.98x10S O.SSxIO8 0.73x10* Nina Revenuee/yr (25c/lb) $30.50x10* $27.25x10* $24.S0x106 •21.25*10* $18.36x10* All Nina Coata (U0/T) $14.4x10* •14.4*10* $14.4x10* $14.4x10* •14.4K10* Operating Proflta $16.10x10* $12.85x10* $10.10x10* •6.85x10* $3.9x10* Taxes (50X of O.P.) $a.osxio* 06.41x10* •5.05x10* $3.43x10* $1.98x10* Nat Profit $8.05x10* $6.43x10* •5.05*10* $3.43x10* $1.98x10* Capital Coat of Nina $2.5x10* • - • -0CF ROR 25.5X 18.9X 13.5X 6.0X •1.5X giving the means for a n t i c i p a t i n g f a i l u r e mechanisms that may occur during the stope extraction. This w i l l r e s u l t in better engineered design of mine structure and support components as well as a safer mining environment. The design concepts developed during t h i s study have been applied with success i n several Noranda mines for actual design. This work i s documented i n Bawden et a l (1988), Bawden, Nantel and Sprott (1988) and i n a series of internal report l i s t e d i n the bibliography. 11.4 FUTURE WORK The future improvements to t h i s design approach should concentrate on the e f f e c t of external factors. Some progress has been made in accounting for the e f f e c t of cable bolts, b l a s t i n g , b a c k f i l l and time i n the design analysis. This has been r e a l i z e d e n t i r e l y based on the i n t e r p r e t a t i o n of case h i s t o r i e s . However, a much greater degree of pr e c i s i o n can be achieved i n accounting for the above e f f e c t s with systematic monitoring programs. In recent years, s i g n i f i c a n t progress has been made i n the development of e f f i c i e n t monitoring tools for underground b l a s t i n g (peak p a r t i c l e v e l o c i t y measurements) which may lead to a b l a s t correction factor i n the design analysis. The range of e f f i c i e n c y of cable bolts has been defined and rough guidelines r e l a t i n g ground conditions, stope size and 304 shape, and the required i n t e n s i t y of b o l t i n g have been developed. Once again, a greater data base and the use of monitoring techniques such as cable bolts s t r a i n and tension gauges can improve the pr e c i s i o n and r e l i a b i l i t y of the cable b o l t design guidelines. There are also a cer t a i n amount of personal interpretation s p e c i f i c a l l y i n the c l a s s i f i c a t i o n of the rock mass, which could be reduced i f an instrumented system for c l a s s i f y i n g the rock mass existed. This i s another important area of research that could improve actual stope design. 11.5 CONCLUDING REM/ARKS The actual trend i n rock mechanics i s towards a greater use of computer technology and numerical modelling. Although very useful i n investigating the e f f e c t of stress, i t i s believed that rock mechanics research should put more emphasis on underground observation, monitoring and the c l a s s i f i c a t i o n of the rock mass, i n order to better understand the behaviour of the rock mass medium. Commenting on the use of f i n i t e element models, Barton (1985) stated: "One problem that arises i s that these methods are so sophisticated that the people working with them, i n my opinion, are not going to have to much time to investigate rock mass properties." This study was lar g e l y based on observational methods and 305 past experience. H i s t o r i c a l l y , mines have been designed from the r e s u l t s of previous designs i n s i m i l a r ground conditions. I t i s the author's opinion that a vast amount of experience and knowledge exists at each mine s i t e and the entire mining industry can benefit from the systematic compilation of t h i s experience. By making such a compilation a v a i l a b l e to the mining operators, i t gives them a broader data base for comparison, increases the confidence i n t h e i r design, and w i l l ultimately reduce the o v e r a l l d i l u t i o n usually associated with open stoping. 306 REFERENCES Barton, N., Lien, R. and Lunde, J . 1974. Engineering c l a s s i f i c a t i o n of rock masses for the design of tunnel support. Rock Mechanics 6, No. 4: 189-236. Barton, N. and Choubey, V. 1977. The shear strength of rock j o i n t s in theory and practic e . Rock Mechanics. 10, 1-54. Barton, N. 1975. Design methods i n rock mechanics, 16th  Symposium on Rock Mechanics, University of Minnesota, September 1975, New-york; American S o c i e t y of C i v i l Engineers. Bawden, W.F., Nantel, J. and Sprott, D. 1988. 90th CIM Annual General Meeting, Edmonton, Alberta. Bawden, W.F., Sauriol, G. , Milne, D. and Germain, P. 1988. P r a c t i c a l rock engineering stope design - case h i s t o r i e s from Noranda Minerals Inc. 90th CIM Annual General Meeting, Edmonton, Alberta. Bieniawski, Z.T. 1973. Engineering c l a s s i f i c a t i o n of jointed rock masses, Trans. S. Afr. Inst. C i v i l Engineers 15, No. 12: 335-344. Brady, B.H.G. 1978. A boundary element method for three-dimensional e l a s t i c analysis of tabular orebody extraction. Proc. 19th U.S. Sym. Rock Mech., 431-438. Brady, B.H.G. and Bray, J.W. 1978. The boundary element method for determining stresses and displacements around long openings i n a t r i a x i a l stress f i e l d . Int. J. Rock Mech. and  Min. S c i . and Geomech. Abstrs. 15, 21-28. Brady, B.H.G. and Brown, E.T. 1985. Rock mechanics for  underground mining. London: George Al l e n & Unwin Ltd. Bray, J.W. 1977. Unpublished notes, Imperial College. Brown, E.T. 1985. From theory to practice i n rock engineering. The Nineteenth S i r J u l i u s Wernher Memorial Lecture of the I n s t i t u t i o n of Mining and Metallurgy, Tunneling '85, Brighton, England. Chappell, B.A. 1979. Load d i s t r i b u t i o n and r e d i s t r i b u t i o n in discontinua. Int. J Rock Mech. Min. S c i . & Geomech. Abstr. 16, No. 6, 391-399. Chappell, B.A. 1987. Structural response and rock bolting of a rock mass. Mining Science Technology, No. 6, 171-191. 307 Coulomb, CA- 1776. Essaie sur une application des regies de maximis et mininis a quelques problemes de statique, r e l a t i f s a 1'architecture. Memories de Mathematique et de Physique,  l'Academie Royale des Sciences. 7, 343-382. Deere, D.U. 1964. Technical descritpion of rock cores for engi n e e r i n g purposes. Rock Mechanics and Engineering  Geology. 1, No. 1, 17-22. Diering, J.A.C. 1987. Advanced e l a s t i c analysis of complex mine excavations using the three-dimensional boundary element technique. PhD. Thesis, Pretoria University, South A f r i c a . Diering, J.A.C. and Laubscher, D.H. 1987. P r a c t i c a l approach to the numerical stress analysis of mass mining operations. Trans. Inst. Min. Metall. 96, A179-A188. Diering, J.A.C. and Stacey, T.R. 1987. Three-dimensional stress analysis: a p r a c t i c a l planning t o o l for mining problems. APCOM 87. Proceedings of the Twentieth International Symposium on the Application of Computers and Mathematics i n the Mineral Industries. Volume 1: Mining. Johannesburg: SAIMM: 33-42. Dowding, CH. 1985. Blast v i b r a t i o n monitoring and control. Englewood C l i f f s : Prentice-Hall, Inc. Fabjanczyk, M. 1981. Review of ground support practice in Australian underground metalliferous mines. Proc. Annual  Conf. Aust. Inst. Min. Metall., Melbourne, 337-349. Fairhurst, C. and Cook, N.G.W. 1966. The phenomenon of rock s p l i t t i n g p a r a l l e l to the d i r e c t i o n of maximum compression in the neighborhood of a s u r f a c e . Proceedings, 1st International Congress on Rock Mechanics. Lisbon, Vol. 1, 687-692. Folk, R.L. 1968. Petrology of sedimentary rocks. University of Texas. F u l l e r , P.G. and Cox, R.H.T. Rock reinforcement design based on contol of j o i n t displacement - a new concept. 3rd  Australian Tunnelling Conference, Sydney, 28-35. F u l l e r , P.G. 1983. Cable support in mining: a keynote lecture, Proc. Int. Symp. on Rock Bolting, Abisko, Sweden, 511-522. G r i f f i t h , A.A. 1924. Theory of rupture. Proc. 1st Int. Con.  App. Mech. Delft, 55-63. 308 Herget, G. 1987. Technical note - Stress assumptions for underground excavations i n the Canadian s h i e l d . Int. J. Rock  Mech. Min. S c i . & Geomech. Abstr. 24, No. 1, 95-97. Hoek, E. 1965. Rock fra c t u r i n g under s t a t i c stress conditions, Nat. Mech. Eng. Res. Inst. Report MEG 383, CSIR, S. A f r i c a . Hoek, E. 1968. B r i t t l e f a i l u r e of rock. Rock Mechanics in  engineering practice (eds K.G. Stagg & O.C.. Zienkiewicz), 99-124. Hoek, E. and Brown, E.T. 1980. Underground Excavations in  Rock, London: I n s t i t u t e of Mining and Metallurgy. Hudyma, M. 1988. Comparison of two and three dimensional boundary element numerical methods. Unpublished report. Hudyma, M. 1988. Development of empirical r i b p i l l a r f a i l u r e c r i t e r i o n for open stope mining. MASc thesis, The University of B r i t i s h Columbia, September 1988. Jeremic, M.L. and Delaire, G.J.P. 1983. F a i l u r e mechanics of cable b o l t systems, Can. Inst. Min. Metall. B u l l . , 76, No. 856, 66-71. Kirsch, G. 1898. Die theorie der e l a s t i z i t a t und die bedurfnisse der f e s t i g k e i t s l e h r e . Veit. Ver. Deut. Ing. 42, 797-807. Lang, L.C., Roach, R.J. and Osoko, M.N. 1977. V e r t i c a l crater retreat an important new mining method. Canadian Mining  Journal. September. Laubscher, D.H. 1976. Geomechanics c l a s s i f i c a t i o n of jointed rock masses - mining applications. Trans. Inst. Min. Metall. No.l, A1-A8. Mathews, K.E., Hoek, E., Wyllie, D.C. and Stewart, S.B.V. 1980. Prediction of stable excavations for mining at depths  below 1000 metres i n hard rock. CANMET Report 802-1571. Matthews, M. , Tillman, V.H. and Worotnicki, G. 1983. A modified cablebolt system for the support of underground openings, Aust. Inst. Min. Metall. Conference, Broken H i l l ,  N.S.W. MacLintock, F.A. and Walsh, J.B. 1962. F r i c t i o n on G r i f f i t h cracks under pressure. Proc. 4th Int. Con. App. Mech. 1015-1021. M i l l e r , D.R. 1984. Design of cable reinforcement patterns to r e s i s t shear f a i l u r e i n open stope walls. S t a b i l i t y in 309 Underground Mining II, Lexington, Kentucky, Ed: A.B. Swilski, CO. Brawner. Murrell, S.A.F. 1965. The e f f e c t l o f t r i a x i a l stress systems on the strength of rock at atmospheric temperatures. Geophy.  J. R. Astr. Soc. 10, 231-281. Pakalnis, R.CT. 1986. Empirical stope design at Ruttan. PhD. Thesis, University of B r i t i s h Columbia. Pakalnis, R.CT. 1987. PCBEM user's manual. Canada/Manitoba Mineral Development Agreement, CANMET Project No. 4-9147-1, Energy, Mines and Resources Canada, Ottawa. Palmstrom, A. 1982. The volumetric j o i n t count - a useful and simple measure of the degree of rock mass j o i n t i n g . Proc.  4th Con. Int. Assoc. Eng. Geol. Volume V, New Delhi, 221-228. Potvin, Y. , Hudyma, M. and M i l l e r , H.D.S. 1987. Progress report of the integrated mine design project. Unpublished report. P r i e s t , S.D. and Hudson, J.A. 197 6. Discontinuity spacings in rock. Int. J . Rock Mech. Min. S c i . 13, 135-148. Stewart, I.J. and Brown, E.T. 1984. A s t a t i c relaxation method for the analysis of excavations i n discontinuous rock. Design and performance of underground excavations: ISRM  symposium, Cambridge. London: B r i t i s h Geotechnical Society, 149-155. Stheeman, W.H. 1982. A p r a c t i c a l solution to cable b o l t i n g problems at Tsumeb Mine. Can. Inst. Min. Metall. B u l l . , 75, No. 838, 65-77. Watson, J.O. and Cowling, R. 1985. Application of three-dimensional boundary element methods to modelling of large mining excavations at depth. Proceedings of the 5th  I n t e r n a t i o n a l C o n f e r e n c e on N u m e r i c a l Methods i n  Geomechanics. 1901-1910. Yu, Y.S., Toews, N.A. and Wong, A.S. 1983. MINTAB user's guide -a mining simulator for determining the e l a s t i c response of s t r a t a surrounding tabular mining excavations (version 4.0, 1982). Division report MRP/MRL 83-25 (TR) , Mining Research Laboratories, CANMET, Energy, Mines and Resources Canada, Ottawa. 310 APPENDIX I OREBODY DIAGRAMS AND ROCK MECHANICS DATA 3 1 1 MINE No. I ORE Rock Type: B r e c c i a BANGING WALL Bock Type: P e r i d o t i t e T v - 2.9 t/m1 - 80 MPa - 46.1 CPa - 0 . 2 6 312 MINE No. 2 QBE (LENS i t II Rock Typei tussive Sulphide T °c E V Q' 4.2 t/m? 200 MP* 61.0 CPs 0.3 7 UANCIWG HALL t ROOP [t.VMK ->f Rock Typei Andeslte Y °t E w 0' 2.9 t/m* 109 MPa 63.0 CPs 0.2S 4 LENS 2 ' ' ' I' • i . 1 ' •'/'„",' -'/' ' ' ". »' > • •115m-OPEN „ , '/<'//;//< A;;/ -,/,,;;"',*V•.'VHk':V$C1 ;s;-'---HANGING WALL * ROOP (LEWS 3) Rock Typei Altered Andeslte Y - 3.0 t/m* o t - 87 MPs E - 84.0 CPs v - 0.28 Q' - 0.9 MINE No. 3 ORB Rock Typei Maaalve Sulphide t - 4.3 t/u* o c - 116 MPa K - 39.0 CPa v - 0.11 0' - 6 N 200m o,=Yn o,„-1.6vh o, B-th • p i h 1050m MINE No. 4 ORE HANGING WALL FW Contact HW Contact Typei Late Granite Dark Norite Breccia Breccia T " 3.4 t>> 3.2 t/m* °c - 131 MPa 81 MPa E - SO.O GPa 53.0 GPa v • 0.26 0.26 0* - 18 18 Rock Type: Dark Norite r O O T WALL Rock Typei relate Gneiss E V 2.7 t/««J 141 MPa 58.8 CPa 0.28 MINE No. 6 O R E Rock Type: B r e c c i a 4 Massive Sulphide T V 0' 3.1 t/m3 125 MPa 9 4 . 0 CPs 0 . 2 2 9 NORTH WALL Rock Type: N o r i t e Y 2< v 0* 2.9 t/m1 113 MPs 5 6 . 0 CPs 0 . 1 7 9 SOOTH WALL Rock Type: G r a n i t e T 2< V 0" 274m Depth 1050 m 316 MINE No. 8 o,'yb 317 03 M MINE No. 10 ORB Hock Typei S i l i c e o u s Ore 3.0 t/m* 41 - »9 M P a 44 - SJ C P S 0.21 - 0.40 HANGING WALL i Hock Typei S i l i c e o u s S e d l M n t Tf " 2 . 8 t/m* o. » 60 MPs 0 S - 6 N P0OT WALL Hock Typei S i l i c e o u s Schis t - 2 . 8 t/m* - 1 4 0 MI'S LON0ITU0INAL LONOHOLE OPEN STOPES • 200m SILL PILLAR SU8LEVEL RETREAT STOPES CONTINUES TO 1000m o,„ -1 .7 th e l o - T h 100m 2Sm • , - » h 100m MINE No. II w MINED OUT (Ne Backfill) <— 200m MINED OUT (Ne Bockflll) PERMANENT PILLAR (No Grode) LONGITUDINAL LONGHOLE STOPE • 30m-H 62 m LONGITUDINAL LONGHOLE STOPE OOm — 200m / f LONGITUDINAL LONGHOLE STOPE -62m 4* _D«plh 925m O R E Rock Type : Porphyry y - 2.72 t/w* o t - 148 MPa E » I B . 5 GPa v - 0.20 Q* - 30 0 , - 1 . I S T O I J o«-l.Syh eio»1.7Yh 320 MINE No. 13 MINE No. 14 3 2 2 MINE No. 16 OR! Rock Typei Maaoive Sulphide j - 4.6 t/mi* o, - 176 MPa B - 119.0 CPa v - 0.24 0* m 20 HANGING WALL Hook Typei Ouarti Porphyry u> w y - 2.9 t/a)' o , - 9 1 MPa K - 68.7 GPa v - 0.19 Q' - 42 FOOT WALL Rock Typei Chlorite Tuff y - 2.9 t/a? o, - 84 MPa E - 68.5 GPa V - 0.25 Q« - 40 Surfoce 850m 1 MINE No. 17 8 7 0 m co ro LONGITUDINAL LONGHOLE OPEN STOPINO J L -IBOOm-O R E Rock Typei Massive Sulphide HALL Rock Typei Gnelaa Y • °c -E -v » O' . 5.3 t/m* 100 HPa 103 GPa 0.31 19 T -"c " E -V • Q" -2.7 t/ai J 52 MPa 105 CPa 0.20 IS o,-yh 2.«th* J . l y h * 'stress based on forauls by Oerget MINE No. 18 ORE . Rock Type: Maaalve Sulphide y - 4.8 l/m* o c - 285 MPa E - 65.5 GPa v - 0.10 Q* - 15 A o„,-3.3th TRANSVERSE LONGHOLE OPEN STOPING MINE No. 19 MINEO OUT A BACKFILLED TO SURFACE 70m to -o 30m •420m LONQITUOINAL S U B - L E V E L ReTRCAT • 150m • LONOITUOINAJL •US-LEVEL RETREAT 2-ISm 110m TRANSVERSAL BLASTHOLE BTOPES -210m. 760m o , - T » ORE Rock Typoi Maaelve Sulphlda NORTH WALL 190*1 O, - 316 MP* E - 232.2 GPa v - 0.16 0' - 44 N Rock Typai Baaaltle Tuff E V SOOTH WALL (90*1 Rock Typoi Rhyolltlo Tuff a, - 90 MPa B - 67.9 CPa v - 0.1S 0 ' - 2 . 2 N MINE No. 20 328 MINE No. 21 T Y P I C A L M I N E CROSS SECTION ORE LONGHOLE tc BLASTHOLE LONGITUDINAL OPEN STOPING Rock Type: Massive Sulphide Oc = 100 MPa E = 88 GPa V = 0.20 Q' = 10-20 HANGING WALL & FOOTWALL Rock Type: Quartz Meta Sediments CTC = 50-135 MPa E = 50-75 GPa y = 0.12-0.34 = 2.5 crv Q' = 0.1-50 329 MINE No. 23 330 MINE No. 30 ORE Rock Y = Oc = E = V = Q' = Type: Massive Sulphide 3.3 t / m 3 160 MPa 80 GPa 0.21 22 TYPICAL MINE CROSS SECTION TRANSVERSE BLASTHOLE OPEN STOPING 1500m HANGING WALL Rock Y = orc = E = v = Q' = Type: Rhyolite 2.7 t / m 5 120-150 MPa 80 GPa 0.14 13-30 FOOTWALL Rock Type: Andesite/Diorite CTV=YH 0\ = 6+0.055H(m) CT2 = 0.8 CT, Y Oc E V Q' 3.0 t / m 3 160 MPa 85 GPa 0.23 14 331 MINE No. 31 TYPICAL MINE C R O S S S E C T I O N ORE Y = 3.5 t / m 3 Oc = 265 MPa E = 63 GPa Q' = 2 5 - 4 0 HANGING WALL Rock Type: TUFF Y = 2.8 t / m 3 CTc = 195 MPa E = 44 GPa Q' = 2 5 - 4 0 FOOTWALL L O N G I T U D I N A L L O N G H O L E O P E N S T O P I N G 850m O Y ^ Y H Rock Type: Iron Formation Y = 2.9 t / m 3 CTC = 275 MPa E = 51 MPa Q' = 2 5 - 4 0 0~„ = 8+l.6YH(m) (isostatic) 3 32 APPENDIX II D E S C R I P T I O N OF THE BOUNDARY ELEMENT PROGRAMS 2 D : B I T E M AND 3 D : B E A P 333 BITEM The 2D d i r e c t b o u n d a r y i n t e g r a l model "BITEM" i s b a s e d on t h e p r o g r a m " B I T E " d e v e l o p e d by P.C. R i c c a r d e l l a a t t h e C a r n e g i e - M e l l o n u n i v e r s i t y i n 1973. I t was e x p a n d e d t o p e r f o r m p i e c e - w i s e h o m o g e n e o u s e l a s t i c i t y a n a l y s e s b y CSIRO (Commonwealth S c i e n t i f i c and I n d u s t r i a l R e s e a r c h O r g a n i z a t i o n , A u s t r a l i a ) i n 1978. The p r o g r a m was s u b s e q u e n t l y m o d i f i e d f o r t h e U.B.C. m a i n f r a m e computer by R. P a k a l n i s (1983) and l a t e r f o r an IBM c o m p a t i b l e c omputer by CANMET u n d e r t h e p r o g r a m name PCBEM ( P a k a l n i s 1987). The b o u n d a r y i n t e g r a l t e c h n i q u e i s d e s i g n e d f o r p r o b l e m s t h a t have one l o n g d i m e n s i o n and a c o n s t a n t c r o s s s e c t i o n a l s h a p e . I t r e q u i r e s t h e d i s c r e t i z a t i o n o f a l l e x c a v a t i o n s u r f a c e s i n t o segments c o n n e c t e d by nodes ( s e e f i g u r e ). An e x p l i c i t s o l u t i o n i s s e l e c t e d t o r e p r e s e n t t h e medium's i n s i t u s t r e s s c o n d i t i o n s . T h e s e f i e l d s t r e s s e s c a n be c o n s t a n t o r c a n v a r y l i n e a r l y w i t h p o s i t i o n . When e x c a v a t i o n s a r e c r e a t e d , t h e s t r e s s p e r p e n d i c u l a r t o t h e b o u n d a r y nodes becomes z e r o . BITEM t h e n c a l c u l a t e s t r a c t i o n s and d i s p l a c e m e n t s a t a l l t h e modes o f a l l t h e b o u n d a r i e s . The b o u n d a r y s o l u t i o n i s d e t e r m i n e d t h r o u g h an i t e r a t i v e p r o c e d u r e i n w h i c h t h e s t r e s s and d i s p l a c e m e n t a t e a c h node i n f l u e n c e s t h e s t r e s s and d i s p l a c e m e n t o f t h e o t h e r nodes o f t h e b o u n d a r y . T h i s p r o c e d u r e ends when t h e d i f f e r e n c e between t h e l a s t two i t e r a t i o n s i s l e s s t h a n a u s e r d e f i n e d c o n v e r g e n c e c r i t e r i o n . 334 Once a boundary solution has been determined, stresses and 335 OPENING TO FIGURE 23. I s o m e t r i c view of an opening t h a t i s lon g i n d i r e c t i o n and t h e d i s c r e t i z a t i o n o f t h e boundary used two d i m e n s i o n a l m o d e l l i n g ( a f t e r Hudyma 1988b). displacements i n t e r n a l to the problem boundary can be determined using the boundary solution and s t r e s s - s t r a i n r e l a t i o n s h i p s . A more detailed description of the boundary in t e g r a l technique i s found in Brady and Bray (1978). 337 BEAP BEAP i s a three dimensional boundary element program developed by J.A.C. D i e r i n g as a PhD t h e s i s , at P r e t o r i a U n i v e r s i t y (1987), i n conjunction with CANMET, INCO (Thompson D i v i s i o n ) and GEMCOM (Pty.) L i m i t e d . Version 1.0, used i n t h i s p r o j e c t , i s due f o r p u b l i c r e l e a s e i n the F a l l 1988. E x c a v a t i o n b o u n d a r i e s are g e n e r a l l y d i s c r e t i z e d by q u a d r i l a t e r a l elements (see f i g u r e ). The problem i s subject to an a r b i t r a r i l y o r i e n t e d s t r e s s f i e l d . The s t r e s s and displacements on the boundary elements vary q u a d r a t i c a l l y and are non-conforming. This means displacements and t r a c t i o n s are assumed to vary according to a quadratic polynomial, and the displacements between adjacent elements are discontinuous. The r e s u l t i n g numerical model has some powerful a b i l i t i e s i n mining r e l a t e d s t r e s s a n a l y s i s , i n c l u d i n g : - the need f o r fewer elements to d i s c r e t i z e an excavation than other 3d boundary element models, - the a b i l i t y to accommodate up to f i v e zones with d i f f e r e n t , m a t e r i a l p r o p e r t i e s , - the use of lumping to reduce data storage requirements, - and the a b i l i t y to determine s t r e s s e s and displacements very c l o s e to an excavation boundary. Further d e t a i l s about BEAP can be found i n D i e r i n g (1987) and D i e r i n g and Stacey (1987). 338 85 FIGURE 25. A t y p i c a l BEAP geometry showing the boundary of the excavations defined by two dimensional quadratic, non-conforming elements i n a three dimensional stress f i e l d ( a f t e r Hudyma 1988b). 339 APPENDIX III PLOT OF INDUCED STRESSES FOR DIFFERENT GEOMETRIES AND K RATIOS 340 H=40 2 3 - ^ L=120 x Ct-28 f 05-29 2 - _ J > ,1? H=40 $1 VV^ 1 7 ^ 5* 1=120 O j - U.7 Ot-2ft H=40 tf L=120 <*-0J<-1Z5 H=40 13 tf 1=120 0,-10 05-: ct-i© T4~3" 349 350 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0081130/manifest

Comment

Related Items