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UBC Theses and Dissertations

Development of empirical rib pillar design criterion for open stope mining Hudyma, Martin Raymond 1988

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DEVELOPMENT OF EMPIRICAL R I B P I L L A R DESIGN CRITERION FOR OPEN STOPE MINING By MARTIN RAYMOND HUDYMA B . A . S c , The 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 , 1986 A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE 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 t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA September 1988 M a r t i n Raymond Hudyma, 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 The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) ABSTRACT The d e s i g n o f open s t o p e r i b p i l l a r s has been done u s i n g many e m p i r i c a l me thods , b u t none o f t h e methods has been v e r i f i e d w i t h a d e s i g n s u r v e y . T h i s t h e s i s u s e s d a t a c o l l e c t e d i n t h e " I n t e g r a t e d M i n e D e s i g n S t u d y " t o d e v e l o p an e m p i r i c a l r i b p i l l a r d e s i g n method f o r open, s t o p e m i n i n g . The method i s c a l l e d t h e " p i l l a r s t a b i l i t y g r a p h " . The d e s i g n v a r i a b l e s i n t h e method a r e : t h e c o m p r e s s i v e s t r e n g t h o f t h e i n t a c t p i l l a r m a t e r i a l , t h e a v e r a g e p i l l a r l o a d d e t e r m i n e d by n u m e r i c a l m o d e l l i n g , t h e p i l l a r w i d t h and t h e p i l l a r h e i g h t . The g r a p h has been r e f i n e d w i t h t h e use o f more t h a n 80 l i t e r a t u r e c a s e h i s t o r i e s o f h a r d r o c k p i l l a r s i n room and p i l l a r m i n i n g . The p i l l a r s t a b i l i t y g r a p h and t h e p i l l a r d a t a base a r e used t o examine t h e a p p l i c a b i l i t y o f e m p i r i c a l methods commonly used i n open s t o p e r i b p i l l a r d e s i g n . The i n v e s t i g a t i o n found t h e p i l l a r s t r e n g t h c u r v e s d e v e l o p e d by Hoek and Brown (1980) may be u s e f u l u n d e r some c o n d i t i o n s f o r t h e d e s i g n o f open s t o p e r i b p i l l a r s b u t f o r m u l a s by H e d l e y ( 1 9 7 2 ) , O b e r t and D u v a l l (1967) and B i e n i a w s k i (1983) a r e n o t a p p l i c a b l e . G u i d e l i n e s , u s i n g t h e p i l l a r s t a b i l i t y g r a p h method , a r e p r o p o s e d f o r t h e d e s i g n o f permanent open s t o p e r i b p i l l a r s , s t a b l e t e m p o r a r y open s t o p e r i b p i l l a r s , and f a i l i n g t e m p o r a r y open s t o p e r i b p i l l a r s . i i i TABLE OF CONTENTS PAGE ABSTRACT i i L I S T OF TABLES v i i L I S T OF FIGURES v i i i ACKNOWLEDGEMENT x i i i CHAPTER 1: INTRODUCTION 1 1.1 C o n t e n t s o f t h e T h e s i s 1 1.2 Open S t o p e M i n i n g 2 1 . 2 . 1 D e f i n i t i o n o f Open S t o p i n g 3 1 . 2 . 2 A p p l i c a b i l i t y o f t h e Open S t o p i n g 4 1 .2 .3 D e s c r i p t i o n o f T y p i c a l Open S t o p e M i n i n g Methods 5 1.3 R o l e o f R i b P i l l a r s i n Open S t o p e M i n i n g 9 CHAPTER 2 : R I B P I L L A R FAILURE 11 2 . 1 F a i l u r e Mechanisms and C h a r a c t e r i s t i c s 11 2 . 1 . 1 Rock F r a c t u r i n g 14 2 . 1 . 2 P i l l a r L o a d - D e f o r m a t i o n C u r v e 17 2 . 1 . 3 L o s s o f L o a d B e a r i n g C a p a c i t y 19 2 . 2 S i g n i f i c a n t V a r i a b l e s i n Open S t o p e P i l l a r S t a b i l i t y 23 2 . 2 . 1 I n t a c t Rock S t r e n g t h 23 2 . 2 . 2 P i l l a r L o a d 23 2 . 2 . 3 P i l l a r Shape and C o n f i n e m e n t 24 2 . 2 . 4 S t r u c t u r a l F e a t u r e s i n P i l l a r s 25 2 . 2 . 5 E f f e c t o f P i l l a r Volume 26 2 . 2 . 6 E f f e c t o f B a c k f i l l 27 2 . 2 . 7 E f f e c t o f B l a s t i n g 30 2 . 3 C h a p t e r Summary 31 CHAPTER 3 : REVIEW OF P I L L A R DESIGN METHODS 32 3 . 1 E m p i r i c a l D e s i g n Methods 32 3 . 1 . 1 P i l l a r S t r e n g t h D e t e r m i n a t i o n 34 3 . 1 . 1 . 1 E m p i r i c a l S t r e n g t h F o r m u l a s 35 3 . 1 . 1 . 2 S a l a m o n ' s F o r m u l a 38 i v 3 . 1 . 1 . 3 H e d l e y ' s F o r m u l a 40 3 . 1 . 1 . 4 O b e r t and D u v a l l Shape E f f e c t F o r m u l a . . 41 3 . 1 . 1 . 5 Hoek and Brown P i l l a r S t r e n g t h C u r v e s . . 43 3 . 1 . 2 P i l l a r Load 45 3 . 1 . 2 . 1 T r i b u t a r y A r e a T h e o r y 45 3 . 1 . 2 . 2 N u m e r i c a l M o d e l l i n g 51 3 . 1 . 3 S a f e t y F a c t o r 51 3 .2 N u m e r i c a l D e s i g n Methods 53 3 . 2 . 1 Types o f N u m e r i c a l Methods 53 3 . 2 . 2 I n t e r p r e t a t i o n o f Boundary E l e m e n t R e s u l t s i n M i n i n g 57 3 . 2 . 2 . 1 P o s t - P r o c e s s i n g F a i l u r e C r i t e r i o n . . . . 57 3 . 2 . 2 . 2 I n t e r a c t i v e F a i l u r e C r i t e r i o n 60 3 . 2 . 2 . 3 P r i n c i p a l S t r e s s M a g n i t u d e 63 3 . 2 . 3 L i m i t a t i o n s o f Bounda ry E l e m e n t M o d e l l i n g . . . 63 3 . 2 . 3 . 1 M o d e l l i n g a Rock Mass 63 3 . 2 . 3 . 2 C o m p u t a t i o n a l A s s u m p t i o n s 66 CHAPTER 4 : OPEN STOPE R I B P I L L A R DATA BASE 68 4 . 1 G e n e r a l D a t a Base I n f o r m a t i o n 68 4 . 2 B a c k g r o u n d D a t a 69 4 . 3 P i l l a r A s s e s s m e n t 73 CHAPTER 5 : BOUNDARY ELEMENT METHODS I N R I B P I L L A R DESIGN. . 78 5 . 1 Bounda ry E l e m e n t Codes Used 79 5 . 1 . 1 BITEM 79 5 . 1 . 2 MINTAB 81 5 . 1 . 3 BEAP 84 5 .2 Open S t o p e R i b P i l l a r M o d e l l i n g 84 5 . 2 . 1 D e f i n i n g t h e Open S t o p e Geometry 86 5 . 2 . 2 D e f i n i n g t h e A v e r a g e P i l l a r S t r e s s 86 5 .3 2D M o d e l l i n g o f 3D S t o p e G e o m e t r i e s 91 5 . 3 . 1 P l a n e S t r a i n S o l u t i o n 92 5 . 3 . 2 C o m p a r i s o n o f 2D and 3D N u m e r i c a l M o d e l l i n g R e s u l t s 93 5 .4 D i s p l a c e m e n t D i s c o n t i n u i t y M o d e l l i n g o f 3D S t o p e G e o m e t r i e s 97 5 . 4 . 1 Seam T h i c k n e s s L i m i t a t i o n s 97 5 . 4 . 2 C o m p a r i s o n o f D i s p l a c e m e n t D i s c o n t i n u i t y and 3D N u m e r i c a l M o d e l l i n g 99 5 .5 P i l l a r L o a d C a l c u l a t i o n s f o r t h e Open S t o p e V D a t a Base 102 5 . 5 . 1 A s s u m p t i o n s 103 5 . 5 . 2 P i l l a r L o a d R e s u l t s 103 5 . 5 . 3 N u m e r i c a l M o d e l C o m p a r i s o n U s i n g t h e Case H i s t o r i e s 107 5 .6 C h a p t e r Summary 110 CHAPTER 6 : DEVELOPMENT OF A P I L L A R DESIGN METHOD 114 6 . 1 C h o i c e o f V a r i a b l e s f o r Open S t o p e P i l l a r D e s i g n . . 115 6 . 1 . 1 A p p l i c a b i l i t y o f S t a t i s t i c a l Methods 115 6 . 1 . 2 D e s i g n V a r i a b l e s 117 6 . 1 . 3 D i s c o u n t e d V a r i a b l e s 118 6 . 1 . 3 . 1 P i l l a r Volume 119 6 . 1 . 3 . 2 S t r u c t u r a l D i s c o n t i n u i t i e s 120 6 .2 P i l l a r S t a b i l i t y Graph 122 6 . 2 . 1 G r a p h i c a l Da ta A n a l y s i s 122 6 . 2 . 2 I n f l u e n c e o f P i l l a r L o a d A p p r o x i m a t i o n s . . . . 126 6 . 2 . 3 I m p o r t a n c e o f Y i e l d i n g P i l l a r Case H i s t o r i e s . 128 6 . 2 . 4 L i m i t a t i o n s o f t h e P i l l a r S t a b i l i t y G r a p h . . . 130 6 .3 D a t a f rom L i t e r a t u r e 131 6 . 3 . 1 D a t a f rom C a n a d i a n Room and P i l l a r M i n i n g . . . 131 6 . 3 . 2 D a t a f rom a Botswana Room and P i l l a r M i n e . . . 134 6 . 3 . 3 D a t a f rom an A u s t r a l i a n Open S t o p e M i n e . . . . 139 6 . 3 . 4 Summary o f A l l t h e D a t a 143 6 .4 C o m p a r i s o n A g a i n s t O t h e r D e s i g n Methods 143 6 . 4 . 1 H e d l e y ' s P i l l a r S t r e n g t h F o r m u l a 146 6 . 4 . 2 Hoek and Brown P i l l a r S t r e n g t h C u r v e s 151 6 . 4 . 3 P i l l a r Shape E f f e c t F o r m u l a s 152 6 .5 C h a p t e r Summary 158 CHAPTER 7: DESIGNING R I B P I L L A R S FOR OPEN STOPE MINING. . . 160 7 . 1 Permanent P i l l a r s 162 7 .2 Tempora ry P i l l a r s 163 7 . 2 . 1 S t a b l e Temporary P i l l a r s 165 7 . 2 . 2 F a i l e d Temporary P i l l a r s 166 7 .3 Case E x a m p l e : T r a n s v e r s e R i b P i l l a r s a t N o r i t a . . . 167 7 . 3 . 1 G e o l o g y and M i n i n g Method 167 7 . 3 . 2 Back A n a l y s i s U s i n g t h e P i l l a r S t a b i l i t y Graph 170 7 . 3 . 3 Comments C o n c e r n i n g t h e P i l l a r D e s i g n 173 v i CHAPTER 8: SUMMARY AND CONCLUSIONS 174 8.1 Summary 174 8.1.1 Open Stope Rib P i l l a r F a i l u r e 174 8.1.2 Current P i l l a r Design Methods 175 8.1.3 I d e n t i f i c a t i o n and Quantification of the Design Varaibles 176 8.1.4 Development of the P i l l a r S t a b i l i t y Graph. . . 177 8.2 Conclusions 179 8.2.1 A p p l i c a b i l i t y of the Method 179 8.2.2 Limitations of the Method 179 8.2.3 Design of Open Stope Rib P i l l a r s 180 8.3 Future Work 181 REFERENCES 183 APPENDIX 1 190 v i i L I S T OF TABLES PAGE TABLE 1. Constants proposed by various authors f o r the 36 s i z e e f f e c t formula (after Babcock, Morgan and Haramy 1981). TABLE 2. Constants proposed by various authors f o r the 37 shape e f f e c t formula (after Babcock, Morgan and Haramy 1981). TABLE 3. Constants proposed by various authors f o r the 37 shape e f f e c t formula (after Babcock, Morgan and Haramy 1981). TABLE 4. The safety factors proposed by various authors 52 for empirical p i l l a r design i n entry mining methods. TABLE 5. Background data for a l l the p i l l a r case 70 h i s t o r i e s . TABLE 6. Comparison of BEAP and BITEM for four sets of 94 d i f f e r e n t orebody geometries. TABLE 7. Comparison of BEAP and MINTAB for the four 98 d i f f e r e n t t e s t s . TABLE 8. P i l l a r load information for a l l the open stope 105 r i b p i l l a r case h i s t o r i e s using BITEM, MINTAB and the Tributary Area Theory. TABLE 9. Comparison of MINTAB and BITEM r e s u l t s , when 107 both programs l i m i t a t i o n s are s a t i s f i e d . TABLE 10. Comparison of BITEM and MINTAB, when the MINTAB 108 l i m i t a t i o n i s met, but the BITEM l i m i t a t i o n i s not met. TABLE 11. Comparison between good BITEM and poor MINTAB 111 geometries shows the average p i l l a r stress varying up to ± 25%. TABLE 12. Data used by Von Kimmelmann et a l . (1984) i n 136 the development of a p i l l a r f a i l u r e c r i t e r i o n . TABLE 13. Comparison of the value of ore for mines using 161 temporary p i l l a r s against mines using permanent p i l l a r s . v i i i L I S T OF FIGURES PAGE FIGURE 1. The elements of an i d e a l i z e d l o n g i t u d i n a l 6 longhole open stoping method showing the b l a s t i n g , mucking and b a c k f i l l i n g operations. FIGURE 2. The elements of an i d e a l i z e d transverse 7 blasthole open stoping method showing the d r i l l i n g , b l a s t i n g , mucking and b a c k f i l l i n g operations. FIGURE 3a. P a r a l l e l f r a c t u r i n g and s p a l l i n g due to a lack 16 of confinement at the p i l l a r walls. FIGURE 3b. Internal s p l i t t i n g and a x i a l cracking of a 16 p i l l a r due to deformable p i l l a r layers or the propagation of p a r a l l e l wall fractures. FIGURE 3c. Diagonal crushing fractures may occur i n 16 confined or massive p i l l a r s . FIGURE 4. A hypothetical load-deformation curve can be 18 used to describe the s t r e s s - s t r a i n c h a r a c t e r i s t i c s of a p i l l a r . FIGURE 5. Wagner (1974) did a series of i n s i t u load- 20 deformation t e s t s on coal p i l l a r s using hydraulic jacks. The graph on the top shows the load-deformation c h a r a c t e r i s t i c s of the p i l l a r i n general. The oblique diagrams give the r e l a t i v e load on each of the 25 jacks at four stages of p i l l a r compression. FIGURE 6. The s t r e s s - s t r a i n curves for laboratory 2 2 specimens loaded under increasing confining pressures show an increase i n peak load and an increase i n the post-peak load bearing capacity. FIGURE 7. There i s a very large influence of specimen 28 s i z e on the strength of i n t a c t rock, f o r small specimen diameters. FIGURE 8. Strength t e s t i n g of samples of increasing 28 specimen length shows a decreasing influence of s i z e . FIGURE 9. Histogram of the safety factors for stable and 39 f a i l e d p i l l a r case h i s t o r i e s i n South Af r i c a n bord and p i l l a r coal mining. ix FIGURE 10. The estimated stress and strength f o r case 42 h i s t o r i e s of p i l l a r s i n room and p i l l a r mining i n the E l l i o t lake uranium mining d i s t r i c t . FIGURE 11. Hoek and Brown (1980) proposed a serie s of 44 p i l l a r strength curves based on the t h e o r e t i c a l d i s t r i b u t i o n of rock mass f a i l u r e i n a p i l l a r . FIGURE 12. The analogy of streamlines i n a smoothly 47 flowing stream obstructed by bridge p i e r s i s often used to describe the concentration of stress i n p i l l a r s . FIGURE 13. The t r i b u t a r y area theory, for average p i l l a r 47 load c a l c u l a t i o n , applied to several d i f f e r e n t p i l l a r layouts. FIGURE 14. Salamon (1974) showed the v a r i a t i o n i n p i l l a r 49 stress caused by increasing the number of p i l l a r s (N) i n a mining panel. The graph shows a d i s t i n c t influence of the l o c a t i o n of a p i l l a r and the number of p i l l a r s on the stress induced. FIGURE 15. A study using two dimensional boundary element 50 numerical modelling shows the influence of p i l l a r shape and the number of p i l l a r s on the average stress. FIGURE 16. An i d e a l i z e d sketch showing the p r i n c i p l e of 54 numerical modelling of underground excavations. FIGURE 17. An empirical f a i l u r e c r i t e r i o n has been 59 applied to the two dimensional stress d i s t r i b u t i o n of a stable open stope r i b p i l l a r . FIGURE 18. The t h e o r e t i c a l d i s t r i b u t i o n of f a i l e d rock i s 59 much greater i n t h i s p i l l a r . FIGURE 19. The peak strength, deformation character- 61 i s t i c s , and e f f e c t of lo c a t i o n used for investigating a p i l l a r case hi s t o r y with a displacement d i s c o n t i n u i t y program. FIGURE 20. The normal stress and the f a i l e d regions 61 estimated with the displacement d i s c o n t i n u i t y program for a s i l l p i l l a r case his t o r y . FIGURE 21. The d i s t r i b u t i o n of normal stress i n a mining 64 block was estimated for two d i f f e r e n t mining sequences to determine the best stope extraction sequence. FIGURE 22. This figure shows the geometrical d e f i n i t i o n 72 for the stope and p i l l a r dimensions used i n t h i s t h e s i s . X FIGURE 23. Isometric view of an opening that i s long i n 80 one d i r e c t i o n and the d i s c r e t i z a t i o n of the boundary used i n two dimensional modelling. FIGURE 24. Oblique view of the MINTAB seam geometry and 83 the stress applied l o c a l l y on each element i n the reef. FIGURE 25. A t y p i c a l BEAP geometry showing the boundary 85 of the excavations defined by two dimensional quadratic, non-conforming elements i n a three dimensional stress f i e l d . FIGURE 26. This figure defines the dimensions f o r stopes 87 and p i l l a r s , and the orientation for the i n s i t u stress regime for t h i s t h e s i s . FIGURE 27a. A r i b p i l l a r i n a horizontal seam loaded by 88 the weight of the overburden. FIGURE 27b. The d i r e c t i o n of loading on a p i l l a r i n a 88 v e r t i c a l orebody. FIGURE 28. The mid-height plane and centerline for t a l l 90 open stope geometries. FIGURE 29. The shaded plane has the greatest influence on 94 the mid-height a v stress. FIGURE 30. Overestimation of average p i l l a r load by the 96 2D "BITEM" boundary element method for the 12 runs i n the four t e s t s . FIGURE 31. The dimensions and geometry of the MINTAB/BEAP 98 comparison t e s t s . FIGURE 32. The difference between the average p i l l a r 101 stress predicted by MINTAB and the average p i l l a r stress predicted by BEAP for the comparison t e s t s . FIGURE 33. Overestimation of average p i l l a r load by the 109 2D "BITEM" boundary element method for the comparison t e s t s and 3 case h i s t o r i e s . FIGURE 34. The difference between the average p i l l a r 112 stress predicted by MINTAB and the average p i l l a r stress predicted by BEAP for the comparison t e s t s and 13 case h i s t o r i e s . FIGURE 35. The p i l l a r s t a b i l i t y graph showing the open 123 stope r i b p i l l a r data base. FIGURE 36. The p i l l a r s t a b i l i t y graph showing the stable 125 and f a i l e d zones and the t r a n s i t i o n area. FIGURE 37. The p i l l a r s t a b i l i t y graph with the p i l l a r 127 load reduced for a l l the data points by the maximum amount l i s t e d i n Table 8. FIGURE 38. The p i l l a r s t a b i l i t y .graph with a l l the case 129 h i s t o r i e s of the 13 y i e l d i n g p i l l a r s joined by s o l i d l i n e s . FIGURE 39. The p i l l a r s t a b i l i t y graph showing the data 133 from room and p i l l a r mining published by Hedley and Grant (1972) i n t h e i r study on the development of a p i l l a r strength formula. FIGURE 40. A plan view of room and p i l l a r mining at BCL 137 Limited, showing the use of long p i l l a r s and square p i l l a r s . FIGURE 41. The p i l l a r s t a b i l i t y graph showing the long 138 p i l l a r data presented by Von Kimmelmann et a l . (1984). FIGURE 42. The square p i l l a r data presented by Von 140 Kimmelmann et a l . (1984) i s plotted on the s t a b i l i t y graph using an e f f e c t i v e width i n the H/W r a t i o . FIGURE 43. The f i v e stages of the S86 p i l l a r i n an open 142 stope p i l l a r t e s t at Mt. Isa (after Brady 1977). FIGURE 44. The t h i r d , fourth, and f i f t h stages of the S86 144 open stope r i b p i l l a r , presented by Brady (1977), are shown on the p i l l a r s t a b i l i t y graph. FIGURE 45. The p i l l a r s t a b i l i t y graph showing the open 145 stope r i b p i l l a r data and the l i t e r a t u r e data. FIGURE 46. The range of r i b p i l l a r dimensions seen i n 17 148 Canadian open stope mines. FIGURE 47. Comparison of the p i l l a r s t a b i l i t y graph and 150 Hedley's formula for two safety factors. FIGURE 48. Three of the Hoek and Brown (1980) p i l l a r 153 strength curves plotted on the p i l l a r s t a b i l i t y graph. FIGURE 49. Comparison between the p i l l a r s t a b i l i t y graph 155 and the Obert and Duval1 (1967) shape e f f e c t formula applied with a safety factor of 1.0. x i i FIGURE 5 0 . The shape e f f e c t f o r m u l a p r o p o s e d by 157 B i e n i a w s k i (1983) a p p l i e d w i t h t h r e e d i f f e r e n t s a f e t y f a c t o r s i s compared a g a i n s t t h e p i l l a r s t a b i l i t y g r a p h . FIGURE 5 1 . The r ange o f t e m p o r a r y r i b p i l l a r d i m e n s i o n s 164 u s e d i n 14 C a n a d i a n open s t o p e m i n e s . FIGURE 5 2 . I s o m e t r i c v i e w o f t r a n s v e r s e b l a s t h o l e open 168 s t o p i n g a t N o r i t a . FIGURE 5 3 . A l o n g i t u d i n a l s e c t i o n o f t h e b l a s t h o l e open 171 s t o p i n g b l o c k a t N o r i t a s h o w i n g t h e p i l l a r c a s e h i s t o r i e s ( 1 0 - 6 , 1 0 - 7 , and 10-8) u s e d i n t h i s c a s e h i s t o r y a n a l y s i s . FIGURE 54 . The p i l l a r s t a b i l i t y g r a p h s h o w i n g t h e 172 l o c a t i o n o f t h e s t a b l e and f a i l e d t r a n s v e r s e p i l l a r c a s e h i s t o r i e s a t N o r i t a . ACKNOWLEDGEMENT The author wishes to acknowledge Noranda Research, Falcon-bridge Limited, the Natural Sciences and Engineering Research Council and the Cy and Emerald Keyes scholarship fund for f i n a n c i a l support during the project. Thanks are extended to the employees of the mines and groups which provided time and information to the study: - Algoma Steel Corp. Limited - G.W. Macleod Mine - Barrick Resources - Camflo Mine - BP Canada Inc. - Mines Selbaie - Cambior - Niobec Mine - Corporation of Falconbridge Copper - Corbet Mine, Lac Shortt Mine - Dome Mines Limited - Falconbridge Limited - East Mine, Fraser Mine, Kidd Creek, Lockerby Mine, Mining Technology Divis i o n , Onaping Mine, Strathcona Mine - Hudson Bay Mining and Smelting - Centennial Mine, Chisel Lake Mine, F l i n Flon Mine, Spruce Point Mine - Inco Limited - L i t t l e Stobie Mine, Mine Research Division, Stobie Mine, Thompson Di v i s i o n - Kiena Gold Mines - Noranda Minerals Inc. - Brunswick Mining and Smelting, Chadbourne Mine, Geco Mine, Golden Giant Mine, Lyon Lake Mine, Mattabi Mine, Mattagami Lake Mine, Mines Gaspe, Mining Technology Divis i o n , Norita Mine - Pamour Porcupine Mines Limited - Ross Mine, No. 1 Mine - S h e r r i t t Gordon - Ruttan Mine - Westmin Resources Limited. Also, thanks to Dr. H.D.S. M i l l e r for h i s e f f o r t s i n sett i n g up the Integrated Mine Design Project. Sincere gratitude i s expressed to Professor Alan Reed for his comments and help i n writing the thesis and the members of the Department of Mining and Mineral Process Engineering at UBC for help and support during the project. Special thanks to my partner Mr. Yves Potvin. His technical contributions and advice have had an immeasurable influence on t h i s t h e s i s and my understanding of mining and rock mechanics. F i n a l l y , and most of a l l , I wish to express my thanks to Harry and N e l l i e Hudyma for t h e i r continuous encouragement and support during a l l my endeavors. 1 CHAPTER 1 INTRODUCTION Open stope mining has been practiced i n Canada since the 1930's. The design of open stope mines i s centered around determining the largest stable stopes and the optimum siz e for p i l l a r s . Systematic methods to design open stopes and t h e i r separating " r i b " p i l l a r s have not been confirmed i n t y p i c a l Canadian open stope mining conditions. In 1986, the Natural Sciences and Engineering Research Council (NSERC), Noranda Research and Falconbridge Limited agreed to sponsor the "Integrated Mine Design Project", a research project at the University of B r i t i s h Columbia under the supervision of Dr. H.D.S. M i l l e r . The goal of the study was to investigate open stope mine design methods by confirming the v a l i d i t y of ex i s t i n g stope and r i b p i l l a r design methods or by developing new empirical methods. This thesis i s a compilation and analysis of the information and data c o l l e c t e d for the design of r i b p i l l a r s i n open stope mining. The f i r s t section of t h i s chapter i s a summary of the contents of the th e s i s . The remainder of the chapter w i l l introduce the problem of designing open stope r i b p i l l a r s by describing open stope mining, and discussing the r o l e of r i b f p i l l a r s i n open stope mining. 1.1 Contents of the Thesis 2 T h i s s t u d y b e g i n s by d e s c r i b i n g open s t o p e m i n i n g and t h e r o l e o f r i b p i l l a r s i n open s t o p e m i n i n g . I n C h a p t e r 2 , t h e c h a r a c t e r i s t i c s o f p r o g r e s s i v e p i l l a r f a i l u r e a r e d i s c u s s e d and t h e f a c t o r s t h a t i n f l u e n c e r i b p i l l a r s t a b i l i t y a r e i d e n t i f i e d . C h a p t e r 3 c o n t a i n s a r e v i e w o f t h e e m p i r i c a l and n u m e r i c a l d e s i g n methods u s e d f o r open s t o p e r i b p i l l a r s . The r i b p i l l a r d a t a c o l l e c t e d i n t h e I n t e g r a t e d M i n e D e s i g n P r o j e c t i s p r e s e n t e d i n C h a p t e r 4 . C h a p t e r 5 d i s c u s s e s t h e use o f boundary e l e m e n t n u m e r i c a l methods t o d e t e r m i n e t h e a v e r a g e s t r e s s i n open s t o p e r i b p i l l a r s . The l o a d i n d u c e d on a l l o f t h e d a t a base p i l l a r s i s e s t i m a t e d i n t h i s s e c t i o n . C h a p t e r 6 shows t h e d e v e l o p m e n t o f a new e m p i r i c a l p i l l a r d e s i g n method c a l l e d t h e " P i l l a r S t a b i l i t y G r a p h " , ba sed on g r a p h i c a l a n a l y s i s o f t h e r i b p i l l a r d a t a and d a t a from l i t e r a t u r e . I t a l s o compares t h e new method w i t h e x i s t i n g e m p i r i c a l d e s i g n methods f o r open s t o p e r i b p i l l a r s . C h a p t e r 7 b r i e f l y d i s c u s s e s t h e a p p l i c a t i o n o f t h e p i l l a r s t a b i l i t y g r a p h f o r t h e d e s i g n o f open s t o p e r i b p i l l a r s . A summary and c o n c l u s i o n o f t h e t h e s i s i s f ound i n C h a p t e r 8. 1.2 Open S t o p e M i n i n g Open s t o p e m i n i n g i s a g e n e r a l name u s e d t o d e s c r i b e a h i g h l y v a r i e d m i n i n g me thod . The re a r e many i m p o r t a n t f e a t u r e s t h a t make up t h e method , and many v a r i a t i o n s on e a c h o f t h e f e a t u r e s . The f o l l o w i n g d i s c u s s i o n o f t h e d e f i n i t i o n , a p p l i c a b i l i t y , and d e s c r i p t i o n o f open s t o p e m i n i n g i s t a k e n l a r g e l y f rom an u n p u b l i s h e d p a p e r on open s t o p e m i n i n g methods , 3 written at U.B.C. (Hudyma 1988a). 1.2.1 D e f i n i t i o n of Open Stoping Three c h a r a c t e r i s t i c s , common to a l l open stoping methods, make i t d i s t i n c t from other mining methods. i) Open stoping i s a non entry mining method. Once stope production has started, a l l a c t i v i t i e s requiring miners are done from the periphery of the stope. The open stope does not need to be entered and at no time are miners exposed to the production face, i i ) I t i s generally a nat u r a l l y supported mining method (although some a r t i f i c i a l support i s occasionally used). Naturally supported means that displacement and deformation of the rock mass i s li m i t e d to e l a s t i c orders of magnitude. The underground structures created are designed to be s t a b l e and self-supporting (in opposition to caving methods) . Mining i s done i n a manner to ensure that unstable release of energy due to mining does not occur (from Brady 1981). i i i ) Stopes are opened to t h e i r f u l l dimensions before a s t a b i l i z i n g f i l l i s introduced. These three c h a r a c t e r i s t i c s d i s t i n g u i s h open stoping from a l l other underground methods. Cut and f i l l , longwall, room and p i l l a r and shrinkage are a l l entry methods that require workers to enter the production face of the stope. Block caving and 4 sublevel caving induce large, unstable movements of rock and include the continual d i s s i p a t i o n of energy as mining proceeds, so they can not be considered nat u r a l l y supported methods. Methods such as AVOCA, which introduces f i l l during extraction to prevent stope i n s t a b i l i t y , or shrinkage stoping, which keeps the stope f u l l of broken ore, are excluded from open stoping because the stope i s never f u l l y open. 1.2.2 A p p l i c a b i l i t y of Open Stoping There are some orebody and geological l i m i t a t i o n s to the a p p l i c a t i o n of open stoping. Modifications of open stoping can be made to mine a wide v a r i e t y of orebodies, but some conditions present d i f f i c u l t problems. Open stoping i s best suited to orebodies that are steep dipping. Stopes i n the orebody must dip s u f f i c i e n t l y above the angle of repose of the broken ore (above 50° to 55°) to permit gravity flow of the ore to the stope bottom. Open stoping can be successful i n shallow dipping orebodies (approximately less than 30°) but the orebody must be quite t h i c k (greater than about 15 metres i n true thickness). I f an orebody i s not steep dipping or t h i c k and f l a t , open stoping can not be used. For mining a steep dipping orebody, the orebody outline must be f a i r l y regular and the orebody needs to be greater than about 5 metres i n width. Irregular orebodies are d i f f i c u l t to delineate and mine. Generally, at widths less than 5 metres, wall rock d i l u t i o n due to d r i l l hole deviation and b l a s t damage 5 becomes too great to use open stoping e f f e c t i v e l y . The rock mass strength of the orebody and the surrounding country rock i s very important i n open stoping. The stronger the rock, the larger the stopes can be made, and consequently, the more productive the method w i l l be. At the l e a s t , f a i r rock mass strength i s needed i n the ore and wall rock to guarantee that the open stopes w i l l be naturally supporting. A f i n a l r e s t r i c t i o n on open stoping i s the orebody must be reasonably large. This i s necessary to get a few working faces (because open stoping i s often a c y c l i c a l method), to take advantage of the large scale of the mining method, and to j u s t i f y the cost of the development associated with open stope mining. 1.2.3 Description of Typical Open Stope Mining Methods Open stoping methods are so dependent on the orebody shape, si z e and orie n t a t i o n that no two mines are exactly the same. Most open stope mining a c t i v i t i e s can be generalized into two basic stages: pre-mining development and production. Open stoping has a large amount of pre-mining development. Typical development usually includes: - sublevel accesses such as ramps, man-way rai s e s (figure 1, note A), and sublevel d r i f t s (figures 1 and 2, note B), - a d r i l l i n g horizon which includes stope access d r i f t s (figures 1 and 2, note C) and d r i l l drives (figure 1, note D) or overcuts (figure 2, note E), LEGEND A - MAN WAY-RAISE F - FOOTWALL HAULAGE DRIFT B - SUBLEVEL DRIFT H - DRAWPOINT C STOPE ACCESS DRIFT I - COLLECTION CONE D - DRILL DRIFTS L - RING DRILL PATTERN FIGURE 1. The elements of an Ideal ized l o n g i t u d i n a l longhole open stoping method showing the b l a s t i n g , mucking and b a c k f i l l i n g operations (after Hudyma 1988a). 3 LEGEND B - SUBLEVEL DRIFT G - FULL STOPE UNDERCUT C - STOPE ACCESS DRIFT H - DRAWPOINT E - FULL STOPE OVERCUT J - SLOT RAISE F - FOOTWALL HAULAGE DRIFT K - PARALLEL DRILL HOLES FIGURE 2. The elements of an i d e a l i z e d transverse blasthole open stoping method showing the d r i l l i n g , b l a s t i n g , mucking and b a c k f i l l i n g operations (af t e r Hudyma 1988a). 8 - a mucking horizon, which may include: - a footwall haulage d r i f t (figures 1 and 2, note F), - stope access undercuts (figure 2, note G) or drawpoints (figures 1 and 2, note H), - stope undercut scrams, V-cuts or c o l l e c t i o n cones (figure 1, note I ) , - the opening of a s l o t r a i s e (figure 2, note J) by staging, drop r a i s i n g , Alimak r a i s e climber or by r a i s e borer. Production mining involves: - using p a r a l l e l d r i l l holes to slash ore into the s l o t r a i s e to form an expansion s l o t which i s opened the f u l l width of the stope, - d r i l l i n g production holes i n p a r a l l e l (figure 2, note K) or rin g patterns (figure 1, note L) . The holes are used to b l a s t ore into the expansion s l o t . Generally, the expansion s l o t i s opened at one end of the stope and ore i s slashed into the s l o t causing a gradual retreat of the production face. This retreat may be longitudinal (along the orebody, as i n figure 1) or transverse (across the orebody, as i n figure 2). As a stope i s blasted, ore i s removed from the bottom of the stope. The ore i s almost always removed with the use of track l e s s load-haul-dump equipment, and taken to an orepass system. There are a few mines using slusher/scraper equipment or continuous mining equipment to move the muck to an orepass, but these operations are quite rare. The ore pass system moves 9 the muck to a central c o l l e c t i o n point for transport out of the mine. When the stope i s completely blasted, i t may be f i l l e d with waste rock or c l a s s i f i e d m i l l t a i l i n g s to permit recovery of p i l l a r s l e f t between stopes (both figures 1 and 2 show the f i l l i n g of stopes). 1.3 Role of Rib P i l l a r s i n Open Stope Mining The most economic open stope method involves mining the enti r e orebody i n one longitudinal stope. I f the use of t h i s f u l l lens mining creates the p o t e n t i a l for serious stope i n s t a b i l i t y , major stope support such as r i b p i l l a r s and b a c k f i l l w i l l l i k e l y be needed. The r o l e of r i b p i l l a r s i n open stope mining i s to provide s t a b i l i t y to a mining block by l i m i t i n g rock mass displacements and r e s t r i c t i n g the exposure of the rock mass i n the stope back and walls. In the past, i f f u l l lens mining was not possible, p i l l a r s had to be l e f t to maintain o v e r a l l mine s t a b i l i t y . Recently, improvements i n mining technology have caused a trend towards the sequencing of extraction so that p i l l a r s are never created, even i n very large orebodies. However, of the 34 Canadian open stope mines investigated i n t h i s study (from 1986-1988), 27 used r i b p i l l a r s to separate stopes i n the orebody. These p i l l a r s varied i n s i z e from about 2000 m3 up to 150,000 m3, depending on factors such as: the orebody geometry, the type of open stoping method, and the mining sequence. The dimensions of the p i l l a r s i n the data base are given i n Chapter 4.1 (Table 5, page 70). 10 I t i s important that r i b p i l l a r s perform t h e i r designed r o l e . Mines using r i b p i l l a r s may leave as much as h a l f of the orebody reserves i n temporary p i l l a r s . The consequences of poor p i l l a r design can serio u s l y a f f e c t the recovery of t h i s ore. A p i l l a r that does not perform i t s intended r o l e may cause: - excessive stope or p i l l a r sloughing, - d i f f i c u l t and expensive p i l l a r recovery, - loss of p i l l a r access, - the need f o r remedial measures such as development r e h a b i l i t a t i o n or a r t i f i c i a l support, - low productivity, - or the loss of ore reserves. 11 CHAPTER 2 RIB PILLAR FAILURE The f i r s t step i n quantifying the variables that influence p i l l a r s t a b i l i t y i s to describe p i l l a r f a i l u r e . While open stope r i b p i l l a r f a i l u r e has not been deeply researched, some of the p r i n c i p l e s of f a i l u r e i n i n t a c t hard rock, s o f t rock and rock masses are applicable to open stope r i b p i l l a r s . The objective of t h i s chapter i s to b r i e f l y discuss the character-i s t i c s of p i l l a r i n s t a b i l i t y and compare them to observations and documentation of f a i l u r e i n open stope r i b p i l l a r s . Using these ideas about p i l l a r f a i l u r e , the factors that influence the s t a b i l i t y of open stope p i l l a r s w i l l be i d e n t i f i e d . 2.1 F a i l u r e Mechanisms and Ch a r a c t e r i s t i c s Rib p i l l a r f a i l u r e can be broken into two basic modes: progressive (stable) f a i l u r e and bursting (unstable) f a i l u r e . Progressive f a i l u r e r e f e r s to gradual d e t e r i o r a t i o n of a rock mass i n a slow, non-violent manner. Bursting f a i l u r e i s the v i o l e n t release of energy causing the instantaneous fracture of rock. Although the conditions associated with each may be very d i f f e r e n t , both modes of f a i l u r e create serious d i f f i c u l t i e s for mining. This thesis w i l l describe and quantify progressive f a i l u r e . Progressive f a i l u r e i s related to the i n s i t u rock properties of the p i l l a r and mine, and the s t a t i c underground stress f i e l d . 12 Both of these factors are quantifiable with reasonable accuracy. Bursting f a i l u r e i s also related to i n s i t u rock properties. However, i t i s also dependent upon factors such as l o c a l stress concentration, the energy released due to the mining and changes i n the dynamic stress f i e l d . I t i s not intended to investigate these factors as they are not quantifiable with technology and budget available for t h i s study. For t h i s reason, the thesis w i l l not attempt to describe or quantify unstable f a i l u r e . Although r i b p i l l a r f a i l u r e i n open stope mining i s not uncommon, i t i s r a r e l y well documented. A reason for the lack of documentation i s that v i s u a l observation and monitoring of p i l l a r s i s d i f f i c u l t i n open stope mining and there i s no t universal method to describe the c h a r a c t e r i s t i c s and e f f e c t s of r i b p i l l a r f a i l u r e . Another pot e n t i a l reason for the absence of documentation i s that the f a i l u r e of r i b p i l l a r s i s often not considered an immediate problem, e s p e c i a l l y with open stope mining methods using b a c k f i l l . In the primary mining, r i b p i l l a r f a i l u r e often does not cause operational problems that are serious enough to warrant changing the mining sequence. Consequently, the operational e f f e c t s of r i b p i l l a r f a i l u r e may not be experienced u n t i l p i l l a r mining s t a r t s . This f a i l u r e often r e s u l t s i n low productivity, waste d i l u t i o n , higher mining costs and possibly l o s t ore. Several signs i n d i c a t i n g p i l l a r s t a b i l i t y problems i n open stope r i b s have been i d e n t i f i e d . These signs of p i l l a r d i s t r e s s 13 are: - cracking and s p a l l i n g of rock i n r i b p i l l a r development and r a i s e s , - audible noise heard i n the p i l l a r s or microseismic events located with monitoring systems, - deformed or plugged d r i l l holes causing d r i l l rods to be stuck and causing problems i n loading holes, - overdraw from primary stopes with the "free" muck being unblasted, oversize material from p i l l a r walls, - stress r e d i s t r i b u t i o n from r i b p i l l a r s a f f e c t i n g nearby p i l l a r s and hanging wall and footwall d r i f t s and raises, - hourglassing and cracking of p i l l a r s seen from development, - major displacements and changes i n stress shown by instrumented monitoring systems such as extensometers, stress meters and sloughmeters. No singl e sign necessarily denotes p i l l a r f a i l u r e , but these signs are commonly reported during p i l l a r f a i l u r e . Progressive p i l l a r f a i l u r e i s a gradual process. Problems may be minor at f i r s t , but get worse with time. P i l l a r damage and d e t e r i o r a t i o n can occur through i n t a c t rock and along e x i s t i n g s t r u c t u r a l d i s c o n t i n u i t i e s . Although p u r e l y 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 s occur i n p i l l a r s , the ov e r a l l influence of geological structure i n open stope p i l l a r s i s not predominant. Stress, p i l l a r loading and development of stress r e l a t e d fractures appears to be predominant. Consequently, the 14 discussion of r i b p i l l a r f a i l u r e w i l l focus on rock fracturing, p i l l a r loading, and the subsequent loss of p i l l a r load bearing a b i l i t y . 2.1.1 Rock Fracturing Rock f r a c t u r i n g i s a primary indicator of p i l l a r f a i l u r e and i s the ultimate reason for the loss of load bearing a b i l i t y and p i l l a r d i s i n t e g r a t i o n . Brady and Brown (1985) define f r a c t u r i n g as " . . . the formation of planes of separation i n the rock material. I t involves the breaking of bonds to form new surfaces." Fracturing generally s t a r t s at the p i l l a r walls where the rock mass i s weakest due to the lack of confinement of p i l l a r material. As f a i l u r e progresses, fractures propagate and develop i n the central parts of the p i l l a r and the s i z e and i n t e n s i t y of e x i s t i n g fractures increases. Krauland and Soder (1987) defined 6 stages to c l a s s i f y p i l l a r f a i l u r e based on v i s u a l observation of p i l l a r f r a c t u r i n g i n room and p i l l a r mines. The stages defined are: "0) No fractures. 1) S l i g h t s p a l l i n g of p i l l a r corners and p i l l a r walls, with short fracture lengths i n r e l a t i o n to p i l l a r height, subparallel to p i l l a r walls. 2) One or a few fractures near surface, d i s t i n c t s p a l l i n g . 3) Fractures appear also i n central parts of the p i l l a r . 4) One or a few fractures occur through central parts of the p i l l a r , d i v i d i n g i t into two or several parts, with rock f a l l s from the p i l l a r . Fractures may be p a r a l l e l to p i l l a r walls or diagonal, i n d i c a t i n g emergence of an hour-glass-shaped p i l l a r . 5) Disintegration of the p i l l a r . Major blocks f a l l out and/or the p i l l a r i s cut o f f by well defined fractures. A l t e r n a t i v e l y , a well developed hour-glass shape may emerge, with central parts completely crushed." 15 Krauland and Soder also noted that although the appearance of p i l l a r f a i l u r e was h i g h l y v a r i a b l e due to g e o l o g i c a l inhomogeneities, the basic pattern of f a i l u r e propagation remained constant for progressive f a i l u r e . This i s perhaps the best documentation and d e f i n i t i o n of an actual mine p i l l a r f a i l u r e mechanism. Use of the Krauland and Soder observational approach to c l a s s i f y open stope p i l l a r s i s not generally possible due to the lack of v i s u a l access. However, the mode of f a i l u r e described above i s s i m i l a r to that seen by the author i n several open stope mines and i s documented i n a few open stope mines (Falmagne 1986; Bray 1967) where s u f f i c i e n t v i s u a l access was av a i l a b l e . The only observation of Krauland and Soder that t h i s author has not seen i n open stope mining i s the d i v i s i o n of p i l l a r s into d i s t i n c t regions due to fr a c t u r i n g . This part of the mechanism i s not l i k e l y to occur i n open stope p i l l a r s . The pot e n t i a l for a fracture to completely sever a p i l l a r i s much lower i n open stope mining than i n room and p i l l a r mining due to the larger scale of open stope p i l l a r s . Fractures would have to be very continuous, f l a t and planar to transect and divide open stope p i l l a r s . From personal observation and l i t e r a t u r e descriptions, some of the most common types of fr a c t u r i n g found i n mine p i l l a r s are: i) surface fr a c t u r i n g and s p a l l i n g (figure 3a) i s usually the f i r s t l o c a t i o n of fracture development (Krauland and Soder 1987) and often a r e s u l t of lack of p i l l a r wall confinement original pillar surface FIGURE 3a. P a r a l l e l f racturing and s p a l l i n g due to a lack of confinement at the p i l l a r walls (after Brady and Brown 1985). -soft partings - internal splitting FIGURE 3b. Internal s p l i t t i n g and a x i a l cracking of a p i l l a r due to deformable p i l l a r layers or the propagation of p a r a l l e l wall fractures (af t e r Brady and Brown 1 9 8 5 ) . FIGURE 3c. Diagonal crushing fractures may occur i n confined or massive p i l l a r s ( a f t e r Brady and Brown 1985) 17 (Fairhurst and Cook 1966). i i ) i n t e r n a l a x i a l cracking (figure 3b) may be caused by highly deformable layers between the p i l l a r and the adjacent wall rock (Brady and Brown 1985) or may be p a r a l l e l surface fractures that propagate or develop i n the centre of the p i l l a r (Agapito 1974). i i i ) diagonal crushing fractures (figure 3c) are often found i n confined or massive p i l l a r s (Coates 1981). 2.1.2 P i l l a r Load-deformation Curve P i l l a r loading can be hypothetically described using a load-deformation (stress-strain) curve (see figure 4) . As a p i l l a r i s loaded, i t compresses according to the l i n e OA. At a load pmax' t n e maximum p i l l a r load bearing capacity i s reached. Beyond t h i s point, p o s t - f a i l u r e deformation of the p i l l a r w i l l occur but at a reduced load. This peak load w i l l be taken as the point of f a i l u r e i n a p i l l a r . Bieniawski (1987) states, "... the ultimate strength i s a state at which the rock specimen or the p i l l a r changes from a gradually increasing load-bearing capacity to a constant or gradually decreasing load-bearing capacity." Determining the actual load-deformation c h a r a c t e r i s t i c s of a hard rock mine p i l l a r i s not possible. Curves f o r small hard rock laboratory specimens are e a s i l y determined and curves for small i n s i t u coal p i l l a r s have been developed (Wagner 1974; Bieniawski and Van Heerden 1975), but i t i s not experimentally 18 FIGURE 4 . A hypothetical load-deformation curve can be used to describe the s t r e s s - s t r a i n c h a r a c t e r i s t i c s of a p i l l a r . The p i l l a r e x h i b i t s l i n e a r e l a s t i c deformation (along l i n e OA) u n t i l the maximum load i s reached ( P m a x ) • P i l l a r deformation continues (along l i n e AB), but with a decreasing load bearing capacity (after S t a r f i e l d and Fairhurst 1968). 19 p r a c t i c a l to conduct load-deformation t e s t s on large samples of j o i n t e d rock (Brady 1977). While t h i s leaves the load-deformation curve of a hard rock mine p i l l a r as a t h e o r e t i c a l concept, i t i s a convenient method to describe p i l l a r f a i l u r e and the loss of p i l l a r load bearing capacity. 2.1.3 Loss of Load Bearing Capacity Ultimately, rock f r a c t u r i n g i s the main reason for loss of p i l l a r load bearing capacity. However, the onset of f r a c t u r i n g does not necessarily s i g n i f y that the p i l l a r has f a i l e d . Agapito (1974), i n h i s study of o i l shale p i l l a r s , found that f r a c t u r i n g started as minor s p a l l i n g i n the p i l l a r perimeter and occurred at stress l e v e l s well below the ultimate load capacity of a p i l l a r . He also noted that as f r a c t u r i n g occurred i n the outer s h e l l of the p i l l a r , monitoring showed that stress concentrations b u i l t up i n the p i l l a r core. Wagner (1974) monitored the i n s i t u stress d i s t r i b u t i o n i n more than 30 underground coal p i l l a r s using a s e r i e s of hydraulic jacks. He found that at several stages of compression, the perimeter of the p i l l a r c a r r i e d r e l a t i v e l y l i t t l e stress compared to the central core of the p i l l a r (figure 5) . He noted that most of the load bearing capacity of a p i l l a r i s found i n the core of the p i l l a r and i s l a r g e l y dependent on the confinement provided by the p i l l a r s h e l l . A f t e r f a i l u r e of the p i l l a r (due to serious i n t e r n a l and surface f r a c t u r i n g ) , Wagner (1974) found that a confined p i l l a r Pillar compression (mm) 2 FIGURE 5 . Wagner (1974) did a series of in situ load-deformation tests on coal p i l l a r s using hydraulic jacks. For this case, 2 5 jacks were put in a 5X5 pattern in a square p i l l a r . The graph on the top shows the load-deformation characteristics of the p i l l a r in general. The oblique diagrams give the relative load on each of the 25 jacks at four stages of p i l l a r compression. The diagrams show that with increasing compression and increasing average p i l l a r stress, the core of the p i l l a r carries an increasing percentage of the load, while the unconfined periphery of the p i l l a r carries less load. Diagram four shows that the p i l l a r core carries a significant load despite the fact that the p i l l a r i s losing i t s overall load bearing capacity (redrawn from Wagner 1974). core had a considerable load bearing capacity. Krauland and Soder (1987) wrote that loss of load bearing capacity i n the post f a i l u r e range of p i l l a r loading depends l a r g e l y upon the slenderness of the p i l l a r s and the presence of f i l l . This i s also supported by the laboratory t e s t i n g of rock specimens i n " s t i f f - t e s t i n g " machines. S t a r f i e l d and Fairhurst (1968) demonstrated that i f confining pressure on a sample i s increased, the peak load capacity increases and the post f a i l u r e load bearing capacity i s greatly enhanced (see figure 6). The loss of load bearing capacity i n open stope r i b p i l l a r s i s also highly dependent on confinement of the p i l l a r core. However, i n open stope mining p i l l a r walls can be very large. Once progressive f a i l u r e s t a r t s , the fractured wall material w i l l peel o f f , preventing confinement of the p i l l a r core, and f i n a l l y r e s u l t i n g i n complete p i l l a r d i s i n t e g r a t i o n . There are methods to prevent fractured wall material from becoming detached from the p i l l a r . These methods include the use of b a c k f i l l , i n s t a l l a t i o n of a r t i f i c i a l support such as cable b o l t s , and leaving open stopes f u l l of broken ore as long as possible to provide some confinement to the p i l l a r walls. The author has seen several examples of f a i l e d r i b p i l l a r s with a considerable load bearing capacity. In these cases, the p i l l a r core had remained confined because the fractured p i l l a r material was confined by b a c k f i l l before i t had the opportunity to slough from the p i l l a r walls. 22 FIGURE 6. The s t r e s s - s t r a i n curves for laboratory specimens loaded under increasing confining pressures show an increase i n peak load and an increase i n the post-peak load bearing capacity (a f t e r S t a r f i e l d and Fairhurst 1968) . 23 2.2 S i g n i f i c a n t Variables i n Open Stope P i l l a r S t a b i l i t y Based on the f a i l u r e c h a r a c t e r i s t i c s described above, there are several variables that could be important i n the design of r i b p i l l a r s . This section w i l l describe the variables and t h e i r p o t e n t i a l influence. 2.2.1 Intact Rock Strength With rock f r a c t u r i n g playing a large r o l e i n the s t a b i l i t y of p i l l a r s , the resistance of the p i l l a r material to fra c t u r i n g and crushing i s an important factor i n p i l l a r strength. The most common index for comparing the strength of d i f f e r e n t rock types i s the u n i a x i a l compressive t e s t . The uni a x i a l compressive s t r e n g t h (UCS) i s the maximum load that a standardized diameter d r i l l core can sustain under un i a x i a l loading conditions. The UCS i s variable upon specimen siz e , so the sample diameter i s standardized to about 54 mm (NX size d r i l l core). Further information about the u n i a x i a l t e s t can be found i n a report by an International Commission on standard-i z a t i o n of laboratory t e s t s (ISRM Commission 1979). 2.2.2 P i l l a r Load P i l l a r load i s a primary factor i n p i l l a r deformation, rock f r a c t u r i n g and p i l l a r f a i l u r e . The d i s t r i b u t i o n of stress i n a p i l l a r may have a s i g n i f i c a n t e f f e c t on the performance and s t a b i l i t y of the p i l l a r . However, there i s no conclusive method to determine stress i n a p i l l a r and there i s no single value 24 that can used to describe the complete loading condition of a p i l l a r . The state of stress i n a p i l l a r v a r i e s upon the stress applied to the p i l l a r as well as the l o c a t i o n inside the p i l l a r . The stress applied to a p i l l a r varies on the pre-mining stress f i e l d and the s i z e and location of stopes, underground workings and other p i l l a r s . The stress inside the p i l l a r i s dependent upon areas of weakness such as geological d i s c o n t i n u i t i e s , the proximity of excavations and the f r a c t u r i n g i n the p i l l a r . With these points kept i n mind, determining the d i s t r i b u t i o n of stress i n a p i l l a r with a high degree of p r e c i s i o n i s not possible. For t h i s thesis, i t was necessary to f i n d a value to represent the load on a p i l l a r . The load was taken as the average stress found at several points along the p i l l a r mid-h e i g h t c e n t e r l i n e , determined u s i n g numerical modelling techniques. The reason i s that t h i s l o c a t i o n has the highest normal stresses i n the p i l l a r , and i s frequently observed as the f i r s t area of f a i l u r e . This choice of stress analysis location w i l l be discussed i n more d e t a i l i n Chapter 5.2.2. 2.2.3 P i l l a r Shape Chapter 2.1.3 described the r o l e of confinement i n p i l l a r s t a b i l i t y and the load bearing capacity. P i l l a r shape has a huge influence on confinement of the p i l l a r core. I t a f f e c t s : - the load-convergence c h a r a c t e r i s t i c s of p i l l a r s at f a i l u r e 25 (Hudson et a l . 1971; S t a r f i e l d and Fairhurst 1968), - the p o s t - f a i l u r e deformation modulus of p i l l a r s (Hudson et a l . 1971; Wagner 1974), - the stress d i s t r i b u t i o n i n a p i l l a r ( S t a r f i e l d and Fairhurst 1968; Wagner 1974), - and the e f f e c t of geological structure and f r a c t u r i n g on p i l l a r s t i f f n e s s and f a i l u r e (Sarkka 1984). This confirms that p i l l a r shape as a s i g n i f i c a n t variable i n p i l l a r s t a b i l i t y . 2.2.4 Structural D i s c o n t i n u i t i e s i n P i l l a r s The e f f e c t of geological structure on r i b p i l l a r s depends upon whether the structure involves major d i s c o n t i n u i t i e s such as f a u l t s and shear zones or minor d i s c o n t i n u i t i e s l i k e j o i n t sets. P i l l a r s intersected by a major structure must be analyzed based on the s p e c i f i c s i t u a t i o n . The or i e n t a t i o n and shear strength of the major structure w i l l play a dominant r o l e i n s t a b i l i t y . However, i n open stoping, i n t e r s e c t i o n of a major structure i s not a common problem and design of such p i l l a r s i s an exception rather than a regular occurrence. When possible, r i b p i l l a r s are located to avoid i n t e r s e c t i o n by major geological d i s c o n t i n u i t i e s . Less prominent d i s c o n t i n u i t i e s such as j o i n t i n g and l o c a l f r a c t u r i n g , are a much more common problem i n p i l l a r design. The influence of minor d i s c o n t i n u i t i e s on r i b p i l l a r s depends upon the orientation, continuity, frequency and shear strength of the structures. At the p i l l a r central core, the e f f e c t of minor d i s c o n t i n u i t i e s on p i l l a r s t a b i l i t y i s small because the t r i a x i a l state of confinement prevents rock movement along the j o i n t s . Geological d i s c o n t i n u i t i e s have a more s i g n i f i c a n t e f f e c t on i n s t a b i l i t y i n unconfined regions of p i l l a r s . A l l c o t t and A r c h i b a l d (1981), Page and Brennan (1981), and Von Kimmelmann (1984) mention s t r u c t u r a l l y c o n t r o l l e d wedge f a i l u r e s from p i l l a r walls. One would expect to f i n d l i t t l e or no confinement of the rock near p i l l a r walls. Consequently, the influence of structure i s best accounted for using wall s t a b i l i t y analyses. An excellent method for wall s t a b i l i t y analysis i s described by Potvin et a l . (1988a). The method quantifies the influence of geological structure, mining induced stress, and stope dimensions to predict the s t a b i l i t y of each surface of an open stope. When the analysis predicts a stable p i l l a r wall, the e f f e c t of minor structure on the s t a b i l i t y of unfractured r i b p i l l a r s w i l l be small. 2.2.5 E f f e c t of P i l l a r Volume P i l l a r s are made of blocks of i n t a c t rock separated by natural and mining induced d i s c o n t i n u i t i e s . So the influence of p i l l a r volume on s t a b i l i t y i s r e a l l y a function of two v a r i a b l e s : the volume e f f e c t on the strength of i n t a c t rock, and the influence of the number of s t r u c t u r a l defects i n the p i l l a r . Laboratory compressive t e s t i n g of small samples has shown an influence of specimen s i z e on the compressive strength of int a c t rock (see figure 7) . However, t e s t i n g of large i n t a c t rock specimens has found that above a " c r i t i c a l " volume, the strength does not decrease s i g n i f i c a n t l y (see figure 8). This concept of asymptotic specimen strength i s reported by Bieniawski (1975) , Herget et a l . (1984), and Pratt et a l . (1972). These authors found the c r i t i c a l volume to be less than one cubic metre. With the volume of blocks i n open stope p i l l a r s usually being much larger than t h i s c r i t i c a l volume, there i s a very limited influence of the volume e f f e c t of i n t a c t rock. The number of s t r u c t u r a l d i s c o n t i n u i t i e s i n a p i l l a r w i l l depend upon the volume of the p i l l a r . Hoek and Brown (1980) suggest that t h i s influence can be quantified through the use of rock mass c l a s s i f i c a t i o n methods. Hardy and Agapito (1977), Stephansson (1985), and other authors have suggested that correction factors to account for p i l l a r volume be used i n p i l l a r strength determination. Both of these ideas w i l l be investigated with open stope r i b p i l l a r case h i s t o r i e s i n Chapter 6.1.3. 2.2.6 E f f e c t of B a c k f i l l The use of f i l l i s very important i n current open stope mining methods. A survey by the Ontario Ministry of Labour (Campbell 1987) found that almost a l l Ontario open stope mines use cemented f i l l to a id i n p i l l a r recovery. The general purpose of f i l l i s used to provide o v e r a l l mine s t a b i l i t y , 0 . 3 Sp*>ol Book O Harbta O Umastona V G r a n l t a A Basalt Basa l t -andas l ta lava Cabbro ftarbla N o r i t a C r a n l t a Quartz d l o r l t a T—t*d by H 0 9 I ' " K o l f M n 1 " B u r e h a r t i at a l ' " K o l f a » n ' " N a l a k l d l a 1 " l l n l c k a y a 1 " l l n i c k a y a 1 " B l a n t a w t k l ' * 7 Hosklns t H o r l n o 1 7 0 Pratt at a l ' * ' ( o e/«cS0) . ( 5 0 / d ) 0 - " 150 2 0 0 2 5 0 Specifwn d l a m t a r d FIGURE 7. There i s a very large influence of specimen si z e on the strength of i n t a c t rock, for small specimen diameters (after Hoek and Brown 1980). 150 100 70 50 - Ix c , • r Johns (1966) Iron ore * Oiorite ° Prott ^ <J/(I972) -•• Bieniowski (1967) _L 0 5 I IS 2 2 5 Specimen side length, m FIGURE 8. Strength t e s t i n g of samples of increasing specimen length shows a decreasing influence of s i z e . Beyond a " c r i t i c a l " length, there i s no s i g n i f i c a n t decrease i n specimen strength. This c r i t i c a l s i z e i s about 1 metre (after Bieniawski and Van Heerden 1975), e s p e c i a l l y i n stope hanging walls and footwalls, by l i m i t i n g spans to stable dimensions and to permit a high r a t i o of extraction of the orebody with p o t e n t i a l l y minimal d i l u t i o n . The r o l e of f i l l i n p i l l a r f a i l u r e i s much les s dramatic. Singh (1976) finds that f i l l : - provides l a t e r a l support to p i l l a r s to i n h i b i t s p a l l i n g and prevent collapse, - acts as a reta i n i n g media to contain fractured rock, thereby retarding the development of f a i l u r e i n surrounding rock, - and reduces energy release rates allowing rock to f a i l i n a non-violent manner. None of these e f f e c t s of f i l l i n g has a large influence on the rock f r a c t u r i n g mode of f a i l u r e described above i n Chapter 2.1.1. F i l l does provide r e s t r a i n t and confinement to fractured rock to prevent sloughing of p i l l a r material and consequently enhances the p o s t - f a i l u r e load bearing capacity of p i l l a r s . Thomas (1979) supports Singh's comments by wri t i n g that f i l l i s not l i k e l y to provide stope wall support before u n r e a l i s t i c f i l l deformation (approximately 20%) has occurred. He finds that f i l l i s most b e n e f i c i a l to mining when i t provides rock confinement causing the rock mass to support i t s e l f . Consolidated and cemented f i l l s have been found more e f f e c t i v e at aiding i n underground s t a b i l i t y (Bharti 1987) . However, the main purpose of consolidated f i l l s i s to be s e l f -supporting and free-standing during p i l l a r recovery operations. 3 0 f a i l u r e due to rock f r a c t u r i n g . I t does give support to f a i l e d p i l l a r s to maintain t h e i r i n t e g r i t y and some load bearing capacity. This aids i n o v e r a l l mine s t a b i l i t y and s i m p l i f i e s p i l l a r recovery operations. 2.2.7 E f f e c t of Blasting Blasting practices are very important i n the success of any mining method. Poor b l a s t i n g practices can turn a stable and e f f i c i e n t design into a very i n e f f i c i e n t design. Some of the ef f e c t s of poor b l a s t i n g i n open stope mining include: poor fragmentation, overbreak beyond stope l i m i t s , need f o r frequent post-blast clean-up and development r e h a b i l i t a t i o n , development of b l a s t induced fractures i n the rock mass, and rock mass disturbance and i n s t a b i l i t y i n stope walls and p i l l a r s due to excessive v i b r a t i o n s . Quantifying poor b l a s t i n g i n an empirical method i s very d i f f i c u l t . There i s no cl e a r d e f i n i t i o n of poor b l a s t i n g , and the consequences are highly varied. The best solution i n describing b l a s t i n g i s to l i s t some of the practices used to minimize the e f f e c t of bl a s t i n g . These practices are often re f e r r e d to as control b l a s t i n g , and include: minimizing the charge weight per delay; using charge decking, decoupling, and/or low density explosives; using e f f i c i e n t hole l o c a t i o n and b l a s t sequencing; and b l a s t i n g to a free face. Although the si g n i f i c a n c e of b l a s t i n g practices i s very great i n mining, there are no c r i t e r i o n to quantify the e f f e c t s 31 of b l a s t i n g on mining. Consequently, b l a s t i n g w i l l not be discussed as a design variable i n t h i s t h e s i s . 2.3 Chapter Summary Progressive f a i l u r e of open stope r i b p i l l a r s i s d i f f i c u l t to observe due to lack of v i s u a l access. Several i n d i r e c t signs of p i l l a r d i s t r e s s have been documented. These signs are d i r e c t l y associated with rock f r a c t u r i n g i n the p i l l a r . Fracturing generally s t a r t s at the p i l l a r walls and propagates or develops i n the p i l l a r core as p i l l a r d e t e r i o r a t i o n progresses. Fractured rock loses some or a l l of i t s load bearing capacity, depending on the confinement of the material. P i l l a r f a i l u r e can be described as the state when a p i l l a r changes from having an increasing load bearing capacity to a constant or decreasing load bearing capacity. F a i l u r e can hypothetically be described using a p i l l a r load-deformation curve. The degree of confinement of a p i l l a r has a large influence on the shape of that curve. Open stope r i b p i l l a r design should be based on the conditions that influence p i l l a r f a i l u r e and load bearing capacity. These conditions are rock f r a c t u r i n g and p i l l a r confinement. The conditions may be influenced by a number of factors, including: the in t a c t strength of the p i l l a r material, the p i l l a r load, the shape of the p i l l a r , the presence of s t r u c t u r a l d i s c o n t i n u i t i e s , and the volume of the p i l l a r . 32 CHAPTER 3 REVIEW OF PILLAR DESIGN METHODS There are two general approaches to current r i b p i l l a r design: empirical methods, and numerical methods. Empirical design i s based on observation of case h i s t o r i e s and previous experience i n s i m i l a r geotechnical conditions. Numerical design i s l a r g e l y based on measured parameters and material properties. However, there i s not a cl e a r d i v i s i o n between the two approaches. Some numerical procedures are occasionally used i n e m p i r i c a l design and some experience and observational information i s used i n numerical techniques. This chapter w i l l discuss the two approaches as they are applied to hard rock p i l l a r design. I t w i l l b r i e f l y describe the background fundamentals i n each method, and give a short discussion of t h e i r respective advantages, disadvantages and l i m i t a t i o n s . 3.1 Empirical Design Methods Empirical design methods are characterized by the fact that they consider a p i l l a r as one unit. I t i s assumed that there i s no v a r i a t i o n i n s t a b i l i t y within a p i l l a r . The s t a b i l i t y of that p i l l a r i s interpreted based on three v a r i a b l e s : i) p i l l a r load, i i ) p i l l a r strength, i i i ) and safety factor. 33 Methods o f c a l c u l a t i n g o r d e t e r m i n i n g each o f t h e s e p a r a m e t e r s a r e b a s e d upon q u a n t i f y i n g u n d e r g r o u n d o b s e r v a t i o n s and p a s t e x p e r i e n c e . T y p i c a l l y , p i l l a r l o a d i s d e t e r m i n e d u s i n g e m p i r i c a l r u l e s o f thumb o r n u m e r i c a l t o o l s . P i l l a r s t r e n g t h and an a p p r o p r i a t e s a f e t y f a c t o r a r e c a l i b r a t e d w i t h c a s e h i s t o r i e s a n d / o r l a b o r a t o r y e x p e r i m e n t s . The s a f e t y f a c t o r i s d e f i n e d a s : S . F . = p i l l a r s t r e n g t h p i l l a r l o a d I t has t h r e e b a s i c p u r p o s e s : - t o expand t h e l o a d and s t r e n g t h d e t e r m i n a t i o n methods t o d i f f e r e n t m i n i n g c o n d i t i o n s , - t o make a d e s i g n more c o n s e r v a t i v e - and t o a c c o u n t f o r t h e i n a c c u r a c y i n t h e i n p u t p a r a m e t e r s . F o r i n s t a n c e , a p i l l a r i n an e n t r y m i n i n g method w o u l d be d e s i g n e d more c o n s e r v a t i v e l y t h a n a p i l l a r i n a n o n - e n t r y m i n i n g m e t h o d . I n o r d e r t o use t h e same s t r e n g t h and l o a d d e t e r m i n a t i o n p r o c e d u r e s f o r t h e d e s i g n o f b o t h s i t u a t i o n s , a h i g h e r s a f e t y f a c t o r w o u l d be d e s i g n e d i n t h e e n t r y method b e c a u s e t h e d e g r e e o f i n s t a b i l i t y a c c e p t a b l e i s l e s s . The c h o i c e o f s a f e t y f a c t o r i s u s u a l l y b a s e d on e x p e r i e n c e w i t h t h e s p e c i f i c d e s i g n method . The f o l l o w i n g s u b - s e c t i o n s w i l l summar ize t h e t e c h n i q u e s d e v e l o p e d f o r c a l c u l a t i n g p i l l a r s t r e n g t h and p i l l a r l o a d and w i l l l i s t t h e s a f e t y f a c t o r s s u g g e s t e d f o r t h e s e d e s i g n p r o c e d u r e s . Because t h e r e a r e a l a r g e number o f d i f f e r e n t t e c h n i q u e s u s e d t o d e t e r m i n e p i l l a r l o a d and s t r e n g t h , emphas i s w i l l be placed on those methods used f o r hard rock design. A more complete discussion of the empirical design methods i s documented by Potvin (1985). 3.1.1 P i l l a r Strength Determination There are many factors that may influence the strength of a mine p i l l a r . These factors include: - s i z e and shape of the p i l l a r , - volume of the p i l l a r , - resistance of i n t a c t p i l l a r material to crushing, - presence of d i s c o n t i n u i t i e s , - strength and orientation of the d i s c o n t i n u i t i e s , - confinement and t r i a x i a l strength of the p i l l a r rock mass, - and the presence of groundwater. The number of p o t e n t i a l l y s i g n i f i c a n t variables makes p i l l a r strength very d i f f i c u l t to determine a n a l y t i c a l l y . Some of these variables are not s i g n i f i c a n t under selected mining conditions. For such si t u a t i o n s , p i l l a r strength may be estimated empirically. The most commonly used empirical p i l l a r strength methods i n hard rock mining are: - Salamon's formula, - Hedley's formula, - Obert and Duvall formula, - and the Hoek and Brown p i l l a r strength curves. The f i r s t three of these methods are v a r i a t i o n s of the empirical s t r e n g t h formulas developed for underground coal mines. Consequently, a b r i e f discussion of the empirical coal formulas i s h e l p f u l , although they see very l i m i t e d use i n hard rock p i l l a r design. 3.1.1.1 Empirical Strength Formulas A major area of p i l l a r design research has been i n underground coal mining. A basic premise of t h i s work was that f u l l s i z e p i l l a r strength could be determined by extrapolating the r e s u l t s from laboratory t e s t i n g of coal specimens. Two forms of the empirical strength equation were developed: - the s i z e e f f e c t formula, - and the shape e f f e c t formula. A) The s i z e e f f e c t formula i s defined as: Op = K * (w a/h b) a f b where: <Tp = p i l l a r strength (psi) , K = u n i a x i a l compressive strength of one cubic foot of p i l l a r material, w = p i l l a r width, h = p i l l a r height, a,b = unequal empirically defined constants. This formula i s based on the fact that rock strength i s dependent on the s i z e of the sample. This i s due to the presence of d i s c o n t i n u i t i e s (such as j o i n t s , f o l i a t i o n s , bedding, b l a s t fractures, and mineralogy). As rock samples of a constant shape increase i n si z e , the strength of the sample decreases. This si z e e f f e c t i s taken into account by giving a d i f f e r e n t weighting to the c o e f f i c i e n t s for w and h i n a shape e f f e c t formula. Table 1 gives the constants a and b proposed by d i f f e r e n t authors. Constants a and b used i n the s i z e e f f e c t formula: ap = K * wa / SOURCE a b Streat (1954) 0.5 1.00 Holland-Gaddy (1962) 0.5 1.00 Greenwald et a l . (1939) 0.5 0.833 Hedley and Grant (1972) 0.5 0.75 Salamon and Munro (1967) 0.46 0.66 Bieniawski (1968) 0.16 0.55 Table 1 (after Babcock, Morgan and Haramy 1981). shape e f f e c t formula, which i s defined as: K * [A + B * (w/h)] K * (w a/h b) a = b ap = p i l l a r strength ( p s i ) , K = u n i a x i a l compressive strength of one cubic foot of p i l l a r material, w = p i l l a r width, h = p i l l a r height, B) The a P = or a B = where: A,B,a,b = empirically defined constants. The shape e f f e c t formula denotes a difference i n strength for p i l l a r s of d i f f e r e n t shape but equal cross-sectional area. The greater the p i l l a r width to p i l l a r height r a t i o , the greater the p i l l a r strength. A change i n mode of f a i l u r e i s one apparent cause of the shape e f f e c t on p i l l a r strength. Slender p i l l a r s tend to f a i l along s t r u c t u r a l d i s c o n t i n u i t i e s i n the rock mass. While for wide p i l l a r s , f a i l u r e i s l i k e l y to be caused by crushing of the p i l l a r material. Tables 2 and 3 give the constants a,b,A,B proposed by d i f f e r e n t authors. Constants a and b used i n the shape e f f e c t formula: oP = K * wa / h b SOURCE a b Zern (1926) Hazen and A r t i e r (1976) Holland (1956) Morrison et a l . 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 Table 2 (after Babcock, Morgan and Haramy 1981). Constants A and B used i n the shape e f f e c t formula: Op = K * [ A + B * (w/h)] SOURCE A B W / h Bunting (1911) Obert et a l . (1960) Bieniawski (1968) Van Heerden (1973) Sorensen and Pariseau (1978) 0.700 0.778 0.556 0.704 0.693 0.300 0.222 0.444 0.296 0.307 0.5 - 1.0 0.5 - 2.0 1.0 - 3.1 1.14 - 3.4 0.5 - 2.0 Table 3 (after Babcock, Morgan and Haramy 1981). 38 The constants and c o e f f i c i e n t s i n each of these formulas were based on p i l l a r case h i s t o r i e s and laboratory t e s t i n g of scale p i l l a r s . Three of the most prominent empirical p i l l a r design studies and surveys provided formulas commonly used i n hard rock p i l l a r strength determination. 3.1.1.2 Salamon 1s Formula In 1967, Salamon published a survey of stable and f a i l e d square coal p i l l a r s i n South A f r i c a n mines. The study investigated 98 stable and 27 collapsed p i l l a r areas. Using a s i z e e f f e c t formula, and assuming the mean safety factor for a l l the f a i l e d cases was 1.0, the c o e f f i c i e n t s K, a and b were ca l i b r a t e d . This gave the formula: strength = K * w 0- 4 6 / h 0 - 6 6 where: strength = p i l l a r strength ( p s i ) , K = 1320 = strength of one cubic foot of p i l l a r material, w = p i l l a r width (feet), h = p i l l a r height (feet). The complete database i s commonly displayed i n a histogram (see figure 9) . To determine a suitable safety factor for t h i s strength formula i n entry mining methods, Salamon averaged the safety factor of the most dense concentration of 50% of the stable p i l l a r s to get an average of 1.57 (see figure 9). He f e l t that t h i s safety factor was adequately conservative to I 1 1 1 1 1 ' 2 2 • «> •* e» o 3DN3aarO00 JO ADN3nD3MJ FIGURE 9. Histogram of the safety factors f o r stable and f a i l e d p i l l a r case h i s t o r i e s i n South A f r i c a n bord and p i l l a r coal mining. The range of safety factors for the most dense concentration of 50% of the stable cases i s between 1.31 and 1.88. Salamon chose the mean of t h i s range, 1.57, as adequately conservative to design stable, permanent p i l l a r s i n room and p i l l a r coal mining (after Salamon 1967). 40 ensure s t a b i l i t y f o r p i l l a r s i n room and p i l l a r coal mines. Despite the fa c t that the study i s based on square p i l l a r s i n bord and p i l l a r coal mining i n South A f r i c a , Salamon's formula has been used for the design of hard rock open stope r i b p i l l a r s . The factor to account f o r the strength of the p i l l a r material i s adjusted to the strength of one cubic foot of int a c t hard rock, but the c o e f f i c i e n t s and safety factor used are those o r i g i n a l l y proposed by Salamon. 3.1.1.3 Hedley's Formula Hedley and Grant (1972) proposed a p i l l a r strength formula based on data from hard rock room and p i l l a r mining at E l l i o t Lake. They empirically c a l i b r a t e d a s i z e e f f e c t formula s i m i l a r to that proposed by Salamon (discussed above). The formula was defined as: Qu = k * w0-5 / h 0 - 7 5 where: Qu = p i l l a r strength ( p s i ) , k = 26,000 = strength of one cubic foot of p i l l a r material ( p s i ) , w = p i l l a r width (feet), h = p i l l a r height (f e e t ) . The data base to develop t h i s formula consisted of 2 3 stable p i l l a r s , 2 p a r t i a l l y f a i l e d p i l l a r s and 3 crushed p i l l a r s . For a p p l i c a t i o n of t h e i r p i l l a r strength formula, Hedley and Grant suggested that p i l l a r s with a safety factor greater than 1.5 are stable and p i l l a r s with a safety factor near 1.0 are crushed. 41 These safety factors are based on i n t e r p r e t a t i o n of the a graphical p l o t of the data base (see figure 10). This strength formula has been further confirmed for room and p i l l a r mining, through studies by Von Kimmelmann et a l . (1984), and Townsend (1982). I t i s the only p i l l a r strength formula developed based on hard rock mining case h i s t o r i e s . So although no published study has confirmed i t s use for open stope p i l l a r s , i t i s widely used i n open stope p i l l a r design. 3.1.1.4 Obert and Duvall Shape E f f e c t Formula Obert et a l . (1946) performed a series of compressive strength t e s t s on specimen coal p i l l a r s with various shapes. I t was determined that the shape e f f e c t of p i l l a r strength follows the empirical r e l a t i o n s h i p : o-p = a± * [0.778 + 0.222(w/h)] where: rjp = p i l l a r strength, o"! = u n i a x i a l strength of a cubical p i l l a r specimen, w = p i l l a r width, h = p i l l a r height. The formula d i d not include any factor to account for the size e f f e c t on strength,, but instead suggested a safety factor between 2 and 4 be used i n p i l l a r design. In hard rock p i l l a r design, t h i s formula has been suggested to account for shape e f f e c t by several authors (Krauland and Soder 1987; Hedley et a l . 1979; Herget et a l . 1984). These authors used additional methods to account f o r p i l l a r strength rsxi ss*J)S JO/IM p>)Dwnsj} FIGURE 10. The estimated stress and strength for case his t o r i e s of p i l l a r s in room and p i l l a r mining in the E l l i o t lake uranium mining d i s t r i c t . Safety factor lines have been drawn on the graph. The chart shows that a l l the case histories with a safety factor above 1.5 are stable (after Hedley and Grant 1972) . 43 si z e dependence. 3.1.1.5 Hoek and Brown P i l l a r Strength Curves Hoek and Brown (1980) proposed a series of curves for the estimation of p i l l a r strength (see figure 11). The curves were developed based on numerical modelling and the d i s t r i b u t i o n of f a i l e d rock inside p i l l a r s of d i f f e r e n t shapes and f o r a range of rock mass q u a l i t i e s , using the empirical rock mass f a i l u r e c r i t e r i a : a p = a2 + ( m * a c * a 3 + s * a c 2 ) ^ where: a p = average p i l l a r strength, a 3 = minimum p r i n c i p a l stress, Oq = u n i a x i a l compressive strength of the i n t a c t p i l l a r material, m & s = empirical constants based on the rock mass qua l i t y of the p i l l a r material. Hoek and Brown proposed these p i l l a r design curves assuming that a p i l l a r has f a i l e d when the stress across the centre of the p i l l a r exceeds the strength of the rock mass. They stated that a safety factor of 1.0 or less would imply that a p i l l a r i s t h e o r e t i c a l l y unstable and that a safety factor i n excess of 1.5 should be used f o r permanent p i l l a r s . However, ' these recommendations do not seem to be confirmed by case history back-analysis. Each curve can be considered a p i l l a r f a i l u r e c r i t e r i o n for a s p e c i f i c rock mass qual i t y . Hoek and Brown proposed that the Intact samples of fine grained igneous crystalline rock m - 17, * - 1 Very good quality rock mas8 m • 8.5, s - 0.1 Good quality rock mass m • 1.7, s » 0.00k Fair quality rock mass m - 0.3^, s » 0.0001 Poor quality rock mass m - 0.09, s - 0.00001 1 2 3 Pi 1lar width/height Wp/h FIGURE 11. Hoek and Brown (1980) proposed a series p i l l a r strength curves based on the theoretical d i s t r i b u t i o n of rock mass f a i l u r e i n a p i l l a r . influence of p i l l a r volume and s t r u c t u r a l defects could be quantified through the use of rock mass c l a s s i f i c a t i o n s . Consequently, the m and s constants account for p i l l a r volume and s t r u c t u r a l defects because they have been rel a t e d to the two most common rock mass c l a s s i f i c a t i o n methods, CSIR by Bieniawski (1973) and NGI by Barton et a l . (1974). O r i g i n a l l y , the strength curves were not supported by case h i s t o r i e s , however p r a c t i c a l a p p l i c a t i on by Potvin (1985) and Page and Brennen (1982) has been successful f o r the good and f a i r rock mass qu a l i t y curves. 3.1.2 P i l l a r Load In underground mine design, i t i s d i f f i c u l t to determine the actual load that w i l l be acting on a p i l l a r . For most safety factor p i l l a r design methods, two procedures are currently used. The f i r s t method, c a l l e d the Tributary Area Theory, uses a s i m p l i f i e d approach to underground stress r e d i s t r i b u t i o n . The other method, generally termed numerical modelling, involves the use of the theory of e l a s t i c i t y to determine s t r e s s r e d i s t r i b u t i o n . In contrast to the s i m p l i c i t y of the t r i b u t a r y area theory, numerical modelling requires the use of a computer due to the s o p h i s t i c a t i o n of the c a l c u l a t i o n process. 3.1.2.1 Tributary Area Theory The Tributary Area Theory assumes that when stopes are opened there i s an equal and symmetric stress r e d i s t r i b u t i o n regardless of the s i z e and location of the p i l l a r s created. I t i s often described using the analogy of a smooth flowing stream obstructed by bridge piers (see figure 12) . To permit a continuous flow rate i n the stream, streamlines are concentrated between the pi e r s ( i e . between the stopes). This causes the flow v e l o c i t y (stress) between the piers ( i n the p i l l a r s ) to increase. The increase i n flow v e l o c i t y i s generally dependent on the r a t i o of the width of the stream (width of the mining area) to the sum of the distances unobstructed by the piers (sum of the p i l l a r widths). So i n a rock mechanics perspective, t h i s theory describes the r e d i s t r i b u t i o n of p r i n c i p a l stress flowlines into p i l l a r s . The average p i l l a r load thus depends on the r a t i o of the t o t a l area extracted to the t o t a l area remaining i n the p i l l a r . Figure 13 shows the application of the Tributary Area Theory to several types of p i l l a r s (including r i b p i l l a r s ) . Due to the s i m p l i c i t y of t h i s theory, some factors that fundamentally influence stress i n p i l l a r s are ignored. These factors are: - the number of p i l l a r s i n the mining block (or the extent of the mining area), - the loc a t i o n of the p i l l a r i n the mining block, - the r e d i s t r i b u t i o n of stress into the abutments, - and the shape of the p i l l a r . A study by Salamon (1974) d e t a i l s the f i r s t three problems by comparing the average stress for a problem predicted by 4 7 FIGURE 12. The analogy of streamlines i n a smoothly flowing stream obstructed by bridge p i e r s i s often used to describe the concentration of stress i n p i l l a r s (after Hoek and Brown 1980). U n i t l e n g t h I-£ RIB PILLARS - o B - Y z O + W ° / W ) 1 • : • U I J . 1 H • E 3 SQUARE PILLARS - 0 p - yz(\ + w o / U p ) : L i r -i t i T - P i l l a r a r e a ^ o / o Rock column a r e a o IRREGULAR PILLARS -Rock column a r e a RECTANGULAR PILLARS - 0 p - Y z ( l + W o / W p ) ( l + L o / L p ) P i l l a r a r e a FIGURE 13. The tr i b u t a r y area theory, f o r average p i l l a r load c a l c u l a t i o n , applied to several d i f f e r e n t p i l l a r layouts (after Hoek and Brown 1980). 48 t r i b u t a r y area to those predicted by an e l e c t r i c analogue model. The stress i n square room and p i l l a r panels of three, seven and eleven square p i l l a r s (in each horizontal direction) were investigated. The average p i l l a r load according to the t r i b u t a r y area theory i s 4 Q 3 3 ( Q 3 3 i s the pre-mining stress component). Figure 14 shows the analogue r e s u l t s of these t e s t s . Stress r e d i s t r i b u t i o n into the abutments r e s u l t s i n the analogue predicted stress always being lower than the t r i b u t a r y area predicted load. As the panel widens (larger number of p i l l a r s ) , the load predicted by the analogue approaches the value of 4Q 3 3. I t i s also demonstrated by t h i s model that the lo c a t i o n of the p i l l a r i n the panel has a s i g n i f i c a n t e f f e c t on i t s load. The influence of the shape of a p i l l a r i s documented i n an in v e s t i g a t i o n of the Tributary Area Theory and two dimensional boundary element modelling of r i b p i l l a r s (Potvin et a l . 1987). Figure 15 shows that as a p i l l a r becomes more slender, the average p i l l a r load predicted by modelling decreases. This e f f e c t i s also discussed by Salamon (1974) and i s attributed to decreasing p i l l a r s t i f f n e s s with increasing p i l l a r slenderness. In summary, the Tributary Area Theory provides a very quick s o l u t i o n for determining p i l l a r load. However, the accuracy of the method i s diminished i f there are a small number of p i l l a r s , a small mining panel, or i f the p i l l a r s are slender i n shape. B i e n i a w s k i (1983) comments t h a t i n c o a l mining, the overestimation of p i l l a r load by t r i b u t a r y area may be as much 49 FIGURE 14. Using an e l e c t r i c analogue model, Salamon (1974) showed the v a r i a t i o n i n p i l l a r stress caused by increasing the number of p i l l a r s (N) i n a mining panel, a i s the p i l l a r stress, and Q 3 3 i s the premining stress. The tr i a n g u l a r symbols correspond to the three p i l l a r s i n panel (a), the c i r c u l a r symbols correspond to the seven p i l l a r s i n panel (b), and the diamond symbols correspond to the eleven p i l l a r s i n panel (c). The graph shows a d i s t i n c t influence of the location of a p i l l a r and the number of p i l l a r s on the stress induced. A 4.0. _ tributary area FIGURE 15. A study using two dimensional boundary element numerical modelling shows the influence of p i l l a r shape and the number of p i l l a r s on the average stress (a f t e r Potvin et a l . 1987). as 40%, while the author has found that the Tributary Area Theory may overestimate the load i n open stope r i b p i l l a r s by as much as 100% (Hudyma 1988b). 3.1.2.2 Numerical Modelling Several types of numerical models are a v a i l a b l e to aid i n the c a l c u l a t i o n of p i l l a r load. Each of these models has 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 a d i f f e r e n t means of c a l c u l a t i o n . The models applicable to hard rock p i l l a r design w i l l be discussed i n chapter 3.2. When used i n empirical design methods, the c a p a b i l i t i e s of numerical models include the a b i l i t y to: - analyze complex mining geometries, - account f o r any number of p i l l a r s and any s i z e of mining seam, - recognize p i l l a r l o c ation i n a mining block, - determine loads i n i n d i v i d u a l p i l l a r s , - and account for variat i o n s i n p i l l a r shape. Numerical modelling removes many of the problems associated with t r i b u t a r y area and i s usually necessary to estimate the p i l l a r load. However, the use of numerical modelling i s a s k i l l that takes a degree of knowledge, experience and c a l i b r a t i o n to use e f f i c i e n t l y i n p i l l a r design. These topics w i l l a l l be discussed i n more depth i n Chapter 3.2 and Chapter 4. 3.1.3 Safety Factor Hoek and Brown (1980) state that, "A safety factor of 1.0 52 implies that the p i l l a r i s t h e o r e t i c a l l y unstable and that the f a i l u r e could propagate across the enti r e p i l l a r The safety factors suggested for various empirical design procedures i n entry mining methods are l i s t e d i n Table 4. The degree of i n s t a b i l i t y acceptable i n entry methods i s much les s than that i n open stope methods. So, although there seems to be an agreement that a safety factor of about 1.5 i s s u f f i c i e n t for p i l l a r design i n entry mining methods, t h i s has not been v e r i f i e d for open stope mining. SOURCE SAFETY FACTOR Salamon (1967) Hedley (1972) Obert and Duvall (1967) Hoek and Brown (1980) Bieniawski (1983) Stacey and Page (1986) 1.6 1.5 2 - 4 1.5 1.5 - 2.0 1.5 Table 4. Safety factors suggested by various authors for p i l l a r design i n entry mining methods. Stacey and Page (1986) state that for p i l l a r s i n non-entry mining methods a minimum safety factor of 1.1 i s necessary and to design p i l l a r s to y i e l d or f a i l , a safety factor of less than 0.5 should be used. However, no data are presented to substantiate these values. Ultimately, none of these formulas or safety factors i s based on observation and experience i n open stope mining. Using a factor of safety adds a conservative cushion against the p o t e n t i a l error associated with empirical design methods. However, a conservative design i s not necessarily the most cost e f f e c t i v e design. Using the safety factors suggested for an entry method p i l l a r s w i l l l i k e l y give a stable design, but experience and c a l i b r a t i o n of an empirical design procedure w i l l provide a better estimate of the safety factor needed. 3.2 Numerical Design Methods In recent years, several .numerical (or computational) methods have been developed s p e c i f i c a l l y f o r use i n underground rock mechanics design. The program codes were created to permit two dimensional or three dimensional stress and displacement investigations around excavations i n rock. In s i m p l i s t i c terms, numerical modelling can be described with figure 16. A region (R) i s defined i n a medium and loading conditions are applied to the region. Excavations (E) are then created i n the medium. The p r i n c i p l e function of numerical modelling i s to calculate the magnitude and orie n t a t i o n of the stresses and displacements acting i n the v i c i n i t y of these excavations. The r e d i s t r i b u t i o n of stresses may be based on e l a s t i c and/or p l a s t i c behaviour of the medium. 3.2.1 Types of Numerical Methods Individual computational methods were developed to analyze problems with respect to s p e c i f i c properties of the medium. Brown (1987) grouped these properties into three broad categories: FIGURE 16. An i d e a l i z e d sketch showing the p r i n c i p l e of numerical modelling of underground excavations a f t e r Potvin et a l . 1987). - d i f f e r e n t i a l continuum methods, - i n t e g r a l methods, - and discontinuum methods. D i f f e r e n t i a l continuum methods (also c a l l e d f i n i t e element and f i n i t e difference methods) require d i s c r e t i z a t i o n of the medium within the region of in t e r e s t , at the boundary of the problem and at a long distance from the boundary of the problem (also termed the f a r f i e l d ) . Continuum methods assume the problem to be solved w i l l not be influenced by d i s c o n t i n u i t i e s i n the rock mass (medium) . This means the rock mass contains few or no s i g n i f i c a n t d i s c o n t i n u i t i e s , or the d i s c o n t i n u i t i e s are so common and uniform that i n d i v i d u a l l y they have no e f f e c t on stress r e d i s t r i b u t i o n . Consequently, for continuum methods, i t i s assumed that the medium can be represented by "equivalent" continuum rock mass material properties. D i f f e r e n t i a l continuum methods permit analysis using e l a s t i c and p l a s t i c theory. However, d i s c r e t i z a t i o n inaccuracies at the boundary and the far f i e l d , extensive data preparation and high computing times make f i n i t e element methods less appealing for rock mechanics design. An extensive discussion of f i n i t e element methods i s presented by Zienkiewicz (1977). Integral methods (or boundary element methods) also use the continuum approach but only r e q u i r e approximations or d i s c r e t i z a t i o n at the problem boundary. This greatly reduces the amount of data needed to describe the problem and consequently the amount of computer time needed to complete the computations. However, they are best suited to l i n e a r and homogeneous (or piece-wise homogeneous) material behaviour. The use of boundary element methods and t h e i r a p p l i c a t i o n i n rock mechanics i s d e t a i l e d i n a book by Crouch and S t a r f i e l d (1983). Discontinuum methods are a sp e c i a l type of d i f f e r e n t i a l technique. They generally assume a rock mass can be modelled by a f i n i t e number of discontinuous blocks. The most common discontinuum approach i s c a l l e d the d i s t i n c t element method. I t uses r i g i d blocks and the laws of motion to determine the forces and displacements applied to the blocks. A good description of the basis of d i s t i n c t element models and a general application i n a rock mass i s given i n Cundall (1987). The most appropriate numerical method for open stope p i l l a r design depends on the i n s i t u medium conditions and the form of stress response expected. As discussed i n Chapter 2, p i l l a r s are not l i k e l y to be i n f l u e n c e d by i n d i v i d u a l minor d i s c o n t i n u i t i e s and are loaded i n a b i a x i a l , e l a s t i c manner. Consequently, the numerical method best suited to open stope p i l l a r design i s a continuum approach using the theory of e l a s t i c i t y . The most e f f i c i e n t approach for these conditions i s the i n t e g r a l method. F i n i t e element methods could perform the computations adequately, but are not as e f f i c i e n t as boundary element methods i n e l a s t i c stress analysis. As a r e s u l t , a l l of the numerical modelling i n t h i s thesis w i l l focus on the a p p l i c a t i o n of boundary element methods. 57 3.2.2 Interpretation of Boundary Element Results i n Mining The boundary element stress analysis technique has been developed to approximate the stress d i s t r i b u t i o n around openings with i r r e g u l a r shapes oriented i n a two dimensional or three dimensional stress f i e l d . However, boundary element methods do not d i r e c t l y determine f a i l u r e . The stress d i s t r i b u t i o n needs to be interpreted to determine the e f f e c t on underground s t a b i l i t y . Many types of f a i l u r e c r i t e r i o n have been applied i n the analysis of stress d i s t r i b u t i o n s . This section w i l l outline the common methods of boundary element i n t e r p r e t a t i o n used i n p i l l a r design. The methods of int e r p r e t a t i o n include: (i) post-processing f a i l u r e c r i t e r i o n , ( i i ) i n t e r a c t i v e f a i l u r e c r i t e r i o n , ( i i i ) and p r i n c i p a l stress magnitudes. 3.2.2.1 Post-Processing F a i l u r e C r i t e r i o n Post processing f a i l u r e c r i t e r i a are applied to the solution a f t e r the stress analysis i s complete. The f a i l u r e c r i t e r i o n does not have any e f f e c t on the stress solution. Generally, continuum material properties, such as i n t a c t rock strength, rock mass strength, d i s c o n t i n u i t y shear strength, or rock mass characterization parameters, are estimated f o r the rock mass behaviour. The f a i l u r e c r i t e r i o n i s c a l i b r a t e d based on the estimated material properties and experience i n s i m i l a r rock conditions. Common f a i l u r e c r i t e r i a used i n post processing were developed by: - Murrell (1965) and Bieniawski (1974) fo r i n t a c t rock, 58 - Hoek and Brown (1980) for j o inted rock masses, - and Coulomb (1776) for d i s c o n t i n u i t i e s . The f a i l u r e c r i t e r i o n i s applied to stresses at many points i n a p i l l a r . Based on the d i s t r i b u t i o n of t h e o r e t i c a l l y f a i l e d rock, p i l l a r s t a b i l i t y i s determined and p o t e n t i a l mining problems are delineated. An example of the a p p l i c a t i o n of a post-processing f a i l u r e c r i t e r i o n i s described by Brady (1977) i n the analysis of an experimental open stope p i l l a r at the Mount Isa Mine in Queensland, A u s t r a l i a . A c r i t e r i o n was c a l i b r a t e d for the f a i l u r e of p i l l a r material based on a formula o r i g i n a l l y proposed by Murrell (1965). From the observation of l o c a l rock s p a l l i n g , the following formula was developed: a x = 9.34a 3 0- 7 5 + 94.0 where, c2_ = the major p r i n c i p a l stress at f a i l u r e (MPa) , 0 3 = the minor p r i n c i p a l stress (MPa). The f a i l u r e c r i t e r i o n was then applied to and a 3 stress d i s t r i b u t i o n s for stable and f a i l e d open stope p i l l a r case h i s t o r i e s f o r v e r i f i c a t i o n . Figure 17 shows the r e s u l t s of applying the c r i t e r i o n to a stable p i l l a r . The points denoted by "F" i n the figure representing the t h e o r e t i c a l zone of f a i l e d rock i n the p i l l a r . The predicted zones of f a i l e d rock are small and i s o l a t e d at the stope periphery, which corresponds well with the stable assessment. Figure 18 shows the c r i t e r i o n applied to the stress d i s t r i b u t i o n of a p i l l a r that f a i l e d . The FIGURE 17. An empirical f a i l u r e c r i t e r i o n has been applied to the two dimensional stress d i s t r i b u t i o n of a stable open stope r i b p i l l a r . Points denoted by M F " represent the area of rock that has t h e o r e t i c a l l y f a i l e d . For t h i s p i l l a r , the f a i l u r e zones are small and i s o l a t e d at the periperhy of the p i l l a r . This corresponds to a generally stable assessment f o r the p i l l a r (after Brady 1977). FIGURE 18. The t h e o r e t i c a l d i s t r i b u t i o n of f a i l e d rock i s much greater i n t h i s p i l l a r . The actual p i l l a r collapsed shortly a f t e r being reduced to t h i s s i z e (after Brady 1977). zone of f a i l e d rock covers a s i g n i f i c a n t portion of the p i l l a r , which also agrees with the actual assessment. Application of a f a i l u r e c r i t e r i o n to the t h e o r e t i c a l stress d i s t r i b u t i o n around underground excavations i s very common for the i n t e r p r e t a t i o n of boundary element solutions. However, i t assumes that load i s e n t i r e l y c a r r i e d by the p i l l a r material and that there i s no stress r e d i s t r i b u t i o n due to destressing of the f a i l e d rock mass. This assumption may not be correct for highly loaded p i l l a r s . 3.2.2.2 Interactive F a i l u r e C r i t e r i o n An i n t e r a c t i v e f a i l u r e c r i t e r i o n works during the numerical computations by adjusting the stress i n regions of the rock mass that f a i l due to high stress. This requires a c r i t e r i o n to determine the peak strength of the rock mass and the post f a i l u r e rock mass c h a r a c t e r i s t i c s . C a l i b r a t i o n of t h i s type of c r i t e r i o n i s very involved and has a fundamental e f f e c t on the r e s u l t s . Documentation of the use of an i n t e r a c t i v e f a i l u r e c r i t e r i o n i s given by Maconachie et a l . (1981) at the C.S.A. mine, Cobar Mines Pty., New South Wales. The displacement discontinuity program "N-Fold" with an i n t e r a c t i v e f a i l u r e c r i t e r i o n was used to investigate the stress condition of a s i l l p i l l a r . The program considers non-linear deformation and b r i t t l e y i e l d i n g of elements. The y i e l d point and post f a i l u r e deformation varies based on the confinement of the element. Figure 60 shows that for increasing confinement (increasing distance from a free BRITTLENESS PEAK MOOULUS IMPol STRENGTH (MPol a EXPOSED CORNER 12-5 72 b EXPOSED SIDE 8-3 90 c RE-ENTRANT CORNER 7-0 126 d ONE BEHIND FREE SIOE 6-3 1S6 FIGURE 19. The peak strength, deformation c h a r a c t e r i s t i c s , and e f f e c t of location used for investigating a p i l l a r case history with a displacement discontinuity program (after Maconachie et a l 1981). | | ELASTIC FIGURE 20. The normal stress and the f a i l e d regions estimated with the displacement discontinuity program for a s i l l p i l l a r case h i s t o r y (after Maconachie et a l 1981). 62 face), the peak strength increases and the post-peak load bearing capacity of the rock improves. The c a l i b r a t i o n of the f a i l u r e c r i t e r i o n was based on estimations of the i n s i t u rock mass strength and laboratory material properties. The material properties were subsequently v e r i f i e d based on observation and monitoring of the s i l l p i l l a r . When applied to a longitudinal section of the s i l l p i l l a r (figure 20), the zones of f a i l e d , and y i e l d i n g rock were outlined and the magnitude of the normal stresses f o r rock under e l a s t i c deformation was determined. The f a i l u r e c r i t e r i o n helped determine the best stope extraction sequence and indicated the need of a pendant p i l l a r to maintain s t a b i l i t y i n the s i l l p i l l a r . While p o t e n t i a l l y very useful i n p i l l a r design, t h i s type of f a i l u r e c r i t e r i o n needs a large amount of c a l i b r a t i o n and v e r i f i c a t i o n before becoming a r e l i a b l e t o o l . Generally, the more s o p h i s t i c a t e d and complex the program and f a i l u r e c r i t e r i o n , the greater the number of assumptions introduced into the s o l u t i o n . 3.2.2.3 P r i n c i p a l Stress Magnitude. The most common and s i m p l i s t i c method of boundary element in t e r p r e t a t i o n i s analysis of p r i n c i p a l stress magnitudes. In p i l l a r s , stress d i s t r i b u t i o n s are plotted on mine plans or sections to reveal areas of high or low p r i n c i p a l stress. Potential mining problems are then estimated based on the stress d i s t r i b u t i o n s . A t y p i c a l example of the use of p r i n c i p a l stress magnitude analysis i s given i n a paper by Bywater et a l . (1983) , at the Mount Isa mine. I t was determined through experience that areas with normal stress greater than 70 MN/m2 generally exhibit s p a l l i n g and are prone to l o c a l rock f a i l u r e . A l i n e a r e l a s t i c displacement d i s c o n t i n u i t y code was used to analyze the p o t e n t i a l stress d i s t r i b u t i o n s i n a new mining block. Figure 21 shows two d i f f e r e n t extraction sequences for the mining block, with the predicted stresses corresponding to the legend. The analysis shows more overstressed areas being developed i n the second sequence which would cause problems e a r l i e r i n the p i l l a r recovery. When the rock mass strength has not been estimated, stresses are f r e q u e n t l y normalized a g a i n s t the i n t a c t u n i a x i a l compressive strength of the rock. Mining problems are l i k e l y to occur i f the normalized major p r i n c i p a l stress i s greater than 1/3 (Bawden et a l . 1988) to 1/2 (Mathews et a l . 1980). 3.2.3 Limitations of Boundary Element Modelling While boundary element modelling i s a sophisticated design t o o l , i t has several l i m i t a t i o n s and p o t e n t i a l sources of inaccuracy i n applied rock mechanics. The l i m i t a t i o n s can be grouped into two basic categories: (i) l i m i t a t i o n s with respect to modelling a rock mass, ( i i ) and l i m i t a t i o n s due to computational assumptions. 3.2.3.1 Modelling a Rock Mass NORMAL • +70 MN/m 2 STRESS £ S 60 - 69 MN/m' / £ ] 50 - 59 MN/m2 40 - 49 MN/m 2 FIGURE 21. The d i s t r i b u t i o n of normal stress i n a mining block was estimated f o r two d i f f e r e n t mining sequences to determine the best stope extraction sequence (after Bywater et a l . 1983). A numerical modelling solution assumes the medium has perfect material properties. In r e a l i t y , a rock mass i s not a perfect material. A number of approximations and assumptions are usually necessary for the estimation of the properties describing the rock mass. The material properties of a rock mass have to be estimated assuming the rock mass behaves as an i s o t r o p i c continuum. This means that the rock mass eithe r has no s i g n i f i c a n t d i s c o n t i n u i t i e s , or the d i s c o n t i n u i t i e s are s u f f i c i e n t l y small, regular and frequent that they have no e f f e c t on s t r e s s . For minor structure such as rock j o i n t s , t h i s may not be a serious l i m i t a t i o n . However for major structure, e s p e c i a l l y f a u l t s that have moved su b s t a n t i a l l y , the rock mass may not act as an i s o t r o p i c continuum at a l l . This could i n v a l i d a t e any numerical solution that did not e x p l i c i t l y model the d i s c o n t i n u i t y . Most boundary element methods give the rock mass l i n e a r e l a s t i c deformational c h a r a c t e r i s t i c s . Laboratory measurements have found that over a range of loading conditions, hard rock samples exhi b i t some non-linear and p l a s t i c deformation. In addition, the p o s t - f a i l u r e load bearing behaviour of an i n s i t u rock mass i s dependent upon several variables that are not r e l a t e d to the e l a s t i c c h a r a c t e r i s t i c s of the rock. For low to medium loading conditions, the use of l i n e a r e l a s t i c i t y i s generally acceptable, but for a discontinuum, highly loaded, or f a i l e d rock mass, l i n e a r e l a s t i c behaviour i s a poor assumption. Parametric studies using boundary element models have shown a large influence of the pre-mining stress regime. This i s an expensive and d i f f i c u l t parameter to measure. The actual i n s i t u stress f i e l d varies with depth and can be profoundly influenced by major s t r u c t u r a l d i s c o n t i n u i t i e s . Consequently, the v i r g i n stress used i n numerical methods w i l l only be an approximation of the actual conditions. I t i s important to be aware of these l i m i t a t i o n s and t h e i r possible e f f e c t on the numerical solution's a b i l i t y to describe the condition of a stressed rock mass. 3.2.3.2 Computational Assumptions Boundary element methods are numerical approximations of the solut i o n to a boundary value problem. Only the simplest excavation geometries can be solved a n a l y t i c a l l y , so for complicated geometries, a solution i s determined through a numerical i t e r a t i o n process. This necessitates d i s c r e t i z i n g the boundary into segments and piecewise modelling of stresses and displacements on each segment. The r e s u l t i s : - the i n t e r i o r s o l u t i o n (stresses o f f the boundary) may not be accurate very near the d i s c r e t i z e d boundary, - and the numerical solution i s only an approximation because the computation i s completed when a s p e c i f i e d convergence c r i t e r i o n i s met. Through the modelling of boundaries with known solutions, i t has been found that the larger the number of elements on a boundary, the greater the accuracy of the numerical model with 67 respect to the known closed form solution. The magnitude of the difference between the numerical model and the closed form solut i o n decreases with an increase i n the number of elements, so there i s a p r a c t i c a l l i m i t to the influence of the number of elements. Above t h i s l i m i t , the addition of extra elements does l i t t l e or nothing to improve the accuracy of the solution. In summary, reading too much d e t a i l i n a numerical solution can be misleading. C a l i b r a t i o n of numerical models with experience and case h i s t o r i e s can be as important as the type of numerical model used or how the r e s u l t s are analyzed. I t should be kept i n perspective that boundary element methods only account for stress related f a i l u r e . S t r u c t u r a l l y controlled f a i l u r e or f a i l u r e due to the combination of stress , and structure may not be interpreted from numerical modelling stress d i s t r i b u t i o n s . 68 CHAPTER 4 OPEN STOPE RIB PILLAR DATA BASE The objective of t h i s chapter i s to present the r i b p i l l a r data c o l l e c t e d during the Integrated Mine Design Study. This w i l l be done by: - d i s c u s s i n g some of the general c h a r a c t e r i s t i c s and information of the p i l l a r case h i s t o r i e s , - presenting the background and physical information on each case h i s t o r y , - defining the q u a l i t a t i v e scale used to give an assessment to the case h i s t o r i e s , - and describing the signs of f a i l u r e f or a l l the case h i s t o r i e s that experienced s t a b i l i t y problems. 4.1 General Data Base Information The o r i g i n a l data used i n t h i s thesis has been c o l l e c t e d i n Canadian open stope mines. The 47 case h i s t o r i e s are only a f r a c t i o n of the t o t a l data c o l l e c t e d during the "Integrated Mine Design Study". Some of the data was rejected because: (i) geotechnical parameters including i n s i t u stress, i n t a c t rock strength and the influence of geological structure could not be estimated with confidence, ( i i ) the actual events of the case h i s t o r y could not be v e r i f i e d , ( i i i ) the stress conditions i n the case h i s t o r y were too complex 69 to be back-analyzed with the means ava i l a b l e at U.B.C. Throughout the course of the study, several mines requested that t h e i r name not appear d i r e c t l y associated with data. To respect t h e i r anonymity, there i s no s p e c i f i c reference to the s i t e of any unpublished data i n t h i s t h e s i s . S p e c i f i c i n f o r m a t i o n about the mining environment, g e o t e c h n i c a l parameters and case h i s t o r i e s i s presented through the use of mine numbers. The data base i s supplemented by information presented i n U.B.C. theses that discuss open stope r i b p i l l a r s , by Goldbeck (1985), Potvin (1985) and Pakalnis (1986). A s i g n i f i c a n t feature of many of the p i l l a r s i n the data base i s that they were stable at one time during the mining and l a t e r f a i l e d . The f a i l u r e was caused by increased extraction near the p i l l a r or mining portions of the p i l l a r . Among the 47 case h i s t o r i e s i n the data base, 30 originate from 13 p i l l a r s at d i f f e r e n t stages of extraction. These " y i e l d i n g p i l l a r s " w i l l be very important to the development of a r i b p i l l a r design method. 4.2 Background Data The background information concerning p i l l a r dimensions, depth, mining environment including r a t i o of extraction and b a c k f i l l , and an assessment of the p i l l a r condition i s given i n Table 5. The dimensions and r a t i o of extraction are defined 70 PILLU KXNI PILLA1 PILL41 SBOMim lAcmix D t P T B EXTRACTION c s n t u c s ASSESSMENT NUKUt NUKBER MAKE ttLLA» sron flLLAI DIP (* mns (•) uno (•*) (MPl) WIDTH { HEIGHT HEICHT ULCM) 2 : 14-3-2/4 43 ! 3' 53 90 NO 820 3tX 62 2 0 0 STABLE 3 2 U-3-2 15 ! 34 49 90 NO 820 57X 62 2 0 0 PAILU1E 7 6 33-176/183 33 ! 50 20 90 12.1 T 1000 25X 64 121 STABLE 8 6 33-176 11 ! 50 20 90 12.1 T 1000 501 64 121 PAILUIX 15 8 23*7 12 ! 50 8 80 32:1 t 210 56Z 77 215 STABLE 16 2549 15 ! 50 7 80 32:1 1 210 571 77 215 STABLE 17 10 062 25 : too 27 65 20:1 1 360 SOX 60 70 SLOUCHINC IS 11 30-203 24 I M 11 90 NO 870 59Z 75 148 STABLE 19 11 30-205 3 5 i 100 12 90 NO (70 60Z 75 148 STABLE 20 16 77-90 15 ! 120 15 90 NO 300 71Z 71 176 SLOUGEDK 21 16 77-92 27 : 1 2 0 40 90 NO 300 SIX 71 176 STABLE 22 16 77-94 30 i 105 40 90 NO 300 49X 71 176 STABLE 23 16 77-92 27 ! 120 40 90 NO 300 68X 71 176 PAILUII 24 16 77-94 30 ! 105 40 90 NO 300 49X 71 176 STABLE 25 16 77-94 30 1 105 40 90 NO 300 84Z 71 176 PAILUU 26 16 80-78 21 ! 135 24 90 NO 210 671 71 176 STABLE 27 16 80-80 15 ! 135 12 90 NO 210 751 71 176 STABLE 28 16 80-82 15 ! '5 27 90 NO 210 71X 71 176 SLOUGHING 29 16 80-84 21 ! 75 39 90 NO. 210 63X 71 176 STABLE 30 16 80-82 15 ! " 27 90 NO 210 82Z 71 176 FAILURE 31 16 80-80 15 135 12 90 NO 210 87Z 71 176 STABLE 32 17 10-20 21 ! ISO 21 90 NO 215 55X 65 100 STABLE 33 17 10-21.5 ! 150 20 90 NO 215 74Z 65 100 FAILURE 17 10-23 15 ! 150 18 90 NO 215 60X 65 1 0 0 SLOUGHING 35 17 10-20 21 : 1 5 0 21 90 NO 215 66X 65 1 0 0 STABLE 36 17 10-20 15 ! 150 30 90 ROCXPILL 215 80Z 65 100 FAILURE 37 17 10-23 15 : i s o 18 90 NO 215 74X 65 100 FAILURE 42 19 LEVEL 11 #8 11 ! 55 23 90 30:1 T 620 501 78 316 FAILURE 43 19 Lll 16-8 33 ! 55 23 90 30.1 T 620 2SX 78 316 STABLE 44 19 Lll (14-16 33 ! 55 IS 90 30:1 T 620 2SX 78 316 STABLE 45 19 LEVEL 11 #14 11 ! 55 18 90 30:1 I 620 502 78 316 FAILURE 46 21 120-13D 32 ! 60 28 70 NO 340 37X 68 90 STABLE 47 21 12D-13S 25 ! 60 28 70 NO 340 46X 68 90 SLOUCHING 48 21 12D-13D 19 ! 60 28 70 NO 340 58X 68 90 FAILURE *9 21 12D-13D 14 ! 60 28 70 NO 340 70X 68 90 FAILURE 22 301 #15 17 ! 35 6 90 TAILINGS 320 66X 63 72 STABLE 51 22 301 116 21 ! 35 5 90 TAILINGS 320 67X 63 72 STABLE 52 22 301 #17 18 ! 35 4 90 TAILINGS 320 61Z 63 72 STABLE 53 22 330 #4-5 24 ! 58 18 90 TAILINGS 520 SIX 69 72 STABLE 54 23 341 VP 17 t 170 10 90 ROOJILL 290 ! 64Z 71 310 STABLE 55 2} 342 VP 20 170 8 90 R0CX7ILL 290 ; 67X 71 310 STABLE 56 31 448 27 I 110 46 90 NO 500 61X 75 26S SLOUGH 57 31 450 24 : n o 52 90 NO 500 : 38X : 75 265 STABLE 58 31 452 30 : n o 44 90 NO 500 ; 38X 75 265 STABLE 59 31 450 24 ; n o 52 90 NO 500 : 73X 75 265 SLOUGH 60 31 452 30 ! n o 44 90 NO 500 ; 75X 75 265 SLOUCH 61 30 2020 PILLAR 24 : n o 38 90 20:1 8 520 59X : 70 ; 160 SLOUGH A r a t i o r a f a r s to a vasta to camant r a t i o T or TAILINGS naans tha b a c k f i l l i n g a a t a r l a l i a p r i m a r i l y c l a a a i f i a d m i l l t a i l l n f a . R or ROCKPILL aaana tha b a c k f i l l i n g a a t a r l a l l a p r l a v a r i l y vaata rock. TABLE 5. Background data for a l l the p i l l a r case h i s t o r i e s . 71 according to figure 22. The dimensions presented are the design dimensions. The actual dimensions may vary s l i g h t l y for most f a i l e d , the actual dimensions (especially p i l l a r width) may be s u b s t a n t i a l l y smaller than the design dimensions, due to excessive sloughing. J u s t i f i c a t i o n for the assessment of the condition of each sloughing and f a i l e d p i l l a r i s given i n chapter 4.3. S p e c i f i c information about the geological s e t t i n g of each case h i s t o r y can be found i n the isometric sketch corresponding to the mine number (see Appendix I ) . Each geological s e t t i n g i s comprised of: - the underground stress regime, - the hanging wall, footwall and orebody material properties and c h a r a c t e r i s t i c s including, cases due to b l a s t induced damage. For p i l l a r s that have - rock type, - i n t a c t u n i a x i a l compressive strength, - e l a s t i c modulus, - poisson's r a t i o , - NGI rock mass c l a s s i f i c a t i o n , - the orebody shape and s i z e , - and the mining methods used i n various parts of the orebody. Several mines use very s i m i l a r stope and p i l l a r dimensions throughout the mine. Inclusion of t h i s data would p o t e n t i a l l y Lo1 = length of stope 1 Lo2 = length of stope 2 Wp = width of pillar Hp = height of pillar, or stope breadth Ho = stope height FIGURE 22. This figure shows the geometrical d e f i n i t i o n for the stope and p i l l a r dimensions used i n t h i s t h e s i s . double or t r i p l e the s i z e of the data base. However, using several case h i s t o r i e s with the exact same information would not broaden the c a p a b i l i t y of the data base to the develop a design method. I t would create problems i n data presentation and d i l u t e the influence of single case h i s t o r i e s . As a re s u l t , only unique cases are presented. 4 . 3 P i l l a r Assessment The signs of r i b p i l l a r i n s t a b i l i t y are l i s t e d i n Chapter 2.1. Based on these signs, three q u a l i t a t i v e assessments have been chosen to categorize the condition of the p i l l a r s i n the data base. A stable assessment i s given to p i l l a r s generally not showing any signs of i n s t a b i l i t y . Any ground control problems are too small to have an e f f e c t on mining near the p i l l a r . A sloughing assessment i s given to p i l l a r s showing one or more of the above signs, but the extent of de t e r i o r a t i o n i s not severe and i s reported i n only a few areas of the p i l l a r . The ground control problems associated with sloughing p i l l a r s have a li m i t e d e f f e c t on mining, such as: d r i l l i n g problems, loss or d i f f i c u l t y i n maintaining some d r i l l holes, the need for development s c a l i n g and r e h a b i l i t a t i o n and some wall sloughing and p i l l a r overbreak. The sloughing assessment i s also used to describe p i l l a r s whose s t a b i l i t y problems are time dependent, becoming more severe as mining continues. Several p i l l a r case h i s t o r i e s have been assessed as sloughing, but have used quick 74 b a c k f i l l i n g to prevent complete p i l l a r f a i l u r e . A f a i l e d assessment i s given to p i l l a r s showing large and severe signs of i n s t a b i l i t y . Their e f f e c t s on mining, include: - loss of ore, - low p r o d u c t i v i t y due to oversize material and overbreak created during mining, the need for frequent r e h a b i l i t a t i o n of development or the use of cable b o l t s to prevent loss of p i l l a r development, - and severe cracking, j o i n t opening, and displacement often needing immediate stope f i l l i n g to prevent complete p i l l a r d i s i n t e g r a t i o n . The assessment of p i l l a r s was based l a r g e l y on documentation and d e s c r i p t i o n by on-site s t a f f and some observations by the author. J u s t i f i c a t i o n of the assessment fo r a l l the sloughing and f a i l e d p i l l a r s i s detailed below, by describing the most serious signs of i n s t a b i l i t y f o r each case h i s t o r y : CASE # 3 Assessment: F a i l u r e . P i l l a r Condition: Sloughing of large slabs from p i l l a r walls into primary stope drawpoints, problems i n maintaining blastholes, wall sloughing intersected development i n the middle of the p i l l a r . (reference: Falmagne 1986). CASE # 8 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : Severe a x i a l c r a c k i n g i n p i l l a r development requiring cable b o l t i n g to maintain overcut and undercut s t a b i l i t y , several feet of overbreak beyond blastholes and hourglass sloughing i n the middle of p i l l a r walls. 75 CASE # 17 Assessment: Sloughing. P i l l a r Condition: Shears and j o i n t s opening i n p i l l a r s , sloughing of p i l l a r walls into primary stopes. Some problems i n d r i l l i n g and maintaining d r i l l holes. (reference: Bawden 1988) . CASE #20 Assessment: Sloughing. P i l l a r Condition: Progressive sloughing of p i l l a r walls into adjacent stopes. (reference: A l l c o t t and Archibald 1981). CASE #23 Assessment: F a i l u r e . P i l l a r Condition: Severe sloughing of p i l l a r walls into adjacent stopes. (reference: A l l c o t t and Archibald 1981). CASE #25 Assessment: F a i l u r e . P i l l a r Condition: Major shear displacement extending over two l e v e l s 45 metres apart, sloughing of p i l l a r walls, (reference: A l l c o t t and Archibald 1981; Potvin 1984). CASE #28 Assessment: Sloughing. P i l l a r C o n d i t i o n : Severe ground f r a c t u r i n g causes abandonment of p i l l a r development, (reference: A l l c o t t and Archibald 1981). CASE #30 Assessment: F a i l u r e . P i l l a r Condition: P i l l a r crushes v i o l e n t l y a f t e r nearby p i l l a r i s recovered by bla s t i n g , (reference: A l l c o t t and Archibald 1981). CASE #33 Assessment: F a i l u r e . P i l l a r Condition: Extensive cracking of p i l l a r , followed by the sloughing of 2 rings of d r i l l holes and major collapse of the upper h a l f of the p i l l a r into adjacent stopes. (reference: Bray 1967). CASE #34 Assessment: Sloughing. P i l l a r Condition: Extensive cracking of the p i l l a r reported, with some sloughing into nearby stopes. (reference: Bray 1967). 76 CASE #36 Assessment: F a i l u r e . P i l l a r Condition: West side of the p i l l a r sloughs into adjacent stope causing breakthrough to a p i l l a r cross-cut. (reference: Bray 1967). CASE #37 Assessment: F a i l u r e . P i l l a r Condition: Wall sloughing creates a hole completely through the p i l l a r , (reference: Bray 1967). CASE # 42,45 Assessment: F a i l u r e . P i l l a r Condition: Severe cracking, s p a l l i n g and j o i n t opening i n p i l l a r development with wooden c r i b s and cable b o l t i n g needed to l i m i t development closure and collapse, heavy overbreak on production b l a s t s . (reference: Bawden and Milne 1987; Chauvin 1986). CASE #47 Assessment: Sloughing. P i l l a r Condition: One v i b r a t i n g wire stressmeter shows decrease i n stress through p i l l a r , (reference: Goldbeck 1985). CASE #48 Assessment: F a i l u r e . P i l l a r Condition: A l l v i b r a t i n g wire stressmeters show decrease i n stress through p i l l a r , (reference: Goldbeck 1985). CASE #49 Assessment: F a i l u r e . P i l l a r Condition: Sharp decrease i n p i l l a r stress shown by v i b r a t i n g wire stressmeters. (reference: Goldbeck 1985). CASE # 56 Assessment: Sloughing. P i l l a r Condition: Serious a x i a l cracking i n p i l l a r as stopes retreated to p i l l a r . CASE # 59 Assessment: Sloughing. P i l l a r Condition: A x i a l cracks i n p i l l a r develop and open a f t e r recovery of a nearby p i l l a r . 77 CASE #60 Assessment: Sloughing. P i l l a r Condition: A x i a l cracks i n p i l l a r develop and open a f t e r recovery of a nearby p i l l a r . CASE # 61 Assessment: Sloughing. P i l l a r Condition: Sloughing of p i l l a r walls as f a r as centre of p i l l a r , overbreak from p i l l a r s during primary mining and severe overbreak during secondary stope mining. 78 CHAPTER 5 BOUNDARY ELEMENT METHODS IN RIB PILLAR DESIGN Boundary element numerical methods are an e f f e c t i v e way to estimate the stress at any point i n a r i b p i l l a r (for reasons described i n Chapter 3.2.3). For each of the case h i s t o r i e s presented i n Chapter 4, a d i r e c t i n t e g r a l two dimensional program (BITEM) and a pseudo-three dimensional displacement d i s c o n t i n u i t y program (MINTAB) method w i l l be used to estimate the average p i l l a r stress. For many r i b p i l l a r geometries, these programs give adequate r e s u l t s . However, BITEM and MINTAB have l i m i t a t i o n s that may cause serious inaccuracies when applied to some three dimensional problems. Ideally, a three dimensional method would be used to determine the stress d i s t r i b u t i o n i n each case his t o r y . However, true three dimensional analysis i s very new technology and the programs have large setup and run times, need quite sophisticated computing f a c i l i t i e s , and are li m i t e d i n program s i z e . To better deine these l i m i t a t i o n s , a three dimensional boundary element code (BEAP) and BITEM and MINTAB w i l l be used to investigate the average stress i n t y p i c a l r i b p i l l a r geometries. This comparison w i l l be used to approximate the error associated with the application of the two dimensional and displacement dis c o n t i n u i t y methods to 3D problems. 79 5.1 Boundary Element Methods Used The following general description of the boundary element methods and numerical codes involved i n the study i s taken l a r g e l y from an unpublished paper written at U.B.C. (Hudyma 1988b). 5.1.1 BITEM The 2D d i r e c t boundary i n t e g r a l model "BITEM" i s based on the program "BITE" developed by P.C. R i c c a r d e l l a at the Carnegie-Mellon u n i v e r s i t y i n 1973. I t was expanded to perform p i e c e - w i s e homogeneous e l a s t i c i t y a n a l y s e s by CSIRO (Commonwealth S c i e n t i f i c and I n d u s t r i a l Research Organization, Australia) i n 1978. The program was subsequently modified for the U.B.C. mainframe computer by R. Pakalnis i n 1983 and l a t e r for an IBM compatible computer by CANMET under the program name PCBEM (Pakalnis 1987). The boundary i n t e g r a l technique i s designed for problems that have one long dimension and a constant cross sectional shape. I t requires the d i s c r e t i z a t i o n of a l l excavation surfaces into segments connected by nodes (see figure 23) . An e x p l i c i t s o l u t i o n i s selected to represent the medium's i n s i t u stress conditions. These f i e l d stresses can be constant or can vary l i n e a r l y with p o s i t i o n . When excavations are created, the stress perpendicular to the boundary nodes becomes zero. BITEM then calculates t r a c t i o n s and displacements at a l l the nodes of a l l the boundaries. The boundary solution i s determined through OPENING TO FIGURE 23. Isometric view of an opening that i s long i n one d i r e c t i o n and the d i s c r e t i z a t i o n of the boundary used i n two dimensional modelling (after Hudyma 1988b). 81 an i t e r a t i v e procedure i n which the stress and displacement at each node influences the stress and displacement of the other nodes of the boundary. This procedure ends when the difference between the l a s t two i t e r a t i o n s i s less than a user defined convergence c r i t e r i o n . Once a boundary solu t i o n has been determined, stresses and displacements i n t e r n a l to the problem boundary can be determined using the boundary solu t i o n 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 det a i l e d d e s c r i p t i o n of the boundary i n t e g r a l technique i s found i n Brady and Bray (1978). 5.1.2 MINTAB Mintab i s a pseudo-three dimensional displacement d i s c o n t i n u i t y boundary element program. The o r i g i n a l code was written by Dr. S.L. Crouch i n South A f r i c a . The program has had several major modifications r e s u l t i n g i n several d i f f e r e n t program names, including: MINSIM, MINTAB, BESOL and N-FOLD. Each v a r i a t i o n has special features such: as the i n c l u s i o n of b a c k f i l l elements, use of a s e m i - i n f i n i t e domain (can account for the surface of the earth), use of multiple en echelon seams, f a u l t s and folds i n the seams and a program i n t e r a c t i v e f a i l u r e c r i t e r i o n with p o s t - f a i l u r e rock mass c h a r a c t e r i s t i c s . The version used f o r t h i s study i s CANMET's MINTAB version 4.0 (1983) which performs only l i n e a r e l a s t i c analysis of one planar seam, i n an i n f i n i t e domain, and with no b u i l t i n f a i l u r e c r i t e r i o n . MINTAB uses the displacement di s c o n t i n u i t y method to solve 82 stresses, s t r a i n s and displacements i n three dimensions around excavations i n tabular orebodies. In MINTAB, 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 (see figure 24) . Each element represents mined or unmined area i n the reef. The t h i r d dimension i s the width of the seam. To give an accurate solution, the seam width 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. The d e f i n i t i o n of a small seam and the l i m i t a t i o n s of displacement d i s c o n t i n u i t y modelling w i l l be discussed i n Chapter 5.4. For p r a c t i c a l purposes, the reef can be considered as two p a r a l l e l planes. Creating excavations i n the g r i d induces movement of the planes. Relative movements between the two planes are broken into two components. Ride components act p a r a l l e l to the plane boundaries and closure components act normal to the planes. The seam elements are subjected to a three dimensional stress f i e l d (see figure 24) . Displacement d i s c 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 displacement between the two planes. I f the two planes do not come i n contact due to displacement, the t r a c t i o n s o"zz, o"yZ, and a x z are a l l zero. Displacements and stresses at unmined points i n the seam are c a l c u l a t e d 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. A more det a i l e d description of the displacement d i s c o n t i n u i t y method i s given by S t a r f i e l d and Crouch (1973). 24. Oblique view of the MINTAB seam geometry and the s applied l o c a l l y on each element i n the reef. 84 5.1.3 BEAP BEAP i s a three dimensional boundary element program developed by J.A.C. Diering as a PhD t h e s i s , at Pretoria University (1987), i n conjunction with CANMET, INCO (Thompson Division) and GEMCOM (Pty.) Limited. Version 1.0, used i n t h i s project, i s due for public release i n the f a l l of 1988. E x c a v a t i o n boundaries 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 figure 25). The problem i s subject to an a r b i t r a r i l y oriented stress f i e l d . The stress and displacements on the boundary elements vary quadratically and are non-conforming. This means displacements and t r a c t i o n s on each element 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 related stress analysis, including: - the need for fewer elements to d i s c r e t i z e an excavation than other three dimensional 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 material properties, - the use of lumping to reduce data storage requirements, - and the a b i l i t y to determine stresses and displacements very close to an excavation boundary. Further d e t a i l s about BEAP can be found i n Diering (1987) and Diering and Stacey (1987). 5.2 Open Stope Rib P i l l a r Modelling 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 in a three dimensional stress f i e l d (after Hudyma 1988b). 86 Boundary element numerical modelling of hard rock excavations r e l i e s l a r g e l y on the problem geometry and the magnitude and orientation of the pre-mining stress. This section describes a consistent method to specify the stope and p i l l a r dimensions and to determine the average load on r i b p i l l a r s i n open stope mining. 5.2.1 Defining the Open Stope Geometry In t h i s t h e s is, the dimensions of stopes and p i l l a r s w i l l be defined according to figure 26. P i l l a r dimensions are defined with respect to the d i r e c t i o n of the greatest induced stress. The p i l l a r height i s t y p i c a l l y defined as p a r a l l e l to the d i r e c t i o n of greatest induced load. Induced load, i n any d i r e c t i o n , i s mostly a function of the s i z e and shape of the excavation surface perpendicular to that load. For small excavation surfaces, the stress r e d i s t r i b u t i o n i s small. For large excavation surfaces, the stress r e d i s t r i b u t i o n w i l l be much larger. In horizontal orebodies (where most of the o r i g i n a l p i l l a r design research was done), the greatest induced load i s v e r t i c a l and the p i l l a r height i s v e r t i c a l (see figure 27a). In steep dipping orebodies, the largest induced load i s horizontal and the p i l l a r height i s horizontal (see figure 27b). For i n c l i n e d orebodies, the p i l l a r height i s defined as the d i r e c t i o n perpendicular to the orebody. 5.2.2 Defining the Average P i l l a r Stress S t o p e 1 L o 1 Wp S t o p e 2 L o 2 Lo1 = length of stope 1 Lo2 = length of stope 2 Wp = width of pillar Hp = height of pillar, or stope breadth FIGURE 26. This figure defines the dimensions for stopes and p i l l a r s , and the orientation f o r the in s i t u s t r e s s regime f o r t h i s thesis. 88 £p 0" = Ugh | Hp FIGURE 27a. A r i b p i l l a r i n a horizontal seam loaded by the weight of the overburden. FIGURE 27b. The d i r e c t i o n of loading on a p i l l a r i n a v e r t i c a l orebody. 89 For an i d e a l i z e d open stope r i b p i l l a r i n a v e r t i c a l orebody, the i n s i t u stress acts i n three basic d i r e c t i o n s : a x, ay, and a 2 (see figure 28) . P i l l a r stress i s a r e s u l t of the pre-mining stress that i s concentrated because of adjacent excavations. Stress concentration i n a d i r e c t i o n i s generally proportional to the s i z e and shape of the stope surfaces normal to that stress d i r e c t i o n . In p i l l a r design, the d i r e c t i o n of greatest importance i s usually the d i r e c t i o n that has the highest s t r e s s . Inside r i b p i l l a r s , the stress acting i n the a x d i r e c t i o n i s the lowest because i t i s p a r a l l e l to the orebody s t r i k e which causes i t to be shadowed by the open stopes. The induced load i n the rjy d i r e c t i o n i s almost always larger than i n the a z d i r e c t i o n , because the pre-mining stress i n the Oy d i r e c t i o n i s t y p i c a l l y much greater than i n the a z d i r e c t i o n . In addition, for s u b - v e r t i c a l l y dipping orebodies, the stope surface normal to the Oy d i r e c t i o n i s much larger than those perpendicular to the a2 d i r e c t i o n . This means the p i l l a r stress i n sub-vertical orebodies i s almost always highest i n the Oy d i r e c t i o n . There i s a large v a r i a t i o n i n the ay stress f i e l d i n a r i b p i l l a r . The best location to determine the average ay stress i s the p i l l a r c enterline at the middle of the stope height (also c a l l e d the p i l l a r "mid-height c e n t e r l i n e " ) , see figure 28. The reasons for t h i s l o c a t i o n are: - i t i s the region of highest normal stress (ay d i r e c t i o n ) , - i t i s the region of lowest confining stress ( a x d i r e c t i o n ) , 90 MID-HEIGHT CENTERLINE MID-HEIGHT PLANE FIGURE 28. The mid-height plane and centerline for t a l l open stope geometries. - i t i s often observed to be one of the f i r s t areas of i n s t a b i l i t y i n a p i l l a r , - the e f f e c t of the excavation corners and stope ends are at a minimum, - t h i s i s usually the plane of analysis when two dimensional modelling (in plane strain) i s used. However, there may be a large v a r i a t i o n i n the a v stress at the mid-height centerline. Hoek and Brown (1980) show that as a p i l l a r becomes more slender ( t a l l e r and narrower), the stress d i s t r i b u t i o n across the mid-height of the p i l l a r becomes more uniform. In a squat p i l l a r , the stress d i s t r i b u t i o n varies s i g n i f i c a n t l y across the p i l l a r mid-height ce n t e r l i n e . They suggest that the average p i l l a r stress should be the average value of the maximum p r i n c i p a l stress (in the ay direction) across the p i l l a r . So for t h i s thesis, the average p i l l a r stress for open stope r i b p i l l a r s w i l l be calculated as the average stress along the mid-height centerline of the p i l l a r . 5.3 2D Modelling of 3D Excavation Geometries Numerical modelling of underground excavations with 3D methods i s a time consuming and expensive procedure. Two dimensional numerical modelling can be used e f f e c t i v e l y to estimate the stress found i n some of the planes of a 3D p i l l a r geometry, and at a much lower cost than 3D numerical methods. One of these planes i s at the mid-height of t a l l open stopes, which i s of primary concern i n open stope r i b p i l l a r design. This sub-section w i l l discuss how 2D modelling can be used to estimate the average p i l l a r stress i n open stope r i b p i l l a r s . I t w i l l also estimate the difference between 2D and 3D numerical modelling for various open stope mining geometries. 5.3.1 Plane S t r a i n Solution To estimate the stress around open stopes, the plane s t r a i n s o l u t i o n i s generally used. Plane s t r a i n conditions assume that around an excavation a l l the mining induced displacements occur i n the plane of the orebody cross-section and the displacements are the same for a l l cross-sections. In a t y p i c a l geometry, a stope i s modelled i n the xy plane (see figure 28) . The assumption i s that i n the 3D s i t u a t i o n , the stope ends have no influence on the cross-section plane. Brown (1985) notes that: "For uniform excavation cross-sections, other than those with extreme a x i a l r a t i o s , the plane s t r a i n boundary stresses usually approximate the correct three-dimensional stress to within l e s s than ten, and sometimes f i v e , per cent at locations removed by at le a s t two excavation 'diameters' from intersections, excavation ends or changes of cross-section." In applying plane s t r a i n conditions to open stope r i b p i l l a r design, the subject of i n t e r e s t i s the influence of the stope ends on the stress at the mid-height centerline of the p i l l a r . I f the mid-height plane i s not s u f f i c i e n t l y removed from the stope ends, some of the mining induced stress r e d i s t r i b u t i o n w i l l occur into the abutments at the stope ends, rather than into the p i l l a r . This means that the stress at the mid-height plane i s greatest when there i s no influence of the stope ends, which i s the case for the 2D plane s t r a i n solution. This i s confirmed i n work done by Watson and Cowling (1985) at Mt. Isa and i s observed i n the r e s u l t s to be discussed i n Chapter 5.3.2. 5.3.2 Comparison of 2D and 3D Numerical Modelling Results A comparison of several d i f f e r e n t stope geometries was done with the 3D model BEAP, and the 2D model BITEM i n plane s t r a i n . The objective was to investigate i n more depth the degree of overestimation predicted by BITEM for d i f f e r e n t stope and p i l l a r geometries. The s i z e of the plane normal to the <7p stress (shaded plane, figure 29) has the greatest influence on stress concentration at the p i l l a r mid-height centerline. To check the influence of the stope ends on the mid-height plane, the r a t i o of stope height to stope length was varied. Four t e s t s , comprised of a t o t a l of 12 d i f f e r e n t stope geometries, were modelled with BITEM and BEAP. The f i r s t t e s t checked the average p i l l a r stress as the height was increased for stopes with a square cross-section. The second t e s t checked the average p i l l a r stress for stopes with a constant height and an increasing longitudinal stope length. The t h i r d t e s t checked the average p i l l a r stress as the height was increased for stopes with a constant longitudinal cross-94 Op H L Wp FIGURE 29. The shaded plane has the greatest influence on the mid-height a y stress. TEST STOPE LENGTH (D STOPE BREADTH (B) STOPE HEIGHT (H) PILLAR WIDTH (Wp) BEAP AVE. PILLAR STRESS INCREASE BITEM H:L RATIO BITEM AVE. PILLAR STRESS INCREASE SQUARE STOPE CROSS-SECTION 10 10 10 10 1.25 1 : 1 1.8 10 10 20 10 1.A5 2 : 1 1.8 10 10 AO 10 1.65 A : 1 1.8 10 10 60 10 1.7 6 : 1 1.8 10 10 80 10 1.7 8 : 1 1.8 LONGIT-UDINAL STOPE CROSS-SECTION 100 10 60 50 1.5 0.6 : 1 2.2 60 10 60 30 1.75 1 : 1 2.A5 30 10 60 15 2.05 2 : 1 2.5 10 10 60 10 1.7 6 : 1 1.8 LONGIT-UDINAL STOPE CROSS-SECTION 30 10 30 15 1.65 1 : 1 2.5 30 10 60 15 2.05 2 : 1 2.5 30 10 120 15 2.3 A : 1 2.5 TRANS-VERSE STOPE CROSS-SECTION 10 10 AO 10 1.6 A : 1 1.8 10 20 AO 10 l.A A : 1 1.6 10 40 AO 10 1.2 A : 1 l.A TABLE 6. Comparison of BEAP and BITEM for four sets of different orebody geometries. section. The f i n a l t e s t checked the average p i l l a r stress as stopes of a constant height and length were increased i n breadth. Table 6 shows the stope and p i l l a r dimensions f o r each run (the dimensions are defined i n figure 29) . Table 6 also shows the average p i l l a r stress increase for BEAP and BITEM and the stope height:length r a t i o . The average p i l l a r stress increase i s defined as the average p i l l a r stress divided by the pre-mining stress i n that d i r e c t i o n ( i e . ay i n figure 28). In a l l 12 cases, the average p i l l a r stress at the mid-height centerline was higher for the 2D plane s t r a i n (BITEM) models than the 3D BEAP models. The overestimation of BEAP by BITEM i s shown for each geometry i n figure 30. The dashed l i n e on figure 3 0 i s an estimate of the maximum overestimation of BEAP by 2D plane s t r a i n modelling for various stope height to stope length r a t i o s . As the stope height to stope length r a t i o increases, the average p i l l a r stress predicted by the 3D models i s closer to the 2D plane s t r a i n solution. As the stope height to length r a t i o increased over 4:1, the 3D stress induced i n the horizontal plane e s s e n t i a l l y remained the same and converged to l e v e l s s i m i l a r the stress predicted by plane s t r a i n modelling. Brown's comment (above) that a stope cross-section needs to be at l e a s t two excavation "diameters" from the stope end, f o r good agreement between 2D plane s t r a i n and 3D modelling r e s u l t s , would correspond to a stope height to stope length r a t i o of 4:1. His estimation of less than 10 % difference between 2D plane aVCn H V n i d 30VH3AV JO NOLLVHI±S3a3AO FIGURE 30. Overestimation of average p i l l a r load by the 2D "BITEM" boundary element method f o r the 12 runs i n the four t e s t s . 97 s t r a i n and 3D modelling agrees well with the r e s u l t s presented i n figure 30. 5.4 Displacement Discontinuity Modelling of 3D Stope Geometries For excavations with i r r e g u l a r cross-sections or small stope length to stope height r a t i o s , the 2D plane s t r a i n method can not e f f e c t i v e l y predict the average stress at the mid-height centerline of a p i l l a r . The displacement d i s c o n t i n u i t y (DD) boundary element method MINTAB may be useful i n these conditions. The DD code can be used to predict three dimensional s t r e s s r e d i s t r i b u t i o n around t h i n , t a b u l a r orebodies. For MINTAB analysis, the orebody must be a single seam with n e g l i g i b l e v a r i a t i o n i n s t r i k e , dip and thickness. In addition, the thickness of the seam must be small compared to the length of excavations made i n the seam. The following sub-sections w i l l investigate the e f f e c t of the seam thickness on ' MINTAB's a b i l i t y t o p r e d i c t stresses at the mid-height centerline of open stope r i b p i l l a r s . 5.4.1 Seam Thickness Limitations To help discuss the influence of the thickness of the reef, the r a t i o of the shortest stope dimension to the seam thickness i s defined as the "seam thickness r a t i o " . In open stope mining, where stopes are t y p i c a l l y t a l l e r than they are long, the seam thickness r a t i o w i l l usually be the r a t i o of stope length to stope breadth (see figure 31). Other authors have discussed the SEAM THICKNESS RATIO = J__ B FIGURE 31. The dimensions and geometry of the MINTAB/BEAP comparison tests. 1 TEST STOPE LENGTH (L) STOPE BREADTH (B) STOPE HEIGHT (H) PILLAR WIDTH (Wp) BEAP 1 MINTAB AVE. | SEAM PILLAR | THICK. STRESS I RATIO INCREASED MINTABI AVE. PILLAR STRESS INCREASE SQUARE STOPE CROSS-SECTION 10 10 10 10 1.25 1.0 1.25 10 10 20 10 1.45 1.0 1.35 10 10 40 10 1.65 1.0 1.5 J 10 10 60 10 1.7 | 1.0 1.65 fl 10 10 80 10 1.7 | 1.0 1.6 | LONGIT-UDINAL STOPE CROSS-SECTION 100 10 60 50 1.5 1 6.0 1.5 60 10 60 30 1.75 | 6.0 1.7 30 10 60 15 2.05 fi 3.0 1 2.0 10 10 60 10 1.7 | 1.0 1.65 LONGIT-UDINAL STOPE CROSS-SECTION 30 10 30 15 1.65 B 3.0 1.65 30 10 60 15 2.05 3.0 2.0 30 10 120 15 2.3 | 3.0 2.2 TRANS-VERSE STOPE CROSS-SECTION 10 10 40 10 1.6 1.0 1.5 10 20 40 10 1.4 0.5 1.45 10 40 40 10 | 1.2 | 0.25 1.45 TABLE 7. Comparison of BEAP and MINTAB for the four different tests. influence of the seam thickness r a t i o . Crouch (1986) states that 3D displacement disc o n t i n u i t y programs: "...can be used to analyze any excavation that has a breadth:thickness r a t i o of 3 or more." When i n v e s t i g a t i n g s t r e s s d i s t r i b u t i o n s around d i f f e r e n t e x c a v a t i o n geometries with the pseudo-3D displacement d i s c o n t i n u i t y method, Brady (1978) was more conservative i n finding that a, "...comparison with r e s u l t s from independent t h r e e -dimensional analyses of these excavation shapes, indicate that the method i s s a t i s f a c t o r y for openings where the span/height r a t i o i s greater than 5." The influence of the seam thickness r a t i o on average p i l l a r stress w i l l be checked through the use of the t e s t s described i n Chapter 5.3.2. 5.4.2 Comparison of Displacement Discontinuity and 3D Numerical Modelling A comparison was made between the three dimensional average p i l l a r stress r e s u l t s from the BEAP runs i n Chapter 5.3.2 and the average p i l l a r stress predicted by MINTAB for the same stope geometries. The goal was to determine the influence that the seam thickness r a t i o has on the accuracy of displacement d i s c o n t i n u i t y modelling. The 12 stope geometries f o r the four t e s t s are summarized i n table 7. This table shows the stope and p i l l a r dimensions, the seam thickness r a t i o f o r each geometry 100 and the average p i l l a r stress for each BEAP and MINTAB run (average p i l l a r stress increase i s calculated as the r a t i o of the average p i l l a r stress to the pre-mining s t r e s s ) . The difference between the two models fo r the various seam thickness r a t i o s i s given i n figure 32. A very rough estimate of the maximum difference between MINTAB and BEAP i s shown i n figure 32. This dashed envelope i s based on the absolute magnitude of the difference (for a l l the points), and plotted as a mirror image above and below the 0% l i n e . In the majority of the t e s t s , there i s l i t t l e difference between the average p i l l a r stresses predicted by BEAP and MINTAB. At a seam thickness of 1.0, there i s l e s s than 10% difference f o r a l l f i v e t e s t s . There i s l e s s than a 5% difference for the f i v e t e s t s having a seam thickness r a t i o equal to or greater than 3.0. Overall, only one t e s t showed a difference of greater than 10%. However, there are only two t e s t s with a seam thickness r a t i o of less than one. Many more tests are needed before any conclusions can be drawn about the a b i l i t y of MINTAB to model stope and p i l l a r geometries with low seam thickness r a t i o s . Considering the minimum seam thickness r a t i o s of 3 and 5 suggested by Crouch and Brady, the difference i n average p i l l a r stress between BEAP and MINTAB i s much les s than expected. Reasons why these authors suggest conservative seam thickness r a t i o s may be: - a high l e v e l of agreement between the DD and 3D solutions was sought i n the analyses done by Crouch and Brady, H •0*0 o H 1 G © (D 5d o. a w O 0 u> ft ft W (D <D • . 0.0. 0* 0* H WHfli > 25 H-•0 H H> 0 hf H » fl> 3 3 S a 8 a ft ^ tr cr O © (D O a t» n < ft» © (D H n 3 p. 0) to «Q O (D 3 ft H- 0» © M < » HID f t » h( 09 0» D CO ft n H> B t-CO ft 0) n ft (D ft 3* <0 m < Z >-ffi Q UJ I-O Q lit CC a. UJ O z Ld 0£ (J U. U. 5 vt V) UJ a: CD 30% 20* H 10X COMPARISON: DD AND 3D NUMERICAL METHODS INFLUENCE OF THE SEAM THICKNESS RATIO - 1 0 * H - 2 0 * H - 3 0 * SEAM THICKNESS RATIO (LENGTH:BREADTH) • 3D TESTS 102 - using the average of several elements to determine the average p i l l a r stress has the e f f e c t of "smoothing out" large differences at i n d i v i d u a l elements i n the p i l l a r , - or the open stope r i b p i l l a r geometries analyzed i n the 12 t e s t s are much simpler and more amenable to DD numerical modelling than the excavation geometries analyzed i n the v e r i f i c a t i o n s by Crouch and Brady. While complex mining geometries have not been investigated, the r e s u l t s of the comparison suggest that using a seam thickness r a t i o of three w i l l give very good agreement between MINTAB and BEAP fo r open stope r i b p i l l a r s . Further checks of the influence of the seam thickness r a t i o w i l l be done i n Chapter 5.5 using case h i s t o r i e s from the data base. 5.5 P i l l a r Load Calculations f o r the Open Stope Data Base There i s no absolute method that can determine the average stress or load i n a mine p i l l a r . As discussed above, and i n Chapter 3, l i n e a r e l a s t i c numerical modelling can often give consistent approximations of the p r e - f a i l u r e load i n hard rock mine p i l l a r s . For p i l l a r s t h a t have a sloughing or de t e r i o r a t i n g condition, load determined by l i n e a r e l a s t i c numerical modelling may be a considerable overestimate. This can be a t t r i b u t e d to the l o c a l loss of load bearing capacity due to rock f r a c t u r i n g and p i l l a r deformation. For f a i l e d p i l l a r s , the l i n e a r e l a s t i c load w i l l not be representative of the stress conditions. A f a i l e d p i l l a r w i l l have l o s t some, or nearly a l l 103 of i t s load bearing capacity, r e s u l t i n g i n stress r e d i s t r i b u t i o n into nearby competent p i l l a r s or abutments. The i n a b i l i t y of l i n e a r e l a s t i c modelling to determine an approximate load for sloughing and e s p e c i a l l y f a i l e d p i l l a r s presents d i f f i c u l t i e s i n developing a r e l i a b l e method of predicting p i l l a r f a i l u r e . 5.5.1 Assumptions In order to set a consistent method for determining loading conditions f o r a l l p i l l a r assessments, i t w i l l be assumed that p i l l a r s a r e i n f i n i t e l y e l a s t i c i n t h e i r deformation c h a r a c t e r i s t i c s . This means that p i l l a r s w i l l not loose t h e i r load bearing capacity regardless of t h e i r physical condition. While not being t e c h n i c a l l y accurate to the actual problem, t h i s assumption w i l l permit the investigation of the stress and geometrical conditions that existed before f a i l u r e and a rudimentary look at the conditions that have resulted i n f a i l u r e of open stope p i l l a r s . Ultimately, i t w i l l provide the basis fo r p r e d i c t i n g conditions that are associated with p i l l a r f a i l u r e . 5.5.2 P i l l a r Load Results The a b i l i t y of BITEM and MINTAB to model each problem geometry i n the data base was evaluated. I f a program could not adequately account for the excavations a f f e c t i n g the stress conditions of the p i l l a r , numerical analysis was not done. This s i t u a t i o n occurred for BITEM when the geometries of a l l the 104 s i g n i f i c a n t excavations could not be included i n the plane of the problem. MINTAB was not used to investigate a stope and p i l l a r geometry when en-echelon stopes were part of the problem geometry, or the orebody had s i g n i f i c a n t changes i n thickness or s i g n i f i c a n t changes i n d i r e c t i o n . For each case h i s t o r y , Table 8 shows: - the pre-mining stress normal to the orebody, - the l i m i t i n g g e ometrical r a t i o s a s s o c i a t e d with the a p p l i c a b i l i t y of MINTAB (the seam thickness rat i o ) and BITEM (the stope height to length r a t i o ) , - the average stress predicted for the p i l l a r by each numerical method and the best estimate of the average p i l l a r stress, - the estimated error associated with the best load due to assumptions associated with modelling three dimensional stope and p i l l a r geometries with numerical methods that are not three dimensional, - the average p i l l a r load calculated using the t r i b u t a r y area theory (chapter 3.1.2.1), - and the error i n the t r i b u t a r y area load compared to the numerically determined load. The best estimate of the average p i l l a r load was chosen based on the l i m i t i n g r a t i o s f o r BITEM and MINTAB. I f a case h i s t o r y had a high stope length to stope width r a t i o , the BITEM load was used. I f a case hi s t o r y had a high seam thickness r a t i o , the MINTAB load was used. I f the stope geometry did not 105 • •" PUB- BITEM MINTAB ESTIMATED AVERAGE TRIBUTARY AREA 1 1 PILLAR MINING HEIGHT: SEAM ! PILLAR LOAD PILLAR LOAD PILLAR j NUMBER STRESS LENGTH LOAD THICK, j LOAD j J ASSESSMENT |(MPa) RATIO (MPa) RATIO | (MPa) (MPa) 1 Z ERROR (MPa) | Z ERROR 2 39 1.4 51 0.3 ; 47 51 ! 25-45Z 62 ! 22Z STABLE i 3 39 1.4 64 0.3 j 55 64 | 25-45Z 90 ; 40Z FAILURE | 7 46 4.5 55 0.6 | 60 55 ! <10Z 61 ; 12Z STABLE ! 8 46 4.5 69 0.6 | 83 69 ; <10Z 92 i 33Z FAILURE ! 15 14 2.6 28 1.5 | 24 28 ! 10-25Z 32 ! 15Z STABLE ! 16 14 1.8 , 29 1.7 ! 24 29 ! 25-45* 33 ! 12Z STABLE ! 17 16 4.0 29 0.9 ! 24 29 ! <10Z 32 ! 10Z SLOUGH ; 18 40 2.0 90 3.0 | 66 66 ! <10Z 98 ! 48Z STABLE ! 19 40 1.7 91 3.3 ! 63 63 | <10Z 99 i 57Z STABLE 1 20 17 2.9 43 0.8 ! 41 *3 ! 10-25Z 58 ! 34Z LOUGH |21 17 4.0 28 0.7 j 28 28 | <10Z 35 ,' 24Z STABLE ! 22 17 3.5 29 0.7 j 26 29 i 10-25Z 33 J 14Z STABLE ! 23 17 1.4 38 0.7 1 31 38 ; 25-45Z 53 ! 39Z FAILURE i 24 17 3.5 33 | 27 33 ! 10-25Z 33 ! OZ STABLE ! 25 17 0.9 57 0.8 ! 30 57 ! >45Z 65 ! 15Z FAILURE ! 26 12 3.0 29 1.8 J 24 29 ! 10-25Z 37 ! 27Z STABLE ! 27 12 3.0 44 3.8 ! 33 33 ! <10Z 48 ! 45Z STABLE 28 12 N A N A 1.1 ! 28 28 | N A j NA SLOUGH ! 29 12 1.8 26 0.8 ; 21 26 ! 25-45Z 33 ! 27Z STABLE ! 30 12 N A N A 1.7 | 31 31 ! N A ; NA FAILURE ! 31 12 0.9 , 60 3.8 ! 37 37 ! <10Z 91 i 146Z STABLE ! 32 15 5.0 26 1.0 | 28 26 ! <10Z 33 ! 27Z , STABLE ,' 33 15 5.0 38 1.1 ! 38 38 i <10Z 57 ! 51Z ! FAILURE j 34 15 6.3 ! 31 1.2 ! 30 31 ! <10Z 38 ; 21Z SLOUGH | 35 15 2.5 31 i.o ! 30 31 ! 10-25Z 44 | 42Z STABLE ] 36 15 1.5 38 1 3 ! 32 38 25-45Z 58 ; 52Z j FAILURE ! 37 15 2.5 40 0.7 ', 35 40 j 10-25Z 57 ! 43Z ; FAILURE ! 42 55 5.0 99 0.5 | 78 99 ! <10Z no ; 11Z ! FAILURE | 43 55 5.0 75 0.5 j 60 75 ! <10Z 73 | -2Z ! STABLE ! 44 55 5.0 76 0.7 [ 59 76 ! <10Z 73 ! -4Z | STABLE ! 45 55 5.0 ! 102 0.6 ; 83 102 ! <10Z 110 | 8Z ! FAILURE ! 46 23 2.1 30 N A ; NA 30 | 10-25Z 36 ! 21Z ! STABLE ! 47 23 2.1 32 N A ! NA 32 j 10-25Z *2 ! 32Z | SLOUGH ! 48 23 1.5 41 N A ; NA 41 ! 25-45Z 55 ! 34Z ] FAILURE j 49 23 1.5 49 N A ; NA 49 i 25-45Z 71 ! 44Z ! FAILURE ! 50 15 N A N A 3-3 j 31 31 ! <10Z NA | NA ! STABLE i 51 15 N A N A 7.0 ! 39 39 ! <10Z NA | NA ! STABLE ! 52 15 N A N A 4.6 ! 48 48 | <10Z NA | NA ! STABLE ! 53 23 N A NA 0.7 ! 36 36 j NA ! NA ! STABLE | 54 18 5.6 43 3.0 ! 46 46 | <10Z 50 ; 8Z ! STABLE j 55 . 18 3.4 44 3.0 i 46 46 <10Z 54 ; 17Z ] STABLE ! 56 30 1.1 59 0.4 | 48 59 | 25-45Z 69 ! 17Z ! SLOUGH ! 57 30 5.8 ! 38 0.2 ] 46 38 ! <10Z 45 | i8z : STABLE ! 58 30 4.4 40 0.2 ! 45 40 ! <10Z 48 ! 20Z J STABLE ! 59 ! 30 0.8 72 0.2 ! 54 72 j >45Z 95 ! 31Z | SLOUGH ! 60 ! 30 0.6 82 0.7 1 53 82 | >45Z 119 ] 45Z ! SLOUGH | 61 35 5.0 70 N A ; NA 70 ! <10Z 88 j 25Z ! SLOUGH i TABLE 8. P i l l a r load information f o r a l l the open stope r i b p i l l a r case h i s t o r i e s using BITEM, MINTAB and the Tributary Area Theory. 106 f i t e i t h e r l i m i t i n g r a t i o , the BITEM load was used. BITEM i s used to estimate the average p i l l a r stress i n these situations because i t accounts for the geometry of these problems better than MINTAB, and the error associated with BITEM (from figure 30) , i s better understood than the error associated with MINTAB (from figure 32). The error associated with the best load i s based on the comparisons of MINTAB and BITEM to a true three dimensional numerical method presented i n chapters 5.3.2 and 5.4.2. The r e s u l t s i n Table 8 show that stable case h i s t o r i e s and primary stoping geometries tend to have a lower degree of error associated with the predicted load. This i s because primary stoping geometries are more regular than secondary and t e r t i a r y geometries and consequently f i t the modelling constraints ( i e . the l i m i t i n g ratios) better. The error i n the best p i l l a r load i s an estimation of the maximum possible error based on figures 30 and 32. The actual error i s smaller for many of the p i l l a r s . For t h i s reason, the load applied i n the development of a p i l l a r design method w i l l not be adjusted for the estimated error. Table 8 shows that the t r i b u t a r y area theory has highly varied r e s u l t s compared to the best load estimated by numerical modelling. I t can be assumed that t r i b u t a r y area overestimates the average p i l l a r load. I t i s also apparent that the greater the stope height:length r a t i o of the case h i s t o r y geometry, the better the agreement between the t r i b u t a r y area theory load and the load predicted by numerical modelling. In general, the 107 overestimation of the predicted stress makes the t r i b u t a r y area theory very un r e l i a b l e i n the estimation of the average load i n open stope r i b p i l l a r s . 5.5.3 Numerical Model Comparison Using the Case H i s t o r i e s Chapters 5.3 and 5.4 gave a de t a i l e d comparison of two dimensional and displacement d i s c o n t i n u i t y numerical modelling against a three dimensional method. Analysis of the data base case h i s t o r i e s provides further information f o r comparison. Two case h i s t o r i e s f i t the MINTAB seam thickness r a t i o l i m i t a t i o n of 3 or greater and also have a large height to length r a t i o (greater than 4) making good BITEM cases. For both of these case h i s t o r i e s , Table 9 shows the stope height to length r a t i o , the seam thickness r a t i o , the average p i l l a r stress predicted by BITEM and MINTAB and the difference i n the predicted stress. This comparison shows good agreement between the average p i l l a r load for the two methods when a stope and p i l l a r geometry meets both of the l i m i t i n g r a t i o s . CASE NUMBER BITEM MINTAB PERCENT DIFFERENCE BETWEEN BITEM AND MINTAB HEIGHT: LENGTH RATIO AVERAGE PILLAR LOAD (MPa) SEAM THICKNESS RATIO AVERAGE PILLAR LOAD (MPa) 54 5.6 43 3.0 46 - 7 % 55 3.4 44 3.0 46 - 5 % Table 9. Comparison of MINTAB and BITEM r e s u l t s when both programs l i m i t a t i o n s are s a t i s f i e d . 108 Three case h i s t o r i e s s a t i s f y the MINTAB seam thickness constraint, but do not have a large height to length r a t i o . These are good MINTAB geometries, but not favorable for BITEM modelling. BITEM w i l l overestimate the average p i l l a r load. For each of these case h i s t o r i e s , Table 10 shows the stope height to length r a t i o , the seam thickness r a t i o , the average p i l l a r s t r e s s p r e d i c t e d by BITEM and MINTAB and the overestimation by BITEM of the MINTAB predicted p i l l a r load. When these three cases are compared against the BITEM overestimation of BEAP graph developed i n Chapter 5.3.2, they p l o t s l i g h t l y above the maximum over-estimation documented i n chapter 5.3.2 (see figure 33). However, considering a pot e n t i a l error of up to 10% for the MINTAB case h i s t o r i e s , the re s u l t s are not very f a r above the l i m i t found i n Chapter 5.3.2. CASE NUMBER BITEM MINTAB PERCENT DIFFERENCE BETWEEN BITEM AND MINTAB HEIGHT: LENGTH RATIO AVERAGE PILLAR LOAD (MPa) SEAM THICKNESS RATIO AVERAGE PILLAR LOAD (MPa) 18 2 . 0 90 3.0 66 + 36 % 19 1.7 91 3 . 3 63 + 44 % 31 0.9 60 3.8 37 + 62 % Table 10. Comparison of BITEM and MINTAB, when the MINTAB l i m i t a t i o n i s met, but the BITEM l i m i t a t i o n i s not met. The overestimation by BITEM i s i n the range estimated i n Chapter 4. 70* COMPARISON: 2D AND 3D NUMERICAL METHODS INFLUENCE OF STOPE HEIGHT:LENGTH RATIO 60* H 50* H 40* H V \ 30* H 20* • • \ \ i o * H § OX • 3D TESTS STOPE HEIGHT:L£NGTH RATIO * DATA BASE t-1 o 110 Many of the case h i s t o r i e s investigated had a large stope height to length r a t i o (making them good geometries for BITEM modelling), but do not f i t the seam thickness c r i t e r i o n needed for accurate MINTAB modelling. By using both numerical methods, the e f f e c t of a low seam thickness r a t i o can be compared against the s a t i s f a c t o r y p i l l a r load r e s u l t s given by BITEM. Table 11 shows the stope height to length r a t i o , the seam thickness r a t i o , the BITEM and MINTAB average p i l l a r stress, and the difference i n the average p i l l a r stress for t h i r t e e n d i f f e r e n t geometries. The r e s u l t s of the MINTAB analysis vary up to ± 25 % with the BITEM r e s u l t s . For the geometries with larger seam thickness r a t i o s (>1.0 but <3.0), the difference i n average p i l l a r stress between the two methods i s l e s s . The maximum difference i n p i l l a r load i s s l i g h t l y higher than the 12 runs i n Chapter 5.4.2, when plotted on the graph of percent difference i n p i l l a r stress versus seam thickness r a t i o (see figure 34) . The envelope showing the maximum error has been redrawn i n figure 34. 5.6 Chapter Summary The three boundary element models (BITEM, MINTAB and BEAP), used i n inve s t i g a t i n g open stope r i b p i l l a r load, have been b r i e f l y described. Conventions for defining open stope r i b p i l l a r geometries and determining the average p i l l a r stress have been presented. The use of three dimensional boundary element modelling i s 111 CASE NUMBER BITEM MINTAB PERCENT DIFFERENCE BETWEEN MINTAB AND BITEM HEIGHT: LENGTH RATIO AVERAGE PILLAR LOAD (MPa) SEAM THICKNESS RATIO AVERAGE PILLAR LOAD (MPa) 7 4.5 55 0.6 60 + 9 % 8 4.5 69 0.6 83 + 20 % 17 4.0 29 0.9 24 - 17 % 21 4.0 28 0.7 28 0 % 32 5.0 26 1.0 28 + 8 % 33 5.0 38 1.1 38 0 % 34 6.3 31 1.2 30 - 3 % 42 5.0 99 0.5 78 - 21 % 43 5.0 75 0.5 60 - 20 % 44 5.0 76 0.7 59 - 22 % 45 5.0 102 0.6 83 - 19 % 57 5.8 38 0.2 46 + 21 % 58 4.4 40 0.2 45 + 13 % Table 11. Comparison between good BITEM and poor MINTAB geometries shows the average p i l l a r stress varying up to ± 25%. BV1NIH A8 0310103yd 30N3y3JJIQ SS381S FIGURE 34. The difference between the average p i l l a r stress predicted by MINTAB and the average p i l l a r stress predicted by BEAP for the comparison tests and 13 case h i s t o r i e s . not possible for the case h i s t o r i e s i n the data base. This i s due to: high program set up and run times, and program space l i m i t a t i o n s . The 2D plane s t r a i n and pseudo-3D displacement d i s c o n t i n u i t y (DD) methods have been used to estimate the load for each p i l l a r case his t o r y . Both of these programs have geometrical l i m i t a t i o n s that may introduce error into the average p i l l a r load. The geometrical l i m i t a t i o n s have been described and the error associated with 2D plane s t r a i n and DD methods has been quantified using 12 t e s t runs and some case h i s t o r i e s from the data base. Figure 33 shows the pote n t i a l error associated with 2D plane s t r a i n modelling for open stope r i b p i l l a r geometries. Figure 34 shows the p o t e n t i a l error associated with the displacement d i s c o n t i n u i t y method for open stope r i b p i l l a r geometries. 114 CHAPTER 6 DEVELOPMENT OF A PILLAR DESIGN METHOD It was stated i n Chapter 3 that a design method for open stope r i b p i l l a r s has not been developed or confirmed. Other authors have shown that the best way to develop and v e r i f y a design procedure i s to conduct a survey and confirm a method with case h i s t o r i e s . There are many examples of p i l l a r design studies, the most notable being: Salamon (1967) i n South African coal mines, Hedley and Grant (1972) i n Canadian hard rock room and p i l l a r mining, and Bieniawski (1983) i n United States coal mines. Each of these studies used experience and c a l i b r a t i o n to develop a method for mining s p e c i f i c conditions. The number of mines v i s i t e d i n the "Integrated Mine Design Study" has resulted i n the c o l l e c t i o n of a substantial amount of data of stable and f a i l e d r i b p i l l a r s from Canadian open stope mines. This data w i l l be used to develop an empirical design method f o r r i b p i l l a r s i n open stope mining. In addition, a wealth of data from hard rock room and p i l l a r mines has been found i n l i t e r a t u r e to help confirm the new empirical method. S p e c i f i c a l l y , the intention of t h i s chapter i s to: - v e r i f y the variables s i g n i f i c a n t i n open stope r i b p i l l a r s based on the data available, - present a method that explains the r e s u l t s of the case h i s t o r i e s i n the data base, - use case h i s t o r i e s from l i t e r a t u r e (mostly from room and 115 p i l l a r mining), to v e r i f y the design concept and r e f i n e the method, - and compare the new method to some of the open stope design procedures commonly used i n the past. 6.1 Choice of Variables Chapter 2.3 discussed variables that may be s i g n i f i c a n t i n the f a i l u r e of open stope r i b p i l l a r s . These variables were: in t a c t rock strength, p i l l a r load, p i l l a r shape and confinement, s t r u c t u r a l d i s c o n t i n u i t i e s , and p i l l a r volume. They w i l l be quantified through the use of: - u n i a x i a l compressive strength f o r i n t a c t rock strength, - boundary element numerical modelling to determine p i l l a r load, - p i l l a r height and width to account for p i l l a r shape and confinement, - empirical rock mass c l a s s i f i c a t i o n methods to account for s t r u c t u r a l d i s c o n t i n u i t i e s , - and the p i l l a r dimensions (from table 5, page 70) can be used to determine the p i l l a r volume. No attempt w i l l be made to quantify the e f f e c t of b a c k f i l l . In Chapter 2, b a c k f i l l was not considered s i g n i f i c a n t i n preventing the f a i l u r e of p i l l a r s , although i t s presence may have a large influence i n preventing p i l l a r d i s i n t e g r a t i o n i f f a i l u r e occurs. 6.1.1 A p p l i c a b i l i t y of S t a t i s t i c a l Methods 116 Ideally, the data base presented i n Chapter 4.2 could be used to t e s t the s i g n i f i c a n c e of each variable i n the s t a b i l i t y of p i l l a r s . Some of the variables are obviously s i g n i f i c a n t . P i l l a r load, p i l l a r width and the strength of the i n t a c t rock are known to have a large influence on the s t a b i l i t y of a p i l l a r . However, the influence of p i l l a r height, p i l l a r volume and minor rock mass d i s c o n t i n u i t i e s (such as j o i n t s ) i n open stope r i b p i l l a r s i s not obvious. The use of s t a t i s t i c s to t e s t the s i g n i f i c a n c e of these three variables was considered, but was l a t e r rejected for a couple of reasons. The f i r s t reason i s the assessment of p i l l a r s t a b i l i t y can not be quantified into a numerical value. The p i l l a r case h i s t o r i e s were assessed with q u a l i t a t i v e categories of stable, sloughing and f a i l e d . These categories l i m i t the use of regression and f a c t o r i a l design methods, because the categories can not be quantified numerically. A system of giving the stable, sloughing and f a i l e d assessments an a r b i t r a r y numerical value and using regression techniques on these values also would not work well. The wide range of i n s t a b i l i t y signs and c h a r a c t e r i s t i c s that are exhibited by the f a i l e d p i l l a r s can not be quantified by a single a r b i t r a r y value and there i s no s a t i s f a c t o r y c r i t e r i o n to determine a representative value for f a i l e d p i l l a r s . The second reason why the use of s t a t i s t i c s i s not f e a s i b l e i s r e l a t e d to the y i e l d i n g p i l l a r case h i s t o r i e s . These are p i l l a r s that were o r i g i n a l l y stable but eventually became 117 unstable due to stopes or p i l l a r s being mined i n the v i c i n i t y or robbing of the p i l l a r . For the y i e l d i n g p i l l a r s , the u n i a x i a l c o m p r e s s i v e s t r e n g t h (UCS) , p i l l a r h e i g h t , rock mass charac t e r i z a t i o n and p i l l a r volume do not change s i g n i f i c a n t l y from the stable to f a i l e d cases. Consequently, a s t a t i s t i c a l method would f i n d that these variables have no s i g n i f i c a n t influence of p i l l a r condition. The only variables that change s i g n i f i c a n t l y for y i e l d i n g case h i s t o r i e s are the average p i l l a r stress and the p i l l a r width. Removing the y i e l d i n g p i l l a r s from the data base reduces the number of case h i s t o r i e s to 12 stable p i l l a r s , 3 sloughing p i l l a r s , and 1 f a i l e d p i l l a r . This i s too small a data base to reach confident s t a t i s t i c a l conclusions about s i g n i f i c a n t variables. The l a s t major problem with using s t a t i s t i c a l methods i n the data base, i s the lack of p r e c i s i o n i n the estimation of some of the data. Chapter 5.5 discusses the determination of average p i l l a r load f o r each case his t o r y . The p o t e n t i a l error associated with t h i s v a r i able varies from l e s s than 10% to greater than 45% (see Table 8, page 105) and implies that a large degree of accuracy should not be used. I t i s not a precise v a r i a b l e and would present s i g n i f i c a n c e problems i f included i n a s t a t i s t i c a l technique. 6.1.2 Design Variables The most important variables i n open stope p i l l a r design are p i l l a r width and the average p i l l a r load. There i s more 118 f l e x i b i l i t y i n choosing and designing these two variables than any of the others. The i n t a c t rock u n i a x i a l compressive strength, rock mass qual i t y and p i l l a r height (orebody width) are a l l a function of the geological s e t t i n g and can not be c o n t r o l l e d or changed. P i l l a r width has a large influence on the l a t e r a l confinement of the p i l l a r core, the p i l l a r s t i f f n e s s , and the modulus of deformation of f a i l i n g p i l l a r s . The magnitude of p i l l a r load has a d i r e c t influence on the degree of f r a c t u r i n g i n a p i l l a r . However, both of these v a r i a b l e s need to be normalized before information from d i f f e r e n t mining conditions can be compared. P i l l a r load i s frequently normalized by comparing i t against the i n t a c t rock strength (discussed i n Chapter 3.2.2.3). This gives a good measure of the state of stress and f r a c t u r i n g i n a p i l l a r . P i l l a r width i s t y p i c a l l y normalized through the use of the r a t i o of the p i l l a r width/height. P i l l a r width/height i s used by many authors to account for the e f f e c t s of p i l l a r shape (see Chapter 3.1.1). 6.1.3 Discounted Variables Two variables have been discounted for design. P i l l a r volume and the influence of geological d i s c o n t i n u i t i e s may be s i g n i f i c a n t i n general p i l l a r design, but t h e i r importance has not been proven for open stope p i l l a r s . Using methods proposed by other authors and information from the data base, i t w i l l be shown that the two discounted variables have a r e l a t i v e l y small 119 v a r i a t i o n i n magnitude i n the open stope p i l l a r data base, and consequently could only have a minor e f f e c t on p i l l a r s t a b i l i t y . 6.1.3.1 P i l l a r Volume Several authors (Hoek and Brown 1980; Agapito and Hardy 1982; Stephansson 1985) have proposed the use of a factor to account f o r the e f f e c t of p i l l a r volume. The reasoning was the rock mass strength decreases with an increase i n p i l l a r volume, due to a larger number of flaws and d i s c o n t i n u i t i e s i n the rock mass. Consequently, the volume e f f e c t i s an i n d i r e c t means of accounting f o r the e f f e c t of d i s c o n t i n u i t i e s . Agapito and Hardy (1982) suggested the following equation to r e l a t e the unconfined u n i a x i a l compressive strength from laboratory t e s t i n g with i n s i t u unconfined compressive p i l l a r strength: °0 = aC ( v l / v l ) a where, OQ = unconfined compressive strength of the p i l l a r , OQ = average laboratory u n i a x i a l compressive strength, V! = volume of the laboratory specimen, Vj = volume of the p i l l a r , a = c o e f f i c i e n t of volume reduction, = 0.12 f o r coal, = 0.08 for o i l shale, = 0.06 for good quality, hard quartzite. Using the formula, we can compare the influence of the v a r i a t i o n of p i l l a r volumes i n the data base. For t h i s data 120 base, the smallest open stope p i l l a r has a volume of about 2500 cubic metres, and the largest open stope p i l l a r has a volume of about 150,000 cubic metres. ^2,500 _ °C (Vi / 2 5 0 0 ) 0 - 0 6 _ — — 1.2 o ^150,000 °C ( V l / 150000) 0' 0 6 So, f o r the f u l l range of p i l l a r volumes i n the data base, t h i s formula shows only a small influence (less than 30%). The lack of s e n s i t i v i t y of volume i s only part of the problem with using t h i s c o e f f i c i e n t of volume reduction method. Any method to account for the influence of flaws or discont-i n u i t i e s i n a rock mass should be based on an assessment of the q u a l i t y of the rock mass. The frequency, orientation, continuity and shear strength of d i s c o n t i n u i t i e s i n a rock mass s h o u l d be c o n s i d e r e d when e s t i m a t i n g the e f f e c t of d i s c o n t i n u i t i e s . This formula does not consider any rock mass c h a r a c t e r i s t i c s and as a r e s u l t , i t does l i t t l e to account for the influence of d i s c o n t i n u i t i e s i n p i l l a r strength. 6.1.3.2 Structural D i s c o n t i n u i t i e s As mentioned above, to account for the influence 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 i n p i l l a r s t r e n g t h , the c h a r a c t e r i s t i c s of the rock mass must be quantified. Currently, the most e f f e c t i v e method of describing a rock mass i s with empirical rock mass c l a s s i f i c a t i o n s . The two most common c l a s s i f i c a t i o n s are the NGI system, developed by Barton, Lien 121 and Lunde of the Norwegian Geotechnical I n s t i t u t e (1974), and the CSIR system, developed by Bieniawski of the South African Council f o r S c i e n t i f i c and I n d u s t r i a l Research (1976). Data for the CSIR rock mass c l a s s i f i c a t i o n was c o l l e c t e d i n the "Integrated Mine Design Study." Herget et a l . (1984) and Stacey and Page (1986) suggest using rock mass c l a s s i f i c a t i o n s as strength reduction factors by applying them against the u n i a x i a l compressive strength of rock. For instance, i f the i n s i t u i n t a c t rock strength i s o0 and the rock mass has a CSIR rock mass r a t i n g of 75%, then the i n s i t u rock mass strength i s (0.75 * o 0 ) . Table 5 (page 70) shows the CSIR geomechanics r a t i n g "RMR" (acronym for rock mass rating) for the p i l l a r s i n the open stope data base. The mean RMR i s 69.6, with a standard deviation of 4.8. This small range i n rock mass ratings i s not u n r e a l i s t i c because the source of the majority of the information i n the data base i s mines i n the Canadian s h i e l d . The c l a s s i f i c a t i o n methods are designed to characterize a much wider range of rock masses. With t h i s small a range of rock mass qua l i t y , however, i t i s not possible to v e r i f y that the i n c l u s i o n of a rock mass strength reduction factor would adequately account for any influence of d i s c o n t i n u i t i e s i n the design of open stope r i b p i l l a r s . Using a strength reduction variable could be an e f f e c t i v e method t o a c c o u n t f o r the i n f l u e n c e of s t r u c t u r a l d i s c o n t i n u i t i e s i n a rock mass. However, the avai l a b l e data 122 could only prove t h i s over a small range of rock mass conditions. Rather than include a variable whose influence can not be e f f e c t i v e l y c a l i b r a t e d or v e r i f i e d , the e f f e c t of s t r u c t u r a l d i s c o n t i n u i t i e s has been omitted. A large amount of data from a much wider v a r i e t y of rock mass conditions i s needed to confirm and c a l i b r a t e the s i g n i f i c a n c e of a strength reduction factor. 6.2 P i l l a r S t a b i l i t y Graph The methodology for the development of an open stope r i b p i l l a r design c r i t e r i o n i s based on the graphical comparison of the s i g n i f i c a n t variables discussed above and the assessment of p i l l a r case h i s t o r i e s . The y-axis of the graph has been chosen to represent the normalized p i l l a r load, while the x-axis i s defined by the p i l l a r width to p i l l a r height r a t i o . Stable p i l l a r s from the data base are plotted with square symbols, sloughing p i l l a r s are represented by cross shaped symbols, and f a i l e d p i l l a r s are located with diamond symbols (see figure 35). By arranging the graph i n t h i s form (and not including correction factors for volume and rock mass q u a l i t y ) , the graph stays i n t u i t i v e l y simple. The influence of varying the design variables i s clear-cut and e x p l i c i t . This graph w i l l be referred to as the " p i l l a r s t a b i l i t y graph". 6.2.1 Graphical Data Analysis Comparison of the shape and the loading condition of o o CO o m o d o O O d o o d s o n / a v o i FIGURE 35. The p i l l a r s t a b i l i t y graph showing the open stope r i b p i l l a r data base. 124 p i l l a r s , using the p i l l a r s t a b i l i t y graph, exposes a trend i n r i b p i l l a r behaviour. The graph shows squat p i l l a r s under low stress conditions as stable (bottom r i g h t region of the graph i n figur e 35) . P i l l a r s become les s stable as t h e i r graphical p o s i t i o n i s located more towards the upper l e f t corner of the graph, which represents highly stressed, slender, and f a i l u r e prone p i l l a r s . The graph has be divided into two zones based on t h i s data (see figure 36) . The upper l e f t side of the graph denotes conditions i n which p i l l a r s have f a i l e d . The bottom r i g h t side of the graph shows conditions i n which p i l l a r s have not suffered any serious i n s t a b i l i t y . The two zones are separated by a t r a n s i t i o n area. The location of t h i s area has been approximated based on the graphical l o c a t i o n and physical condition of the case h i s t o r i e s . No s t a t i s t i c a l methods have been used to locate the t r a n s i t i o n area. The bottom l i n e of the t r a n s i t i o n area corresponds to the region where major p i l l a r s t a b i l i t y problems are f i r s t encountered. Only one sloughing p i l l a r , no f a i l e d p i l l a r s , and a l l but four of the stable p i l l a r s p l o t below t h i s l i n e . This bottom l i n e does not necessarily s i g n i f y p i l l a r f a i l u r e , but rather the onset of mining problems due to p i l l a r i n s t a b i l i t y . Sloughing or de t e r i o r a t i n g p i l l a r s could carry an even greater load (as reported by Goel and Page 1981) , but displacement, rock f r a c t u r i n g and p i l l a r deformation w i l l increase. The top l i n e roughly defines a c r i t e r i o n where p i l l a r f a i l u r e has been H 3 G H> 0) U> H-M • (D O. N 3* O (D 3 10 K-M 0) H* 3 0) a it f t to 3* f t cr f t H-*1 M JD |_u 3 f t to p -rtvQ H* ^ O B» 3 1 5 3* 0) ^ CO (D 3* 0> O • C H-3 tQ f t 3" (D to f t &» tr M fO o D \ Q < o _l 0.60 0.50 0.40 H 0.30 H 0.20 H 0.10 H PILLAR STABILITY GRAPH OPEN STOPE RIB PILLAR DATA • 0.00 - | 1 p 0.0 0.4 i 1 r 0.8 ' i i 1 1 1 r 1.2 1.6 2.0 • STABLE PILLAR WIDTH/PILLAR HEIGHT + SLOUGHING O FAILURE 126 observed i n the case h i s t o r i e s of the data base. No stable case h i s t o r i e s , four of the nine sloughing p i l l a r s and a l l but three of the f a i l e d p i l l a r s are found above t h i s l i n e . P i l l a r s p l o t t i n g above t h i s l i n e generally have: - started to lose load bearing capacity, - suffered a large amount of frac t u r i n g , - experienced large displacements of rock, - and had severe sloughing of p i l l a r walls (unless confined by b a c k f i l l ) . In regions of the graph where s u f f i c i e n t r i b p i l l a r data i s not a v a i l a b l e to l o c a t e the t r a n s i t i o n zone, i t has been approximated with dashed l i n e s . 6.2.2 Influence of P i l l a r Load Approximations In Chapter 5.5.2, the maximum error i n the average p i l l a r load was estimated for each case h i s t o r y . To check the influence of t h i s error, the average p i l l a r load i s decreased by the maximum amount of the error shown i n Table 8 (page 105) . The reason f o r the decrease i s that the majority of p i l l a r loads are estimated by BITEM, which overestimated the actual p i l l a r load. Data i n which the error could not be reasonably estimated were omitted. This occurred for 6 of the 47 data points. Figure 37 i s a pl o t of the p i l l a r s t a b i l i t y graph using the reduced average p i l l a r load with the o r i g i n a l t r a n s i t i o n area. The modified data s t i l l f i t s the graph well, with only three sloughing cases and one f a i l e d case below the t r a n s i t i o n zone. son/avcn 128 I t should be kept i n mind that the adjusted load was decreased by an estimate of the maximum error, and most cases w i l l have an error smaller than the maximum. We can conclude that the error i n the average p i l l a r load does not s i g n i f i c a n t l y change the method proposed. I t also demonstrates the fac t that the p i l l a r loading conditions has less of an e f f e c t on p i l l a r s t a b i l i t y than the p i l l a r shape (width/height r a t i o ) . 6.2.3 Importance of Yielding P i l l a r Case H i s t o r i e s As discussed i n the data base description (Chapter 4.1), there are 13 p i l l a r s that were stable and subsequently f a i l e d due to mining. These p i l l a r s comprise 30 of the 47 case h i s t o r i e s i n the open stope data base. The y i e l d i n g p i l l a r case h i s t o r i e s are very useful i n developing a design method because the stable and f a i l e d cases should p l o t i n t h e i r respective zones separated by the t r a n s i t i o n area. Figure 38 i s a p l o t of the e n t i r e data base with the stages of each y i e l d i n g p i l l a r joined by a s o l i d l i n e . The y i e l d i n g p i l l a r endpoints correspond well to the stable and f a i l e d zones which reinforces the l o c a t i o n of the t r a n s i t i o n area. As a p i l l a r f a i l s , i t s loc a t i o n moves from the stable zone, through the t r a n s i t i o n area, and into the f a i l e d zone. The y i e l d i n g p i l l a r s also demonstrate the s e n s i t i v i t y of the graph to predict p i l l a r f a i l u r e . s o n / a v o i FIGURE 38. The p i l l a r s t a b i l i t y graph with a l l the case h i s t o r i e s of the 13 y i e l d i n g p i l l a r s joined by s o l i d l i n e s . This reinforces the l o c a t i o n of the t r a n s i t i o n zone and shows the s e n s i t i v i t y of the method to predict f a i l u r e . 130 6.2.4 Limitations of the P i l l a r S t a b i l i t y Graph There are a few comments to be made concerning the l i m i t -ations of the p i l l a r s t a b i l i t y graph. F i r s t l y , the data i n and near the t r a n s i t i o n zone shows a v a r i e t y of behaviour. This suggests that a great degree of pre c i s i o n i s not inherent to the graph. This lack of pr e c i s i o n i s a function of inaccuracy i n the input data and the broad assessments used to categorize p i l l a r s . The s i z e of the t r a n s i t i o n zone could be considered a measure of the accuracy of the p i l l a r s t a b i l i t y graph. I t should be emphasized that t h i s i s an empirically developed r e l a t i o n s h i p and i s more r e l i a b l e when applied i n conditions s i m i l a r to those i n the data base. S p e c i f i c a l l y , the range of the various data i s : 70 MPA < UCS < 316 MPa, 9 metres < Wp < 45 metres, 60 < RMR < 78 where, UCS = the i n t a c t rock u n i a x i a l compressive strength, Wp = the p i l l a r width, RMR = a measure of the rock mass competency using the CSIR rock mass c l a s s i f i c a t i o n . A f i n a l note about the p i l l a r s t a b i l i t y graph i s that there are almost no stable p i l l a r s with an (average p i l l a r load/UCS) r a t i o greater than 0.5, and very few stable p i l l a r s with an (average load/UCS) r a t i o greater than 0.33. This suggests that there i s a p r a c t i c a l l i m i t to the maximum normalized load for a 131 stable open stope r i b p i l l a r . These values correspond well with suggestions by Mathews et a l . (1980) and Bawden et a l . (1988), of the maximum normalized major p r i n c i p a l stress allowable before stress related mining problems become excessive. 6.3 Data from L i t e r a t u r e Very few open stope p i l l a r case h i s t o r i e s found i n l i t e r a t u r e provide s u f f i c i e n t information that they can applied to the p i l l a r s t a b i l i t y graph. F u l l y documented room and p i l l a r mining case h i s t o r i e s are more common. Three studies of hard rock p i l l a r design have been found which contain the p i l l a r l o a d , u n i a x i a l compressive rock s t r e n g t h , p i l l a r shape information and an assessment of the p i l l a r s t a b i l i t y . The two largest studies deal with room and p i l l a r mining while the t h i r d i s a smaller and more det a i l e d study that deals with open stope r i b p i l l a r design. 6.3.1 Data from Canadian Room and P i l l a r Mining In the 1960's, a major rock mechanics in v e s t i g a t i o n was undertaken i n the E l l i o t Lake uranium mining d i s t r i c t to determine stable stope and p i l l a r configurations. One of the re s u l t s was a p i l l a r strength formula (described i n Chapters 3.1.1.3, and 6.4.1). The d e t a i l s of the formula development and the data base were published by Hedley and Grant (1972). Their data base consisted of 23 stable p i l l a r s , 2 p i l l a r s that were p a r t i a l l y f a i l e d , and 3 p i l l a r s that were crushed. P i l l a r s i n 132 the uranium mines are very long i n one d i r e c t i o n which i s the same shape as p i l l a r s i n open stope mines. However, the p i l l a r dimensions and volume are s u b s t a n t i a l l y lower i n room and p i l l a r mining. Using the data i n the paper (Hedley and Grant 1972) , the case h i s t o r i e s were plotted on the p i l l a r s t a b i l i t y graph (see figure 39) . The E l l i o t Lake data f i t s the p i l l a r s t a b i l i t y graph quite well with a l l of the stable p i l l a r s p l o t t i n g below the t r a n s i t i o n area, and most of the p a r t i a l l y f a i l e d and crushed p i l l a r s p l o t t i n g i n the t r a n s i t i o n area. Ideally, for t h i s data, the t r a n s i t i o n zone would probably be s l i g h t l y lower. This would give a better separation between the stable and unstable p i l l a r s . However, there i s not s u f f i c i e n t data near the t r a n s i t i o n zone to warrant adjusting i t s l o c a t i o n . The rock mass qu a l i t y for the E l l i o t Lake mines i s s i m i l a r to that found i n the "Integrated Mine Design Study". A discussion on p i l l a r s t a b i l i t y at the Denison Mine (Townsend 1982), which i s one of the mines i n Hedley's study, gives the p i l l a r s an NGI rock mass qu a l i t y of 45. This i s roughly equivalent to a CSIR ra t i n g of 78, based on a r e l a t i o n s h i p proposed by Bieniawski (1976). An RMR of 78 i s within the range of the rock mass q u a l i t i e s found i n the open stope p i l l a r data base. Due to the variable nature of a rock mass, i t i s wrong to assume an RMR of 78 for a l l p i l l a r s i n the E l l i o t Lake data base. However, i t can be concluded that the general rock mass conditions between the two data bases are s i m i l a r . s o n / a v c n FIGURE 39. The p i l l a r s t a b i l i t y graph shoving the data from room and p i l l a r mining published by Hedley and Grant (1972) i n t h e i r study on the development of a p i l l a r strength formula. 134 An i n t e r e s t i n g observation can be made concerning the influence of p i l l a r volume. The volume of an average p i l l a r i n the E l l i o t Lake data base i s approximately 25 to 50 times smaller than the average volume of the open stope data base (« 1000 - 2000 m3 for room and p i l l a r , and » 50,000 m3 f o r open stoping). A r e l a t i v e increase of p i l l a r strength due to the smaller volume should r a i s e the r e l a t i v e p o s i t i o n of the t r a n s i t i o n zone. This does not correspond with the cases of p a r t i a l l y f a i l e d and crushed E l l i o t Lake p i l l a r s . According to the Hedley data, the t r a n s i t i o n zone should probably be s l i g h t l y lower. Based on t h i s observation, there appears to be l i t t l e d i fference i n the influence of p i l l a r volume between p i l l a r s i n open stope and room and p i l l a r mining. 6.3.2 Data from a Botswana Room and P i l l a r Mine A paper by Von Kimmelmann et a l . (1984) discussed the development of a p i l l a r design c r i t e r i o n at BCL Limited i n Botswana. Back analysis of a large number of e x i s t i n g p i l l a r s was performed using the pseudo-three dimensional displacement d i s c o n t i n u i t y numerical method. P i l l a r d e t e r i o r a t i o n was assessed with the following c r i t e r i o n : "Group A ( i n t a c t p i l l a r s ) d i s p l a y e d minor s p a l l i n g p a r t i c u l a r l y associated with any overbreak into the hanging wall or footwall gneisses. No j o i n t opening was observed. Group B p i l l a r s exhibited prominent s p a l l i n g generally 135 associated with s t r u c t u r a l features. S l i g h t opening of the j o i n t s into the p i l l a r was also noted. Group C p i l l a r s displayed severe s p a l l i n g of i n t a c t rock, pronounced opening of j o i n t s and deformation of d r i l l holes." The Group A assessment corresponds reasonably well with stable p i l l a r s , Group B with sloughing p i l l a r s , and Group C with f a i l e d p i l l a r s . Table 12 gives the p i l l a r c l a s s i f i c a t i o n , p i l l a r shape, p i l l a r load, and remarks on the p i l l a r s t a b i l i t y for the complete data base presented by Von Kimmelmann (1984). Two d i f f e r e n t types of p i l l a r s were investigated. P i l l a r s that were near square (when viewed i n plan) and p i l l a r s that were very long i n one dimension (see figure 40) . The long p i l l a r s were applied d i r e c t l y to the p i l l a r s t a b i l i t y graph (see figure 41) . Using the t r a n s i t i o n zone for the open stope p i l l a r s , one stable p i l l a r i s above the t r a n s i t i o n zone and f i v e stable case h i s t o r i e s are i n the t r a n s i t i o n zone. These case h i s t o r i e s suggest the t r a n s i t i o n zone could be located s l i g h t l y h i g h e r making the current p i l l a r s t a b i l i t y graph a b i t conservative f o r t h i s data. The square p i l l a r s can not be d i r e c t l y applied to the p i l l a r s t a b i l i t y graph. Several authors have noted that rectangular p i l l a r s are s i g n i f i c a n t l y stronger than square p i l l a r s (Wagner 1974; Salamon 1983; Kersten 1984; Stacey and Page 1986). To account f o r the difference during design, these authors have suggested the use of an e f f e c t i v e p i l l a r width: CLASSIFICATION OF SQUARE PILLARS 136 PILLAR NO. CLASSIFICATION W/H ESTIMATED PILLAR STRESS (MPA) REMARKS 1 B 0,80 28 Opening of Joint* 2 A 1.70 26 Joints tight 3 A 1.70 30 Minor spalling 4 B 1.2* 34 Spalling i n gneiss 5 B 1.00 34 Spalling i n M.S. Joints tight 6 B 1.30 35 Fractured M.S. Assoc. with joi n t i n g 7 C 1,20 55 Sever* spalling 8 C 0,96 55 Severe spalling 9 c 1,00 58 Severe spalling 10 c 1.50 58 Severe spalling 4 opening of Joints 11 c 0,50 58 Failed p i l l a r 12 c 1,26 53 Marked hangingvall deterioration 13 B 1,40 48 Bangingvall deterioration 14 c 1,60 58 Severe spalling 15 c 1,40 55 Severe spalling 16 c 0,76 50 Slabbing Assoc. vitb fault 17 A 1,40 37 ) 18 B 1.74 40 )Spalling Assoc. with structural 19 A 2,50 35 )features 20 C 0,6"0 48 ) 21 C 0,90 0,60 0,60 48 .Severe spalling Assoc. with 22 C 48 23 C 48 ^deterioration of hangingvall 24 B/C 1.32 55 H/W i n s t a b i l i t y + deformed boreholes 25 B 1.50 47 Spalling 26 B 1.67 48 Joints opening 27 A 1,60 35 Minor spalling i n footvall gneiss 28 A 2,00 35 Minor spalling 29 C 1,00 59 Severe spalling 30 C 1,00 59 Assoc. with bad hangingvall conditions 31 C 1,00 59 Severe spalling 32 C 1,00 59 Failed 33 B 0,80 54 Large p i l l a r 34 B/C 0,92 55 Assoc. with bad hangingvall consitions 35 B/C 1.20 54 Severe spalling 36 C 1,00 55 Severe spalling 37 B 0,92 55 SpalfTng and local slabbing 38 C 0,60 60 Failed 39 B/C 1.30 56 Spalling of gneiss overbreak 40 C 2,27 60 Severe spalling 41 C 1.2C 63 Severe spalling 42 B/C 1.50 63 Severe spelling 43 C 2,00 59 Severe spalling 44 B 1,20 56 Spalling Assoc. with Joint opening 45 B/C 1,40 63 Prominent spalling in gneiss and M.S. 46 B 1,80 53 Spalling 47 A 2,60 60 Minor spalling CLASSIFICATION OF LONG PILLARS (L»W) PILLAR NO. CLASSIFICATION W/H ESTIMATED PILLAR STRESS (MPa) REMARKS 1 A 1,00 25 V. minor spalling 2 A 1,50 29 V. minor spalling 3 A 1,25 40 Joints opening 4 B 0,43 35 Spalling 5 B 0,40 50 Spalling 6 A 0,90 28 Minor spalling in M.S. 7 A 1,00 45 Slight movement on hangingvall contact • 8 A 1.48 48 Minor spalling Assoc. with joints 9 A 1,30 50 No borehole deformation 10 A 1,20 47 Stable TABLE 12. Data used by Von Kimmelmann et a l . (1984) i n the development of a p i l l a r f a i l u r e c r i t e r i o n . 137 FIGURE 40. A plan view of room and p i l l a r mining at BCL Limited, showing the use of long p i l l a r s and square p i l l a r s (after Von Kimmelmann 1984). 138 son/avcn 139 W e f f = 4 * A C where: W eff = the e f f e c t i v e p i l l a r width, A = p i l l a r cross sectional area, C = p i l l a r circumference. The reasoning i s that for very long p i l l a r s (and open stope r i b p i l l a r s ) , a p i l l a r i s e f f e c t i v e l y exposed on only two walls and consequently stronger than square p i l l a r s , which are exposed on four walls. Using t h i s concept, square p i l l a r s have h a l f the e f f e c t i v e width of a long p i l l a r having the same p i l l a r height to width r a t i o . In figure 42, the square p i l l a r s at BCL Limited have been plotted on the p i l l a r s t a b i l i t y graph using t h e i r e f f e c t i v e p i l l a r width/ h e i g h t r a t i o ( i e . the a c t u a l width/height r a t i o ) . The adjusted square p i l l a r data agrees reasonably well with the o r i g i n a l t r a n s i t i o n zone on the p i l l a r s t a b i l i t y graph. Three stable square p i l l a r case h i s t o r i e s p l o t above the f a i l u r e l i n e on the t r a n s i t i o n zone, while a l l the y i e l d i n g and f a i l e d p i l l a r s p l o t above the t r a n s i t i o n area. The e f f e c t i v e width adjustment for square p i l l a r s on the p i l l a r s t a b i l i t y graph adequately explains the assessment for t h i s data. As with the long p i l l a r s , the adjusted square p i l l a r data suggests the t r a n s i t i o n zone could be located s l i g h t l y higher. However, t h i s inaccuracy i s on the conservative side f o r stable p i l l a r design. 6.3.3 Data from an Australian Open Stope Mine 140 IN O M son/avcn FIGURE 42. The square p i l l a r Kimmelmann et a l . (1984) i s using an e f f e c t i v e width i n data presented by Von plotted on the s t a b i l i t y graph the H/W r a t i o . 141 A t e s t open stoping block at Mt. Isa i s described i n depth by Brady (1977). The objective of the t r i a l mining block was to obtain information for r i b p i l l a r design and c a l i b r a t e a f a i l u r e c r i t e r i o n f o r the rock mass. Figure 43 shows the t e s t broken into f i v e stages. Stage 1 (problem No. 1) shows the development of two s l o t r a i s e s , and the S86 r a i s e to observe p i l l a r conditions. Stage 2 contains the opening of the S85 stope. Stage 3 shows the opening of S87 stope which creates the S86 p i l l a r . Stage 4 i s the expansion of the S87 stope, with the S86 p i l l a r remaining stable and i n t a c t . Stage 5 shows the robbing of the S86 p i l l a r which resulted i n f a i l u r e of the p i l l a r . Brady presented s u f f i c i e n t information that stages 3, 4 and 5 could be modelled with BITEM to determine the average p i l l a r load. The stope height:length r a t i o for a l l three cases i s greater than 3, so less than 20% error i s expected i n the average p i l l a r load determined by BITEM (the error i s estimated using figure 33, page 109). The modelling r e s u l t s were i n good agreement with a p r i n c i p a l stress contour diagram i n the o r i g i n a l paper. The rock mass, as described i n the paper by Brady, has s i m i l a r c h a r a c t e r i s t i c s and qu a l i t y to the t y p i c a l rock mass 142 192 0 7 0/B MICAF 610 1 10-0 -1920 Problem No. 1 k -26-2 . ; 1 -Boundary of S84 • pillar area 1 6 65 30-2 S85 slope Problem No. 2 -I 1 i < i SB7 Cut-off rais« (1 81 Dia.) , Boundary of S86 < \ J pillar area S86 raise _ J i | 15.1 '4-8 I — n n 0— r — - S 87 stopt Problem No 3 J •1920 26.2 10-0 Problem No 4 1 1 6-65 i _ •34-4 SBS 6-7 S 6 6 O 1 r 1 37-8 ! ses ; , 1 58b o i S87 r 1 420 sen Problem No. 5 Scole 10m FIGURE 43. The f i v e stages of the S86 p i l l a r i n an open stope p i l l a r t e s t at Mt. Isa ( a f t e r Brady 1977). 143 found i n the data base. The volume of the A u s t r a l i a p i l l a r s i s also s i m i l a r to that i n the data base. So, these two variables are not l i k e l y to have a s i g n i f i c a n t influence i n p l o t t i n g the data on the p i l l a r s t a b i l i t y graph. The three stages are plotted on a p i l l a r s t a b i l i t y graph i n figure 44. The S86 p i l l a r p l o t s i n the stable region for stages 3 and 4, and p l o t s i n the f a i l u r e zone a f t e r stage 5. This agrees very well with Brady's description of the p i l l a r during the t e s t . 6.3.4 Summary of A l l the Data A p l o t of the open stope data and a l l the data from l i t e r a t u r e i s given i n figure 45. The data from l i t e r a t u r e helps confirm the location of the t r a n s i t i o n area over a greater area. In the e n t i r e data base of 135 p i l l a r s , four stable case h i s t o r i e s are found above the t r a n s i t i o n zone and one sloughing p i l l a r i s found below the t r a n s i t i o n zone. Consequently, the s o l i d design l i n e s f o r the t r a n s i t i o n zone have been extended. The success of the p i l l a r s t a b i l i t y graph i n separating the d i f f e r e n t p i l l a r assessments supports the decision to discount the influence of p i l l a r volume and rock mass qu a l i t y as i n s i g n i f i c a n t i n hard rock p i l l a r design. 6.4 Comparison Against Other Design Methods A number of empirical design methods are frequently used for r i b p i l l a r s . However, none of these methods was based on open 144 son/avon FIGURE 4 4 . The t h i r d , fourth and f i f t h stages of the S86 open stope r i b p i l l a r , presented by Brady (1977), are shown on the p i l l a r s t a b i l i t y graph. The data agrees very well with the s t a b i l i t y graph. • CD • 145 CM son/avoT F I sSL 4rib !m P i lh r l a b i l i t y graph showing the open Hedlly M9?2J V o n a K ? t h e l i t e r a t ^ e data presented by tieaiey (1972), Von Kimmelmann (1984), and Brady (1977). 146 stope mining case h i s t o r i e s . The following comparison of the methods a g a i n s t the p i l l a r s t a b i l i t y graph, shows the a p p l i c a b i l i t y of the other methods to the design of open stope r i b p i l l a r s . Any negative evaluation should not be taken as a c r i t i c i s m of other methods, but rather i t serves to show the l i m i t a t i o n s of these methods when applied to the design of open stope r i b p i l l a r s . 6.4.1 Hedley's P i l l a r Strength Formula The p i l l a r strength formula developed by Hedley and Grant (1972) was based on data from room and p i l l a r mining at E l l i o t Lake and has been discussed i n Chapters 3.1.1.3 and 6.3.1. The formula i s defined as: Qu = k * wa / h b where: Qu = p i l l a r strength k = strength of 1 f t . cube (UCS 1 2) w = p i l l a r width (ft) h = p i l l a r height (ft) a = empirical constant = 0.5 b = empirical constant = 0.75 To get UCS 1 2, several authors have used a s c a l i n g factor from the compressive strength of a 2 inch diameter specimen (UCS 2): 147 u c s 1 2 0.7 * UCS 2 This r e l a t i o n s h i p has been found i n works by Hedley and Grant (1972), Hedley et a l . (1979), Hoek and Brown (1980), and Von Kimmelmann et a l . (1984). Hedley's formula i s a siz e e f f e c t formula, which means that i t accounts f o r the actual dimensions of a p i l l a r and not just the p i l l a r shape. To apply t h i s to open stope r i b p i l l a r s , the s i z e of t y p i c a l open stope r i b p i l l a r s must be determined. The range of r i b p i l l a r sizes seen i n 17 d i f f e r e n t Canadian open stope mines i s presented i n figure 46. The dimensions of permanent p i l l a r s are denoted by the symbol "P" and the dimensions of p i l l a r s i n mining methods using b a c k f i l l and temporary p i l l a r s are denoted by the symbol "B". The dashed l i n e s give the upper and lower bound of p i l l a r dimensions used i n the 17 Canadian open stope mines. For various p i l l a r width to p i l l a r height r a t i o s ( i e . p i l l a r s t r i k e length to orebody width r a t i o s ) , the minimum and maximum p i l l a r dimensions can be determined and applied to Hedley's s i z e e f f e c t formula. For a p p l i c a t i o n of t h e i r p i l l a r strength formula, Hedley and Grant suggest that p i l l a r s with a safety factor greater than 1.5 are stable and p i l l a r s with a safety factor near 1.0 are crushed. Rearrangement of the safety factor formula, S.F. Qu 0.7 * UCS 2 * w a c r p aP * h b H rt»0 O O 3* ct> o» c ft 3 0> W o> a fl) fD o> o> •3 fl) . 3 <D f t O (D H - n> f ) H 3 O r-< 0» Cft M (0 f t oi r ( B 0 3 (D •» TJ *0 Q> CD fl) < « 3* B O H * H * H * M> ft M 3 3* fl> fl> >1 f t f t • KT 3" 3* <t> fl) *0 w a> » M <o r t o» f t H r ) ~ fl) fl) f t O. f t 0> 03 i o> 3 * 10 O M » a T J H - fl) 3 0 M 3 3 M O D. W • f t (!) fl) 3 CO W O CD f t fl) • d ff> 3 H * 0) 0) 01 3 u. O o z - I ui or r-45 40 35 -30 -25 -20 -15 -10 -5 -PILLAR DIMENSIONS BASED ON 17 CANADIAN OPEN STOPE MINES B B B \ B B P P B B B B P P P B B \ B \ B B B B B k B \ B \ \ B = BACKFILLED —] 1 1 1— 20 40 OREBODY WIDTH (m) P = PERMANENT 60 149 permits p l o t t i n g of safety factor l i n e s for 1.0 and 1.5, for the maximum and minimum r i b p i l l a r sizes observed i n open stoping, against the data base (figure 47). The upper shaded zone shows the possible l o c a t i o n of open stope r i b p i l l a r s when designed with a safety factor of 1.0. The lower zone shows the possible l o c a t i o n of open stope r i b p i l l a r s when designed with a safety factor of 1.5. Size e f f e c t formulas assume that smaller p i l l a r s are stronger than large p i l l a r s . So, the upper l i n e of each zone corresponds to the minimum p i l l a r sizes seen i n Canadian open stope mines, while the lower l i n e of each zone corresponds to the maximum p i l l a r sizes seen i n Canadian open stope mines. The graph shows that, for open stope r i b p i l l a r design, Hedley's formula i s conservative r e l a t i v e to the p i l l a r s t a b i l i t y graph. In defense of Hedley's formula, i t was designed f o r much smaller p i l l a r s and i t i s le s s conservative when applied i n room and p i l l a r mining (due to the nature of the s i z e e f f e c t formula). Comparison of the p i l l a r s t a b i l i t y graph against Salamon's formula (Chapter 3.1.1.2) would give a s i m i l a r conclusion. Hedley and Salamon used the same method to determine the strength v a r i a b l e "K" and Salamon has very s i m i l a r values for the empirical constants (a=0.46 and b=0.66). Salamon's method i s a c t u a l l y a b i t more conservative than Hedley's formula because Salamon recommended the use of a safety factor of 1.6 to ensure stable design and used a p i l l a r height c o e f f i c i e n t of s o n / a v o n FIGURE 47. Comparison of the p i l l a r s t a b i l i t y graph and Hedley 1s formula for two safety factors. Hedley's formula i s a s i z e e f f e c t formula, so there i s a range of p i l l a r strength f o r each safety f a c t o r based on the s i z e of open stope r i b p i l l a r s observed i n 17 Canadian mines. b=0.66 compared to b=0.75 suggested by Hedley. 151 6.4.2 Hoek and Brown P i l l a r Strength Curves Hoek and Brown (1980) proposed a serie s of curves (figure 11, page 44) for the estimation of p i l l a r strength. These curves are discussed i n more depth i n Chapter 3.1.1.5. The curves were developed based on numerical modelling, rock mass f a i l u r e d i s t r i b u t i o n s inside p i l l a r s of d i f f e r e n t shapes, and for a range of rock mass q u a l i t i e s , using the f a i l u r e c r i t e r i a : °P = CT3 + ( m * aC * a3 + s * CTC2)!s where: ffp = average p i l l a r strength o~3 = minimum p r i n c i p l e stress a c = u n i a x i a l compressive strength of i n t a c t p i l l a r material m & s = empirical constants based on the rock mass qua l i t y . The m & s empirical constants have been rel a t e d to the NGI and CSIR rock mass c l a s s i f i c a t i o n s . Hoek and Brown proposed these p i l l a r design l i n e s assuming that a p i l l a r i s f a i l e d when the stress across the centre of the p i l l a r exceeds the strength of the rock mass. Each curve corresponds to a f a i l u r e l i n e f or a d i f f e r e n t rock mass qual i t y . 152 Since Hoek and Brown used input parameters s i m i l a r to those i n the p i l l a r s t a b i l i t y graph, i t was possible to reproduce some of t h e i r design curves on the design chart (see figure 48). The f i r s t observation i s that Hoek and Brown design l i n e f or good rock mass qu a l i t y (RMR « 60 - 80) corresponds reasonably well with the t r a n s i t i o n zone of the p i l l a r s t a b i l i t y graph. The majority of p i l l a r s i n the open stope r i b data base have a good rock mass qu a l i t y . However, Hoek and Brown suggest a safety factor of 1.5 for permanent mine p i l l a r s . While t h i s safety factor may be needed for the design of permanent p i l l a r s i n entry mining methods, use of t h i s safety factor would make Hoek and Brown curves quite conservative for open stope r i b p i l l a r design. Hoek and Brown suggest a very large influence of the rock mass q u a l i t y on p i l l a r strength. The design curve for a f a i r rock mass q u a l i t y i s well below the t r a n s i t i o n zone of the p i l l a r s t a b i l i t y graph and the design curve for a very good rock mass q u a l i t y i s f a r above the t r a n s i t i o n zone. There are very few p i l l a r case h i s t o r i e s with f a i r or very good rock mass q u a l i t i e s i n the data base, so the a p p l i c a b i l i t y of these curves for p i l l a r design can not be v e r i f i e d . A substantial number of case h i s t o r i e s of p i l l a r s i n f a i r and very good rock masses are needed before these two curves could be used confidently i n open stope r i b p i l l a r design. 6.4.3 P i l l a r Shape E f f e c t Formulas son/avoi FIGURE 48. Three of the Hoek and Brown (1980) p i l l a r strength curves plo t t e d on the p i l l a r s t a b i l i t y graph. The t r a n s i t i o n zone of the p i l l a r s t a b i l i t y graph and the good rock nass q u a l i t y curve are very close to each other. 154 There are several v a r i a t i o n s of the shape e f f e c t formula (see Chapter 3.1.1.1). Two of the most common va r i a t i o n s were developed by Obert and Duvall (1967) and Bieniawski (1983). Obert and Duvall (1967) presented a formula to account for the influence of p i l l a r shape. I t i s based on compressive t e s t i n g of coal specimen p i l l a r s of various shape by Obert et a l . (1946). The proposed re l a t i o n s h i p was: dp = a 1 * [A + B * (w / h)] where: CTp = p i l l a r strength, = u n i a x i a l strength of a cubical p i l l a r , w = p i l l a r width, h = p i l l a r height, A = empirical constant = 0.778 B = empirical constant = 0.222. The formula has been used by several authors ( l i s t e d i n Chapter 3.1.1.4) to account for the shape e f f e c t i n hard rock p i l l a r design. The formula assumes that the strength of a cubical p i l l a r (o~l) i s known. I f we assume the maximum cubical p i l l a r strength on the p i l l a r s t a b i l i t y graph i s found at the i n t e r s e c t i o n of w/h = 1 and the f a i l u r e l i n e (top of the t r a n s i t i o n zone) , the Obert and Duvall formula can be compared to the p i l l a r s t a b i l i t y graph and the data base. Figure 49 shows the Obert and Duvall formula plotted on the p i l l a r s t a b i l i t y graph. I t does not compare well with the p i l l a r data or the lo c a t i o n of the 155 son/avon FIGURE 49. Comparison between the p i l l a r s t a b i l i t y graph and the Obert and Duvall (1967) shape e f f e c t formula applied with a safety factor of 1.0. 156 t r a n s i t i o n zone. The Obert and Duvall formula assumes a much higher strength for slender p i l l a r s than that shown by the case h i s t o r i e s and the p i l l a r s t a b i l i t y graph t r a n s i t i o n zone. There are many f a i l e d and sloughing p i l l a r s below the f a i l u r e l i n e proposed by Obert and Duvall. This formula i s not applicable to the design of open stope r i b p i l l a r s . A major coal p i l l a r design study was c a r r i e d out by Bieniawski (1983) at Pennsylvania State University i n the la t e 1970's. One of the major r e s u l t s of the study was the development of a shape e f f e c t p i l l a r strength formula. Bieniawski used a formula s i m i l a r to that proposed by Obert and Duvall. Bieniawski's formula i s : (Tp = K * [ 0.64 + ( 0.36 * W )] H where: Op = the p i l l a r strength, K = UCS 1 2 = the compressive strength of 1 cubic foot of i n t a c t p i l l a r material, W = p i l l a r width, H = p i l l a r height. Assuming UCS 1 2 ~ °' 7 * UCS 2 (shown i n Chapter 6.4.1), a f a i l u r e l i n e can be plotted on the p i l l a r s t a b i l i t y graph. Bieniawski's formula i s plotted i n figure 50, f o r a safety f a c t o r of 1.0, 1.5 and 2.0. This formula does not compare well with the p i l l a r data or the t r a n s i t i o n zone. For each safety factor, there are many p i l l a r case h i s t o r i e s that can not be 157 son/avon FI?VoLf°* T h e s n a p e e f f e c t forumla proposed by Bieniawski (1983) applied with three d i f f e r e n t safety factors i s compared against the p i l l a r s t a b i l i t y graph. 158 explained by Bieniawski's formula. The conditions under which these formula were developed can explain t h e i r inadequacy for open stope r i b p i l l a r design. Both of the formulas i s more applicable f o r p i l l a r s with a width/height r a t i o of much greater than one. For p i l l a r s with a width/height r a t i o of l e s s than one, the shape e f f e c t formulas w i l l overestimate p i l l a r strength by large amounts. Generally, these formulas are not well suited to open stope r i b p i l l a r design. 6.5 Chapter Summary The variables that are s i g n i f i c a n t for open stope r i b p i l l a r design are: the p i l l a r width and p i l l a r height (defined according to figure 26, page 87), the compressive strength of the i n t a c t rock material and the load induced on the p i l l a r . The volume of a p i l l a r and the presence of geological d i s c o n t i n u i t i e s do not appear to be s i g n i f i c a n t f o r open stope r i b p i l l a r design, over the range observed for these variables i n Canadian open stope mines. A p i l l a r design chart has been developed based on open stope r i b p i l l a r s and v e r i f i e d and refined based on hard rock room and p i l l a r mining data found i n l i t e r a t u r e . The t o t a l data base consists of 135 p i l l a r case h i s t o r i e s . The p i l l a r s t a b i l i t y graph contains stable and f a i l e d design areas separated by a t r a n s i t i o n zone, which shows a v a r i e t y of p i l l a r behaviour. The 159 t r a n s i t i o n zone i s represented by a s o l i d l i n e where i t s l o c a t i o n i s well defined by data. The t r a n s i t i o n zone i s represented by dashed l i n e s where i t s exact l o c a t i o n i s not v e r i f i e d by the data. The compatibility of a number of e x i s t i n g open stope r i b p i l l a r design methods with the p i l l a r s t a b i l i t y graph and the complete p i l l a r data base was checked. Hedley's s i z e e f f e c t formula (1972) was found to be quite conservative f o r open stope r i b p i l l a r design. The Hoek and Brown (1980) p i l l a r strength curve for a good rock mass qu a l i t y agreed well with the p i l l a r s t a b i l i t y graph. However, the a p p l i c a b i l i t y of the strength curves f o r the other rock mass q u a l i t i e s could not be v e r i f i e d . The p i l l a r shape e f f e c t formulas proposed by Obert and Duvall (1967) and Bieniawski (1983) are not applicable to open stope r i b p i l l a r design. 160 CHAPTER 7 DESIGNING RIB PILLARS FOR OPEN STOPE MINING The design of r i b p i l l a r s depends on the duration of the support to be provided. Rib p i l l a r s may be designed to give permanent support to provide long-term s t a b i l i t y to open stopes, to provide regional s t a b i l i t y to the ore block and to protect access to the stopes. Conversely, r i b s may be designed to give temporary support to a mining block u n t i l stope support i s provided by b a c k f i l l . The p i l l a r i s then recovered. The decision to use permanent or temporary p i l l a r s i s l a r g e l y based on economics. In a r e l a t i v e l y low grade orebody, a permanent p i l l a r may be the most economical form of support because of the high costs associated with b a c k f i l l and p i l l a r recovery methods. In higher grade orebodies, temporary p i l l a r s are t y p i c a l l y used because the cost of b a c k f i l l i n g can be j u s t i f i e d and the maximum extraction of the orebody i s desired. This i s shown e x p l i c i t l y i n a comparison of the approximate value of ore per ton found i n Canadian open stope mines using permanent and temporary p i l l a r s (Table 13) . The average value per tonne i n the mines using temporary p i l l a r s and f i l l i s almost double that of the mines using permanent p i l l a r s . Because permanent and temporary p i l l a r s have d i f f e r e n t purposes, t h e i r designs can be quite d i f f e r e n t . The following chapter w i l l discuss the design of permanent and temporary 161 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 PERMANENT PILLARS APPROXIMATE VALUE OF ORE ($US/ton) RUTTAN $ 43 ALGOMA $ 25 HEATH STEELE $ 92 SELBAIE - ZONE A $ 47 MEAN $ 52 Table 13. 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 . The mine grades are from the 1987 Canadian Mines Handbook, and the pri c e of the metals i s from the January 1988 Engineering and Mining Journal (after Potvin et a l . 1988b). 162 p i l l a r s i n Canadian open stope mines and suggest some guidelines for using the p i l l a r s t a b i l i t y graph method. An example of the use of temporary p i l l a r s i s also given. 7.1 Permanent P i l l a r s The maximum possible orebody extraction around permanent p i l l a r s i s about 80%. Any remaining ore w i l l be l e f t i n place, so i d e a l l y , permanent p i l l a r s should be located i n low grade ore or waste. Oversize (conservative) p i l l a r dimensions are permissible under these conditions. However, the design of permanent p i l l a r s i n ore must be a compromise between conservative dimensions, to maintain the s t a b i l i t y of the mining blo c k f o r a long p e r i o d of time, and non-conservative dimensions, to minimize the loss of ore i n the p i l l a r . In a preliminary design, i t i s suggested that permanent p i l l a r s should p l o t below the t r a n s i t i o n zone, i n the stable area of the p i l l a r s t a b i l i t y graph. The distance below the t r a n s i t i o n zone should be a function of the degree of confidence i n the input data (especially the u n i a x i a l compressive strength of the rock and the induced stress) . The les s confident the input data, the further below the t r a n s i t i o n zone a p i l l a r should p l o t . Ultimately, the best design for permanent p i l l a r s i s optimised according to mining experience i n the l o c a l ground conditions. A good example of using l o c a l experience i n p i l l a r design i s documented by Pakalnis (1986) at Ruttan. The r i b 163 p i l l a r s gradually f a i l as the longitudinal stopes are opened to t h e i r planned l i m i t s . However) the p i l l a r s r e t a i n s u f f i c i e n t rock mass competency that they remain r e l a t i v e l y i n t a c t , without the use of b a c k f i l l , and continue to provide stope support and regional mine support. In most mines, fr a c t u r i n g due to p i l l a r f a i l u r e would combine with geological structure to cause severe p i l l a r sloughing and eventually complete p i l l a r d i s i n t e g r a t i o n . At Ruttan, sloughing of f a i l e d p i l l a r material i s not a problem, so the r i b p i l l a r s can be designed to gradually f a i l because they w i l l remain int a c t and s t i l l provide the necessary stope support. 7.2 Temporary P i l l a r s Temporary r i b p i l l a r s are used when i t i s intended to recover the e n t i r e orebody. This type of open stope mining involves the use of b a c k f i l l and the extraction of ore must be c a r e f u l l y sequenced. An optimum mining sequence gives a high rate of mining, while avoiding stope and p i l l a r i n s t a b i l i t y . One of the primary concerns for the design of temporary p i l l a r s i s the ease of recovery of the p i l l a r . Small p i l l a r s are more d i f f i c u l t and more expensive to recover. Figure 51 shows the range of temporary p i l l a r dimensions used i n 14 Canadian open stope mines. Generally, temporary r i b p i l l a r s are designed with a s t r i k e length of greater than 8-10 metres and l e s s than 25 metres. P i l l a r height ( i e . orebody width) varies from l e s s than 5 metres to 60 metres. 164 CD CD O to m m CD CD CD e 1 r-Q com a o CD U Of O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CN CD CD CD m to O I D C M O in FIGURE 51. The range of temporary r i b p i l l a r dimensions used i n 14 Canadian open stope mines. The maximum s t r i k e length ( p i l l a r width) i s about 25 metres, while the maximum orebody width ( p i l l a r height) i s about 60 metres. 165 The design of temporary p i l l a r s depends on whether the p i l l a r i s intended to be stable or to f a i l . Both approaches are used i n open stoping i n Canada, and there are d i f f e r e n t recommendations that can be made i n the design of each type of temporary p i l l a r . 7.2.1 Stable Temporary P i l l a r s The majority of temporary r i b p i l l a r s are designed to be stable. However, the mine operator's philosophy plays a large r o l e i n determining the s i z e of temporary r i b p i l l a r s . P i l l a r s may be designed larger than necessary, or t h e i r dimensions may be minimized. Use of oversize r i b p i l l a r s permits easier p i l l a r recovery. In addition, the s t a b i l i t y provided by the extra s i z e means that the primary stopes may not need immediate f i l l i n g , leaving some f l e x i b i l i t y i n the f i l l i n g cycle. However, minimizing temporary p i l l a r dimensions gives a higher primary mining volume and a quicker payback on c a p i t a l and development costs. Minimizing p i l l a r dimensions can become c o s t l y i f the p i l l a r s f a i l unexpectedly or i f the p i l l a r s are d i f f i c u l t to recover due to t h e i r small s i z e . The consequences of f a i l e d temporary p i l l a r s may include: - the loss of reserves, - a high mining cost, - the need for remedial s t a b i l i t y measures such as cable b o l t i n g , - regional i n s t a b i l i t y such as hanging wall and back caving, 166 - and a low rate mining. Cases of r i b p i l l a r i n s t a b i l i t y and recovery problems are documented by many authors including Falmagne (1986), Brady (1977) and Bray (1967). 7.2.2 F a i l e d Temporary P i l l a r s A r e l a t i v e l y new concept i n open stoping i s to design the r i b p i l l a r s to f a i l . The consequences of f a i l e d p i l l a r s described above can often be minimized i f f a i l u r e i s planned. The advantage i s that i n a high stress environment, the p i l l a r w i l l not become overstressed and w i l l be easier to recover. Designing r i b p i l l a r s to destress or f a i l has been documented at INCO's Frood mine (Grace and Taylor 1985) and Falconbridge•s Strathcona mine (Bharti 1987). To design a f a i l i n g p i l l a r with the p i l l a r s t a b i l i t y graph, i t i s suggested that a p i l l a r p l o t well above the t r a n s i t i o n area, have a low p i l l a r width to height r a t i o while having a p i l l a r width large enough to permit easy recover. Although there are no p i l l a r s designed to f a i l i n the data base, several p i l l a r case h i s t o r i e s that were discarded from the data base f i t the above design suggestions. There are a few q u a l i t a t i v e recommendations and comments to add to the design of f a i l i n g p i l l a r s : - i t i s very important to f i l l the surrounding stopes as quickly as possible. The f i l l w i l l provide l a t e r a l constraint on the p i l l a r walls and w i l l reduce sloughing of the fractured p i l l a r 167 material, - control b l a s t i n g should be used near the p i l l a r walls to minimize wall damage due to b l a s t v i b r a t i o n s , - development i n p i l l a r s w i l l l i k e l y need f u l l f r i c t i o n a r t i f i c i a l support such as cable bol t s and grouted rebar, as p i l l a r f r a c t u r i n g could s u b s t a n t i a l l y a f f e c t development s t a b i l i t y , - and d r i l l hole closure and displacement could cause severe problems f o r longhole (small diameter d r i l l hole) open stoping methods. Large diameter blastholes w i l l l i k e l y be needed for recovery of f a i l e d p i l l a r s . 7.3 Case Example: Transverse Rib P i l l a r s at Norita 7.3.1 Geology and Mining Method The Norita mine i s located i n the Mattagami mining d i s t r i c t i n north western Quebec. The geological s e t t i n g f o r the copper-zinc orebody i s shown i n Mine #19 i n Appendix I. More d e t a i l can be found i n papers by Bawden and Milne (1987) , Chauvin (1986), and Goodier and Dube (1984). In recent years, the mine has converted to a transverse blasthole open stoping method. This case h i s t o r y w i l l focus on the transverse p i l l a r s i n the open stoping between l e v e l s 9 and 11 of the orebody (figure 52). The mining block was divided into two l e v e l s with 17 stopes per l e v e l . The basic sequence of extraction for the mining block i s shown by the roman numbers on figure 52. Primary FIGURE 52. Isometric view of transverse blasthole open stoping at Norita. The basic sequence of stope extraction i s shown i n roman numbers. 169 stopes were extracted every fourth stope. Stopes were f i l l e d with a 30:1 r a t i o of m i l l t a i l i n g s and waste rock to cement. Temporary p i l l a r s (composed of three consecutive unmined stopes) are formed by the extraction of the primary stopes. S t a b i l i t y problems were not reported during the primary mining and the temporary p i l l a r s have been assessed as stable. The next phase i n the mining was to extract the middle (secondary) stope of the temporary p i l l a r s . The b l a s t i n g of the secondary stopes was done c a r e f u l l y using control b l a s t i n g methods. Explosives were decked with a maximum detonation per delay of 90 kilograms. Afte r the stopes were emptied, they were b a c k f i l l e d with a 30:1 r a t i o of m i l l t a i l i n g s and waste rock to cement. With the commencement of primary mining between l e v e l s 9 and 10 (stage IV) and t e r t i a r y stope mining between l e v e l s 10 and 11 (stage I I I ) , det e r i o r a t i o n of drawpoint p i l l a r s on l e v e l 10 necessitated frequent r e h a b i l i t a t i o n . Mining of the t e r t i a r y stopes encountered heavy b l a s t overbreak (3.3 metre p u l l on 2 metre rounds) . The ore was described as badly broken and fractured. This damage was induced by mining since the ground was c l a s s i f i e d as very good (Q « 40 and RMR « 75) before mining had started. With continued mining between l e v e l s 9 and 11 (stages I I I , IV, and V) , development d r i f t s i n the 8-8 s i l l p i l l a r ( d i r e c t l y above l e v e l 9) deteriorated due to stress shedding from the transverse mining area. This was confirmed by s t r e s s c e l l s i n s t a l l e d near the t r a n s v e r s e p i l l a r s . 170 Extensometer monitoring of the 8-8 s i l l p i l l a r showed that the de t e r i o r a t i o n was d i r e c t l y related to mining events i n the t r a n s v e r s e mining block. Based on these observations (documented by Bawden and Milne 1987), the t e r t i a r y p i l l a r s i n the transverse mining area were assumed to have f a i l e d . 7.3.2 Back Analysis Using the P i l l a r S t a b i l i t y Graph Back analysis w i l l focus on representative p i l l a r s i n the mining block. A f t e r the primary mining between l e v e l s 10 and 11 was completed, stopes 10-5 and 10-9 had been extracted leaving a stable temporary p i l l a r made of stopes 10-6, 10-7, and 10-8 (see figure 53). The p i l l a r dimensions were: 55-60 metres i n (stope) height, 33 metres i n ( p i l l a r ) width and 23 metres i n ( p i l l a r ) height (according to the convention i n figure 26, page 87). The average load was estimated by two dimensional plane s t r a i n modelling (BITEM) at 75 MPa (case 43 from Table 8, page 105). The p i l l a r p l o t s well inside the stable zone of the p i l l a r s t a b i l i t y graph (figure 54). During secondary mining stope 10-7 was extracted leaving the t e r t i a r y p i l l a r s 10-6 and 10-8 (figure 53) , which were given a f a i l e d assessment. The p i l l a r dimensions were: 55-60 metres (stope) height, 11 metres i n ( p i l l a r width) and 23 metres i n ( p i l l a r ) height. The t h e o r e t i c a l average p i l l a r load on the 10-8 p i l l a r was estimated at 99 MPa (case 42 from Table 8, page 165) . This i s a t h e o r e t i c a l average p i l l a r load because i n p r a c t i c e the p i l l a r has f a i l e d and destressed and therefore w i l l FIGURE 53. A longitudinal section of the blasthole open s t o p i n g block at Norita showing the p i l l a r case h i s t o r i e s (10-6, 10-7, and 10-8) used i n t h i s case hist o r y analysis (after Goodier and Dube 1984). 172 S O n / Q V O T F I o ? ^ f 4 \ K ? 6 P 4 l a r s t a b i l i t y graph showing the l o c a t i o n 173 have a much lower actual load (see Chapter 5.5.1 for a more complete discussion of t h i s assumption). The p i l l a r p l o t s above the t r a n s i t i o n zone i n the f a i l e d area (see figure 54) . This agrees very well with the f a i l e d assessment f o r the t e r t i a r y stopes. 7.3.3 Comments Concerning the P i l l a r Design This y i e l d i n g p i l l a r case hi s t o r y i l l u s t r a t e s the use of f a i l e d p i l l a r s i n open stope mining. There are several comments and observations to make that are a consequence of the p i l l a r design: 1 - Cable b o l t i n g of the t e r t i a r y stope backs was necessary, due to severe cracking and j o i n t opening. 2 - Heavy overbreak during the p i l l a r ( t e r t i a r y stope) mining was encountered. 3 - Blastholes (6h inch diameter) were used for the entire mining block and were necessary to avoid the loss of d r i l l holes due to crushing and f r a c t u r i n g during the t e r t i a r y p i l l a r recovery. 4 - The stopes were f i l l e d quickly with waste rock and cemented m i l l t a i l i n g s . 5 - The mining of the f a i l e d p i l l a r s was generally successful. 174 CHAPTER 8 SUMMARY AND CONCLUSIONS a.i summary The purpose of t h i s study i s to investigate the s t a b i l i t y of r i b p i l l a r s i n open stope mining and develop guidelines for the optimization of r i b p i l l a r dimensions. This i s accomplished through four major steps: - d e s c r i p t i o n of the f a i l u r e mechanism i n open stope r i b p i l l a r s , - i n v e s t i g a t i o n of the methods currently used i n open stope r i b p i l l a r design, - q u a n t i f i c a t i o n of the s i g n i f i c a n t design variables, - and formulation and v e r i f i c a t i o n of a new method based on open stope r i b p i l l a r data and case h i s t o r i e s . 8.1.1 Open Stope Rib P i l l a r F a i l u r e There are two basic types of f a i l u r e i n hard rock p i l l a r s . Progressive f a i l u r e r e f e r s to gradual d e t e r i o r a t i o n of a p i l l a r i n a slow, non-violent manner. Bursting f a i l u r e i s character-ized by the v i o l e n t release of energy causing instantaneous fracture of rock. This thesis only investigates progressive f a i l u r e . Open stope r i b p i l l a r i n s t a b i l i t y i s a progressive mechanism. P i l l a r f a i l u r e i s defined as the point at which progressive f a i l u r e causes a p i l l a r to s t a r t l o s i n g i t s load 175 bearing capacity. The decrease i n load bearing capacity i s l a r g e l y due to f r a c t u r i n g of the rock mass i n the p i l l a r . Several signs of increasing p i l l a r i n s t a b i l i t y have been i d e n t i f i e d , including: - cracking and s p a l l i n g of rock i n p i l l a r development, - audible noise heard i n the p i l l a r s or microseismic events detected with monitoring systems, - deformed or plugged d r i l l holes, - overdraw from stopes consisting of unblasted, oversize ore, - stress r e d i s t r i b u t i o n from p i l l a r s a f f e c t i n g nearby p i l l a r s or development, - hourglassing and cracking of p i l l a r s , - and d i s p l a c e m e n t s or changes i n s t r e s s shown by instrumentation. 8.1.2 Current P i l l a r Design Methods Design methods used for open stope r i b p i l l a r s were based on empirical p i l l a r design studies or the use of numerical modelling and empirical f a i l u r e c r i t e r i o n . Empirical p i l l a r design methods were developed based on laboratory t e s t i n g and/or i n v e s t i g a t i o n of actual mine p i l l a r s . These methods were developed for s p e c i f i c mining conditions and are not necessarily applicable f o r open stope r i b p i l l a r design. Numerical methods b a s i c a l l y assume e l a s t i c and/or p l a s t i c rock mass behaviour to determine stress r e d i s t r i b u t i o n and rock mass displacement around underground excavations. Empirical f a i l u r e c r i t e r i o n are 176 applied to the stress or displacement r e s u l t s to determine rock mass f a i l u r e . However, i t i s d i f f i c u l t to v e r i f y an i n s i t u rock mass f a i l u r e c r i t e r i o n . Consequently, numerical design methods need extensive s i t e c a l i b r a t i o n before they can be used e f f e c t i v e l y to design r i b p i l l a r s i n open stope mining. The design methodology chosen for t h i s t h e s i s i s a combination of numerical and empirical methods. Numerical techniques are used to determine p i l l a r load, while p i l l a r f a i l u r e i s determined from empirical back analysis of open stope r i b p i l l a r case h i s t o r i e s . 8.1.3 I d e n t i f i c a t i o n and Quantification of the Design Variables Based on the data and case h i s t o r i e s c o l l e c t e d i n the Integrated Mine Design Project, the factors that are s i g n i f i c a n t for open stope r i b p i l l a r design are: - the compressive strength of i n t a c t p i l l a r material (UCS), - the average p i l l a r stress (determined with boundary element numerical modelling), - the p i l l a r height, - and the p i l l a r width. Three factors were discounted as i n s i g n i f i c a n t i n r i b p i l l a r f a i l u r e : the presence of minor geological d i s c o n t i n u i t i e s (such as j o i n t s ) , the e f f e c t of p i l l a r volume, and the e f f e c t of b a c k f i l l . The open stope r i b p i l l a r data and case h i s t o r i e s did not prove these factors as being important i n p i l l a r f a i l u r e . The background information for a l l the p i l l a r s i n the data base 177 i s presented i n Table 5 (page 70) and the geological settings of a l l of the p i l l a r case h i s t o r i e s are shown i n oblique orebody diagrams i n Appendix I. Three of the four design variables are quite easy to quantify. The UCS can be determined by laboratory t e s t i n g of i n t a c t rock samples or estimated with the point load t e s t . The p i l l a r height and p i l l a r width are measured from mine plans. The most d i f f i c u l t factor to quantify i s the average p i l l a r s t r e s s . A method to determine average p i l l a r stress i s proposed i n Chapter 5. The two dimensional boundary element code BITEM and the pseudo-three dimensional displacement d i s c o n t i n u i t y boundary element model "MINTAB" have been used to estimate the p i l l a r load for a l l the p i l l a r s i n the data base. However, these methods have l i m i t a t i o n s when modelling some p i l l a r geometries. The major geometrical l i m i t a t i o n s associated with two dimensional (2D) and displacement d i s c o n t i n u i t y (DD) numerical modelling have been i d e n t i f i e d . In addition, a rough error associated with these l i m i t a t i o n s i s given i n figure 33, page 109 (for 2D modelling), and i n figure 34, page 112 (for DD modelling). These error estimates are based on a comparison of the 2D and DD models to 12 runs of the three dimensional boundary element code "BEAP". 8.1.4 Development of the P i l l a r S t a b i l i t y Graph The open stope r i b p i l l a r data c o l l e c t e d has been empir-i c a l l y analyzed and a p i l l a r design graph has been developed 178 (figure 36, page 125) . The design chart has been c a l l e d the " P i l l a r S t a b i l i t y Graph". I t contains stable and f a i l e d design areas separated by a t r a n s i t i o n zone. The p i l l a r s t a b i l i t y graph has been v e r i f i e d and refined based on more than 80 hard rock room and p i l l a r case h i s t o r i e s from l i t e r a t u r e . The complete data base of about 135 p i l l a r s i s shown i n figure 45 (page 145). The design chart explains the s t a b i l i t y condition of the data base case h i s t o r i e s very well and i s quite s e n s i t i v e i n p r e d i c t i n g p i l l a r f a i l u r e . Empirical design methods used for open stope r i b p i l l a r design have been compared to the complete p i l l a r data base and the p i l l a r s t a b i l i t y graph. The good rock mass q u a l i t y design l i n e of the p i l l a r strength curves proposed by Hoek and Brown (1980) agrees quite well with the data base and p i l l a r s t a b i l i t y graph. However, the Hedley and Grant (1972) s i z e e f f e c t p i l l a r strength formula and the shape e f f e c t p i l l a r strength formula's by Obert and Duvall (1967) and Bieniawski (1983) do not compare well with the p i l l a r data or the p i l l a r s t a b i l i t y graph. Open stope r i b p i l l a r s may be designed to be permanent and s t a b l e , temporary and stable, or temporary and f a i l i n g . Guidelines have been suggested for the design of each type of r i b p i l l a r using the p i l l a r s t a b i l i t y graph. A case history discussing the use of stable and f a i l e d temporary r i b p i l l a r s i s also presented. 179 8.2 Conclusions 8.2.1 A p p l i c a b i l i t y of the Method The p i l l a r s t a b i l i t y graph uses factors that are r e l a t i v e l y easy to quantify data to predict the s t a b i l i t y of open stope r i b p i l l a r s . The method i s most e f f e c t i v e when rough predictions of s t a b i l i t y are required. Minor problems such as l o c a l f r a c t u r i n g w i l l not be predicted, but gross changes i n p i l l a r s t a b i l i t y are recognized. The method i s designed to predict f a i l u r e of open stope r i b p i l l a r s , but can be applied to some other types of p i l l a r s . I t should be applicable for the design of open stope s i l l p i l l a r s , and r i b and s i l l p i l l a r s i n non-entry methods such as V e r t i c a l Crater Retreat. The mechanism of p i l l a r f a i l u r e for these types of p i l l a r s i s the same as the mechanism of f a i l u r e i n open stope r i b p i l l a r s . This design method has not been developed or confirmed for p i l l a r s i n entry methods such as shrinkage and room and p i l l a r mining. The p i l l a r s t a b i l i t y graph would l i k e l y need the development of a safety factor before i t could be applied to p i l l a r design i n entry mining methods. 8.2.2 Limitations of the Method An empirical design method i s more r e l i a b l e when applied to conditions s i m i l a r to those found i n the o r i g i n a l work. Consequently, the following l i m i t a t i o n s are suggested f o r the p i l l a r s t a b i l i t y graph: 180 70 MPa < UCS < 316 MPa, 9 metres < Wp < 45 metres, 60 < RMR < 78, (Average P i l l a r Load / UCS) < 0.5. where, UCS = the i n t a c t rock u n i a x i a l compressive strength, Wp = the p i l l a r width, RMR = a measure of the rock mass competency using the CSIR rock mass c l a s s i f i c a t i o n , Average P i l l a r Load i s determined using two dimensional or displacement dis c o n t i n u i t y boundary element numerical modelling. The p i l l a r s t a b i l i t y graph method may work s a t i s f a c t o r i l y outside these l i m i t a t i o n s , but the current open stope data base generally does not extend outside these l i m i t s . F i n a l l y , i t should be kept i n perspective that t h i s i s a preliminary design method. The assumptions and p o t e n t i a l error associated with the variables and design chart l i m i t the usefulness of the p i l l a r s t a b i l i t y graph for f i n a l design. 8.2.3 Design of Open Stope Rib P i l l a r s The design of open stope r i b p i l l a r s i s dependent upon the ro l e of that p i l l a r i n the s t a b i l i t y of the mine. Rib p i l l a r s may be designed to be give permanent support to open stopes, or they may be designed to give temporary stope support u n t i l b a c k f i l l i s i n place. This decision i s l a r g e l y one of 181 economics. Low grade orebodies cannot be mined using b a c k f i l l and p i l l a r recovery methods due to the higher mining cost. Medium and high grade mines can a f f o r d the cost of b a c k f i l l and p i l l a r recovery, so temporary p i l l a r s can be designed. In some instances, temporary p i l l a r s have been designed to f a i l to avoid stress b u i l d up. There are a few consequences of designing p i l l a r s to f a i l , including: - the need f o r quick b a c k f i l l i n g a f t e r the stope i s extracted, - the use of a r t i f i c i a l support i n p i l l a r development, - and the use of large diameter d r i l l holes and control b l a s t i n g p ractices. 8.3 Future Work There i s a l i m i t to the value of c o l l e c t i n g further general p i l l a r case h i s t o r i e s to r e f i n e the p i l l a r s t a b i l i t y graph. More cases of open stope p i l l a r s are not l i k e l y to s i g n i f i c a n t l y improve the accuracy of the e x i s t i n g graph or reduce the s i z e of the t r a n s i t i o n area. This i s not to say that p i l l a r design at s p e c i f i c s i t e s can not be aided by case h i s t o r i e s from that s i t e or from s i m i l a r ground conditions. Past experience i s the best way to r e f i n e p i l l a r design methods to l o c a l conditions. The understanding of one of the possible design factors may be improved by c o l l e c t i n g s p e c i f i c case h i s t o r i e s . The influence of rock mass c h a r a c t e r i s t i c s was not found to be s i g n i f i c a n t (Chapter 6.1.3.2), but varied over only a small range of rock mass q u a l i t i e s . Analysis of p i l l a r case h i s t o r i e s 182 i n f a i r or very good q u a l i t y rock masses may show that the qu a l i t y of the rock mass i s s i g n i f i c a n t i n open stope r i b p i l l a r design. I f t h i s can be proven, a correction factor to the ex i s t i n g p i l l a r s t a b i l i t y graph could be developed to account for the e f f e c t of rock mass qual i t y . Assessment of the p i l l a r s i n the data base was sometimes d i f f i c u l t , and a substantial amount of data could not be applied because a r e l i a b l e assessment could not be determined. A more de t a i l e d i n v e s t i g a t i o n into p i l l a r f a i l u r e mechanisms and i n s i t u rock mass f r a c t u r i n g could improve p i l l a r design methods. A better d e f i n i t i o n of f a i l u r e can be developed through systematic i n s i t u p i l l a r monitoring using v i s u a l techniques (as shown by Krauland and Soder 1987) or through the use of instrumentation such as stressmeters (as shown by Agapito 1974), extensometers (as shown by A l l c o t t and Archibald 1981) or microseismics. The use of microseismic systems f o r i n s i t u m onitoring shows great p o t e n t i a l through quantifying the decrease of rock mass qu a l i t y due to rock f r a c t u r i n g , and monitoring the changes i n the load bearing condition of p i l l a r s . Both of these topics can be investigated with the microseismic technology currently available. 183 REFERENCES Agapito, J.F.T. 1974. Rock mechanics applications to the design of o i l shape p i l l a r s . 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London: McGraw-Hill. 190 APPENDIX I S p e c i f i c information about the geological s e t t i n g of each case h i s t o r y can be found i n the isometric sketch corresponding to the mine number. Each geological s e t t i n g i s comprised of: - the underground stress regime, - the hanging wall, footwall and orebody material properties and c h a r a c t e r i s t i c s including (when a v a i l a b l e ) : - rock type, - i n t a c t u n i a x i a l compressive strength, - e l a s t i c modulus, - poisson's r a t i o , - NGI rock mass c l a s s i f i c a t i o n , - stereonet of the major j o i n t sets, - the orebody shape and siz e , - and the mining methods used i n various parts of the orebody. Mine #22 does not have an isometric orebody sketch due to the complexity of the orebody and the v a r i a b i l i t y of the material properties and stress f i e l d . MINE No. 2 ORE (LENS 2 * 3 ) Rock Type: 1 = °c = E = V = Q' = Massive Sulphide 4.2 t/m3 200 MPa 61.0 GPa 0.3 HANGING WALL t, ROOF (LENS 2) Rock Type: Andes i t e y E v Q" o»=ifh om=2.3yt\ 70m 01,2=2. 2th 2.9 t/m3 109 MPa 63.0 GPa 0.25 4 LENS 2 -H5m LONGITUDINAL OPEN STOPE A* 0 0* HANGING WALL t ROOF (LENS 3) Rock Type: A l t e r e d A n d e s i t e Y = 3.0 t/m3 o c = 87 MPa E - 84.0 GPa v = 0.28 192 MINE No. 6 ORE Rock Type: Breccia 4 Massive Sulphide T • 2 e : V • Q' -3.1 t/m3 125 MPa 94.0 GPa 0.22 9 WORTH WALL Rock Type: Norite T -*: V • Q' • 2.9 t/m3 113 MPa S6.0 GPa 0.17 9 SOOTH WALL T V 2.7 t/m3 184 MPa 73.0 GPa 0.23 25 ISOm Rock Type: Granite 274 m Depth 1050 m MINE No. 8 N MINE No. 11 MINED OUT (No Backfill) 200m r MINED OUT ! T (No Backfill) PERMANENT PILLAR (No Grodo) 71 LONGITUDINAL LONGH<SLE STOPE • 30m-H 62m LONGITUDINAL LONGHO STOPE OOm / / LONGITUDINAL LONGHOLE STOPE 4* -33m — 2O0m -62m _Dtplh 925m ORE Rock Type: Porphyry 7 - 2.72 t/«3 o, - 148 MPa Z » 18.S GPa v • 0.20 Q* - 30 0,'1.15-rh ' » e«»1.5Yh o.a-1.7th MINE No. 16 ORB  Rock Typei Kaaalva Sulphlda Surfoca y -°c -8 • v • 0* -4.6 t/«' 176 MPa 119.0 CP* 0.24 20 HANGING HALL Book Type• Quarta Porphyry y - 2.9 t/aj1 o c - 91 MPa B - 68.7 GPa v - 0.19 0' - 42 080m FOOT WALL Rook Typai Chlorlta Tuff Y - 2.9 t/m1 o e - 84 MPa E - 68.5 GPa v - 0.2S 0 ' - 40 MINE No. 17 870m LONGITUDINAL LONOHOLE OPEN STOPING -1600m-ORg WALL  Rock Typai Maaelva Sulphide Rock Typei Cnalaa y - S.3 t/«* y - 2.7 t/m1 o t - 100 MPa ot - 52 MPa E - 103 CPa E - 105 GPa v - 0.31 v - 0.20 0' - 19 Q" - 18 o,-th 2.6th* foraula by Berget MINE No. 19 o s - » h 1 30m MINED OUT a BACKFILLED TO SURFACE •MI-3-3YI» 420m 70m LONOITUDINAL SUB-LEVEL RETREAT 30m • 180m • LONOITUDINAL SUB-LEVEL RETREAT 2-18 m 110m ORB Rock Typoi Maaalva Bulphlda Oapih 780m WORTH WALL (10») o, - 316 MP* E - 232.2 GPa v - 0.16 0' - 44 N Rock Typos Baaaltlo Tuff o c - 11B MPa B - 95.0 GPa v - 0.26 0* - 4.0 N SOUTH WALL ISO*) Rook Typai Rhyolltio Tuff o c - 98 MPa B - 67.9 GPa v - 0.15 0 * -MINE No. 21 199 TYPICAL MINE CROSS SECTION LONGHOLE tc BLASTHOLE LONGITUDINAL OPEN STOPING ORE  Rock Type: Massive Sulphide 0*c = 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 V = 0.12-0.34 Q' = 0.1-50 = 2.5 0"v MINE No. 23 200 Rock Type: Massive Sulphide UCS =310 MPa Q' = 20 FOOTWALL & HANGING WALL Rock Type: Argy1ite UCS =75 MPa Q' = 0.6 MINE No. 30 ORE Rock Type: Massive Sulphide Y = C c = E = V = Q' = 3.3 t / m ' 160 MPa 80 GPa 0.21 22 TYPICAL MINE CROSS SECTION TRANSVERSE BLASTHOLE OPEN STOPING 1500m HANGING WALL Rock Y = 0"c = E = V = Q' = Type: Rhyolite 2.7 t / m s 120-150 MPa 80 GPa 0.14 13-30 FOOTWAa Rock Type: Andesite/Diorite (TV=YH 0\ = 6+O.055H(m) Y E V Q' 3.0 t / m ' 160 MPa 85 GPa 0.23 14 0"j = 0.80", 2 0 2 MINE No. 31 

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