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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 E M P I R I C A L R I B P I L L A R DESIGN  CRITERION  FOR OPEN STOPE MINING By MARTIN RAYMOND HUDYMA B.A.Sc,  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 P A R T I A L FULFILLMENT OF THE REQUIREMENTS  FOR THE DEGREE OF  MASTER OF A P P L I E D  SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MINING AND MINERAL PROCESS We a c c e p t t h i s t h e s i s a s to the  required  conforming  standard  THE UNIVERSITY OF B R I T I S H September  ENGINEERING  COLUMBIA  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 many  design  empirical  verified in  the  rib  with  The  methods,  "pillar  of  determined  the by  and p i l l a r  intact  none  of  has  the  This thesis to  been  done  using  has  been  methods uses data  develop  open, s t o p e m i n i n g .  collected  an  empirical  The m e t h o d  is  graph".  in  the  method  material,  modelling,  The g r a p h has  been  histories  are: the  the  the  average  pillar  pillar  width  r e f i n e d w i t h the of hard  compressive load  and  use  of  rock p i l l a r s  the more  i n room  mining.  to  examine  in  open  s t a b i l i t y g r a p h and t h e p i l l a r  the  stope  rib  strength  useful  under but  pillar  conditions  formulas  and B i e n i a w s k i  (1983)  Guidelines, the  for  by H e d l e y are not  using  temporary  open s t o p e r i b  design.  The  the  design  investigation  open  pillars.  stope  design  (1972),  Obert  of  found  (1980)  open  may be  stope  and D u v a l l  the  rib  (1967)  applicable.  pillar of  the  used  commonly u s e d  c u r v e s d e v e l o p e d b y Hoek a n d Brown  some  for  data base are  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  pillar  stable  for  pillar  case  pillars  Design Study"  numerical  The p i l l a r  proposed  Mine  stability  literature  pillars  but  variables  height.  80  rib  a design survey.  design  strength  stope  d e s i g n method  c a l l e d the  pillar  open  "Integrated  pillar  than  of  stability  permanent rib  open  pillars,  and  graph stope  method, rib  failing  are  pillars, temporary  iii TABLE OF CONTENTS PAGE ABSTRACT  i i  L I S T OF TABLES  v i i  L I S T OF FIGURES  viii  ACKNOWLEDGEMENT  xiii  CHAPTER 1:  INTRODUCTION  1.1  Contents  1.2  Open S t o p e M i n i n g 1 . 2 . 1 D e f i n i t i o n o f Open S t o p i n g 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 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  2 3 4  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  1.3  of the  1 Thesis  CHAPTER 2 : R I B P I L L A R F A I L U R E 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 2 . 1 . 1 Rock F r a c t u r i n g 2.1.2 P i l l a r Load-Deformation Curve 2 . 1 . 3 Loss o f Load B e a r i n g C a p a c i t y 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 Stability 2 . 2 . 1 I n t a c t Rock S t r e n g t h 2 . 2 . 2 P i l l a r Load 2 . 2 . 3 P i l l a r Shape and C o n f i n e m e n t 2.2.4 Structural Features i n P i l l a r s 2 . 2 . 5 E f f e c t o f P i l l a r Volume 2.2.6 Effect of B a c k f i l l 2.2.7 Effect of Blasting  2 . 3 Chapter  Summary  CHAPTER 3 : REVIEW OF P I L L A R DESIGN METHODS 3.1 E m p i r i c a l D e s i g n Methods 3.1.1 P i l l a r Strength Determination 3 . 1 . 1 . 1 E m p i r i c a l Strength Formulas 3 . 1 . 1 . 2 Salamon's Formula  1  5  11 11 14 17 19 23 23 23 24 25 26 27 30 31 32 32 34 35 38  iv 3.1.1.3 3.1.1.4 3.1.1.5 3.1.2 P i l l a r 3.1.2.1 3.1.2.2 3.1.3 Safety 3.2  H e d l e y ' s Formula O b e r t a n d D u v a l l Shape E f f e c t F o r m u l a . Hoek a n d Brown P i l l a r S t r e n g t h C u r v e s . Load T r i b u t a r y Area Theory Numerical Modelling Factor  . .  N u m e r i c a l D e s i g n Methods 3 . 2 . 1 Types o f N u m e r i c a l Methods 3 . 2 . 2 I n t e r p r e t a t i o n o f Boundary Element R e s u l t s in Mining 3.2.2.1 Post-Processing Failure C r i t e r i o n . . . . 3.2.2.2 Interactive Failure Criterion 3 . 2 . 2 . 3 P r i n c i p a l S t r e s s Magnitude 3.2.3 L i m i t a t i o n s o f Boundary Element M o d e l l i n g . . . 3 . 2 . 3 . 1 M o d e l l i n g a Rock Mass 3 . 2 . 3 . 2 Computational Assumptions  CHAPTER 4 : OPEN STOPE R I B P I L L A R DATA BASE  40 41 43 45 45 51 51 53 53 57 57 60 63 63 63 66 68  4 . 1 G e n e r a l Data Base I n f o r m a t i o n  68  4.2  Background Data  69  4.3  P i l l a r Assessment  73  CHAPTER 5 : BOUNDARY ELEMENT METHODS I N R I B P I L L A R DESIGN.  .  78  5.1  Boundary Element Codes Used 5 . 1 . 1 BITEM 5 . 1 . 2 MINTAB 5 . 1 . 3 BEAP  79 79 81 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 5 . 2 . 1 D e f i n i n g t h e Open S t o p e G e o m e t r y 5.2.2 D e f i n i n g the Average P i l l a r S t r e s s  84 86 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 5.3.1 Plane S t r a i n S o l u t i o n 5 . 3 . 2 C o m p a r i s o n o f 2D a n d 3D N u m e r i c a l M o d e l l i n g Results  91 92  5.4  5.5  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 Geometries 5 . 4 . 1 Seam T h i c k n e s s L i m i t a t i o n s 5.4.2 Comparison of Displacement D i s c o n t i n u i t y a n d 3D N u m e r i c a l M o d e l l i n g Pillar  Load C a l c u l a t i o n s f o r the  Open  Stope  93 97 97 99  V  Data Base 5.5.1 Assumptions 5.5.2 P i l l a r Load R e s u l t s 5.5.3 Numerical Model Comparison U s i n g the Histories 5.6  102 103 103  Case  107  C h a p t e r Summary  CHAPTER 6 :  110  DEVELOPMENT OF A P I L L A R DESIGN METHOD  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 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 6.1.2 Design V a r i a b l e s 6.1.3 Discounted Variables 6 . 1 . 3 . 1 P i l l a r Volume 6.1.3.2 Structural Discontinuities  6.2  Pillar 6.2.1 6.2.2 6.2.3 6.2.4  6.3  Data from L i t e r a t u r e 6 . 3 . 1 D a t a f r o m C a n a d i a n Room a n d P i l l a r M i n i n g . 6 . 3 . 2 D a t a f r o m a B o t s w a n a Room a n d P i l l a r M i n e . 6 . 3 . 3 D a t a f r o m an A u s t r a l i a n Open S t o p e M i n e . . 6 . 3 . 4 Summary o f A l l t h e D a t a  114 .  .  115 115 117 118 119 120  S t a b i l i t y Graph G r a p h i c a l Data A n a l y s i s I n f l u e n c e o f P i l l a r Load A p p r o x i m a t i o n s . . . . Importance 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 . L i m i t a t i o n s of the P i l l a r S t a b i l i t y Graph. . .  122 122 126 128 130  . . .  . . .  131 131 134 139 143  6.4  Comparison A g a i n s t Other D e s i g n Methods 6.4.1 H e d l e y ' s P i l l a r S t r e n g t h Formula 6 . 4 . 2 Hoek a n d Brown P i l l a r S t r e n g t h C u r v e s 6 . 4 . 3 P i l l a r Shape E f f e c t F o r m u l a s  143 146 151 152  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 M I N I N G .  .  .  160  7.1  Permanent P i l l a r s  162  7.2  Temporary P i l l a r s 7 . 2 . 1 S t a b l e Temporary 7 . 2 . 2 F a i l e d Temporary  163 165 166  7.3  Pillars Pillars  Case Example: 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 . 7 . 3 . 1 G e o l o g y and M i n i n g M e t h o d 7 . 3 . 2 Back A n a l y s i s U s i n g the P i l l a r S t a b i l i t y Graph 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  .  .  167 167 170 173  vi CHAPTER 8: SUMMARY AND CONCLUSIONS  174  8.1 Summary 8.1.1 Open Stope R i b P i l l a r F a i l u r e 8.1.2 C u r r e n t P i l l a r Design Methods 8.1.3 I d e n t i f i c a t i o n and Q u a n t i f i c a t i o n o f t h e Design V a r a i b l e s 8.1.4 Development o f t h e P i l l a r S t a b i l i t y Graph. . .  174 174 175  8.2 C o n c l u s i o n s 8.2.1 A p p l i c a b i l i t y o f t h e Method 8.2.2 L i m i t a t i o n s o f t h e Method 8.2.3 Design o f Open Stope R i b P i l l a r s  179 179 179 180  8.3 F u t u r e Work  181  176 177  REFERENCES  183  APPENDIX 1  190  vii L I S T OF TABLES PAGE TABLE 1. Constants proposed by v a r i o u s authors f o r t h e s i z e e f f e c t formula ( a f t e r Babcock, Morgan and Haramy 1981).  36  TABLE 2. Constants proposed by v a r i o u s authors f o r t h e shape e f f e c t formula ( a f t e r Babcock, Morgan and Haramy 1981).  37  TABLE 3. Constants proposed by v a r i o u s authors f o r t h e shape e f f e c t formula ( a f t e r Babcock, Morgan and Haramy 1981).  37  TABLE 4. The s a f e t y f a c t o r s proposed by v a r i o u s authors f o r e m p i r i c a l p i l l a r d e s i g n i n e n t r y mining methods.  52  TABLE 5. Background data f o r a l l t h e p i l l a r case histories.  70  TABLE 6. Comparison o f BEAP and BITEM f o r f o u r s e t s o f d i f f e r e n t orebody geometries.  94  TABLE 7. Comparison of BEAP and MINTAB f o r t h e f o u r different tests.  98  TABLE 8. P i l l a r l o a d i n f o r m a t i o n f o r a l l t h e open stope r i b p i l l a r case h i s t o r i e s u s i n g BITEM, MINTAB and t h e T r i b u t a r y Area Theory.  105  TABLE 9. Comparison o f MINTAB and BITEM r e s u l t s , when both programs l i m i t a t i o n s a r e s a t i s f i e d .  107  TABLE 10. Comparison o f BITEM and MINTAB, when t h e 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 t h e average p i l l a r s t r e s s v a r y i n g up t o ± 25%. TABLE 12. Data used by Von Kimmelmann e t a l . (1984) i n the development o f a p i l l a r f a i l u r e c r i t e r i o n .  136  TABLE 13. Comparison o f t h e v a l u e o f ore f o r mines u s i n g 161 temporary p i l l a r s a g a i n s t mines u s i n g permanent p i l l a r s .  viii L I S T OF FIGURES PAGE FIGURE 1. The elements o f an i d e a l i z e d l o n g i t u d i n a l longhole open s t o p i n g method showing t h e b l a s t i n g , mucking and b a c k f i l l i n g o p e r a t i o n s .  6  FIGURE 2. The elements o f an i d e a l i z e d t r a n s v e r s e b l a s t h o l e open s t o p i n g method showing t h e 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 o p e r a t i o n s .  7  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 t o a l a c k of confinement a t the p i l l a r w a l l s .  16  FIGURE 3b. I n t e r n a l s p l i t t i n g and a x i a l c r a c k i n g o f a p i l l a r due t o deformable p i l l a r l a y e r s o r t h e propagation of p a r a l l e l wall f r a c t u r e s .  16  FIGURE 3c. Diagonal c r u s h i n g f r a c t u r e s may occur i n c o n f i n e d o r massive p i l l a r s .  16  FIGURE 4. A h y p o t h e t i c a l l o a d - d e f o r m a t i o n curve can be used t o d e s c r i b e t h e 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 o f a pillar.  18  FIGURE 5. Wagner (1974) d i d a s e r i e s o f i n s i t u l o a d deformation t e s t s on c o a l p i l l a r s u s i n g h y d r a u l i c j a c k s . The graph on t h e t o p shows t h e l o a d - d e f o r m a t i o n c h a r a c t e r i s t i c s o f the p i l l a r i n g e n e r a l . The o b l i q u e diagrams g i v e t h e r e l a t i v e l o a d on each o f t h e 25 j a c k s at f o u r stages o f p i l l a r compression.  20  FIGURE 6. The s t r e s s - s t r a i n curves f o r l a b o r a t o r y specimens loaded under i n c r e a s i n g c o n f i n i n g p r e s s u r e s show an i n c r e a s e i n peak l o a d and an i n c r e a s e i n t h e post-peak l o a d b e a r i n g c a p a c i t y .  22  FIGURE 7. There i s a very l a r g e i n f l u e n c e o f specimen s i z e on t h e s t r e n g t h o f i n t a c t rock, f o r s m a l l specimen diameters.  28  FIGURE 8. S t r e n g t h t e s t i n g o f samples o f i n c r e a s i n g specimen l e n g t h shows a d e c r e a s i n g i n f l u e n c e o f s i z e .  28  FIGURE 9. Histogram o f t h e s a f e t y f a c t o r s f o r s t a b l e 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 c o a l mining.  39  ix FIGURE 10. The estimated s t r e s s and s t r e n g t h f o r case h i s t o r i e s o f p i l l a r s i n room and p i l l a r mining i n t h e E l l i o t l a k e uranium mining d i s t r i c t .  42  FIGURE 11. Hoek and Brown (1980) proposed a s e r i e s o f p i l l a r s t r e n g t h curves based on t h e t h e o r e t i c a l d i s t r i b u t i o n o f rock mass f a i l u r e i n a p i l l a r .  44  FIGURE 12. The analogy o f s t r e a m l i n e s i n a smoothly f l o w i n g stream o b s t r u c t e d by b r i d g e p i e r s i s o f t e n used to d e s c r i b e t h e c o n c e n t r a t i o n o f s t r e s s i n p i l l a r s .  47  FIGURE 13. The t r 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 t o several d i f f e r e n t p i l l a r layouts.  47  FIGURE 14. Salamon (1974) showed t h e v a r i a t i o n i n p i l l a r s t r e s s caused by i n c r e a s i n g t h e number o f p i l l a r s (N) i n a mining p a n e l . The graph shows a d i s t i n c t i n f l u e n c e o f the l o c a t i o n o f a p i l l a r and t h e number o f p i l l a r s on the s t r e s s induced.  49  FIGURE 15. A study u s i n g two dimensional boundary element numerical m o d e l l i n g shows t h e i n f l u e n c e o f p i l l a r shape and t h e number o f p i l l a r s on t h e average s t r e s s .  50  FIGURE 16. An i d e a l i z e d s k e t c h showing t h e p r i n c i p l e o f numerical m o d e l l i n g o f underground e x c a v a t i o n s .  54  FIGURE 17. An e m p i r i c a l f a i l u r e c r i t e r i o n has been a p p l i e d t o t h e two dimensional s t r e s s d i s t r i b u t i o n o f a s t a b l e open stope r i b p i l l a r .  59  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 o f f a i l e d r o c k i s much g r e a t e r i n t h i s p i l l a r .  59  FIGURE 19. The peak s t r e n g t h , deformation c h a r a c t e r i s t i c s , and e f f e c t o f l o c a t i o n used f o r i n v e s t i g a t i n g a p i l l a r case h i s t o r y w i t h a displacement d i s c o n t i n u i t y program.  61  FIGURE 20. The normal s t r e s s and t h e f a i l e d r e g i o n s e s t i m a t e d w i t h t h e displacement d i s c o n t i n u i t y program f o r a s i l l p i l l a r case h i s t o r y .  61  FIGURE 21. The d i s t r i b u t i o n o f normal s t r e s s i n a mining b l o c k was e s t i m a t e d f o r two d i f f e r e n t mining sequences t o determine t h e b e s t stope e x t r a c t i o n sequence.  64  FIGURE 22. T h i s f i g u r e shows t h e g e o m e t r i c a l d e f i n i t i o n f o r t h e stope and p i l l a r dimensions used i n t h i s t h e s i s .  72  X  FIGURE 23. I s o m e t r i c view o f an opening t h a t i s l o n g i n one d i r e c t i o n and t h e d i s c r e t i z a t i o n o f t h e boundary used i n two d i m e n s i o n a l m o d e l l i n g .  80  FIGURE 24. O b l i q u e view o f t h e MINTAB seam geometry and the s t r e s s a p p l i e d l o c a l l y on each element i n t h e r e e f .  83  FIGURE 25. A t y p i c a l BEAP geometry showing t h e boundary of t h e e x c a v a t i o n s d e f i n e d by two d i m e n s i o n a l q u a d r a t i c , non-conforming elements i n a t h r e e d i m e n s i o n a l s t r e s s field.  85  FIGURE 26. T h i s f i g u r e d e f i n e s t h e dimensions f o r stopes and p i l l a r s , and t h e o r i e n t a t i o n f o r t h e i n s i t u s t r e s s regime f o r t h i s t h e s i s .  87  FIGURE 27a. A r i b p i l l a r i n a h o r i z o n t a l seam loaded by the weight o f the overburden.  88  FIGURE 27b. The d i r e c t i o n o f l o a d i n g on a p i l l a r i n a v e r t i c a l orebody.  88  FIGURE 28. The mid-height p l a n e and c e n t e r l i n e f o r t a l l open stope geometries.  90  FIGURE 29. The shaded p l a n e has t h e g r e a t e s t i n f l u e n c e on the mid-height a s t r e s s .  94  FIGURE 30. O v e r e s t i m a t i o n o f average p i l l a r l o a d by t h e 2D "BITEM" boundary element method f o r t h e 12 runs i n the f o u r t e s t s .  96  FIGURE 31. The dimensions and geometry comparison t e s t s .  98  v  o f t h e MINTAB/BEAP  FIGURE 32. The d i f f e r e n c e between t h e average p i l l a r 101 s t r e s s p r e d i c t e d by MINTAB and t h e average p i l l a r s t r e s s p r e d i c t e d by BEAP f o r t h e comparison t e s t s . FIGURE 33. O v e r e s t i m a t i o n o f average p i l l a r l o a d by t h e 2D "BITEM" boundary element method f o r t h e comparison t e s t s and 3 case h i s t o r i e s .  109  FIGURE 34. The d i f f e r e n c e between t h e average p i l l a r 112 s t r e s s p r e d i c t e d by MINTAB and t h e average p i l l a r s t r e s s p r e d i c t e d by BEAP f o r t h e comparison t e s t s and 13 case histories. FIGURE 35. The p i l l a r s t a b i l i t y graph showing t h e open stope r i b p i l l a r data base.  123  FIGURE 36. The p i l l a r s t a b i l i t y graph showing t h e s t a b l e and f a i l e d zones and t h e t r a n s i t i o n a r e a .  125  FIGURE 37. The p i l l a r s t a b i l i t y graph w i t h t h e p i l l a r l o a d reduced f o r a l l t h e data p o i n t s by t h e maximum amount l i s t e d i n T a b l e 8.  127  FIGURE 38. The p i l l a r s t a b i l i t y .graph w i t h a l l t h e case h i s t o r i e s o f t h e 13 y i e l d i n g p i l l a r s j o i n e d by s o l i d lines.  129  FIGURE 39. The p i l l a r s t a b i l i t y graph showing t h e d a t a from room and p i l l a r mining p u b l i s h e d by Hedley and Grant (1972) i n t h e i r study on t h e development o f a p i l l a r s t r e n g t h formula.  133  FIGURE 40. A p l a n view o f room and p i l l a r mining a t BCL L i m i t e d , showing t h e use o f l o n g p i l l a r s and square pillars.  137  FIGURE 41. The p i l l a r s t a b i l i t y graph showing t h e l o n g p i l l a r data p r e s e n t e d by Von Kimmelmann e t a l . (1984).  138  FIGURE 42. The square p i l l a r data p r e s e n t e d by Von Kimmelmann e t a l . (1984) i s p l o t t e d on t h e s t a b i l i t y graph u s i n g an e f f e c t i v e width i n t h e H/W r a t i o .  140  FIGURE 43. The f i v e stages o f t h e S86 p i l l a r i n an open stope p i l l a r t e s t a t Mt. I s a ( a f t e r Brady 1977).  142  FIGURE 44. The t h i r d , fourth, and f i f t h s t a g e s o f t h e S86 open stope r i b p i l l a r , p r e s e n t e d by Brady (1977), a r e shown on t h e p i l l a r s t a b i l i t y graph.  144  FIGURE 45. The p i l l a r s t a b i l i t y graph showing t h e open stope r i b p i l l a r data and t h e l i t e r a t u r e d a t a .  145  FIGURE 46. The range o f r i b p i l l a r dimensions seen i n 17 Canadian open stope mines. FIGURE 47. Comparison o f t h e p i l l a r s t a b i l i t y Hedley's formula f o r two s a f e t y f a c t o r s .  148  graph and  150  FIGURE 48. Three o f the Hoek and Brown (1980) p i l l a r s t r e n g t h curves p l o t t e d on t h e p i l l a r s t a b i l i t y graph.  153  FIGURE 49. Comparison between t h e p i l l a r s t a b i l i t y graph and t h e Obert and Duval1 (1967) shape e f f e c t formula a p p l i e d w i t h a s a f e t y f a c t o r o f 1.0.  155  xii FIGURE 5 0 . The s h a p e e f f e c t f o r m u l a p r o p o s e d b y 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 .  157  FIGURE 5 1 . The r a n g e o f t e m p o r a r y r i b p i l l a r u s e d i n 14 C a n a d i a n o p e n s t o p e m i n e s .  164  FIGURE 5 2 . Isometric view of transverse stoping at N o r i t a .  dimensions  b l a s t h o l e open  168  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 s t o p i n g b l o c k at N o r i t a showing the p i l l a r case 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 history analysis.  171  FIGURE 5 4 . 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 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 case h i s t o r i e s at N o r i t a .  172  ACKNOWLEDGEMENT The author wishes t o acknowledge Noranda Research, F a l c o n b r i d g e L i m i t e d , t h e N a t u r a l S c i e n c e s and E n g i n e e r i n g Research C o u n c i l and t h e Cy and Emerald Keyes s c h o l a r s h i p fund f o r f i n a n c i a l support d u r i n g t h e p r o j e c t . Thanks a r e extended t o t h e employees o f t h e mines and groups which p r o v i d e d time and i n f o r m a t i o n t o t h e study: - Algoma S t e e l Corp. L i m i t e d - G.W. Macleod Mine - B a r r i c k Resources - Camflo Mine - BP Canada Inc. - Mines S e l b a i e - Cambior - Niobec Mine - C o r p o r a t i o n o f F a l c o n b r i d g e Copper - Corbet Mine, Lac S h o r t t Mine - Dome Mines L i m i t e d - F a l c o n b r i d g e L i m i t e d - E a s t Mine, F r a s e r Mine, Kidd Creek, Lockerby Mine, Mining Technology D i v i s i o n , Onaping Mine, S t r a t h c o n a Mine - Hudson Bay Mining and Smelting - C e n t e n n i a l Mine, C h i s e l Lake Mine, F l i n F l o n Mine, Spruce P o i n t Mine - Inco L i m i t e d - L i t t l e S t o b i e Mine, Mine Research D i v i s i o n , S t o b i e Mine, Thompson D i v i s i o n - Kiena Gold Mines - Noranda M i n e r a l s I n c . - Brunswick M i n i n g and Smelting, Chadbourne Mine, Geco Mine, Golden G i a n t Mine, Lyon Lake Mine, M a t t a b i Mine, Mattagami Lake Mine, Mines Gaspe, Mining Technology D i v i s i o n , N o r i t a Mine - Pamour Porcupine Mines L i m i t e d - Ross Mine, No. 1 Mine - S h e r r i t t Gordon - Ruttan Mine - Westmin Resources L i m i t e d . A l s o , thanks t o Dr. H.D.S. M i l l e r f o r h i s e f f o r t s i n s e t t i n g up the I n t e g r a t e d Mine Design P r o j e c t . his the for  S i n c e r e g r a t i t u d e i s expressed t o P r o f e s s o r A l a n Reed f o r comments and h e l p i n w r i t i n g t h e t h e s i s and t h e members o f Department o f Mining and M i n e r a l Process E n g i n e e r i n g a t UBC h e l p and support d u r i n g t h e p r o j e c t .  S p e c i a l thanks t o my p a r t n e r Mr. Yves P o t v i n . His technical c o n t r i b u t i o n s and a d v i c e have had an immeasurable i n f l u e n c e on t h i s t h e s i s and my understanding o f mining and rock mechanics. F i n a l l y , and most o f a l l , I wish t o express my thanks t o Harry and N e l l i e Hudyma f o r t h e i r continuous encouragement and support d u r i n g a l l my endeavors.  1 CHAPTER 1 INTRODUCTION  Open  stope  1930's.  mining  The d e s i g n  has been p r a c t i c e d o f open  determining the l a r g e s t pillars.  Systematic  separating  stable  methods  "rib"pillars  Canadian  open  Sciences  and  Research  stope  "Integrated University  mining  Design  of B r i t i s h  H.D.S. M i l l e r .  t o design  i s centered  open  not been  conditions. Research  Falconbridge  Mine  mines  since the  stopes and t h e optimum  have  Engineering  and  stope  i n Canada  Columbia  confirmed  a  under  size for and t h e i r  i n typical  In 1986, t h e N a t u r a l  Council  Limited  Project",  stopes  around  (NSERC),  agreed  to  research  Noranda  sponsor  project  the  a t the  t h e s u p e r v i s i o n o f Dr.  The g o a l o f t h e study was t o i n v e s t i g a t e  open  stope mine d e s i g n methods by c o n f i r m i n g t h e v a l i d i t y o f e x i s t i n g stope  and  rib pillar  e m p i r i c a l methods.  design  methods  or  by  developing  new  T h i s t h e s i s i s a c o m p i l a t i o n and a n a l y s i s o f  the i n f o r m a t i o n and data c o l l e c t e d f o r t h e d e s i g n o f r i b p i l l a r s i n open stope mining. The  first  contents  describing  1.1  of  of the t h e s i s .  introduce  pillars  section  t h e problem open  stope  this  chapter  The  remainder  o f d e s i g n i n g open mining,  i n open stope mining.  Contents o f t h e T h e s i s  is a  o f the  of the chapter stope  and d i s c u s s i n g f  summary  r i b pillars the r o l e  will by  of r i b  2 This role  study  of  rib  begins  pillars  characteristics the  factors  Chapter  3  that  collected  element open  a  rib  base p i l l a r s i s  the  In  2,  the  discussed  and  s t a b i l i t y are  the  empirical  rib pillars.  Integrated  Mine  and  Design  methods  to  determine  pillars.  The  load  estimated  in this  the  average  induced  on  is  boundary  stress  of  the  in data  the  S t a b i l i t y G r a p h " , based on g r a p h i c a l a n a l y s i s o f t h e  rib  of  a new e m p i r i c a l  and d a t a  from  section.  all  pillar  Project  Chapter 5 d i s c u s s e s the use o f  pillar  literature.  It  Chapter  7 briefly  discusses  A summary a n d c o n c l u s i o n o f t h e t h e s i s  Open S t o p e Open  a l s o compares t h e  the  mining  is  a  general  v a r i e d m i n i n g method. up  features. applicability, from  new  f o r open s t o p e  rib  application of  the  rib  pillars.  i s found i n Chapter  8.  Mining  stope  make  largely  numerical  The r i b  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  highly  identified.  d e s i g n method c a l l e d  pillars.  that  the  Chapter  f a i l u r e are  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  1.2  and  the  data  pillar  mining  C h a p t e r 6 shows  development  pillar  of  stope  mining.  pillar  review  i n Chapter 4.  stope  stope  f o r open s t o p e  in  numerical  "Pillar  open  influence r i b p i l l a r  contains  presented  in  d e s c r i b i n g open  of progressive  d e s i g n methods u s e d data  by  the The and  method,  name  There are  and  following description  many  variations  an u n p u b l i s h e d paper  open  to  describe  many i m p o r t a n t  discussion of  used  of stope  on o p e n s t o p e  on the  a  features  each  of  the  definition,  mining mining  is  taken  methods,  3  w r i t t e n a t U.B.C. (Hudyma 1988a).  1.2.1  D e f i n i t i o n o f Open S t o p i n g  Three  characteristics,  common t o a l l open s t o p i n g methods,  make i t d i s t i n c t from o t h e r mining methods. i ) Open  stoping  is a  non  e n t r y mining  method.  Once  stope  p r o d u c t i o n has s t a r t e d , a l l a c t i v i t i e s r e q u i r i n g miners done from the p e r i p h e r y of the stope.  The  are  open stope does  not need t o be entered and a t no time are miners exposed t o the p r o d u c t i o n f a c e , ii)  It  is  generally  (although  a  naturally  some a r t i f i c i a l  supported  support  mining  i s occasionally  N a t u r a l l y supported means t h a t displacement and of  method used).  deformation  the rock mass i s l i m i t e d t o e l a s t i c o r d e r s of magnitude.  The  underground  stable  and  methods) . unstable  structures  created  self-supporting Mining  r e l e a s e of  is  done  energy  (in in  a  due  are  designed  opposition manner  t o mining  to  to  to  be  caving  ensure  does not  that occur  (from Brady 1981). iii)  Stopes  are  opened  stabilizing f i l l  These  three  to  to  and  enter  full  dimensions  before  a  i s introduced.  characteristics  a l l o t h e r underground methods. pillar  their  distinguish Cut and f i l l ,  open  stoping  from  l o n g w a l l , room and  shrinkage are a l l e n t r y methods t h a t r e q u i r e workers the  production  f a c e of the  stope.  Block  caving  and  4  sublevel  caving  induce  large,  unstable  movements  of  rock  and  i n c l u d e the c o n t i n u a l d i s s i p a t i o n of energy  as mining  proceeds,  so  supported  methods.  they  can  Methods such to  not  be  considered  as AVOCA, which i n t r o d u c e s f i l l  prevent stope i n s t a b i l i t y ,  the  stope  naturally  full  of  broken  extraction  or shrinkage s t o p i n g , which keeps  ore,  are  because the stope i s never f u l l y  1.2.2  during  excluded  from  open s t o p i n g  open.  A p p l i c a b i l i t y of Open S t o p i n g  There  are  some orebody  and  a p p l i c a t i o n o f open s t o p i n g .  geological  limitations  to  the  M o d i f i c a t i o n s o f open s t o p i n g can  be made t o mine a wide v a r i e t y of o r e b o d i e s , but some c o n d i t i o n s present d i f f i c u l t Open  stoping  dipping.  Stopes  angle of repose gravity be  30°)  about  i s best  suited  to  orebodies  but  that  are  steep  i n the orebody must d i p s u f f i c i e n t l y above the of the broken  ore  (above  50°  t o 55°)  flow of the ore t o the stope bottom.  successful  than  problems.  i n shallow d i p p i n g o r e b o d i e s the  orebody  must  be  15 metres i n t r u e t h i c k n e s s ) .  t o permit  Open s t o p i n g can  (approximately  quite thick  less  ( g r e a t e r than  I f an orebody i s not steep  d i p p i n g o r t h i c k and f l a t , open s t o p i n g can not be  used.  For mining a steep d i p p i n g orebody, the orebody o u t l i n e must be f a i r l y 5  r e g u l a r and the orebody needs t o be g r e a t e r than  metres  in  delineate  and  width. mine.  w a l l r o c k d i l u t i o n due  Irregular  orebodies  G e n e r a l l y , a t widths to d r i l l  are  less  about  difficult than  5  to  metres,  h o l e d e v i a t i o n and b l a s t damage  5  becomes t o o g r e a t t o use open s t o p i n g e f f e c t i v e l y . The  r o c k mass s t r e n g t h of the  country  rock  i s very  the rock, the  important  orebody  and  the  i n open s t o p i n g .  l a r g e r the stopes can be made, and  surrounding The  stronger  consequently,  the more p r o d u c t i v e the method w i l l be.  At the l e a s t ,  fair  mass s t r e n g t h i s needed  w a l l rock t o  guarantee  i n the ore and  rock  t h a t t h e open stopes w i l l be n a t u r a l l y s u p p o r t i n g . A  final  restriction  reasonably l a r g e . (because  open  advantage justify  of  on  open s t o p i n g i s the orebody must  T h i s i s necessary t o get a few working  stoping the  is  large  often  scale  a of  cyclical the  method),  mining  faces  to  method,  be  take  and  to  the c o s t of the development a s s o c i a t e d w i t h open stope  mining.  1.2.3  D e s c r i p t i o n of T y p i c a l Open Stope M i n i n g Methods  Open s t o p i n g methods are so dependent on the orebody shape, size  and  Most  open  basic  orientation  that  stope mining  stages:  s t o p i n g has  a large  two  activities  pre-mining  development u s u a l l y - sublevel  no  (figures  be  exactly  the  same.  generalized into  and  production.  development.  two Open  Typical  includes: such  horizon  1 and  are  amount of pre-mining  accesses  drilling  can  development  as ramps, man-way r a i s e s  note A), and s u b l e v e l d r i f t s - a  mines  which  2, note C)  (figure  1,  ( f i g u r e s 1 and 2, note B), includes  and d r i l l  D) or o v e r c u t s ( f i g u r e 2, note E ) ,  stope drives  access  drifts  ( f i g u r e 1,  note  3  LEGEND A - MAN WAY-RAISE - SUBLEVEL DRIFT STOPE ACCESS DRIFT C D - DRILL DRIFTS  B  F H I L  -  FOOTWALL HAULAGE DRIFT DRAWPOINT COLLECTION CONE RING DRILL PATTERN  FIGURE 1. The elements o f an I d e a l i z e d l o n g i t u d i n a l l o n g h o l e open s t o p i n g method showing t h e b l a s t i n g , mucking and b a c k f i l l i n g o p e r a t i o n s ( a f t e r Hudyma 1988a).  LEGEND B C E F  -  SUBLEVEL DRIFT STOPE ACCESS DRIFT FULL STOPE OVERCUT FOOTWALL HAULAGE DRIFT  G H J K  -  FULL STOPE UNDERCUT DRAWPOINT SLOT RAISE PARALLEL DRILL HOLES  FIGURE 2. The elements o f an i d e a l i z e d t r a n s v e r s e b l a s t h o l e open s t o p i n g method showing t h e 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 o p e r a t i o n s ( a f t e r Hudyma 1988a).  8 - a mucking h o r i z o n , which may i n c l u d e : - a f o o t w a l l haulage d r i f t  ( f i g u r e s 1 and 2, note F ) ,  - stope access undercuts ( f i g u r e 2, note G) o r drawpoints  ( f i g u r e s 1 and 2, note H),  - stope undercut scrams, V - c u t s o r c o l l e c t i o n  cones  ( f i g u r e 1, note I ) , - t h e opening  of a s l o t  raise  ( f i g u r e 2, note J) by s t a g i n g ,  drop r a i s i n g , Alimak r a i s e c l i m b e r o r by r a i s e b o r e r . P r o d u c t i o n mining  involves:  - using p a r a l l e l to  d r i l l holes t o slash ore into the s l o t  form an expansion s l o t which  the  raise  i s opened t h e f u l l width o f  stope,  - drilling ring  production holes i n p a r a l l e l  patterns  (figure  1, note  b l a s t o r e i n t o t h e expansion Generally,  t h e expansion s l o t  and  ore i s slashed  the  production face.  the  orebody,  The h o l e s a r e used t o  slot.  i s opened a t one end o f t h e stope  into the s l o t This  L) .  ( f i g u r e 2, note K) o r  causing a gradual r e t r e a t of  retreat  may be l o n g i t u d i n a l  (along  as i n f i g u r e 1) o r t r a n s v e r s e (across t h e orebody,  as i n f i g u r e 2 ) . As a stope i s b l a s t e d , o r e i s removed from t h e bottom stope. trackless system. or  The  o r e i s almost  load-haul-dump There  always  equipment,  removed  with  and taken  of the  t h e use o f  t o an  orepass  a r e a few mines u s i n g s l u s h e r / s c r a p e r equipment  c o n t i n u o u s mining  equipment t o move t h e muck t o an orepass,  but t h e s e o p e r a t i o n s a r e q u i t e r a r e .  The o r e pass system moves  9 the muck t o a c e n t r a l c o l l e c t i o n p o i n t f o r t r a n s p o r t out of the mine.  When the stope  i s completely b l a s t e d ,  w i t h waste r o c k o r c l a s s i f i e d of  pillars  filling  1.3  left  mill  between stopes  i t may  be  t a i l i n g s t o permit  (both f i g u r e s  1 and  filled  recovery  2 show the  of s t o p e s ) .  R o l e o f R i b P i l l a r s i n Open Stope M i n i n g The  entire full  most  economic  orebody  i n one  lens  mining  open  stope  longitudinal  creates  major  backfill  l i k e l y be needed.  stope  mining  is  to  stope  the  instability, will  method stope.  I f the use  potential  support  provide  i n v o l v e s mining  such  for as  of  serious  rib  to  a  this stope  pillars  The r o l e of r i b p i l l a r s  stability  the  mining  and  i n open  block  by  l i m i t i n g r o c k mass displacements and r e s t r i c t i n g the exposure  of  the r o c k mass i n the stope back and w a l l s . In had  the p a s t ,  t o be  left  improvements  i f full  to maintain  i n mining  the sequencing  l e n s mining was overall  technology  mine s t a b i l i t y . have caused  of e x t r a c t i o n so t h a t p i l l a r s  even i n v e r y l a r g e o r e b o d i e s .  pillars  to  separate  stopes  v a r i e d i n s i z e from about 2000 m factors  pillars  Recently,  a t r e n d towards  are never c r e a t e d ,  However, o f the 34 Canadian  stope mines i n v e s t i g a t e d i n t h i s study rib  not p o s s i b l e ,  (from 1986-1988), 27  i n the orebody. 3  These  up t o 150,000 m , 3  open used  pillars  depending  on  such as: the orebody geometry, the type of open s t o p i n g  method, and  the mining  sequence.  The dimensions  i n the data base are g i v e n i n Chapter 4.1  o f the  pillars  (Table 5, page 70).  10 It role.  is  important  that  rib pillars  Mines u s i n g r i b p i l l a r s  may  d e s i g n can s e r i o u s l y  - l o s s of p i l l a r - the  need  consequences of poor A  cause:  sloughing,  pillar  recovery,  access,  for  remedial  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 - low  The  i t s intended r o l e may  - e x c e s s i v e stope or p i l l a r and expensive  designed  a f f e c t the r e c o v e r y of t h i s ore.  p i l l a r t h a t does not perform  - difficult  their  l e a v e as much as h a l f of the  orebody r e s e r v e s i n temporary p i l l a r s . pillar  perform  productivity,  - or t h e l o s s of ore r e s e r v e s .  measures support,  such  as  development  11 CHAPTER 2 RIB PILLAR FAILURE  The f i r s t pillar  step  stability  i n quantifying the v a r i a b l e s that i s t o describe  pillar  failure.  stope r i b p i l l a r f a i l u r e has n o t been deeply the  principles  rock  masses  objective istics and  of f a i l u r e  i n intact  are applicable  of t h i s  chapter  While  researched, rock,  stope  soft  open  some of rock and  rib pillars.  The  i s to b r i e f l y discuss the character-  of p i l l a r i n s t a b i l i t y  documentation o f f a i l u r e  these  t o open  hard  influence  and compare i n open stope  them  to  observations  rib pillars.  Using  i d e a s about p i l l a r f a i l u r e , t h e f a c t o r s t h a t i n f l u e n c e the  s t a b i l i t y o f open stope p i l l a r s w i l l be  identified.  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 Rib  pillar  failure  progressive  (stable)  Progressive  failure  mass  i n a slow,  violent rock.  can be  failure  broken  and b u r s t i n g  r e f e r s t o gradual  non-violent  into  manner.  two  basic  (unstable)  modes: failure.  d e t e r i o r a t i o n of a Bursting  failure  r e l e a s e o f energy c a u s i n g t h e instantaneous  rock  i s the  fracture of  Although t h e c o n d i t i o n s a s s o c i a t e d w i t h each may be very  different,  both modes o f f a i l u r e c r e a t e s e r i o u s d i f f i c u l t i e s f o r  mining. T h i s t h e s i s w i l l d e s c r i b e and q u a n t i f y p r o g r e s s i v e  failure.  P r o g r e s s i v e f a i l u r e i s r e l a t e d t o t h e i n s i t u rock p r o p e r t i e s o f the  p i l l a r and mine,  and t h e s t a t i c  underground  stress  field.  12 Both of these f a c t o r s are q u a n t i f i a b l e w i t h r e a s o n a b l e accuracy. Bursting  failure  i s also  related  to  in situ  rock  properties.  However, i t i s a l s o dependent upon f a c t o r s such as l o c a l concentration, changes  the  i n the  investigate  and  the  unstable  dynamic  these  technology reason,  energy  released  stress  factors  budget  thesis  as  they  not  the  I t i s not  are  for  attempt  to  not  this to  mining  and  intended  to  quantifiable study.  describe  with  For or  this  quantify  failure.  Although  rib pillar  failure  uncommon, i t i s r a r e l y w e l l of  field.  available  will  due  stress  documentation  pillars  is  i s that  difficult  in  i n open  stope  documented.  visual open  A reason  observation stope  mining  mining  and  i s not  f o r the  lack  monitoring  and  there  is  of no  t universal  method t o d e s c r i b e  rib p i l l a r failure. documentation considered  Another p o t e n t i a l reason f o r the absence of  i s that  an  methods  using  pillar  failure  often  serious  Consequently, not  be  the  immediate  mining  are  enough  failure  backfill. does to  of  problem,  not  until  rib pillars  especially In  cause  warrant  the o p e r a t i o n a l  experienced  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  the  with  primary  operational  changing  i s often  the  mining  rib  problems  that  mining  starts.  stope  mining,  e f f e c t s of r i b p i l l a r  pillar  open  not  sequence.  failure This  may  failure  o f t e n r e s u l t s i n low p r o d u c t i v i t y , waste d i l u t i o n , h i g h e r mining c o s t s and p o s s i b l y l o s t ore. Several  signs  indicating p i l l a r  stope r i b s have been i d e n t i f i e d .  stability  problems i n open  These s i g n s of p i l l a r d i s t r e s s  13 are: - c r a c k i n g and s p a l l i n g o f rock i n r i b p i l l a r development and  raises,  - a u d i b l e n o i s e heard i n t h e p i l l a r s  or microseismic  events  l o c a t e d w i t h m o n i t o r i n g systems, - deformed o r plugged d r i l l  holes causing d r i l l  rods t o be  s t u c k and c a u s i n g problems i n l o a d i n g h o l e s , - overdraw from primary stopes w i t h t h e " f r e e " muck b e i n g u n b l a s t e d , o v e r s i z e m a t e r i a l from p i l l a r w a l l s , - s t r e s s 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 pillars  a f f e c t i n g nearby  and hanging w a l l and f o o t w a l l d r i f t s  - h o u r g l a s s i n g and c r a c k i n g o f p i l l a r s  seen  and r a i s e s ,  from  development, - major displacements  and changes i n s t r e s s shown by  instrumented m o n i t o r i n g systems such as s t r e s s meters and No  single  sign  sloughmeters.  necessarily  denotes  pillar  s i g n s a r e commonly r e p o r t e d d u r i n g p i l l a r Progressive p i l l a r may be minor a t f i r s t , and  deterioration  existing  structural  structurally influence  controlled  of geological  predominant. related  can  extensometers,  failure  failure,  failure.  i s a gradual process.  but g e t worse w i t h time. occur  but these  through  intact  discontinuities. failures  occur  Problems  Pillar rock  and  Although  in pillars,  f r a c t u r e s appears  along purely  the o v e r a l l  s t r u c t u r e i n open stope p i l l a r s  Stress, p i l l a r  damage  i s not  l o a d i n g and development o f s t r e s s  t o be predominant.  Consequently,  the  14 d i s c u s s i o n of r i b p i l l a r pillar  loading,  and  the  failure will  focus  on r o c k f r a c t u r i n g ,  subsequent l o s s of p i l l a r  load  bearing  ability.  2.1.1  Rock F r a c t u r i n g Rock f r a c t u r i n g i s a primary i n d i c a t o r of p i l l a r  i s the u l t i m a t e pillar  reason f o r the l o s s of l o a d b e a r i n g  disintegration.  fracturing  as  "...  the  rock m a t e r i a l .  new  surfaces."  the  Brady formation  I t involves  the  As  pillar  and  (1985)  define  separation  of bonds t o  central  parts  of  and  Soder  p i l l a r mines.  walls  the  pillar  and  the  size  and and  increases.  (1987)  The  in  form  f r a c t u r e s propagate  defined  6  f a i l u r e based on v i s u a l o b s e r v a t i o n  i n room and  ability  t o the l a c k of confinement of  f a i l u r e progresses,  i n t e n s i t y of e x i s t i n g f r a c t u r e s Krauland  breaking  and  F r a c t u r i n g g e n e r a l l y s t a r t s a t the p i l l a r  p i l l a r material. in  Brown  of p l a n e s of  the  where the r o c k mass i s weakest due  develop  and  failure  stages  to  classify  of p i l l a r f r a c t u r i n g  stages d e f i n e d  are:  "0) No f r a c t u r e s . 1) S l i g h t s p a l l i n g of p i l l a r c o r n e r s and p i l l a r w a l l s , w i t h s h o r t f r a c t u r e lengths i n r e l a t i o n t o p i l l a r h e i g h t , s u b p a r a l l e l to p i l l a r walls. 2) One or a few f r a c t u r e s near s u r f a c e , d i s t i n c t s p a l l i n g . 3) F r a c t u r e s appear a l s o i n c e n t r a l p a r t s o f the p i l l a r . 4) One or a few f r a c t u r e s occur through c e n t r a l p a r t s of the p i l l a r , d i v i d i n g i t i n t o two or s e v e r a l p a r t s , w i t h rock f a l l s from the p i l l a r . F r a c t u r e s may be p a r a l l e l t o p i l l a r w a l l s or d i a g o n a l , i n d i c a t i n g emergence of an hour-glass-shaped p i l l a r . 5) D i s i n t e g r a t i o n of the p i l l a r . Major b l o c k s f a l l out and/or the p i l l a r i s cut o f f by w e l l d e f i n e d f r a c t u r e s . A l t e r n a t i v e l y , a w e l l developed h o u r - g l a s s shape may emerge, w i t h c e n t r a l p a r t s completely crushed."  15 Krauland  and Soder a l s o  pillar  failure  was  inhomogeneities,  the  remained best  noted highly  basic  that  although  variable pattern  due  of  f a i l u r e mechanism. approach  to  and  definition  to  failure  constant f o r progressive f a i l u r e .  documentation  t h e appearance o f  o f an  geological propagation  T h i s i s perhaps the actual  mine  pillar  Use o f t h e Krauland and Soder o b s e r v a t i o n a l  classify  open  stope  pillars  p o s s i b l e due t o t h e l a c k o f v i s u a l a c c e s s .  i s not g e n e r a l l y However, t h e mode o f  f a i l u r e d e s c r i b e d above i s s i m i l a r t o t h a t seen by t h e author i n several mines  open stope mines and i s documented i n a few open  (Falmagne 1986; Bray  was a v a i l a b l e .  1967) where s u f f i c i e n t v i s u a l  stope access  The o n l y o b s e r v a t i o n o f Krauland and Soder t h a t  t h i s author has not seen i n open stope mining i s t h e d i v i s i o n o f pillars  into  distinct  r e g i o n s due t o f r a c t u r i n g .  the mechanism i s not l i k e l y potential  f o r a fracture  This part of  t o occur i n open stope p i l l a r s .  t o completely  sever a p i l l a r  The  i s much  lower i n open stope mining than i n room and p i l l a r mining due t o the l a r g e r s c a l e o f open stope p i l l a r s .  F r a c t u r e s would have t o  be v e r y continuous, f l a t and p l a n a r t o t r a n s e c t and d i v i d e open stope  pillars.  From p e r s o n a l o b s e r v a t i o n and l i t e r a t u r e d e s c r i p t i o n s , of  t h e most  common types  of fracturing  found  i n mine  some  pillars  are: i) the 1987)  surface fracturing  first  location  and  often a  and s p a l l i n g  (figure  o f f r a c t u r e development r e s u l t of  lack of  3a) i s u s u a l l y  (Krauland and Soder  p i l l a r wall  confinement  original pillar surface  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 t o a l a c k o f confinement a t t h e p i l l a r w a l l s ( a f t e r Brady and Brown 1985). -soft partings  - i n t e r n a l splitting  FIGURE 3b. I n t e r n a l s p l i t t i n g and a x i a l c r a c k i n g o f a p i l l a r due t o deformable p i l l a r l a y e r s o r the p r o p a g a t i o n o f p a r a l l e l w a l l f r a c t u r e s ( a f t e r Brady and Brown 1 9 8 5 ) .  FIGURE 3c. Diagonal c r u s h i n g f r a c t u r e s may occur i n c o n f i n e d o r massive p i l l a r s ( a f t e r Brady and Brown 1985)  17 ( F a i r h u r s t and Cook 1966). ii)  internal axial  highly wall  deformable  rock  cracking  layers  (Brady  ( f i g u r e 3b) may be caused by  between  and Brown  the p i l l a r  1985) o r may  and t h e  adjacent  be p a r a l l e l  surface  f r a c t u r e s t h a t propagate o r develop i n t h e c e n t r e (Agapito  1974).  iii)  diagonal  in confined  2.1.2  of the p i l l a r  crushing  f r a c t u r e s ( f i g u r e 3c) a r e o f t e n found  o r massive p i l l a r s  (Coates 1981).  P i l l a r Load-deformation Curve P i l l a r l o a d i n g can be h y p o t h e t i c a l l y d e s c r i b e d u s i n g a l o a d -  deformation is p  ( s t r e s s - s t r a i n ) curve  loaded,  max'  t  n  i t compresses a c c o r d i n g maximum  e  Beyond t h i s  point,  pillar  point  "...  of f a i l u r e  load.  capacity  bearing  This  At a load  i s reached.  constant  will  Bieniawski  will  be taken as  (1987)  states,  i s a s t a t e a t which t h e r o c k specimen  changes from a g r a d u a l l y  to a  OA.  capacity  peak l o a d  in a pillar.  the ultimate strength  or t h e p i l l a r  load  t o the l i n e  As a p i l l a r  p o s t - f a i l u r e deformation o f t h e p i l l a r  occur but a t a reduced the  (see f i g u r e 4) .  or gradually  increasing decreasing  load-bearing load-bearing  capacity." Determining t h e a c t u a l load-deformation c h a r a c t e r i s t i c s o f a hard  r o c k mine p i l l a r  rock l a b o r a t o r y small  i n situ  Bieniawski  and  i s not p o s s i b l e .  specimens a r e e a s i l y coal  pillars  Curves f o r s m a l l  determined  have been  Van Heerden 1975), but  developed  hard  and curves f o r (Wagner 1974;  i t i s not e x p e r i m e n t a l l y  18  FIGURE 4 . A h y p o t h e t i c a l load-deformation curve can be used to d e s c r i b e 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 o f 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 l o a d i s reached ( P )• Pillar deformation c o n t i n u e s (along l i n e AB), but w i t h a d e c r e a s i n g l o a d b e a r i n g c a p a c i t y ( a f t e r S t a r f i e l d and F a i r h u r s t 1968). m a x  19 practical  t o conduct load-deformation t e s t s on  jointed  rock  deformation concept, and  (Brady  curve  i t is a  1977).  of  a hard  pillar does  rock  load bearing not  Agapito  (1974),  the  load-  a theoretical pillar  failure  capacity.  Capacity  capacity.  study  main reason f o r l o s s of  However, the  signify  in his  as  describe  f r a c t u r i n g i s the  necessarily  leaves  rock mine p i l l a r  load bearing  Loss o f Load Bearing Ultimately,  this  convenient method t o  the l o s s o f p i l l a r  2.1.3  While  l a r g e samples of  that of  the  onset of f r a c t u r i n g pillar  o i l shale  has  pillars,  failed.  found  that  f r a c t u r i n g s t a r t e d as minor s p a l l i n g i n the p i l l a r p e r i m e t e r occurred  a t s t r e s s l e v e l s w e l l below the u l t i m a t e  of a p i l l a r . outer  He  shell  of  a l s o noted t h a t as the  concentrations  built  monitored  in  the  pillar, up  situ  in  stress  capacity  f r a c t u r i n g occurred  monitoring the  load  pillar  showed core.  in  that  more  the  stress  Wagner  distribution in  and  (1974)  than  30  underground c o a l p i l l a r s u s i n g a s e r i e s of h y d r a u l i c j a c k s .  He  found  of  the  that  at  pillar  central  carried  core  the  load  the  pillar  of the  bearing and  by the p i l l a r After surface  several  stages  of  relatively pillar  capacity  compression, little  stress  ( f i g u r e 5) . of  a pillar  the  He  perimeter  compared  to  noted t h a t most  i s found  i n the  i s l a r g e l y dependent on the confinement  core  the of of  provided  shell.  failure  of  fracturing),  the  pillar  (due  to  serious  internal  Wagner (1974) found t h a t a c o n f i n e d  and  pillar  Pillar compression (mm)  2  FIGURE 5 . Wagner (1974) d i d a s e r i e s of i n s i t u l o a d deformation t e s t s on coal p i l l a r s using hydraulic jacks. For t h i s case, 2 5 jacks were put i n a 5X5 pattern i n a square p i l l a r . The graph on the top shows the l o a d deformation c h a r a c t e r i s t i c s o f 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 o f the 25 jacks a t four stages of p i l l a r compression. The diagrams show that with i n c r e a s i n g compression and i n c r e a s i n g average p i l l a r s t r e s s , the core of the p i l l a r c a r r i e s an i n c r e a s i n g percentage of the load, while the unconfined periphery of the p i l l a r c a r r i e s l e s s load. Diagram four shows that the p i l l a r core c a r r i e s a s i g n i f i c a n t load despite the f a c t that the p i l l a r i s l o s i n g i t s o v e r a l l load bearing capacity (redrawn from Wagner 1974).  core  had  Soder post  a  considerable  (1987) wrote failure  slenderness also  range of of  the  supported  demonstrated  is  bearing  pillar  the  that  loading  and  the  laboratory  if  the  depends l a r g e l y upon  the  presence of  t e s t i n g of  confining  capacity  i n open  will  peel  fill.  rock  and  This  is  specimens  in  Fairhurst  pressure  on  a  capacity  on  the p o s t  detached  failure  prevent  from  backfill,  pillar  starts,  of  walls  the  the can  fractured  confinement  the  leaving  p o s s i b l e to provide has  considerable core had  fractured  pillar.  installation  and  of  the  seen  open  wall  be  very  wall  pillar  These  of  material  methods  artificial  stopes  full  of  broken  some confinement t o the  several  load bearing  examples o f capacity.  failed  by b a c k f i l l  from the p i l l a r  walls.  before  i t had  large.  core,  and  There  are  becoming  the  such ore  core.  material  from  include  support  pillars  pillar  use  as as  long  rib pillars  In t h e s e cases,  the o p p o r t u n i t y  with  the  of  cable  p i l l a r walls.  remained c o n f i n e d because the f r a c t u r e d p i l l a r  confined  is  failure  i n open stope r i b  confinement  stope mining  o f f , preventing  to  (1968)  sample  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 .  methods  and  in  Starfield  dependent  progressive  finally  load  Krauland  c a p a c i t y i s g r e a t l y enhanced (see f i g u r e 6).  Once  was  of  machines.  highly  However,  author  loss  l o s s of l o a d b e a r i n g  also  bolts,  capacity.  the peak l o a d c a p a c i t y i n c r e a s e s and  load bearing The  bearing  pillars  by  "stiff-testing"  increased,  that  load  as The a  pillar  material t o slough  22  FIGURE 6. The s t r e s s - s t r a i n c u r v e s f o r l a b o r a t o r y specimens l o a d e d under i n c r e a s i n g c o n f i n i n g pressures show an i n c r e a s e i n peak l o a d and an i n c r e a s e i n t h e post-peak l o a d bearing c a p a c i t y ( a f t e r S t a r f i e l d and F a i r h u r s t 1968) .  23 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 Stope P i l l a r  Stability  Based on t h e f a i l u r e c h a r a c t e r i s t i c s d e s c r i b e d are  several variables that  rib pillars. potential  2.2.1  of p i l l a r s ,  Strength  fracturing playing  i s an important  most common index is  the  uniaxial  strength  standardized  diameter  conditions.  sample core).  found  i n a report  in pillar  compressive  (UCS) drill  i s the  core  strength.  The  o f d i f f e r e n t rock  test.  The  maximum  load  can s u s t a i n  under  uniaxial that  a  uniaxial  The UCS i s v a r i a b l e upon specimen s i z e , so  diameter  drill  factor  f o r comparing t h e s t r e n g t h  compressive  the  a large r o l e i n the s t a b i l i t y  the resistance of the p i l l a r material t o f r a c t u r i n g  crushing  loading  i n t h e d e s i g n of  influence.  I n t a c t Rock  types  there  T h i s s e c t i o n w i l l d e s c r i b e t h e v a r i a b l e s and t h e i r  With r o c k  and  c o u l d be important  above,  i s standardized  Further  information  t o about  54 mm  (NX s i z e  about t h e u n i a x i a l t e s t can be  by an I n t e r n a t i o n a l  Commission  on standard-  i z a t i o n o f l a b o r a t o r y t e s t s (ISRM Commission 1979).  2.2.2  Pillar Pillar  fracturing pillar  may  Load  load  i s a primary f a c t o r i n p i l l a r deformation,  and p i l l a r have  a  failure.  to  determine  stress  The d i s t r i b u t i o n o f s t r e s s i n a  significant  s t a b i l i t y of the p i l l a r .  rock  effect  on t h e performance and  However, t h e r e i s no c o n c l u s i v e method  in a pillar  and t h e r e  i s no s i n g l e  value  24 that  can  used  to  describe  state  of  stress  the  complete l o a d i n g  condition  of  a  pillar. The  the  stress  a p p l i e d t o the p i l l a r as w e l l as the l o c a t i o n i n s i d e the  pillar.  The  stress  field and  and  applied the  to  a  pillar  a p i l l a r varies  s i z e and  other p i l l a r s .  in  The  stress  p r o x i m i t y of e x c a v a t i o n s and points  stress  in  kept  a  in  pillar  on  upon  the  pre-mining  stress  l o c a t i o n of stopes, underground workings i n s i d e the  upon areas of weakness such as  these  varies  the  mind,  with  geological  i s dependent  discontinuities,  f r a c t u r i n g i n the p i l l a r .  determining  a  pillar  high  degree  the  the With  distribution  of  precision  to  find  of  is  not  possible. For  this  represent  the  thesis,  it  load  a  on  average  stress  height  centerline,  techniques.  The  normal s t r e s s e s first  found  necessary  pillar.  The  several  i s that  This  using  was  along  a  value  taken  the  numerical  i s frequently  to  as  pillar  t h i s l o c a t i o n has  i n the p i l l a r , and  area of f a i l u r e .  load  points  determined  reason  w i l l be d i s c u s s e d  2.2.3  at  was  the mid-  modelling the  highest  observed as  c h o i c e of s t r e s s a n a l y s i s  the  location  i n more d e t a i l i n Chapter 5.2.2.  P i l l a r Shape Chapter  stability  2.1.3  and  the  described load  the  bearing  role  of  confinement  capacity.  Pillar  huge i n f l u e n c e on confinement o f the p i l l a r c o r e . - the  load-convergence  c h a r a c t e r i s t i c s of  in  pillar  shape has  a  It affects:  pillars  at  failure  25 (Hudson e t a l . 1971; S t a r f i e l d and F a i r h u r s t 1968), - t h e p o s t - f a i l u r e deformation modulus o f p i l l a r s al.  (Hudson e t  1971; Wagner 1974),  - the s t r e s s 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 F a i r h u r s t  1968; Wagner 1974), - and  the  effect  of geological  p i l l a r s t i f f n e s s and f a i l u r e This  confirms  pillar  2.2.4  pillar  and  fracturing  on  significant variable  in  (Sarkka 1984).  shape  as a  stability.  Structural Discontinuities i n P i l l a r s  The  effect  upon whether as  that  structure  of g e o l o g i c a l  the structure  f a u l t s and  structure  involves  on r i b p i l l a r s  depends  major d i s c o n t i n u i t i e s such  shear zones o r minor d i s c o n t i n u i t i e s l i k e  joint  sets.  P i l l a r s i n t e r s e c t e d by a major s t r u c t u r e must be analyzed  based  on  strength  the  o f the major  stability. structure  However,  structure i n open  The  will  stoping,  orientation  play  and  a dominant  shear  role in  i n t e r s e c t i o n o f a major  i s not a common problem and d e s i g n o f such p i l l a r s i s  an e x c e p t i o n rib  specific situation.  rather  pillars  are  than a r e g u l a r located  to  occurrence.  avoid  When p o s s i b l e ,  intersection  by  major  geological discontinuities. Less  prominent d i s c o n t i n u i t i e s such as  fracturing, The  a r e a much more common problem  influence  o f minor  upon t h e o r i e n t a t i o n ,  j o i n t i n g and  local  in pillar  design.  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  continuity,  frequency and shear  strength  of  the  structures.  At  the  minor d i s c o n t i n u i t i e s on triaxial  state  joints.  of  Archibald  stability  i s small  e f f e c t of the  confinement prevents rock movement a l o n g  the  Geological  pillar  the  because  d i s c o n t i n u i t i e s have  e f f e c t on i n s t a b i l i t y and  p i l l a r c e n t r a l core,  i n unconfined r e g i o n s  (1981),  Page  and  a  more s i g n i f i c a n t  of p i l l a r s .  Brennan  (1981),  Allcott 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  pillar  walls.  confinement influence  the  of  stability analysis  of  One  expect  to  find  rock near p i l l a r w a l l s .  structure  analyses. is  would  An  described  by  is  best  Potvin  method  et  al.  or  no  Consequently,  accounted  excellent  little  for  for  using  wall  (1988a).  the wall  stability The  method  q u a n t i f i e s the i n f l u e n c e of g e o l o g i c a l s t r u c t u r e , mining induced stress,  and  surface  of  pillar  dimensions t o  open stope. the  predict  When the  the  of  analysis predicts a  e f f e c t o f minor s t r u c t u r e  r i b p i l l a r s w i l l be  stability  on  the  each  stable  stability  of  separated  by  small.  E f f e c t o f P i l l a r Volume Pillars  n a t u r a l and pillar  the  are  made  of  blocks  of  intact  mining induced d i s c o n t i n u i t i e s .  volume  variables: and  an  wall,  unfractured  2.2.5  stope  the  on  stability  is  volume e f f e c t on  influence  of  the  number  really the of  rock So the  a  strength  influence  function of  of  of two  i n t a c t rock,  s t r u c t u r a l defects  in  the  pillar. L a b o r a t o r y compressive t e s t i n g o f s m a l l samples has  shown an  i n f l u e n c e o f specimen s i z e on t h e compressive s t r e n g t h o f i n t a c t rock  (see f i g u r e  7) .  However,  testing  of  large  intact  rock  specimens has found t h a t above a " c r i t i c a l " volume, t h e s t r e n g t h does not decrease s i g n i f i c a n t l y asymptotic Herget  (see f i g u r e 8 ) .  T h i s concept of  specimen s t r e n g t h i s r e p o r t e d by B i e n i a w s k i  e t a l . (1984),  and P r a t t  e t a l . (1972).  (1975) ,  These authors  found t h e c r i t i c a l volume t o be l e s s than one c u b i c metre. the volume larger  o f b l o c k s i n open stope p i l l a r s  than  this  critical  volume,  there  With  u s u a l l y b e i n g much is a  very  limited  i n f l u e n c e o f the volume e f f e c t o f i n t a c t rock. The depend  number upon  of s t r u c t u r a l  the volume  discontinuities  o f the p i l l a r .  in a pillar  Hoek and Brown  will (1980)  suggest t h a t t h i s i n f l u e n c e can be q u a n t i f i e d through t h e use o f rock  mass  classification  Stephansson  (1985),  correction pillar  methods.  and  factors  to  other  account  authors  with  open  stope  and  Both  Agapito  have  for pillar  strength determination.  investigated  Hardy  of  rib pillar  (1977),  suggested  volume these case  be  that  used  in  ideas w i l l  be  histories  in  Chapter 6.1.3.  2.2.6 E f f e c t o f B a c k f i l l The mining  use  fill  methods.  (Campbell use  of  1987)  cemented  purpose o f  A  survey  found t h a t  fill  fill  i s very  is  to  important  by  the O n t a r i o M i n i s t r y  almost  stope  o f Labour  a l l O n t a r i o open stope mines  aid in pillar  used t o  i n c u r r e n t open  provide  recovery. overall  mine  The  general  stability,  Sp*>ol Book  T—t*d by  Harbta Umastona Granlta Basalt Basalt-andaslta Cabbro ftarbla Norita Cranlta Quartz d l o r l t a  O O V A  ( e/«cS0) . o  H09I'" KolfMn " Bureharti at a l ' " Kolfa»n'" Nalakldla " llnlckaya " llnickaya " Blantawtkl'* Hosklns t H o r l n o P r a t t at a l ' * ' 1  lava  1  1  1  7  1 7 0  (50/d) -" 0  0.3  150  Specifwn  dlamtar  200  250  d  FIGURE 7. There i s a v e r y l a r g e i n f l u e n c e of specimen s i z e on t h e s t r e n g t h o f i n t a c t rock, f o r small specimen diameters ( a f t e r Hoek and Brown 1980). 150 100 70 50  Ix , • Iron ore  r  *  Johns (1966)  Oiorite  ° Prott ^<J/(I972)  -••  Bieniowski (1967)  c 05  I IS 2 Specimen side length, m  _L 25  FIGURE 8. S t r e n g t h t e s t i n g o f samples of i n c r e a s i n g specimen l e n g t h shows a d e c r e a s i n g i n f l u e n c e o f s i z e . Beyond a " c r i t i c a l " l e n g t h , t h e r e i s no s i g n i f i c a n t decrease i n specimen s t r e n g t h . T h i s c r i t i c a l s i z e i s about 1 metre ( a f t e r B i e n i a w s k i and Van Heerden 1975),  especially spans  i n stope  to  stable  hanging  walls  dimensions  and  and f o o t w a l l s , to  permit  a  high  e x t r a c t i o n o f t h e orebody w i t h p o t e n t i a l l y minimal The Singh  role  of f i l l  in pillar  (1976) f i n d s t h a t  - provides l a t e r a l prevent  failure  by  limiting ratio  of  dilution.  i s much l e s s  dramatic.  fill:  support t o p i l l a r s t o i n h i b i t s p a l l i n g and  collapse,  - a c t s as a r e t a i n i n g media t o c o n t a i n f r a c t u r e d rock, thereby r e t a r d i n g t h e development o f f a i l u r e i n s u r r o u n d i n g rock, - and reduces  energy  r e l e a s e r a t e s a l l o w i n g rock t o f a i l  in a  n o n - v i o l e n t manner. None o f these rock  fracturing  2.1.1. rock  effects  Fill  Thomas  of  failure  has a l a r g e described  influence above  does p r o v i d e r e s t r a i n t and confinement  t o prevent  enhances  mode  of f i l l i n g  sloughing of p i l l a r  the p o s t - f a i l u r e  load  in  on the Chapter  to fractured  m a t e r i a l and consequently  bearing  capacity  of  pillars.  (1979) supports Singh's comments by w r i t i n g t h a t f i l l i s  not l i k e l y t o p r o v i d e stope w a l l support b e f o r e u n r e a l i s t i c  fill  deformation  finds  that  i t provides  rock  fill  (approximately  i s most  confinement  beneficial  to  mining  when  c a u s i n g t h e rock mass t o support  Consolidated effective  20%) has o c c u r r e d .  at  and  aiding  cemented  fills  i n underground  However, t h e main purpose  itself.  have  been  stability  of consolidated f i l l s  s u p p o r t i n g and f r e e - s t a n d i n g d u r i n g p i l l a r  He  found  (Bharti  more 1987) .  i s t o be s e l f -  recovery operations.  30  f a i l u r e due t o rock f r a c t u r i n g . pillars  to  maintain  capacity.  This  their  aids  I t does g i v e support t o f a i l e d  integrity  i n o v e r a l l mine  and  some  stability  load  bearing  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 o f B l a s t i n g Blasting  practices  mining method. efficient effects  a r e v e r y important i n t h e success o f any  Poor b l a s t i n g  design  into  o f poor  a very  blasting  practices  can t u r n  a s t a b l e and  design.  Some o f the  inefficient  i n open  stope  mining  fragmentation, overbreak beyond stope l i m i t s , post-blast of  blast  include:  poor  need f o r frequent  clean-up and development r e h a b i l i t a t i o n , development induced  disturbance  fractures  i n t h e rock  and i n s t a b i l i t y  mass,  i n stope w a l l s  and rock  and p i l l a r s  mass  due t o  excessive vibrations. Quantifying difficult. the  poor  are highly  blasting the e f f e c t  referred  t o as c o n t r o l weight  blasting, using  explosives;  Although  the s i g n i f i c a n c e  The  These  best  i s very  solution  practices  and i n c l u d e : charge  in  used t o  are often  minimizing the  decking,  decoupling,  u s i n g e f f i c i e n t h o l e l o c a t i o n and  b l a s t sequencing; and b l a s t i n g t o a f r e e  great  method  some o f t h e p r a c t i c e s  of blasting.  per delay;  and/or low d e n s i t y  varied.  i s to l i s t  minimize  charge  i n an e m p i r i c a l  There i s no c l e a r d e f i n i t i o n o f poor b l a s t i n g , and  consequences  describing  blasting  face.  of b l a s t i n g  practices  i n mining, t h e r e a r e no c r i t e r i o n t o q u a n t i f y  i s very  the e f f e c t s  31 of  blasting  discussed  2.3  on mining.  Consequently,  blasting  Chapter Summary failure  o f open stope r i b p i l l a r s  t o observe due t o l a c k o f v i s u a l access. pillar  distress  directly  have  associated  Fracturing generally or  not be  as a d e s i g n v a r i a b l e i n t h i s t h e s i s .  Progressive  of  will  develops  in  progresses. bearing  with  documented.  rock  the  Fractured  pillar rock  These  fracturing  s t a r t s a t the p i l l a r core  as  loses  some  indirect  in  signs  signs  the  are  pillar.  walls  and propagates  pillar  deterioration  or a l l of i t s load  c a p a c i t y , depending on t h e confinement o f t h e m a t e r i a l .  Pillar changes  been  Several  i s difficult  failure  from  constant  having  an i n c r e a s i n g  or decreasing  hypothetically curve.  can be d e s c r i b e d  be  load  described  The degree  as t h e s t a t e when a p i l l a r load  bearing using  o f confinement  bearing  capacity  capacity.  a  pillar  to a  F a i l u r e can  load-deformation  of a p i l l a r  has a  large  i n f l u e n c e on t h e shape o f t h a t curve. Open  stope  conditions capacity.  the  that These  confinement. factors,  rib pillar influence conditions  The c o n d i t i o n s  design pillar  should failure  are rock  load,  t h e shape  and  based  on t h e  load  bearing  fracturing  may be i n f l u e n c e d  i n c l u d i n g : the i n t a c t strength  pillar  be  and  by a number o f  of the p i l l a r  of the p i l l a r ,  pillar  material,  t h e presence  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 t h e volume o f t h e p i l l a r .  of  32  CHAPTER 3 REVIEW OF PILLAR DESIGN METHODS  There design: design  a r e two g e n e r a l  empirical i s based  approaches  methods,  t o current  and numerical  on o b s e r v a t i o n  r i b pillar  methods.  o f case h i s t o r i e s and  experience i n s i m i l a r geotechnical  conditions.  there  approaches.  i s not  a  clear  design  information  i s used i n numerical  applied the  design  properties.  between  t h e two  Some numerical procedures a r e o c c a s i o n a l l y used i n  empirical  This  division  previous  Numerical  i s l a r g e l y based on measured parameters and m a t e r i a l However,  Empirical  chapter t o hard  background  discussion  and  will  some  discuss  rock p i l l a r fundamentals  of their  experience  and  observational  techniques. t h e two approaches  design. i n each  respective  It will method,  advantages,  as they a r e  briefly and g i v e  describe a  short  disadvantages and  limitations.  3.1 E m p i r i c a l Design Methods Empirical they c o n s i d e r  design  methods a r e c h a r a c t e r i z e d by t h e f a c t  a p i l l a r as one u n i t .  no v a r i a t i o n i n s t a b i l i t y  within  I t i s assumed t h a t t h e r e i s a pillar.  The s t a b i l i t y  t h a t p i l l a r i s i n t e r p r e t e d based on t h r e e v a r i a b l e s : i) p i l l a r ii) pillar iii)  load, strength,  and s a f e t y f a c t o r .  that  of  33 Methods are  of  c a l c u l a t i n g or  based  upon  quantifying  experience. empirical and  underground  Typically,  rules  an  d e t e r m i n i n g each  of  thumb  appropriate  pillar or  safety  safety  S.F. It  factor  is  are  i s defined  l o a d and s t r e n g t h  calibrated  instance,  a  pillar  inaccuracy i n the  in  an  entry  In  determination  the  The  to  procedures factor degree  safety  case  to  use for  would of  factor  the be  the  strength  design of  instability  method  would  i n a non-entry  same  designed  parameters.  mining  and  load  both s i t u a t i o n s , in  the  acceptable  entry  is  be  a  method  less.  The  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  the  d e s i g n method. following  developed will  order  safety  specific  with  input  mining  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  of  strength  mining conditions,  and t o account f o r t h e  choice  Pillar  using  d e t e r m i n a t i o n methods  -  because  determined  as:  t o make a d e s i g n more c o n s e r v a t i v e  higher  past  experiments.  -  method.  and  purposes:  t o expand the different  For  observations  load  factor  parameters  = p i l l a r strength p i l l a r load  has t h r e e b a s i c -  these  numerical t o o l s .  h i s t o r i e s and/or laboratory The  of  list  procedures. techniques  for  sub-sections  calculating pillar  the  safety  Because used t o  factors there  determine  are  will  summarize  strength suggested a  pillar  large  and  the  techniques  pillar  for number  load  these of  l o a d and s t r e n g t h ,  and  design  different emphasis  will  be p l a c e d on those methods used  more  complete  discussion  documented by P o t v i n  3.1.1 P i l l a r There  of  f o r hard  the empirical  rock d e s i g n .  design  A  methods i s  (1985).  S t r e n g t h Determination  a r e many f a c t o r s t h a t may  mine p i l l a r .  These f a c t o r s  i n f l u e n c e t h e s t r e n g t h of a  include:  - s i z e and shape o f t h e p i l l a r , - volume o f t h e p i l l a r , - resistance of i n t a c t p i l l a r material to crushing, - presence o f d i s c o n t i n u i t i e s , - s t r e n g t h and o r i e n t a t i o n o f t h e 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 s t r e n g t h o f t h e p i l l a r  rock  mass, - and t h e presence o f groundwater. The  number  strength these  of p o t e n t i a l l y  very  difficult  variables  conditions.  are  For  estimated e m p i r i c a l l y .  to  not  such  significant determine  variables  analytically.  significant  situations,  makes  under pillar  The most commonly  pillar  Some of  selected strength  mining may  used e m p i r i c a l  be  pillar  s t r e n g t h methods i n hard rock mining a r e : - Salamon's formula, - Hedley's  formula,  - Obert and D u v a l l formula, - and t h e Hoek and Brown p i l l a r s t r e n g t h c u r v e s . The f i r s t t h r e e o f these methods a r e v a r i a t i o n s o f t h e e m p i r i c a l  strength  formulas  Consequently, is  helpful,  pillar  developed  f o r underground  coal  mines.  a b r i e f d i s c u s s i o n of the empirical coal although  they  see v e r y  limited  formulas  use i n hard  rock  design.  3.1.1.1 E m p i r i c a l S t r e n g t h Formulas A  major  area  of  pillar  underground c o a l mining. full the  size  pillar  results  from  design  research  A b a s i c premise  been  in  o f t h i s work was t h a t  s t r e n g t h c o u l d be determined laboratory testing  has  by  of coal  extrapolating  specimens.  Two  forms o f t h e e m p i r i c a l s t r e n g t h equation were developed: - the s i z e e f f e c t  formula,  - and t h e shape e f f e c t  A)  formula.  The s i z e e f f e c t formula i s d e f i n e d as: Op = K * (w /h ) a  a f b  b  where: <Tp = p i l l a r s t r e n g t h (psi) , K = u n i a x i a l compressive pillar w = pillar  s t r e n g t h o f one c u b i c f o o t o f  material, width,  h = p i l l a r height, a,b = unequal This  formula  dependent  on  presence  of  empirically defined constants.  i s based the s i z e  on  the  fact  that  o f t h e sample.  discontinuities  (such  as  bedding, b l a s t f r a c t u r e s , and m i n e r a l o g y ) .  rock  This  strength i s  i s due  joints,  t o the  foliations,  As r o c k samples o f a  constant  shape  decreases. different  increase  This size weighting  e f f e c t formula. different  i n size,  effect  t h e s t r e n g t h o f t h e sample  i s taken  into  t o the c o e f f i c i e n t s  account  by g i v i n g  a  f o r w and h i n a shape  T a b l e 1 g i v e s t h e c o n s t a n t s a and b proposed by  authors.  Constants a and b used i n t h e s i z e e f f e c t ap = K * w /  formula:  a  SOURCE  a  b  S t r e a t (1954) Holland-Gaddy (1962) Greenwald e t a l . (1939) Hedley and Grant (1972) Salamon and Munro (1967) B i e n i a w s k i (1968)  0.5 0.5 0.5 0.5 0.46 0.16  1.00 1.00 0.833 0.75 0.66 0.55  T a b l e 1 ( a f t e r Babcock, Morgan and Haramy 1981).  B)  The shape e f f e c t formula, which i s d e f i n e d a s : a  P  = K * [A + B * (w/h)]  a  B  = K * (w /h )  or a  a = b  b  where: ap = p i l l a r s t r e n g t h K = uniaxial  compressive  p i l l a r material, w = pillar  (psi),  width,  h = p i l l a r height,  s t r e n g t h o f one c u b i c f o o t of  A,B,a,b = e m p i r i c a l l y d e f i n e d c o n s t a n t s . The  shape e f f e c t  pillars  formula  of different  denotes a d i f f e r e n c e  i n strength f o r  shape but equal c r o s s - s e c t i o n a l a r e a .  The  g r e a t e r t h e p i l l a r width t o p i l l a r h e i g h t r a t i o , t h e g r e a t e r t h e pillar  strength.  A change i n mode o f f a i l u r e  cause o f t h e shape e f f e c t tend t o f a i l While  along s t r u c t u r a l  f o r wide  crushing  on p i l l a r  pillars,  of the p i l l a r  c o n s t a n t s a,b,A,B proposed  strength.  discontinuities  failure  Tables  by d i f f e r e n t  Slender  t o be 2 and  pillars  caused  formula:  b  SOURCE  a  b  Zern (1926) Hazen and A r t i e r (1976) H o l l a n d (1956) Morrison e t a l .  0.5 0.5 0.5 0.5  0.5 0.5 0.5 0.5  T a b l e 2 ( a f t e r Babcock, Morgan and Haramy 1981).  Constants A and B used i n t h e shape e f f e c t Op = K * [ A + B * (w/h)] SOURCE  A  B  Bunting (1911) Obert e t a l . (1960) B i e n i a w s k i (1968) Van Heerden (1973) Sorensen and P a r i s e a u (1978)  0.700 0.778 0.556 0.704 0.693  0.300 0.222 0.444 0.296 0.307  by  3 g i v e the  authors.  Constants a and b used i n t h e shape e f f e c t oP = K * w / h a  apparent  i n t h e rock mass.  i s likely  material.  i s one  formula: W/h 0.5 0.5 1.0 1.14 0.5  -  1.0 2.0 3.1 3.4 2.0  T a b l e 3 ( a f t e r Babcock, Morgan and Haramy 1981).  38  The  constants  were based scale  on  pillar  pillars.  design  and  coefficients case  Three  s t u d i e s and  i n each  histories  of  the  surveys  and  of  formulas  laboratory testing  most prominent  provided  these  empirical  formulas  of  pillar  commonly used  in  hard r o c k 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 . 3.1.1.2 Salamon s 1  Formula  In  1967,  Salamon  square  coal  pillars  investigated  98  published a in  survey  South  s t a b l e and  African  of  stable  and  failed  The  study  mines.  27 c o l l a p s e d p i l l a r  areas.  Using a  s i z e e f f e c t formula, and assuming the mean s a f e t y f a c t o r f o r a l l the  failed  cases  calibrated.  was  1.0,  the  coefficients  K,  a  and  b  were  T h i s gave the formula:  strength = K * w 0  46  /  h 0  6 6  where: strength = p i l l a r strength (psi), K = 1320  = s t r e n g t h of one c u b i c f o o t o f p i l l a r material,  w = p i l l a r width  (feet),  h = p i l l a r height The  complete  figure  database  9) .  strength  To  safety  factor  stable  pillars  felt  that  of  this  i s commonly d i s p l a y e d i n a histogram  determine  formula  (feet).  a  suitable  i n e n t r y mining the  to get safety  most an  factor  for  methods, Salamon averaged  dense  average  factor  safety  was  concentration of of  1.57  (see  adequately  50%  figure  (see this the  of  the  9).  He  conservative to  I  2  1  2  1  1  1  1  •  «>  •*  e»  '  o  3DN3aarO00 JO ADN3nD3MJ  FIGURE 9. Histogram o f the s a f e t y f a c t o r s f o r s t a b l e 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 c o a l mining. The range of s a f e t y f a c t o r s f o r the most dense c o n c e n t r a t i o n o f 50% of the s t a b l e cases i s between 1.31 and 1.88. Salamon chose the mean o f t h i s range, 1.57, as adequately c o n s e r v a t i v e t o d e s i g n s t a b l e , permanent p i l l a r s i n room and p i l l a r c o a l mining ( a f t e r 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 c o a l mines. D e s p i t e the in  bord  and  fact  pillar  that  the study i s based  coal  mining  in  South  on square Africa,  pillars  Salamon's  formula has been used f o r the d e s i g n of hard r o c k open stope r i b pillars.  The  f a c t o r t o account  f o r the s t r e n g t h of the  pillar  m a t e r i a l i s a d j u s t e d t o the s t r e n g t h of one c u b i c f o o t o f i n t a c t hard rock, but the c o e f f i c i e n t s and s a f e t y f a c t o r used are those o r i g i n a l l y proposed by Salamon. 3.1.1.3 Hedley's Hedley based Lake. to  on  and data  Formula  Grant  (1972) proposed  from hard  a pillar  rock room and  pillar  s t r e n g t h formula mining  at  Elliot  They e m p i r i c a l l y 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  t h a t proposed by Salamon ( d i s c u s s e d above).  The  formula  was  d e f i n e d as: Qu = k * w 0  5  /  h 0  7 5  where: Qu = p i l l a r s t r e n g t h ( p s i ) , k = 26,000 = s t r e n g t h of one c u b i c f o o t o f p i l l a r material w = p i l l a r width  (feet),  h = p i l l a r height The  data  pillars,  base  to  develop  2 partially  application  of t h e i r  (psi),  (feet). this  formula  f a i l e d p i l l a r s and pillar  consisted  of  23  stable  3 crushed p i l l a r s .  s t r e n g t h formula, Hedley  and  For Grant  suggested t h a t p i l l a r s w i t h a s a f e t y f a c t o r g r e a t e r than 1.5 stable  and  pillars  with a safety  f a c t o r near  1.0  are  are  crushed.  41 These  safety  factors  are  based  g r a p h i c a l p l o t o f the data base This and  strength  pillar  (1984),  formula has  mining,  and  through  Townsend  on  interpretation  of  the  a  (see f i g u r e 10). been  studies  (1982).  further by  confirmed  Von  I t i s the  f o r room  Kimmelmann  only p i l l a r  et a l . strength  formula developed based on hard rock mining case h i s t o r i e s .  So  although no p u b l i s h e d study has confirmed i t s use f o r open stope pillars,  i t i s w i d e l y used i n open stope p i l l a r d e s i g n .  3.1.1.4 Obert and D u v a l l Shape E f f e c t Obert  et  al.  (1946)  performed  Formula a  series  of  compressive  s t r e n g t h t e s t s on specimen c o a l p i l l a r s w i t h v a r i o u s shapes. was  determined  the  empirical  t h a t the shape e f f e c t o f p i l l a r s t r e n g t h  It  follows  relationship:  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 s t r e n g t h o f a c u b i c a l 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 i n c l u d e any  effect  on  strength,,  but  f a c t o r t o account  instead  suggested  a  f o r the  safety  size  factor  between 2 and 4 be used i n p i l l a r d e s i g n . In to  hard rock p i l l a r d e s i g n , t h i s formula has been suggested  account  Soder  1987;  f o r shape Hedley  et  effect  by  a l . 1979;  several Herget  authors  (Krauland  e t a l . 1984).  a u t h o r s used a d d i t i o n a l methods t o account f o r p i l l a r  and  These  strength  rsxi ss*J)S  JO/IM  p>)Dwnsj}  FIGURE 10. The estimated s t r e s s and strength f o r case 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 . Safety f a c t o r l i n e s have been drawn on the graph. The chart shows that a l l the case h i s t o r i e s with a s a f e t y f a c t o r above 1.5 are s t a b l e ( a f t e r Hedley and Grant 1972) .  43 s i z e dependence. 3.1.1.5 Hoek and Brown P i l l a r S t r e n g t h Hoek and Brown  (1980) proposed  estimation of p i l l a r developed failed of  based  rock  Curves  a series  o f curves  s t r e n g t h (see f i g u r e 11).  f o r the  The curves were  on numerical m o d e l l i n g and t h e d i s t r i b u t i o n o f  inside p i l l a r s  rock mass q u a l i t i e s ,  of d i f f e r e n t  shapes and f o r a range  using the empirical  r o c k mass  failure  criteria: a  p  = a2 + ( m * a  a  p  = average p i l l a r s t r e n g t h ,  a  3  = minimum p r i n c i p a l  c  * a3 + s * a  2 c  )^  where:  Oq  stress,  = u n i a x i a l compressive pillar  strength of the i n t a c t  material,  m & s = e m p i r i c a l c o n s t a n t s based on t h e r o c k mass q u a l i t y of the p i l l a r Hoek and Brown proposed a  pillar  pillar a  has f a i l e d  material.  these p i l l a r d e s i g n curves assuming t h a t  when t h e s t r e s s  a c r o s s t h e c e n t r e o f the  exceeds t h e s t r e n g t h o f t h e rock mass.  safety  factor  o f 1.0  or less  would  imply  They s t a t e d that  that  a pillar is  t h e o r e t i c a l l y u n s t a b l e and t h a t a s a f e t y f a c t o r i n excess o f 1.5 should  be  used  recommendations  do  for  permanent  not seem  t o be  pillars. confirmed  However, ' these by case  history  back-analysis. Each curve can be c o n s i d e r e d a p i l l a r a s p e c i f i c r o c k mass q u a l i t y .  failure criterion for  Hoek and Brown proposed  that the  Intact fine  samples  of  grained  crystalline  igneous rock  m - 17, * - 1  Very  good  quality  rock mas8 m • 8 . 5 , s - 0.1  Good quality m • 1.7,  Fair  rock s »  quality  mass  0.00k  rock  mass  m - 0.3^, s » 0.0001 Poor  quality  rock  mass  m - 0.09, s - 0.00001  1  2  Pi 1lar width/height  3 W /h p  FIGURE 11. Hoek and Brown (1980) proposed a s e r i e s p i l l a r s t r e n g t h 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 o f rock mass f a i l u r e i n a p i l l a r .  influence  of  quantified  pillar  volume  through  the  the  and  Consequently,  m  and  use  structural  of  rock  s constants  defects  mass  account  could  be  classifications. for p i l l a r  volume  and s t r u c t u r a l d e f e c t s because they have been r e l a t e d t o the most common rock mass c l a s s i f i c a t i o n methods, CSIR by (1973) and NGI  Page and  the  s t r e n g t h curves  however p r a c t i c a l Brennen  (1982) has  f a i r rock mass q u a l i t y  3.1.2  Pillar  Bieniawski  by Barton e t a l . (1974).  Originally, histories,  two  were not  application been  supported  by  Potvin  by  case  (1985)  s u c c e s s f u l f o r the  good  and and  curves.  Load  In underground mine d e s i g n , i t i s d i f f i c u l t t o determine the actual  load that w i l l  be  a c t i n g on  a pillar.  f a c t o r p i l l a r d e s i g n methods, two procedures The  first  simplified  method,  called  the  For most s a f e t y  are c u r r e n t l y used.  T r i b u t a r y Area  approach t o underground s t r e s s  Theory,  uses  redistribution.  a The  o t h e r method, g e n e r a l l y termed numerical m o d e l l i n g , i n v o l v e s the use  of  the  theory  redistribution. area t h e o r y ,  of  elasticity  to  determine  In c o n t r a s t t o the s i m p l i c i t y o f the  numerical  m o d e l l i n g r e q u i r e s the use  stress tributary  of a computer  due t o 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 p r o c e s s . 3.1.2.1 T r i b u t a r y Area The opened  Tributary there  i s an  Theory  Area  Theory  equal  r e g a r d l e s s of the s i z e and  and  assumes symmetric  that  when  stress  l o c a t i o n of the p i l l a r s  stopes  are  redistribution created.  It  is  o f t e n d e s c r i b e d u s i n g t h e analogy  obstructed continuous between flow  bridge  piers  (see f i g u r e  12) .  velocity  ( i e . between t h e s t o p e s ) .  ( s t r e s s ) between t h e p i e r s  The i n c r e a s e i n flow v e l o c i t y  the r a t i o  o f t h e width  This  the p i l l a r So  permit  a  causes the  ( i n the p i l l a r s )  to  i s g e n e r a l l y dependent  o f t h e stream  (width  area) t o t h e sum o f t h e d i s t a n c e s unobstructed of  To  stream  flow r a t e i n the stream, s t r e a m l i n e s a r e c o n c e n t r a t e d  the p i e r s  increase. on  by  o f a smooth f l o w i n g  o f t h e mining  by t h e p i e r s (sum  widths).  i n a rock  mechanics p e r s p e c t i v e , t h i s  describes  the  redistribution  of principal  The  average p i l l a r  l o a d thus depends on t h e r a t i o o f t h e t o t a l  area  extracted  to  the t o t a l  stress  theory  area  flowlines into  remaining  i n the  pillars.  pillar.  F i g u r e 13 shows t h e a p p l i c a t i o n o f t h e T r i b u t a r y Area Theory t o s e v e r a l types o f p i l l a r s Due  (including r i b p i l l a r s ) .  to the s i m p l i c i t y  fundamentally  of t h i s  influence stress  theory,  in pillars  some  factors  are ignored.  that These  factors are: - t h e number o f p i l l a r s the mining  i n t h e mining  block  (or t h e extent o f  area),  - t h e l o c a t i o n o f t h e p i l l a r i n t h e mining  block,  - t h e r e d i s t r i b u t i o n o f s t r e s s i n t o t h e abutments, - and t h e shape o f t h e p i l l a r .  A by  study  comparing  by Salamon  (1974) d e t a i l s  t h e average  stress  the f i r s t  for a  problem  t h r e e problems p r e d i c t e d by  47  FIGURE 12. The analogy o f s t r e a m l i n e s i n a smoothly f l o w i n g stream o b s t r u c t e d by b r i d g e p i e r s i s o f t e n used t o describe the concentration of s t r e s s i n p i l l a r s (after Hoek and Brown 1980).  Unit  length  £ I-  RIB PILLARS  - o  1  •  1  H  - Y z O + °/W ) W  B  :  •  I  J.  •  SQUARE P I L L A R S -  E3 0  p  - yz(\  -Pillar  ^  Li r i t i  U  + o/U ) w  :  p  Rock c o l u m n area  area  o / o  -  o  T  IRREGULAR P I L L A R S Rock c o l u m n RECTANGULAR P I L L A R S - 0 - Y z ( l + o / W ) ( l + o / L ) W  p  L  p  Pillar  area  area  p  FIGURE 13. The t r 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 t o several d i f f e r e n t p i l l a r l a y o u t s ( a f t e r Hoek and Brown 1980).  48 t r i b u t a r y area t o those p r e d i c t e d by an e l e c t r i c analogue model. The  s t r e s s i n square  eleven  square  pillars  investigated. tributary  The  area  (in  each  average  theory  component). tests.  room and p i l l a r panels of t h r e e , seven  Figure  is 14  horizontal  pillar  4 Q 3 3  shows  load  according  i s the  ( Q 3 3  the  results  were  to  pre-mining  analogue  the  stress  of  these  S t r e s s r e d i s t r i b u t i o n i n t o the abutments r e s u l t s i n the  analogue p r e d i c t e d s t r e s s always b e i n g lower area  direction)  and  predicted  pillars),  the  load. load  value of 4 Q .  the  predicted  panel by  widens  the  (larger  analogue  tributary number  approaches  of the  I t i s a l s o demonstrated by t h i s model t h a t the  3 3  location  As  than the  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  i n f l u e n c e o f the shape of a p i l l a r  investigation  of the T r i b u t a r y Area  boundary element m o d e l l i n g Figure  15  average effect  shows  pillar  that load  as  Theory and  of r i b p i l l a r s a  pillar  predicted  by  i s documented i n an two  dimensional  ( P o t v i n e t a l . 1987).  becomes  more  modelling  i s a l s o d i s c u s s e d by Salamon (1974) and  slender,  decreases.  This  i s attributed to  decreasing p i l l a r s t i f f n e s s with i n c r e a s i n g p i l l a r  slenderness.  In summary, the T r i b u t a r y Area Theory p r o v i d e s a v e r y solution  f o r determining  pillar  load.  s m a l l mining  Bieniawski  panel,  (1983)  or  i f the p i l l a r s  comments  that  quick  However, the accuracy  the method i s d i m i n i s h e d i f t h e r e are a s m a l l number o f a  the  in  are  of  pillars,  s l e n d e r i n shape.  coal  o v e r e s t i m a t i o n o f p i l l a r l o a d by t r i b u t a r y area may  mining,  the  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 s t r e s s caused by i n c r e a s i n g 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 s t r e s s , and Q i s the premining s t r e s s . The t r i a n g u l a r symbols correspond t o the t h r e e p i l l a r s i n panel ( a ) , the c i r c u l a r symbols correspond t o the seven p i l l a r s i n panel (b), and the diamond symbols correspond t o 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 i n f l u e n c e of the l o c a t i o n o f a p i l l a r and the number of p i l l a r s on the s t r e s s induced. 3 3  A 4.0. _  tributary area  FIGURE 15. A study u s i n g two dimensional boundary element n u m e r i c a l m o d e l l i n g shows t h e i n f l u e n c e o f p i l l a r shape and t h e number o f p i l l a r s on t h e average s t r e s s ( a f t e r P o t v i n e t a l . 1987).  as  40%,  while  Theory may  the  author  has  found  that  the  Tributary  Area  o v e r e s t i m a t e the l o a d i n open stope r i b p i l l a r s  much as 100%  by as  (Hudyma 1988b).  3.1.2.2 Numerical M o d e l l i n g Several the  types  calculation  different The  o f numerical of  pillar  load.  c h a r a c t e r i s t i c s and  models  applicable  d i s c u s s e d i n chapter When used  models are  to  Each  hard  these  models  has  rock  pillar  design  will  be  3.2.  i n empirical  - a n a l y z e complex mining f o r any  of  to a i d i n  a d i f f e r e n t means o f c a l c u l a t i o n .  d e s i g n methods, the c a p a b i l i t i e s  numerical models i n c l u d e the a b i l i t y  - account  available  of  to:  geometries,  number  of  pillars  and  any  size  of  mining  seam, - r e c o g n i z e p i l l a r l o c a t i o n i n a mining b l o c k , - determine  loads i n i n d i v i d u a l  - and account  pillars,  f o r v a r i a t i o n s i n p i l l a r shape.  Numerical m o d e l l i n g removes many of the problems a s s o c i a t e d w i t h tributary load.  area and  i s usually  necessary  pillar  However, the use of numerical m o d e l l i n g i s a s k i l l  takes a degree efficiently  in  of knowledge, experience pillar  design.  and  These  d i s c u s s e d i n more depth i n Chapter 3.2  3.1.3  t o e s t i m a t e the  that  c a l i b r a t i o n to  topics  and Chapter  will  all  use be  4.  Safety Factor  Hoek and  Brown  (1980) s t a t e  that,  "A  safety  f a c t o r of  1.0  52 implies  that  the p i l l a r  failure  could  propagate  i s theoretically across  the  u n s t a b l e and t h a t the  entire  pillar  The  s a f e t y f a c t o r s suggested f o r v a r i o u s e m p i r i c a l d e s i g n procedures in  e n t r y mining  instability in  open  methods  are l i s t e d  i n Table  a c c e p t a b l e i n e n t r y methods  stope  methods.  agreement t h a t  a safety  pillar  in  design  So,  entry  there  o f about  mining  The degree of  i s much l e s s than  although  factor  4.  1.5  methods,  seems  that  t o be  an  i s sufficient for  this  has  not  been  v e r i f i e d f o r open stope mining. SOURCE  SAFETY FACTOR  Salamon (1967) Hedley (1972) Obert and D u v a l l (1967) Hoek and Brown (1980) B i e n i a w s k i (1983) Stacey and Page (1986) T a b l e 4.  Stacey mining to 0.5  and  S a f e t y f a c t o r s suggested by v a r i o u s authors f o r p i l l a r d e s i g n i n e n t r y mining methods.  Page  methods  (1986)  state  that  a minimum s a f e t y  design p i l l a r s should  1.6 1.5 2-4 1.5 1.5 - 2.0 1.5  be  f a c t o r o f 1.1  t o y i e l d or f a i l , used.  for pillars  However,  in  non-entry  i s necessary and  a s a f e t y f a c t o r o f l e s s than no  data  are  presented  to  s u b s t a n t i a t e these v a l u e s . Ultimately,  none  of  these  formulas  or  safety  factors  based on o b s e r v a t i o n and experience i n open stope mining. a  factor  potential  of  safety  error  adds  a  associated  conservative with  cushion  empirical  Using  against  design  is  the  methods.  However, a c o n s e r v a t i v e d e s i g n i s not n e c e s s a r i l y the most c o s t effective entry  design.  method  Using  pillars  the  will  safety factors  likely  give  a  suggested  stable  for  design,  an but  e x p e r i e n c e and c a l i b r a t i o n o f an e m p i r i c a l d e s i g n procedure  will  p r o v i d e a b e t t e r estimate o f the s a f e t y f a c t o r needed.  3.2  Numerical In  Design Methods  recent  years,  several  methods have been developed rock mechanics d e s i g n . two  dimensional  or  .numerical  specifically  (or  f o r use  computational) i n underground  The program codes were c r e a t e d t o permit  three  dimensional  stress  and  displacement  i n v e s t i g a t i o n s around e x c a v a t i o n s i n rock. In  simplistic  w i t h f i g u r e 16.  terms,  numerical  modelling  in  modelling stresses  the  medium.  The  i s to calculate and  excavations.  be  described  A r e g i o n (R) i s d e f i n e d i n a medium and l o a d i n g  c o n d i t i o n s are a p p l i e d t o the r e g i o n . created  can  principle  acting  redistribution  of  in  (E) are  f u n c t i o n of  the magnitude and  displacements The  Excavations  the  then  numerical  o r i e n t a t i o n of the vicinity  s t r e s s e s may  of  be  these  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 o f Numerical  Individual problems Brown  with (1987)  categories:  Methods  computational respect grouped  to  methods were developed  specific these  p r o p e r t i e s of  properties  into  to  analyze  the  medium.  three  broad  FIGURE 16. An i d e a l i z e d s k e t c h showing the p r i n c i p l e o f numerical m o d e l l i n g o f underground e x c a v a t i o n s a f t e r P o t v i n e t 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. Differential and  finite  continuum methods  difference  medium w i t h i n  methods)  the region  of  (also  require  interest,  called  finite  element  discretization a t t h e boundary  of  the  o f the  problem and a t a l o n g d i s t a n c e from t h e boundary o f the problem (also  termed  problem t o be in  the  far field).  solved w i l l  t h e r o c k mass  methods  not be i n f l u e n c e d by  (medium) .  significant  Continuum  assume  discontinuities  T h i s means the r o c k mass c o n t a i n s  few  o r no  discontinuities,  are  so common and u n i f o r m t h a t i n d i v i d u a l l y they have no  on s t r e s s r e d i s t r i b u t i o n . it  or the  discontinuities  continuum r o c k mass m a t e r i a l p r o p e r t i e s . permit  analysis  effect  Consequently, f o r continuum methods,  i s assumed t h a t the medium can be r e p r e s e n t e d by  methods  the  using  elastic  "equivalent"  Differential and  continuum  plastic  theory.  However, d i s c r e t i z a t i o n i n a c c u r a c i e s a t the boundary and the f a r field,  e x t e n s i v e data p r e p a r a t i o n and h i g h computing times make  f i n i t e element methods l e s s a p p e a l i n g f o r r o c k mechanics d e s i g n . An  extensive discussion of f i n i t e  element methods i s p r e s e n t e d  by Z i e n k i e w i c z (1977). I n t e g r a l methods continuum  approach  discretization the  amount  (or boundary but  only  a t t h e problem of  data  needed  element methods) a l s o use the require  boundary. to  c o n s e q u e n t l y t h e amount o f computer  approximations This  describe  greatly  the  or  reduces  problem  and  time needed t o complete the  computations.  linear  and  homogeneous (or p i e c e - w i s e homogeneous) m a t e r i a l behaviour.  The  use  However,  o f boundary  they  are  best  element methods and  suited  their  to  application  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 Discontinuum technique. a  finite  methods  are  a  special  type  of  differential  number  of  discontinuous  blocks.  The  most  displacements  a p p l i e d t o the b l o c k s .  the b a s i s of d i s t i n c t  It  the f o r c e s  A good d e s c r i p t i o n of  element models and  i n a rock mass i s g i v e n i n C u n d a l l  by  common  i s c a l l e d the d i s t i n c t element method.  uses r i g i d b l o c k s and the laws o f motion t o determine  The  (1983).  They g e n e r a l l y assume a rock mass can be modelled  discontinuum approach  and  i n rock  a general  application  (1987).  most a p p r o p r i a t e numerical method f o r open stope  pillar  d e s i g n depends on the i n s i t u medium c o n d i t i o n s and the form of stress are  response  not  likely  discontinuities Consequently, pillar  expected.  and  the  design  to  is  As  be  are  influenced  loaded  numerical a  d i s c u s s e d i n Chapter  in a  method  continuum  by  approach  elasticity.  The most e f f i c i e n t approach  the  method.  integral  computations  Finite  adequately,  but  numerical  modelling  in  elastic  suited  to  using  the  minor manner.  open  stope  theory  element methods c o u l d perform are  not  this  as  thesis  a p p l i c a t i o n of boundary element methods.  of  f o r these c o n d i t i o n s i s  efficient  element methods i n e l a s t i c s t r e s s a n a l y s i s . the  pillars  individual  biaxial,  best  2,  as  the  boundary  As a r e s u l t , a l l of will  focus  on  the  57 3.2.2  I n t e r p r e t a t i o n o f Boundary Element R e s u l t s The  boundary  element  stress  analysis  i n Mining  technique  has been  developed t o approximate t h e s t r e s s d i s t r i b u t i o n around openings with  irregular  shapes  dimensional s t r e s s  oriented  field.  d i r e c t l y determine f a i l u r e .  to  be  stability.  to  The s t r e s s  determine  d i s t r i b u t i o n needs  the e f f e c t  on  underground  Many types o f f a i l u r e c r i t e r i o n have been a p p l i e d i n  the a n a l y s i s o f s t r e s s d i s t r i b u t i o n s . the  or three  However, boundary element methods do  not  interpreted  i n a two d i m e n s i o n a l  common methods o f boundary  p i l l a r design.  This section w i l l  element  (ii) (iii)  i n t e r p r e t a t i o n used i n  The methods o f i n t e r p r e t a t i o n  (i) post-processing f a i l u r e interactive failure  outline  include:  criterion,  criterion,  and p r i n c i p a l s t r e s s magnitudes.  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 Post p r o c e s s i n g after does  the stress n o t have  continuum  analysis  material  characterization  estimated  properties,  parameters,  material Common  such  discontinuity  The f a i l u r e  conditions.  i s complete.  The f a i l u r e  any e f f e c t on t h e s t r e s s  r o c k mass s t r e n g t h ,  behaviour.  f a i l u r e c r i t e r i a are applied t o the solution  failure  as i n t a c t  is  strength,  o r rock mass  f o r t h e rock  used  i n similar  i n post  (1965) and B i e n i a w s k i  rock  processing  were developed by: - Murrell  mass  c a l i b r a t e d based on t h e  and experience criteria  Generally,  rock  shear s t r e n g t h ,  a r e estimated  criterion  properties  solution.  criterion  (1974) f o r i n t a c t rock,  58 - Hoek and - and The  Brown (1980) f o r j o i n t e d rock masses,  Coulomb (1776) f o r  failure criterion  pillar.  i s a p p l i e d t o s t r e s s e s a t many p o i n t s i n a  Based on the  pillar  discontinuities.  distribution  s t a b i l i t y i s determined and  of t h e o r e t i c a l l y  f a i l e d rock,  p o t e n t i a l mining problems  are  delineated. An  example of  criterion  is  the  described  experimental  open  Australia.  failure  pillar  of  spalling, a  pillar A  0  7 5  a post-processing  (1977) at  based  +  in  the  the  failure  analysis  Mount  was on  From the  f o l l o w i n g formula was 3  of  criterion  (1965).  = 9.34a -  x  Brady  material  Murrell  the  by  stope  Queensland,  proposed by  application  Isa  calibrated a  formula  of  an  Mine  in  for  the  originally  o b s e r v a t i o n of  local  rock  developed:  94.0  where,  The  c2_ = the  major p r i n c i p a l  s t r e s s at  03  minor p r i n c i p a l  stress  = the  failure  criterion  was  distributions  for  histories  verification.  for  a p p l y i n g the by  "F"  rock small  i n the in and  the  criterion  a p p l i e d t o the  to  and  failed Figure  pillar.  The at  the  to  open 17  stope  s t a b l e assessment. stress distribution  and stope  shows  a stable p i l l a r .  predicted  (MPa) ,  (MPa).  applied  f i g u r e r e p r e s e n t i n g the  isolated  w e l l w i t h the  stable  then  failure  The  theoretical zones  periphery, F i g u r e 18  of  a  pillar  the  case  results  points  failed  of  denoted  zone of  which  stress  3  failed  rock  are  corresponds  shows the  criterion  of a p i l l a r t h a t f a i l e d .  The  FIGURE 17. An e m p i r i c a l f a i l u r e c r i t e r i o n has been a p p l i e d t o the two d i m e n s i o n a l s t r e s s d i s t r i b u t i o n o f a s t a b l e open stope r i b p i l l a r . P o i n t s denoted by F " r e p r e s e n t the area o f r o c k t h a t 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 , t h e f a i l u r e zones a r e s m a l l and i s o l a t e d a t t h e periperhy of the p i l l a r . T h i s corresponds t o a g e n e r a l l y s t a b l e assessment f o r t h e p i l l a r ( a f t e r Brady 1977). M  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 o f f a i l e d rock i s much g r e a t e r i n t h i s p i l l a r . The a c t u a l p i l l a r c o l l a p s e d s h o r t l y a f t e r b e i n g reduced t o t h i s s i z e ( a f t e r Brady 1977).  zone of  f a i l e d r o c k covers a s i g n i f i c a n t p o r t i o n  of the  pillar,  which a l s o agrees w i t h the a c t u a l assessment. A p p l i c a t i o n o f a f a i l u r e c r i t e r i o n t o the t h e o r e t i c a l s t r e s s distribution the  around underground  excavations  i s very  i n t e r p r e t a t i o n o f boundary element s o l u t i o n s .  common f o r However, i t  assumes t h a t l o a d 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 m a t e r i a l  and  t h a t t h e r e i s no s t r e s s r e d i s t r i b u t i o n due  the  f a i l e d rock mass. loaded  T h i s assumption may  to destressing  of  not be c o r r e c t f o r h i g h l y  pillars.  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 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 d u r i n g  computations by a d j u s t i n g that  fail  due  to  determine  the  peak  failure  high  i s very  numerical  the s t r e s s i n r e g i o n s o f the rock mass stress.  strength  This  requires  the  rock  of  r o c k mass c h a r a c t e r i s t i c s .  criterion  the  involved  and  has  a  mass  criterion and  the  to  post  C a l i b r a t i o n of t h i s type of a fundamental e f f e c t on  the  results. Documentation of the use is  g i v e n by  Mines  Maconachie e t a l . (1981) a t the  Pty.,  New  South  Wales.  program "N-Fold" w i t h an to  investigate  the  program c o n s i d e r s elements. based on for  of an i n t e r a c t i v e f a i l u r e  The the  stress  point  condition  displacement  confinement  of  a  deformation and and  confinement of the  increasing  C.S.A. mine, Cobar discontinuity  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  non-linear  yield  The  criterion  post  sill  pillar.  The  b r i t t l e y i e l d i n g of  f a i l u r e deformation  element.  (increasing  used  Figure distance  60  varies  shows t h a t  from  a  free  BRITTLENESS MOOULUS IMPol 12-5  PEAK STRENGTH (MPol 72  a  EXPOSED CORNER  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 s t r e n g t h , deformation c h a r a c t e r i s t i c s , and e f f e c t o f l o c a t i o n used f o r i n v e s t i g a t i n g a p i l l a r case h i s t o r y w i t h a displacement d i s c o n t i n u i t y program ( a f t e r Maconachie e t a l 1981). |  | ELASTIC  FIGURE 20. The normal s t r e s s and t h e f a i l e d r e g i o n s e s t i m a t e d w i t h the displacement d i s c o n t i n u i t y program f o r a s i l l p i l l a r case h i s t o r y ( a f t e r Maconachie e t a l 1981).  62 face),  t h e peak  bearing  capacity  failure  criterion  mass s t r e n g t h properties  strength  and t h e post-peak  o f t h e rock improves.  of the i n s i t u  and l a b o r a t o r y m a t e r i a l p r o p e r t i e s .  were subsequently v e r i f i e d  When a p p l i e d  load  The c a l i b r a t i o n o f t h e  was based on e s t i m a t i o n s  monitoring of the s i l l  (figure  increases  rock  The m a t e r i a l  based on o b s e r v a t i o n and  pillar.  to a longitudinal section  20), t h e zones  of  failed,  of the s i l l  and y i e l d i n g  pillar  rock  were  o u t l i n e d and t h e magnitude o f t h e normal s t r e s s e s f o r rock under elastic  deformation  helped  determine  was the  determined. best  stope  The  failure  extraction  criterion  sequence  and  i n d i c a t e d t h e need o f a pendant p i l l a r t o m a i n t a i n s t a b i l i t y i n the s i l l  pillar.  While p o t e n t i a l l y v e r y u s e f u l i n p i l l a r d e s i g n , failure  criterion  verification more  needs  before  sophisticated  a  large  becoming and  amount  a reliable  complex  the  t h i s type o f  o f c a l i b r a t i o n and  tool. program  Generally, the and  failure  c r i t e r i o n , t h e g r e a t e r t h e number o f assumptions i n t r o d u c e d  into  the s o l u t i o n . 3.2.2.3 P r i n c i p a l S t r e s s Magnitude. The  most  interpretation  common and s i m p l i s t i c  method o f boundary  element  i s a n a l y s i s o f p r i n c i p a l s t r e s s magnitudes.  pillars,  stress  d i s t r i b u t i o n s are plotted  sections  t o reveal  areas  of high  on mine  plans  o r low p r i n c i p a l  In or  stress.  P o t e n t i a l mining problems a r e then estimated based on t h e s t r e s s distributions.  A typical analysis  example of the use  i s given  Mount I s a mine. with  normal  spalling  i n a paper by  I t was  stress  of p r i n c i p a l  Bywater e t a l . (1983) , a t  determined  greater  discontinuity  than  70  MN/m  2  code  was  p o t e n t i a l s t r e s s d i s t r i b u t i o n s i n a new shows two  different  the  generally  exhibit  A linear  elastic  used  to  analyze  mining b l o c k .  shows more o v e r s t r e s s e d areas  t o the  being  the  F i g u r e 21  sequences f o r the mining  p r e d i c t e d s t r e s s e s corresponding  analysis second  extraction  the  through e x p e r i e n c e t h a t areas  and are prone t o l o c a l rock f a i l u r e .  displacement  with  s t r e s s magnitude  block,  legend.  developed  The  i n the  sequence which would cause problems e a r l i e r i n the  pillar  recovery. When the rock mass s t r e n g t h has not been estimated, s t r e s s e s are  frequently  compressive occur 1/3  normalized  s t r e n g t h of the rock.  i f the n o r m a l i z e d  (Bawden e t a l . 1988)  3.2.3  against  intact  uniaxial  Mining problems are l i k e l y t o  major p r i n c i p a l t o 1/2  the  stress  i s g r e a t e r than  (Mathews e t a l . 1980).  L i m i t a t i o n s of Boundary Element M o d e l l i n g  While tool,  boundary  it  inaccuracy  has  element m o d e l l i n g  several  limitations  i s a sophisticated and  i n a p p l i e d rock mechanics.  potential The  design  sources  limitations  can  grouped i n t o two b a s i c c a t e g o r i e s : ( i ) l i m i t a t i o n s w i t h r e s p e c t t o m o d e l l i n g a rock mass, (ii)  and l i m i t a t i o n s due t o computational  3.2.3.1 M o d e l l i n g a Rock Mass  assumptions.  of be  NORMAL STRESS  • +70 MN/m £ S 60 - 69 MN/m' 2  / £ ] 50 - 59 MN/m 40 - 49 MN/m  2  2  FIGURE 21. The d i s t r i b u t i o n o f normal s t r e s s i n a mining b l o c k was e s t i m a t e d f o r two d i f f e r e n t mining sequences t o determine t h e b e s t stope e x t r a c t i o n sequence ( a f t e r Bywater e t a l . 1983).  A  numerical  modelling  perfect material perfect are  describing  isotropic  A  the  r o c k mass.  significant  e f f e c t on s t r e s s . may  not  be  especially may  not  a  serious  material  of  the  properties of  a  rock  rock mass behaves as  the  an  an  rock mass e i t h e r  has  discontinuities  are  frequent  limitation.  a  assumptions  properties  T h i s means t h a t the  and  and  that  they  have  no this  However f o r major s t r u c t u r e ,  t h a t have moved s u b s t a n t i a l l y , the  as  i n v a l i d a t e any  The  regular  has  For minor s t r u c t u r e such as r o c k j o i n t s ,  faults  act  estimation  or  medium  a r o c k mass i s not  the  discontinuities,  small,  the  approximations  estimated assuming the  continuum.  sufficiently  for  assumes  In r e a l i t y ,  number o f  necessary  mass have t o be  no  properties.  material.  usually  solution  i s o t r o p i c continuum  at  all.  numerical s o l u t i o n t h a t d i d not  r o c k mass This  could  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 elastic have  boundary  deformational  found  samples  that  mass  the is  loading  generally  methods  give  characteristics. a  range of  some n o n - l i n e a r  dependent  upon  the  loading and  several  acceptable,  but  the  use  mass  conditions,  plastic  linear  hard  rock  deformation.  In  behaviour of an variables  e l a s t i c c h a r a c t e r i s t i c s of the conditions,  rock  L a b o r a t o r y measurements  p o s t - f a i l u r e load bearing  r e l a t e d t o the medium  over  exhibit  addition, rock  element  of  that  rock.  linear  in situ are  For low  elasticity  f o r a discontinuum, h i g h l y loaded,  not to is or  f a i l e d r o c k 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 l a r g e i n f l u e n c e of the pre-mining expensive situ  and  stress  influenced the  field  by  virgin  parameter  varies  with  major s t r u c t u r a l  stress  approximation It  difficult  used  s t r e s s regime. t o measure.  depth  and  T h i s i s an  The  can  be  discontinuities.  i n numerical  methods  actual  in  profoundly  Consequently,  will  only  be  an  o f the a c t u a l c o n d i t i o n s .  i s important  possible effect  t o be aware of these l i m i t a t i o n s  and  their  on the numerical s o l u t i o n ' s a b i l i t y t o d e s c r i b e  the c o n d i t i o n o f a s t r e s s e d rock mass. 3.2.3.2 Computational  Assumptions  Boundary element methods are numerical approximations solution  to  excavation  a  boundary  geometries  complicated  value  can  geometries,  be  a  into  segments and  is  Only  the  simplest  analytically, determined  so  for  through  This necessitates d i s c r e t i z i n g piecewise modelling  d i s p l a c e m e n t s on each segment. - the i n t e r i o r s o l u t i o n  solved  solution  numerical i t e r a t i o n process. boundary  problem.  o f the  a the  of s t r e s s e s and  The r e s u l t i s :  ( s t r e s s e s o f f the boundary) may  not  be  a c c u r a t e v e r y near the d i s c r e t i z e d boundary, - and  the numerical  the  computation  solution  i s o n l y an approximation  i s completed  when a  specified  because  convergence  c r i t e r i o n i s met.  Through the m o d e l l i n g of boundaries w i t h known s o l u t i o n s , i t has  been  found  that  the  boundary, the g r e a t e r the  larger  the  accuracy  number  of  elements  on  a  of the numerical model with  67 r e s p e c t t o the known c l o s e d form s o l u t i o n . difference solution  between  decreases  the  numerical  w i t h an  model  The magnitude of the and  the  closed  i n c r e a s e i n the number of  form  elements,  so t h e r e i s a p r a c t i c a l l i m i t t o the i n f l u e n c e o f the number of elements.  Above t h i s l i m i t , the a d d i t i o n of e x t r a elements does  l i t t l e or n o t h i n g t o improve the accuracy of the  In summary, r e a d i n g too much d e t a i l can  be  misleading.  Calibration  of  solution.  i n a numerical numerical  solution  models  with  e x p e r i e n c e and case h i s t o r i e s can be as important as the type of n u m e r i c a l model used or how be  kept  in  perspective  account  for  stress  failure  or  failure  s t r u c t u r e may distributions.  the r e s u l t s are a n a l y z e d . that  related due  to  boundary  failure. the  element  methods  Structurally  combination  of  I t should only  controlled s t r e s s , and  not be i n t e r p r e t e d from numerical m o d e l l i n g s t r e s s  68 CHAPTER 4 OPEN STOPE RIB PILLAR DATA BASE  The data  objective of t h i s  collected  chapter  i s t o present the r i b p i l l a r  d u r i n g t h e I n t e g r a t e d Mine Design  Study.  This  w i l l be done by: - discussing  some  of  the  general  characteristics  and  i n f o r m a t i o n o f t h e p i l l a r case h i s t o r i e s , - p r e s e n t i n g t h e background  and p h y s i c a l  i n f o r m a t i o n on each  case h i s t o r y , - d e f i n i n g t h e q u a l i t a t i v e s c a l e used t o g i v e an assessment t o the case h i s t o r i e s , - and  describing  the  signs  of  failure  f o r a l l the  case  h i s t o r i e s t h a t experienced s t a b i l i t y problems.  4.1 G e n e r a l Data Base I n f o r m a t i o n The  original  Canadian  open  data used  stope  i n t h i s t h e s i s has been c o l l e c t e d i n  mines.  The 47 case  histories  are only a  f r a c t i o n o f t h e t o t a l data c o l l e c t e d d u r i n g t h e " I n t e g r a t e d Mine Design Study".  Some o f t h e data was r e j e c t e d because:  ( i ) g e o t e c h n i c a l parameters rock  including  in situ  stress,  intact  s t r e n g t h and the i n f l u e n c e o f g e o l o g i c a l s t r u c t u r e  c o u l d not be estimated w i t h c o n f i d e n c e , (ii)  the actual  events  of  t h e case  history  could  not be  verified, (iii)  t h e s t r e s s c o n d i t i o n s i n t h e case h i s t o r y were t o o complex  69 t o be back-analyzed w i t h t h e means a v a i l a b l e a t U.B.C.  Throughout t h e course o f t h e study, s e v e r a l mines requested that  their  name not appear d i r e c t l y  respect t h e i r site  of  any  information parameters  a s s o c i a t e d with data.  anonymity, t h e r e i s no s p e c i f i c unpublished about  the  and case  data mining  histories  in  this  reference t o the  thesis.  environment,  i s presented  To  Specific  geotechnical  through  t h e use o f  mine numbers. The  data  base  i s supplemented by i n f o r m a t i o n presented i n  U.B.C. t h e s e s t h a t d i s c u s s open stope  rib pillars,  by Goldbeck  (1985), P o t v i n (1985) and P a k a l n i s (1986). A  significant  f e a t u r e o f many o f t h e p i l l a r s  i n t h e data  base i s t h a t they were s t a b l e a t one time d u r i n g t h e mining and later  failed.  The f a i l u r e was caused  by i n c r e a s e d e x t r a c t i o n  near t h e p i l l a r o r mining p o r t i o n s o f t h e p i l l a r . case h i s t o r i e s different be  very  Among t h e 47  i n t h e data base, 30 o r i g i n a t e from 13 p i l l a r s a t  stages o f e x t r a c t i o n . important  These " y i e l d i n g  t o t h e development  pillars"  of a r i b p i l l a r  will  design  method.  4.2 Background Data The depth,  background mining  backfill, Table  5.  information  environment  concerning  including  ratio  pillar  dimensions,  of extraction  and  and an assessment o f t h e p i l l a r c o n d i t i o n i s g i v e n i n The dimensions  and r a t i o  of extraction  are defined  70  PILLU  NUKUt 2 3 7  8 15 16 17 IS  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 37 42 43 44 45 46 47 48 *9 51 52 53 54 55 56 57 58 59 60 61  KXNI NUKBER  PILLA1 MAKE  PILL41  ttLLA» sron  WIDTH  :  2  6 6  8 10 11 11 16 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 19 19 19 19 21 21 21 21 22 22 22 22 23 2} 31 31 31 31 31 30  14-3-2/4 U-3-2 33-176/183 33-176 23*7 2549 062 30-203 30-205 77-90 77-92 77-94 77-92  77-94  77-94 80-78 80-80 80-82 80-84 80-82 80-80 10-20 10-21.5 10-23 10-20 10-20 10-23 LEVEL 11 #8  Lll  16-8  Lll (14-16 LEVEL 11 #14 120-13D 12D-13S 12D-13D 12D-13D 301 #15 301 116 301 #17 330 #4-5 341 VP 342 VP  448  450 452 450 452 2020 PILLAR  43  !  3'  15  !  34  ! 11 ! 12 ! 15 ! 25 : 24 I 35 i  50 50 50 50 too  33  15 27  !  15 21 15 15 11 33 33  11  32 25 19 14 17 21 18  24  :  ! !  1  120  105 120 105 105 135 135 '5 75  ! ! !  135 ISO 150 150  !  "  :  150  !  150  :  iso  ! ! ! ! ! !  55 55 55 55 60 60  !  ! ! ! ! !  60  60 35 35 35 58  53 49 20 20 8 7 27 11 12 15 40 40 40 40 40  24  12 27 39 27 12 21 20 18 21 30 18 23 23 IS 18 28 28 28 28 6 5  4  n o  !  n o  44  :  n o  38  24  :  170 170  I  110  :  n o  ;  n o  DIP  HEICHT  18 10 8 46 52 44 52  t  A r a t i o r a f a r s t o a v a s t a t o camant r a t i o T o r TAILINGS naans t h a b a c k f i l l i n g a a t a r l a l R o r ROCKPILL aaana t h a b a c k f i l l i n g a a t a r l a l  TABLE 5.  120  ! ! ! !  17 20 27 30 24 30 24  M  100  30 i 27 30 30 21 15 15 21 15 15 21  SBOMim flLLAI  { HEIGHT  90 90 90 90 80 80 65 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 70 70 70 70 90 90 90 90 90 90 90 90 90 90 90 90  lAcmix  (* mns ULCM) NO NO  12.1 12.1  T T  32:1 t 32:1 1 20:1 1 NO  NO NO NO NO NO NO NO  NO  NO  NO  NO. NO NO NO NO NO  NO  ROCXPILL NO 30:1 T 30.1 T 30:1 T 30:1 I NO NO NO NO TAILINGS TAILINGS TAILINGS TAILINGS ROOJILL R0CX7ILL NO NO NO NO NO 20:1  8  i a primarily claaaifiad mill l a p r l a v a r i l y vaata rock.  EXTRACTION  DtPTB  (•) 820  3tX  210 210  57X 25X 501 56Z 571  870 (70 300  59Z 60Z 71Z  820 1000 1000 360  SIX  ! ; : ; : ;  49X 68X 49X 84Z 671 751 71X 63X 82Z 87Z 55X 74Z 60X 66X 80Z 74X 501 2SX 2SX 502 37X 46X 58X 70X 66X 67X 61Z SIX 64Z 67X 61X 38X 38X 73X 75X 59X  ucs  (•*)  SOX  300  300 300 300 300 210 210 210 210 210 210 215 215 215 215 215 215 620 620 620 620 340 340 340 340 320 320 320 520 290 290 500 500 500 500 500 520  csnt  uno  :  :  62 62 64 64 77 77 60 75 75 71 71 71 71 71 71 71 71 71 71 71 71 65 65 65 65 65 65 78 78 78 78 68 68 68 68 63 63 63 69 71 71 75 75 75 75 75 70  ASSESSMENT  (MPl)  200 200 121 121  215 215 70 148 148 176 176 176 176 176 176 176 176 176 176 176 176 100 100 100 100 100 100  ;  316 316 316 316 90 90 90 90 72 72 72 72 310 310 26S 265 265 265 265 160  STABLE PAILU1E STABLE PAILUIX STABLE STABLE SLOUCHINC STABLE STABLE  SLOUGEDK  STABLE STABLE PAILUII STABLE PAILUU STABLE STABLE SLOUGHING STABLE FAILURE STABLE STABLE FAILURE SLOUGHING STABLE FAILURE FAILURE FAILURE STABLE STABLE FAILURE STABLE SLOUCHING FAILURE FAILURE STABLE STABLE STABLE STABLE STABLE STABLE SLOUGH STABLE STABLE SLOUGH SLOUCH SLOUGH  taillnfa.  Background d a t a f o r a l l the p i l l a r case  histories.  71 a c c o r d i n g t o f i g u r e 22.  The dimensions  dimensions.  dimensions  cases  The  due  failed,  to  the  blast  actual  substantially excessive condition chapter  actual  induced  smaller  sloughing. of  each  than  may  damage.  dimensions  p r e s e n t e d are the d e s i g n vary For  slightly pillars  (especially p i l l a r the  design  Justification  sloughing  and  f o r most that  have  width) may  dimensions,  due  be to  f o r the assessment of the  failed  pillar  is  given  in  4.3.  Specific case h i s t o r y  i n f o r m a t i o n about can be found  the  setting  i n the i s o m e t r i c s k e t c h  t o the mine number (see Appendix I ) . comprised  geological  of  each  corresponding  Each g e o l o g i c a l s e t t i n g i s  of:  - the underground s t r e s s regime, - the hanging w a l l , f o o t w a l l and orebody m a t e r i a l p r o p e r t i e s and c h a r a c t e r i s t i c s  including,  - 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 - NGI  ratio,  rock mass c l a s s i f i c a t i o n ,  - the orebody shape and -  size,  and the mining methods used i n v a r i o u s p a r t s o f the orebody.  S e v e r a l mines use throughout  the mine.  very  similar  stope  and  pillar  dimensions  I n c l u s i o n 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. T h i s f i g u r e shows t h e g e o m e t r i c a l d e f i n i t i o n f o r 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  o f t h e data  base.  However, u s i n g  s e v e r a l case h i s t o r i e s w i t h t h e exact same i n f o r m a t i o n would not broaden t h e c a p a b i l i t y o f t h e data base t o t h e develop method. dilute  I t would  create  problems  the influence of single  i n data  case  a design  presentation  histories.  As a  and  result,  o n l y unique cases a r e presented.  4 . 3 P i l l a r Assessment The 2.1.  signs  of r i b p i l l a r  Based on these  instability  are l i s t e d  signs, three q u a l i t a t i v e  i n Chapter  assessments have  been chosen t o c a t e g o r i z e t h e c o n d i t i o n o f t h e p i l l a r s  i n the  data base. A  stable  assessment  i s given  showing any s i g n s o f i n s t a b i l i t y .  to  pillars  g e n e r a l l y not  Any ground c o n t r o l problems  are t o o s m a l l t o have an e f f e c t on mining near t h e p i l l a r . A  sloughing  assessment  i s given  to p i l l a r s  showing  one o r  more o f t h e above s i g n s , but t h e extent o f d e t e r i o r a t i o n i s not severe  and i s r e p o r t e d  i n o n l y a few areas  of the p i l l a r .  The  ground c o n t r o l problems a s s o c i a t e d w i t h s l o u g h i n g p i l l a r s have a limited  effect  on mining,  difficulty  in  development  scaling  and  maintaining  pillars  histories  some  drill  problems,  holes,  the  and some w a l l  l o s s or  need  for  sloughing  The s l o u g h i n g assessment i s a l s o used t o  whose  becoming more severe  as: d r i l l i n g  and r e h a b i l i t a t i o n  p i l l a r overbreak.  describe  such  stability  problems  as mining c o n t i n u e s .  have been assessed  as s l o u g h i n g ,  a r e time  dependent,  Several p i l l a r but have used  case quick  74 backfilling A  failed  t o prevent complete p i l l a r assessment  i s given  severe s i g n s o f i n s t a b i l i t y . - l o s s of - low  pillars  showing  T h e i r e f f e c t s on mining,  large  and  include:  ore,  productivity  created  to  failure.  during  due  to  oversize  material  mining, the need f o r frequent  o f development or the use  and  overbreak  rehabilitation  o f c a b l e b o l t s t o prevent l o s s of  p i l l a r development, - and  severe  needing  cracking,  immediate  joint  stope  opening,  filling  and  displacement  often  t o prevent complete  pillar  disintegration.  The and  d e s c r i p t i o n by  author. and  assessment of p i l l a r s was on-site  Justification  failed  pillars  of  staff the  based l a r g e l y on documentation and  some o b s e r v a t i o n s  assessment  i s d e t a i l e d below,  by  f o r a l l the describing  by  the  sloughing the  most  s e r i o u s s i g n s 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 C o n d i t i o n : Sloughing of l a r g e s l a b s from p i l l a r w a l l s i n t o primary stope drawpoints, problems i n m a i n t a i n i n g b l a s t h o l e s , w a l l s l o u g h i n g i n t e r s e c t e d development i n the middle of the p i l l a r . ( r e f e r e n c e : Falmagne 1986). CASE # 8 Assessment: F a i l u r e . Pillar Condition: Severe axial cracking in pillar development r e q u i r i n g c a b l e b o l t i n g t o m a i n t a i n overcut and undercut s t a b i l i t y , several f e e t of overbreak beyond b l a s t h o l e s and h o u r g l a s s s l o u g h i n g i n the middle of p i l l a r w a l l s .  75 CASE # 17 Assessment: Sloughing. P i l l a r C o n d i t i o n : Shears and j o i n t s opening i n p i l l a r s , s l o u g h i n g o f p i l l a r w a l l s i n t o primary s t o p e s . Some problems i n d r i l l i n g and m a i n t a i n i n g d r i l l h o l e s . ( r e f e r e n c e : Bawden 1988) . CASE # 2 0 Assessment: Sloughing. P i l l a r Condition: Progressive sloughing of p i l l a r walls into adjacent stopes. ( r e f e r e n c e : A l l c o t t and A r c h i b a l d 1981). CASE # 2 3 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : Severe s l o u g h i n g o f p i l l a r adjacent stopes. ( r e f e r e n c e : A l l c o t t and A r c h i b a l d 1981). CASE  walls  into  #25 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : Major shear displacement extending over two l e v e l s 45 metres a p a r t , s l o u g h i n g o f p i l l a r w a l l s , ( r e f e r e n c e : A l l c o t t and A r c h i b a l d 1981; P o t v i n 1984).  CASE  #28 Assessment: Sloughing. Pillar Condition: Severe ground fracturing abandonment o f p i l l a r development, ( r e f e r e n c e : A l l c o t t and A r c h i b a l d 1981).  CASE # 3 0 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : P i l l a r crushes v i o l e n t l y p i l l a r i s recovered by b l a s t i n g , ( r e f e r e n c e : A l l c o t t and A r c h i b a l d 1981).  after  causes  nearby  CASE # 3 3 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : E x t e n s i v e c r a c k i n g o f p i l l a r , f o l l o w e d by the s l o u g h i n g o f 2 r i n g s o f d r i l l h o l e s and major c o l l a p s e o f t h e upper h a l f o f t h e p i l l a r i n t o adjacent stopes. ( r e f e r e n c e : Bray 1967). CASE  #34 Assessment: Sloughing. P i l l a r Condition: Extensive cracking of the p i l l a r reported, w i t h some s l o u g h i n g i n t o nearby s t o p e s . ( r e f e r e n c e : Bray 1967).  76 CASE  #36 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : West s i d e o f t h e p i l l a r sloughs i n t o a d j a c e n t stope c a u s i n g breakthrough t o a p i l l a r c r o s s cut. ( r e f e r e n c e : Bray 1967).  CASE  #37 Assessment: F a i l u r e . P i l l a r Condition: Wall sloughing creates through t h e p i l l a r , ( r e f e r e n c e : Bray 1967).  a hole  completely  CASE # 42,45 Assessment: F a i l u r e . Pillar Condition: Severe c r a c k i n g , spalling and joint opening i n p i l l a r development w i t h wooden c r i b s and c a b l e b o l t i n g needed t o l i m i t development c l o s u r e and c o l l a p s e , heavy overbreak on p r o d u c t i o n b l a s t s . ( r e f e r e n c e : Bawden and M i l n e 1987; Chauvin 1986). CASE  CASE  CASE  #47 Assessment: Sloughing. Pillar C o n d i t i o n : One v i b r a t i n g w i r e decrease i n s t r e s s through p i l l a r , ( r e f e r e n c e : Goldbeck 1985).  stressmeter  #48 Assessment: F a i l u r e . Pillar Condition: A l l v i b r a t i n g wire decrease i n s t r e s s through p i l l a r , ( r e f e r e n c e : Goldbeck 1985).  stressmeters  #49 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : Sharp decrease i n p i l l a r v i b r a t i n g wire stressmeters. ( r e f e r e n c e : Goldbeck 1985).  stress  shows  show  shown by  CASE # 56 Assessment: Sloughing. P i l l a r C o n d i t i o n : S e r i o u s a x i a l c r a c k i n g 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 a f t e r r e c o v e r y o f a nearby p i l l a r .  develop and open  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 a f t e r r e c o v e r y o f a nearby p i l l a r .  develop  and open  CASE # 61 Assessment: S l o u g h i n g . P i l l a r C o n d i t i o n : Sloughing o f p i l l a r w a l l s as f a r as c e n t r e of p i l l a r , overbreak from p i l l a r s d u r i n g primary mining and severe overbreak d u r i n g secondary stope mining.  78  CHAPTER 5 BOUNDARY ELEMENT METHODS IN RIB PILLAR DESIGN  Boundary element numerical estimate  the stress  described  program  3.2.3).  i n Chapter (BITEM)  discontinuity the  a t any p o i n t i n a r i b p i l l a r  i n Chapter  presented  average  methods a r e an e f f e c t i v e way t o  4,  and a  program pillar  F o r each  a  direct  (MINTAB) method w i l l  stress.  limitations  applied  F o r many  may  cause  t o some t h r e e dimensional  dimensional  method  distribution dimensional have  that  large  in  would  each  analysis setup  be  case  i s very  and  two  dimensional  t h e s e programs g i v e adequate r e s u l t s . have  o f t h e case  integral  pseudo-three  ( f o r reasons histories  dimensional displacement  be used  t o estimate  r i bp i l l a r  geometries,  However, BITEM and MINTAB serious  problems.  used  to  history.  Ideally,  when  a three  determine  the  stress  However,  true  three  new technology  r u n times,  inaccuracies  need  and t h e programs  quite  sophisticated  computing f a c i l i t i e s , and a r e l i m i t e d i n program s i z e . To  better  deine  boundary element code to  investigate  geometries.  the  these  limitations,  a  three  dimensional  (BEAP) and BITEM and MINTAB w i l l average  stress  T h i s comparison w i l l  i n typical  be used  be used  r i b pillar  t o approximate t h e  e r r o r a s s o c i a t e d w i t h t h e a p p l i c a t i o n o f t h e two dimensional and displacement  d i s c o n t i n u i t y methods t o 3D problems.  79 5.1 Boundary Element Methods Used The  following  methods  and  largely  from  general  numerical an  description  codes  o f t h e boundary  involved  unpublished  paper  i n the  written  at  element  study  i s taken  U.B.C.  (Hudyma  1988b).  5.1.1  BITEM  The the  2D  direct  program  boundary  "BITE"  developed  Carnegie-Mellon u n i v e r s i t y piece-wise  Scientific  i n 1978.  the U.B.C. mainframe  by  i n 1973.  homogeneous  (Commonwealth Australia)  integral  model  "BITEM" i s based  P.C.  Riccardella  I t was  elasticity  and  Industrial  The program computer  was  by R.  at  on the  expanded t o perform  analyses  by  CSIRO  Research O r g a n i z a t i o n ,  subsequently m o d i f i e d f o r P a k a l n i s i n 1983  and  later  f o r an IBM compatible computer by CANMET under the program name PCBEM ( P a k a l n i s 1987). The that  boundary  have  shape.  one  integral  long  t e c h n i q u e i s d e s i g n e d f o r problems  dimension  It  requires  surfaces  into  segments  explicit  solution  the  and  a  constant  discretization  connected by nodes  of  cross  sectional  a l l excavation  (see f i g u r e 23) .  An  i s s e l e c t e d t o r e p r e s e n t t h e medium's i n s i t u  stress conditions.  These f i e l d  vary l i n e a r l y with p o s i t i o n .  s t r e s s e s can be c o n s t a n t o r can  When e x c a v a t i o n s a r e c r e a t e d ,  s t r e s s p e r p e n d i c u l a r t o the boundary nodes becomes zero.  the BITEM  then c a l c u l a t e s t r a c t i o n s and d i s p l a c e m e n t s a t a l l t h e nodes o f a l l the boundaries.  The boundary s o l u t i o n i s determined through  OPENING TO  FIGURE 23. I s o m e t r i c view o f an opening t h a t 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 o f the boundary used i n two dimensional modelling ( a f t e r Hudyma 1988b).  81 an  i t e r a t i v e procedure  each  node  influences  i n which  the  nodes o f the boundary. between  the  last  convergence  stress  iterations  stresses  can  be  Once  and  5.1.2  i s less  a  than  boundary  a  user  solution  defined  has  determined  using  the  boundary  been  problem  solution  and  A more d e t a i l e d d e s c r i p t i o n o f the (1978).  MINTAB is  discontinuity written  pseudo-three element  dimensional  program.  The  by Dr. S.L. Crouch i n South A f r i c a . major  program  names,  modifications  variation  backfill  including: has  elements,  f o r the s u r f a c e f a u l t s and criterion version  a  boundary  several  resulting  use  of  in  MINTAB,  features  such:  a semi-infinite  several BESOL  as  different  and  the  N-FOLD.  inclusion  domain  o f the e a r t h ) , use o f m u l t i p l e  of  (can account  en e c h e l o n seams,  f o l d s 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 with  used  in  was  The program has had  MINSIM,  special  displacement  o r i g i n a l code  post-failure  for this  rock  study  is  mass  characteristics.  CANMET's  MINTAB  (1983) which performs o n l y l i n e a r e l a s t i c a n a l y s i s seam,  difference  i n t e g r a l technique i s found i n Brady and Bray  Mintab  Each  displacement o f the o t h e r  displacements i n t e r n a l t o the  stress-strain relationships. boundary  and  and displacement a t  T h i s procedure ends when the  criterion.  determined, boundary  two  the s t r e s s  an  infinite  domain,  and  with  no  version  The 4.0  o f one p l a n a r  built  in  failure  criterion. MINTAB uses  the displacement d i s c o n t i n u i t y  method t o  solve  82 stresses,  strains  and  displacements  i n t h r e e dimensions  excavations  i n t a b u l a r orebodies.  discretized  i n t o a g r i d of square two  figure the  24) .  Each element  reef.  The  an  accurate  give  third  In MINTAB, the  d i m e n s i o n a l elements  dimension  i s the width  the  seam  width  of the must  r e l a t i o n t o the o v e r a l l s i z e of the problem. the  limitations  parallel  planes.  movement  of  planes  are  parallel normal three  planes.  the  the  the  Creating  broken  to  to  purposes,  the  into plane  dimensional  can  excavations  Relative two  seam  field  seam.  be  in  the  grid  movements between  and  the  two  components  act  c l o s u r e components  act  Ride  elements  (see  the  two  planes  displacement,  the  tractions  Displacements  and  stresses  calculated  as  discontinuities  a of  do  are  figure  o" , zz  not  subjected to  24) .  Z  a t unmined  linear a l l the  elements  in  and  Displacement  a  contact are  x z  p o i n t s i n the  combination  of in  a  are a s s o c i a t e d w i t h  come  o"y ,  two  induces  each element and r e p r e s e n t r e l a t i v e displacement between the If  in  discontinuity  c o n s i d e r e d as  d i s c o n t i n u i t y components i n t h r e e dimensions  planes.  To  small  be  components.  The  stress  (see  5.4.  reef  boundaries  planes.  is  The d e f i n i t i o n of  of displacement  m o d e l l i n g w i l l be d i s c u s s e d i n Chapter For p r a c t i c a l  orebody  r e p r e s e n t s mined o r unmined area i n  solution,  a s m a l l seam and  around  the  the  due  two to  a l l zero. seam  are  displacement  seam.  A  more  d e t a i l e d d e s c r i p t i o n of the displacement d i s c o n t i n u i t y method i s g i v e n by S t a r f i e l d and Crouch  (1973).  24. O b l i q u e view o f the MINTAB seam geometry and the s a p p l i e d l o c a l l y on each element i n the r e e f .  84 5.1.3  BEAP BEAP  is  developed  by  University Division)  a  three  J.A.C.  (1987), and  an  boundaries  elements  on  element  the  polynomial,  are  and  discontinuous.  are  PhD  thesis, CANMET,  stress  boundary  Pretoria  INCO  (Thompson  a b i l i t i e s i n mining  The  to  vary  1988. by  problem i s s u b j e c t  field.  The  T h i s means displacements assumed  used i n t h i s  discretized  elements v a r y  the displacements The  generally  program  at  V e r s i o n 1.0,  (see f i g u r e 25).  oriented  are non-conforming. each  a  i n conjunction with  arbitrarily  displacements  as  element  f o r p u b l i c r e l e a s e i n the f a l l of  Excavation  to  Diering  boundary  GEMCOM (Pty.) L i m i t e d .  p r o j e c t , i s due  quadrilateral  dimensional  according  stress  and  quadratically  and  and  tractions  to  a  on  quadratic  between a d j a c e n t elements are  r e s u l t i n g numerical model has related stress analysis,  some powerful  including:  - the need f o r fewer elements t o d i s c r e t i z e an e x c a v a t i o n  than  o t h e r t h r e e dimensional boundary element models, - the  ability  to  accommodate up  to  five  zones w i t h  different  material properties, - the use o f lumping t o reduce data s t o r a g e - and  the a b i l i t y  requirements,  t o determine s t r e s s e s and displacements  very  c l o s e t o an e x c a v a t i o n boundary. Further  details  about  D i e r i n g and Stacey  5.2  BEAP can  be  (1987).  Open Stope R i b P i l l a r M o d e l l i n g  found  i n D i e r i n g (1987)  and  85  FIGURE 25. A t y p i c a l BEAP geometry showing t h e boundary o f t h e e x c a v a t i o n s d e f i n e d by two d i m e n s i o n a l q u a d r a t i c , non conforming elements i n a t h r e e d i m e n s i o n a l s t r e s s f i e l d ( a f t e r Hudyma 1988b).  86 Boundary excavations magnitude section pillar  element relies  and  largely  orientation  describes  modelling  and  to  of  on  the  problem  of  the  pre-mining  a c o n s i s t e n t method t o  dimensions  pillars  numerical  determine  hard  geometry  and  average  This  stope  load  on  rib  D e f i n i n g the Open Stope Geometry In t h i s t h e s i s , the dimensions of stopes and p i l l a r s  defined with  according  respect  The  to  pillar  direction  to the  height of  f i g u r e 26.  is  excavation  surface  large much  surfaces,  excavation larger.  original p i l l a r load 27a).  is vertical In steep  a  the  horizontal  design  research  and  the p i l l a r  dipping  orebodies,  d i r e c t i o n perpendicular  size  that  stress  to  the  in  any  and  shape of  the  load.  For  was  load,  (where  most  done), the g r e a t e s t  height the  small  i s small.  redistribution  orebodies  stress.  parallel  redistribution  orebodies,  the  as  is vertical  of  t o the orebody.  D e f i n i n g the Average P i l l a r  Stress  be the  induced  (see f i g u r e  l a r g e s t induced  height  For  will  load i s  i s h o r i z o n t a l (see f i g u r e  pillar  be  defined  induced  Induced  the  to  stress  h o r i z o n t a l and the p i l l a r h e i g h t inclined  of  perpendicular the  greatest  load.  function  will  dimensions are  defined  induced  surfaces, In  the  typically  greatest  i s mostly  excavation  Pillar  d i r e c t i o n of  direction,  5.2.2  and  i n open stope mining.  5.2.1  For  the  stress.  s p e c i f y the  the  rock  i s defined  as  27b). the  S t o p e  S t o p e  1  2  Lo2  Lo1  Wp  Lo1 = length of stope 1 Lo2 = length of stope 2 Wp = width of pillar Hp = height of pillar, or stope breadth  FIGURE 26. T h i s f i g u r e d e f i n e s t h e dimensions f o r s t o p e s and p i l l a r s , and t h e o r i e n t a t i o n f o r t h e i n s i t u s t r e s s regime f o r t h i s t h e s i s .  88  £p  |  0" =  Ugh  Hp  FIGURE 27a. A r i b p i l l a r i n a h o r i z o n t a l weight o f the overburden.  FIGURE 27b. The d i r e c t i o n o f l o a d i n g v e r t i c a l orebody.  seam loaded by t h e  on a p i l l a r  in a  89 For  an  idealized  open  stope  rib pillar  in a  orebody, t h e i n s i t u s t r e s s a c t s i n t h r e e b a s i c ay,  and a  (see f i g u r e  2  pre-mining  stress  excavations. proportional to  that  highest  that  stress  i s concentrated  directions: a , x  i s a r e s u l t o f the  because  i n a direction  direction.  importance  In p i l l a r  i s usually  design,  i s generally  the d i r e c t i o n  that  has the  stress.  lowest because  the stress acting  i t i s parallel  t h e rjy d i r e c t i o n  direction, typically  i n the a  i s almost  much g r e a t e r than  sub-vertically  to  t h e Oy d i r e c t i o n a2 d i r e c t i o n .  dipping  always  i n the a orebodies,  i s much l a r g e r  direction i s  x  t o t h e orebody s t r i k e which  z  The induced  larger  because t h e pre-mining s t r e s s  for  the  adjacent  the d i r e c t i o n of  causes i t t o be shadowed by t h e open stopes. in  of  t o t h e s i z e and shape o f t h e stope s u r f a c e s normal  Inside r i b p i l l a r s , the  Pillar  Stress concentration  stress  greatest  28) .  vertical  than  load  i n the a  z  i n t h e Oy d i r e c t i o n i s  direction.  In a d d i t i o n ,  t h e stope s u r f a c e  normal  than those p e r p e n d i c u l a r t o  T h i s means t h e p i l l a r  stress  i n sub-vertical  o r e b o d i e s i s almost always h i g h e s t i n t h e Oy d i r e c t i o n . There i s a l a r g e pillar. the  i n t h e ay s t r e s s  field  in a rib  The b e s t l o c a t i o n t o determine t h e average ay s t r e s s i s  pillar  called  variation  centerline  the p i l l a r  a t t h e middle o f t h e stope h e i g h t  "mid-height c e n t e r l i n e " ) ,  see f i g u r e  28.  (also The  reasons f o r t h i s l o c a t i o n a r e : - i t i s t h e r e g i o n o f h i g h e s t normal s t r e s s - i t i s t h e r e g i o n o f lowest c o n f i n i n g  (ay d i r e c t i o n ) ,  stress  ( a direction), x  90  MID-HEIGHT CENTERLINE  MIDHEIGHT PLANE  FIGURE 28. The mid-height plane and c e n t e r l i n e f o r t a l l open stope geometries.  - it  is  often  observed  to  be  one  of  the  first  areas  of  instability in a pillar, - the e f f e c t o f the e x c a v a t i o n c o r n e r s and  stope ends are a t a  minimum, - this  i s usually  modelling  the  the mid-height  distribution  centerline.  across  In  significantly suggest value  a  the  the  the  stress  f o r open  5.3  squat  (taller  mid-height the  and  dimensional  narrower),  distribution  varies  centerline.  They  average  pillar  stress  should  principal  stress  ( i n the  stope  thesis,  rib pillars  s t r e s s a l o n g the mid-height  stress  stress  mid-height  for this  the  pillar  pillar  So  s t r e s s at  v  of the  the  pillar.  will  the  be  becomes more  be  the  ay  average  direction)  average  pillar  calculated  c e n t e r l i n e o f the  as  the  pillar.  2D M o d e l l i n g o f 3D E x c a v a t i o n Geometries Numerical  methods  is  dimensional  modelling a  time  geometry, of  and  these  of  underground  consuming  numerical  e s t i m a t e the s t r e s s  One  when two  Hoek and Brown (1980) show t h a t as a  pillar,  maximum  across  average  the  across  that of  analysis  be a l a r g e v a r i a t i o n i n the a  becomes more s l e n d e r  uniform.  of  ( i n plane s t r a i n ) i s used.  However, t h e r e may  pillar  plane  modelling  found  expensive can  be  with  procedure.  used  c o s t than  i s a t the mid-height  3D  numerical  of t a l l  open  3D Two  effectively  i n some of the p l a n e s of a 3D  a t a much lower planes  and  excavations  to  pillar  methods. stopes,  which This  i s o f primary  concern  sub-section w i l l  estimate It w i l l  the  average  i n open  d i s c u s s how pillar  stope  2D  stress  design.  m o d e l l i n g can be used  i n open stope  to  rib pillars.  a l s o e s t i m a t e the d i f f e r e n c e between 2D and 3D numerical  m o d e l l i n g f o r v a r i o u s open stope mining  5.3.1  rib pillar  geometries.  Plane S t r a i n S o l u t i o n  To e s t i m a t e the s t r e s s around open stopes, the plane s o l u t i o n i s g e n e r a l l y used.  strain  Plane s t r a i n c o n d i t i o n s assume t h a t  around an e x c a v a t i o n a l l the mining induced d i s p l a c e m e n t s occur in  the p l a n e of the orebody c r o s s - s e c t i o n and the displacements  are  the  stope  same f o r a l l c r o s s - s e c t i o n s .  is  modelled  assumption  i s that  in  the  xy  plane  (see  i n the 3D s i t u a t i o n ,  i n f l u e n c e on the c r o s s - s e c t i o n p l a n e . "For  In a t y p i c a l  axial  ratios,  usually  approximate the  within  less  than  the  ten,  plane  correct and  28) .  The  the stope ends have no  Brown (1985) notes t h a t :  uniform excavation c r o s s - s e c t i o n s ,  extreme  figure  geometry, a  o t h e r than those with  strain  boundary  stresses  three-dimensional stress  sometimes  five,  per  cent  to at  l o c a t i o n s removed by a t l e a s t two e x c a v a t i o n 'diameters' from i n t e r s e c t i o n s , e x c a v a t i o n ends or changes o f c r o s s - s e c t i o n . "  In  a p p l y i n g p l a n e s t r a i n c o n d i t i o n s t o open stope r i b p i l l a r  design,  the  ends on  the s t r e s s  If  the  s u b j e c t of  mid-height  interest  i s the  a t the mid-height plane  i s not  influence  o f the  c e n t e r l i n e of the  sufficiently  removed  stope  pillar. from  the  stope  ends,  will  occur  some into  of  the  the  i n t o the p i l l a r .  mining  abutments  induced  at  i s g r e a t e s t when t h e r e i s no  which  i s the  case  5.3.2  ends,  r a t h e r than  f o r the  2D  mid-height  i n f l u e n c e o f the stope ends,  plane  strain  i n work done by Watson and  and i s observed  stope  redistribution  T h i s means t h a t the s t r e s s a t the  plane  confirmed  the  stress  solution.  Cowling  This i s  (1985) a t Mt.  i n the r e s u l t s t o be d i s c u s s e d i n Chapter 5.3.2.  Comparison of 2D and 3D Numerical M o d e l l i n g R e s u l t s  A comparison  of s e v e r a l d i f f e r e n t stope geometries was  w i t h the 3D model BEAP, and the 2D model BITEM i n p l a n e The  Isa  objective  was  to  investigate  i n more depth  the  done  strain.  degree  o v e r e s t i m a t i o n p r e d i c t e d by BITEM f o r d i f f e r e n t stope and  of  pillar  geometries. The s i z e of the plane normal t o the <7p s t r e s s  (shaded plane,  f i g u r e 29) has the g r e a t e s t i n f l u e n c e on s t r e s s c o n c e n t r a t i o n a t the p i l l a r mid-height  centerline.  To check the i n f l u e n c e of the  stope ends on the mid-height plane, the r a t i o o f stope h e i g h t t o stope l e n g t h was  varied.  Four t e s t s , comprised  different  stope geometries,  The  first  test  was  increased  second  test  constant  checked for  checked  height test  and  were modelled  the average  stopes  with  a  checked  increasing  The  third  the average  was  i n c r e a s e d f o r stopes  with  a  BITEM and  BEAP.  pillar  s t r e s s as the h e i g h t  square  cross-section.  the average p i l l a r an  with  of a t o t a l of 12  The  s t r e s s f o r stopes w i t h a  longitudinal pillar  constant  stope  length.  s t r e s s as the h e i g h t longitudinal  cross-  94 Op H  Wp  L  FIGURE 29. The shaded plane has the greatest i n f l u e n c e on the mid-height a s t r e s s . y  TEST  SQUARE STOPE CROSSSECTION  LONGITUDINAL STOPE CROSSSECTION LONGITUDINAL STOPE CROSSSECTION TRANSVERSE STOPE CROSSSECTION  BEAP BITEM BITEM AVE. H:L AVE. PILLAR RATIO PILLAR STRESS STRESS INCREASE INCREASE  STOPE LENGTH  (D  STOPE BREADTH (B)  STOPE HEIGHT (H)  PILLAR WIDTH (Wp)  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  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  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  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 f o r four sets of d i f f e r e n t orebody geometries.  section. stopes  The of  a  final  test  constant  checked  height  the average  and  length  pillar  were  stress  as  increased  in  f o r each  run  breadth. Table (the the  6 shows the  dimensions average  stope and p i l l a r  are d e f i n e d i n f i g u r e 29) .  pillar  stress  defined  as  the  The  average  average  pillar  mining s t r e s s i n t h a t d i r e c t i o n In  T a b l e 6 a l s o shows  i n c r e a s e f o r BEAP and  stope h e i g h t : l e n g t h r a t i o . is  dimensions  pillar  stress  BITEM and  stress increase  divided  by  the  was  higher  f o r the  than the 3D BEAP models.  2D  plane  strain  mid-height  (BITEM) models  The o v e r e s t i m a t i o n of BEAP by BITEM i s  shown f o r each geometry i n f i g u r e 30. 3 0 i s an  pre-  ( i e . ay i n f i g u r e 28).  a l l 12 cases, the average p i l l a r s t r e s s a t the  centerline  the  The dashed l i n e on  figure  e s t i m a t e of the maximum o v e r e s t i m a t i o n o f BEAP by  2D  p l a n e s t r a i n m o d e l l i n g f o r v a r i o u s stope h e i g h t t o stope l e n g t h ratios.  As  the average to  the  stope h e i g h t t o stope  pillar  s t r e s s p r e d i c t e d by the 3D models i s c l o s e r  the 2D p l a n e s t r a i n s o l u t i o n .  ratio  increased  over  4:1,  h o r i z o n t a l plane e s s e n t i a l l y levels  similar  Brown's comment at  length r a t i o increases,  the s t r e s s  As the stope h e i g h t t o l e n g t h  the  3D  remained  stress  plane  strain  between  2D  plane  to  a stope c r o s s - s e c t i o n needs t o be  strain  and  3D  modelling  f o r good results,  would correspond t o a stope h e i g h t t o stope l e n g t h r a t i o of His  the  modelling.  l e a s t two e x c a v a t i o n "diameters" from the stope end,  agreement  in  the same and converged  p r e d i c t e d by  (above) t h a t  induced  e s t i m a t i o n of l e s s than 10 % d i f f e r e n c e between 2D plane  4:1.  aVCn H V n i d 30VH3AV J O NOLLVHI±S3a3AO FIGURE 30. O v e r e s t i m a t i o n o f average p i l l a r l o a d by t h e 2D "BITEM" boundary element method f o r t h e 12 runs i n t h e four tests.  97 strain  and 3D m o d e l l i n g agrees  well with the r e s u l t s  presented  i n f i g u r e 30.  5.4 Displacement  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 Stope  Geometries  For e x c a v a t i o n s w i t h i r r e g u l a r c r o s s - s e c t i o n s o r s m a l l stope length not  t o stope  effectively  centerline  height r a t i o s , predict  element  conditions.  The  dimensional  stress  orebodies.  t h e average  of a p i l l a r .  boundary  stress  The displacement  method DD  t h e 2D p l a n e  MINTAB  code  can  may be  redistribution  F o r MINTAB a n a l y s i s ,  s t r a i n method can a t t h e mid-height discontinuity  be  used  useful to  around  in  predict thin,  (DD) these three  tabular  t h e orebody must be a s i n g l e  seam w i t h 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 , d i p and t h i c k n e s s . In addition,  t h e t h i c k n e s s o f t h e seam must be s m a l l compared t o  the l e n g t h o f e x c a v a t i o n s made i n t h e seam. sections MINTAB's  will  investigate  ability  to  the e f f e c t  predict  The f o l l o w i n g sub-  o f t h e seam  stresses  at  t h i c k n e s s on '  the  mid-height  c e n t e r l i n e o f open stope r i b p i l l a r s .  5.4.1 Seam T h i c k n e s s L i m i t a t i o n s To h e l p d i s c u s s t h e i n f l u e n c e o f t h e t h i c k n e s s o f t h e r e e f , the r a t i o o f t h e s h o r t e s t stope dimension  t o t h e seam t h i c k n e s s  i s d e f i n e d as t h e "seam t h i c k n e s s r a t i o " .  I n open stope mining,  where stopes a r e t y p i c a l l y thickness  ratio  stope breadth  will  taller  usually  than they a r e l o n g , t h e seam  be t h e r a t i o  o f stope  length to  (see f i g u r e 31). Other authors have d i s c u s s e d t h e  SEAM THICKNESS RATIO = J__ B FIGURE 31. The dimensions and geometry of the MINTAB/BEAP comparison tests.  1  BEAP 1 MINTAB AVE. | SEAM PILLAR | THICK. STRESS I RATIO INCREASED  MINTABI  STOPE LENGTH (L)  STOPE BREADTH (B)  STOPE HEIGHT (H)  PILLAR WIDTH (Wp)  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  10  10  60  10  1.7  |  1.0  1.65 fl  10  10  80  10  1.7  |  1.0  1.6  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  3.0  2.0  10  10  60  10  1.7  fi 1 |  1.0  1.65  LONGITUDINAL STOPE CROSSSECTION  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  TRANSVERSE STOPE CROSSSECTION  10  10  40  10  1.6  1.0  1.5  10  20  40  10  1.4  0.5  1.45  10  40  40  10  TEST  SQUARE STOPE CROSSSECTION  LONGITUDINAL STOPE CROSSSECTION  |  1.2  |  | 0.25  AVE. PILLAR STRESS INCREASE  1.45  TABLE 7. Comparison of BEAP and MINTAB for the four different t e s t s .  J |  influence  of  the  seam t h i c k n e s s  ratio.  Crouch  (1986)  states  t h a t 3D 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 programs: "...can  be  used  to  analyze  any  excavation  that  has  a  b r e a d t h : t h i c k n e s s r a t i o o f 3 o r more." When  investigating  excavation  stress  geometries  discontinuity  method,  distributions  with  Brady  the  around  pseudo-3D  (1978)  was  more  different  displacement  conservative  in  f i n d i n g t h a t a, "...comparison dimensional that  the  with  results  analyses of  method  is  from  these  influence  of  the  satisfactory  seam  three-  e x c a v a t i o n shapes,  span/height r a t i o i s g r e a t e r than The  independent  for  openings  indicate where  the  5."  thickness  ratio  on  average  pillar  s t r e s s w i l l be checked through the use o f the t e s t s d e s c r i b e d i n Chapter 5.3.2.  5.4.2  Comparison of Displacement D i s c o n t i n u i t y and 3D Numerical  Modelling A comparison pillar the  stress  was  results  average p i l l a r  geometries. seam  made between the t h r e e d i m e n s i o n a l average  The  thickness  from the BEAP runs i n Chapter 5.3.2  s t r e s s p r e d i c t e d by MINTAB f o r the same stope goal  ratio  was  t o determine the i n f l u e n c e t h a t  has  d i s c o n t i n u i t y modelling.  on The  the 12  t e s t s a r e summarized i n t a b l e 7. pillar  and  dimensions,  the  seam  accuracy  of  the  displacement  stope geometries f o r the  four  T h i s t a b l e shows the stope and  thickness  ratio  f o r each  geometry  100 and  the  average  (average  pillar  pillar  stress  for  stress increase  each  BEAP  i s c a l c u l a t e d as  the average p i l l a r s t r e s s t o the pre-mining The  d i f f e r e n c e between the  thickness ratios of  the  figure  i s given  and  two  MINTAB  the  run  ratio  of  stress).  models f o r the v a r i o u s seam  i n f i g u r e 32.  A very  rough  estimate  maximum d i f f e r e n c e between MINTAB and  BEAP i s shown i n  32.  on  This  dashed  envelope  is  based  the  absolute  magnitude o f the d i f f e r e n c e ( f o r a l l the p o i n t s ) , and p l o t t e d as a m i r r o r image above and below the 0%  line.  In the m a j o r i t y of  the t e s t s , t h e r e i s l i t t l e d i f f e r e n c e between the average p i l l a r s t r e s s e s p r e d i c t e d by 1.0,  there  is  less  There i s l e s s than seam t h i c k n e s s  BEAP and than  10%  MINTAB.  At a seam t h i c k n e s s  difference for  a 5% d i f f e r e n c e f o r the  ratio  equal  to  or  greater  a l l five  are  only  than one. be  two  tests  with  a  tests.  f i v e t e s t s having than  3.0.  seam t h i c k n e s s  However,  ratio  of  less  Many more t e s t s are needed b e f o r e any c o n c l u s i o n s  drawn about the a b i l i t y  a  Overall,  o n l y one t e s t showed a d i f f e r e n c e of g r e a t e r than 10%. there  of  of MINTAB t o model stope  and  can  pillar  geometries w i t h low seam t h i c k n e s s r a t i o s . Considering suggested stress Reasons  by  r a t i o s may  minimum  Crouch and  between why  the  BEAP  these  seam t h i c k n e s s  ratios  of  3 and  Brady, the d i f f e r e n c e i n average  and  authors  MINTAB suggest  is  much  less  conservative  5  pillar  than  expected.  seam  thickness  be:  - a h i g h l e v e l of agreement between the DD and sought i n the a n a l y s e s done by Crouch and  3D s o l u t i o n s was  Brady,  COMPARISON: DD AND 3D NUMERICAL METHODS  H  •0*0 o H 1 G © (D 5d  INFLUENCE OF THE SEAM THICKNESS RATIO  30%  o. a w  O 0 u> ft ft W (D <D • . 0.0. m 0* 0* H < Z WHfli > 25 H•0 H H> >-  20* H  ffi  Q hf UJ fl> I3 3 O S 8 Q a ft lit C C ^ tr cr O © ft (D a. O a t» (D UJ n < O ft» © (D zLd H n ft 3 0£ (J 3 * p. 0) <0 U. U. to «Q 5 O (D 3 ft H- 0» vt V) © M< UJ » HID a: f t » h( 09 0» CD D CO ft 0  H »  10X  a  -10*  H  -20*  H  n H>  B  t-  -30*  CO  ft 0)  n  SEAM THICKNESS RATIO (LENGTH:BREADTH) • 3D TESTS  102 - using  the  average  of  several  elements  to  determine  average p i l l a r s t r e s s has the e f f e c t o f "smoothing  the  out" l a r g e  d i f f e r e n c e s a t i n d i v i d u a l elements i n the p i l l a r , - o r the open tests  are  modelling  stope r i b p i l l a r  much  simpler  than  the  and  geometries more  excavation  v e r i f i c a t i o n s by Crouch and  a n a l y z e d i n the  amenable  to  geometries  DD  numerical  analyzed  in  o f the comparison  r a t i o of three w i l l BEAP  for  influence  open  suggest  that  using a  the  seam t h i c k n e s s  g i v e v e r y good agreement between MINTAB and  stope  o f the  the  Brady.  While complex mining geometries have not been i n v e s t i g a t e d , results  12  rib  pillars.  Further  seam t h i c k n e s s r a t i o  will  be  checks  of  the  done i n Chapter  5.5 u s i n g case h i s t o r i e s from the d a t a base.  5.5 P i l l a r Load C a l c u l a t i o n s f o r t h e Open Stope Data Base There stress  i s no  or  Chapter  load  3,  elastic  can determine the  As  numerical  deteriorating  For  pillars  condition,  m o d e l l i n g may  load be  average  d i s c u s s e d above, m o d e l l i n g can  approximations o f the p r e - f a i l u r e  pillars.  numerical  i n a mine p i l l a r .  linear  consistent mine  a b s o l u t e method t h a t  that  give  load  i n hard  rock  a  sloughing  by  linear  a considerable overestimate.  the  r o c k f r a c t u r i n g and p i l l a r deformation. l i n e a r e l a s t i c load w i l l  conditions.  A failed  For f a i l e d  or  elastic  can be a t t r i b u t e d t o the l o c a l 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 to  in  often  have  determined  and  This due  pillars,  not be r e p r e s e n t a t i v e o f the s t r e s s  pillar will  have l o s t some, o r n e a r l y a l l  103 of i t s l o a d b e a r i n g into  nearby  linear  competent p i l l a r s  elastic  sloughing  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  modelling  o r abutments.  The i n a b i l i t y o f  t o determine an approximate  and e s p e c i a l l y f a i l e d p i l l a r s p r e s e n t s  developing  load f o r  difficulties in  a r e l i a b l e method o f p r e d i c t i n g p i l l a r  failure.  5.5.1 Assumptions In o r d e r conditions pillars  t o s e t a c o n s i s t e n t method f o r d e t e r m i n i n g  for a l l pillar are  infinitely  characteristics. load  bearing  assumption geometrical  elastic  i t will in  regardless  will  permit  conditions  will  of t h e i r  t e c h n i c a l l y accurate  deformation  not l o o s e  physical  their  condition.  t o t h e a c t u a l problem, t h i s  the i n v e s t i g a t i o n that  be assumed t h a t  their  T h i s means t h a t p i l l a r s  capacity  While n o t b e i n g  assessments,  loading  existed  of  before  the stress failure  and  and  a  rudimentary look a t t h e c o n d i t i o n s t h a t have r e s u l t e d i n f a i l u r e of for  open  stope p i l l a r s .  predicting  Ultimately,  conditions  that  i twill  provide  are  associated  and MINTAB  t o model  the basis  with  pillar  failure.  5.5.2 P i l l a r Load The  ability  Results of  BITEM  geometry i n t h e data base was e v a l u a t e d . adequately  account  f o r the excavations  conditions of the p i l l a r , situation  occurred  each  problem  I f a program c o u l d not affecting  the stress  numerical a n a l y s i s was n o t done.  f o r BITEM  when  t h e geometries  This  o f a l l the  104 significant the  excavations  problem.  pillar  c o u l d n o t be i n c l u d e d i n t h e plane o f  MINTAB was n o t used  geometry when en-echelon  to investigate  a stope and  stopes were p a r t o f t h e problem  geometry, o r t h e orebody had s i g n i f i c a n t changes i n t h i c k n e s s o r significant  changes i n d i r e c t i o n .  F o r each case h i s t o r y ,  Table  8 shows: - t h e pre-mining - the  limiting  applicability (the  s t r e s s normal t o t h e orebody, geometrical o f MINTAB  ratios  associated  with  the  (the seam t h i c k n e s s r a t i o ) and BITEM  stope h e i g h t t o l e n g t h r a t i o ) ,  - t h e average  s t r e s s p r e d i c t e d f o r t h e p i l l a r by each numerical  method and t h e b e s t estimate o f t h e average - the estimated  error  associated with  pillar  the best  stress,  load  due t o  assumptions a s s o c i a t e d w i t h m o d e l l i n g t h r e e d i m e n s i o n a l and  pillar  geometries  with  numerical  methods  that  stope  a r e not  three dimensional, - t h e average theory  pillar  load calculated  i n the t r i b u t a r y  n u m e r i c a l l y determined  based  area  (chapter 3.1.2.1),  - and t h e e r r o r  The  using the t r i b u t a r y  best  estimate  on t h e l i m i t i n g  area  load  compared t o t h e  load.  o f t h e average ratios  pillar  l o a d was  f o r BITEM and MINTAB.  chosen  I f a case  h i s t o r y had a h i g h stope l e n g t h t o stope width r a t i o ,  t h e BITEM  load  thickness  was used.  I f a case  history  r a t i o , t h e MINTAB l o a d was used.  had a h i g h  seam  I f t h e stope geometry d i d not  105  •  •"  PUBMINING STRESS (MPa)  PILLAR NUMBER  2 3 7 8 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61  .  ! !  39 39 46 46 14 14 16 40 40 17 17 17 17 17 17 12 12 12 12 12 12 15 15 15 15 15 15 55 55 55 55 23 23 23 23 15 15 15 23 18 18 30 30 30 30 30 35  BITEM HEIGHT: LOAD LENGTH (MPa) RATIO 1.4 1.4 4.5 4.5 2.6 1.8 4.0 2.0 1.7 2.9 4.0 3.5 1.4 3.5 0.9 3.0 3.0 NA 1.8 NA 0.9 5.0 5.0 6.3 2.5 1.5 2.5 5.0 5.0 5.0 5.0 2.1 2.1 1.5 1.5 NA NA NA NA 5.6 3.4 1.1 5.8 4.4 0.8 0.6 5.0  ,  ,  !  !  !  51 64 55 69 28 29 29 90 91 43 28 29 38 33 57 29 44 NA 26 NA 60 26 38 31 31 38 40 99 75 76 102 30 32 41 49 NA NA NA NA 43 44 59 38 40 72 82 70  MINTAB SEAM ! THICK, j LOAD RATIO | (MPa) 0.3 ; 0.3 j 0.6 | 0.6 | 1.5 | 1.7 ! 0.9 ! 3.0 | 3.3 ! 0.8 ! 0.7 j 0.7 j  1  0.7 | 0.8 ! 1.8 J 3.8 ! 1.1 ! 0.8 ; 1.7 | 3.8 ! 1.0 | 1.1 ! 1.2 !  i.o !  1.3 0.7 0.5 0.5 0.7 0.6 NA NA NA NA 3-3 7.0 4.6 0.7 3.0 3.0 0.4 0.2 0.2 0.2  ! ', | j [ ; ; ! ; ; j ! ! ! ! i | ] ! !  N0.7 A  ;  1  47 55 60 83 24 24 24 66 63 41 28 26 31 27 30 24 33 28 21 31 37 28 38 30 30 32 35 78 60 59 83 NA NA NA NA 31 39 48 36 46 46 48 46 45 54 53 NA  ESTIMATED AVERAGE PILLAR LOAD j Z ERROR (MPa) 51 ! 25-45Z 64 | 25-45Z <10Z 55 ! 69 ; <10Z 28 ! 10-25Z 29 ! 25-45* 29 ! <10Z 66 ! <10Z 63 | <10Z *3 ! 10-25Z <10Z 28 | 29 i 10-25Z 38 ; 25-45Z 33 ! 10-25Z 57 ! >45Z 29 ! 10-25Z 33 ! <10Z 28 | 26 ! 25-45Z 31 ! 37 ! <10Z 26 ! <10Z 38 i <10Z <10Z 31 ! 31 ! 10-25Z 38 25-45Z 40 j 10-25Z 99 ! <10Z 75 ! <10Z 76 ! <10Z 102 ! <10Z 30 | 10-25Z 32 j 10-25Z 41 ! 25-45Z 49 i 25-45Z <10Z 31 ! <10Z 39 ! 48 | <10Z 36 j 46 | <10Z 46 <10Z 59 | 25-45Z 38 ! <10Z 40 ! <10Z 72 j >45Z 82 | >45Z 70 ! <10Z  1  TRIBUTARY AREA PILLAR LOAD J (MPa) | Z ERROR 62 90 61 92 32 33 32 98 99 58 35 33 53 33 65 37 48 NA 33 NA 91 33 57 38 44 58 57  ! ; ; i ! ! ! ! i ! ,' J ! ! ! ! ! j ! ; i ! ! ; | ; !  no ;  73 | 73 ! 110 | 36 ! *2 ! 55 ! 71 ! NA | NA | NA | NA ! 50 ; 54 ; 69 ! 45 | 48 ! 95 ! 119 ] 88 j  22Z 40Z 12Z 33Z 15Z 12Z 10Z 48Z 57Z 34Z 24Z 14Z 39Z OZ 15Z 27Z 45Z  1  1  PILLAR j ASSESSMENT |  STABLE FAILURE STABLE FAILURE STABLE STABLE SLOUGH STABLE  i | ! ! ! ! ; !  STABLE SLOUGH STABLE STABLE FAILURE STABLE FAILURE STABLE STABLE NA SLOUGH 27Z STABLE NA FAILURE 146Z STABLE 27Z , STABLE 51Z ! FAILURE 21Z SLOUGH 42Z STABLE 52Z j FAILURE 43Z ; FAILURE 11Z ! FAILURE -2Z ! STABLE -4Z | STABLE 8Z ! FAILURE 21Z ! STABLE 32Z | SLOUGH 34Z ] FAILURE 44Z ! FAILURE NA ! STABLE NA ! STABLE NA ! STABLE NA ! STABLE 8Z ! STABLE 17Z ] STABLE 17Z ! SLOUGH STABLE i8z : 20Z J STABLE 31Z | SLOUGH 45Z ! SLOUGH 25Z ! SLOUGH  1| ! ! i ! ! !  TABLE 8. P i l l a r l o a d i n f o r m a t i o n 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 u s i n g BITEM, MINTAB and the T r i b u t a r y Area Theory.  ! ! ! ! ,' j | ] ! ! | ! ! ! ! ! j ! i ! ! | j ! ! ! ! ! | i  106 fit  either limiting  ratio,  used t o  e s t i m a t e the  because  i t accounts  than MINTAB, and  the  BITEM l o a d was  average p i l l a r f o r the  the  error  used.  BITEM i s  s t r e s s i n these s i t u a t i o n s  geometry o f associated  these problems  with  BITEM  (from  better figure  30) , i s b e t t e r understood than the e r r o r a s s o c i a t e d w i t h MINTAB (from f i g u r e The  error  comparisons numerical results  MINTAB  with  and  with  tend  30 and  best to  load  i s based  a  true  three  i n chapters  5.3.2  and  the  to  have  predicted  on  a  load.  lower This  and  consequently  estimation 32.  The  f i t the  5.4.2.  degree  The  The  primary  of  i s because  modelling  the  dimensional  geometries are more r e g u l a r than secondary and  l i m i t i n g ratios) better. an  the  BITEM  presented  geometries  geometries  is  of  method  associated stoping  associated  i n T a b l e 8 show t h a t s t a b l e case h i s t o r i e s and  stoping  the  32).  error primary  tertiary  constraints  (ie.  e r r o r i n the b e s t p i l l a r  load  of the maximum p o s s i b l e e r r o r based on actual error i s smaller  f o r many of the  figures pillars.  For t h i s reason, the l o a d a p p l i e d i n the development of a p i l l a r d e s i g n method w i l l not be a d j u s t e d Table varied  8  shows  that  tributary  r e s u l t s compared t o the b e s t  modelling.  I t can be  the  average p i l l a r  the  stope h e i g h t : l e n g t h  b e t t e r the the  the  f o r the e s t i m a t e d e r r o r .  load  area  theory  l o a d e s t i m a t e d by  assumed t h a t t r i b u t a r y area  load.  by  highly  numerical  overestimates  I t i s a l s o apparent t h a t the  greater  r a t i o of the case h i s t o r y geometry,  agreement between the t r i b u t a r y area predicted  has  numerical  modelling.  theory In  load  general,  the and the  107 o v e r e s t i m a t i o n o f t h e p r e d i c t e d s t r e s s makes t h e t r i b u t a r y t h e o r y v e r y u n r e l i a b l e i n t h e e s t i m a t i o n o f t h e average  area  load i n  open stope r i b p i l l a r s .  5.5.3  Numerical Chapters  5.3  dimensional against  Model Comparison U s i n g t h e Case H i s t o r i e s and 5.4 gave  and displacement  a t h r e e dimensional  a detailed  discontinuity method.  comparison numerical  case  limitation  histories  length r a t i o of  these  length  f i t t h e MINTAB  of 3 or greater  modelling  A n a l y s i s o f t h e data base  case h i s t o r i e s p r o v i d e s f u r t h e r i n f o r m a t i o n f o r Two  and a l s o  seam  have  comparison. thickness  ratio,  histories,  Table  t h e seam  9 shows  thickness  ratio,  ratio  a large height t o  ( g r e a t e r than 4) making good BITEM c a s e s .  case  o f two  t h e stope  F o r both height t o  t h e average  s t r e s s p r e d i c t e d by BITEM and MINTAB and t h e d i f f e r e n c e  pillar i n the  predicted stress.  T h i s comparison shows good agreement between  the  load  average  pillar  f o r t h e two methods when a stope and  p i l l a r geometry meets both o f t h e l i m i t i n g  CASE NUMBER  BITEM HEIGHT: LENGTH RATIO  ratios.  MINTAB  AVERAGE PILLAR LOAD (MPa)  SEAM THICKNESS RATIO  AVERAGE PILLAR LOAD (MPa)  PERCENT DIFFERENCE BETWEEN BITEM AND MINTAB  54  5.6  43  3.0  46  - 7 %  55  3.4  44  3.0  46  - 5 %  T a b l e 9. Comparison o f MINTAB and BITEM programs l i m i t a t i o n s a r e s a t i s f i e d .  results  when  both  108 Three  case  constraint,  histories  satisfy  b u t do n o t have a l a r g e  These a r e good MINTAB geometries, modelling. For  each  BITEM  t o length  pillar  stress  overestimation these  ratio,  slightly  histories,  by  BITEM  o f BEAP graph  developed  above t h e maximum  load.  t h e average and t h e  pillar  against  load.  t h e BITEM 5.3.2,  they  documented i n  However, c o n s i d e r i n g a p o t e n t i a l  BITEM  histories,  SEAM THICKNESS RATIO  the results  i n Chapter 5.3.2.  MINTAB  AVERAGE PILLAR LOAD (MPa)  f o r BITEM  t h e stope  MINTAB  over-estimation  are n o t v e r y f a r above t h e l i m i t found  HEIGHT: LENGTH RATIO  ratio,  i n Chapter  o f up t o 10% f o r t h e MINTAB case  CASE NUMBER  10 shows  and  a r e compared  c h a p t e r 5.3.2 (see f i g u r e 33). error  Table  ratio.  pillar  o f t h e MINTAB p r e d i c t e d  cases  thickness  t o length  t h e average  t h e seam t h i c k n e s s  predicted  three  height  seam  but not favorable  overestimate  case  by BITEM  overestimation plot  will  o f these  height  When  t h e MINTAB  AVERAGE PILLAR LOAD (MPa)  PERCENT DIFFERENCE BETWEEN BITEM AND MINTAB  18  2. 0  90  3.0  66  + 36 %  19  1.7  91  3. 3  63  + 44 %  31  0.9  60  3.8  37  + 62 %  T a b l e 10. Comparison o f BITEM and MINTAB, when t h e MINTAB l i m i t a t i o n i s met, but t h e BITEM l i m i t a t i o n i s n o t met. The o v e r e s t i m a t i o n by BITEM i s i n t h e range estimated i n Chapter 4.  COMPARISON: 2D AND 3D NUMERICAL METHODS INFLUENCE OF STOPE HEIGHT:LENGTH RATIO  70*  60*  V  H  \  50* H  40* H  30* H  • •  20*  io* H  \  \ §  OX  •  3D TESTS  STOPE HEIGHT:L£NGTH RATIO * DATA BASE  to  1  110 Many o f t h e case height  to length r a t i o  modelling), for  histories  investigated  had a l a r g e  (making them good geometries  f o r BITEM  but do not f i t t h e seam t h i c k n e s s c r i t e r i o n  a c c u r a t e MINTAB m o d e l l i n g .  stope  needed  By u s i n g both numerical methods,  the e f f e c t o f a low seam t h i c k n e s s r a t i o can be compared a g a i n s t the  satisfactory  shows  pillar  t h e stope  ratio,  height  t h e BITEM  difference  l o a d r e s u l t s g i v e n by BITEM. t o length  and MINTAB  i n t h e average  geometries.  The  average  pillar  ± 25 % w i t h t h e BITEM r e s u l t s .  pillar  stress  Chapter in The  stress  envelope  analysis  F o r t h e geometries  t h e two methods  and t h e different  vary  up t o  with  larger  i s less.  The maximum  l o a d i s s l i g h t l y h i g h e r than t h e 12 runs i n  5.4.2, when p l o t t e d  pillar  stress,  for thirteen  MINTAB  thickness  (>1.0 but <3.0), t h e d i f f e r e n c e i n average  between  difference i n p i l l a r  t h e seam  pillar  stress  r e s u l t s of the  seam t h i c k n e s s r a t i o s  ratio,  T a b l e 11  versus  showing  on t h e graph  of percent  seam t h i c k n e s s r a t i o  t h e maximum  error  difference  (see f i g u r e  has been  34) .  redrawn i n  f i g u r e 34.  5.6 Chapter The used  Summary  t h r e e boundary element models (BITEM, MINTAB and BEAP),  i n investigating  briefly  described.  p i l l a r geometries  open  stope  Conventions  rib pillar  load,  f o r defining  open  and determining t h e average  have  been  stope r i b  p i l l a r s t r e s s have  been p r e s e n t e d . The use o f  t h r e e dimensional boundary  element m o d e l l i n g i s  111  CASE NUMBER  MINTAB  BITEM HEIGHT: LENGTH RATIO  AVERAGE PILLAR LOAD (MPa)  SEAM THICKNESS RATIO  AVERAGE PILLAR LOAD (MPa)  PERCENT DIFFERENCE BETWEEN MINTAB AND BITEM  7  4.5  55  0.6  60  +  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  33  5.0  38  1.1  38  34  6.3  31  1.2  30  -  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  +  9 %  8 % 0 % 3 %  11. Comparison between good BITEM and poor MINTAB geometries shows t h e average p i l l a r stress varying up t o ± 25%.  BV1NIH A8 0310103yd 30N3y3JJIQ SS381S  FIGURE 34. The d i f f e r e n c e between t h e average p i l l a r s t r e s s p r e d i c t e d by MINTAB and the average p i l l a r s t r e s s p r e d i c t e d by BEAP f o r the comparison t e s t s and 13 case histories.  not p o s s i b l e f o r the case h i s t o r i e s i n the data base. to:  high  program  limitations.  set  The  discontinuity  2D  up plane  run  strain  times, and  and  program  pseudo-3D  space  displacement  (DD) methods have been used t o e s t i m a t e the l o a d f o r  each p i l l a r case h i s t o r y . l i m i t a t i o n s t h a t may The  and  T h i s i s due  geometrical  Both of these programs have g e o m e t r i c a l  i n t r o d u c e e r r o r i n t o the average p i l l a r l o a d .  limitations  have  been  described  and  the  error  a s s o c i a t e d w i t h 2D plane s t r a i n and DD methods has been q u a n t i f i e d using Figure  12  test  33  runs  shows  and  the  some case  potential  histories  error  the  potential  error  the  associated with  s t r a i n m o d e l l i n g f o r open stope r i b p i l l a r shows  from  associated  geometries. with  d i s c o n t i n u i t y method f o r open stope r i b p i l l a r  the  data  base.  2D  plane  F i g u r e 34  displacement  geometries.  114 CHAPTER 6 DEVELOPMENT OF A PILLAR DESIGN METHOD  It stope  was s t a t e d  i n Chapter  r i bpillars  authors design  have  a d e s i g n method  has not been developed  shown t h a t  procedure  3 that  w i t h case h i s t o r i e s .  o r confirmed.  t h e b e s t way t o develop  i s t o conduct  a survey  f o r open Other  and v e r i f y  a  and c o n f i r m a method  There a r e many examples o f p i l l a r  s t u d i e s , t h e most n o t a b l e b e i n g : Salamon (1967) i n South  African  c o a l mines, Hedley  and Grant  and  and B i e n i a w s k i (1983) i n U n i t e d S t a t e s c o a l  pillar  mines.  mining,  (1972) i n Canadian  design  hard rock room  Each o f these s t u d i e s used e x p e r i e n c e and c a l i b r a t i o n t o  develop a method f o r mining s p e c i f i c The number o f mines v i s i t e d  conditions.  i n t h e " I n t e g r a t e d Mine  Design  Study" has r e s u l t e d i n t h e c o l l e c t i o n o f a s u b s t a n t i a l amount o f data  o f s t a b l e and f a i l e d  mines.  T h i s data w i l l  method  for r i bpillars  wealth  o f data  from  rib pillars  be used  from Canadian  t o develop  an e m p i r i c a l  i n open stope mining.  hard  rock room  open stope  and p i l l a r  design  In a d d i t i o n ,  a  mines has been  found i n l i t e r a t u r e t o h e l p c o n f i r m t h e new e m p i r i c a l  method.  S p e c i f i c a l l y , the i n t e n t i o n of t h i s chapter i s t o : - verify  the variables  significant  i n open stope r i b p i l l a r s  based on t h e data a v a i l a b l e , - present  a  method  that  explains the r e s u l t s  o f t h e case  h i s t o r i e s i n t h e data base, - use case  histories  from  literature  (mostly  from  room and  115 p i l l a r m i n i n g ) , t o v e r i f y the d e s i g n concept and r e f i n e the method, - and compare the new  method t o some o f the open stope d e s i g n  procedures commonly used i n the p a s t .  6.1  Choice o f V a r i a b l e s Chapter  2.3  failure  o f open stope r i b p i l l a r s .  the  discussed variables  t h a t may  be  These  significant variables  i n t a c t r o c k s t r e n g t h , p i l l a r l o a d , p i l l a r shape and structural  discontinuities,  and  pillar  volume.  in  were:  confinement, They  will  be  q u a n t i f i e d through the use o f : - u n i a x i a l compressive s t r e n g t h f o r i n t a c t r o c k s t r e n g t h , - boundary  element  numerical  modelling  to  determine  pillar  load, - pillar  height  and  width  to  account  for p i l l a r  shape  and  account  for  confinement, - empirical  rock mass c l a s s i f i c a t i o n  structural - and  the  methods  to  discontinuities,  pillar  dimensions  (from t a b l e  5,  page  70)  can  be  used t o determine the p i l l a r volume. No attempt w i l l  be made t o q u a n t i f y the e f f e c t o f b a c k f i l l .  Chapter 2, b a c k f i l l was the  failure  of p i l l a r s ,  In  not c o n s i d e r e d s i g n i f i c a n t i n p r e v e n t i n g although i t s presence may  have a l a r g e  i n f l u e n c e 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 o f S t a t i s t i c a l Methods  116 Ideally,  the  data  base presented  i n Chapter  4.2  could  used t o t e s t the s i g n i f i c a n c e of each v a r i a b l e i n the of  pillars.  Pillar are  the v a r i a b l e s are  l o a d , p i l l a r width  known  pillar. and  Some of  to  have  a  and  large  the  minor  rock  mass d i s c o n t i n u i t i e s  rock  stability  of  a  was  l a t e r r e j e c t e d f o r a couple of The  first  be  of  reason  quantified  histories  and  r e g r e s s i o n and be  as  joints)  i n open  considered,  but  i s the assessment of p i l l a r s t a b i l i t y  can  into  s l o u g h i n g and  value.  qualitative  These  factorial  reasons.  numerical  with  failed.  quantified  t h r e e v a r i a b l e s was  a  were assessed  sloughing  not  these  (such  The use of s t a t i s t i c s t o t e s t  significance  stable,  intact  However, the i n f l u e n c e o f p i l l a r h e i g h t , p i l l a r volume  the  can  the  stability  significant.  s t r e n g t h of the  i n f l u e n c e on  stope r i b p i l l a r s i s not obvious.  not  obviously  be  The  pillar  categories of  categories  limit  case  stable,  the  use  of  d e s i g n methods, because the c a t e g o r i e s numerically.  failed  A  system  of  giving  assessments an a r b i t r a r y  the  numerical  v a l u e and u s i n g r e g r e s s i o n techniques on these v a l u e s a l s o would not  work  well.  The  wide  range  of  instability  signs  c h a r a c t e r i s t i c s t h a t are e x h i b i t e d by the f a i l e d p i l l a r s can be  quantified  satisfactory failed The is  a  single  criterion  arbitrary  value  and  there  is  t o determine a r e p r e s e n t a t i v e v a l u e  not no for  pillars. second reason why  related  pillars  by  and  to  that  the were  the use of s t a t i s t i c s  yielding  pillar  originally  case  stable  i s not  histories. but  feasible These  eventually  are  became  117 u n s t a b l e due t o stopes o r p i l l a r s r o b b i n g o f the p i l l a r . compressive  and  from  to  the  method  stable  would  influence  For the y i e l d i n g p i l l a r s ,  strength  characterization  (UCS) ,  pillar  that  of p i l l a r  pillar  volume do  failed  find  b e i n g mined i n the v i c i n i t y  cases. these  height,  not  The  have  uniaxial  rock  change  a  statistical  no  significant  o n l y v a r i a b l e s t h a t change  s i g n i f i c a n t l y f o r y i e l d i n g case h i s t o r i e s are the average s t r e s s and the p i l l a r width.  pillar  Removing the y i e l d i n g p i l l a r s  the d a t a base reduces the number o f case h i s t o r i e s t o 12 pillars,  3 sloughing p i l l a r s ,  and  small  data  confident  a  base  about s i g n i f i c a n t The  to  reach  mass  significantly  Consequently,  variables  condition.  the  or  1 failed  pillar.  from  stable  T h i s i s too  statistical  conclusions  variables.  l a s t major problem w i t h u s i n g s t a t i s t i c a l  methods i n the  data base, i s t h e l a c k of p r e c i s i o n i n t h e e s t i m a t i o n of some of the  data.  pillar  load  associated greater large  Chapter  with  than  degree  precise  for  5.5  d i s c u s s e s the  each this  45% of  variable  (see  case  and  varies  Table  page  8,  should  would  included i n a s t a t i s t i c a l  6.1.2  history.  variable  accuracy  determination The from 105)  not  present  be  of  average  potential less  and  than  error 10%  to  implies that  used.  It  significance  i s not  problems  a a if  technique.  Design V a r i a b l e s The most important v a r i a b l e s i n open stope p i l l a r d e s i g n are  pillar  width  and  the  average  pillar  load.  There  is  more  118 flexibility any  of  the  strength, are  others.  rock  all a  lateral  The  and  of  the  Pillar ratio  the  Pillar  width  state  Chapter of  is typically  can  not  be  influence  on  the  failing  on  of  the these  information Pillar  i t a g a i n s t the This  fracturing through  Pillar  pillars.  both  compared.  normalized  pillar  influence  before  and  width)  from  load  intact  is  rock  gives  a  in  pillar.  the  a use  width/height  good  of  the  i s used  f o r the e f f e c t s o f p i l l a r shape  (see  3.1.1).  Discounted V a r i a b l e s Two  volume  variables and  significant  the  have  influence  been  discounted  of g e o l o g i c a l  i n general p i l l a r  not been proven by  direct  3.2.2.3).  width/height.  and  However,  be  stress  (orebody  core, of  than  compressive  a large  pillar  a  comparing  by many authors t o account  6.1.3  has  normalized  by  height setting  pillar.  c o n d i t i o n s can  o f the p i l l a r  Chapter  has  variables  uniaxial  of deformation  a  be  (discussed i n the  the  load  in  pillar  width  of  pillar  normalized  of  and  rock  geological  modulus  to  mining  frequently  measure  of  need  different  strength  of  fracturing  variables  intact  confinement  magnitude  degree  The  or changed.  stiffness,  d e s i g n i n g these two  mass q u a l i t y  function  controlled the  i n choosing and  shown t h a t the two  design.  discontinuities  d e s i g n , but  f o r open stope p i l l a r s .  o t h e r authors and  for  their  Pillar may  importance  U s i n g methods  i n f o r m a t i o n from the data base,  be has  proposed  i t will  be  d i s c o u n t e d v a r i a b l e s have a r e l a t i v e l y s m a l l  119 variation  i n magnitude i n the open stope p i l l a r  data base,  consequently c o u l d o n l y have a minor e f f e c t on p i l l a r  and  stability.  6.1.3.1 P i l l a r Volume Several  authors  1982; Stephansson account  (Hoek  and  1985) have  Brown  proposed  1980;  Agapito  the use  f o r t h e e f f e c t of p i l l a r volume.  of  a  and  factor  mass.  number o f flaws and d i s c o n t i n u i t i e s  Consequently,  t h e volume e f f e c t  to  The r e a s o n i n g was the  r o c k mass s t r e n g t h decreases w i t h an i n c r e a s e i n p i l l a r due t o a l a r g e r  Hardy  volume,  i n the rock  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 . A g a p i t o and Hardy (1982) suggested t h e f o l l o w i n g e q u a t i o n t o relate  the  laboratory  unconfined  testing  uniaxial  with  in situ  compressive unconfined  strength  compressive  from pillar  strength: °0  = C a  ( l/ l ) v  v  a  where, OQ = u n c o n f i n e d compressive OQ = average  s t r e n g t h of t h e p i l l a r ,  laboratory uniaxial  compressive s t r e n g t h ,  V! = volume o f t h e l a b o r a t o r y specimen, V j = volume o f the p i l l a r , a = c o e f f i c i e n t o f volume r e d u c t i o n , = 0.12  f o r coal,  = 0.08  f o r o i l shale,  = 0.06 f o r good q u a l i t y , hard Using variation  the  formula,  of p i l l a r  we  volumes  can  compare  quartzite. the  influence  i n the data base.  o f the  For t h i s  data  120 base,  the s m a l l e s t open stope p i l l a r has a volume o f about  c u b i c metres, about  and the l a r g e s t open stope p i l l a r has a volume of  150,000 c u b i c metres.  ^2,500  °C  _ —  °C  ^150,000  So,  f o r the f u l l  (Vi / 2 5 0 0 ) 0  ( l /  The problem  lack  _ —  0 6  150000) '  V  0  1.2 o  0 6  range of p i l l a r volumes i n the data base,  formula shows o n l y a s m a l l i n f l u e n c e  Any  2500  of  sensitivity  of  this  ( l e s s than 30%).  volume  is  only  part  of  the  w i t h u s i n g t h i s c o e f f i c i e n t of volume r e d u c t i o n method.  method  to  account  f o r the  influence  i n u i t i e s i n a r o c k mass should be based quality  of  the  c o n t i n u i t y and should  be  rock  mass.  The  of  flaws  or d i s c o n t -  on an assessment of the frequency,  orientation,  shear s t r e n g t h of d i s c o n t i n u i t i e s i n a rock mass considered  discontinuities. characteristics  when  T h i s formula and  estimating  does not  as a r e s u l t ,  the  effect  c o n s i d e r any  i t does l i t t l e  of  rock mass  t o account f o r  the i n f l u e n c e o f 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 . 6.1.3.2 S t r u c t u r a l As  mentioned  geological  Discontinuities above,  to  account  discontinuities  in  for  the  pillar  influence  strength,  c h a r a c t e r i s t i c s of the rock mass must be q u a n t i f i e d . the  most  empirical  effective rock  classifications  method  mass are  of  describing  classifications. the  NGI  system,  a  rock  The  developed  two by  of the  Currently,  mass most  i s with common  Barton,  Lien  121 and  Lunde  of  the  the  CSIR system,  Norwegian G e o t e c h n i c a l developed  by  Institute  B i e n i a w s k i o f the  C o u n c i l 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  South  " I n t e g r a t e d Mine Design  Stacey as  and  Page  strength  uniaxial situ  (1986) suggest  reduction  compressive  intact  rock  *  o ).  Table  5  Herget  by  applying  s t r e n g t h of rock.  strength i s o  0  and  African  collected in  e t a l . (1984)  u s i n g rock mass  factors  rock mass r a t i n g of 75%, (0.75  Study."  and  (1976).  Data f o r the CSIR rock mass c l a s s i f i c a t i o n was the  (1974),  and  classifications  them  against  the  For i n s t a n c e , i f the i n the  rock mass has  a CSIR  then the i n s i t u rock mass s t r e n g t h i s  0  (page 70)  shows the  CSIR geomechanics r a t i n g  "RMR"  (acronym f o r rock mass r a t i n g ) f o r the p i l l a r s i n the open stope data base. 4.8.  The  mean RMR  i s 69.6,  w i t h a standard d e v i a t i o n of  T h i s s m a l l range i n rock mass r a t i n g s i s not  because  the  data base  source  of  the  majority  of  the  i s mines i n the Canadian s h i e l d .  i n f o r m a t i o n i n the The  classification  methods are designed t o c h a r a c t e r i z e a much wider masses. it  influence  range of rock  With t h i s s m a l l a range o f rock mass q u a l i t y ,  i s not p o s s i b l e t o v e r i f y  strength  unrealistic  reduction of  factor  however,  t h a t the i n c l u s i o n o f a rock mass would  discontinuities  adequately  i n the  design  account of  open  for  any  stope r i b  pillars. Using method  a to  strength reduction variable account  discontinuities  in a  for rock  the mass.  c o u l d be  influence However,  the  of  an  effective structural  available  data  122 could  only  prove  conditions. not  be  this  a  small  range  of  rock  mass  Rather than i n c l u d e a v a r i a b l e whose i n f l u e n c e can  effectively  structural  over  calibrated  or  verified,  d i s c o n t i n u i t i e s has been o m i t t e d .  the  effect  of  A l a r g e amount o f  data from a much wider v a r i e t y o f rock mass c o n d i t i o n s i s needed to  confirm  reduction  and  calibrate  pillar  significance  of  a  strength  factor.  6.2 P i l l a r S t a b i l i t y The  the  methodology  Graph f o r t h e development  design c r i t e r i o n  o f an open  stope r i b  i s based on t h e g r a p h i c a l comparison o f  the s i g n i f i c a n t v a r i a b l e s d i s c u s s e d above and t h e assessment o f pillar to  case h i s t o r i e s .  represent  The y - a x i s o f t h e graph has been  the normalized p i l l a r  defined  by t h e p i l l a r  width  pillars  from  base  t h e data  sloughing p i l l a r s  load,  to p i l l a r  while the x-axis i s  height  ratio.  Stable  with  square  symbols,  are p l o t t e d  a r e r e p r e s e n t e d by c r o s s  shaped  f a i l e d p i l l a r s a r e l o c a t e d w i t h diamond symbols By  arranging  correction stays  the  factors  intuitively  variables  graph  in  this  chosen  form  symbols, and  (see f i g u r e 35).  (and  not  including  f o r volume and rock mass q u a l i t y ) , t h e graph simple.  i s clear-cut  The i n f l u e n c e and  explicit.  of varying the design This  graph  will  be  condition  of  r e f e r r e d t o as t h e " p i l l a r s t a b i l i t y graph".  6.2.1 G r a p h i c a l Data A n a l y s i s Comparison  of  the  shape  and  the  loading  o  o  CO  om  o d  o  O  O  d  o o d  son/avoi  FIGURE 3 5 . The p i l l a r s t a b i l i t y stope r i b p i l l a r data base.  graph showing t h e open  124 pillars, rib  using  pillar  the p i l l a r  behaviour.  stability  35) .  position graph,  Pillars  i s located  which  a trend i n  The graph shows squat p i l l a r s  s t r e s s c o n d i t i o n s as s t a b l e figure  graph, exposes  (bottom r i g h t r e g i o n o f t h e graph i n  become  less  stable  as  their  more towards the upper l e f t  represents  under low  highly  stressed,  graphical  c o r n e r o f the  slender,  and  failure  prone p i l l a r s . The graph has be d i v i d e d (see  figure  conditions  36) .  The  i n t o two  upper  left  zones based on t h i s  side  of  i n which p i l l a r s have f a i l e d .  the  graph  data  denotes  The bottom r i g h t  side  of t h e graph shows c o n d i t i o n s i n which p i l l a r s have not s u f f e r e d any  serious  transition approximated condition  instability.  The  area.  location  The  based  on  the  two  zones of  graphical  o f t h e case h i s t o r i e s .  No  this  stability  area  problems  pillar,  no  pillars  plot  failed  necessarily mining  corresponds t o t h e are f i r s t  below  this  signify  problems  to  deteriorating  pillars  reported  Goel  by  fracturing roughly  and p i l l a r  defines  a  pillar  could  and  region  This  failure,  Page  1981) ,  criterion  four  rather  where  even but  deformation w i l l  a  been  physical  methods  major  Only one  bottom  but  an  has  and  where  instability.  carry  by  have  The bottom l i n e o f the  a l l but  line.  pillar  due  and  area  statistical  encountered.  pillars,  separated  location  been used t o l o c a t e the t r a n s i t i o n a r e a . transition  are  sloughing  the  line the  stable  does  load  displacement, The top  failure  not  onset of  Sloughing  greater  increase.  pillar  of  pillar  has  or (as rock line been  PILLAR STABILITY GRAPH  H  3  G  OPEN STOPE RIB PILLAR DATA  0.60  H>  0) U> HM •  (D O.  0.50  N 3* O (D 3 10 K-  •  M  0) H* 3 0)  a it  to  0.40  H  0.30  H  0.20  H  0.10  H  0.00  -|  ft 3* f t  cr  f t H*1 M  JD |_u  tpo- f t 3  rtvQ H* ^ O B» 315 3* 0)  ^  o D \ Q < o _l  CO  (D 3* 0> O • C H-  3  tQ  ft 3" (D  to ft &»  tr  1  0.0  p  0.4  i  1 0.8  M fO  r  '  1.2  i  i  1  1.6  1 2.0  PILLAR WIDTH/PILLAR HEIGHT •  STABLE  +  SLOUGHING  O  FAILURE  1  r  126 observed  i n t h e case h i s t o r i e s o f t h e data base.  histories, of  No s t a b l e case  f o u r o f t h e nine s l o u g h i n g p i l l a r s and a l l but t h r e e  the f a i l e d  pillars  a r e found  above  this  line.  Pillars  p l o t t i n g above t h i s l i n e g e n e r a l l y have: - started t o lose load bearing capacity, - s u f f e r e d a l a r g e amount o f f r a c t u r i n g , - e x p e r i e n c e d l a r g e displacements o f rock, - and had severe s l o u g h i n g o f p i l l a r w a l l s (unless c o n f i n e d by  backfill).  In r e g i o n s o f t h e 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 available  to  approximated  6.2.2  w i t h dashed  the  transition  Chapter  was  i t has  been  Approximations  5.5.2, t h e maximum e r r o r  estimated  zone,  lines.  I n f l u e n c e o f P i l l a r Load  In load  locate  f o r each  case  i n t h e average  history.  To  pillar  check t h e  i n f l u e n c e o f t h i s e r r o r , t h e average p i l l a r l o a d i s decreased by the  maximum  amount o f t h e e r r o r  The reason f o r t h e decrease are e s t i m a t e d load.  by BITEM,  shown i n T a b l e  (page  105) .  i s that the majority of p i l l a r  loads  which o v e r e s t i m a t e d  8  the actual  Data i n which t h e e r r o r c o u l d not be r e a s o n a b l y  were o m i t t e d .  pillar  estimated  T h i s o c c u r r e d f o r 6 o f t h e 47 data p o i n t s .  F i g u r e 37 i s a p l o t o f t h e p i l l a r s t a b i l i t y graph u s i n g t h e reduced The  average  modified  pillar  data  still  load with the o r i g i n a l fits  t h e graph  well,  transition with  only  area. three  s l o u g h i n g cases and one f a i l e d case below t h e t r a n s i t i o n zone.  son/avcn  128 It  s h o u l d be kept  i n mind t h a t t h e a d j u s t e d l o a d was decreased  by an e s t i m a t e o f t h e maximum e r r o r , and most cases w i l l have an e r r o r s m a l l e r than t h e maximum. We does  can conclude  not s i g n i f i c a n t l y  demonstrates less  the fact  o f an e f f e c t  (width/height  6.2.3  the error change  that  i n t h e average  t h e method  the p i l l a r  on p i l l a r  pillar  proposed.  load  I t also  l o a d i n g c o n d i t i o n s has  stability  than  the p i l l a r  shape  ratio).  Importance 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  As there due  that  discussed  i n t h e data  a r e 13 p i l l a r s  t o mining.  that  These  base  description  were s t a b l e  pillars  and subsequently  comprise  h i s t o r i e s i n t h e open stope data base.  (Chapter 4.1),  30  failed  o f t h e 47  case  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 a r e v e r y u s e f u l i n d e v e l o p i n g a d e s i g n method because the  stable  and f a i l e d  cases  should  plot  zones s e p a r a t e d by t h e t r a n s i t i o n a r e a . the  entire  joined  data  by  a  base w i t h  solid  t h e stages  line.  The  F i g u r e 38 i s a p l o t o f o f each  yielding  correspond w e l l t o t h e s t a b l e and f a i l e d the  location  location area,  of the t r a n s i t i o n  moves  and i n t o  demonstrate failure.  from  area.  the stable  the f a i l e d  the s e n s i t i v i t y  zone.  i n their respective  zone,  yielding  pillar  pillar  endpoints  zones which  reinforces  As a p i l l a r through  the t r a n s i t i o n  The y i e l d i n g  o f t h e graph  fails, i t s  pillars  to predict  also pillar  son/avoi  FIGURE 38. The p i l l a r s t a b i l i t y graph w i t h a l l the case h i s t o r i e s o f t h e 13 y i e l d i n g p i l l a r s j o i n e d by s o l i d lines. T h i s r e i n f o r c e s the l o c a t i o n o f 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 o f t h e method t o p r e d i c t failure.  130 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 Graph  There a r e a few comments t o be made c o n c e r n i n g 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 graph. near  the t r a n s i t i o n  zone  Firstly,  shows a v a r i e t y  the l i m i t -  t h e d a t a i n and  o f behaviour.  This  suggests t h a t a g r e a t degree o f p r e c i s i o n i s not i n h e r e n t t o the graph. the  This  input  pillars.  lack of precision  data  and t h e broad  i s a function of inaccuracy i n assessments  The s i z e o f t h e t r a n s i t i o n  used  zone c o u l d be c o n s i d e r e d a  measure o f t h e accuracy o f t h e p i l l a r s t a b i l i t y It  should  developed  be  emphasized  relationship  and  that  i s more  to categorize  this  graph.  is  reliable  c o n d i t i o n s s i m i l a r t o those i n t h e data base.  an  empirically  when  applied i n  S p e c i f i c a l l y , the  range o f t h e v a r i o u s data i s : 70 MPA  <  UCS  <  316 MPa,  9 metres <  Wp  <  45 metres,  RMR  <  78  60  <  where, UCS = t h e i n t a c t rock u n i a x i a l compressive Wp = t h e p i l l a r  strength,  width,  RMR = a measure o f t h e rock mass competency u s i n g the CSIR rock mass c l a s s i f i c a t i o n . A final are almost ratio  note about t h e p i l l a r no s t a b l e p i l l a r s  greater  (average  than  0.5,  s t a b i l i t y graph  with  an (average  and v e r y  few s t a b l e  load/UCS) r a t i o g r e a t e r than 0.33.  i s that there  pillar  load/UCS)  pillars  with  an  T h i s suggests t h a t  t h e r e i s a p r a c t i c a l l i m i t t o t h e maximum n o r m a l i z e d  load f o r a  131 s t a b l e open stope r i b p i l l a r .  These v a l u e s correspond w e l l with  s u g g e s t i o n s by Mathews e t a l . (1980) and Bawden e t a l . (1988), of  t h e maximum  normalized  major  principal  stress  allowable  b e f o r e s t r e s s r e l a t e d mining problems become e x c e s s i v e .  6.3 Data from Very  Literature  few  open  stope  pillar  l i t e r a t u r e provide s u f f i c i e n t to  the p i l l a r s t a b i l i t y  mining rock  case  pillar  load,  histories design  uniaxial  case  histories  in  i n f o r m a t i o n t h a t they can a p p l i e d  graph.  F u l l y documented room and p i l l a r  a r e more common.  have  found  been  found  compressive  rock  Three  which  s t u d i e s o f hard  contain the p i l l a r  strength,  pillar  i n f o r m a t i o n and an assessment o f t h e p i l l a r s t a b i l i t y .  shape The two  l a r g e s t s t u d i e s d e a l w i t h room and p i l l a r mining w h i l e t h e t h i r d is  a s m a l l e r and more d e t a i l e d study t h a t d e a l s w i t h 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 In  t h e 1960's,  undertaken determine results  a major  i n the E l l i o t stable  stope  was a p i l l a r  3.1.1.3, and 6.4.1).  rock Lake  mechanics uranium  and p i l l a r strength  base  partially  formula  mining  district  was to  One o f t h e  ( d e s c r i b e d i n Chapters  The d e t a i l s o f t h e formula development and  c o n s i s t e d o f 23 s t a b l e failed,  investigation  configurations.  the data base were p u b l i s h e d by Hedley data  Mining  and 3 p i l l a r s  and Grant  pillars,  (1972).  2 pillars  t h a t were crushed.  that  Their were  Pillars in  132 the  uranium mines are v e r y  same shape as p i l l a r s dimensions  l o n g i n one  d i r e c t i o n which i s the  i n open stope mines.  However, the  pillar  and volume are s u b s t a n t i a l l y lower i n room and  pillar  mining. Using  the  data  i n the  paper  case h i s t o r i e s were p l o t t e d figure  39) .  graph the  The  Elliot  quite well with transition  area,  crushed p i l l a r s  (Hedley  on the p i l l a r  Lake  data  fits  a l l of the s t a b l e and  plotting  and  most  of  Grant  stability the  graph  pillar  pillars  the  1972) , the  stability  p l o t t i n g below  partially  i n the t r a n s i t i o n a r e a .  failed  and  Ideally,  for  t h i s data, the t r a n s i t i o n zone would p r o b a b l y be s l i g h t l y This  would  unstable  give  a  pillars.  better  s e p a r a t i o n between  However, t h e r e  i s not  (see  the  lower.  stable  and  s u f f i c i e n t data  near  the t r a n s i t i o n zone t o warrant a d j u s t i n g i t s l o c a t i o n . The to  r o c k mass q u a l i t y  that  found  in  on  pillar  discussion  1982), which pillars  an  equivalent  the  i s one NGI  to  "Integrated  stability  CSIR  mass  the  base.  rating  assume an base.  of  t o the v a r i a b l e RMR  of  78  78,  An RMR  r o c k mass q u a l i t i e s found Due  Mine  the  quality  proposed by B i e n i a w s k i (1976). of  at  Lake mines i s s i m i l a r Design  Denison  o f the mines i n Hedley's  rock a  f o r the E l l i o t  of  A  Mine  (Townsend  study,  g i v e s the  45.  based  Study".  This on  a  is  roughly  relationship  of 78 i s w i t h i n the  i n the open stope p i l l a r  range data  nature of a rock mass, i t i s wrong t o  for a l l pillars  i n the  Elliot  Lake  data  However, i t can be concluded t h a t the g e n e r a l rock mass  c o n d i t i o n s between the two data bases are s i m i l a r .  son/avcn  FIGURE 39. The p i l l a r s t a b i l i t y graph shoving the d a t a from room and p i l l a r mining p u b l i s h e d by Hedley and Grant (1972) i n t h e i r study on the development o f a p i l l a r s t r e n g t h formula.  134 An  interesting  observation  can  be  made  concerning  i n f l u e n c e o f p i l l a r volume.  The volume o f an average  the  i s approximately  Elliot  Lake  s m a l l e r than  smaller  volume  partially  zone.  raise  25  pillar in  t o 50  times  open stope data base  and » 50,000 m  increase of p i l l a r  should  failed  volume o f t h e  f o r room and p i l l a r ,  3  A relative  transition  base  t h e average  (« 1000 - 2000 m stoping).  data  the  f o r open  3  s t r e n g t h due t o t h e  the r e l a t i v e  position  T h i s does not correspond  with  of the  t h e cases o f  and crushed E l l i o t Lake p i l l a r s .  According to  the Hedley data, t h e t r a n s i t i o n zone should p r o b a b l y be s l i g h t l y lower.  Based  difference  on t h i s  o b s e r v a t i o n , t h e r e appears  t o be  little  i n t h e i n f l u e n c e o f 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  development Botswana. was  Von Kimmelmann  of a  pillar  design  Back a n a l y s i s  performed  using  e t a l . (1984) criterion  discussed the  a t BCL L i m i t e d i n  o f a l a r g e number o f e x i s t i n g  t h e pseudo-three  dimensional  pillars  displacement  d i s c o n t i n u i t y numerical method. Pillar  deterioration  was  assessed  with  the  following  minor  spalling  criterion: "Group  A  (intact  particularly  pillars)  a s s o c i a t e d w i t h any overbreak  wall or footwall gneisses. Group  B  displayed  pillars  exhibited  i n t o t h e hanging  No j o i n t opening was observed. prominent  spalling  generally  135 associated with s t r u c t u r a l j o i n t s i n t o the p i l l a r was Group  C  pillars  pronounced  features. a l s o noted.  displayed  opening  of  S l i g h t opening of the  severe  joints  spalling  and  of  intact  deformation  rock,  of  drill  reasonably w e l l with  stable  holes." The  Group A assessment  pillars,  corresponds  Group B w i t h s l o u g h i n g p i l l a r s ,  pillars.  Table  shape, p i l l a r complete Two  12  gives  the  pillar  and Group C w i t h  failed  classification,  pillar  l o a d , and remarks on the p i l l a r  stability  data base p r e s e n t e d by Von Kimmelmann different  that  were near  were  very  types of p i l l a r s  square  long  dimension  (1984).  were i n v e s t i g a t e d .  (when viewed  i n one  i n plan) (see  and  figure  40) .  were a p p l i e d d i r e c t l y t o the p i l l a r s t a b i l i t y  figure  41) .  pillars, stable  transition  zone  for  the  The graph open  histories  histories  are  i n the t r a n s i t i o n  suggest the t r a n s i t i o n  making  the  current  zone.  These  zone c o u l d be l o c a t e d  pillar  stability  graph  that long (see stope  one s t a b l e p i l l a r i s above the t r a n s i t i o n zone and  case  higher  the  Pillars  pillars  pillars  Using  f o r the  five case  slightly a  bit  conservative f o r t h i s data. The square p i l l a r s stability pillars 1974;  graph. are  S e v e r a l authors have noted  significantly  Salamon  account  can not be d i r e c t l y a p p l i e d t o the p i l l a r  1983;  f o r the  s t r o n g e r than  Kersten  difference  1984;  square  Stacey  during design,  suggested the use o f an e f f e c t i v e p i l l a r  and  that rectangular pillars Page  these  width:  (Wagner  1986).  authors  To have  CLASSIFICATION OF SQUARE PILLARS  PILLAR NO. 1 2 3 4 5 6  7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  CLASSIFICATION B A A B  B B C C  c c c c B  c c c  A B A C C C C B/C B B A A C C C C B B/C B/C C B C B/C C C B/C C B B/C B A  W/H 0,80 1.70 1.70 1.2* 1.00 1.30 1,20 0,96 1,00 1.50 0,50 1,26 1,40 1,60 1,40 0,76 1,40 1.74 2,50 0,6"0 0,90 0,60 0,60 1.32 1.50 1.67 1,60 2,00 1,00 1,00 1,00 1,00 0,80 0,92 1.20 1,00 0,92 0,60 1.30 2,27 1.2C 1.50 2,00 1,20 1,40 1,80 2,60  ESTIMATED PILLAR STRESS (MPA) 28 26  30 34 34 35 55 55 58 58 58 53 48 58 55 50 37 40 35 48 48 48 48 55 47 48 35 35 59 59 59 59 54 55 54 55 55 60 56 60 63 63 59 56 63 53 60  REMARKS Opening of J o i n t * Joints t i g h t Minor s p a l l i n g S p a l l i n g i n gneiss S p a l l i n g i n M.S. Joints t i g h t Fractured M.S. Assoc. with j o i n t i n g Sever* s p a l l i n g Severe s p a l l i n g Severe s p a l l i n g Severe s p a l l i n g 4 opening of J o i n t s Failed p i l l a r Marked hangingvall d e t e r i o r a t i o n Bangingvall d e t e r i o r a t i o n Severe s p a l l i n g Severe s p a l l i n g Slabbing Assoc. v i t b f a u l t ) ) S p a l l i n g Assoc. with s t r u c t u r a l )features ) .Severe s p a l l i n g Assoc. with ^ d e t e r i o r a t i o n of hangingvall H/W i n s t a b i l i t y + deformed boreholes Spalling Joints opening Minor s p a l l i n g i n f o o t v a l l gneiss Minor s p a l l i n g Severe s p a l l i n g Assoc. with bad hangingvall c o n d i t i o n s Severe s p a l l i n g Failed Large p i l l a r Assoc. with bad hangingvall c o n s i t i o n s Severe s p a l l i n g Severe s p a l l i n g SpalfTng and l o c a l slabbing Failed S p a l l i n g of gneiss overbreak Severe s p a l l i n g Severe s p a l l i n g Severe s p e l l i n g Severe s p a l l i n g S p a l l i n g Assoc. with Joint opening Prominent s p a l l i n g i n gneiss and M.S. Spalling Minor s p a l l i n g  CLASSIFICATION OF LONG PILLARS ( L » W )  PILLAR NO. 1 2 3 4 5 6 7 • 8 9 10  CLASSIFICATION A A A B B A A A A A  W/H 1,00 1,50 1,25 0,43 0,40 0,90 1,00 1.48 1,30 1,20  ESTIMATED REMARKS PILLAR STRESS (MPa) 25 29 40 35 50 28 45 48 50 47  V. minor s p a l l i n g V. minor s p a l l i n g Joints opening Spalling Spalling Minor s p a l l i n g i n M.S. Slight movement on hangingvall contact Minor s p a l l i n g Assoc. with j o i n t s No borehole deformation Stable  TABLE 12. Data used by Von Kimmelmann e t a l . (1984) i n t h e development o f a p i l l a r f a i l u r e c r i t e r i o n .  136  137  FIGURE 40. A p l a n view o f room and p i l l a r mining a t BCL L i m i t e d , showing t h e use o f l o n g p i l l a r s and square p i l l a r s ( a f t e r Von Kimmelmann 1984).  138  son/avcn  139 W  eff  =  4 * A C  where: W f f = the e f f e c t i v e p i l l a r width, e  A = p i l l a r cross sectional  area,  C = p i l l a r circumference. The  reasoning i s that f o r very long p i l l a r s  pillars),  a pillar  i s e f f e c t i v e l y exposed  on o n l y two w a l l s  consequently s t r o n g e r than square p i l l a r s , four walls. effective  Using t h i s  width  t o width r a t i o . have  concept,  of a long p i l l a r In f i g u r e  been  plotted  effective  pillar  on  (and open stope r i b  which  a r e exposed  square p i l l a r s  pillar  width/  on the  having the same p i l l a r h e i g h t  42, the square p i l l a r s  the  have h a l f  and  stability  height  ratio  a t BCL  Limited  graph  using  (ie.  the  their actual  width/height r a t i o ) . The the  a d j u s t e d square p i l l a r  original  transition  zone  data agrees r e a s o n a b l y w e l l w i t h on  the  pillar  stability  graph.  Three s t a b l e 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 line  on the t r a n s i t i o n  pillars  plot  adjustment  above  for  the  square  zone, w h i l e a l l the y i e l d i n g transition pillars  on  adequately e x p l a i n s the assessment long  pillars,  the  adjusted  square  area. the  The  pillar  failed  effective  width  stability  graph  f o r t h i s data. pillar  and  data  t r a n s i t i o n zone c o u l d be l o c a t e d s l i g h t l y h i g h e r .  As w i t h the suggests  the  However, t h i s  i n a c c u r a c y i s on the c o n s e r v a t i v e s i d e f o r s t a b l e p i l l a r d e s i g n .  6.3.3  Data from an A u s t r a l i a n Open Stope Mine  140 IN  O M  son/avcn FIGURE 42. The square p i l l a r data p r e s e n t e d by Von Kimmelmann e t a l . (1984) i s p l o t t e d on the s t a b i l i t y u s i n g an e f f e c t i v e width i n the H/W r a t i o .  graph  141 A test by Brady  open s t o p i n g b l o c k a t Mt. I s a i s d e s c r i b e d i n depth  (1977).  The o b j e c t i v e o f t h e t r i a l mining b l o c k was t o  o b t a i n i n f o r m a t i o n f o r r i b p i l l a r d e s i g n and c a l i b r a t e a f a i l u r e criterion  f o r t h e rock mass.  F i g u r e 43 shows t h e t e s t  broken  i n t o f i v e stages.  Stage  1  (problem  No.  1)  shows  t h e development  r a i s e s , and t h e S86 r a i s e t o observe p i l l a r  of  two  slot  conditions.  Stage 2 c o n t a i n s t h e opening o f t h e S85 stope. Stage  3 shows t h e opening  o f S87 stope which  c r e a t e s t h e S86  pillar. Stage  4 i s t h e expansion  o f the S87 stope, w i t h t h e S86  pillar  remaining s t a b l e and i n t a c t . Stage  5 shows t h e r o b b i n g o f t h e S86 p i l l a r  which r e s u l t e d i n  f a i l u r e of the p i l l a r .  Brady p r e s e n t e d s u f f i c i e n t 5 c o u l d be modelled load.  The  stope  greater  than  average  pillar  using  w i t h BITEM t o determine  height:length r a t i o  3,  so  less  than  l o a d determined  f i g u r e 33, page 109).  agreement original The similar  with  i n f o r m a t i o n t h a t stages 3, 4 and  a  principal  20%  t h e average  f o r a l l three error  pillar  cases i s  i s expected  i n the  by BITEM (the e r r o r i s estimated  The m o d e l l i n g r e s u l t s were i n good stress  contour  diagram  i n the  paper. rock  mass,  as d e s c r i b e d  characteristics  i n t h e paper  and q u a l i t y  by  to the t y p i c a l  Brady,  has  rock  mass  142  192 0  610  -I  1  7 0/B MICAF  1  i  10-0  i <  , \  k  -26-2  . ; 1 -  Boundary of S86 pillar area  J S86 raise  Problem No. 1 -1920  SB7 Cut-off rais« (1 81 Dia.)  <  30-2 1 6 65  S85 slope _ J  Boundary of S84 • pillar area  Problem No. 2  n  i  |  15.1  '4-8 I —  n  0  — r — - S 87 stopt  Problem No 3  1  J  !  r  ses  ,  ; 1  37-8  1  58b o  i r  S87 1  Problem No 4 •1920  1  26.2  10-0  1 6-65  i_  •34-4  SBS  Problem No. 5  6-7  420  S66  sen  O  Scole  10m  FIGURE 43. The f i v e stages o f t h e S86 p i l l a r i n an open s t o p e p i l l a r t e s t a t 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  a l s o s i m i l a r t o t h a t i n the data base. a r e not  likely  t o have a s i g n i f i c a n t  d a t a on the p i l l a r s t a b i l i t y The  and  4,  agrees  influence  variables  in plotting  the  graph.  t h r e e stages are p l o t t e d on a p i l l a r  f i g u r e 44. 3  So, t h e s e two  is  stability  graph i n  The S86 p i l l a r p l o t s i n the s t a b l e r e g i o n f o r stages and  plots  i n the  very well with  failure  Brady's  zone a f t e r  description  stage  5.  of the p i l l a r  This during  the t e s t .  6.3.4  Summary o f A l l the A  plot  literature  of  the  Data  open  i s given  in  stope  figure  data 45.  and The  a l l the data  data  from  from  literature  h e l p s c o n f i r m the l o c a t i o n of the t r a n s i t i o n area over a g r e a t e r area.  In the e n t i r e data base of 135 p i l l a r s ,  histories pillar solid The  i s found  success  of  pillar  influence  above the t r a n s i t i o n zone and one  below the  design l i n e s  different the  are found  the  transition  f o r the t r a n s i t i o n pillar  stability  assessments of  four stable  pillar  zone.  graph  and  rock  mass  the  extended.  i n separating  supports the d e c i s i o n  volume  sloughing  Consequently,  zone have been  case  the  to discount quality  as  i n s i g n i f i c a n t i n hard r o c k p i l l a r d e s i g n .  6.4  Comparison A g a i n s t Other Design Methods A number of e m p i r i c a l d e s i g n methods are f r e q u e n t l y used f o r  rib pillars.  However, none of these methods was  based on open  144  son/avon FIGURE 4 4 . The t h i r d , f o u r t h and f i f t h stages o f t h e S86 open stope r i b p i l l a r , p r e s e n t e d by Brady (1977), a r e shown on the p i l l a r s t a b i l i t y graph. The data agrees v e r y w e l l w i t h the s t a b i l i t y graph.  • CD  145  • CM  son/avoT FI  sSL rib 4  !m h Pil  r  graph showing t h e open H e d l l y M9?2J V o n K ? ^ e data p r e s e n t e d by tieaiey (1972), Von Kimmelmann (1984), and Brady (1977). a  lability t  h  e  l  i  t  e  r  a  t  146 stope mining methods  case h i s t o r i e s .  against  the  The  pillar  following  stability  comparison graph,  o f the  shows  the  applicability  o f the o t h e r methods t o the d e s i g n o f open stope  rib  Any  pillars.  criticism  of  n e g a t i v e e v a l u a t i o n s h o u l d not be taken as a  o t h e r methods,  but  rather  i t s e r v e s t o show the  l i m i t a t i o n s o f t h e s e methods when a p p l i e d t o the d e s i g n o f open stope r i b p i l l a r s .  6.4.1  Hedley's P i l l a r S t r e n g t h Formula  The  pillar  (1972) was  strength  formula developed by  Hedley  and  Grant  based on data from room and p i l l a r mining a t E l l i o t  Lake and has been d i s c u s s e d  i n Chapters 3.1.1.3 and 6.3.1.  The  formula i s d e f i n e d as: Qu = k * w  a  /  h  b  where: Qu = p i l l a r  strength  k = s t r e n g t h o f 1 f t . cube  (UCS ) 12  w = p i l l a r width ( f t ) h = p i l l a r height (ft)  To from  get  the  (UCS ): 2  a = empirical constant =  0.5  b = empirical constant =  0.75  UCS , 12  several  compressive  authors have used  strength  of  a  2  inch  a  scaling  diameter  factor specimen  147  ucs  This  relationship  (1972),  Hedley  0.7 * UCS  1 2  has been  2  found  e t a l . (1979),  i n works by Hedley  Hoek and Brown  and Grant  (1980),  and Von  Kimmelmann e t a l . (1984). Hedley's it  accounts  the  pillar  formula i s a s i z e e f f e c t formula, which means t h a t f o r t h e a c t u a l dimensions  shape.  s i z e of t y p i c a l  open stope r i b p i l l a r s  of r i b p i l l a r  stope  mines  temporary lines  sizes  seen  i s presented  pillars  dimensions  of  are  pillars  pillars  in  t h e 17 Canadian  to  pillar  width r a t i o s ) ,  must be determined.  i n 17 d i f f e r e n t  i n figure  denoted  by  i n mining  a r e denoted  g i v e t h e upper  height  and not j u s t  To a p p l y t h i s t o open stope r i b p i l l a r s , the  range  permanent  of a p i l l a r  46. the  The  ratios  "P"  The  strike  dimensions  length  to  and  dashed  For various p i l l a r  (ie. pillar  of  and the  backfill  "B".  and lower bound o f p i l l a r  open  dimensions  using  by t h e symbol  open stope mines.  Canadian  symbol  methods  The  used width  orebody  t h e minimum and maximum p i l l a r dimensions can be  determined and a p p l i e d t o 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 o f t h e i r p i l l a r s t r e n g t h formula, Hedley and  Grant suggest t h a t p i l l a r s are  stable  crushed.  S.F.  and  pillars  w i t h a s a f e t y f a c t o r g r e a t e r than 1.5 with  a  safety  factor  near  Rearrangement o f t h e s a f e t y f a c t o r formula,  Qu c r  p  0.7 * UCS a  P  2  * h  * w b  a  1.0 a r e  PILLAR DIMENSIONS H  BASED ON 17 CANADIAN OPEN STOPE MINES  rt»0 O O 3* ct> o» c  45  ft 3 0> W o> a  fl) . fD 3 o> o> <D f t  O  40  •3  (D H - n> f ) H 3 fl) O r< 0» Cft M (0 f t oi r ( B 0 3 (D •» TJ *0 Q> CD fl) < « 3* B O  3  H * H * H * M>  35  -  30  -  ft M  u. O  25  -  <t>fl)*0  o z  20  -  3 3*fl>fl>>1 f t f t • KT 3" 3*  w >o» < oa rt ft H r)  ~fl)fl) ft  ft  O.  0> 03 i o>  O  3  * 10  a TJ fl) 0 3 3 M O D. W • f t (!) fl) 3 CO W O CD f t fl) • d ff> 3 M» H-  »  M  15  -  or  H*  B  \  B  P  B  k  B  B P  P  P  P B  B  B  10  5  \  B  -  -  B  B  B\ B  r-  3  M  B  B  -I  ui  B B  \  B  —]  0)  20  0)  1  1  1—  OREBODY WIDTH (m)  01  B = BACKFILLED  \  B  40  P = PERMANENT  \  60  149  p e r m i t s p l o t t i n g o f s a f e t y f a c t o r l i n e s f o r 1.0  and 1.5,  maximum and  i n open s t o p i n g ,  minimum r i b p i l l a r  sizes  a g a i n s t the data base ( f i g u r e 47). the p o s s i b l e  location  The  rib pillars  zone shows  when designed  when designed w i t h a  safety  S i z e e f f e c t formulas assume t h a t s m a l l e r p i l l a r s  s t r o n g e r than  zone corresponds  large  pillars.  So,  the upper  t o the minimum p i l l a r  sizes  open stope mines, w h i l e the lower l i n e to  shaded  lower zone shows the p o s s i b l e  of open stope r i b p i l l a r s  f a c t o r of 1.5. are  The upper  o f open stope  w i t h a s a f e t y f a c t o r of 1.0. location  observed  f o r the  line  seen  in  of  each  Canadian  of each zone corresponds  the maximum p i l l a r s i z e s seen i n Canadian open stope mines. The  graph  shows  Hedley's  formula  stability  graph.  designed  that, is  f o r open  stope  conservative  In  defense  of  rib pillar  relative Hedley's  f o r much s m a l l e r p i l l a r s  and  to  the  formula,  design, pillar it  was  i t i s less conservative  when a p p l i e d i n room and p i l l a r mining  (due t o the n a t u r e of the  s i z e e f f e c t formula). Comparison formula  (Chapter  Hedley  and  strength  variable  actually  because ensure  3.1.1.2)  Salamon  the e m p i r i c a l is  of the p i l l a r  "K"  used and  constants a  bit  stability  would the  give  same  a  very  b=0.66).  conservative  a g a i n s t Salamon's  similar  method  Salamon has  (a=0.46 and  more  graph  than  to  conclusion.  determine  similar  values for  Salamon's method Hedley's  formula  Salamon recommended the use of a s a f e t y f a c t o r o f 1.6 stable  design  and  used  a pillar  the  height c o e f f i c i e n t  to of  son/avon  FIGURE 47. Comparison of the p i l l a r s t a b i l i t y graph and H e d l e y s formula f o r two s a f e t y f a c t o r s . Hedley's formula i s a s i z e e f f e c t formula, so t h e r e i s a range o f p i l l a r s t r e n g t h f o r each s a f e t y f a c t o r based on the s i z e o f open stope r i b p i l l a r s observed i n 17 Canadian mines. 1  151 b=0.66 compared t o b=0.75 suggested by Hedley.  6.4.2 Hoek and Brown P i l l a r S t r e n g t h Curves Hoek and Brown 11,  page  44)  (1980) proposed  f o r the estimation  curves  are discussed  curves  were developed  failure for  i n more based  distributions  a series of p i l l a r  depth  pillars  =  CT  3  +  (  m  * C a  * 3 a  +  s  *  These  3.1.1.5.  modelling,  of d i f f e r e n t  rock  The mass  shapes, and  a range o f rock mass q u a l i t i e s , u s i n g t h e f a i l u r e  °P  (figure  strength.  i n Chapter  on numerical  inside  o f curves  criteria:  C)  CT  2  !s  where: ffp = average p i l l a r s t r e n g t h o~3 = minimum p r i n c i p l e a  c  stress  = u n i a x i a l compressive  strength of i n t a c t  pillar  material m & s = e m p i r i c a l c o n s t a n t s based  on t h e rock mass  quality.  The  m & s e m p i r i c a l c o n s t a n t s have been r e l a t e d t o t h e 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 d e s i g n l i n e s  assuming  t h a t a p i l l a r i s f a i l e d when t h e s t r e s s a c r o s s t h e c e n t r e o f the pillar  exceeds  corresponds  the strength  o f t h e rock  mass.  Each  curve  t o a f a i l u r e l i n e f o r a d i f f e r e n t rock mass q u a l i t y .  152 S i n c e Hoek and Brown used in the p i l l a r s t a b i l i t y of  graph,  i n p u t parameters s i m i l a r t o those i t was p o s s i b l e t o reproduce some  t h e i r d e s i g n curves on t h e d e s i g n c h a r t (see f i g u r e 48). The  first  o b s e r v a t i o n i s t h a t Hoek and Brown d e s i g n  rock mass q u a l i t y with  (RMR  the t r a n s i t i o n  majority of p i l l a r s rock  mass  « 60 - 80) corresponds  zone  of the p i l l a r  However, Hoek  and Brown  o f 1.5  f o r permanent mine p i l l a r s .  factor  may  needed  and  reasonably  stability  factor  e n t r y mining  f o r good well  graph.  The  i n t h e open stope r i b data base have a good  quality.  be  line  f o r the design  suggest While  a safety  this  o f permanent  safety  pillars  in  methods, use o f t h i s s a f e t y f a c t o r would make Hoek  Brown curves  q u i t e c o n s e r v a t i v e f o r open stope  rib pillar  design. Hoek and Brown suggest mass q u a l i t y rock  mass  on p i l l a r  quality  pillar stability mass q u a l i t y few  pillar  a very  strength.  i s well  below  l a r g e i n f l u e n c e o f t h e rock The d e s i g n curve the t r a n s i t i o n  zone  histories  with  fair  zone.  o f the  or very  There a r e v e r y good  rock  q u a l i t i e s i n t h e data base, so t h e a p p l i c a b i l i t y o f these for  fair  graph and t h e d e s i g n curve f o r a v e r y good rock  i s f a r above t h e t r a n s i t i o n case  for a  p i l l a r d e s i g n can not be v e r i f i e d .  case h i s t o r i e s o f p i l l a r s  mass curves  A s u b s t a n t i a l number o f  i n f a i r and v e r y good rock masses are  needed b e f o r e these two curves c o u l d be used c o n f i d e n t l y i n open stope r i b p i l l a r d e s i g n .  6.4.3 P i l l a r Shape E f f e c t Formulas  son/avoi FIGURE 48. Three o f t h e Hoek and Brown (1980) p i l l a r s t r e n g t h c u r v e s p l o t t e d on t h e 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 o f t h e p i l l a r s t a b i l i t y graph and t h e good r o c k nass q u a l i t y c u r v e a r e v e r y c l o s e t o each o t h e r .  154 There (see  are  Chapter  several  variations  3.1.1.1).  Two  the  Duvall  influence  testing al.  and  of  of c o a l  (1946).  the  =  pillar  1  *  formula  (1967) p r e s e n t e d a formula t o account f o r shape.  specimen  a  effect  (1967) and B i e n i a w s k i (1983).  It  pillars  [A  +  i s based  on  compressive  o f v a r i o u s shape by Obert e t  The proposed r e l a t i o n s h i p  dp  shape  o f the most common v a r i a t i o n s were  developed by Obert and D u v a l l Obert  of  was:  B * (w / h)]  where: CTp = p i l l a r  strength,  = u n i a x i a l strength of a c u b i c a l  pillar,  w = p i l l a r width, h = p i l l a r height, A = e m p i r i c a l c o n s t a n t = 0.778 B = e m p i r i c a l c o n s t a n t = 0.222. The  formula has been used by s e v e r a l authors  3.1.1.4) t o  account  f o r the  shape  effect  (listed  i n hard  i n Chapter rock  pillar  of a c u b i c a l  pillar  design. The (o~l) on w/h  formula assumes t h a t  i s known. the p i l l a r = 1 and  the  strength  I f we assume the maximum c u b i c a l p i l l a r stability  the f a i l u r e  graph line  i s found a t the i n t e r s e c t i o n (top o f the t r a n s i t i o n  formula  plotted  compare  well  F i g u r e 49  on  the  pillar  with  the  pillar  data  stability  shows the Obert and  stability or  graph. the  of  zone) , the  Obert and D u v a l l formula can be compared t o the p i l l a r graph and the d a t a base.  strength  Duvall  I t does  location  of  not 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 D u v a l l (1967) shape e f f e c t formula a p p l i e d with a s a f e t y f a c t o r o f 1.0.  156 transition  zone.  The Obert  and D u v a l l formula assumes a much  higher strength f o r slender p i l l a r s  than t h a t shown by t h e case  h i s t o r i e s and t h e 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. are  many  failed  and s l o u g h i n g p i l l a r s  proposed by Obert and D u v a l l .  below  There  the f a i l u r e  line  T h i s formula i s n o t a p p l i c a b l e t o  the d e s i g n o f open stope r i b p i l l a r s .  A  major  Bieniawski 1970's.  coal  design  study  was  carried  (1983) a t P e n n s y l v a n i a S t a t e U n i v e r s i t y One  development  of of  B i e n i a w s k i used Duvall.  pillar  t h e major a  shape  results  effect  of  the  pillar  out by  i n the l a t e  study  was the  strength  formula.  a formula s i m i l a r t o t h a t proposed  by Obert and  B i e n i a w s k i ' s formula i s : (Tp  = K * [ 0.64 + ( 0.36 * W )] H  where: Op = t h e p i l l a r s t r e n g t h , K = UCS  t h e compressive s t r e n g t h o f 1 c u b i c f o o t  = 1 2  of  intact p i l l a r material,  W = p i l l a r width, H = p i l l a r height. Assuming failure  line  Bieniawski's  UCS  1 2  ~  can be formula  °'  7  * UCS  plotted  with  the p i l l a r  factor,  there  on  i s plotted  f a c t o r o f 1.0, 1.5 and 2.0.  2  (shown  the p i l l a r i n figure  6.4.1),  stability 50,  for a  a  graph. safety  T h i s formula does not compare w e l l  data o r t h e t r a n s i t i o n  a r e many  i n Chapter  pillar  case  zone.  histories  F o r each that  safety  can not be  157  son/avon  ?VoLf°* (1983) a p p l i e d w i t h  FI  c t forumla proposed by B i e n i a w s k i three d i f f e r e n t safety factors 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 graph. T  h  e  s  n  a  p  e  e  f  f  e  158 e x p l a i n e d by B i e n i a w s k i ' s formula.  The  c o n d i t i o n s under which these formula were developed  e x p l a i n t h e i r inadequacy of  the  formulas  f o r open stope r i b p i l l a r d e s i g n .  is  more  applicable  for  w i d t h / h e i g h t r a t i o of much g r e a t e r than one. width/height will  ratio  of l e s s  overestimate p i l l a r  these  formulas  are  not  than one,  pillars  well  suited  the shape e f f e c t  to  open  Both  with  For p i l l a r s  s t r e n g t h by l a r g e amounts.  can  a  with a  formulas  Generally,  stope  rib  pillar  design.  6.5  Chapter Summary The v a r i a b l e s t h a t are 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  are:  according the  to  intact  The  the figure  volume  pillar  width  26,  page 87),  rock m a t e r i a l of  discontinuities rib  pillar  a do  and  pillar  the and  not appear  and the  the  height  compressive  load  t o be  d e s i g n , over the range  pillar  induced presence  s t r e n g t h of the  of  significant  observed  on  (defined  pillar.  geological  f o r open stope  f o r these v a r i a b l e s  i n Canadian open stope mines. A p i l l a r d e s i g n c h a r t has been developed based on open stope rib pillars pillar  mining  consists graph  and v e r i f i e d and r e f i n e d based on hard rock room and  of  data 135  found  pillar  contains stable  in literature.  case and  histories.  failed  The The  total pillar  d e s i g n areas  data  base  stability  s e p a r a t e d by  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.  a The  159 transition location  zone is  represented  is  well by  represented  defined  dashed  by  lines  by  a  data. where  solid The  line  where  transition  i t s exact  its  zone  is  is  not  stope  rib  location  v e r i f i e d by the d a t a . The pillar  compatibility design  complete formula rib  curve  The  data  (1972) was design.  number the  base was  graph.  of  pillar  existing  open  stability  checked.  graph  Hedley's  and  size  the  effect  found t o be q u i t e c o n s e r v a t i v e f o r open stope The  Hoek and  f o r a good rock mass q u a l i t y  stability curves  a  methods w i t h  pillar  pillar  of  However,  the  Brown  (1980) p i l l a r  agreed  strength  w e l l w i t h the  applicability  of  the  pillar  strength  f o r the o t h e r rock mass q u a l i t i e s c o u l d not be v e r i f i e d .  pillar  (1967) and rib p i l l a r  shape e f f e c t Bieniawski design.  formulas  (1983) are  proposed not  by  Obert  applicable to  and open  Duvall stope  160  CHAPTER 7 DESIGNING RIB PILLARS FOR  The  design  support  to  of  be  rib pillars  provided.  OPEN STOPE MINING  depends  Rib  pillars  on  the  may  d u r a t i o n of  be  designed  permanent support t o p r o v i d e long-term  stability  to  ore b l o c k  provide  access  regional s t a b i l i t y  t o the s t o p e s .  temporary  support  Conversely,  to  a  p r o v i d e d by b a c k f i l l . The  decision  to  mining  r e c o v e r y methods. are  typically  justified This  is  value  ore  or  In a r e l a t i v e l y  be  the  costs associated with  support  is  pillars  is  low grade orebody,  most economical  because  the  explicitly  per  ton  in  found  a  form of  backfill  cost  of  support  and  backfilling  pillar pillars can  be  per  the  in  mines  comparison  of  the  approximate  i n Canadian open stope mines u s i n g  temporary p i l l a r s  almost  stope  temporary  permanent and tonne  until  to give  the maximum e x t r a c t i o n of the orebody i s d e s i r e d .  shown  of  be designed  use  permanent  to protect  In h i g h e r grade o r e b o d i e s , temporary  used  and  block  and  recovered.  a permanent p i l l a r may high  r i b s may  give  t o open stopes,  The p i l l a r i s then  l a r g e l y based on economics.  because o f the  t o the  to  the  using  (Table 13) . temporary  The  pillars  average v a l u e and  fill  is  double t h a t of the mines u s i n g permanent p i l l a r s .  Because purposes,  permanent  their  designs  and can  temporary be  pillars  quite different.  c h a p t e r w i l l d i s c u s s the d e s i g n of permanent and  have  different  The f o l l o w i n g temporary  161  MINES USING BACKFILL NORITA MATTAGAMI LAKE MINES GASPE WESMIN CORBET KIDD CREEK KIENA LOCKERBY LAC SHORTT GOLDEN GIANT LYON LAKE GECO BRUNSWICK CENTENNIAL SELBAIE - ZONE B FALCONBRIDGE  $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $  88 60 68 128 108 125 69 123 69 114 144 70 125 54 100 129  MEAN  $  98  MINES USING PERMANENT PILLARS  Table  APPROXIMATE VALUE OF ORE ($US/ton)  APPROXIMATE VALUE OF ORE ($US/ton)  RUTTAN ALGOMA HEATH STEELE SELBAIE - ZONE A  $ $ $ $  43 25 92 47  MEAN  $  52  13. Comparison o f t h e v a l u e o f o r e ($US/ton) f o r mines u s i n g b a c k f i l l a g a i n s t mines u s i n g permanent p i l l a r s . The mine grades a r e from t h e 1987 Canadian Mines Handbook, and t h e p r i c e o f t h e metals i s from the January 1988 E n g i n e e r i n g and M i n i n g J o u r n a l (after P o t v i n e t a l . 1988b).  162 pillars for  i n Canadian open stope mines and suggest some g u i d e l i n e s  using the p i l l a r s t a b i l i t y  use o f temporary p i l l a r s  7.1 Permanent The pillars  Pillars  maximum  possible  i s about 80%.  waste.  orebody  permanent  under  in  for  a  long  around  permanent  be l e f t  i n place,  should be l o c a t e d i n low grade ore  conditions. ore  period  of  pillar  dimensions  However,  must  c o n s e r v a t i v e dimensions, t o m a i n t a i n block  ore w i l l  (conservative)  these  pillars  extraction  Any remaining  Oversize  permissible  An example o f t h e  i s also given.  so i d e a l l y , permanent p i l l a r s or  graph method.  be  a  the design  compromise  the s t a b i l i t y time,  and  are of  between  o f t h e mining  non-conservative  dimensions, t o minimize t h e l o s s o f o r e i n t h e p i l l a r . In pillars area  a  preliminary  should  plot  of the p i l l a r  design, below  i t i s suggested  the t r a n s i t i o n  stability  graph.  zone,  that  permanent  i n the stable  The d i s t a n c e  below t h e  t r a n s i t i o n zone should be a f u n c t i o n o f t h e degree o f confidence in  t h e i n p u t data  of  t h e rock  input should  data,  and t h e induced the further  stress) .  below  The l e s s  the t r a n s i t i o n  strength  confident the zone  a  pillar  plot.  Ultimately, optimised  the  according  conditions. design  ( e s p e c i a l l y t h e u n i a x i a l compressive  best  design  t o mining  f o r permanent  experience  pillars  i n the l o c a l  A good example o f u s i n g l o c a l experience  i s documented  by P a k a l n i s  (1986)  a t Ruttan.  is  ground  in pillar The r i b  163 pillars their  gradually f a i l  planned  as t h e l o n g i t u d i n a l stopes are opened t o  limits.  However) the p i l l a r s  retain  sufficient  r o c k mass competency t h a t they remain r e l a t i v e l y i n t a c t , t h e use  of b a c k f i l l ,  and  r e g i o n a l mine support.  without  c o n t i n u e t o p r o v i d e stope support  In most mines, f r a c t u r i n g due t o p i l l a r  f a i l u r e would combine w i t h g e o l o g i c a l s t r u c t u r e t o cause pillar  s l o u g h i n g and  e v e n t u a l l y complete  At Ruttan, s l o u g h i n g o f f a i l e d so  the  they  rib pillars  will  remain  and  can  be  intact  disintegration.  p i l l a r m a t e r i a l i s not a problem,  designed  and  pillar  severe  still  to  gradually f a i l  p r o v i d e the  because  necessary  stope  support.  7.2  Temporary  Pillars  Temporary  rib  recover  the  entire  i n v o l v e s the use carefully  pillars  are  orebody.  of b a c k f i l l  sequenced.  An  used This  and  when type  it  of  open  of  pillars are  the  i s the  primary  optimum mining  ease  more d i f f i c u l t  shows  the  range  concerns  of  Canadian  open stope mines.  designed  with  less  than  a  strike  25 metres.  f o r the  more expensive  temporary  pillar  to  height metres.  of  mining  high  temporary  Small  recover.  dimensions  l e n g t h of g r e a t e r than  from l e s s than 5 metres t o 60  to  instability.  design  G e n e r a l l y , temporary  Pillar  stope  sequence g i v e s a  of r e c o v e r y of the p i l l a r . and  intended  the e x t r a c t i o n o f ore must be  r a t e of mining, w h i l e a v o i d i n g stope and p i l l a r One  is  pillars  Figure used  in  rib pillars 8-10  metres  ( i e . orebody width)  51 14 are and  varies  164  O  CD CD  to  m  CD CD  m  CD  e  1 r-  Q  a o CD U Of O  com CD CD  CD  CD CD CD  CD  CD CD  CD  CD  CD CD CD  O CN  CD CD  CD CD CD CD CD  m to  O  ID CM  O  in  FIGURE 51. The range o f 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 l e n g t h ( p i l l a r width) i s about 25 metres, w h i l e t h e maximum orebody w i d t h ( p i l l a r height) i s about 60 metres.  165 The pillar used  design  of  temporary  pillars  depends  i s intended t o be s t a b l e or t o f a i l . in  open  stoping  in  Canada,  and  on  whether  the  Both approaches are there  are  different  recommendations t h a t can be made i n the d e s i g n o f each type  of  temporary p i l l a r .  7.2.1  S t a b l e Temporary  The  majority  stable. role may  of  Pillars  temporary  rib pillars  However, the mine o p e r a t o r ' s  are  designed  designed  be minimized. recovery.  Use  some  minimizing mining  than  necessary,  Pillars  or t h e i r dimensions  may  of o v e r s i z e r i b p i l l a r s p e r m i t s e a s i e r p i l l a r  In a d d i t i o n , the s t a b i l i t y p r o v i d e d by the e x t r a s i z e  means t h a t the leaving  larger  be  philosophy plays a large  i n d e t e r m i n i n g the s i z e o f temporary r i b p i l l a r s . be  to  primary  stopes  flexibility  temporary  volume and  costs.  Minimizing  pillars  fail  recover  due  in  pillar  not  the  need  filling  dimensions  gives  immediate  pillar  dimensions can  their  temporary p i l l a r s may  or  small  i f the  size.  a  However,  higher and  are  primary  development  become c o s t l y  pillars  The  filling,  cycle.  a q u i c k e r payback on c a p i t a l  unexpectedly to  may  i f the  difficult  consequences  of  to  failed  include:  - the l o s s o f r e s e r v e s , - a h i g h mining  cost,  - the need f o r remedial s t a b i l i t y measures such as c a b l e bolting, - regional instability  such as hanging w a l l and back c a v i n g ,  166 - and a low r a t e mining. Cases  of  rib  documented  pillar  by  many  (1977) and Bray  7.2.2  pillars  will  to  not  new  well  above  (1986),  The  consequences  o f t e n be  Brady  minimized  of  failed  i f failure  is  the  and  will  be  easier to  the  pillars planned. pillar  recover.  t o d e s t r e s s or f a i l has been documented a t  (Grace  and  ( B h a r t i 1987).  stability  graph,  transition  h e i g h t r a t i o w h i l e having easy r e c o v e r .  are  i n open s t o p i n g i s t o d e s i g n  overstressed  mine  S t r a t h c o n a mine the p i l l a r  Falmagne  problems  i s t h a t i n a h i g h s t r e s s environment, the  become  Frood  including  concept  Designing r i b p i l l a r s INCO's  recovery  Pillars  fail.  above can  advantage  and  (1967).  relatively  described The  authors  F a i l e d Temporary A  rib  instability  Although  Taylor  1985)  and  Falconbridge•s  To d e s i g n a f a i l i n g  i t i s suggested area,  have  a p i l l a r width  a  pillar  with  that a p i l l a r  plot  low  pillar  width  l a r g e enough t o  t h e r e are no p i l l a r s  to  permit  designed t o f a i l i n  the data base, s e v e r a l p i l l a r case h i s t o r i e s t h a t were d i s c a r d e d from the data base f i t the above d e s i g n There are a few  q u a l i t a t i v e recommendations and  add t o the d e s i g n of f a i l i n g  - i t i s v e r y important as p o s s i b l e .  The  suggestions.  p i l l a r w a l l s and w i l l  pillars:  to f i l l  fill  will  comments t o  the surrounding stopes as q u i c k l y provide l a t e r a l  c o n s t r a i n t on  the  reduce s l o u g h i n g of the f r a c t u r e d p i l l a r  167 material, - control  blasting  should  be  used  near  the  pillar  walls  to  minimize w a l l damage due t o b l a s t v i b r a t i o n s , - development  in  artificial pillar  pillars  will  likely  need  support such as c a b l e b o l t s  fracturing  could  full  friction  and grouted r e b a r , as  substantially  affect  development  stability, - and  drill  problems  hole  closure  displacement  could  cause  Large diameter b l a s t h o l e s w i l l  recovery of f a i l e d  l i k e l y be needed f o r  pillars.  Case Example: 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  7.3.1  Geology and M i n i n g Method  The N o r i t a mine i s l o c a t e d i n the Mattagami mining i n n o r t h western Quebec. zinc can  orebody be  found  i s shown i n Mine #19 i n papers  converted  This  case  to  a  history  by  i n Appendix  Bawden  and  Milne  focus on  I.  (1987) ,  open  stoping  the t r a n s v e r s e p i l l a r s  open s t o p i n g between l e v e l s 9 and 11 o f the orebody The mining b l o c k was per  level.  block  The  i s shown  basic by  the  d i v i d e d i n t o two sequence roman  More  of  detail Chauvin  In r e c e n t y e a r s , the mine  transverse blasthole  will  district  The g e o l o g i c a l s e t t i n g f o r the copper-  (1986), and Goodier and Dube (1984). has  severe  f o r l o n g h o l e (small diameter d r i l l hole) open s t o p i n g  methods.  7.3  and  on  i n the  ( f i g u r e 52).  l e v e l s w i t h 17 stopes  extraction  numbers  method.  f o r the  figure  52.  mining Primary  FIGURE 52. Isometric view o f t r a n s v e r s e b l a s t h o l e open stoping at Norita. The b a s i c sequence o f stope e x t r a c t i o n i s shown i n roman numbers.  169 stopes were e x t r a c t e d every with  a 30:1 r a t i o  Temporary p i l l a r s are  of m i l l  fourth  stope.  tailings  Stopes  were  temporary The  filled  and waste rock t o cement.  (composed o f t h r e e c o n s e c u t i v e unmined stopes)  formed by t h e e x t r a c t i o n o f t h e primary  problems  were  stopes.  not r e p o r t e d d u r i n g t h e primary  Stability  mining  and the  p i l l a r s have been assessed as s t a b l e . next  (secondary) secondary  phase  stope o f t h e temporary stopes  methods.  i n t h e mining  was  done  to extract  pillars.  carefully  E x p l o s i v e s were decked  d e l a y o f 90 k i l o g r a m s .  was  with  t h e middle  The b l a s t i n g o f the  using  control  blasting  a maximum d e t o n a t i o n p e r  A f t e r t h e stopes were emptied,  they were  b a c k f i l l e d w i t h a 30:1 r a t i o o f m i l l t a i l i n g s and waste rock t o cement. With t h e commencement o f 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  III), deterioration  necessitated stopes metre  frequent  encountered rounds) .  fractured.  rehabilitation.  heavy b l a s t The  o r e was  started.  (stages pillar  Mining  With  cells  level  installed  10  of the t e r t i a r y  described  as b a d l y  on 2  broken  and  s i n c e t h e ground  (Q « 40 and RMR « 75) b e f o r e mining  continued  above  level  (3.3 metre p u l l  mining  I I I , IV, and V) , development (directly  on  overbreak  9)  between drifts  deteriorated  shedding from t h e t r a n s v e r s e mining a r e a . stress  pillars  T h i s damage was induced by mining  was c l a s s i f i e d as v e r y good had  o f drawpoint  near  the  levels  9 and 11  i n t h e 8-8 due  to  sill  stress  T h i s was confirmed by transverse  pillars.  170 Extensometer m o n i t o r i n g of the deterioration transverse  was  directly  mining  (documented by  8-8  pillar  to  mining  related  block.  Bawden and  sill  Based  Milne  on  showed t h a t events  these  Back A n a l y s i s U s i n g the P i l l a r S t a b i l i t y Back  analysis  will  focus  in  the  observations  1987), the t e r t i a r y p i l l a r s  the t r a n s v e r s e mining area were assumed t o have  7.3.2  the  on  in  failed.  Graph  representative p i l l a r s  i n the  mining b l o c k .  A f t e r the primary mining between l e v e l s 10 and  was  stopes 10-5  completed,  s t a b l e temporary f i g u r e 53). height, height  33  had been e x t r a c t e d l e a v i n g a  p i l l a r made o f stopes 10-6,  The p i l l a r dimensions metres  in  (pillar)  load  modelling  stability  was  estimated  (BITEM) a t 75 MPa  pillar  tertiary  plots  graph  pillars  well  height,  (pillar)  10-6  11  height.  pillar  165) .  (see  width  and  23  metres i n  (pillar)  by  two  dimensional  (case 43  inside  the  was  This  from  plane  Table  stable  zone  8, of  strain  page the  The  105). pillar  ( f i g u r e 54).  assessment.  (stope)  8  and 10-8  were: 55-60 metres i n (stope)  During secondary mining stope 10-7  failed  10-7,  ( a c c o r d i n g t o the convention i n f i g u r e 26, page 87).  average  The  and 10-9  11  and The  in  e x t r a c t e d l e a v i n g the  ( f i g u r e 53) , which were g i v e n a  pillar  metres  dimensions  (pillar  were:  width)  and  55-60 23  metres  metres i n  The t h e o r e t i c a l average p i l l a r l o a d on the  estimated is a  10-8  was  a t 99  theoretical  p r a c t i c e the p i l l a r has f a i l e d  MPa  (case 42  average  from  pillar  Table  load  8,  10page  because  in  and d e s t r e s s e d and t h e r e f o r e w i l l  FIGURE 53. A l o n g i t u d i n a l s e c t i o n o f the b l a s t h o l e stoping block at Norita showing the p i l l a r histories (10-6, 10-7, and 10-8) used i n t h i s h i s t o r y a n a l y s i s ( a f t e r Goodier and Dube 1984).  open case case  172  SOn/QVOT F  I  o ? ^ f  4  \  K?  6  P4  l a r  s t a b i l i t y graph showing t h e l o c a t i o n  173 have  a  much  lower  actual  load  (see Chapter  complete d i s c u s s i o n o f t h i s assumption). the  transition  agrees  very  zone i n the  well  w i t h the  5.5.1  f o r a more  The p i l l a r p l o t s above  failed  area  (see f i g u r e  failed  assessment  54) .  f o r the  This  tertiary  stopes.  7.3.3  Comments Concerning the P i l l a r Design  This  yielding  pillar  case  history  f a i l e d p i l l a r s i n open stope mining. and  o b s e r v a t i o n s t o make t h a t  illustrates  the  use  of  There a r e s e v e r a l comments  a r e a consequence  o f the p i l l a r  design: 1 - Cable b o l t i n g o f the t e r t i a r y to 2  severe c r a c k i n g and j o i n t  - Heavy overbreak was  stope backs was  necessary, due  opening.  d u r i n g the p i l l a r  (tertiary  stope)  mining  encountered.  3 - Blastholes  (6h  inch  diameter)  were  used  for  the  entire  mining b l o c k and were necessary t o a v o i d the l o s s o f holes  due  to  c r u s h i n g and  fracturing  d u r i n g the  drill  tertiary  p i l l a r recovery. 4 - The mill  stopes were f i l l e d  q u i c k l y w i t h waste r o c k and cemented  tailings.  5 - The mining o f 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 rib  pillars  i s t o i n v e s t i g a t e the s t a b i l i t y  of  i n open stope mining and develop g u i d e l i n e s f o r the  optimization  of  rib pillar  dimensions.  This  is  accomplished  through f o u r major s t e p s : - description  of  the  failure  mechanism  in  open  stope  rib  pillars, - i n v e s t i g a t i o n of rib pillar  the  methods  c u r r e n t l y used  i n open  stope  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 d e s i g n v a r i a b l e s , - and  formulation  and  verification  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  Progressive in  two  b a s i c types  failure  r e f e r s to gradual  a slow, n o n - v i o l e n t  ized  by  fracture  the of  violent rock.  of f a i l u r e  manner. release  This  i n hard  rock  d e t e r i o r a t i o n of a  Bursting f a i l u r e of  thesis  pillars.  energy only  pillar  i s character-  causing  instantaneous  investigates  progressive  failure. Open  stope  rib  pillar  mechanism.  Pillar  failure  progressive  failure  causes  instability  i s defined a pillar  to  as  is the  start  a  progressive  point losing  at  which  i t s load  175 bearing  capacity.  largely  due  Several  to  signs  identified,  The  decrease  fracturing of  of  in  the  increasing  load rock  pillar  bearing mass  capacity  in  the  instability  is  pillar.  have  been  including:  - c r a c k i n g and s p a l l i n g of r o c k i n p i l l a r development, - a u d i b l e n o i s e heard  i n the p i l l a r s  or microseismic  events  d e t e c t e d w i t h m o n i t o r i n g systems, - deformed o r plugged d r i l l h o l e s , - overdraw from stopes c o n s i s t i n g of u n b l a s t e d , o v e r s i z e ore, - stress redistribution or  from p i l l a r s  a f f e c t i n g nearby  pillars  development,  - h o u r g l a s s i n g and c r a c k i n g of - and  displacements  or  pillars,  changes  in  stress  shown  by  instrumentation.  8.1.2  C u r r e n t P i l l a r Design Methods  Design methods used f o r open stope r i b p i l l a r s empirical modelling  pillar and  design  empirical  studies failure  or  the  use  criterion.  were based of  numerical  Empirical  d e s i g n methods were developed based on l a b o r a t o r y t e s t i n g investigation  of  actual  mine  pillars.  These  on  methods  pillar and/or were  developed f o r s p e c i f i c mining c o n d i t i o n s and are not n e c e s s a r i l y applicable basically determine  f o r open stope r i b p i l l a r d e s i g n . assume e l a s t i c stress  around underground  and/or  redistribution excavations.  plastic and  Numerical methods  r o c k mass behaviour rock  mass  to  displacement  E m p i r i c a l f a i l u r e c r i t e r i o n are  176 a p p l i e d t o the s t r e s s or displacement r e s u l t s t o determine  rock  mass  failure.  situ  rock  mass  However,  failure  i t is difficult  criterion.  to v e r i f y  Consequently,  an  in  numerical  design  methods need e x t e n s i v e s i t e c a l i b r a t i o n b e f o r e they can be e f f e c t i v e l y to design r i b p i l l a r s The  design  combination  of  techniques  methodology numerical  are  used  to  f a i l u r e i s determined  i n open stope mining.  chosen  and  used  for  empirical  determine  this  thesis  methods.  pillar  load,  is  a  Numerical  while  pillar  from e m p i r i c a l back a n a l y s i s o f 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 Q u a n t i f i c a t i o n o f the Design V a r i a b l e s Based  on  the  data  and  case  histories  collected  in  the  I n t e g r a t e d Mine Design P r o j e c t , the f a c t o r s t h a t are s i g n i f i c a n t for  open stope r i b p i l l a r d e s i g n a r e : - the compressive  s t r e n g t h of i n t a c t p i l l a r m a t e r i a l (UCS),  - the average p i l l a r s t r e s s  (determined w i t h boundary  element numerical m o d e l l i n g ) , - the p i l l a r h e i g h t , - and the p i l l a r Three  factors  failure: as  were  width. discounted  the presence  joints),  the  as  insignificant  in rib  of minor 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  effect  of  pillar  volume,  and  the  pillar (such  effect  of  backfill.  The open stope r i b p i l l a r data and case h i s t o r i e s d i d  not  prove  these  The  background i n f o r m a t i o n f o r a l l the p i l l a r s  factors  as  being  important  in pillar  failure.  i n the data base  177 i s p r e s e n t e d i n T a b l e 5 (page 70) and the g e o l o g i c a l s e t t i n g s of all  of the  pillar  case  histories  are shown i n o b l i q u e orebody  diagrams i n Appendix I. Three  of  quantify.  the  The  four  UCS  can  design be  variables  determined  by  are  quite  easy  laboratory testing  intact  rock samples or estimated w i t h the p o i n t l o a d t e s t .  pillar  height  The  most  stress.  and  pillar  difficult  width  factor  to  A method t o determine  in  Chapter  and  the  5.  The  two  pseudo-three  are  measured  quantify average  dimensional  from  i s the  load  these  methods  geometries. two  have  The  pillars  limitations  (2D)  and  i n the when  data  limitations  displacement  a s s o c i a t e d w i t h these  page 109  limitations  ( f o r 2D m o d e l l i n g ) , and  12  some  runs  of  pillar  a s s o c i a t e d with  i n f i g u r e 34, page 112  DD  to  However,  (DD)  i s given i n figure  the  models  base.  the  In a d d i t i o n , a rough  These e r r o r e s t i m a t e s are based  and  t o estimate  discontinuity  modelling). 2D  pillar  discontinuity  modelling  n u m e r i c a l m o d e l l i n g have been i d e n t i f i e d . error  plans.  average  displacement  major g e o m e t r i c a l  dimensional  The  boundary element code BITEM  dimensional  f o r a l l the  of  p i l l a r s t r e s s i s proposed  boundary element model "MINTAB" have been used pillar  mine  to  the  33,  ( f o r DD  on a comparison of three  dimensional  boundary element code "BEAP".  8.1.4  Development o f the P i l l a r S t a b i l i t y Graph The  ically  open  stope  analyzed  and  rib pillar a  pillar  data design  collected graph  has  has  been  been  empir-  developed  178 (figure  36,  page  "Pillar  Stability  areas  separated  graph  has  rock  room  complete  The  Graph". by  a  and  data  design  pillar  and  zone.  The  r e f i n e d based  case  histories  base o f about The  c h a r t has  been c a l l e d  I t c o n t a i n s s t a b l e and  transition  been v e r i f i e d  (page 145). of  125) .  135  pillar  design  stability  on more than 80  from  pillars  failed  the  hard  literature.  The  i s shown i n f i g u r e  d e s i g n c h a r t e x p l a i n s the s t a b i l i t y  45  condition  the data base case h i s t o r i e s v e r y w e l l and i s q u i t e s e n s i t i v e  in predicting p i l l a r Empirical  failure.  design  methods  used  f o r open  stope  d e s i g n have been compared t o the complete p i l l a r the p i l l a r line  stability  of the  pillar  graph.  The  rib  data base  good rock mass q u a l i t y  s t r e n g t h curves  proposed  by  However, the Hedley  s t r e n g t h formula by Obert  and  and D u v a l l  and Grant  (1967) and  Bieniawski  strength  stable,  temporary  Guidelines rib  rib pillars  pillar  and  may  stable,  have been suggested using  the  be designed  pillar  or  f o r the  stability  d i s c u s s i n g the use of s t a b l e and f a i l e d also  presented.  pillar  formula's  (1983) do not compare  w e l l w i t h 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 Open stope  Brown  stability  (1972) s i z e e f f e c t  the shape e f f e c t p i l l a r  and  design  Hoek and  (1980) agrees q u i t e w e l l w i t h the data base and p i l l a r graph.  pillar  graph.  t o be permanent  temporary  and  failing.  d e s i g n o f each type graph.  A  case  and  of  history  temporary r i b p i l l a r s i s  179 8.2  Conclusions  8.2.1 A p p l i c a b i l i t y o f t h e Method The p i l l a r  stability  graph  uses f a c t o r s t h a t a r e r e l a t i v e l y  easy t o q u a n t i f y data t o p r e d i c t t h e s t a b i l i t y  o f open stope r i b  pillars.  The method i s most e f f e c t i v e when rough p r e d i c t i o n s o f  stability  are required.  will  fracturing  n o t be p r e d i c t e d , b u t g r o s s changes i n p i l l a r s t a b i l i t y a r e  recognized. stope  The method  r i b pillars,  pillars. sill  Minor problems such as l o c a l  i s designed t o p r e d i c t  but can be a p p l i e d  f a i l u r e o f open  t o some o t h e r t y p e s o f  I t should be a p p l i c a b l e f o r t h e d e s i g n o f open stope  pillars,  and r i b and s i l l  as V e r t i c a l C r a t e r R e t r e a t . these types  of p i l l a r s  pillars  i n non-entry methods such  The mechanism o f p i l l a r f a i l u r e f o r  i s t h e same as t h e mechanism o f f a i l u r e  i n open stope r i b p i l l a r s . T h i s d e s i g n method has n o t been developed pillars  o r confirmed f o r  i n e n t r y methods such as shrinkage and room and p i l l a r  mining.  The  development  pillar  stability  of a safety  factor  graph  would  before  likely  need t h e  i t c o u l d be a p p l i e d t o  p i l l a r d e s i g n i n e n t r y mining methods.  8.2.2 L i m i t a t i o n s o f t h e Method An e m p i r i c a l conditions  d e s i g n method i s more r e l i a b l e when a p p l i e d t o  similar  Consequently,  to  those  the following  pillar stability  graph:  found  in  limitations  the  original  a r e suggested  work. f o r the  180 70 MPa  <  UCS  <  316  9 metres  <  Wp  <  45  60  <  RMR  <  78,  MPa, metres,  (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 s t r e n g t h ,  Wp  = the p i l l a r width,  RMR  = a measure of the rock mass competency u s i n g the CSIR rock mass  classification,  Average P i l l a r Load i s determined  u s i n g two d i m e n s i o n a l or  displacement d i s c o n t i n u i t y boundary element numerical modelling. The  pillar  stability  graph  outside these l i m i t a t i o n s ,  method  may  i t should be  p r e l i m i n a r y d e s i g n method. associated  with  the  satisfactorily  but the c u r r e n t open stope data base  g e n e r a l l y does not extend o u t s i d e these Finally,  work  kept  limits.  i n perspective that  The assumptions  variables  and  this  and p o t e n t i a l  design  chart  is a error  limit  the  u s e f u l n e s s of the p i l l a r s t a b i l i t y graph f o r f i n a l d e s i g n .  8.2.3  Design o f Open Stope Rib  The role may they  Pillars  d e s i g n of open stope r i b p i l l a r s  o f t h a t p i l l a r i n the s t a b i l i t y  i s dependent upon the  of the mine.  Rib  pillars  be designed t o be g i v e permanent support t o open stopes, or may  backfill  be  designed  is  in  to  place.  give This  temporary decision  stope is  support  largely  until  one  of  181 economics.  Low  and  recovery  pillar  grade orebodies methods  cannot  due  to  be mined u s i n g the  higher  backfill  mining  cost.  Medium and h i g h grade mines can a f f o r d the c o s t of b a c k f i l l pillar  and  r e c o v e r y , so temporary p i l l a r s can be designed.  In some  i n s t a n c e s , temporary p i l l a r s have been designed t o f a i l  to avoid  stress  build  up.  p i l l a r s to f a i l ,  There  are  a  few  consequences  of  designing  including:  - the need f o r q u i c k b a c k f i l l i n g a f t e r the stope i s e x t r a c t e d , - the use o f a r t i f i c i a l - and  the  blasting  8.3  use  of  support i n p i l l a r development,  large  diameter  drill  holes  and  control  practices.  F u t u r e Work There i s a l i m i t t o the v a l u e o f c o l l e c t i n g  pillar  case  histories  to  refine  the  pillar  further general  stability  graph.  More cases of open stope p i l l a r s are not l i k e l y t o 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 t h e s i z e of the t r a n s i t i o n  area.  T h i s i s not t o say t h a t p i l l a r  design at  s p e c i f i c s i t e s can not be a i d e d by case h i s t o r i e s from t h a t s i t e or way  from  Past e x p e r i e n c e  i s the b e s t  t o r e f i n e p i l l a r d e s i g n methods t o l o c a l c o n d i t i o n s . The  be  s i m i l a r ground c o n d i t i o n s .  understanding  improved  influence significant  of  by rock  of one  collecting mass  (Chapter  of the p o s s i b l e d e s i g n f a c t o r s specific  characteristics  6.1.3.2),  range o f rock mass q u a l i t i e s .  but  case was  varied  histories. not over  The  found only  A n a l y s i s of p i l l a r case  may  to a  be  small  histories  182 in  fair  or very  good  quality  rock  masses may  show  t h a t the  q u a l i t y o f t h e 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 this  existing  pillar  can be  stability  proven, graph  a correction  factor  c o u l d be developed  t o the  t o account  f o r t h e e f f e c t o f rock mass q u a l i t y . Assessment difficult,  of the p i l l a r s  situ A  base was  sometimes  and a s u b s t a n t i a l amount o f data c o u l d not be a p p l i e d  because a r e l i a b l e detailed  i n t h e data  assessment c o u l d not be determined.  investigation  into  rock mass f r a c t u r i n g  better  definition  of  pillar  failure  mechanisms and i n  c o u l d improve p i l l a r failure  can  A more  be  d e s i g n methods.  developed  through  s y s t e m a t i c i n s i t u p i l l a r m o n i t o r i n g u s i n g v i s u a l t e c h n i q u e s (as shown  by  Krauland  and  Soder  1987)  or  through  t h e use o f  i n s t r u m e n t a t i o n such as s t r e s s m e t e r s (as shown by A g a p i t o 1974), extensometers  (as  microseismics. monitoring decrease  of  shown  by  Allcott  and  The use o f m i c r o s e i s m i c  shows rock  great mass  potential quality  due  Archibald systems  through to  rock  1981)  or  for i n situ  quantifying  the  fracturing,  and  m o n i t o r i n g t h e changes i n t h e l o a d b e a r i n g c o n d i t i o n o f p i l l a r s . 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Washington: N a t i o n a l Academy o f S c i e n c e s , 1076-1081. Watson, J.O. and Cowling, R. 1985. A p p l i c a t i o n o f t h r e e d i m e n s i o n a l boundary element methods t o m o d e l l i n g o f l a r g e mining e x c a v a t i o n s a t depth. Proceedings o f t h e 5 t h I n t e r n a t i o n a l Conference on Numerical Methods i n Geomechanics. 1901-1910. Yu, Y.S., Toews, N.A. and Wong, A.S. 1983. MINTAB u s e r ' s guide -a mining s i m u l a t o r f o r d e t e r m i n i n g t h e e l a s t i c response o f s t r a t a s u r r o u n d i n g t a b u l a r mining e x c a v a t i o n s ( v e r s i o n 4.0, 1982). D i v i s i o n r e p o r t MRP/MRL 83-25 (TR), M i n i n g Research L a b o r a t o r i e s , CANMET, Energy, Mines and Resources Canada, Ottawa. Z i e n k i e w i c z , O.C. McGraw-Hill.  1977. The F i n i t e Element Method.  London:  190  APPENDIX I  Specific case h i s t o r y  information  about  the g e o l o g i c a l  setting  of  each  can be found i n the i s o m e t r i c s k e t c h c o r r e s p o n d i n g  t o t h e mine number.  Each g e o l o g i c a l s e t t i n g i s comprised o f :  - the underground s t r e s s regime, - t h e hanging w a l l , f o o t w a l l and orebody m a t e r i a l p r o p e r t i e s and c h a r a c t e r i s t i c s i n c l u d i n g  (when a v a i l a b l e ) :  - r o c k type, - i n t a c t u n i a x i a l compressive s t r e n g t h , - elastic  modulus,  - poisson's r a t i o , - NGI r o c k mass c l a s s i f i c a t i o n , - s t e r e o n e t o f the major j o i n t  sets,  - the orebody shape and s i z e , - and t h e mining methods used i n v a r i o u s p a r t s o f the orebody. Mine  #22  does  complexity  not have  an i s o m e t r i c  o f the orebody  p r o p e r t i e s and s t r e s s  and  field.  orebody  s k e t c h due  the v a r i a b i l i t y  t o the  of the material  MINE No. 2 ORE (LENS 2 * 3 ) Rock Type: 1  =  E  =  HANGING WALL t, ROOF (LENS 2)  Massive Sulphide 4.2 t/m 200 MPa 61.0 GPa 0.3 3  °c =  V =  Rock Type:  Andesite 2.9 t/m 109 MPa 63.0 GPa 0.25 4 3  y  E v Q"  Q' =  LENS  0*  2  -H5m o»=ifh o =2.3yt\ m  70m  LONGITUDINAL OPEN STOPE  01,2=2. 2th  A*  0 HANGING WALL t ROOF (LENS 3) Rock Type: Y o E v  c  = = =  Altered Andesite 3.0 t/m 87 MPa 84.0 GPa 0.28 3  192  MINE  No. 6  ORE Rock Type:  T • 2e: V •  Q'  -  Breccia 4 Massive Sulphide 3.1 t/m 125 MPa 94.0 GPa 0.22 9 3  ISOm  WORTH WALL Rock Type:  T -  *:  V •  Q'  Norite 2.9 t/m 113 MPa S6.0 GPa 0.17 9 3  •  274 m  SOOTH WALL Rock Type:  T V  Granite 2.7 t/m 184 MPa 73.0 GPa 0.23 25 3  Depth  1050 m  MINE No. 8  N  MINE No. 11  MINED OUT (No Backfill)  /  /  T  r  MINED OUT ! (No Backfill)  PERMANENT  PILLAR  (No Grodo)  200m  71 LONGITUDINAL LONGH<SLE 62m STOPE  LONGITUDINAL LONGHO OOm STOPE  LONGITUDINAL LONGHOLE STOPE  4*  _Dtplh 925m -33m  • 30m-H  -62m  — 2O0m ORE  0,'1.15-rh  Rock Type: 7  Porphyry  - 2.72 t/« o , - 148 MPa Z » 18.S GPa v • 0.20 Q* - 30  ' » e«»1.5Yh 3  o.a-1.7th  MINE No. 16 ORB  Surfoca  Rock Typei y  -  8 v  • •  °c -  0* -  Kaaalva  Sulphlda  4.6 t/«' 176 MPa 119.0 CP* 0.24 20  HANGING HALL Book Type• y o B v 0' c  Quarta Porphyry  - 2.9 t/aj - 91 MPa - 68.7 GPa - 0.19 - 42 1  FOOT WALL Rook Typai  Chlorlta Tuff  - 2.9 t/m - 84 MPa - 68.5 GPa - 0.2S 0 ' - 40 Y o E v  e  1  080m  MINE No. 17 o,-th 2.6th*  LONGITUDINAL LONOHOLE OPEN STOPING  870m  f o r a u l a by Berget  -1600m-  ORg  WALL  Rock Typai  y  o E v 0' t  -  Maaelva Sulphide S.3 t/«* 100 MPa 103 CPa 0.31 19  Rock Typei  y  o E v Q" t  -  Cnalaa 2.7 t/m 52 MPa 105 GPa 0.20 18  1  MINE No. 19  1  o -»h s  MINED  •MI-3-3YI»  OUT a  BACKFILLED  TO SURFACE  30m  420m  • 180m •  LONOITUDINAL  70m  SUB-LEVEL  LONOITUDINAL  RETREAT  2-18 m  SUB-LEVEL RETREAT  30m  110m  Oapih 780m ORB Rock Typoi  Maaalva Bulphlda  o, - 316 MP* E - 232.2 GPa v - 0.16 0' - 44 N  WORTH WALL (10»)  SOUTH WALL ISO*)  Rock Typos  Rook Typai  o B v 0* c  Baaaltlo Tuff  - 11B MPa - 95.0 GPa - 0.26 - 4.0 N  Rhyolltio Tuff  o - 98 MPa B - 67.9 GPa v - 0.15 0* c  MINE No. 21  199  TYPICAL MINE CROSS SECTION  LONGHOLE tc BLASTHOLE LONGITUDINAL OPEN STOPING  ORE Rock 0* = E = V = Q' = c  Type: Massive Sulphide 100 MPa 88 GPa 0.20 10-20  HANGING WALL & FOOTWALL Rock Type: Quartz Meta Sediments CT = 5 0 - 1 3 5 MPa E = 5 0 - 7 5 GPa V = 0.12-0.34 Q' = 0.1-50 C  = 2.5 0"  v  200  MINE No. 23  Rock Type:  Massive S u l p h i d e  UCS = 3 1 0 MPa Q' = 20  FOOTWALL & HANGING WALL Rock Type:  Argy1ite  UCS = 7 5 MPa Q' = 0.6  MINE No. 30  TYPICAL MINE CROSS SECTION  TRANSVERSE BLASTHOLE OPEN STOPING  ORE Rock Type: Massive Sulphide Y = 3.3 t / m ' C = 160 MPa E = 80 GPa V = 0.21 Q' = 22 c  HANGING WALL Rock Type: Rhyolite Y = 2.7 t / m 0"c = 120-150 MPa E = 80 GPa V = 0.14 Q' = 13-30  1500m  s  FOOTWAa Rock Type: Andesite/Diorite 3.0 t / m ' Y 160 MPa 85 GPa E V 0.23 14 Q'  (T =YH V  0"j = 0.80", 0\ = 6+O.055H(m)  2 0 2  MINE No. 31  

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