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Investigation of underground mine pillar design procedures Potvin, Yves 1985

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INVESTIGATION OF UNDERGROUND MINE PILLAR DESIGN PROCEDURES By YVES POTVIN B.Sc,  LAVAL U n i v e r s i t y , QUEBEC 1981  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF A«ii«MASTER OF^SCIENCE J  in THE FACULTY OF GRADUATE STUDIES Mining  and M i n e r a l Process  We accept  Engineering  t h i s t h e s i s as conforming  tq the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA March  ©  1985  Yves P o t v i n ,  1985  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the  requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t t h e L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by t h e head o f my department o r by h i s o r her r e p r e s e n t a t i v e s .  It i s  understood t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l n o t be allowed without my w r i t t e n  permission.  Department o f M i n i n g and M i n e r a l P r o c e s s  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6 (3/81)  Columbia  Engineering  ABSTRACT  The p r i n c i p a l f u n c t i o n s o f underground mine p i l l a r s a r e to  s t a b i l i z e openings and t o c a r r y t h e l o a d o f o v e r l y i n g r o c k  s t r a t a . They a r e o f t e n ( p a r t i a l l y o r c o m p l e t e l y ) r e c o v e r e d a t a l a t e r s t a g e when t h e i r s t a b i l i z i n g e f f e c t i s no l o n g e r r e q u i r e d . For economic r e a s o n s , an optimum-sized p i l l a r i s t h e s m a l l e s t one s a t i s f y i n g s a f e t y r e q u i r e m e n t s . Thus t h e p i l l a r d e s i g n problem c o n s i s t s o f d e t e r m i n i n g the p i l l a r ' s  minimum dimensions  a s t h e l o a d approaches t h e u l t i -  mate p i l l a r s t r e n g t h . Because t h e p i l l a r ' s  s t r e n g t h and t h e l o a d a c t i n g upon  i t a r e b o t h f u n c t i o n s o f many i n t e r r e l a t e d f a c t o r s , which may vary as mining progresses, the determination o f p i l l a r  dimensions  i s a complex t a s k . Furthermore,  t h e m u l t i p l i c i t y o f p i l l a r shapes, s i z e s ,  r o c k m a t e r i a l and f u n c t i o n s add t o t h e d e s i g n e r s ' problem. Consequently,  p i l l a r d e s i g n programs a r e s t i l l g e n e r a l l y  performed a s a t r i a l - a n d - e r r o r p r o c e s s . In  o r d e r , t o improve t h e p r e s e n t p i l l a r d e s i g n p r a c t i c e s  (1) - A A p i l l a r c l a s s i f i c a t i o n i s proposed t o s t a n d a r d i z e the design (2)  procedure  The p r i n c i p a l d e s i g n methods, d i v i d e d i n t o f o u r groups, a r e summarized and t h e i r  is  i s defined  (3)  A f i v e - p h a s e d e s i g n procedure is  (4)  with design charts  developed  The d e s i g n p r o c e d u r e case  applicability  histories  i s a p p l i e d i n a n a l y s i n g two  TABLE OF CONTENTS  CHAPTER 1. CHAPTER 2.  Introduction The C l a s s i f i c a t i o n and D e f i n i t i o n o f P i l l a r s  2.1  Pillar  2.2  Category 1:  2.3  Classification  2.2.1  Description  2.2.2  Definitions  Category 2:  2.4  Description  2.3.2  Definitions  Description  2.4.2  Definitions  Category 4:  2.6  Discussion  3.1  "Stub  2.4.1  2.5  Pillars"  "Separation P i l l a r s "  2.3.1  Category 3:  CHAPTER 3.  "Plate  Pillars"  "Inclined  Pillars"  Review o f P i l l a r Design Methods Introduction  3.2  Group 1.  Experience Methods  3.3  Group 2.  Empirical  3.4  3.5  Methods  3.3.1  Empirical  strength  3.3.2  Empirical  s t r e s s formulas  3.3.3  Empirical  dimensioning formulas  Group 3.  Theoretical  formulas  Methods  3.4.1  Theoretical strength  3.4.2  T h e o r e t i c a l s t r e s s formulas  Group 4.  Computer Methods  formulas  Page  CHAPTER 4.  Pillar  Design  Procedure  4.1  Philosophy of P i l l a r Design  42  4.2  Design Procedure  42  4.3 CHAPTER 5. 5.1  4.2.1  Phase 1.  Experience Design  4.2.2  Phase 2.  P i l l a r Structural  Analysis  4.2.2.1  P i l l a r Transection V e r i f i c a t i o n  4.2.2.2  Shear S t a b i l i t y  4.2.3  Phase 3.  Empirical  4.2.4  Phase 4.  Theoretical  4.2.5  Phase 5.  Computer Design  Analysis  Design Design  46  Design Charts Heath S t e e l e Case H i s t o r y A n a l y s i s  53  Geology 5.1.1  Regional  Geology  5.1.2  Mine's  5.1.3  Structural  5.1.4  Jointing  Geology Geology  5.2  Mining Method and Underground S t r u c t u r e s Dimension  57  5.3  Rock Mechanics  59  Data  5.3.1  Rock S t r e n g t h  Parameters  5.3.2  Laboratory T e s t i n g  5.3.3  Rock Mass C l a s s i f i c a t i o n  5.3.4  V i r g i n Stress  5.4  P i l l a r Characteristics  63  5.5  Mining Sequence  63  5.6  F a i l u r e H i s t o r y and P i l l a r  Geometry  64  Page 5.7  5.8  68  P i l l a r Design Study 5.7.1  Phase 1.  Experience Design  5.7.2  Phase 2.  P i l l a r Structural  5.7.3  Phase 3.  E m p i r i c a l Methods  Analysis  5.7.3.1  E s t i m a t i o n of P i l l a r Load by the T r i b u t a r y Area Formula  5.7.3.2  Estimation of P i l l a r  5.7.4  T h e o r e t i c a l Methods  5.7.5  Computer Methods  Strength  90  D i s c u s s i o n o f the R e s u l t s  CHAPTER 6. 6.1  Geco Case H i s t o r y A n a l y s i s 98  Geology 6.1.1  Regional Geology  6.1.2  Mine Geology  6.1.3  Structural  Geology  6.2  Mining Method and Underground  6.3  Rock Mechanics Data  S t r u c t u r e Dimension  102 102  6.5.1  Rock S t r e n g t h Parameters  6.3.2  L a b o r a t o r y Test  6.3.3  Rock Mass C l a s s i f i c a t i o n  6.3.4  Virgin  Stress  6.4  P i l l a r Characteristics  108  6.5  Mining Sequence  108  6.6  F a i l u r e H i s t o r i e s and P i l l a r Geometries  113  6.7  Pillar  Design Study  120  6.7.1  Phase 1 .  Experience Design  6.7.2  Phase 2.  Pillar  Structural  Analysis  VI fa.ge  6.7.3  6.8  Phase 3.  E m p i r i c a l Methods  6.7.3.1  E s t i m a t i o n o f P i l l a r Load by the E x t r a c t i o n Ratio Formula  6.7.3.2  Estimation of P i l l a r Hoek's Method.  6.7.4  T h e o r e t i c a l Methods  6.7.5  Computer Methods  Strength;  Discussion of Results  CHAPTER 7.  ^30  Summary and C o n c l u s i o n 135  7.1  Design Procedure  7.2  Case H i s t o r i e s  I36  7.3  Design Methods  137  APPENDIX A.  Review o f L i t e r a t u r e  APPENDIX B.  Determination o f the Geco s t r e s s regime a t 700 f t . depth  APPENDIX C.  I l l u s t r a t i o n of P i l l a r s  APPENDIX D.  "BITEM", 2-D, Boundary Element Program  vii  LIST OF  Figure  FIGURES  Description  Page 9  1  P i l l a r category  1 "Plate P i l l a r s "  2  P i l l a r category  2 "Separation  3  P i l l a r category  3 "Stub P i l l a r s "  4  P i l l a r category  4 "Inclined P i l l a r s "  5  Hard Rock P i l l a r s  (Appendix  C)  6  Hard Rock P i l l a r s  (Appendix  C)  7  Soft Rock P i l l a r s  (Appendix  C)  8  Influence o f P i l l a r Width to Height Ratio on Average P i l l a r Strength  26  9  Average V e r t i c a l P i l l a r Layouts.  28  Pillars"  P i l l a r Stresses  10 13 '  in Typical  15  10  Determination of Load on Chain P i l l a r s by the " F i r s t P a n e l " Load Concept  29  11  Observed Value o f W f o r Coal Seams 7 f t . Thick and having a Crushing Strength i n the  32  3 - i n . Cube of 3,000 p s i  ±10%  12  P i l l a r transected  by a s i n g l e plane o f weakness  13  I n t e r s e c t i n g planes  14  Design c h a r t f o r " P l a t e P i l l a r s " ,  15  Design c h a r t f o r "Separation Category 2  16  Design c h a r t f o r "Stub P i l l a r s " ,  17  Design c h a r t f o r " I n c l i n e d P i l l a r s " ,  18  Heath S t e e l e Geology  54  19  Plan View of Heath S t e e l e Orebody  56  20  V i r g i n S t r e s s at Heath S t e e l e  62  21  L o n g i t u d i n a l View o f the Heath S t e e l e  65  of weakness  44 44  Category 1  Pillars",  Category 3 Category 4  I n v e s t i g a t e d Area at  47 ^  ^9 50  viii Figure  Description  Page  22  E x t r a c t i o n Flowchart o f 77-89, 77-91, 77-93 and 77-95 Stopes  66  23  Estimated failed.  Layout when 77-92 Rib P i l l a r  69  24  Estimated failed  Layout when 77-94 Rib P i l l a r  70  25  S  26  The E f f e c t of S F r a c t u r e s on 30 m. wide Rib P i l l a r s  (100 f t )  27  The E f f e c t o f S F r a c t u r e s on 60 m. wide Rib P i l l a r s  (200 f t )  28  S  29  Combined E f f e c t of S  30  77-90 Rib P i l l a r S l i d i n g  77  31  77-90 Rib P i l l a r Deformation versus Time  78  32  P i l l a r s E x t r a c t i o n Numbers f o r the 77-90 p i l l a r f a i l u r e geometry.  0  1  33  P i l l a r s E x t r a c t i o n Numbers f o r the 77-92 p i l l a r f a i l u r e geometry.  8  2  34  P i l l a r s E x t r a c t i o n Numbers f o r the 77-94 p i l l a r f a i l u r e geometry  35  The E f f e c t of the Width to Height average p i l l a r s t r e n g t h  36  Computer Output of the 77-90 p i l l a r f a i l u r e geometry. (Stress simulation)  87  37  Computer Output o f the 77-92 p i l l a r f a i l u r e geometry. (Stress simulation)  88  38  Computer Output of the 77-94 p i l l a r f a i l u r e geometry. (Stress simulation)  8  39  P i l l a r Deformation versus E x t r a c t i o n Number (N)  ^3  40  S a f e t y F a c t o r versus  9^  41  S a f e t y F a c t o r versus E x t r a c t i o n Ratio  42  Schematic S t r a t i g r a p h i c Columns i l l u s t r a t i n g g e n e r a l i z e d r e l a t i o n s h i p s of s u l p h i d e zones, Geco Mine  3  72  F r a c t u r e System 3  3  5  73  ^  7  75  F r a c t u r e System 3  and  S  5  76  Fractures  Ratio on  E x t r a c t i o n Number (N) (e)  ^  8  84  ?  96 99  ix  Figure  Description  Page 107  43  Assumed S t r e s s Regime at Geco  44  Longitudinal at Geco  45  E x t r a c t i o n Flowchart o f 10-19.5, 10-21, 10-22 and 10-23.5 stopes  46  Estimated Layout when 10-21.5 P i l l a r  47  Estimated Layout when 10-23 P i l l a r F a i l e d  H8  48  Estimated Layout when 10-20 P i l l a r F a i l e d  H9  49  P i l l a r s E x t r a c t i o n Numbers f o r the 10-21.5 p i l l a r f a i l u r e geometry  122  50  P i l l a r s E x t r a c t i o n Numbers f o r the 10-23 p i l l a r f a i l u r e geometry  123  51  P i l l a r s E x t r a c t i o n Numbers f o r the 10-20 p i l l a r f a i l u r e geometry  l  52  Computer Output o f the 10-21.5 P i l l a r F a i l u r e Geometry ( S t r e s s s i m u l a t i o n )  53  Computer Output o f the 10-23 P i l l a r Geometry ( S t r e s s s i m u l a t i o n )  Failure  54  Computer Output o f the 10-20 P i l l a r Geometry (Stress s i m u l a t i o n )  Failure  55  Safety  56  Comparison o f Heath S t e e l e , Geco Case h i s t o r i e s a n a l y s i s r e s u l t s  View o f the I n v e s t i g a t e d  Area  109  Failed  F a c t o r versus E x t r a c t i o n Ratio  H?  i  7  2  i  i  2 l +  2  2  8  9  133 138  X  LIST OF TABLES Table  Description  Page  1  Rock Mechanic S t u d i e s i n Noranda Underground Mines  3  2  P i l l a r and Opening D e s i g n i n g Methods used by Noranda Underground Mines  4  3  P i l l a r C l a s s i f i c a t i o n Summary  17  4  Constants A and B used i n the " S i z e E f f e c t Formula"  22  5  Constants a and b used i n the "Shape E f f e c t Formula"  23  6  Characteristic  38  7  Summary o f Computer Methods  39  8  Mining Sequence  of the Panel  64  9  Approximate Stope and P i l l a r Dimensions when 77-92 P i l l a r F a i l e d  6?  10  Approximate Stope and P i l l a r Dimension when 77-94 P i l l a r F a i l e d  68  11  Heath S t e e l e P i l l a r A n a l y s i s R e s u l t s  91  12  Summary o f the Geology at Geco  13  Stope 10-19.5 Mining Sequence  14  Stope 10-21 Mining Sequence  15  Stope 10-22 Mining Sequence  16  Stope 10-23.5 Mining Sequence  17  Approximate Stope and P i l l a r Dimensions when 10-21.5 P i l l a r F a i l e d  18  Approximate Stope and P i l l a r 10-23 P i l l a r F a i l e d  19  Approximate Stope and P i l l a r Dimensions when 10-20 P i l l a r F a i l e d  20  Geco P i l l a r A n a l y s i s R e s u l t s  Input Data f o r Computer Methods  -'-00 HO 1  1  0  HI 112  Dimensions when  '  H5 -^6  xi  ACKNOWLEDGEMENTS The author f i r s t Group, who  wishes to thank Noranda Research  Mining  Division  have made t h i s p r o j e c t f e a s i b l e by f i n a n c i n g the r e s e a r c h , pro-  v i d i n g an impressive amount of i n f o r m a t i o n and f o r t h e i r o u t s t a n d i n g cooperation.  The  involvement  of the f o l l o w i n g Noranda mines and  a s s i s t a n c e of t h e i r employees was  also appreciated:  Brunswick Mining and -  Heath S t e e l e Mine  -  Geco D i v i s i o n Goldstream  the  Smelting  Mine.  As w e l l , s p e c i a l acknowledgements to Dr. H.D.S. M i l l e r f o r h i s s u p e r v i s i o n of the r e s e a r c h p r o j e c t , the p e r t i n e n t advice given, and f o r h i s s t i m u l a t i n g approach towards rock mechanics. The author wishes to thank the f o l l o w i n g s c h o l a r s h i p funds f o r financial  support: -  Cy and  Emerald  Keyes  F r e d e r i c k Armand McDiarmid George E. In a d d i t i o n , thanks  Winkler to the members o f the Department of Mining  and  M i n e r a l Process E n g i n e e r i n g f o r t h e i r h e l p f u l a t t i t u d e , to W. M. Cumming f o r p r o o f r e a d i n g , and f i n a l l y t o Jacques and Jeannine tinuous encouragement and  support.  Potvin f o r their  con-  1  CHAPTER  1  Introduction  2  The p r i n c i p a l f u n c t i o n s o f underground mine p i l l a r s openings,  and t o c a r r y the l o a d o f o v e r l y i n g s t r a t a .  t i a l l y o r completely)  are t o s t a b i l i z e  They are o f t e n (par-  recovered a t a l a t e r stage when t h e i r  stabilizing  e f f e c t i s no l o n g e r necessary. For economic reasons, an optimum-sized p i l l a r i s the s m a l l e s t one t h a t s a t i s f i e s s a f e t y requirements. Thus, t h e p i l l a r design problem c o n s i s t s o f determining the p i l l a r ' s minimum dimension  as the l o a d reaches  Because t h e p i l l a r ' s  the u l t i m a t e p i l l a r s t r e n g t h .  s t r e n g t h , and l o a d a c t i n g upon i t are both  t i o n s o f many i n t e r r e l a t e d f a c t o r s , which vary as mining p r o g r e s s e s , dimensioning  is a difficult  Furthermore,  funcpillar  task.  the m u l t i p l i c i t y o f p i l l a r shapes, s i z e s , rock m a t e r i a l  and a p p l i c a t i o n s add t o the d e s i g n e r s ' c o n f u s i o n . Consequently,  p i l l a r design programs are s t i l l  generally a t r i a l - a n d -  error process. In  September 1982, a research p r o j e c t was undertaken,  under the super-  v i s i o n o f Dr. H. D. S. M i l l e r , with the c o l l a b o r a t i o n and f i n a n c i a l o f Noranda Research, design procedure.  Mining D i v i s i o n , t o develop a comprehensive  support  pillar  The p r o j e c t ' s f i r s t y e a r was e n t i r e l y d e d i c a t e d t o a com-  p l e t e review o f the p i l l a r design methods a v a i l a b l e . T h i s i s reproduced  i n appendix A.  Another o f the p r o j e c t design procedures  tasks was to i n v e s t i g a t e the c u r r e n t p i l l a r  and the r o l e o f rock mechanics techniques i n mine p i l l a r  design. To achieve t h i s g o a l , a q u e s t i o n n a i r e was mailed to seven Noranda underground o p e r a t i o n s .  The i n f o r m a t i o n was completed  mines i n New Brunswick, Quebec, O n t a r i o and B r i t i s h  by v i s i t i n g  four  Columbia.  Table 1 shows t h a t a f a i r amount o f rock mechanic s t u d i e s had been com-  3  X  X  X  i n Noranda Underground  PARAMETER STRENGTH INVESTIGATIONS STRESS LABORATORY TEST  Matagami  Mattabi  u  X  X  X  X  Poisson's Ratio  ?  X  X  X  X  In-Situ  X  Measurement  P h o t o - E l a s t i c Model Computer M o d e l l i n g  X  Compress. S t r e n g t h  o°  X  X  X  Tensile Strength  •-4 C O T r i a x i a l Strength  o ID  Shear S t r e n g t h  X  X  X  X  X  X  ^  X  X  X  X  X  X  N G I  X  X  Criterion  X  X  X  X  X  X  C S I R  X  Laubscher  Extensom.  X  X  X  Compression Pad Closure S t a t i o n  X  X  X  L e v e l l i n g Survey S t a t i o n  X  Piezometer  X  X  Multi-Wire  X  Mapping  X  Structural  X  MONITORING  X  X  Boroscope Observ.  5.  X  E l a s t i c Mod  Failure R Q D ROCK MASS CLASSIFICATION  X  U n i t Weight  X  4.  3.  2.  1.  ROCK  Goldstream  Mines  Heath Steele  Brunswick (BM 5 S)  Rock Mechanic S t u d i e s  Geco  1  Mines Gaspe ,  T A B L E  X  X  pleted. to  However, i t must be emphasized t h a t these experiments  are  related  the o p e r a t i o n s ' s i z e and age, as w e l l as the s t a b i l i t y problems encoun-  tered. T a b l e 2 confirms that the mines r e l y mainly upon p r e v i o u s for  experience  design, l e a v i n g the more s o p h i s t i c a t e d methods to mining c o n s u l t a n t s .  •Table  2  P i l l a r and Opening Designing Methods Used by Noranda Underground Mines Experience Methods Group 1 t/1 M CO  Empirical Methods Group 2  OO  in  •fi c c  rt  C  o  M  Analytical Methods Group 3  in  c  •H  t/1  u  rt  c a. o M  c •H  Computer Methods Group 4 in  u  TO  in  M C  c  ID  c  CL,  O  o  Goldstream  M  Mattabi  M  M  Matagarni  M  M  Mines Gaspe  M  M  C  c  Brunswick  M  M  C  c  Heath S t e e l e  M  M  Geco  M  M  Note:  M  M  -  The mine's s t a f f performed  C  -  C o n s u l t a n t performed  the d e s i g n .  the d e s i g n .  In o r d e r to improve the a c t u a l p i l l a r design p r a c t i c e s : a pillar classification design  system i s proposed  t o s t a n d a r d i z e the  procedure  the p r i n c i p a l design methods are summarized and t h e i r i s defined  applicability  a f i v e - p h a s e design procedure with design charts i s developed the procedure i s a p p l i e d i n a n a l y s i n g two  case h i s t o r i e s .  6  CHAPTER 2 The  C l a s s i f i c a t i o n and  Definition  of  Pillars  7 2.1  Pillar The  Classification  l i t e r a t u r e p r o v i d e s no standard d e f i n i t i o n f o r the term, "under-  ground p i l l a r . "  I f one  attempts to e l a b o r a t e a general d e f i n i t i o n , i t  should be borne i n mind t h a t the p i l l a r may be permanent o r temporary, but i n any notion o f s t a b i l i t y Regardless  and  o r may  not be m i n e r a l i z e d ,  may  event r e f e r e n c e must be made to the  security.  o f which mining method i s used, every mine must leave  l a r s to s t a b i l i z e underground s t r u c t u r e s . However, because o f the  pil-  vari-  able ground c o n d i t i o n s , s t r e s s , and the m u l t i p l e p i l l a r a p p l i c a t i o n s r e l a t e d to mining methods and orebody geometry, no two  pillars  are i d e n -  tical . In the documents reviewed, kinds o f p i l l a r s  more than twenty names d e s c r i b i n g v a r i o u s  were encountered.  T h i s wide v a r i e t y o f p i l l a r s  e l a b o r a t i o n o f a standard design procedure  a difficult  The p i l l a r shape, the l o a d a c t i n g on the p i l l a r , the p i l l a r m e t e r i a l are the three most important  makes the  task. and the s t r e n g t h o f  f a c t o r s to be  considered  when d e s i g n i n g a p i l l a r . A simple c l a s s i f i c a t i o n  ( f o r p i l l a r design purposes) i s  regrouping under the same " c a t e g o r y " p i l l a r s submitted  to s i m i l a r l o a d i n g s i t u a t i o n s .  suggested,  of s i m i l a r shape which are  In t h i s manner, every p i l l a r i n  each category can be designed u s i n g i d e n t i c a l equations  and a given metho-  dology . Because the behaviour  o f hard rock d i f f e r s g r e a t l y from t h a t o f s o f t  rock, each category i s broken i n t o two l a r s , and Note:  (b) s o f t rock  sub-categories:  (a) hard rock  pil-  pillars.  The width, h e i g h t and l e n g t h o f the p i l l a r s  w i t h i n a category, but the general shape must be  may  similar.  vary g r e a t l y  8  2.2  Category 1. 2.2.1  "Plate  Pillars"  Description  Figure  1 shows that " P l a t e P i l l a r s " are submitted t o a b i a x i a l h o r i -  zontal stress f i e l d . However, t h i s i s not  The  top and  the bottom o f the p i l l a r s  to s u r f i c i a l  overburden.  of t h i s f a c t when dimensioning a s u r f a c e  T h i s i s due  which r a r e l y r e q u i r e p l a t e  2.2.2  The  designer  should be aware  pillar.  cases of s o f t rock " P l a t e P i l l a r s "  the l i t e r a t u r e .  (Category IB) were found i n  p r i n c i p a l l y to the s o f t rock mining methods  pillars.  Definitions Category 1A:  Hard Rock  - Crown P i l l a r s , Roof P i l l a r s , Horizontal P i l l a r s :  Level P i l l a r s ,  Strike  These are h o r i z o n t a l s l i c e s of v a r y i n g t h i c k n e s s , the excavated area  to p r o v i d e  t h e i r support f u n c t i o n i s no o f t e n used to d e f i n e the den  load  support. longer  shallowest  Pillars,  l e f t above  They are g e n e r a l l y recovered  required.  The  after  term "crown p i l l a r " i s  h o r i z o n t a l p i l l a r c a r r y i n g the  overbur-  (surface p i l l a r ) . - Sill Sill  Pillars:  pillars  s i t u a t e d underneath the  2.3  loaded.  t r u e i n the case of s u r f a c e p i l l a r s , which must bear  the v e r t i c a l load due  No  are not  Category 2. 2.3.1  are very  s i m i l a r to crown p i l l a r s but they are  stopes at each s u b l e v e l .  "Separation  Pillars"  Description  Separation h o r i z o n t a l load.  pillars  (Category 2) are subjected  to a v e r t i c a l  They are open on t h e i r l o n g i t u d i n a l s i d e  and  (Figure 2).  It  9  CATEGORY "plate  category CROWN ROOF  I  (hard rock)  pillar"  cotegory  PILLARS PILLARS  LEVEL  PILLARS  STRIKE  PILLARS  HORIZONTAL SILL  Q.  P.  PILLARS  SURFACE  FIGURE 1  PILLARS  Pillar  Category  1  " Plate  I  Pillars"  I b.  Isoft  rock)  10  CATEGORY 11  category 2 a  separation  (hard  rock  2  pillar category  RIB  PILLARS  BARRIER  DIP  PILLARS  ENTRY  TRANSVERSE ABUTMENT  FIGURE 2  PILLARS PILLARS  P i l l a r Category 2  "Separation P i l l a r s '  2b  PILLARS PILLARS  uoft  rock  should be noted t h a t the hard rock pillars  (Category 2A) and  (Category 2B) do not possess  s o f t rock p i l l a r s  s o f t rock s e p a r a t i o n  i d e n t i c a l c h a r a c t e r i s t i c shapes, s i n c e  are u s u a l l y lower and wider  (Figure 2).  In the case of a v e r y long s e p a r a t i o n p i l l a r dimensions) lem may  the h o r i z o n t a l s t r e s s may  be c o n s i d e r e d to be two  2.3.2  (compared to the other  have a n e g l i g i b l e e f f e c t and the  dimensional.  Definitions Category  2A:  Hard Rock  - Rib P i l l a r s ,  Dip P i l l a r s ,  Transverse  Pillars:  A r i b p i l l a r i s a s e p a r a t i n g w a l l between two the r i b i s u s u a l l y i n the orebody d i p d i r e c t i o n and pillars  t r a n s f e r the v e r t i c a l  They may  The  l e n g t h of  i s continuous.  The r i b  stabilizing  be recovered at a l a t e r  stage  mining. Category  2B:  - Barrier  S o f t Rock  Pillars:  Barrier p i l l a r s  are used t o i s o l a t e c o a l mine p a n e l s .  u s u a l l y permanent p i l l a r s which c o n t r o l r o o f s t a b i l i t y in  stopes.  load from the r o o f to the f l o o r ,  the rock o v e r l y i n g the stoped area. of  prob-  They are  and p l a y a major r o l e  ventilation. - Entry These p i l l a r s  Pillars: r e f e r to the l o n g w a l l mining method.  They p r o v i d e a  p r o t e c t i o n t o the panel e n t r i e s and are recovered d u r i n g the panel's e x p l o i t a t i o n stage.  final  12 2.4  Category 2.4.1 The  lar to  3. "Stub  Pillars"  Description shape o f "stub p i l l a r s "  (Figure 3).  They are open on the f o u r v e r t i c a l  a u n i a x i a l compressive 2.4.2  stress  - Centre These p i l l a r s  s i d e s and are s u b j e c t e d  field.  3A:  Hard Rock  Pillars: have the same f u n c t i o n as r i b p i l l a r s , but are  ated i n the middle of the stopes. c a r r y the r o o f l o a d .  the c e n t r e p i l l a r s  They reduce the span of openings  C o n t r a r y to the r i b p i l l a r s which are  are t r a n s e c t e d by c r o s s - c u t s or  - (Room and The  be square or rectangu-  Definitions Category  to  (Category 3) may  stub p i l l a r s  Pillar] may  Pillars,  Stub  and  help  continuous,  drifts.  Pillars:  r e f e r to a uniform room and p i l l a r panel or  simply be l e f t randomly wherever s t a b i l i z a t i o n  i s needed.  Their length,  width, h e i g h t , shape and composition vary a c c o r d i n g t o the s i t e ments.  situ-  They support the v e r t i c a l  and r e q u i r e -  l o a d o f o v e r l y i n g rock, and may  be perma-  nent or r e c o v e r a b l e . - Post P i l l a r s , These p i l l a r s  Yielding  Pillars:  r e f e r to the "post p i l l a r " mining method.  v i d e temporary support to the immediate r o o f . bottom up, the post p i l l a r s  s t a r t to y i e l d  the bottom, where they are c o n f i n e d by Category - Panel  3B:  As mining progresses from  the  and f i n a l l y c o l l a p s e " g e n t l y " at  backfill.  S o f t Rock  Pillars:  These temporary p i l l a r s panel.  They pro-  are u n i f o r m l y d i s t r i b u t e d w i t h i n a longwall  They support the panel's immediate r o o f and w i l l be removed at a  13  CATEGORY  3  "stub p i l l a r s "  H EIGHT  category CENTER  3a  PILLARS  (ROOM S PILLAR) POST  category  (hard roc k )  PANEL PILLARS  SPLIT  PILLARS  FIGURE 3  P i l l a r Category 3  PILLARS PILLARS  REMNANT CHAIN  "Stub  Pillars"  3 b  PILLARS  PILLARS  (soft  rock'  later  stage. - Split  Pillars:  During longwall split  are the r e s i d u a l p o r t i o n o f s p l i t p i l l a r s .  r e t r e a t s , they e i t h e r c o l l a p s e or are completely - Chain  continuous p i l l a r . pillars  may  This provides  "Inclined  i n s t e a d of a long, massive,  the highest  extraction ratio.  The  Pillars"  Description  Inclined p i l l a r s mitted  small p i l l a r s  but they are  be designed to y i e l d , p e r m i t t i n g the r o o f to deform.  Category 4. 2.5.1  As min-  recovered.  p l a y the same r o l e as b a r r i e r p i l l a r s ,  composed o f a s e r i e s o f a l i g n e d  do not have a p a r t i c u l a r shape or are not  to a p a r t i c u l a r l o a d i n g s i t u a t i o n .  i n t o the three preceding  a t i o n f o r design  sub-  However, because they do  c a t e g o r i e s , and  they T e q u i r e  because of t h e i r i n c l i n a t i o n ,  f o u r t h category o f the p i l l a r c l a s s i f i c a t i o n  2.6  two  Pillars:  These p i l l a r s  fit  are cut i n t o  Pillars:  Remnant p i l l a r s  2.5  the panel p i l l a r s  pillars. - Remnant  ing  p i l l a r recovery,  special  inclined pillars  not  consider-  form  the  (Figure 4 ) .  Discussion The  illustrated  author i s aware t h a t p i l l a r s  i n the forementioned c a t e g o r i e s  with i d e a l i z e d shapes, which i s not  ground p i l l a r s .  In a d d i t i o n , i t should  the case f o r r e a l under-  be r e a l i z e d that the  a p i l l a r i s a f u n c t i o n of s e v e r a l f a c t o r s : - Virgin stress - S t r e s s induced by mining  are  load a c t i n g on  15  CATEGORY inclined  4  pillar  11  I HEIGHT  category  FIGURE 4  4a  (hard  rock)  P i l l a r Category -  "Inclined  category  Pillars"  4b  (soft  rock)  - Geological - Pillar  features  shape and  - Openings and  orientation  general  mine s t r u c t u r e s  - Ground water. However, i t i s b e l i e v e d that every p i l l a r may above f o u r c a t e g o r i e s , l o a d i n g mechanism and  i n t o one  of  the  even though the c l a s s i f i c a t i o n o v e r s i m p l i f i e s the the p i l l a r geometry.  F i n a l l y , because s h a f t p i l l a r s other p i l l a r s ,  fall  they are not  included  are fundamentally d i f f e r e n t from  in this classification.  Nevertheless,  the f o l l o w i n g d e f i n i t i o n i s proposed: Shaft  Pillars:  These are permanent p i l l a r s system. pillars  The  s h a f t and  the  s h a f t p i l l a r may  become l a r g e r with i n c r e a s e d  Because the  shaft i s a v i t a l  are designed with a high  p r o v i d i n g p r o t e c t i o n to the mine s h a f t be v e r t i c a l or i n c l i n e d .  depth, and  t h e i r shapes are v a r i a b l e .  component i n underground mines, these  and  pillars  safety factor.  Table 3 summarizes the p i l l a r c l a s s i f i c a t i o n . ogy  Shaft  design  methodol-  dimensioning formulas a p p l i c a b l e to each category w i l l be  developed  i n the f o l l o w i n g  chapters.  Most o f the p r e v i o u s Mines A s s o c i a t e s "  The  p i l l a r d e f i n i t i o n s were taken from "Roche  (1984)^ as w e l l as F i g u r e s  5,  Appendix C, which i l l u s t r a t e the d i f f e r e n t kinds  6, and  7 reproduced i n  of p i l l a r .  TABLE 3 PILLAR CLASSIFICATION SUMMARY Category 1 Plate P i l l a r s A Hard Rock  B Soft Rock  Category 2 Separation P i l l a r s  Category 3 Stub P i l l a r s  Category 4 Inclined P i l l a r s  A Hard Rock  B Soft Rock  A Hard Rock  B S o f t Rock  A Hard Rock  B S o f t Rock  Crown  Rib  Barrier  Centre  Panel  Inclined  Inclined  Roof  Dip  Entry  Stub  Split  Level  Transverse  "Pillar"  Remnant  Strike  (R+P)  Abutment  Horizontal  Chain  Post  Sill Surface  /  4 ^  •  —-* t  1  /  +  / t  III  CHAPTER 3 Review of P i l l a r Design Methods  19 3.1  Introduction The p r i n c i p l e f o r d e s i g n i n g any underground s t r u c t u r e i s strength stress Thus, a p i l l a r w i l l  long term load b e a r i n g pillar's  simple:  ^  >  remain s t a b l e i f the load a p p l i e d i s l e s s than i t s  capability.  Difficulties  a r i s e i n estimating  the  u l t i m a t e s t r e n g t h as w e l l as the p r e c i s e load a c t i n g upon i t .  Pillar  strength:  Because of the rock m a t e r i a l ' s complexity t i o n o f rock mass s t r e n g t h i s p e r p l e x i n g .  and  variability,  the  evalua-  Furthermore, the t r u e s t r e n g t h  a p i l l a r can o n l y be c a l c u l a t e d a f t e r c o n s i d e r i n g the s t r e n g t h o f the m a t e r i a l together  p r o b a b i l i t y o f i n c l u d i n g a weakness zone  i n the - The  pillar  deformation and  pillar  triaxial  s t r e n g t h of  the  material  - The  geometry of the  - The  p i l l a r as p a r t o f the general  A l s o , environmental f a c t o r s may pillar  pillar  with:  - The  pillar rock  structure.  cause a time dependent a l t e r a t i o n of the  strength.  Pillar  load:  As mentioned i n Chapter 2, the load a c t i n g on a p i l l a r of: - The  v i r g i n stress  - The  s t r e s s induced  - Geological - Pillar  by mining  features  shape and  - Openings and - Ground water.  orientations  general mine s t r u c t u r e  of  i s a function  20 Hence, the s t r e s s l e v e l induced i n p i l l a r s  ( p i l l a r l o a d ) , changes as mining  progresses. Although s e v e r a l techniques can be used t o measure i n s i t u  stress,  these a r e expensive, and the r e s u l t s a r e not always r e l i a b l e . Because t h e r e are so many f a c t o r s i n v o l v e d i n the complex mechanism o f p i l l a r l o a d i n g (and deformation) as w e l l as p i l l a r  s t r e n g t h , the d e s i g n e r  must depend upon numerous methods t o account f o r these  factors.  The f o l l o w i n g summarizes the most important d e s i g n i n g methods. are d i v i d e d  i n t o f o u r groups,  They  according to t h e i r l e v e l o f s o p h i s t i c a t i o n .  Group 1 - Experience Methods Group 2 - E m p i r i c a l Methods Group 3 - T h e o r e t i c a l Methods Group 4 - Computer Methods. It should be noted that every method, i f used c o r r e c t l y , i s capable o f producing adequately s i z e d p i l l a r s with r e s p e c t t o s a f e t y .  3.2  Group 1.  Experience Methods  T h i s i s by f a r the most widely used and the l e a s t s o p h i s t i c a t e d method. Based on o b s e r v a t i o n s , h i s t o r y , and on the d e s i g n e r ' s " f e e l i n g " f o r the rock, i t a l s o r e l a t e s to s i m i l a r work completed situations.  A c o n s e r v a t i v e dimensioning  i n corresponding geological is first  may have t o be made a c c o r d i n g t o the requirements signed  l a i d out and m o d i f i c a t i o n s and performance  o f the de-  structure.  No s p e c i f i c  experience method i s proposed,  but i t i s s t r o n g l y  recommended  that d e t a i l e d a c t i v e f i l e s be kept on i n f o r m a t i o n concerning the mine ity:  failures,  s l a b b i n g , squeezing, c a v i n g , convergence,  et c e t e r a .  stabil-  This w i l l empirical  3.3  improve the f u t u r e experience  design and may lead to an  approach.  Group 2.  E m p i r i c a l Methods  An e m p i r i c a l method i s the q u a n t i f i c a t i o n o f experience formulas or curves.  into designing  Because most o f these methods do not take i n t o account  many important f a c t o r s , one should be aware o f the c o n d i t i o n s i n which they were developed. While the m a j o r i t y o f e m p i r i c a l p i l l a r design methods  considers  s t r e n g t h and s t r e s s s e p a r a t e l y , some do i n c o r p o r a t e s t r e n g t h and s t r e s s i n t o a dimensioning  formula.  The f o l l o w i n g i s a review o f the most important e m p i r i c a l methods. b r i e f d e s c r i p t i o n , the formula(s)  and the parameters are given.  ( r e f e r r i n g to Chapter 2's p i l l a r c l a s s i f i c a t i o n ) , the p i l l a r  As w e l l  categories  which can be designed by each method a r e i n d i c a t e d .  3.3.1  E m p i r i c a l Strength  Formulas.  E m p i r i c a l p i l l a r s t r e n g t h formulas e s s e n t i a l l y i n v o l v e e x t r a p o l a t i n g the r e s u l t s o f l a b o r a t o r y t e s t s on rock  specimens, t o f u l l - s i z e mine  pillars. A)  S i z e E f f e c t Formula  a  p  = a  where:  (Appendix A.  S e c t i o n 3.1)  [A + B(£)]  c  Op  =  Pillar  o  =  U n i a x i a l compressive s t r e n g t h o f a cube o f p i l l a r m a t e r i a l  W  =  Pillar  width  h  =  Pillar  height  A, B  =  Constants given i n u n i t s o f p i l l a r s t r e n g t h (Table 4 ) .  c  strength (psi)  A  Description: Rocks have a n a t u r a l s t r e n g t h a n i s o t r o p y which i s predominantly due t the  presence o f d i s c o n t i n u i t i e s  ( i . e . j o i n t s , c l e a t s , b l a s t f r a c t u r e s , et  c e t e r a ) but can a l s o be a t t r i b u t e d to v a r i a t i o n s i n rock f a b r i c ( i . e . f o l i a t i o n , bedding p l a n e s , et c e t e r a ) and mineralogy.  As rock samples o f  constant shape i n c r e a s e i n s i z e , the s t r e n g t h o f the specimen decreases. T a b l e 4 g i v e s the c o n s t a n t s proposed by d i f f e r e n t authors t o model t h i s be haviour.  TABLE 4 CONSTANTS A AND B USED IN THE "SIZE EFFECT FORMULA"  SOURCE Bunting  FORMULA  (1911)  + 0,.222  Obert et a l (1960)  0,.778  Bieniawski  0,.556 + 0,.444  (1968)  Van Heerden (1973)  0..704  Sorensen 5 P a r i s e a u (1978)  0..693 + 0..307  - Applicable to p i l l a r  B)  0..700 + 0..300  categories:  Shape E f f e c t Formula  where:  + 0,.296  W/H w h w h w h w h w h  3.  Stub  4.  Inclined  0,.5  - 1 .0  0,.5  - 2..0  1 .0  - 3,.1  1 .14 - 3 .4 0 .5  - 2,.0  Pillars Pillars.  (Appendix A, S e c t i o n 3.2)  Op  =  P i l l a T strength (psi)  K  =  Constant r e l a t e d t o the p i l l a r  W  =  Pillar  h  =  P i l l a r height  a, b  =  Dimensionless c o n s t a n t s  width  material  23  Description: The shape e f f e c t denotes a d i f f e r e n c e i n the u n i t strength o f d i f f e r e n t shape but equal c r o s s - s e c t i o n . one apparent cause o f shape e f f e c t . of a l i m i t e d number o f f r a c t u r e s .  A change i n mode o f f a i l u r e i s  Slender p i l l a r s tend t o f a i l by means For wide p i l l a r s the p r o b a b i l i t y o f  d e v e l o p i n g a s i n g l e continuous f r a c t u r e plane i s l e s s . p i l l a r r e s u l t s from c r u s h i n g pillar  strength.  core a l s o c o n t r i b u t e s  Thus, f a i l u r e o f the  of the p i l l a r m a t e r i a l , thereby  The t r i a x i a l  for pillars  increasing  s t a t e o f s t r e s s i n a squat p i l l a r ' s  t o an i n c r e a s e  i n p i l l a r strength.  inner  Table 5 gives the  c o n s t a n t s a and b proposed by d i f f e r e n t authors to model t h i s behaviour. TABLE 5 CONSTANTS a AND b USED IN THE "SHAPE EFFECT FORMULA" SOURCE Streat  FORMULA  (1954)  Holland-Gaddy  (1962)  kh"  1  . o o  kh'  1  .oo o.  w  a  o . 5  w  b  0,.5  1. 00  5  0,.5  1. 00  Greenwald et a l (1939)  kh-°  . 6 3  5  0,.5  0.833  Hedley 6 Grant  kh-°  .75 0- S  0,.5  0.75  Salamon § Munro (1967)  kh"  .66 0. » S  0..46  0.66  Bieniawski  kh-° • w ° -  16  0..16  0.,55  (1972)  (1968)  0  w  0 .  w  w  5 5  M o r r i s o n et a l  kh"°  .5  w  0 . 5  0..5  0.5  Zern (1926)  kh"°  .5  w  0 . 5  0..5  0.,5  Hazen d, A r t i e r (1976)  kh"°  •5  w  0 . 5  0,.5  0..5  Holland  kh  .5  w  0 . 5  0..5  0..5  (1956)  - Applicable  - 0  to p i l l a r categories:  3.  Stub  Pillars  4.  Inclined  Pillars  C)  Salamon " M o d i f i e d " Shape E f f e c t Formula  o  p  =  K —£• , h  where:  where We  (Appendix A, S e c t i o n 3.3.4)  = /W .W a  2  Op  =  Pillar  K  =  Constant r e l a t e d t o the p i l l a r compressive s t r e n g t h  Wi,W  =  C r o s s - s e c t i o n s i d e s o f the p i l l a r s  We  =  The e q u i v a l e n t pillar  h  =  Pillar  a,b  =  Dimensionless  2  strength ( p s i ) material  width f o r a r e c t a n g u l a r  height constants  Description: 2 The  r e s u l t s o f underground t e s t s (Wagner, 1974)  shown that p i l l a r s square p i l l a r s  on c o a l p i l l a r s  have  o f r e c t a n g u l a r c r o s s - s e c t i o n s a r e about 40% stronger  o f the same width and h e i g h t .  the s t r e n g t h o f r e c t a n g u l a r p i l l a r s  A reasonably  can be obtained  than  good estimate o f  by s u b s t i t u t i n g the  square r o o t o f the c r o s s - s e c t i o n a l area o f the p i l l a r f o r W, i n t h e shape effect  formula.  - Applicable to p i l l a r categories:  D)  3.  Stub  4.  Inclined  Sheorey and Singh " M o d i f i e d " Shape E f f e c t Formula  °P whe r e :  •  Pillars Pillars  (Appendix A, S e c t i o n 3.3.4)  .b h Op  =  Pillar  K  =  Constant r e l a t e d t o the a x i a l compressive s t r e n g t h o f the p i l l a r m a t e r i a l  =  C r o s s - s e c t i o n s i d e s o f the p i l l a r  =  Pillar  Wi,W  2  h  strength (psi)  height  a,b  =  Dimensionless constants  (Table 5)  Description: This method as the Salamon m o d i f i e d e q u i v a l e n t width.  formula uses the concept o f an  However, Sheorey and Singh recommend u s i n g the average  value o f the r e c t a n g u l a r c r o s s - s e c t i o n s i d e s as e q u i v a l e n t - A p p l i c a b l e to p i l l a r c a t e g o r i e s :  E)  3.  Stub  4.  Inclined P i l l a r s  Heek and Brown Curves (Appendix A, S e c t i o n  Ci  =  a  + v ma a /  3  c  3  o  3.3.7)  stress at f a i l u r e  = Minor p r i n c i p a l s t r e s s at f a i l u r e  3  o"  c  = The u n i a x i a l compressive strength o f i n t a c t rock m a t e r i a l  m and s a r e constants  which depend upon the p r o p e r t i e s o f  the rock and upon the extent f o r e being  Pillars  + sa£  0\ = Major p r i n c i p a l  where:  width.  subjected  t o which i t has been broken be-  t o the s t r e s s e s o*i and a . 3  Description: 3 The  Hoek and Brown  the o v e r a l l  curves were developed based on the assumption that  strength o f a p i l l a r  s t r e n g t h across  i s approximately equal  the c e n t r e o f the p i l l a r .  t o the average  Figure 8 shows the r e s u l t s o f a  s e r i e s o f c a l c u l a t i o n s u s i n g s t r e s s d i s t r i b u t i o n from computer together  with Hoek's f a i l u r e c r i t e r i o n .  f i n e d , one may determine the p i l l a r  modelling,  Once the rock mass q u a l i t y i s de-  strength f o r d i f f e r e n t p i l l a r  - Applicable to p i l l a r categories:  2.  Separation  3.  Stub P i l l a r s  4.  Incl-ined P i l l a r s .  dimensions.  Pillars  26  -p  3.0r  so  E (D U +»  I n t a c t samples o f f i n e g r a i n e d igneous c r y s t a l l i n e rock m=l? , s = l  W  > -H W W <D  U  e o o  Very good q u a l i t y rock mass m=8.5  x  , s=0.1  rt 3 +> bD P  Good q u a l i t y rock mass m=1.7 , s=0.004  w  F a i r q u a l i t y rock mass m=0.34 , s=0.0001  ft  Poor q u a l i t y rock mass m=0.09 , s=0.00001  rt >  Pillar  FIGURE 8  width/height  ;  W^/h  I n f l u e n c e o f P i l l a r Width t o Height r a t i o on Average P i l l a r  Strength.  A f t e r Hoek and Brown  (1980)^  27  3.3.2 A)  E m p i r i c a l S t r e s s Formulas  The E x t r a c t i o n Ratio Formula o r T r i b u t a r y Area  _  °p -  (Appendix A, S e c t i o n 1.3.4)  TH (W+BHL+B)  inn—  where:  a  =  Pillar  Y  =  U n i t weight o f the rock  H  =  Depth below s u r f a c e  B  =  Width o f the opening  L  =  Pillar  length  W  =  Pillar  width.  p  load  Description: I f a l a r g e area i s mined out with a reasonably pillars,  uniform p a t t e r n o f  i t can be s a i d t h a t n e a r l y the whole weight o f the overburden  be c a r r i e d by the p i l l a r s  i n equal p r o p o r t i o n s .  (1980)^ g i v e s the e x t r a c t i o n r a t i o formula  F i g u r e 9, Hoek and Brown  f o r d i f f e r e n t p i l l a r shapes.  should be noted t h a t the t r i b u t a r y area theory r e p r e s e n t s the average p i l l a r  stress.  (Overestimates  will  It  the upper l i m i t o f  the load on p i l l a r s  by about 4 0 % ) .  4 Bieniawski ing  (1983) .  The t r i b u t a r y area does not take i n t o account the a r c h -  e f f e c t , o r any other mechanical behaviour o f the o v e r l y i n g s t r a t a . - Applicable to p i l l a r categories:  B)  Chain P i l l a r Formula  U  = -1  P  where:  Separation  3.  Stub  (Appendix A, S e c t i o n Swilski  a  2.  2  yH  v  (1983)  1.3.8)  5  vh  ' (Lp+S)(Wp+2W +3S) p  Op  =  Pillar  load ( p s i )  Y  =  Unit weight o f the rock  Pillars  Pillars.  RIB  PILLARS  crp- = / M l +  FIGURE 9  SQUARE PILLARS W o  /w  }  Average V e r t i c a l P i l l a r Layouts. After  crp =y z { l +  w  Vw )  Stresses i n Typical  I l l u s t r a t i o n s are a l l p l a n views.  Hoek and Brown (1980)-  3  p  Pillar  29  H  =  w = p  L  P "  S  =  w = F  Depth below s u r f a c e P i l l a r width Pillar  length  Spacing  between chain  Width o f the f a c e .  Z  y  IL T -J-s  COAL  I P  RIBSIDE  pillars  I a r e a  o f  strata load  - J  i  \  '  \  COAL FACE  COAL PANEL w Ch§in p i l l d t s  FIGURE 10.  ¥  Tail  Entry  Determination o f Load on Chain P i l l a r s by the " f i r s t p a n e l " Load Concept. A f t e r S z w i l s k i (1983)  5  Description: The it  c h a i n p i l l a r formula  i s based on the e x t r a c t i o n r a t i o formula but  c o n s i d e r s the e x t r a load a c t i n g on the c h a i n p i l l a r s by the c a n t i l e v e r  a c t i o n o f the immediate r o o f .  However, t h i s s i m p l i f i e d procedure  ignores  the e f f e c t o f the gob support, gob  t o the nearest -  C)  solid  creating a pressure  coal panel.  A p p l i c a b l e t o p i l l a r category:  Subsidence Formula  arch from the compacted  3B  -  (Appendix A, S e c t i o n 10.3)  Chain  Pillars.  Whittaker and Singh (1981) 6  0  p  imrp  =  For W/D and  a  = 9.81 y  p  (  p  +  w  )  •  D  •  1  /  4  w  2  +  c  o  t  *  -  p  < 2 t a n <f>  For W/D where:  2  PfP.D +  Dtancf0 2  > 2 t a n <f>  o"p  =  Pillar  load (psi)  Y  =  Average d e n s i t y o f the overburden  <j>  =  Angle o f shear o f r o o f s t r a t a at edge o f longw a l l e x t r a c t i o n and measured t o v e r t i c a l  P  =  Width o f b a r r i e r  W  =  Width o f longwall e x t r a c t i o n  D  =  Depth below s u r f a c e .  pillar  Description: The to  subsidence theory has been a p p l i e d t o the b a r r i e r p i l l a r  a s c e r t a i n the extent  of s t r a t a pressure  t r a c t i o n t o produce l o a d i n g o f the adjacent  situation  a r c h i n g a c r o s s a longwall exbarrier  pillars.  B a s i c a l l y , t h i s approach assumes that the goaf area behind  the longwall  i s loaded by a t r i a n g u l a r roof mass which shears at an angle 4> t o the vertical.  The l o a d i n g developed by the mass o f r o o f s t r a t a o u t s i d e the  t r i a n g u l a r r e g i o n i s presumed t o be t r a n s f e r r e d t o the b a r r i e r -  A p p l i c a b l e t o p i l l a r category:  2B - B a r r i e r  pillars.  Pillars  3.3.3  E m p i r i c a l Dimensioning  Formulas.  Other e m p i r i c a l formulas do not c o n s i d e r s t r e s s and s t r e n g t h P i l l a r dimensioning formulas are o f t e n used to d e s i g n c o a l b a r r i e r  A)  Mines' I n s p e c t o r Formula  W  =  (Appendix A, S e c t i o n 10.2)  20 + 4T +  where:  separately pillars.  A s h l e y (1930)  3  0.1D  W  =  Width o f p i l l a r  (feet)  T  =  Bed Thickness  (feet)  D  =  Thickness o f the overburden  (feet)  Description: The Ashley formula was developed from experiments i n the P e n n s y l v a n i a coal f i e l d s .  It i s based on the c o n s e r v a t i v e assumption that an a r c h o f  height equal to h a l f the panel width w i l l t i o n s based on the above assumption r e s u l t  stabilize.  Simple hand c a l c u l a -  in pillar  s i z e s with width to  height r a t i o s of approximately three t o f i v e depending upon depth,  pillar  height and panel width. - A p p l i c a b l e to p i l l a r  B)  H o l l a n d Formula  D  category:  (Appendix A, S e c t i o n  =  1ST  or  =  2B  -  Barrier  Pillars  10.2)  ±%L™JL  K log e where:  D  =  Width o f B a r r i e r P i l l a r  (feet)  T  =  Thickness o f p i l l a r  W2  =  The estimated convergence on the h i g h s t r e s s s i d e o f the p i l l a r (mm). (W may be estimated with F i g . 11)  (feet)  2  K  =  Constant = 0.09 i f c a v i n g f o l l o w i n g mining i s permitted = 0.08 i f s t r i p packs are b u i l t = 0.07 i f h y d r a u l i c stowage i s c a r r i e d out.  32 Description: The H o l l a n d f o r m u l a i s based on t h e convergence s t u d i e s by B e l i n s k i and B o r e c k i (1964) . Compared w i t h A s h l e y ' s f o r m u l a , i t g i v e s a more r e a l i s t i c p i l l a r w i d t h and c o n s i d e r s p i l l a r t h i c k n e s s , a s w e l l a s o t h e r p e r t i n e n t f a c t o r s . H o l l a n d ' s f o r m u l a , however, i s i n c o m p l e t e i n t h a t i t d i s r e g a r d s t h e p r o p e r t i e s o f the p i l l a r r o c k . Consequently,  t h i s method s h o u l d be a p p l i e d  o n l y i n c o n d i t i o n s s i m i l a r t o those i n which H o l l a n d  experimented.  (Figure l l )  HS: H y d r a u l i c Stowage  1000 700 5 00 400 300  C : Caved SP: S t r i p Packed  0  PJ?s Room & P i l l a r  200  L : Longwall  100 60  40 30 20 0 0  400 800 1200 1600 2000 T h i c k n e s s o f Overburden ( F t . )  FIGURE 11  Observed Value o f W  2  2400  2800  f o r C o a l seams  7 f t . T h i c k and Having a C r u s h i n g S t r e n g t h i n the 3 i n . Cube o f 3000 p s i . + 10%  - Applicable to p i l l a r  category:  2b - B a r r i e r  Pillars.  33 C)  Morrison,  C o r l e t t and W  =  Rice.  j D  where:  (Appendix A, S e c t i o n  10.2)  f o r D < 4000 f e e t  W  =  Width of p i l l a r  (feet)  D  =  Depth below s u r f a c e  (feet)  Description: The  two  previous  formulas were developed s p e c i f i c a l l y f o r c o a l .  Morrison,  C o r l e t t and  o f rock.  Nonetheless, i t o v e r s i m p l i f i e s the problem and  Rice formula g i v e s s a t i s f a c t o r y r e s u l t s i n most kinds  a guide or p r e l i m i n a r y e s t i m a t i o n  2a)  -  b)  D)  Not  a p p l i c a b l e to Rib E n t r y and  B a r r i e r P i l l a r Formula W  =  I  i  where:  D  +  should  be used  as  only.  - A p p l i c a b l e to p i l l a r c a t e g o r i e s :  Note  The  (Appendix A,  Dip  Section  Abutment Barrier  Pillars Pillars  Pillars.  10.2)  15  W  =  Width of p i l l a r  (feet)  D  =  Depth below s u r f a c e  (feet)  Description: T h i s formula i s c i t e d  i n the l i t e r a t u r e as a t r a d i t i o n a l r u l e of thumb  approach to d e s i g n i n g b a r r i e r p i l l a r s . should -  be used as a rough e s t i m a t i o n  Again i t i s o v e r s i m p l i f i e d and  only.  A p p l i c a b l e to p i l l a r category:  2B  - Barrier  Pillars  34 3.4  Group 3.  T h e o r e t i c a l Methods  The t h e o r e t i c a l methods attempt  to evaluate mathematically  f a c t o r s a f f e c t i n g the s t r e s s and s t r e n g t h o f p i l l a r s . i s then proposed.  the p r i n c i p a l  A more r e a l i s t i c  However, the behaviours of p i l l a r s  are very  model  complicated  and t o be c o n s i s t e n t with the theory, the methods need a f a i r number o f i n put parameters.  C o l l e c t i n g data i n a mining  e a r l y stage o f a mine's l i f e ) are too expensive  environment  ( e s p e c i a l l y at the  i s not an easy t a s k , and o f t e n the techniques  or not adequately advanced to p r o v i d e a c c u r a t e data.  Because the t h e o r e t i c a l methods are complex and d i f f i c u l t s u l t s are o f t e n not r e l i a b l e .  They are u s e f u l  to apply, the r e -  i n f u r t h e r comprehending the  mechanism i n v o l v e d i n p i l l a r d e s i g n . 3.4.1  T h e o r e t i c a l S t r e n g t h Formulas  At l e a s t f o u r t h e o r e t i c a l methods have been reviewed  i n the  literature  research: Appendix A  It was  - Coates  ( S e c t i o n 3.3.3)  - Grobbelaar  ( S e c t i o n 3.5.1)  - Wilson  ( S e c t i o n 3.5.2)  - Panek  ( S e c t i o n 3.5.3)  noted t h a t o n l y Wilson's method has been used by designers, and  a b r i e f d e s c r i p t i o n of t h i s method i s g i v e n below. A)  Confined Core Method Y h  "  (Wilson)  1 (tan B ) - = (tan B - l ) u  y =  where:  u  i _  '  n  c^ a. o J  The depth o f y i e l d zone from r i b s i d e (feet)  the  h  =  Seam h e i g h t  (feet)  Ov  =  The maximum p i l l a r s t r e s s ( p s i ) ( s i t u a t e d at the y i e l d zone/confined core i n t e r f a c e )  Oo  =  Unconfined  compressive  strength (psi)  •Tan 3 =  Triaxial  stress coefficient  1 + s i n (j) 1 - sin $ <}) i s .the a n g l e o f i n t e r n a l f r i c t i o n o f t h e c o a l .  Description: T h i s concept r e c o g n i z e s around t h e p e r i p h e r y  t h a t a " y i e l d " o r " f r a c t u r e " zone d e v e l o p s  o f a p i l l a r which c o n f i n e s  a central elastic  Because o f t h i s confinement t h e i n n e r core i s s u b j e c t e d  core.  to t r i a x i a l  stress  conditions. The  limit  o f t h e average c o r e s t r e s s i s reasoned t o be equal t o t h e  p i l l a r peak abutment s t r e s s , which i s l o c a t e d a t t h e y i e l d core i n t e r f a c e .  Based on t h i s assumption, p i l l a r  strengths  zone/confined can be c a l -  culated .  - Applicable  3.4.2  to p i l l a r category:  Theoretical  Stress  2B.  Barrier  Pillars  Formula  F i v e t h e o r e t i c a l methods t o e v a l u a t e t h e s t r e s s a c t i n g on a p i l l a r have been reviewed  i n the l i t e r a t u r e  research. Appendix A  The  - Beam and P l a t e Theory  ( S e c t i o n 1.3.5)  - Wall d e f l e c t i o n t h e o r y  (Section  - Photoelastic  ( S e c t i o n 1.3.7)  data  1.3.6)  - Pariseau  (Section  9.2)  - Hedley  (Section  9.3)  w a l l d e f l e c t i o n formula and t h e p h o t o e l a s t i c t e c h n i q u e were r e l a -  t i v e l y p o p u l a r i n t h e p a s t but they a r e no longer w i l l not be r e v i e w e d . A l t h o u g h they p l a y e d  w i d e l y used.  an i m p o r t a n t r o l e i n t h e e a r l y  development o f r o c k mechanics, they can now be r e p l a c e d techniques.  Thus t h e y  by more e f f i c i e n t  A)  Beam and  P l a t e Theory Method  Description: A number o f equations were d e r i v e d Some o f them may the  Pariseau  beam theory. describe  A complete understanding o f the  theory  i m p l i c a t i o n s of the input parameters are e s s e n t i a l .  - Applicable  B)  engineering  be used to design p i l l a r s i f they r e a l i s t i c a l l y  i n s i t u underground s i t u a t i o n .  as w e l l as the  from C i v i l  to p i l l a r c a t e g o r i e s :  Inclined P i l l a r Y  S  h  Plate  Pillars  2.  Separation  Pillars  Formulas  * Kp)+  ( 1  1.  (1 - Kg)  P  cos  2*  1-R  y  Cl-Ko) s i n  h  2cQ  1 - R where:  Sp  =  Average p i l l a r s t r e s s i n the normal d i r e c t i o n  tp  =  Average p i l l a r shear s t r e s s  Y  =  Unit weight o f the  h  =  Depth below  KQ  =  Ratio of h o r i z o n t a l over v e r t i c a l v i r g i n  R  =  Extraction  «  =  I n c l i n a t i o n of the seam  rock  surface stress  ratio  Description: Pariseau ratio  proposed an extension  o f the a p p l i c a b i l i t y o f the  extraction  (or t r i b u t a r y area) formula to i n c l i n e d seams of a r b i t r a r y d i p .  shear f o r c e s caused by the seam's i n c l i n a t i o n i s accounted f o r . -  Applicable  to p i l l a r category:  4.  Inclined  Pillars  The  3? C)  Hedley's M o d i f i e d  Formula f o r I n c l i n e d yh c o s ^ + OH  sin *  2  P  Pillars  2  1 - R  where:  Average p i l l a r direction  aP  s t r e s s i n the  Y  Unit weight o f the  h  Depth below  R  Extraction ratio Horizontal  rock  surface  v i r g i n stress  I n c l i n a t i o n o f the  CC  normal  orebody  Description: The  pre-mining s t r e s s f i e l d and  factors affecting p i l l a r the  stress.  normal s t r e s s a c t i n g on the  vertical  s t r e s s and  horizontal  e x t r a c t i o n r a t i o are the two  For  i n c l i n e d workings Hedley stated  3.5  Group 4. The  stress.  T h i s combination i s used i n the  to p i l l a r c a t e g o r y :  4.  Inclined  A l s o , the use  of d i g i t a l  from the mathematical p o i n t  stress. Pillars  may  be adapted to every p i l l a r  computers i n underground mine design i s ,  of view, the most p r e c i s e method.  However, the accuracy of the r e s u l t s i s r e l a t e d d i r e c t l y to the of the  input  ex-  Computer Methods  computer methods are v e r s a t i l e and  category.  that  seam i s a combination of the components o f  t r a c t i o n r a t i o formula to determine the average p i l l a r - Applicable  principal  data. Table  6 gives  quality  the c h a r a c t e r i s t i c input d a t a r e q u i r e d  by  computer models. Numerous computer programs are used by rock mechanic s p e c i a l i s t s . methods are  summarized i n Table 7 and  are d i v i d e d  - i n t e g r a l methods  i n t o two  groups:  The  - d e r i v a t i v e methods At present, very few Canadian mines have t h e i r own computer models. Mine d e s i g n e r s  g e n e r a l l y p r e f e r to r e l y on c o n s u l t a n t s ' e x p e r t i s e f o r the  s o p h i s t i c a t e d methods. More i n f o r m a t i o n on "BITEM", the boundary element gram used i n t h i s study  i s a v a i l a b l e i n APPENDIX D . TABLE 6  CHARACTERISTIC INPUT DATA FOR COMPUTER METHODS  1.  2.  Rock(s) Strength  Parameters:  - U n i a x i a l compressive s t r e n g t h  (a )  - Unit weight  (y)  c  Virgin Stress: V e r t i c a l Stress  (a ) v (a„)  Horizontal stress  n  3.  General  Mine Geology  4.  General  S t r u c t u r e and Geometry o f the Mine  5.  Rock Deformation A.  B.  Elastic:  Plastic  Indices - E l a s t i c Modulus  (E)  - Poisson's  (v)  - Creep Constants - Viscosity  6.  Ratio  constants  Others - m and s Indices - Friction  angle.  (Hoek c r i t e r i a )  39 TABLE 7 SUMMARY OF COMPUTER METHODS  I n t e g r a l Methods - Boundary elements  - 2 dimensional - 3 dimensional  - Displacement  discontinuities  - 2 dimensional - 3 dimensional  D e r i v a t i v e Methods - F i n i t e elements  '  - 2 dimensional - 3 dimensional  - Finite difference  - 2 dimensional - 3 dimensional  Hybrid Methods - Mixed Boundary and F i n i t e elements been developed  Programs have  recently.  F i n a l l y , a summary i s given below o f the p r i n c i p a l reviewed  i n this  d e s i g n methods  chapter.  F u r t h e r i n f o r m a t i o n on these methods, formulas and curves a r e a v a i l a b l e i n the l i t e r a t u r e review, Appendix A.  GROUP 1.  EXPERIENCE METHODS  GROUP 2.  EMPIRICAL METHODS  STRENGTH  PILLAR CATEGORY  a)  Size  (3,4)  a)  Extraction r a t i o ( t r i b u t a r y area)  (2,3)  a)  Ashley  (2b)  b)  Shape E f f e c t  (3,4)  b)  Chain  (3b)  b)  Holland  (2b)  c)  Salamon Modified  c)  Subsidence  (2b)  c)  (3b,4)  Morrison, C o r l e t t , Rice  (Abutment Pillar)  d)  Sheorey,  d)  Barrier  (2b)  e)  Hoek curves  Effect  STRESS  PILLAR CATEGORY  Pillar  Singh (3b,4) (2,3,4)  GROUP 3. STRENGTH a)  Wilson  *  PILLAR CATEGORY (2b)  THEORETICAL METHODS STRESS  PILLAR CATEGORY  a) Beam Theory  (1,2)  Grobbelaar  b) Pariseau  (4)  *  Coates  c) Hedley  (4)  *  Panek  * Photoelastic analysis * Wall d e f l e c t i o n GROUP 4.  *  DIMENSIONING  Are no longer widely used.  COMPUTER METHODS  (Coates)  Pillar  PILLAR CATEGORY  CHAPTER 4 PILLAR DESIGN PROCEDURE  42 4.1  Philosophy o f P i l l a r  Design  Hoek and Brown (1980)  have d e s c r i b e d the p h i l o s o p h y of underground  3  s t r u c t u r e d e s i g n as f o l l o w s : "The basic the rock  aim of any  i t s e l f as the principal  l i t t l e disturbance ing  as  as possible  l i t t l e as possible  The extent gical  to which  conditions  awareness  and  cannot  this  during  design  aim  on site  should  material,  he to u t i l i z e  creating  the excavation  process  or steel  as and add-  support.  can be met depends upon the  and  of these  the extent  of the  designer's  must consider  and one  in which  even those  all  elements  effi-  An optimum s i z e d p i l l a r might be d e f i n e d as the s m a l l e s t one  s a t i s f i e s safety  4.2  which  "  A good p i l l a r d e s i g n i s one p r o p e r l y s i z e d f o r both s a f e t y and ciency.  Design  geolo-  conditions.  is one of balance  Designers  be quantified.  design  structural  design  consideration  interact.  structure  in the way of concrete  existing  "A good engineering factors  underground  that  requirements.  Procedure  Many p i l l a r d e s i g n methods, formulas and curves have been reviewed i n Chapter t h r e e , but none o f these i s completely  independent.  In the f o l l o w i n g f i v e phase d e s i g n procedure, the designer uses  several  methods which become more s o p h i s t i c a t e d as experience w i t h the rock m a t e r i a l is for  gained.  A l s o , d e s i g n c h a r t s are i n c l u d e d to help s e l e c t  s u i t a b l e methods  each type o f p i l l a r . 4.2.1  Phase 1.  Experience  Design.  I n i t i a l l y a f a i r amount o f u n c e r t a i n t y e x i s t s concerning the mechanical behaviour o f rock on a l a r g e s c a l e , and on the l o c a t i o n , a t t i t u d e , and prop e r t i e s o f f a u l t s or j o i n t s .  Hence, at t h i s stage, o n l y a c o n s e r v a t i v e p r e l i m i n a r y design i s p o s s i b l e , u s i n g the d e s i g n e r ' s experience and the study o f s i m i l a r  case  histories. A l s o d u r i n g t h i s phase, the c o l l e c t i o n o f rock mechanics data should be undertaken  to prepare f o r the f o l l o w i n g phases of d e s i g n , which employ  more s o p h i s t i c a t e d methods. 4.2.2 The  Phase 2.  P i l l a r Structural Analysis  second phase o b j e c t i v e i s t o determine  whether p l a n e ( s ) of weakness  ( f a u l t s or major d i s c o n t i n u i t i e s ) c o n t r o l the p i l l a r ' s discontinuities affect to s l i d i n g  the p i l l a r  (shear f a i l u r e ) . 1.  stability.  s t r e n g t h because they reduce  T h i s can occur i n two  These  the r e s i s t a n c e  ways:  By a s i n g l e plane and movement that takes p l a c e along the plane  2.  (Figure 12)  By i n t e r s e c t i n g planes  The movement may  (Figure 13).  be i n the d i r e c t i o n of the t r e n d and plunge  of t h e i r  i n t e r s e c t i o n s , or along one o f the s i n g l e p l a n e s . 4.2.2.1  P i l l a r Transection V e r i f i c a t i o n  For v e r y simple c a s e s , a s c a l e drawing may whether the p i l l a r  f a i l u r e may  be s u f f i c i e n t to  be s t r u c t u r a l l y c o n t r o l l e d .  determine  However, f o r  more complicated s i t u a t i o n s a s t e r o g r a p h i c method w i l l be r e q u i r e d .  Com-  prehensive i n s t r u c t i o n s f o r u s i n g the s t e r e o g r a p h i c technique i s reproduced g  i n Appendix VI of the l i t e r a t u r e review, J . A. T o u s s e u i l . Because the plane must i n t e r s e c t both s i d e s of the p i l l a r and be  con-  tinuous over i t s e n t i r e l e n g t h , p i l l a r s having a h i g h width to height r a t i o are not l i k e l y to f a i l  by  sliding.  FIGURE 12  P i l l a r Transected of Weakness.  by a S i n g l e Plane  After Touseull  9  45 4.2.2.2  Shear S t a b i l i t y A n a l y s i s  I f t r a n s e c t i o n o c c u r r e d , Hoek and Brown (1980)  3  suggest  e v a l u a t i n g the  shear s t a b i l i t y along a f a u l t or major d i s c o n t i n u i t y u s i n g the f o l l o w i n g technique: - estimate these parameters on s e v e r a l p o i n t s along t h e f a u l t d  : major p r i n c i p a l  stress  03  : minor p r i n c i p a l  stress  6  : angle between the f a u l t  and O j  Assume t h a t Shear S t r e s s :  T = 1/2  (o"i - a ) s i n 2B  Normal S t r e s s : a - 1/2 and  (1)  3  (Ci+a ) - ( a i - a ) 3  3  the shear s t r e n g t h TS o f the f a u l t  cos 2B  (2)  i s d e f i n e d by:  xs = c + a Tan <> j  (3)  where: c i s the cohesion <> j i s the angle o f f r i c t i o n o i s the normal  stress  - Equation 3 i n Equation 2 TS = c + l / 2 ( ( a i + o )  - ( O i - a ) cos 2 6 ) t a n c f >  3  3  - Then, a f a c t o r o f s a f e t y ( T S / ) can be c a l c u l a t e d along the f a u l t t  and  g i v e s an i n d i c a t i o n o f the p o t e n t i a l f o r s l i p on the f a u l t .  T h i s a n a l y s i s should be used to ensure  i n c o n j u n c t i o n with a s t r u c t u r a l  t h a t wedges which a r e f r e e to f a l l  analysis  o r s l i d e are not formed by the  f a u l t and other f a u l t s or j o i n t s .  4.2.3 The  Phase 3. E m p i r i c a l Design  rock mechanics data c o l l e c t i o n program should now be adequately ad-  vanced t o p r o v i d e the input parameters r e q u i r e d by the e m p i r i c a l methods, which may be s e l e c t e d u s i n g the c h a r t s (Figures 14, 15, 16, 17).  46 I f none o f the e m p i r i c a l formulas reviewed l a r s i t u a t i o n , the d e s i g n e r may adapted ing  attempt  are a p p l i c a b l e to a p a r t i c u -  to develop h i s own  curves or  to h i s c o n d i t i o n s by monitoring, many o b s e r v a t i o n s and good  formulas, engineer-  judgement.  4.2.4  Phase 4.  Theoretical  Design  The r e a l aim of t h e o r e t i c a l design methods i s to a i d i n understanding the complexity o f the problem and to p r o v i d e a mathematical behaviours.  model f o r rock  However, because i t r e q u i r e s advanced mathematics as well as a  c o n s i d e r a b l e amount o f input data, o n l y a few t h e o r e t i c a l methods have been adapted  to mine d e s i g n .  In any case, i t i s a v a l u a b l e e x e r c i s e to " p l a y " with a t h e o r e t i c a l method at t h i s stage o f d e s i g n .  4.2.5  Phase 5.  Computer Design  During t h i s phase the p i l l a r dimensions model w i l l  be "adapted"  w i l l be o p t i m i z e d .  to the mine's p i l l a r s .  First,  A computer  i t should be used  to  analyze case h i s t o r i e s i n order to g a i n confidence i n the model and to i n v e s t i g a t e the rock mass behaviour. F i n a l l y , c a r e f u l underground o b s e r v a t i o n s , m o n i t o r i n g and measurements should p r o v i d e feedback  4.3  Design  on each computer d e s i g n .  Charts  The c h a r t s ( F i g u r e s 14 to 17) procedure. ation,  A c h a r t r e p r e s e n t i n g each p i l l a r category  (3) Stub,  formulas  summarize the p r e c e d i n g f i v e phase design ((1) P l a t e ,  (2)  (4) I n c l i n e d ) i n d i c a t e s the methods, r e l a t i o n s h i p s  that should be used  i n the f i v e phase  procedure.  Separ-  and  PILLAR  FIGURE lk  CATEGORY I  "plate pillars" category l a . (hord  rock)  PHASE I  PHASE 2  EXPERIENCE  STRUCTURAL  PHASE 3  PHASE 4  PHASE 5  SURFACE PILLAR CROWN PILLAR LEVEL  PILLAR  STRIKE PILLAR HORIZONTAL P. ROOF PILLAR SILL  PILLAR  METHOD  ANALYSIS  EMPIRICAL METHOD  no melhods\ ovoiloble /  THEORETICAL METHOD beam theory  COMPUTER METHOD  PILLAR  FIGURE 13  CATEGORY 2  "separation category 2a ( hard  RIB OIP  rock)  PILLAR PILLAR  PHASE I  PHASE 2  EXPERIENCE  STRUCTURAL  METHOD  ANALYSIS  PHASE 3 EMPIRICAL  METHOD Hoek's curves  TRANSVERSE ABUTMENT-  pillars" PHASE 4 THEORETICAL  METHOD beam  PHASE 5 COMPUTER METHOD  theory  tributary area  EXPERIENCE  Morrison,c.,R.  METHOD  category 2 b (soft  rock)  E X P E R I E N C E  BARRIER ENTRY  P. PILLAR  METHOD  STRUCTURAL ANALYSIS  EMPIRICAL METHOD  ME  THOD  Hoek's c u r v e s  beom  tributary  Wilson  oreo  subsidence Ashley Holland bar rier p i l l a r  IM  T H EO R E T I C Al  theory  C O M P U T E R ME  THOD  PILLAR  FIGURE 1^  CATEGORY  "stub category 3a (hard  rock )  CENTER  PILLAF  PHASE E X P E R I E N C E M E T H O D  pillar"  PHASE 2  PHASE 3  S T R U C T U R A L  E M P I R I C A L M  A N A L Y S I S  ROOM & PILLAR  E  T  H  O  D  tribulory Hoek's  PILLAR  size  areo  PHASE 4  T I  T H E O R E T I C A L M  E  (no  T  H  O  PHASE 5 C  O  D  M  P  U  T  M  E  T  H  E O  M  P  U  T  E  M  E  T  H  O  R O  methods)  curves  shape  POST  3  effect effect  category 3b (soft  rock)  •quare  plllpr  E M P I R I C A L M  E  T  H  O  D  tributary  PANEL  PILLAR  Hoek's E X P E R I E N C E M  SPLIT  E  T  H  O  D  shape  S T R U C T U R A L  T H E O R E T I C A L  effect  size  A N A L Y S I S  area curves  effect  M  PILLAR  (no i  P.  reclangular  pillar  I |  CHAIN  PILLAR  >  I  M  E  T  H  O  tributary  H  O  area  1  Hoek's  curves  j  modified  '  S h e o r e y ft S i n g h  pillar  D  methods)  D  Salomon  chain  T  >  E M P I R I C A L  REMNANT  E  '  ->-  C  O  R D  FIGURE  PILLAR  1?  CATEGORY  inclined category 4 P H A S E  PHASE  pillar  2  squore  4  II  PHASE 3  pillar  PHASE  4  PHASE 5  EMPIRICAL METHOD  INCLINED  P.  EXPERIENCE  STRUCTURAL  METHOD  ANALYSIS  —J J  I  Hoek's curves shape effect size effect  pil)ar  COMPUTE R  METHOD  METHOD  Panseau  Hedley  EMPIRICAL rectongular  THEORETICAL  METHOD Hoek's curves Salomon modified Sheorey 8 S i n g h  I  CHAPTER 5 HEATH STEELE CASE HISTORY ANALYSES  INTRODUCTION During the summer o f 1984,  f o u r Noranda underground  seeking p i l l a r f a i l u r e case h i s t o r i e s . the Bray  e a r l y 60's, was (1967) . 1 0  s e l e c t e d because  mines were v i s i t e d  The Geco "B-Block", mined out i n  the f a i l u r e s were w e l l documented by  The 77-92 and 77-94 r i b p i l l a r f a i l u r e s at Heath  were a l s o chosen to take advantage  o f A l l c o t and A r c h i b a l d  Steele  (1981)  11  pillar  d e s i g n study. The examination of case h i s t o r i e s may information f o r future designs. ter  generate p e r t i n e n t and  Geco (Chapter 6) and Heath  5) case h i s t o r i e s are analyzed u s i n g the f o l l o w i n g procedure: Review of General Information  1.  Steele  Geology 1.1  Regional geology  1.2  Mine geology  1.3  Structural  geology  2.  Mining method and underground  3.  Rock Mechanics  structures  dimensions.  Data  3.1  Rock s t r e n g t h  parameters  3.2  Laboratory t e s t s  3.3  Rock Mass C l a s s i f i c a t i o n  3.4  Virgin  stress  Review o f P i l l a r Information 4.  Pillar  Characteristics  5.  Mining  sequence  6.  Failure  h i s t o r y and p i l l a r  geometry  useful (Chap-  53 P i l l a r Design 7 .1  Phase 1  Experience method  7 .2  Phase 2  P i l l a r structural  7 .3  Phase 3  E m p i r i c a l methods  7 .4  Phase 4  T h e o r e t i c a l methods  7 .5  Phase 5  Computer methods  5.1  Study  analysis  Geology ( A f t e r A l l c o t t and A r c h i b a l d ( 1 9 8 1 ) ) 11  5.1.1  Regional  Geology  The massive s u l p h i d e s t r a t i f o r m d e p o s i t s of n o r t h e r n New hosted by the Tetagouche rock group.  Brunswick are  T h i s rock group i s h i g h l y f o l d e d ,  middle O r d o v i c i a n i n age and covers a c i r c u l a r area approximately  56  km.  (35 m i l e s ) i n diameter. The Tetagouche rock group i s broken i n t o three l i t h o l o g i c a l Sedimentary, Metabasalt, and  5.1.2  units:  Rhyolitic.  Mine Geology  The massive s u l p h i d e d e p o s i t s l i e w i t h i n the r h y o l i t e u n i t i n c l o s e p r o x i m i t y to the quartz f e l d s p a r c r y s t a l t u f f , which i s a l s o known as Augen S c h i s t and The  Porphyry.  s t r a t i g r a p h i c rock u n i t s i n the ore zone area top towards the  n o r t h , which i s i n d i c a t e d by the metal bedding  i n the sediments.  as f o l l o w s : 1.  zoning i n the s u l p h i d e s and  These u n i t s l i s t e d from youngest  graded  to o l d e s t are  ( F i g u r e 18)  Banded Quartz  Feldspar C r y s t a l Tuff  T h i s rock u n i t i s banded i n p l a c e s with 5-10  cm.  bands,  interlaid  with v a r y i n g g r a i n s i z e and p r o p o r t i o n s o f quartz and f e l d s p a r phenocrysts.  7800 LEVEL  5. A c i d T u f f 6. Sediments  FIGURE 18  Heath S t e e l e Geology  Banded Quartz  Crystal Tuff  The  quartz c r y s t a l t u f f occurs as a 9 to 15 m.  bed  on the hanging w a l l s i d e o f the massive s u l p h i d e s .  phyry  The por-  i s q u i t e competent and f r e s h i n appearance, with a com-  p r e s s i v e s t r e n g t h o f 56.5 MPa (8200 p s i ) .  However, the f r a c t u r i n g  tends t o be b l o c k y when exposed on the stope's  Iron  (30-50 f t . ) t h i c k  wall.  Formation  T h i s zone i s present as a d i s c o n t i n u o u s t h i n band along the upper margin o f the massive s u l p h i d e f o r m a t i o n . i n small patches zone.  along the f o o t w a l l c o n t a c t and w i t h i n the s u l p h i d e  T h i s i s a competent bed, but i s too t h i n and d i s c o n t i n u o u s  to be r e l i e d upon as a s t a b i l i z i n g  Massive  However, i t a l s o occurs  unit.  Sulphides  The massive s u l p h i d e s a r e v e r y f i n e g r a i n e d , with a  compressive  s t r e n g t h o f 177 MPa (22,917 p s i ) , and form the most competent u n i t i n the mine.  Very l i t t l e  rock  sloughing occurs where the w a l l s o f  the stopes c o n s i s t o f massive s u l p h i d e s .  Acid Tuff T h i s i s the l e a s t competent rock u n i t  i n the mine, and tends to be  s o f t and sloughs r e a d i l y when exposed on the w a l l s o f stopes.  It  forms a 1.5 t o 21 m. (5-70 f t . ) t h i c k bed on the f o o t w a l l o f the s u l p h i d e s and becomes d i s c o n t i n u o u s i n p l a c e s .  C l a s t i c Sedimentary Rocks The  sedimentary  rocks i n the f o o t w a l l below the a c i d t u f f are i n t e r -  c a l a t e d with quartz f e l d s p a r c r y s t a l t u f f s and form a band a p p r o x i mately 366 m. (1200 f t . ) t h i c k .  56 5.1.3  S t r u c t u r a l Geology  The B Zone i s a t a b u l a r shaped v e r t i c a l or steep n o r t h e r l y d i p p i n g massive s u l p h i d e body, which s t r i k e s a t N 73°E. a s t r i k e l e n g t h o f a p p r o x i m a t e l y 1150 m. from a few c e n t i m e t e r s depth o f 1097 m.  to 75 meters  The massive s u l p h i d e s  have  (3,800 f t . ) , v a r y i n t h i c k n e s s  (250 f t . ) and have been t r a c e d to a  (3,600 f t . ) .  F o l d i n g i s the primary s t r u c t u r a l c o n t r o l and although there  i s minor  f a u l t i n g , f a u l t s have had no major i n f l u e n c e on the shape o f displacement o f the ore zone.  The orebody  has undergone  f i v e p e r i o d s o f f o l d i n g which a r e  numbered one to f i v e i n time sequence as they o c c u r r e d .  (Figure  19)  FIGURE 19. .Diagramatical P l a n View o f Heath S t e e l e Orebody, Si:  Showing O r i e n t a t i o n o f F o l d i n g  The f i r s t p e r i o d o f f o l d i n g l e f t the massive s u l p h i d e . f o l d i n g i s a few f l a t  very l i t t l e  i f any imprint  on  The o n l y r e a l evidence f o r t h i s p e r i o d o f lying relict  cleavage planes  i n the host  rocks. S2:  The second p e r i o d o f f o l d i n g had the g r e a t e s t e f f e c t on the shape of the orebody.  T h i s p e r i o d has shaped the orebody i n t o a number  o f shaped i s o c l i n a l f o l d s which plunge at approximately 60° i n a S 73° W d i r e c t i o n .  S3:  The t h i r d p e r i o d o f deformation produced f o l d s which plunged  s t e e p l y northwest  open or t i g h t c o n c e n t r i c  or southeast.  This folding-  leads to some d i l u t i o n problems i n mining as the f o l d s are d i f f i c u l t to d e f i n e with the normal f i f t e e n meters (SO f t . ) spaced d e f i n i t i o n diamond S4:  drilling.  The f o u r t h p e r i o d o f deformation r e s u l t e d i n a s e r i e s of open, conc e n t r i c f o l d s , which plunged t o the northwest  and appeared  as not  more than g e n t l e warps. Sj:  The f i f t h p e r i o d of f o l d i n g produced in a northeasterly direction.  open f o l d s which plunged  T h i s p e r i o d o f deformation  70°  produced  o n l y r a r e f o l d s i n the mine a r e a . - JOINTING  Golder A s s o c i a t e s  There are two major j o i n t s t e e p l y d i p p i n g , with one  (1981)  1 2  s e t s evident throughout  h o r i z o n t a l j o i n t s appeared  d i r e c t i o n and  Both are  set approximately p a r a l l e l t o the s t r i k e o f the  orebody and one approximately t r a n s v e r s e to the s t r i k e .  The j o i n t  the mine.  set p a r a l l e l  to be more prominent  A t h i r d set o f near  i n the s u l p h i d e s .  to the s t r i k e i n d i c a t e d a spread i n s t r i k e  i s p r o b a b l y a combination  o f two  joint  sets.  J o i n t s are u s u a l l y p l a n a r or s l i g h t l y u n d u l a t i n g and spaced at about 1 B . to 3 a .  5.2  (3.3 - 9.8  ft.).  Mining Method and Underground S t r u c t u r e s Dimension A f t e r A l l c o t t and A r c h i b a l d  (1981)  11  Mining o f Heath S t e e l e B Zone orebody proceeded s t o p i n g method, with l a t e r s e l e c t e d area f i l l i n g . from the upper l e v e l s t o the lower maintained  on two  with b l a s t hole open  E x t r a c t i o n progressed  l e v e l s and east t o west with p r o d u c t i o n  to three l e v e l s s i m u l t a n e o u s l y .  The p r o d u c t i o n r a t e  was  3000 tons per day from 1970 to 1976, i n c r e a s e d to 3,500 tons per day i n 1977,  and f i n a l l y reached 4,200 tons per day i n 1982. Mining  of 8600 p r o d u c t i o n  completed without  level,  110 m.  (360 f t . ) below s u r f a c e , was  any s e r i o u s s t a b i l i t y problems and a d i l u t i o n f a c t o r o f  10% was adequate compensation f o r overbreak or minor f a l l s o f waste. centimeters  (2 inches) diameter b l a s t h o l e r i n g s were used, and underground  ore haulage was by Track equipment. 30 m.  (40 f t . ) r i b p i l l a r s were l e f t  low  Stope dimensions were g e n e r a l l y about  (100 f t . ) on s t r i k e and up t o 45 m.  Mining  (150 f t . ) h i g h .  to separate  advanced to the 8300 p r o d u c t i o n  s u r f a c e , u s i n g the same method.  l e v e l , a t 200 m.  the 10% d i l u t i o n was s t i l l  sloughing  (650 f t . ) be-  Stope height was i n c r e a s e d to 60 m. introduced.  Although i t had been easy to mine adjacent stopes with an i n t e r v e n i n g 15 m.  Twelve meters  the stopes.  (200 f t . ) and t r a c k l e s s load-haul-dump was  and  Five  f o o t w a l l and hanging w a l l  (50 f t . ) p i l l a r of low grade s u l p h i d e s  s a t i s f a c t o r y , at t h i s stage  s t a r t e d from the west s i d e o f 83-78 r i b p i l l a r .  small s c a l e The cause was  a s c r i b e d to the i n t e r s e c t i o n o f j o i n t s at the face o f the p i l l a r , but not to  loading. Mining  from s u r f a c e .  s t a r t e d on 8050 p r o d u c t i o n  I t was decided  to remove s i l l  level,  p i l l a r s under 8300 l e v e l so  t h a t the new stope h e i g h t s would be i n c r e a s e d t o 140 m. time the s t r i k e l e n g t h was 45 m.  275 m (900 f t . )  (450 f t . ) .  At t h i s  (150 f t . ) and the r i b p i l l a r s were 15 m.  (50 f t . ) wide. Real  s t a b i l i t y problems occurred when r e c o v e r i n g r i b p i l l a r s between  primary stopes.  In the f i r s t  b l a s t e d caused the adjacent back extending  over a 150 m.  i n s t a n c e a r i b p i l l a r t h a t was  instantaneously  r i b p i l l a r to b u r s t and i n i t i a t e d a cave i n the (500 f t . ) s t r i k e l e n g t h .  After this,  stope  lengths were l i m i t e d to 43 m. rib pillar  (140 f t . ) , and 85 m.  l e n g t h s were i n c r e a s e d to 18 m.  (280 f t . ) h e i g h t .  The  (60 f t . )  Ground problems were encountered with i n c r e a s i n g frequency as the depth from s u r f a c e  increased.  The l a s t procedure u t i l i z e d b a c k f i l l i n g the c r i t i c a l  area and removing  r i b p i l l a r s o n l y between f i l l e d stopes. At  l e v e l 7430 the stope dimensions were presumed to be 30 m.  l o n g , 60 m.  5.3  (200 f t . ) h i g h and separated by 30 m.  Rock Mechanics 5.3.1  (100 f t . )  (100 f t . ) r i b p i l l a r s .  Data  Rock S t r e n g t h Parameters - Density  Ore:  Waste:  y  = 4581  k g / 3 (286  |p-)  y = 2883 k g / 3 ( 1 7 9  i|f)  m  m  - E l a s t i c Modulus F-W C h l o r i t e T u f f  E = 68,536 MPa  (9.9 M. p s i )  Ore Massive Sulphide E =119,284 MPa  (17.3M. p s i )  H-W  (9.9 M. p s i )  Q t z . Porphyry  E = 68,743 MPa  - Poisson's Ratio v =  0.25  Ore Massive S u l p h i d e v =  0.24  v =  0.19  F-W C h l o r i t e T u f f  H-W  5.3.2  Q t z . Porphyry  Laboratory T e s t i n g - Unconfined Compressive S t r e n g t h F-W C h l o r i t e T u f f  o  c  =  Ore Massive Sulphide H-W  Qtz. Porphyry  o  84 MPa 176.5 MPa  c  =  91 MPa  (12,182 p s i ) (25,598 p s i ) (13,198 p s i )  60  5.3.3  Rock Mass C l a s s i f i c a t i o n  The f o o t w a l l , hanging wall and orebody rocks were c l a s s i f i e d by  Golder  12 A s s o c i a t e s (1981)  u s i n g the NGI  system.  R e s u l t s are given below as well  as an estimated CSIR r a t i n g f o r comparison purposes. 77-92 Cross-.Cut Footwall - C h l o r i t e T u f f NGI RQD Jn Jr Ja Jw SRF Q  95 3 2 0..75 1..0 1..0  90 6 2 0..75 1..0 1..0  84  40  CSIR I n t a c t Strength RQD Spacing o f J o i n t s Condition of Joints Ground Water  7 20 25 6 1_0 68  77-92 Cross-Cut  Sulphides NGI  RQD Jn Jr Ja Jw SRF  85 6 1 0.75 1.0 1.0  95 6 1 0.75 1.0 1.0  Q  18.9  21 CSIR  Intact Strength RQD Spacing J o i n t s C o n d i t i o n of J o i n t s Ground Water  12 17 25 6 7 67  61  I  77-92  Gross-Gut H a n g i n g w a l l P o r p h y r y NGI RQD Jn Jr Ja Jw SRF  95 6  95 3.0 1.0  2.0 0.75 1.0 1.0  0.75 1.0 1.0  42  42 GSIR 7  Intact Strength RQD Spacing o f J o i n t s Condition o f J o i n t s Ground Water  5.3«4  Virgin  20  25 6 10  w  Stress  No v i r g i n s t r e s s measurements have been made a t t h e mine.  Measurements  have been a c h i e v e d a t Brunswick M i n i n g , which i s located, i n t h e same r o c k f o r m a t i o n about  50  km  depth a r e a s f o l l o w s :  ( 3 0 miles)  away. The r e s u l t s a t  7 0 0 m. ( 2 3 0 0  ft.)  (Figure 2 0 )  - To determine t h e v i r g i n s t r e s s a t Heath S t e e l e , t h e f o l l o w i n g assumpt i o n has t o be made: "The r a t i o o f s t r e s s e s ( v e r t i c a l and h o r i z o n t a l s ) a t Brunswick i s comp a r a b l e w i t h the r a t i o o f s t r e s s e s a t Heath Thus, the s t r e s s regime o  vv  = a, = v ^ waste 1  = o  Note:  3  2883  = 8.79  KPSF = k i l o  Steele".  3 0 0 m. ( 1 0 0 0 f t . )  x  (depth below r  kg/m x 10  5  3  below s u r f a c e a t Heath  surface)  x 305 m = 8.79 x 1 0 kg/m  2  = 8.62 MP a  pounds p e r square f o o t  5  kg/m  2  (180 KPSF)*  Steele  62  FIGURE 20  V i r g i n S t r e s s at Heath S t e e l e  63  °H  (north-south)  ° '  =  a'i = °H  (east-west)  0 2  0  5.4  Pillar  2  =  2  17.24 MPa 1-Sxa  =  =  ° '  x  8  12.93 MPa  =  2 x 8.62 MPa (360 KPSF)  = 1 . 5 x 8 . 6 2 MPa (272 KPSF)  Characteristics  - Ribs: O r i g i n a l l y 12 m.  (40 f t . ) x 61 m. (200 f t . ) h i g h x ore width  Laterally  (90 f t . ) x 76 m.  27 m.  (250 f t . ) h i g h x ore width  - Sills/Crowns: P r o d u c t i o n l e v e l up c o n t a i n s cones o r trough u s u a l l y extending up  15 meters  (50 f t . ) above l e v e l .  Below l e v e l u s u a l l y 15 t o  23 meters (50 to 75 f e e t ) depending on ore widths and l o c a l geometry. - Pillar  Support: G e n e r a l l y no systematic support  i s given.  areas some c a b l e b o l t i n g has been used.  In s p e c i f i c problem In some small  pillars  i n the room and p i l l a r o v e r c u t s , some perimeter s t r a p p i n g has been done i n i s o l a t e d problem areas. of  ( 5 or 8 f t . ) 1.5 t o 2.5 m.  use mechanical  The  E a r l y p r a c t i c e was to  b o l t s and s t r a p s o r p l a t e s .  anchored r e b a r p i n s a r e almost  Mining  support  development w i t h i n p i l l a r areas has been the use o f standard  rock b o l t s  5.5  Otherwise l o c a l  Latterly  resin  e x c l u s i v e l y used.  Sequence  i n v e s t i g a t e d area c o n s i s t s o f f o u r open stopes  77-89) separated by three r i b p i l l a r s from 245 m. (800 f t . ) t o 366 m.  (77-95, 77-93, 77-91,  (77-94, 77-92, 77-90).  The depth v a r i e s  (1200 f t . ) below s u r f a c e , and a 300 m.  (1000  f t . ) depth was assumed f o r c a l c u l a t i o n  purposes.  F i g u r e 21 i s a l o n g i t u d i n a l view o f the s t o p e / p i l l a r panel l a y o u t , and Table 8 summarizes the mining  sequence (from B l a s t i n g  Record).  TABLE 8 MINING SEQUENCE OF THE PANEL STOPE  5.6  START DATE  FINISH DATE  77-95  May, 1977  Nov. 1978  77-93  Dec. 1976  May, 1978  77-91  Apr. 1976  Apr. 1978  77-89  May, 1975  Dec. 1977  77-92 ( P i l l a r Recovery)  Apr. 1978  Apr. 1978  F a i l u r e H i s t o r y and P i l l a r Geometry - November 1977:  77-92 Rib P i l l a r  It was d i s c o v e r e d t h a t t h e r e was e x c e s s i v e wedge type sloughing from the w a l l s o f t h i s p i l l a r  i n t o the stopes on each s i d e t o the extent  that i t was c o n s i d e r e d not t o be p r o v i d i n g  any support.  Accordingly, i t  was decided t o b l a s t out t h i s p i l l a r and t o stop f u r t h e r mining west i n 77-93 stope to i n c r e a s e the 77-94 p i l l a r . - A p r i l 1978:  The 77-92 r i b was b l a s t e d , and r e c o v e r e d .  - September, 1978:  77-94 Rib P i l l a r  A f t e r the 77-92 r i b was b l a s t e d , mining continued i n 77-95 stope. On September 23/78, a b l a s t i n 77-95 stope appeared  t o have t r i g g e r e d a  v i o l e n t r e a c t i o n i n 77-94 r i b c a u s i n g s e i s m i c i t y and b u c k l i n g o f t r a c k rails  i n t h i s p i l l a r on both 7950 and 7800 l e v e l s . - J u l y 1980:  77-96 Rib P i l l a r ,  (supplementary  A c t i v i t y i n t h i s r i b on 7700 l e v e l developed  information) i n J u l y 1980 and was  65  FIGURE 21  Schematic Longitudinal View of the Investigated Area at Heath Steele. (Mining method: Blast hole Open stoping)  Scale: 1 i n . = 100 f t .  8200  66  - 77-9^ P i l l a r deteriorates  77-92  Pillar  recovered  w <u  ft  o -p CO  »A ON I <S-  c ON I  o-  H ON I  ON  00  £>o  -p  u d x: o  o  c o  •H o  rtJ  -p  CM CM  3 O I—I  77-92  Pillar  failed  6?  associated  with the b l a s t i n g o f 74-97 stope.  From the F i g u r e 22 E x t r a c t i o n Flowchart the stope and p i l l a r and dimensions  geometries  were estimated: a)  when the 77-92 r i b p i l l a r f a i l e d (Figure 23, Table 9)  b)  when the 77-94 p i l l a r c o l l a p s e d i n September 1978 (Figure 24, Table 10).  The d e s i g n study w i l l  i n November 1977  c o n c e n t r a t e on these two p a r t i c u l a r cases, and  because the major p r i n c i p a l s t r e s s i s h o r i z o n t a l i n the N-S a x i s d i r e c t i o n , o n l y the p l a n view needs t o be c o n s i d e r e d .  TABLE 9 APPROXIMATE  STOPE + PILLAR DIMENSIONS WHEN 77-92 PILLAR FAILED (NOVEMBER, 1977)  Length  Width  Height  Stopes 77-89  43m.  (140 f t )  15m.  (50 f t )  110m.  (360 f t )  77-91  30m.  (100 f t )  40m.  (130 f t )  120m.  (395 f t )  77-93  27m.  ( 90 f t )  40m.  (130 f t )  120m.  (395 f t )  77-95  18m.  ( 60 f t )  40m.  (130 f t )  90m.  (300 f t )  77-90  15m.  ( 50 f t )  15m.  ( 50 f t )  117m.  (385 f t )  77-92  27m.  ( 90 f t )  40m.  (130 f t )  122m.  (400 f t )  77-94  30m.  (100 f t )  40m.  (130 f t )  107m.  (350 f t )  Pillars  68 TABLE 10 APPROXIMATE STOPE AND PILLAR DIMENSIONS WHEN 77-94 PILLAR FAILED (SEPTEMBER, 1978)  Length  Width  77-89  43m.. (140 f t )  15m.. ( 50 f t )  137m.  (450 f t ) caved  77-91) ) 77-93)  98m.. (320 f t )  40m.. (130 f t )  168m.  (550 f t )  77-95  43m.  (140 f t )  40m.. (130 f t )  90m.  (300 f t )  15m.  ( 50 f t )  15m., ( 50 f t )  122m.  (400 f t )  122m.  (400 f t )  Height  Stopes  Pillars 77-90  PAT i c n r t\ x  77-92 77-94  5.7  18m.  . (130 f t ) 40m.  P i l l a r Design A n a l y s i s Every p i l l a r  fied  ( 60 f t )  i n v o l v e d i n the Heath S t e e l e case h i s t o r y may be  as " s e p a r a t i o n p i l l a r s "  (Category  2 o f the p i l l a r  A c c o r d i n g to the d e s i g n c h a r t s o f Chapter ing  classi-  classification).  t h r e e , the f o l l o w i n g design-  methods should be used. 5.7.1  Phase 1.  Experience  Design  From the d e s c r i p t i o n o f the mining method ( S e c t i o n 5.2), the most r e cent p r a c t i c e a t Heath S t e e l e was b a c k f i l l i n g the c r i t i c a l area and r e c o v e r ing  r i b pillars  be 30m. rib  o n l y between primary  (100 f t ) long, 60m.  pillars.  filled  stopes, which were estimated t o  (200 f t ) h i g h and separated by 30m.  (100 f t )  FIGURE 2 3  Estimated Layout When 7 7 - 9 2 Rib P i l l a r  Failed  FIGURE 24  E s t i m a t e d Layout When  77-94  Rib P i l l a r  Failed  71 5.7.2  Phase 2.  P i l l a r Structural Analysis A f t e r A l l c o t t and  The  Archibald  p i l l a r s c o n s i s t of massive s u l p h i d e s  s t r e n g t h o f 176.5  MPa  (1981)  11  which have a compressive  (25598 p s i ) , the s t r o n g e s t  u n i t i n the g e o l o g i c a l  sequence. The  most important f a c t o r a f f e c t i n g the  f r a c t u r e systems, more s p e c i f i c a l l y S The N-S  S  3  3  and  s t r e n g t h o f the p i l l a r s i s the S. 5  f r a c t u r e s s t r i k e at N 30°W, which i s approximately 15° to  a x i s o f the r i b p i l l a r s and  a c t i n g on the p i l l a r s  (Figure  the d i r e c t i o n o f the compressive  w a l l and  (60 f t ) have the S  w a l l and  f t ) (Tables  voke s l i d i n g The  3  Ss  cases,  9 and  i n the  the p i l l a r lengths  10).  east-  (200  f t ) and  an  How-  east-west  f r a c t u r e s supported on both the hanging  f o o t w a l l over a s t r i k e length o f only  In the present (130  the S  f t ) and  (33 f t ) (Figure 26).  ever, a p i l l a r with a n o r t h - s o u t h a x i s of 60 m. (60 f t ) has  (100  f r a c t u r e s supported on both hanging  3  f o o t w a l l over a s t r i k e l e n g t h of 10m  a x i s of 18m.  forces  25).  Note that p i l l a r s with a north-south a x i s of 30m. west a x i s o f 18m  the  Thus, the S  3  2m. (N-S  (7 f t ) (Figure  27).  a x i s ) never exceed  f r a c t u r e s alone should  not  40m. pro-  pillars.  (N 40°E) f r a c t u r e s s t r i k e at about 60°  o f the r i b p i l l a r s and  to the north-south a x i s  d i p s t e e p l y to the northwest.  are much l e s s w e l l developed than the S5  f r a c t u r e s and  (Figure 28).  They  are at a f l a t t e r  angle to the d i r e c t i o n of the compressive f o r c e s . The  i n t e r s e c t i o n of the  S  3  and  S  5  f r a c t u r e s near the s i d e s of the r i b  p i l l a r s sometimes r e s u l t i n s p a l l i n g and (Figure  29).  d e t e r i o r a t i o n of the  pillars.  P I L L A R  P L A N  V I E W  COMPRESSIVE  FORCES  1  COMPRESSI VE FIGURE 2 5 .  S  F r a c t u r e System  FORCES  PILLAR PLAN VIEW  H A N G I N G  i  A/  W A L L  S T O P E  60'-  |*  *|  F O O T W A L L  FIGURE 2 6  The E f f e c t o f S  3  F r a c t u r e s on 3 0 m. ( 1 0 0 f t . )  Wide R i b P i l l a r s . ( A f t e r A l l c o t t & A r c h i b a l d )  1  1  73  PILLAR PLAN VIEW  HANGING  WALL  STO  6 0  '  1  FOOTWALL The E f f e c t o f Wide R i b P i l l a r s  F r a c t u r e s on 6 0 m. ( 2 0 0 f t . ) (After A l l c o t t & Archibald)  1  1  PILLAR PLAN  VIEW  C O M P R E S S I V E  COMPRESSIVE FIGURE 28.  S  5  F O R C E S  F O R C E S  F r a c t u r e System  PILLAR PLAN  VIEW  COMPRESSIVE  COMPRESSIVE FIGURE 2 9  FORCES  FORCES  Combined E f f e c t o f S- and S- F r a c t u r e s  77  LINKAGE  I  OF  S  3  SLIPS  50 ft  1  PLAN VIEW FIGURE 3 0  7 7 - 9 0 Rib P i l l a r S l i d i n g .  (After A l l c o t t & Archibald)  FIGURE 31  co m co t q  fi  CO  E-i £5 CO  s;  6 0 0  6  5 0 0  5  (After A l l c o t t & Archibald)  1 : L  stess factor a strain . t i m e vs  ( 7 7 - 9 0 rib)  4 0 0  3 0 0  2 0 0  1 0 0  2  I  o o  ro  O O  o o  in  8 DAYS g (0  o o  no  o o CT)  a o o  o o  o o  CM  Because the 77-90 p i l l a r  i s only  15m.  (50 f t ) wide (east-west  these wedge f a i l u r e s may induce major s t a b i l i t y pillar  sliding  The  axis),  problems, and provoke  (Figure 30).  deformation o f the 77-90 r i b p i l l a r was monitored and F i g u r e 31  c l e a r l y shows that the p i l l a r 5.7.3  Phase 3:  s l i d i n g described  previously,  occurred.  E m p i r i c a l Methods  E m p i r i c a l methods may be used t o estimate the l o a d a c t i n g on a p i l l a r , and  i t s ultimate  were r e p o r t e d ure  strength at f a i l u r e .  failed  Since  a) 77-92 and b) 77-94  pillars  ( S e c t i o n 5.6), and c) 77-90 s u f f e r e d s t r u c t u r a l f a i l -  ( S e c t i o n 5.7.2), the e m p i r i c a l methods w i l l  be a p p l i e d to these  three  cases. 5.7.3.1 The  Estimation  of P i l l a r  Load by the E x t r a c t i o n Ratio  s t r e s s can be c a l c u l a t e d f o r each p i l l a r , u s i n g  Formula  the f o l l o w i n g r e -  lationship : a  p  =  0"i . N  where * N = E x t r a c t i o n number Op  (Figures 32, 33, 34)  = Average p i l l a r s t r e s s Sum o f 1/2 s t r i k e length o f each _ Adjacent stopes + s t r i k e length o f p i l l a r S t r i k e Length o f P i l l a r  Oi A)  77-90 P i l l a r  =  17.24 MPa  (360 KPSF)  F a i l u r e Geometry (Figure 32)  Pillar  N  Oi(MPa)  77-90  3.4  17.24  58.48  77-92  2.1  17.24  36.20  77-94  1.9  17.24  32.76  a  p  (MPa)  ( S e c t i o n 5.3.4)  80 B)  77-92 P i l l a r F a i l u r e Geometry (Figure 35) Pillar  N  g (MPa)  77_90  C)  F A I L E D 3.1  17.24  53.44  77-94  1.9  17.24  32.76  F a i l u r e Geometry (Figure 34)  Pillar  N  Oi(MPa)  77-90  a (MPa) p  F A I L E D  77-92  --  77-94  F a i l e d and Recovered  6.3  17.24  Estimation of P i l l a r  The p i l l a r  ---  77-92  77-94 P i l l a r  5.7.3.2  (MPa)  r  108.61  Strength; Hoek's Method  s t r e n g t h may be estimated  u s i n g the curves  developed by  3 Hoek S Brown (1980)  (Figure 35).  The p i l l a r m a t e r i a l was c l a s s i f i e d by  12 Golder  Associates  (1981)  as a good q u a l i t y rock mass  (Q - 20), and the  u n i a x i a l compressive s t r e n g t h i s : a A)  c  =  176.5 MPa  (25598 p s i )  77-90 P i l l a r F a i l u r e Geometry  ,,,„ Pillar D  w  W/H /  u  P i l l a r Strength/a  c  Pillar (  Strength M  P  A  )  77-90  1.0  0.3  52.95  77-92  0.75  0.25  44.13  77-94  0.75  0.25  44.13  FIGURE 3 2  PLAN VIEW  P i l l a r s E x t r a c t i o n Numbers f o r the  7 7 - 9 0 P i l l a r F a i l u r e Geometry.  a, =  17.2  MPa  FIGURE 33  P i l l a r s E x t r a c t i o n Numbers  |  PLAN VIEW  f o r the 77-92 P i l l a r F a i l u r e Geometry• co ro  O] = I 7.2 M P ,  FIGURE 34  P i l l a r s E x t r a c t i o n Numbers for  the  ?7-94  PLAN VIEW  P i l l a r Failure  Geometry.  CT. = 17.2  M Pa  84  Intact samples of f i n e grained igneous c r y s t a l l i n e rock m=17 , s=l  Very good q u a l i t y rock mass m=8.5 , s = 0 . 1  Good q u a l i t y rock mass m=1.7 , s=0.004 F a i r q u a l i t y rock mass m=0.> , s=0.0001 Poor q u a l i t y rock mass m=0.09 , s=0.00001  P i l l a r width/height  FIGURE 35  i  The E f f e c t  W^/h  o f the Width to H e i g h t  on. Average P i l l a r  Strength.  Ratio  85 B)  77-92  Pillar  Failure  W/H  Pillar  P  i  l  l  a  77-90  Geometry  Strength/a  r  c  Pillar  Strength  F A I L E D  77-92  0.75  0.25  44.13  77-94  0.75  0.25  44.13  C) 77-94 P i l l a r  p  .  P  l  1 1 a T  .  w  /  l  r  W  /  l  a  Failure  Geometry  Pillar  77-90  5.7.4  FAILED AND 0.5  Strength (MPa)  RECOVERED --  0.15  Theoretical  It was s t a t e d  Pillar  F A I L E D  77-92 77-94  Strength/a.  H  26.48  Methods  i n Chapter 3 that the t h e o r e t i c a l methods are u s e f u l f o r  b e t t e r understanding the mechanism  involved i n p i l l a r  design.  However, the complexity and the great amount o f data r e q u i r e d make them i m p r a c t i c a l , d i f f i c u l t to apply, and i n a c c u r a t e .  Thus, no t h e o r e t i c a l  methods have been used f o r the Heath S t e e l e case h i s t o r y 5.7.5  Phase 5.  Computer  analysis.  Methods  The computer s t r e s s a n a l y s i s program used was  "BITEM", a two-dimension-  a l boundary element program developed by the C.S.I.R.O.  T h i s program has  been m o d i f i e d and adapted t o the U.B.C. main frame I.B.M. computer by R. Pakalnis.  Again, the three s i t u a t i o n s modelled were the p i l l a r  geometries of 77-90, 77-92 and 77-94.  The p i l l a r  failure  s t r e s s i s taken as the  86 average v a l u e o f 30 nodal s t r e s s e s d i s t r i b u t e d w i t h i n each p i l l a r . N.B.  The s t r e s s u n i t s o f the computer output are i n k i l o pounds per square f o o t (KPSF). F i g u r e s 36, 37, 38.  A)  77-90  P i l l a r F a i l u r e Geometry (Figure 36)  Pillar  B)  77-92  Stress  77-90  43.09 MPa  900 (KPSF)  77-92  27.77 MPa  580 (KPSF)  77-94  28.73 MPa  600 (KPSF)  P i l l a r F a i l u r e Geometry (Figure 37)  Pillar  77-90  C)  Op Average P i l l a r  . „.?P Average P i l l a r  Stress  Failed  77-92  38.30 MPa  800 (KPSF)  77-94  32.85 MPa  687 (KPSF)  77-94 P i l l a r F a i l u r e Geometry (Figure 38)  Pillar  . „.?P Average P i l l a r  77-90  F a i l e d ---  77-92  Recovered-  77-94  57.46 MPa  Stress  1200 (KPSF)  PLAN VIEW  36  Computer Output o f the 77-90 P i l l a r F a i l u r e Geometry. P r i n c i p a l Major S t r e s s Contour. co  PLAN VIEW  FIGURE 3 7  Computer Output o f the 7 7 - 9 2 P i l l a r F a i l u r e Geometry. P r i n c i p a l Major S t r e s s Contour.  PLAN VIEW  Computer Output o f the 77-94 P i l l a r F a i l u r e Geometry. P r i n c i p a l Major S t r e s s Contour.  90  5.8  D i s c u s s i o n o f the  Results  Before d i s c u s s i n g the rock mechanics r e s u l t s of A] 77-90, B) 77-92 and C) 77-94 p i l l a r f a i l u r e s , the r e q u i r e d assumptions must be reviewed. 1.  The  2.  v i r g i n s t r e s s was  estimated  from measurements at  Brunswick Mining  and  For every p i l l a r  f a i l u r e case r e p o r t e d ,  dimensions were  Smelting. stopes  and  pillars'  assessed.  For each s i t u a t i o n the p i l l a r loads were c a l c u l a t e d u s i n g two methods, t r i b u t a r y area and c o r r o b o r a t e very w e l l  computer s i m u l a t i o n .  (Table 11). The  The  different  r e s u l t s of both methods  p i l l a r s t r e n g t h s were estimated  using  3 Hoek and  Brown (1980)  r a t i o of the p i l l a r calculated. equals  curves.  s t r e n g t h over the p i l l a r load at a given time was  A s a f e t y f a c t o r of 1 means that the load a c t i n g on the  i t s u l t i m a t e s t r e n g t h and  The  A s o - c a l l e d " s a f e t y f a c t o r " which i s the  pillar  f a i l u r e i s imminent.  f a i l u r e h i s t o r y can then be r e c o n s t r u c t e d u s i n g Table  A) 77-90  also  P i l l a r F a i l u r e Geometry (Nov.  The  f i r s t p i l l a r to c o l l a p s e was  The  f a i l u r e was  1977)  77-90 (S.F. = 1.04)  not documented, probably  11:  (November, 1977).  because i t was  n o n - v i o l e n t , and caused by s l i d i n g along the S  3  progressive,  f r a c t u r e (Figures  30,  31). B) 77-92 P i l l a r F a i l u r e Geometry (Nov.  1977)  A f t e r the 77-90 p i l l a r p a r t i a l l y l o s t  i t s bearing c a p a b i l i t y , a part  of the load was  the 77-92 p i l l a r to  r e d i s t r i b u t e d causing  fail.  (S.F. = 0.96). C)  77-94  According  Pillar  F a i l u r e Geometry (Sept.  1978)  to the a c t u a l geometry of the p a n e l , Table  77-94 p i l l a r had  previously f a i l e d .  (S.F. = 0.46).  11 shows that  the  TABLE 11 HEATH STEELE PILLAR ANALYSIS RESULTS  Pillar  A)  Extraction Number  Tributary Area (MPa)  Computer Stress (MPa)  IV/H (Plan View)  Pillar Strength (MPa)  Safety Factor  1  52.95  1.04  Extraction Ratio %  Remarks  77-90 P i l l a r F a i l u r e Geometry, November 1977  77-90  3.4  58.48  43.09  77-92  2.1  36.20  27.77  77-94  1.9  32.76  28.73  B)  Mean (1) Stress (MPa)  77-92 P i l l a r  50.79 x  31.99  0.75  30.75  0.75  44.13  1.38  71 51  P i l l a r Slide Stable  44.13  1.44  49  Stable  F a i l u r e Geometry, November 1977  77-90  F A I L E D  77-92  3.1  53.44  38.30  45.87  0.75  44.13  0.96  68  Pillar  77-94  1.9  32.76  32.85  32.80  0.75  44.13  1.35  49  Stable  0.46  84  Pillar  C)  A c t u a l Geometry (77-94 F a i l e d ) September 1978  77-90  F A I L E D  77-92 77-94  (1)  (2)  Failed  F A I L E D 6.3  108.61 - ' (  2  )  57.46  57.46  and R E C O V E R E 0.5  26.48  D  The mean s t r e s s i s assumed to be the average value of computer and t r i b u t a r y area methods. Only the computer s t r e s s was considered i n C) A c t u a l Geometry 77-94, the t r i b u t a r y area v a l u e was judged irrelevant. I r r e l e v a n t value.  Failed  These c o n c l u s i o n s from the r e s u l t s of computational d e s i g n methods (Table 11) a r e i n agreement w i t h the i n s t a b i l i t y events experienced at Heath S t e e l e (according to the documentation) which suggest that the and  dimensions  s t r e s s v a l u e s assumed were c o r r e c t . Furthermore,  A l l c o t t and A r c h i b a l d ( 1 9 8 1 )  1 1  attempted  to e l a b o r a t e an  e m p i r i c a l d e s i g n curve f o r Heath S t e e l e p i l l a r s , u s i n g bore-hole extensomet e r s ' deformation r e c o r d s .  From the o b s e r v a t i o n s of f a i l i n g  p i l l a r s , four  stages of d e t e r i o r a t i o n have been d e f i n e d . Stage 1:  Intact  Pillar  No v i s i b l e or a u d i b l e evidence of movement, although may  register  Stage 2:  extensometers  convergence.  Pillar  Failure  Sound and movement are observed.  It i s s t i l l  p o s s i b l e to  drill,  b l a s t and muck the p i l l a r m a t e r i a l , but at times continuous movement w i l l prevent t h i s . Stage 3:  Post  A f t e r s t a b i l i z a t i o n r e c o v e r y can begin a g a i n .  Failure  Manageable r e c o v e r y i s no l o n g e r p o s s i b l e , but s t a b i l i z a t i o n a l l o w r e t e n t i o n of f i l l Stage  will  or through a c c e s s .  4:  No r e l i a b l e use remains  i n the  pillar.  Combining these q u a l i t a t i v e o b s e r v a t i o n s with the deformation v e r s u s e x t r a c t i o n numb er lars failed (N) of 3.3.  curve  ( F i g u r e 3 9),  A l l c o t t and A r c h i b a l d n o t i c e s that  pil-  at Stage 2 of d e t e r i o r a t i o n corresponding to an e x t r a c t i o n number T a b l e 11 r e s u l t s c o n f i r m A l l c o t t and A r c h i b a l d ' s o b s e r v a t i o n s .  F i g u r e 40 d e p i c t s a p l o t of the e x t r a c t i o n number v e r s u s s a f e t y showing that p i l l a r f a i l u r e t i o n number N = 3.3.  (S.F. = 1) e f f e c t i v e l y occurred around  factor,  an e x t r a c -  €6  FIGURE  40  EXTRACTION NUMBER VS SAFETY FACTOR  i  CD CD CD -P  cn  _c +-> fd  OJ  X  +  r\-  cn I  cn  <  m CE rcn  1  l_  cn  in cu  OJ  in  Ul _j  NS RB  C3 CO 1  LE  cu. IE  r-  ZD  95 Because s e v e r a l methods have been employed which g i v e s u b s t a n t i a l l y t h e same r e s u l t as t h e A l l c o t t and A r c h i b a l d experiments, t h e p i l l a r d e s i g n p r o cedure and imput parameters  can be c o n s i d e r e d c a l i b r a t e d a t Heath S t e e l e .  F i n a l l y , F i g u r e 41 r e p r e s e n t s a p l o t o f t h e l o c a l e x t r a c t i o n r a t i o "e" v e r s u s t h e s a f e t y f a c t o r o f each p i l l a r a t d i f f e r e n t s t a g e s o f e x t r a c t i o n . Note:  e = 100 x  ( °f l / ^ w i d t h o f each a d j a c e n t stope) sum o f l / 2 w i d t h o f each a d j a c e n t stope + the width o f p i l l a r s u m  F i g u r e 41 i n d i c a t e s t h a t a t 3 0 0 m ( 1 0 0 0 f t . ) depth, i n s t a b i l i t y i s initiated  when t h e e x t r a c t i o n r a t i o exceeds 65 - 7 0 % . Thus i t i s suggested  to l i m i t p r i m a r y e x t r a c t i o n t o 65% a t t h i s depth. T h i s w i l l minimize-  sta-  b i l i t y problems t h a t have caused e x t r a support c o s t s , m i n i n g d e l a y , l o s s of o r e r e s e r v e s as w e l l a s making p i l l a r s  recovery very  difficult.  Curves s i m i l a r t o F i g u r e 41 s h o u l d be developed i n o r d e r t o determine the optimum percentage o f e x t r a c t i o n a t d i f f e r e n t depths ( 6 0 0 m, 9 0 0 m , 1 2 0 0 at Heath S t e e l e .  m)  CHAPTER 6 GECO CASE HISTORY ANALYSIS  98 6.1  Geology ( a f t e r Bray 6.1.1  (1967)  1 0  R e g i o n a l Geology  The Manitouwadge S y n c l i n e i s a broad sediments and m e t a v o l c a n i c s , and  The  e a s t e r l y p l u n g i n g s y n c l i n e of meta-  s u r r o u n d i n g c o u n t r y r o c k s a r e mainly g r a n i t e  t r o n d j e m i t e , showing evidence of g r a n i t i z a t i o n near the s y n c l i n e i n the  form of g n e i s s i c g r a n i t e and  migmatite.  The metasediments c o n s i s t of quartz f e l d s p a r b i o t i t e g n e i s s , q u a r t z i t e s w i t h v a r y i n g amounts of b i o t i t e ,  i r o n f o r m a t i o n and  the quartz muscovite  group  which i s host r o c k f o r the Geco orebody. The m e t a v o l c a n i c s a r e o l d e r than t h e metasediments and blende  s c h i s t and  6.1.2  c o n t a i n horn-  amphibolite.  Mine Geology  The Geco orebody i s l o c a t e d i n the s e r i c i t e s c h i s t group of r o c k s on  the  south limb of the Manitouwadge s y n c l i n e .  A l a r g e open drag f o l d  l y 760 m.  t o the east i s the host s t r u c t u r e  (2500 f t ) l o n g and  f o r the orebody.  p l u n g i n g 35°  approximate-  '  The orebody i s l a r g e and and a s u r r o u n d i n g envelope  s t e e p l y d i p p i n g w i t h a c o r e of massive s u l p h i d e s  of d i s s e m i n a t e d  sulphides.  m i n e r a l s mined a r e c h a l c o p y r i t e , s p h a l e r i t e and A c r o s s - S e c t i o n from  The major economic  galena.  south to n o r t h a c r o s s t h e Geco orebody shows t h e  f o l l o w i n g sequence of f o r m a t i o n s : - g  r e  y gneiss (including b i o t i t i c quartzite)  - sericite schist  ( c o n t a i n i n g the orebody)  - b i o t i t e amphibole garnet g n e i s s . I n t r u s i v e i n t o t h e s e f o r m a t i o n s a r e b a s i c dykes, g r a n i t e , pegmatite dykes and d i a b a s e dykes.  T a b l e 12 and  F i g u r e 42 summarize the Geco  geology.  99  FIGURE  42  Schematic S t r a t i g r a p h i c Columns I l l u s t r a t i n g G e n e r a l i z e d R e l a t i o n s h i p s o f S u l p h i d e Zones, Geco Mine  100 The orebody forms a t a b u l a r mass l y i n g more or l e s s v e r t i c a l , and raking eastward a t from 20 degrees to 30 degrees.  In c r o s s - s e c t i o n , t h e o r e -  body has t h e shape of an onion, with t h e bulbous bottom p o r t i o n s conforming to t h e c u r v a t u r e of the d r a g f o l d . The massive s u l p h i d e c o r e (orebody) v a r i e s i n t h i c k n e s s from a few inches t o about 45 m. (150 f t ) w i t h an average t h i c k n e s s of 12 m. (40 f t ) . The grade of t h e o r e averages b e t t e r than 2 percent copper, 4 percent z i n c and 2 oz/ton of s i l v e r . TABLE 12 SUMMARY OF THE GEOLOGY AT GECO Rock Types GRANITE GROUP 1)  Granite  2)  B i o t i t e garnet g n e i s s  3)  B i o t i t e s i l l i m a n i t e gneiss  SERICITE SCHIST GROUP 4)  Quartz b i o t i t e a n t h o p h y l l i t e h o r n f e l s  5)  Sericite  6)  Chalcopyrite  7)  Sphalerite  8)  Pyrite, pyrrhotite, sphalerite,  schist  GREY GNEISS GROUP 9)  Quartz f e l d s p a r b i o t i t e g n e i s s  10)  Biotitic  quartzite  11)  Iron f o r m a t i o n  INTRUSIVES 12)  Diabase  13)  Pegmatite  14)  Quartz  diorite  chalcopyrite  - 101 6.1.3  S t r u c t u r a l Geology  M u l t i p l e f o l d i n g i n the o r e bearing s c h i s t , t r a n s v e r s e t o the main d r a g f o l d i n g , aggravates  the ground weaknesses induced by f a u l t i n g and f r a c -  t u r i n g , and i n some p l a c e s i n c r e a s e s the tendency As a r u l e , t h e pegmatite  dykes a r e not m i n e r a l i z e d , except where i n •  contact w i t h the massive s u l p h i d e c o r e . cluded  to slough.  They a r e , t h e r e f o r e , r a r e l y i n -  i n a stope, but may form a stope w a l l .  S i n c e the l a r g e dykes (over  1 m. (3 f t ) a r e e x t e n s i v e l y f r a c t u r e d , they tend t o s l a b and break o f f when exposed over a wide s u r f a c e .  By c o n t r a s t , the massive s u l p h i d e c o r e of the  orebody i s r e l a t i v e l y f r e e from j o i n t s and f r a c t u r e s and has been observed standing s o l i d l y over h o r i z o n t a l l e n g t h s of 21 m. (70 f t ) and v e r t i c a l h e i g h t s of over 90 m. (300 f t ) . Ground c o n t r o l i n the mine i s a l s o a d v e r s e l y a f f e c t e d , e s p e c i a l l y when we have f o l d i n g i n the area of the top of t h e stope. schist  i s not standing v e r t i c a l l y ,  load as s t e e p l y d i p p i n g s c h i s t s .  Because the f o l d e d  i t w i l l not support T h i s problem w i l l  the same v e r t i c a l  i n c r e a s e with depth and  more i n t e n s e f o l d i n g . Thus, t h e s t r u c t u r a l weaknesses of the o r e - b e a r i n g formation c o n s i s t s of: (a)  f o l i a t i o n and some f a u l t i n g  i n an east-west  direction.  (b)  j o i n t i n g and minor f a u l t i n g i n a n o r t h - s o u t h d i r e c t i o n .  (c)  weak c o n t a c t s along diabase dykes and along d i o r i t e / q u a r t z muscovite s c h i s t c o n t a c t s .  (d)  r e g i o n a l , drag and c r o s s f o l d i n g .  (e)  i r r e g u l a r f r a c t u r e s and j o i n t s i n broad  quartz  pegmatites.  12 - Jointing.  A f t e r Golder A s s o c i a t e s (1981)  There a r e two s t e e p l y d i p p i n g j o i n t  sets.  The f i r s t  west s t r i k e , the other s t r i k e s roughly n o r t h - s o u t h .  one has an e a s t -  No p e r s i s t e n t  near  102  horizontal joint 6.2  s e t s were found at Geco.  Mining Method and Underground S t r u c t u r e Dimension The p r i n c i p a l mining method at Geco i s b l a s t h o l e mining, but where the  ore narrows to 8 m (25 f t ) or l e s s i t i s necessary to use a cut and  fill  method. The r o c k s a t Geco are not the best s u i t e d to open s t o p i n g as they w i l l slough r e a d i l y when exposed  i n the l a r g e areas of a stope w a l l .  Geco have  overcome the problem by modifying the mining method by i n t r o d u c i n g f i l l the ore i s drawn; thus keeping the stopes f u l l at a l l times. stability  as  To prevent i n -  i n the backs, they are c a b l e b o l t e d u s i n g tensioned 9.1 m long  cable bolts. The orebody Mining s t a r t e d progressed  i s divided  i n 1957  i n t o b l o c k s f o r convenience of  at the west e x t r e m i t y of the orebody  (Block A) and  eastward.  A t y p i c a l b l o c k i s about  150 to 180 m.  (500 f t ) h i g h , c o n s i s t i n g of  t h r e e 21 m (70 f t ) wide primary stopes separated by two p i l l a r s and f l a n k e d by two stopes a r e mined f i r s t  boundary p i l l a r s 46 m  and drawn under rock f i l l  the i n t r o d u c t i o n of cemented h y d r a u l i c f i l l . are  identification.  then removed between the f i l l e d  stopes.  37 m (120 f t )  (150 f t ) wide.  The  primary  and then c o n s o l i d a t e d w i t h  The two 37 m (120 f t ) p i l l a r s These p i l l a r s a r e u s u a l l y mined  i n 60 to 90 m (200 to 300 f t ) l i f t s to minimize d i l u t i o n from the f i l l To date most of the primary s t o p i n g i s completed  walls.  and p i l l a r mining  t r i b u t e s a l a r g e share of the p r o d u c t i o n .  6.3  Rock Mechanics 6.3.1  Data  Rock S t r e n g t h - Density  Parameters Ore Massive S u l p h i d e = 5334 kg/m  3  (333  lbs/ft )  Disseminated ore  3  (200  lbs/ft )  = 3204 kg/m  3  3  con-  Waste:  Hanging w a l l = 2666 kg/m and f o o t w a l l  3  (166 l b s / f t ) 3  - E l a s t i c Modulus and Poisson's R a t i o Ore:  Waste:  E  =  103425 MPa  v  =  0.31  E  =  105340 MPa*  v  =  0.2*  (15M. p s i )  12 6.3.2  Laboratory T e s t .  - Unconfined Ore:  A f t e r Golder A s s o c i a t e s (1981)  Compressive S t r e n g t h a  =  c  100 MPa  Quartz b i o t i t e  (psi) 6,000  schist  Quartzite  (MPa) 41  23,000  159  4,000  27  7,500  52  15,500  107  Hornblende b i o t i t e q t z s c h i s t  7,000  48  Granite  (gneiss)  9,000  62  Granite  biotite  10,500  72  27,000  186  13,500  93  Sericite Quartz  biotite  gneiss  Quartz b i o t i t e  Quartz  biotite  Quartz muscovite - T e n s i l e Strength  muscovite  schists  Ore: a  = 8 MPa  t  - T r i a x i a l Compressive S t r e n g t h Ore:  0  3  =  6.9 MPa  = 150 MPa O i = 232 MPa  a  3  = 13.8 MPa  a  3  = 20.7 MPa  • a  l  = 307 MPa  Estimated from the t y p i c a l value o f E l a s t i c Modulus and Poisson Ratio f o r g n e i s s rock. (Hoek and Brown (1980) , p. 262,267) 3  104 6.3.3  Rock Mass C l a s s i f i c a t i o n  The f o o t w a l l , hanging w a l l and orebody rocks were c l a s s i f i e d by Golder 12 Associates  (1980)  2850 l e v e l 28-54.5 C r o s s - c u t S e r i c i t e Schist  (Two Ratings)  NGI RQD Jn Jr Ja Jw SRF Q  =  NGI  60 4 2 0.75 1.0 2  50 6 2 1.0 1.0 1.0  20  16.7 CSIR  Intact Strength RQD Spacing o f J o i n t s Condition of Joints Ground Water  7 13 10 12 10 52  Hangingwall  Ramp Below 2850 L Biotite  RQD Jn Jr Ja Jw SRF Q  =  Garnet Gneiss  (Two Ratings)  NGI  NGI  60 6 3 1 1 2.5  90 4 2 0.75 1 1  12  60 CSIR  Intact Strength RQD Spacing o f J o i n t s Condition of Joints Ground Water  7 13 20 6 10 56  1850 Level Hangingwall Hangingwall  D r i f t o f f 18-36 Cross-Cut  Schist  (Two Ratings)  NGI  NGI  RQD Jn Jr Ja Jw SRF  90 2 1 1 1 2.5  60 3 1.5 2 1 2.5  Q  18  6 CSIR  Intact Strength RQD Spacing o f J o i n t s C o n d i t i o n of J o i n t s Ground Water  7 20 20 6 10_ 63  1850 L e v e l i n Footwall o f 19-40 P i l l a r Footwall S e r i c i t e  Schist  RQD Jn Jr Ja Jw SRF Q  =  (Two Ratings)  NGI  NGI  75 4 1 4 1 2.5  60 3 2 2 1 2.5  1.9  8 CSIR  I n t a c t Strength RQD Spacing o f J o i n t s Condition of Joints Ground Water  Stope  7 13 20 6 10 56  106  1850 Level 44 P i l l a r Massive  Sill  Sulphides  RQD Jn Jr Ja Jw SRF Q  =  (Two  Ratings)  NGI  NGI  60 9 1 2.0 1.0 4.0  80 9 1.5 0.75 1 1  0.8  17.8 CSIR  Intact Strength RQD Spacing of J o i n t s Condition of Joints Ground Water  7 13 20 6 10 56  2250 Level 27-61  Stope  Footwall S c h i s t  RQD Jn Jr Ja SRF Q  =  (Two Rating NGI  NGI  50 4 1 4 2.5  70 3 2 3 2.5  1.3  6.2 CSIR  I n t a c t Strength RQD Spacing o f J o i n t s Condition of Joints Ground Water  7 13 20 6 10 56  Values obtained f o r the f o o t w a l l s c h i s t v a r i e d from 1.3 to 20 (poor to good r o c k ) ; 0.8 to 17 f o r the s u l p h i d e s (poor to good r o c k ) ; and from 6 to 60 f o r the hangingwall  schist  (poor to v e r y good r o c k ) .  107 6.3.4  V i r g i n Stress  No s t r e s s measurements have been performed at Geco. vertical  However, the  s t r e s s i s assumed to be equal to the weight o f the o v e r l y i n g rock.  c  =  v  where:  The major p r i n c i p a l  yh  = a  3  y -  d e n s i t y o f the waste rock  h =  depth below s u r f a c e  s t r e s s a\ and i n t e r m e d i a t e p r i n c i p a l s t r e s s o , 2  both h o r i z o n t a l , are estimated u s i n g two d i f f e r e n t Appendix B.  The mean v a l u e s a r e : a1 =  2.6 a  v  a  2.1 o  v  2  =  fsee F i g u r e 431  FIGURE 4 3  Assumed S t r e s s Regime a t Geco  sources, d e s c r i b e d i n  108  At 215 metres a  (700 f t ) depth, the s t r e s s regime i s : «= y.h «= 2660 kg/m  3  3  a 01  «= 2.6a  0  « 2.1o «  2  6.4  Pillar Six  The  «= 5.72 x 1 0  3  5  x 215 m «= 5.72 x 1 0 kg/m  2  «=  5  kg/m  2  5.66 MPa (116 KPSF)  «= 14.73 MPa (302 KPSF)  3  3  11.89 MPa (244 KPSF)  Characteristics  stopes with i n t e r v e n i n g p i l l a r s  were used t o mine t h e 'B' Block.  stopes' i n i t i a l dimensions were 21m. (70 f t ) long and up to 150 m.  (500 f t ) high  (vertical).  The r i b p i l l a r s , designed  t o be recovered at a subsequent stage, were  37 m. (12 f t ) l o n g . The p i l l a r m a t e r i a l i s a massive s u l p h i d e which i s r e l a t i v e l y s t r o n g (a  c  6.5  «= 100 MPa) .  Mining The  Sequence  i n v e s t i g a t e d area c o n s i s t s o f f o u r open stopes  10 - 22 and 10 - 23.5) separated by three r i b p i l l a r s 10 - 23).  (10 - 19.5, 10 - 21,  (10 - 20, 10 - 21.5,  The depth v a r i e s from 150 m. (500 f t ) t o 320 m. (1050 f t ) below  s u r f a c e , and a 215 m (700 f t ) depth was assumed f o r c a l c u l a t i o n F i g u r e 44 i s a l o n g i t u d i n a l view o f the s t o p e / p i l l a r / p a n e l Tables 13 to 16 summarize the mining  sequence.  purposes. layout and  FIGURE 44  L o n g i t u d i n a l View of t h e I n v e s t i g a t e d Area a t Geco .  TABLE 13 STOPE 10-19.5 MINING SEQUENCE Date Feb.  Broken Ore  T o t a l Tons  1960  8,050  March 1960  20,150  28,200  April  1960  60,030  88,230  Sept.  1960  10,000  98,230  Oct.  1960  105,630  203,860  Dec.  1960  6,820  210,680  1  1  Sept. 1961  Remarks  Sloughing  TABLE 14 STOPE 10-21 MINING SEQUENCE  Date  Broken Ore  T o t a l Tons  Nov.  1959  3,890  3,890  Dec.  1959  11,500  15,390  Jan.  1960  19,903  35,293  Feb.  1960  18,678  53,971  Mar.  1960  67,027  120,998  Sept. 1960  20,000  140,998  Remarks  Oct.  1960  5,000  145,998  Small amount o f sloughing from north s i d e  Nov.  1960  15,230  161,228  10-21.5 p i l l a r  cracked  Dec.  1960  32,390  193,618  10-21.5 p i l l a r  failed  10--21 SOUTH STOPE March 1961  27,677  221,295  April  1961  3,100  224,395  May  1961  9,400  233,795  June  1961  24,640  258,435  TABLE 15 STOPE 10-22 MINING SEQUENCE  Date  Broken Ore  T o t a l Tons  March 1960  1,930  1,930  June  1960  3,250  5,180  July  1960  7,500  12,680  August 1960  15,000  27,680  Sept.  1960  48,350  76,030  Nov.  1960  15,000  91,030  Dec.  1960  35,800  126,830  March  1961  3,074  129,904  Remarks  10-23 P i l l a r  Failed  'Caving'  10-22 SOUTH STOPE  June 1961  6,990  136,894  J u l y , 1961  14,340  151,234  August 1961  50,220  201,454  10-21.5 PILLAR Dec.  1960  50,000  50,000  April  1961  10,000  60,000  June  1961  30,000  90,000  10-21.5 p i l l a r  recovery  112  TABLE 16 STOPE 10-23.5 MINING SEQUENCE  Date May-  Broken Ore  T o t a l Tons  Remarks  1960  250  250  June 1960  2,285  2,535  Aug. 1960  10,600  13,135  Sept. 1960  16,300  29,435  Oct.  1960  38,945  68,380  Dec.  1960  19,140  87,520  Jan.  1961  13,550  101,070  March 1961  12,830  113,900  May  1961  26,455  140,355  July  1961  22,619  162,974  Aug.  1961  407  163,381  Over Break  Sept. 1961  1,395  164,776  Over Break  10--23 PILLAR  Dec . 1960  5,000  5,000  Feb. 1961  20,000  25,000  March 1961  17,889  42,889  April  10,000  52,889  1961  10-23 P i l l a r  Failed  6.6  F a i l u r e H i s t o r i e s and P i l l a r ( A f t e r Bray 1 9 6 7 )  Geometries  1 0  - October, 1960:  sloughing s t a r t e d i n 10-21 stope.  - November, 1960:  extensive cracking o f :  . 10-21.5 p i l l a r . 10-23  850 l e v e l , major remedial  pillar  work on: . 10-21.5 n i l l a r  December, 1960:  10-21.5 p i l l a r c o l l a p s e d from the 7A to 5A sublevel.  (The upper h a l f o f the p i l l a r ) .  650 l e v e l ,  10-23 p i l l a r  showed extensive  sloughing. - January, 1961:  A f u l l r a i s e was d r i v e n to s u r f a c e t o backfill  - March, 1961:  10-22 stope.  10-22 stope cave to the e l e v a t i o n o f the 450 l e v e l .  - September, 1961:  The  The f i l l  r a i s e acted as a s l o t .  west s i d e o f the 10-20.5 p i l l a r s u f f e r e d  sloughing. - A p r i l , 1962:  10-19.5 stope cave t o the e l e v a t i o n o f 450  - October, 1963:  level.  Caving  reached  the 250 l e v e l  cross-cut.  From F i g u r e 45 e x t r a c t i o n f l o w c h a r t , the stope and p i l l a r and  dimensions were a)  geometries  estimated:  when 10-21.5 r i b p i l l a r f a i l e d ,  i n November, 1960 (Figure 46,  Table 17). b)  when 10-23 r i b p i l l a r f a i l e d ,  i n November, 1960 (Figure 47,  Table 18). c)  when 10-20 r i b p i l l a r f a i l e d ,  i n August, 1961 (Figure 48, Table 19).  T h i s design study w i l l concentrate on these three p a r t i c u l a r cases, and because the major p r i n c i p a l  s t r e s s i s h o r i z o n t a l i n the north-south  t i o n , o n l y the p l a n view needs t o be c o n s i d e r e d .  direc-  114  o -p w  10-20.5 P i l l a r deteriorates  10-22 Stope cave to 450 l e v e l  10-21.5 P i l l a r recovered 10-21.5 & 10-23 failed  115  TABLE 17 APPROXIMATE STOPE AND PILLAR DIMENSIONS WHEN 10-21.5 PILLAR FAILED (November, 1960)  Stopes  Length  Width  Height  10-19.5  21 m.  ( 70 f t . .)  20 m.  ( 65 f t , •)  150 m. (500 f t .• )  10-21  30 m.  (100 f t .•)  20 m. ( 65 f t .•)  150 m. (500 f t .• )  10-22  21 m.  ( 70 f t . 0  17 m. ( 55 f t . 0  150 m.  10-23.5  24 m.  ( 80 f t . • )  14 m.  150 m. (500 f t ..)  ( 45 f t , •)  (500 f t .0  Pillars  10-20 10-21.5 10-23  21 m. ( 70 f t . •) 9 m. ( 30 f t , •) 15 m.  ( 50 f t . •)  21 m. ( 70 f t , •)  150 m.  20 m.  150 m. (500 f t .• )  ( 65 f t , •)  18 m. ( 60 f t .0  (500 f t ..)  150 m. (500 f t .• )  TABLE 18 APPROXIMATE STOPE AND PILLAR DIMENSIONS WHEN 10-23 PILLAR FAILED (November, 1960)  Stopes  Length  10-19.5  Width  Height  21 m. ( 70 f t . )  20 m. (65 f t . )  150 m. (500 f t . )  10-22 )  61 m. (200 f t . )  18 m. (60 f t . )  150 m. (500 f t . )  10-23.5  24 m. ( 80 f t . )  14 m. (45 f t . )  150 m. (500 f t . )  10-20 10-21.5  21 m. ( 70 f t . )  21 m. (70 f t . ) F a i l e d  150 m. (500 f t . ) -  10-23  15 m. ( 50 f t . )  18 m. (60 f t . )  150 m. (500 f t . )  1  0  -  2  1  1  Pillars  TABLE 19 APPROXIMATE STOPE AND PILLAR DIMENSIONS WHEN 10-20 PILLAR FAILED (August, 1961)  Pillars  Length  Width  10-20  15 m. (50 f t . )  30 m. (100 f t . )  10-21.5  ---  F a i 1 e d  10-23  Height 150 m. (500 f t . )  F a i l e d  Stopes 10-19.5  24m. (80 f t . )  2 0 m. ( 6 5 f t . )  1 5 0 m. ( 5 0 0 f t . )  100 m. ( 3 3 3 f t . )  3 0 m. (100 f t . )  240 m. (80 f t . )  10-21 1 0  _22  10-23.5  S c a l e : 1 i n . = 100 f t .  PLAN VIEW  FIGURE 46  Estimated Layout When 10-21.5 P i l l a r  Failed.  Estimated Layout When 10-20 P i l l a r  Failed  120 6.7  Pillar  Design Study  The three r i b p i l l a r s 10-23) may be c l a s s i f i e d  involved  i n the present study  as " s e p a r a t i o n  pillars'  (10-20, 10-21.5,  (Category two).  A c c o r d i n g to the design c h a r t s , the f o l l o w i n g design methods should be applied. 6.7.1  Phase 1.  Experience Design  From the d e s c r i p t i o n of the mining method "block"  i s mined u s i n g three  by 37 m. ft.) and  (120 f t . ) p i l l a r s  wide.  and f l a n k e d  by two boundary p i l l a r s  with the i n t r o d u c t i o n o f h y d r a u l i c  (120 f t . ) p i l l a r s  6.7.2  (70 f t . ) wide primary stopes separated  Phase 2.  Structural  Empirical  of p i l l a r  The two  (Section  6.1.3).  core which Thus, i t i s  ( f a u l t s , j o i n t s and d i s c o n t i n u i t i e s ) do not  p l a y an important r o l e i n p i l l a r s t a b i l i t y Phase 3.  at Geco.  Methods.  load by the e x t r a c t i o n r a t i o formula  (Tributary  area) o  p  «=  where:  oi . N N «= e x t r a c t i o n number Op «= average p i l l a r Oi  fill  stopes.  are l o c a t e d mostly i n the massive sulphide  b e l i e v e d t h a t the s t r u c t u r e s  (150  Analysis  i s r e l a t i v e l y f r e e from j o i n t s and f r a c t u r e s  Estimation  fill.  are then removed between the f i l l e d  Pillar  The r i b p i l l a r s  6.7.3  46 m.  The primary stopes are mined f i r s t and drawn under rock  then c o n s o l i d a t e d  37 m.  21 m.  ( S e c t i o n 6.2) a t y p i c a l  •= 14.74 MPa  stress  (302 KPSF) ( S e c t i o n 6.3.4)  12 A)  B)  10-21.5 P i l l a r  Failure  Geometry (Figure 49)  N  10-20  2.4  14.74  35.38  10-21.5  3.8  14.74  56.01  10-23  2.5  14.74  36.85  10-23 P i l l a r  Failure  Pillar  N  10-20  2.9  10-20 P i l l a r  3.8  Failure  10-21.5 10-23  p  (MPa)  a (MPa) p  14.74  42.75  and Recovered 14.74  56.01  Geometry (Figure 51)  Pillar 10-20  a  Oi(MPa)  Failed  10-23  (MPa)  Geometry (Figure 50)  10-21.5  C)  Oi  Pillar  N 5  o i (MPa) 14.74 F a i l e d and Recovered Failed  a  p  (MPa) 73.70  N = 2.4  N = 3.8  N = 2.5  4—  1-  10-20  10-23  O; = 14.7 MPa FIGURE 49  P i l l a r s E x t r a c t i o n Numbers f o r the 10-21.5 P i l l a r F a i l u r e Geometry. P L A N VIEW  ro ro  O; = 14.7 MPa FIGURE 5 0  P i l l a r s E x t r a c t i o n Numbers f o r the 1 0 - 2 3  Pillar  F a i l u r e Geometry. PLAN VIEW ro  «  1  —1  10-20  ,1  ft ' ' .''''V'-.'•. .'  G[  FIGURE 5 1  -  17.4  1  M  Pa  P i l l a r s E x t r a c t i o n Numbers f o r the F a i l u r e Geometry. PLAN VIEW  10-20  Pillar  125  6.7.3.2  Estimation of P i l l a r  The p i l l a r s ' curves  S t r e n g t h ; Hoek's Method  s t r e n g t h can be estimated u s i n g Hoek and Brown (1980)  (Figure 8 ) .  The p i l l a r m a t e r i a l was c l a s s i f i e d  ( S e c t i o n 6.3.3) and  the Rock Q u a l i t y Index v a r i e s from Q « 0.8 to Q « 17.8.  A good q u a l i t y  rock mass i s then assumed, and the u n i a x i a l compressive  s t r e n g t h i s o*=  100 MPa A)  B)  (2105 KPSF).  10-21.5  Pillar  Pillar  W/H  10-20  1  0.3  30  10-21.5  0.5  0.2  20  10-23  0.8  0.25  25  10-23  Pillar  Pillar  W/H  10-20  1  10-21.5 10-23  C)  F a i l u r e Geometry  P i l l a r Strength (MPa)  F a i l u r e Geometry  P i l l a r Strength/a  c  P i l l a r Strength (MPa)  0.3  0.8  Pillar  W/H  10-20  0.5  10-23  c  30  F a i l e d and Recovered  10-20 P i l l a r  10-21.5  P i l l a r Strength/o  0.25  25  F a i l u r e Geometry  Pillar  Strength/a  c  P i l l a r Strength (MPa)  0.2  20  F a i l e d and Recovered Failed  c  126 6.7.4 As  Theoretical  Methods  i n Heath S t e e l e ' s case h i s t o r y , no t h e o r e t i c a l methods have been  used f o r the Geco p i l l a r f a i l u r e  6.7.5 The  Computer Methods  two-dimensional boundary elements program "BITEM" was used again  to model the three s i t u a t i o n s : p i l l a r f a i l u r e geometry. A)  (a)  (Figure  10-21.5, (b) 10-23 and (c) 10-20  52,53,54).  10-21.5 P i l l a r F a i l u r e Geometry (Figure  Pillar  B)  analysis.  10-23 P i l l a r  op P i l l a r Load  (MPa)  10-20  26.33 (550 KPSF)  10-21.5  38.30 (800 KPSF)  10-23  31.12 (650 KPSF)  F a i l u r e Geometry (Figure  Pillar Pillar 10-20 10-21.5 10-23  C)  52)  Op Load  (MPa)  31.12 (650 KPSF) Failed 39.84 (832 KPSF)  10-20 P i l l a r F a i l u r e Geometry (Figure  Pillar Pillar 10-20  53)  54)  Op Load  (MPa)  38.30 (800 KPSF)  10-21.5  Failed  10-23  Failed  FIGURE 5 2  COMPUTER OUTPUT OF THE 1 0 - 2 1 . 5 PILLAR FAILURE GEOMETRY MAJOR PRINCIPAL STRESS CONTOUR  53  COMPUTER OUTPUT OF THE 1 0 - 2 3 PILLAR FAILURE GEOMETRY MAJOR PRINCIPAL STRESS CONTOUR  FIGURE 5 4  COMPUTER OUTPUT OF THE 1 0 - 2 0 PILLAR FAILURE GEOMETRY MAJOR PRINCIPAL STRESS CONTOUR  130  6.8  D i s c u s s i o n of the R e s u l t s Before d i s c u s s i n g the rock mechanics r e s u l t s of A)  and C) 10-23  10-20, B) 10-21.5  p i l l a r f a i l u r e s , we must review the assumptions r e q u i r e d .  - The v i r g i n s t r e s s was i n Appendix  estimated f o l l o w i n g the procedure d e s c r i b e d  B.  - E l a s t i c Modulus and Poisson Ratio were s e l e c t e d u s i n g Hoek and 3 Brown (1980) t y p i c a l v a l u e s f o r g n e i s s rock i n t h i s a r e a . - Each time a p i l l a r was  r e p o r t e d f a i l e d , stope and p i l l a r  dimensions  were assessed. The p i l l a r load was lation.  The  c a l c u l a t e d u s i n g t r i b u t a r y area and computer simu-  load values determined  by the t r i b u t a r y area are about  h i g h e r than those from computer s i m u l a t i o n .  30%  Since the t r i b u t a r y area  s i m p l i f i e s the problem and r e p r e s e n t s the upper l i m i t of the average s t r e s s , the load values from computer s i m u l a t i o n are judged more and kept as mean v a l u e s .  The p i l l a r  s t r e n g t h was  overpillar  realistic  estimated u s i n g Hoek and  3 Brown (1980) The  c u r v e s , and each p i l l a r ' s  s a f e t y f a c t o r was  determined.  sequence of f a i l u r e events, a c c o r d i n g to the computational  methods  summarized i n Table 20 are as f o l l o w s : A)  10-21.5 P i l l a r  F a i l u r e Geometry (November  According to the documentation pillars  failed  p i l l a r to f a i l  i n November, 1960. (S.F. «= 0.53).  metry assumed at f a i l u r e was l e s s , the r e s u l t s are s t i l l failures.  1960)  (Bray ( 1 9 6 7 ) ) , both 10-21.5 and 1 0  T a b l e 20 shows t h a t 10-21.5 was  the  10-23 first  T h i s low s a f e t y f a c t o r i n d i c a t e s that the geonot exact  (S.F. should be around 1).  Neverthe-  capable of r e c o n s t r u c t i n g the h i s t o r y of the  TABLE 20 GECO PILLAR ANALYSIS RESULTS  Pillar  A)  Extraction Number "N"  Tributary Area (MPa)  Computer Stress (MPa)  Mean Stress (MPa)  W/H (Plan View)  Pillar Strength (MPa)  Safety Factor  Extraction Ratio %  Remarks  21.5 P i l l a r F a i l u r e Geometry, November 1960  10-20  2.4  35.38  26.33  26.33  1  30  1.15  55  Stable  10-21.5  3.8  56.01  38.30  38.30  0.5  20  0.53  74  Pillar  10-23  2.5  36.85  31 .12  31.12  0.8  25  0.81  60  Failure initiated  31.12  1  30  0.97  66  Stable  B)  23 P i l l a r F a i l u r e Geometry, November 1960  10-20  2.9  42.75  31.12  10-21.5 10-23  C)  failed  F a i l e d 3.8  56.01  39.84  39.84  and R e c o v e r e d  •  0.8  25  0.63  74  Pillar  failed  0.5  20  0.53  80  Pillar  failed  10-20 P i l l a r F a i l u r e Geometry, August 1961  10-20  5  73.70  38.30  38.30  132  B)  10-23 P i l l a r  F a i l u r e Geometry (November 1960)  J u s t a f t e r the 10-21.5 p i l l a r c o l l a p s e d , the s t r e s s r e d i s t r i b u t i o n caused the complete f a i l u r e o f 10-23 p i l l a r  (S.F. = 0.63), and the 10-20  p i l l a r p r o b a b l y s t a r t e d to show some i n s t a b i l i t y  C)  10-20 P i l l a r The  the  (S.F. = 0.97)  F a i l u r e Geometry (August 1961)  10-20 p i l l a r  load had a l r e a d y  s a f e t y f a c t o r o f 0.53 i n d i c a t e s that i n August 1961, l a r g e l y exceeded the bearing  c a p a b i l i t y o f the p i l l a r .  Although these r e s u l t s are not as p r e c i s e as those o f Heath S t e e l e ' s h i s t o r y , they a r e c o n s i s t e n t with the f a i l u r e events at Geco. accuracy o f the design r e s u l t s are valuable Figure  procedure and input data must s t i l l  as a s t a r t i n g p o i n t f o r f u t u r e  While the  be improved, the  designs.  55 i s a p l o t o f the l o c a l e x t r a c t i o n r a t i o "e"* versus the  s a f e t y f a c t o r o f each p i l l a r observed that at t h i s depth t r a c t i o n r a t i o exceeds 55%. at  case  d i f f e r e n t depths using  at d i f f e r e n t stages o f e x t r a c t i o n .  I t can be  (±300 m) s t a b i l i t y problems begin when the exPermissible  e x t r a c t i o n r a t i o can be determined  the same procedure.  Geco a c t u a l l y l i m i t s primary  mining to an e x t r a c t i o n r a t i o o f 37%. It should curve pillar  *  be n o t i c e d that a l a c k o f p o i n t s  (Figure 55) i s due t o the i n a c c u r a t e  i n the upper part o f the  estimation  dimensions i n s i t u a t i o n A: (10-21.5 P i l l a r  Defined  i n S e c t i o n 5.8  o f the stope and  F a i l u r e Geometry).  Geco  3  x +  2.5  A  2  10-20  10-2  1.5  10-23  r-  O  4->  U rd L_  1  . 5  >, <U <+fd LO  5  r-  0  100 Extraction  Ratio  C4)  CHAPTER 7 SUMMARY AND  CONCLUSIONS  135  7.1  Design  Procedure  In the context of the North American mining pillars  are s t i l l  designed u s i n g a t r i a l  i n d u s t r y , most underground  and e r r o r p r o c e s s .  Three major o b s t a c l e s i n d e s i g n i n g p i l l a r s  are r e s p o n s i b l e f o r t h i s  situation. Accurate e s t i m a t i o n o f p i l l a r s t r e n g t h E v a l u a t i o n of p i l l a r load The m u l t i p l i c i t y of  pillars.  T h i s study aims to improve the a c t u a l p i l l a r d e s i g n p r a c t i c e s . - A classification  system was  f i r s t proposed  which d i v i d e s p i l l a r s  into four categories: Category  1.  Plate  Category  2.  Separation  Category  3.  Stub  Category 4. This c l a s s i f i c a t i o n  Pillars Pillars  Pillars  Inclined  Pillars.  r e s o l v e s the problem of the m u l t i p l i c i t y o f  and a l l o w s s t a n d a r d i z a t i o n of the p i l l a r design - A f i v e phase design procedure  was  pillars  procedure.  developed.  It suggests that every  s u i t a b l e d e s i g n i n g method should be used, becoming more s o p h i s t i c a t e d as p e r i e n c e i s gained with the rock m a t e r i a l .  ex-  Also, design charts provide a  g u i d e l i n e f o r the s e l e c t i o n of the p e r t i n e n t methods.  T h i s procedure  per-  mits : i) ii)  A standard design process f o r a l l p i l l a r A more a c c u r a t e e s t i m a t i o n o f p i l l a r  load and  s e v e r a l methods which take i n t o account iii)  types. s t r e n g t h by using  different  factors.  An o p t i m i z a t i o n of the rock mechanics data employed as a design tool.  Thus, the procedure helps to overcome the three major o b s t a c l e s i n designing p i l l a r s . of misconstruing  7.2  A l s o , i t i s simple the  to apply and minimizes the  possibility  results.  Case H i s t o r i e s T h i s p i l l a r design procedure was  ure at Heath S t e e l e andGeco D i v i s i o n . documented and design  i n v o l v e d simple  a p p l i e d i n back-analysing  geometry, the input parameters a f f e c t i n g the  A p l o t d e p i c t i n g e x t r a c t i o n r a t i o versus stages  fail-  Because both case h i s t o r i e s were w e l l  of p i l l a r s c o u l d be understood, c o n t r o l l e d and  p i l l a r at d i f f e r e n t  pillar  adjusted.  " s a f e t y f a c t o r " f o r each  of e x t r a c t i o n appears to be an e f f i c i e n t manner  of s y n t h e s i z i n g the a n a l y s i s r e s u l t s .  As w e l l , the curves i n d i c a t e the  l i m i t of e x t r a c t i o n p e r m i s s i b l e at a given depth. Both mines--Heath S t e e l e and ures r e s u l t i n g i n p r o d u c t i o n reserves before  Geco--had experienced  costly p i l l a r  d e l a y s , e x t r a ground support  and  l o s s of ore  they were able to determine a safe e x t r a c t i o n r a t i o .  because i t i s based on experience  37% at Geco) w i l l  Although f u r t h e r r e s e a r c h v a r i e t y o f p i l l a r s and  (50% at  i s r e q u i r e d i n order to o b t a i n a wider versus  a method of o p t i m i z i n g primary e x t r a c t i o n ,  a v o i d i n g major s t a b i l i t y problems. The  the  remain safe f o r primary e x t r a c t i o n .  rock mass q u a l i t i e s , the e x t r a c t i o n r a t i o  s a f e t y f a c t o r curves r e p r e s e n t  Also,  o n l y , t h e r e i s no i n d i c a t i o n whether  p i l l a r s are overdesigned, or to which depth t h i s e x t r a c t i o n r a t i o Heath S t e e l e and  fail-  curves take the f o l l o w i n g f a c t o r s i n t o account: - virgin stress - s t r e s s induced  by mining  • - strength of p i l l a r  material  13?  - rock mass q u a l i t y - structural  discontinuities  - percentage o f e x t r a c t i o n - e f f e c t o f adjacent  openings  - o v e r a l l geometry and o r i e n t a t i o n of the underground s t r u c t u r e s - p i l l a r width to h e i g h t r a t i o - depth below s u r f a c e . However, damage c r e a t e d by b l a s t i n g , as w e l l as groundwater e f f e c t s were ignored because  they are d i f f i c u l t  part i n p i l l a r  stability.  to q u a n t i f y .  They may  p l a y an important  The use o f rock mass c l a s s i f i c a t i o n allows r e s u l t s from s i t e s to be compared.  different  F i g u r e 56 combines the curves from both case h i s t o r i e s .  The rock mass q u a l i t y i s i n d i c a t e d f o r each case.  7.3  Design Methods A review o f the p r i n c i p a l p i l l a r d e s i g n methods i s g i v e n i n Chapter  3.  They are s u b d i v i d e d i n t o four groups a c c o r d i n g to t h e i r l e v e l o f s o p h i s t i c a t i o n , and t h i s study makes the f o l l o w i n g c o n c l u s i o n s : Group 1. Experience Methods - Most mines s t i l l  r e l y p r i n c i p a l l y upon experience d e s i g n .  - Keeping d e t a i l e d f i l e s on a l l i n f o r m a t i o n concerning the mine stability gence w i l l Group 2.  such as f a i l u r e , improve  s l a b b i n g , squeezing, c a v i n g , conver-  the experience d e s i g n .  E m p i r i c a l Methods  - Because e m p i r i c a l methods ignore many f a c t o r s i n f l u e n c i n g stability, developed  pillar  the knowledge o f the c o n d i t i o n s i n which they were is essential.  Heath x .5  St ee 1 e  77-90  & Ge c  o  10-20  + 77-92  •  10-2 1.  A 77-94  o  10-23  —  RMR =  0  5  68  Heath RMR =  STRBLE  Steele  56  UNSTABLE  Geco  0  ... i  0  10  i  i  1  1  20  30  40  50  Extraction  Ratio  —1  60  L_  70  1  .  80  90  100  Group 3. -  T h e o r e t i c a l Methods The t h e o r e t i c a l and a n a l y t i c a l methods are complex and to  apply, and t h e i r r e s u l t s are o f t e n not r e l i a b l e .  ful  difficult  They are use-  i n f u r t h e r comprehending the mechanism i n v o l v e d i n p i l l a r  design. -  To determine  t h e o r e t i c a l l y p i l l a r strengths; only  has been widely -  Wilson's  formula  used.  The Coates' w a l l d e f l e c t i o n formula and the p h o t o e l a s t i c technique to  determine  pillar  load were r e l a t i v e l y popular i n the past but  are no longer employed. I f the p i l l a r ' s  s t r u c t u r e can be r e a l i s t i c a l l y  represented by  the  beam or p l a t e theory, i t i s a w e l l - a c c e p t e d method of d e s i g n i n g pillars.  Group 4. - The  Computer Methods computer methods are v e r s a t i l e and may  be adapted  to every  category o f p i l l a r . - Although  they are mathematically p r e c i s e , the accuracy of the r e s u l t s  i s . r e l a t e d to the q u a l i t y of the input data and designer's s k i l l s . F i n a l l y , - i t i s important t o remember t h a t d e s i g n i n g underground i s a p r o g r e s s i v e task. results will  pillars  The accuracy and the d e s i g n e r ' s confidence i n the  improve c o n c u r r e n t l y with the c o n t i n u i n g a p p l i c a t i o n of the  design procedure.  C a r e f u l underground o b s e r v a t i o n s , monitoring and measure-  ments should p r o v i d e feedback  on each d e s i g n .  140  REFERENCES 1.  Roche Mines A s s o c i l s l t e e  (1984)  ; E t a t de l a Question sur l e  Dimensionnement e t l a S t a b i l i t y Energy Mines and Resources 2.  WAGNER, H.  (197^)  Load-Deformation  o f C o a l P i l l a r s , Advances i n Rock Mech.,  I n t e r n a t i o n a l S o c i e t y o f Rock Mech., pp. 1 0 7 6 -  113., 19?4  1081,  3.  Canada, F e v r i e r 1 9 8 4  ; Determination o f the Complete  Charactiristics Vol.  des P i l l i e r s de s u r f a c e .  (1980)  HOEK, E . BROWN, E.T. f  5 Underground E x c a v a t i o n i n Rock ,  I n s t i t u t e o f Mining and M e t a l l u r g y , London, 5 2 7 p . 4.  BIENIAWSKI , Z.T. ( 1 9 8 3 ) Mines f o r U.S.  i  Improve Design o f Room and P i l l a r C o a l  Conditions , S t a b i l i t y  i n Underground  Mining, S o c i e t y o f M i n i n g Eng. o f AIME, 5.  SZWILSKI, T.B. ( 1 9 8 3 )  ;  S i z i n g o f Chain P i l l a r ,  I983 Stability  i n Under-  Mining, Chapt. 2 5 , S o c i e t y o f Mining Eng. o f AIME, 1983,  6.  PP. 5 3 9 - 5 5 7  SINGH, R.N. ( 1 9 8 1 )  WITTAKER, B.N.,  ; Stability  o f Longwall  Mining Gate Roadways i n R e l a t i o n t o R i b P i l l a r S i z e ,  7.  Int.  J o u r n a l Rock Mech., Min. S c i . and Geomech. a b s t r . ,  Vol.  18, pp. 3 3 1 - 3 3 4  ASHLEY, G.H. ( 1 9 3 0 )  ; B a r r i e r P i l l a r L e g i s l a t i o n i n Pennsylvania  Trans. AIME, C o a l Div., 1 9 3 0 , pp. 7 6 - 9 6 8.  BELINSKI, A.,  BORECKI, M. ( 1 9 6 4 )  j Results of Investigation  on Rock P r e s s u r e by the Longwall System o f C o a l Mining i n the Upper S i l e s i a n Conference  TOUSEULL, J.A.,  ;  , Proceeding 4 t h . I n t .  on S t r a t a C o n t r o l and Rock Mech., Columbia  University, 9.  Coal F i e l d  1 9 6 4 , pp.85-88  S t e r e o g r a p h i c Method o f Determining Wether  Planes o f Weakness T r a n s e c t P i l l a r s  , U.S. Bureau o f  Mines, Denver, Colorado. 10.  BRAY, R.C.E. ( 1 9 6 7 ) , Annual Geology  ;  C o n t r o l o f Ground Movement a t the Geco Mine  General Meeting, Dept., Ottawa 1 9 6 7  Noranda Mines, Geco D i v .  141  11.  ARCHIBALD, TJ.E. ( l 9 8 l )  ALLCOTT, G.A.,  ;  D e s c r i p t i o n of P i l l a r  Behaviour a t Heath S t e e l e Mines, CIM B u l l e t i n , 80-87  pp.  12.  Oct. 1 9 8 1 ,  Golder A s s o c i a t e s ( 1 9 8 1 )  ;  P r e d i c t i o n of S t a b l e E x c a v a t i o n Spans  f o r M i n i n g a t Depth Below 1 0 0 0 Meters i n Hard Rock, Canada C e n t e r f o r M i n e r a l and Energy Technology, Canmet C o n t r a c t no. 80-00081, A p r i l 13.  COATES, D.F.  (1966)  ;  1 3 4 p.  P i l l a r Loading: I I Model S t u d i e s ,  Branch Research Report R - 1 7 0 , 1966  1981,  Mines  Queen's P r i n t e r , Ottawa  142  APPENDIX A REVIEW OF LITERATURE (See "LITERATURE RESEARCH REPORT" June 1984)  143  APPENDIX B Determination o f the Geco S t r e s s  Regime a t 700 f t . Depth  No s t r e s s i n v e s t i g a t i o n s have been performed s t r e s s e s a r e estimated u s i n g the f o l l o w i n g 1.  From Herget  at Geco.  Both h o r i z o n t a l  methods:  (1983)  R e s u l t s from groundstress d e t e r m i n a t i o n s i n the Canadian S h i e l d a r e analyzed i n regard t o change with depth o f the r a t i o s t r e s s t o measured v e r t i c a l  stress  to measured v e r t i c a l  (o^ min/^v)-  at 215 m. £L  O-3  2.  a n <  253.87 C°h max/°v) « depth (m)  + 1.45  frr /rr 1 lo-h min/<V  + 0.88  Hfinaxl  _  =  279.82 depth (m)  253.87 depth  0-3  0_2_  a  m  3 minimum h o r i z o n t a l  stress  (700 f t . ) depth g  c  stress  (o^ a x / v )  o f maximum h o r i z o n t a l  H(min) o  =  v  279.82 depth  + 1.45  2.64  + 0.88 «= 2.20  From Hoek and Brown (1980) In s i t u s t r e s s measurements have been done at Wawa Mine, not f a r from  Geco, and the shallow depth r e s u l t s (^300 m.) tend t o c o n f i r m s t r e s s values determined  by Herget's  formulas. Depth (m.)  G.W. MacLeod M i n e , Wawa, G.W. MacLeod M i n e , Wawa, G.W. MacLeod M i n e , Wawa, G.W. MacLeod M i n e , Wawa, G.W. MacLeod M i n e , Wawa, G.W. MacLeod M i n e , Wawa, Wawa, O n t a r i o E l l i o t Lake, Ontar i o El 1 i o t Lake, O n t a r i o El 1 l o t Lake, O n t a r i o  Ontario Ontario Ontario Ontario Ontario Ontario  h  370  16.1  1Z°_  '5-1  S i der i t e Tuff Tuff Tuff Meta-diorite Chert Granite  575 575 1*80 575 3^5  Sandstone  TTB  Quartz i te D i a b a s e dyke  a  7ST  1(00  21.5  1A. 6  Vcr 1.29 1.23 1.25  18.7  26.6 20.0  1.52 2.50  ( 1 1 . 0 ) * 2.56  r 1r7r. 2r r  T77o1.90  ref.  81  AL 81  81 81 81 82 8 3  "ST 8^  144  APPENDIX C ILLUSTRATION OF PILLARS ( a f t e r Roche Mines A s s o c i a t e s  (1984) ) 1  lk-5  MAIN SHAFT SURFACE PILLAR, RIB PILLAR -,  SHAFT PILLAR -,  CENTER PILLAR, ROOF PILLAR, SILL PILLAR OVERBURDEN -, MINERALIZED ZONE  II  IP in  FIGURE 5  HARD ROCK PILLAR  146  RIB PILLAR  STOPE  FIGURE 6 • HARD ROCK PILLARS  FIGURE 7  SOFT ROCK PILLARS  148  APPENDIX D "BITEM", 2-D Boundary Element Program  DESCRIPTION OF BITEM Program BITEM i s based on program BITE, which was developed by P.C. Riccardella during PhD studies at Carnegie-Mellon University and has been released through CSIRO. BITE performs e l a s t i c i t y analyses f o r homogeneous solids only; BITEM has been developed at CSIRO to analyse systems consisting of a number of regions with d i f f e r e n t material properties. The boundary i n t e g r a l technique uses only information r e l a t i n g to the boundary surface to enable an analysis of the whole s o l i d . The net effect i s a reduction i n the dimension of the problem posed. As applied i n BITEM the boundary integral equation technique enables a two-dimensional analysis of plane s t r a i n (or stress) l i n e a r e l a s t i c i t y problems given only a description  of the (one-dimensional)boundary surfaces of  the s o l i d . Advantages of t h i s technique over other available stress analysis methods, which require as input data a s p e c i f i c a t i o n of the whole body, are as followst 1.  Reduction i n volume of input data, and thus greater ease modelling problems  2.  Savings i n computer time and storage  PROGRAM CAPABILITY Program BITEM solves two-dimensional e l a s t i c i t y problems f o r a piecewise homogeneous isotropic l i n e a r l y e l a s t i c material, using the boundary i n t e g r a l equation technique. Data required by the program include the elastic•properties of each i n d i v i d u a l homogeneous domain, a description of the geometry of the boundary surface of each such domain, and some  o f the displacement  and t r a c t i o n boundary c o n d i t i o n s a l o n g these boun-  d a r i e s . Such boundary c o n d i t i o n s p e c i f i c a t i o n s need o n l y be made on those s u r f a c e s which do not i n t e r f a c e s between a d j o i n i n g r e g i o n s , e.g. on e x c a v a t i o n boundaries i n mining a p p l i c a t i o n s . The program i s capable o f g e n e r a t i n g t h e remaining t r a c t i o n and d i s p l a c e m e n t unknowns on a l l boundaries o f the s o l i d , i n t e r f a c e o r o t h e r w i s e , t o g e t h e r w i t h s t r e s s c a l c u l a t i o n s on the boundaries and s t r e s s and displacement  solutions  f o r s p e c i f i e d l o c a t i o n s w i t h i n the s o l i d . L i n e a r l y v a r y i n g ( r a t h e r than c o n s t a n t v a l u e ) displacements and t r a c t i o n s a r e assumed over the d i s c r e t i z e d segments o f the boundaries. T h i s l i n e a r boundary value approach i s more a c c u r a t e than the constant boundary v a l u e approach,  while r e -  q u i r i n g l i t t l e o r no i n c r e a s e i n computer r u n n i n g times and storage requirements.  In a d d i t i o n t o i t s a p p l i c a b i l i t y i n normal geomechanics  problems,  BITEM i s a b l e t o s o l v e s e v e r a l i n c l u s i o n - t y p e problems;  f o r example,  the problem o f an i n c l u s i o n which has been s t r e s s e d p r i o r t o i t s i n s e r tion i n a solid.  

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