DEVELOPMENT OF EMPIRICAL R I B P I L L A R DESIGN CRITERION
FOR OPEN STOPE MINING
By
MARTIN RAYMOND HUDYMA
B . A . S c , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1986
A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
i n
THE FACULTY OF GRADUATE STUDIES
DEPARTMENT OF MINING AND MINERAL PROCESS ENGINEERING
We a c c e p t t h i s t h e s i s as c o n f o r m i n g
t o t h e r e q u i r e d s t a n d a r d
THE UNIVERSITY OF BRITISH COLUMBIA
September 1988
M a r t i n Raymond Hudyma, 1988
In presenting this thesis in partial fulfilment of the requirements for an advanced
degree at the University of British Columbia, I agree that the Library shall make it
freely available for reference and study. I further agree that permission for extensive
copying of this thesis for scholarly purposes may be granted by the head of my
department or by his or her representatives. It is understood that copying or
publication of this thesis for financial gain shall not be allowed without my written
permission.
Department
The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3
DE-6(3/81)
ABSTRACT
The d e s i g n o f open s t o p e r i b p i l l a r s has been done u s i n g
many e m p i r i c a l me thods , b u t none o f t h e methods has been
v e r i f i e d w i t h a d e s i g n s u r v e y . T h i s t h e s i s u s e s d a t a c o l l e c t e d
i n t h e " I n t e g r a t e d M i n e D e s i g n S t u d y " t o d e v e l o p an e m p i r i c a l
r i b p i l l a r d e s i g n method f o r open, s t o p e m i n i n g . The method i s
c a l l e d t h e " p i l l a r s t a b i l i t y g r a p h " .
The d e s i g n v a r i a b l e s i n t h e method a r e : t h e c o m p r e s s i v e
s t r e n g t h o f t h e i n t a c t p i l l a r m a t e r i a l , t h e a v e r a g e p i l l a r l o a d
d e t e r m i n e d by n u m e r i c a l m o d e l l i n g , t h e p i l l a r w i d t h and t h e
p i l l a r h e i g h t . The g r a p h has been r e f i n e d w i t h t h e use o f more
t h a n 80 l i t e r a t u r e c a s e h i s t o r i e s o f h a r d r o c k p i l l a r s i n room
and p i l l a r m i n i n g .
The p i l l a r s t a b i l i t y g r a p h and t h e p i l l a r d a t a base a r e used
t o examine t h e a p p l i c a b i l i t y o f e m p i r i c a l methods commonly used
i n open s t o p e r i b p i l l a r d e s i g n . The i n v e s t i g a t i o n found t h e
p i l l a r s t r e n g t h c u r v e s d e v e l o p e d by Hoek and Brown (1980) may be
u s e f u l u n d e r some c o n d i t i o n s f o r t h e d e s i g n o f open s t o p e r i b
p i l l a r s b u t f o r m u l a s by H e d l e y ( 1 9 7 2 ) , O b e r t and D u v a l l (1967)
and B i e n i a w s k i (1983) a r e n o t a p p l i c a b l e .
G u i d e l i n e s , u s i n g t h e p i l l a r s t a b i l i t y g r a p h method , a r e
p r o p o s e d f o r t h e d e s i g n o f permanent open s t o p e r i b p i l l a r s ,
s t a b l e t e m p o r a r y open s t o p e r i b p i l l a r s , and f a i l i n g t e m p o r a r y
open s t o p e r i b p i l l a r s .
i i i
TABLE OF CONTENTS
PAGE
ABSTRACT i i
L I S T OF TABLES v i i
L I S T OF FIGURES v i i i
ACKNOWLEDGEMENT x i i i
CHAPTER 1: INTRODUCTION 1
1.1 C o n t e n t s o f t h e T h e s i s 1
1.2 Open S t o p e M i n i n g 2 1 . 2 . 1 D e f i n i t i o n o f Open S t o p i n g 3 1 . 2 . 2 A p p l i c a b i l i t y o f t h e Open S t o p i n g 4 1 .2 .3 D e s c r i p t i o n o f T y p i c a l Open S t o p e
M i n i n g Methods 5
1.3 R o l e o f R i b P i l l a r s i n Open S t o p e M i n i n g 9
CHAPTER 2 : R I B P I L L A R FAILURE 11
2 . 1 F a i l u r e Mechanisms and C h a r a c t e r i s t i c s 11 2 . 1 . 1 Rock F r a c t u r i n g 14 2 . 1 . 2 P i l l a r L o a d - D e f o r m a t i o n C u r v e 17 2 . 1 . 3 L o s s o f L o a d B e a r i n g C a p a c i t y 19
2 . 2 S i g n i f i c a n t V a r i a b l e s i n Open S t o p e P i l l a r S t a b i l i t y 23 2 . 2 . 1 I n t a c t Rock S t r e n g t h 23 2 . 2 . 2 P i l l a r L o a d 23 2 . 2 . 3 P i l l a r Shape and C o n f i n e m e n t 24 2 . 2 . 4 S t r u c t u r a l F e a t u r e s i n P i l l a r s 25 2 . 2 . 5 E f f e c t o f P i l l a r Volume 26 2 . 2 . 6 E f f e c t o f B a c k f i l l 27 2 . 2 . 7 E f f e c t o f B l a s t i n g 30
2 . 3 C h a p t e r Summary 31
CHAPTER 3 : REVIEW OF P I L L A R DESIGN METHODS 32
3 . 1 E m p i r i c a l D e s i g n Methods 32 3 . 1 . 1 P i l l a r S t r e n g t h D e t e r m i n a t i o n 34
3 . 1 . 1 . 1 E m p i r i c a l S t r e n g t h F o r m u l a s 35 3 . 1 . 1 . 2 S a l a m o n ' s F o r m u l a 38
i v
3 . 1 . 1 . 3 H e d l e y ' s F o r m u l a 40 3 . 1 . 1 . 4 O b e r t and D u v a l l Shape E f f e c t F o r m u l a . . 41 3 . 1 . 1 . 5 Hoek and Brown P i l l a r S t r e n g t h C u r v e s . . 43
3 . 1 . 2 P i l l a r Load 45 3 . 1 . 2 . 1 T r i b u t a r y A r e a T h e o r y 45 3 . 1 . 2 . 2 N u m e r i c a l M o d e l l i n g 51
3 . 1 . 3 S a f e t y F a c t o r 51
3 .2 N u m e r i c a l D e s i g n Methods 53 3 . 2 . 1 Types o f N u m e r i c a l Methods 53 3 . 2 . 2 I n t e r p r e t a t i o n o f Boundary E l e m e n t R e s u l t s
i n M i n i n g 57 3 . 2 . 2 . 1 P o s t - P r o c e s s i n g F a i l u r e C r i t e r i o n . . . . 57 3 . 2 . 2 . 2 I n t e r a c t i v e F a i l u r e C r i t e r i o n 60 3 . 2 . 2 . 3 P r i n c i p a l S t r e s s M a g n i t u d e 63
3 . 2 . 3 L i m i t a t i o n s o f Bounda ry E l e m e n t M o d e l l i n g . . . 63 3 . 2 . 3 . 1 M o d e l l i n g a Rock Mass 63 3 . 2 . 3 . 2 C o m p u t a t i o n a l A s s u m p t i o n s 66
CHAPTER 4 : OPEN STOPE R I B P I L L A R DATA BASE 68
4 . 1 G e n e r a l D a t a Base I n f o r m a t i o n 68
4 . 2 B a c k g r o u n d D a t a 69
4 . 3 P i l l a r A s s e s s m e n t 73
CHAPTER 5 : BOUNDARY ELEMENT METHODS I N R I B P I L L A R DESIGN. . 78
5 . 1 Bounda ry E l e m e n t Codes Used 79 5 . 1 . 1 BITEM 79 5 . 1 . 2 MINTAB 81 5 . 1 . 3 BEAP 84
5 .2 Open S t o p e R i b P i l l a r M o d e l l i n g 84 5 . 2 . 1 D e f i n i n g t h e Open S t o p e Geometry 86 5 . 2 . 2 D e f i n i n g t h e A v e r a g e P i l l a r S t r e s s 86
5 .3 2D M o d e l l i n g o f 3D S t o p e G e o m e t r i e s 91 5 . 3 . 1 P l a n e S t r a i n S o l u t i o n 92 5 . 3 . 2 C o m p a r i s o n o f 2D and 3D N u m e r i c a l M o d e l l i n g
R e s u l t s 93
5 .4 D i s p l a c e m e n t D i s c o n t i n u i t y M o d e l l i n g o f 3D S t o p e G e o m e t r i e s 97 5 . 4 . 1 Seam T h i c k n e s s L i m i t a t i o n s 97 5 . 4 . 2 C o m p a r i s o n o f D i s p l a c e m e n t D i s c o n t i n u i t y
and 3D N u m e r i c a l M o d e l l i n g 99
5 .5 P i l l a r L o a d C a l c u l a t i o n s f o r t h e Open S t o p e
V
D a t a Base 102 5 . 5 . 1 A s s u m p t i o n s 103 5 . 5 . 2 P i l l a r L o a d R e s u l t s 103 5 . 5 . 3 N u m e r i c a l M o d e l C o m p a r i s o n U s i n g t h e Case
H i s t o r i e s 107
5 .6 C h a p t e r Summary 110
CHAPTER 6 : DEVELOPMENT OF A P I L L A R DESIGN METHOD 114
6 . 1 C h o i c e o f V a r i a b l e s f o r Open S t o p e P i l l a r D e s i g n . . 115 6 . 1 . 1 A p p l i c a b i l i t y o f S t a t i s t i c a l Methods 115 6 . 1 . 2 D e s i g n V a r i a b l e s 117 6 . 1 . 3 D i s c o u n t e d V a r i a b l e s 118
6 . 1 . 3 . 1 P i l l a r Volume 119 6 . 1 . 3 . 2 S t r u c t u r a l D i s c o n t i n u i t i e s 120
6 .2 P i l l a r S t a b i l i t y Graph 122 6 . 2 . 1 G r a p h i c a l Da ta A n a l y s i s 122 6 . 2 . 2 I n f l u e n c e o f P i l l a r L o a d A p p r o x i m a t i o n s . . . . 126 6 . 2 . 3 I m p o r t a n c e o f Y i e l d i n g P i l l a r Case H i s t o r i e s . 128 6 . 2 . 4 L i m i t a t i o n s o f t h e P i l l a r S t a b i l i t y G r a p h . . . 130
6 .3 D a t a f rom L i t e r a t u r e 131 6 . 3 . 1 D a t a f rom C a n a d i a n Room and P i l l a r M i n i n g . . . 131 6 . 3 . 2 D a t a f rom a Botswana Room and P i l l a r M i n e . . . 134 6 . 3 . 3 D a t a f rom an A u s t r a l i a n Open S t o p e M i n e . . . . 139 6 . 3 . 4 Summary o f A l l t h e D a t a 143
6 .4 C o m p a r i s o n A g a i n s t O t h e r D e s i g n Methods 143 6 . 4 . 1 H e d l e y ' s P i l l a r S t r e n g t h F o r m u l a 146 6 . 4 . 2 Hoek and Brown P i l l a r S t r e n g t h C u r v e s 151 6 . 4 . 3 P i l l a r Shape E f f e c t F o r m u l a s 152
6 .5 C h a p t e r Summary 158
CHAPTER 7: DESIGNING R I B P I L L A R S FOR OPEN STOPE MINING. . . 160
7 . 1 Permanent P i l l a r s 162
7 .2 Tempora ry P i l l a r s 163 7 . 2 . 1 S t a b l e Temporary P i l l a r s 165 7 . 2 . 2 F a i l e d Temporary P i l l a r s 166
7 .3 Case E x a m p l e : T r a n s v e r s e R i b P i l l a r s a t N o r i t a . . . 167 7 . 3 . 1 G e o l o g y and M i n i n g Method 167 7 . 3 . 2 Back A n a l y s i s U s i n g t h e P i l l a r S t a b i l i t y
Graph 170 7 . 3 . 3 Comments C o n c e r n i n g t h e P i l l a r D e s i g n 173
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CHAPTER 8: SUMMARY AND CONCLUSIONS 174
8.1 Summary 174 8.1.1 Open Stope Rib P i l l a r F a i l u r e 174 8.1.2 Current P i l l a r Design Methods 175 8.1.3 I d e n t i f i c a t i o n and Quantification of the
Design Varaibles 176 8.1.4 Development of the P i l l a r S t a b i l i t y Graph. . . 177
8.2 Conclusions 179 8.2.1 A p p l i c a b i l i t y of the Method 179 8.2.2 Limitations of the Method 179 8.2.3 Design of Open Stope Rib P i l l a r s 180
8.3 Future Work 181
REFERENCES 183
APPENDIX 1 190
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L I S T OF TABLES
PAGE
TABLE 1. Constants proposed by various authors f o r the 36 s i z e e f f e c t formula (after Babcock, Morgan and Haramy 1981).
TABLE 2. Constants proposed by various authors f o r the 37 shape e f f e c t formula (after Babcock, Morgan and Haramy 1981).
TABLE 3. Constants proposed by various authors f o r the 37 shape e f f e c t formula (after Babcock, Morgan and Haramy 1981).
TABLE 4. The safety factors proposed by various authors 52 for empirical p i l l a r design i n entry mining methods.
TABLE 5. Background data for a l l the p i l l a r case 70 h i s t o r i e s .
TABLE 6. Comparison of BEAP and BITEM for four sets of 94 d i f f e r e n t orebody geometries.
TABLE 7. Comparison of BEAP and MINTAB for the four 98 d i f f e r e n t t e s t s .
TABLE 8. P i l l a r load information for a l l the open stope 105 r i b p i l l a r case h i s t o r i e s using BITEM, MINTAB and the Tributary Area Theory.
TABLE 9. Comparison of MINTAB and BITEM r e s u l t s , when 107 both programs l i m i t a t i o n s are s a t i s f i e d .
TABLE 10. Comparison of BITEM and MINTAB, when the MINTAB 108 l i m i t a t i o n i s met, but the BITEM l i m i t a t i o n i s not met.
TABLE 11. Comparison between good BITEM and poor MINTAB 111 geometries shows the average p i l l a r stress varying up to ± 25%.
TABLE 12. Data used by Von Kimmelmann et a l . (1984) i n 136 the development of a p i l l a r f a i l u r e c r i t e r i o n .
TABLE 13. Comparison of the value of ore for mines using 161 temporary p i l l a r s against mines using permanent p i l l a r s .
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L I S T OF FIGURES
PAGE
FIGURE 1. The elements of an i d e a l i z e d l o n g i t u d i n a l 6 longhole open stoping method showing the b l a s t i n g , mucking and b a c k f i l l i n g operations.
FIGURE 2. The elements of an i d e a l i z e d transverse 7 blasthole open stoping method showing the d r i l l i n g , b l a s t i n g , mucking and b a c k f i l l i n g operations.
FIGURE 3a. P a r a l l e l f r a c t u r i n g and s p a l l i n g due to a lack 16 of confinement at the p i l l a r walls.
FIGURE 3b. Internal s p l i t t i n g and a x i a l cracking of a 16 p i l l a r due to deformable p i l l a r layers or the propagation of p a r a l l e l wall fractures.
FIGURE 3c. Diagonal crushing fractures may occur i n 16 confined or massive p i l l a r s .
FIGURE 4. A hypothetical load-deformation curve can be 18 used to describe the s t r e s s - s t r a i n c h a r a c t e r i s t i c s of a p i l l a r .
FIGURE 5. Wagner (1974) did a series of i n s i t u load- 20 deformation t e s t s on coal p i l l a r s using hydraulic jacks. The graph on the top shows the load-deformation c h a r a c t e r i s t i c s of the p i l l a r i n general. The oblique diagrams give the r e l a t i v e load on each of the 25 jacks at four stages of p i l l a r compression.
FIGURE 6. The s t r e s s - s t r a i n curves for laboratory 2 2 specimens loaded under increasing confining pressures show an increase i n peak load and an increase i n the post-peak load bearing capacity.
FIGURE 7. There i s a very large influence of specimen 28 s i z e on the strength of i n t a c t rock, f o r small specimen diameters.
FIGURE 8. Strength t e s t i n g of samples of increasing 28 specimen length shows a decreasing influence of s i z e .
FIGURE 9. Histogram of the safety factors for stable and 39 f a i l e d p i l l a r case h i s t o r i e s i n South Af r i c a n bord and p i l l a r coal mining.
ix
FIGURE 10. The estimated stress and strength f o r case 42 h i s t o r i e s of p i l l a r s i n room and p i l l a r mining i n the E l l i o t lake uranium mining d i s t r i c t .
FIGURE 11. Hoek and Brown (1980) proposed a serie s of 44 p i l l a r strength curves based on the t h e o r e t i c a l d i s t r i b u t i o n of rock mass f a i l u r e i n a p i l l a r .
FIGURE 12. The analogy of streamlines i n a smoothly 47 flowing stream obstructed by bridge p i e r s i s often used to describe the concentration of stress i n p i l l a r s .
FIGURE 13. The t r i b u t a r y area theory, for average p i l l a r 47 load c a l c u l a t i o n , applied to several d i f f e r e n t p i l l a r layouts.
FIGURE 14. Salamon (1974) showed the v a r i a t i o n i n p i l l a r 49 stress caused by increasing the number of p i l l a r s (N) i n a mining panel. The graph shows a d i s t i n c t influence of the l o c a t i o n of a p i l l a r and the number of p i l l a r s on the stress induced.
FIGURE 15. A study using two dimensional boundary element 50 numerical modelling shows the influence of p i l l a r shape and the number of p i l l a r s on the average stress.
FIGURE 16. An i d e a l i z e d sketch showing the p r i n c i p l e of 54 numerical modelling of underground excavations.
FIGURE 17. An empirical f a i l u r e c r i t e r i o n has been 59 applied to the two dimensional stress d i s t r i b u t i o n of a stable open stope r i b p i l l a r .
FIGURE 18. The t h e o r e t i c a l d i s t r i b u t i o n of f a i l e d rock i s 59 much greater i n t h i s p i l l a r .
FIGURE 19. The peak strength, deformation character- 61 i s t i c s , and e f f e c t of lo c a t i o n used for investigating a p i l l a r case hi s t o r y with a displacement d i s c o n t i n u i t y program.
FIGURE 20. The normal stress and the f a i l e d regions 61 estimated with the displacement d i s c o n t i n u i t y program for a s i l l p i l l a r case his t o r y .
FIGURE 21. The d i s t r i b u t i o n of normal stress i n a mining 64 block was estimated for two d i f f e r e n t mining sequences to determine the best stope extraction sequence.
FIGURE 22. This figure shows the geometrical d e f i n i t i o n 72 for the stope and p i l l a r dimensions used i n t h i s t h e s i s .
X
FIGURE 23. Isometric view of an opening that i s long i n 80 one d i r e c t i o n and the d i s c r e t i z a t i o n of the boundary used i n two dimensional modelling.
FIGURE 24. Oblique view of the MINTAB seam geometry and 83 the stress applied l o c a l l y on each element i n the reef.
FIGURE 25. A t y p i c a l BEAP geometry showing the boundary 85 of the excavations defined by two dimensional quadratic, non-conforming elements i n a three dimensional stress f i e l d .
FIGURE 26. This figure defines the dimensions f o r stopes 87 and p i l l a r s , and the orientation for the i n s i t u stress regime for t h i s t h e s i s .
FIGURE 27a. A r i b p i l l a r i n a horizontal seam loaded by 88 the weight of the overburden.
FIGURE 27b. The d i r e c t i o n of loading on a p i l l a r i n a 88 v e r t i c a l orebody.
FIGURE 28. The mid-height plane and centerline for t a l l 90 open stope geometries.
FIGURE 29. The shaded plane has the greatest influence on 94 the mid-height a v stress.
FIGURE 30. Overestimation of average p i l l a r load by the 96 2D "BITEM" boundary element method for the 12 runs i n the four t e s t s .
FIGURE 31. The dimensions and geometry of the MINTAB/BEAP 98 comparison t e s t s .
FIGURE 32. The difference between the average p i l l a r 101 stress predicted by MINTAB and the average p i l l a r stress predicted by BEAP for the comparison t e s t s .
FIGURE 33. Overestimation of average p i l l a r load by the 109 2D "BITEM" boundary element method for the comparison t e s t s and 3 case h i s t o r i e s .
FIGURE 34. The difference between the average p i l l a r 112 stress predicted by MINTAB and the average p i l l a r stress predicted by BEAP for the comparison t e s t s and 13 case h i s t o r i e s .
FIGURE 35. The p i l l a r s t a b i l i t y graph showing the open 123 stope r i b p i l l a r data base.
FIGURE 36. The p i l l a r s t a b i l i t y graph showing the stable 125 and f a i l e d zones and the t r a n s i t i o n area.
FIGURE 37. The p i l l a r s t a b i l i t y graph with the p i l l a r 127 load reduced for a l l the data points by the maximum amount l i s t e d i n Table 8.
FIGURE 38. The p i l l a r s t a b i l i t y .graph with a l l the case 129 h i s t o r i e s of the 13 y i e l d i n g p i l l a r s joined by s o l i d l i n e s .
FIGURE 39. The p i l l a r s t a b i l i t y graph showing the data 133 from room and p i l l a r mining published by Hedley and Grant (1972) i n t h e i r study on the development of a p i l l a r strength formula.
FIGURE 40. A plan view of room and p i l l a r mining at BCL 137 Limited, showing the use of long p i l l a r s and square p i l l a r s .
FIGURE 41. The p i l l a r s t a b i l i t y graph showing the long 138 p i l l a r data presented by Von Kimmelmann et a l . (1984).
FIGURE 42. The square p i l l a r data presented by Von 140 Kimmelmann et a l . (1984) i s plotted on the s t a b i l i t y graph using an e f f e c t i v e width i n the H/W r a t i o .
FIGURE 43. The f i v e stages of the S86 p i l l a r i n an open 142 stope p i l l a r t e s t at Mt. Isa (after Brady 1977).
FIGURE 44. The t h i r d , fourth, and f i f t h stages of the S86 144 open stope r i b p i l l a r , presented by Brady (1977), are shown on the p i l l a r s t a b i l i t y graph.
FIGURE 45. The p i l l a r s t a b i l i t y graph showing the open 145 stope r i b p i l l a r data and the l i t e r a t u r e data.
FIGURE 46. The range of r i b p i l l a r dimensions seen i n 17 148 Canadian open stope mines.
FIGURE 47. Comparison of the p i l l a r s t a b i l i t y graph and 150 Hedley's formula for two safety factors.
FIGURE 48. Three of the Hoek and Brown (1980) p i l l a r 153 strength curves plotted on the p i l l a r s t a b i l i t y graph.
FIGURE 49. Comparison between the p i l l a r s t a b i l i t y graph 155 and the Obert and Duval1 (1967) shape e f f e c t formula applied with a safety factor of 1.0.
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FIGURE 5 0 . The shape e f f e c t f o r m u l a p r o p o s e d by 157 B i e n i a w s k i (1983) a p p l i e d w i t h t h r e e d i f f e r e n t s a f e t y f a c t o r s i s compared a g a i n s t t h e p i l l a r s t a b i l i t y g r a p h .
FIGURE 5 1 . The r ange o f t e m p o r a r y r i b p i l l a r d i m e n s i o n s 164 u s e d i n 14 C a n a d i a n open s t o p e m i n e s .
FIGURE 5 2 . I s o m e t r i c v i e w o f t r a n s v e r s e b l a s t h o l e open 168 s t o p i n g a t N o r i t a .
FIGURE 5 3 . A l o n g i t u d i n a l s e c t i o n o f t h e b l a s t h o l e open 171 s t o p i n g b l o c k a t N o r i t a s h o w i n g t h e p i l l a r c a s e h i s t o r i e s ( 1 0 - 6 , 1 0 - 7 , and 10-8) u s e d i n t h i s c a s e h i s t o r y a n a l y s i s .
FIGURE 54 . The p i l l a r s t a b i l i t y g r a p h s h o w i n g t h e 172 l o c a t i o n o f t h e s t a b l e and f a i l e d t r a n s v e r s e p i l l a r c a s e h i s t o r i e s a t N o r i t a .
ACKNOWLEDGEMENT
The author wishes to acknowledge Noranda Research, Falcon-bridge Limited, the Natural Sciences and Engineering Research Council and the Cy and Emerald Keyes scholarship fund for f i n a n c i a l support during the project.
Thanks are extended to the employees of the mines and groups which provided time and information to the study:
- Algoma Steel Corp. Limited - G.W. Macleod Mine - Barrick Resources - Camflo Mine - BP Canada Inc. - Mines Selbaie - Cambior - Niobec Mine - Corporation of Falconbridge Copper - Corbet Mine, Lac
Shortt Mine - Dome Mines Limited - Falconbridge Limited - East Mine, Fraser Mine, Kidd Creek,
Lockerby Mine, Mining Technology Divis i o n , Onaping Mine, Strathcona Mine
- Hudson Bay Mining and Smelting - Centennial Mine, Chisel Lake Mine, F l i n Flon Mine, Spruce Point Mine
- Inco Limited - L i t t l e Stobie Mine, Mine Research Division, Stobie Mine, Thompson Di v i s i o n
- Kiena Gold Mines - Noranda Minerals Inc. - Brunswick Mining and Smelting,
Chadbourne Mine, Geco Mine, Golden Giant Mine, Lyon Lake Mine, Mattabi Mine, Mattagami Lake Mine, Mines Gaspe, Mining Technology Divis i o n , Norita Mine
- Pamour Porcupine Mines Limited - Ross Mine, No. 1 Mine - S h e r r i t t Gordon - Ruttan Mine - Westmin Resources Limited.
Also, thanks to Dr. H.D.S. M i l l e r for h i s e f f o r t s i n sett i n g up the Integrated Mine Design Project.
Sincere gratitude i s expressed to Professor Alan Reed for his comments and help i n writing the thesis and the members of the Department of Mining and Mineral Process Engineering at UBC for help and support during the project.
Special thanks to my partner Mr. Yves Potvin. His technical contributions and advice have had an immeasurable influence on t h i s t h e s i s and my understanding of mining and rock mechanics.
F i n a l l y , and most of a l l , I wish to express my thanks to Harry and N e l l i e Hudyma for t h e i r continuous encouragement and support during a l l my endeavors.
1
CHAPTER 1
INTRODUCTION
Open stope mining has been practiced i n Canada since the
1930's. The design of open stope mines i s centered around
determining the largest stable stopes and the optimum siz e for
p i l l a r s . Systematic methods to design open stopes and t h e i r
separating " r i b " p i l l a r s have not been confirmed i n t y p i c a l
Canadian open stope mining conditions. In 1986, the Natural
Sciences and Engineering Research Council (NSERC), Noranda
Research and Falconbridge Limited agreed to sponsor the
"Integrated Mine Design Project", a research project at the
University of B r i t i s h Columbia under the supervision of Dr.
H.D.S. M i l l e r . The goal of the study was to investigate open
stope mine design methods by confirming the v a l i d i t y of ex i s t i n g
stope and r i b p i l l a r design methods or by developing new
empirical methods. This thesis i s a compilation and analysis of
the information and data c o l l e c t e d for the design of r i b p i l l a r s
i n open stope mining.
The f i r s t section of t h i s chapter i s a summary of the
contents of the th e s i s . The remainder of the chapter w i l l
introduce the problem of designing open stope r i b p i l l a r s by
describing open stope mining, and discussing the r o l e of r i b f
p i l l a r s i n open stope mining.
1.1 Contents of the Thesis
2
T h i s s t u d y b e g i n s by d e s c r i b i n g open s t o p e m i n i n g and t h e
r o l e o f r i b p i l l a r s i n open s t o p e m i n i n g . I n C h a p t e r 2 , t h e
c h a r a c t e r i s t i c s o f p r o g r e s s i v e p i l l a r f a i l u r e a r e d i s c u s s e d and
t h e f a c t o r s t h a t i n f l u e n c e r i b p i l l a r s t a b i l i t y a r e i d e n t i f i e d .
C h a p t e r 3 c o n t a i n s a r e v i e w o f t h e e m p i r i c a l and n u m e r i c a l
d e s i g n methods u s e d f o r open s t o p e r i b p i l l a r s . The r i b p i l l a r
d a t a c o l l e c t e d i n t h e I n t e g r a t e d M i n e D e s i g n P r o j e c t i s
p r e s e n t e d i n C h a p t e r 4 . C h a p t e r 5 d i s c u s s e s t h e use o f boundary
e l e m e n t n u m e r i c a l methods t o d e t e r m i n e t h e a v e r a g e s t r e s s i n
open s t o p e r i b p i l l a r s . The l o a d i n d u c e d on a l l o f t h e d a t a
base p i l l a r s i s e s t i m a t e d i n t h i s s e c t i o n . C h a p t e r 6 shows t h e
d e v e l o p m e n t o f a new e m p i r i c a l p i l l a r d e s i g n method c a l l e d t h e
" P i l l a r S t a b i l i t y G r a p h " , ba sed on g r a p h i c a l a n a l y s i s o f t h e r i b
p i l l a r d a t a and d a t a from l i t e r a t u r e . I t a l s o compares t h e new
method w i t h e x i s t i n g e m p i r i c a l d e s i g n methods f o r open s t o p e r i b
p i l l a r s . C h a p t e r 7 b r i e f l y d i s c u s s e s t h e a p p l i c a t i o n o f t h e
p i l l a r s t a b i l i t y g r a p h f o r t h e d e s i g n o f open s t o p e r i b p i l l a r s .
A summary and c o n c l u s i o n o f t h e t h e s i s i s f ound i n C h a p t e r 8.
1.2 Open S t o p e M i n i n g
Open s t o p e m i n i n g i s a g e n e r a l name u s e d t o d e s c r i b e a
h i g h l y v a r i e d m i n i n g me thod . The re a r e many i m p o r t a n t f e a t u r e s
t h a t make up t h e method , and many v a r i a t i o n s on e a c h o f t h e
f e a t u r e s . The f o l l o w i n g d i s c u s s i o n o f t h e d e f i n i t i o n ,
a p p l i c a b i l i t y , and d e s c r i p t i o n o f open s t o p e m i n i n g i s t a k e n
l a r g e l y f rom an u n p u b l i s h e d p a p e r on open s t o p e m i n i n g methods ,
3
written at U.B.C. (Hudyma 1988a).
1.2.1 D e f i n i t i o n of Open Stoping
Three c h a r a c t e r i s t i c s , common to a l l open stoping methods,
make i t d i s t i n c t from other mining methods.
i) Open stoping i s a non entry mining method. Once stope
production has started, a l l a c t i v i t i e s requiring miners are
done from the periphery of the stope. The open stope does
not need to be entered and at no time are miners exposed to
the production face,
i i ) I t i s generally a nat u r a l l y supported mining method
(although some a r t i f i c i a l support i s occasionally used).
Naturally supported means that displacement and deformation
of the rock mass i s li m i t e d to e l a s t i c orders of magnitude.
The underground structures created are designed to be
s t a b l e and self-supporting (in opposition to caving
methods) . Mining i s done i n a manner to ensure that
unstable release of energy due to mining does not occur
(from Brady 1981).
i i i ) Stopes are opened to t h e i r f u l l dimensions before a
s t a b i l i z i n g f i l l i s introduced.
These three c h a r a c t e r i s t i c s d i s t i n g u i s h open stoping from
a l l other underground methods. Cut and f i l l , longwall, room and
p i l l a r and shrinkage are a l l entry methods that require workers
to enter the production face of the stope. Block caving and
4
sublevel caving induce large, unstable movements of rock and
include the continual d i s s i p a t i o n of energy as mining proceeds,
so they can not be considered nat u r a l l y supported methods.
Methods such as AVOCA, which introduces f i l l during extraction
to prevent stope i n s t a b i l i t y , or shrinkage stoping, which keeps
the stope f u l l of broken ore, are excluded from open stoping
because the stope i s never f u l l y open.
1.2.2 A p p l i c a b i l i t y of Open Stoping
There are some orebody and geological l i m i t a t i o n s to the
a p p l i c a t i o n of open stoping. Modifications of open stoping can
be made to mine a wide v a r i e t y of orebodies, but some conditions
present d i f f i c u l t problems.
Open stoping i s best suited to orebodies that are steep
dipping. Stopes i n the orebody must dip s u f f i c i e n t l y above the
angle of repose of the broken ore (above 50° to 55°) to permit
gravity flow of the ore to the stope bottom. Open stoping can
be successful i n shallow dipping orebodies (approximately less
than 30°) but the orebody must be quite t h i c k (greater than
about 15 metres i n true thickness). I f an orebody i s not steep
dipping or t h i c k and f l a t , open stoping can not be used.
For mining a steep dipping orebody, the orebody outline must
be f a i r l y regular and the orebody needs to be greater than about
5 metres i n width. Irregular orebodies are d i f f i c u l t to
delineate and mine. Generally, at widths less than 5 metres,
wall rock d i l u t i o n due to d r i l l hole deviation and b l a s t damage
5
becomes too great to use open stoping e f f e c t i v e l y .
The rock mass strength of the orebody and the surrounding
country rock i s very important i n open stoping. The stronger
the rock, the larger the stopes can be made, and consequently,
the more productive the method w i l l be. At the l e a s t , f a i r rock
mass strength i s needed i n the ore and wall rock to guarantee
that the open stopes w i l l be naturally supporting.
A f i n a l r e s t r i c t i o n on open stoping i s the orebody must be
reasonably large. This i s necessary to get a few working faces
(because open stoping i s often a c y c l i c a l method), to take
advantage of the large scale of the mining method, and to
j u s t i f y the cost of the development associated with open stope
mining.
1.2.3 Description of Typical Open Stope Mining Methods
Open stoping methods are so dependent on the orebody shape,
si z e and orie n t a t i o n that no two mines are exactly the same.
Most open stope mining a c t i v i t i e s can be generalized into two
basic stages: pre-mining development and production. Open
stoping has a large amount of pre-mining development. Typical
development usually includes:
- sublevel accesses such as ramps, man-way rai s e s (figure 1,
note A), and sublevel d r i f t s (figures 1 and 2, note B),
- a d r i l l i n g horizon which includes stope access d r i f t s
(figures 1 and 2, note C) and d r i l l drives (figure 1, note
D) or overcuts (figure 2, note E),
LEGEND
A - MAN WAY-RAISE F - FOOTWALL HAULAGE DRIFT B - SUBLEVEL DRIFT H - DRAWPOINT C STOPE ACCESS DRIFT I - COLLECTION CONE D - DRILL DRIFTS L - RING DRILL PATTERN
FIGURE 1. The elements of an Ideal ized l o n g i t u d i n a l longhole open stoping method showing the b l a s t i n g , mucking and b a c k f i l l i n g operations (after Hudyma 1988a).
3
LEGEND
B - SUBLEVEL DRIFT G - FULL STOPE UNDERCUT C - STOPE ACCESS DRIFT H - DRAWPOINT E - FULL STOPE OVERCUT J - SLOT RAISE F - FOOTWALL HAULAGE DRIFT K - PARALLEL DRILL HOLES
FIGURE 2. The elements of an i d e a l i z e d transverse blasthole open stoping method showing the d r i l l i n g , b l a s t i n g , mucking and b a c k f i l l i n g operations (af t e r Hudyma 1988a).
8
- a mucking horizon, which may include:
- a footwall haulage d r i f t (figures 1 and 2, note F),
- stope access undercuts (figure 2, note G) or
drawpoints (figures 1 and 2, note H),
- stope undercut scrams, V-cuts or c o l l e c t i o n cones
(figure 1, note I ) ,
- the opening of a s l o t r a i s e (figure 2, note J) by staging,
drop r a i s i n g , Alimak r a i s e climber or by r a i s e borer.
Production mining involves:
- using p a r a l l e l d r i l l holes to slash ore into the s l o t r a i s e
to form an expansion s l o t which i s opened the f u l l width of
the stope,
- d r i l l i n g production holes i n p a r a l l e l (figure 2, note K) or
rin g patterns (figure 1, note L) . The holes are used to
b l a s t ore into the expansion s l o t .
Generally, the expansion s l o t i s opened at one end of the stope
and ore i s slashed into the s l o t causing a gradual retreat of
the production face. This retreat may be longitudinal (along
the orebody, as i n figure 1) or transverse (across the orebody,
as i n figure 2).
As a stope i s blasted, ore i s removed from the bottom of the
stope. The ore i s almost always removed with the use of
track l e s s load-haul-dump equipment, and taken to an orepass
system. There are a few mines using slusher/scraper equipment
or continuous mining equipment to move the muck to an orepass,
but these operations are quite rare. The ore pass system moves
9
the muck to a central c o l l e c t i o n point for transport out of the
mine. When the stope i s completely blasted, i t may be f i l l e d
with waste rock or c l a s s i f i e d m i l l t a i l i n g s to permit recovery
of p i l l a r s l e f t between stopes (both figures 1 and 2 show the
f i l l i n g of stopes).
1.3 Role of Rib P i l l a r s i n Open Stope Mining
The most economic open stope method involves mining the
enti r e orebody i n one longitudinal stope. I f the use of t h i s
f u l l lens mining creates the p o t e n t i a l for serious stope
i n s t a b i l i t y , major stope support such as r i b p i l l a r s and
b a c k f i l l w i l l l i k e l y be needed. The r o l e of r i b p i l l a r s i n open
stope mining i s to provide s t a b i l i t y to a mining block by
l i m i t i n g rock mass displacements and r e s t r i c t i n g the exposure of
the rock mass i n the stope back and walls.
In the past, i f f u l l lens mining was not possible, p i l l a r s
had to be l e f t to maintain o v e r a l l mine s t a b i l i t y . Recently,
improvements i n mining technology have caused a trend towards
the sequencing of extraction so that p i l l a r s are never created,
even i n very large orebodies. However, of the 34 Canadian open
stope mines investigated i n t h i s study (from 1986-1988), 27 used
r i b p i l l a r s to separate stopes i n the orebody. These p i l l a r s
varied i n s i z e from about 2000 m3 up to 150,000 m3, depending on
factors such as: the orebody geometry, the type of open stoping
method, and the mining sequence. The dimensions of the p i l l a r s
i n the data base are given i n Chapter 4.1 (Table 5, page 70).
10
I t i s important that r i b p i l l a r s perform t h e i r designed
r o l e . Mines using r i b p i l l a r s may leave as much as h a l f of the
orebody reserves i n temporary p i l l a r s . The consequences of poor
p i l l a r design can serio u s l y a f f e c t the recovery of t h i s ore. A
p i l l a r that does not perform i t s intended r o l e may cause:
- excessive stope or p i l l a r sloughing,
- d i f f i c u l t and expensive p i l l a r recovery,
- loss of p i l l a r access,
- the need f o r remedial measures such as development
r e h a b i l i t a t i o n or a r t i f i c i a l support,
- low productivity,
- or the loss of ore reserves.
11
CHAPTER 2
RIB PILLAR FAILURE
The f i r s t step i n quantifying the variables that influence
p i l l a r s t a b i l i t y i s to describe p i l l a r f a i l u r e . While open
stope r i b p i l l a r f a i l u r e has not been deeply researched, some of
the p r i n c i p l e s of f a i l u r e i n i n t a c t hard rock, s o f t rock and
rock masses are applicable to open stope r i b p i l l a r s . The
objective of t h i s chapter i s to b r i e f l y discuss the character
i s t i c s of p i l l a r i n s t a b i l i t y and compare them to observations
and documentation of f a i l u r e i n open stope r i b p i l l a r s . Using
these ideas about p i l l a r f a i l u r e , the factors that influence the
s t a b i l i t y of open stope p i l l a r s w i l l be i d e n t i f i e d .
2.1 F a i l u r e Mechanisms and Ch a r a c t e r i s t i c s
Rib p i l l a r f a i l u r e can be broken into two basic modes:
progressive (stable) f a i l u r e and bursting (unstable) f a i l u r e .
Progressive f a i l u r e r e f e r s to gradual d e t e r i o r a t i o n of a rock
mass i n a slow, non-violent manner. Bursting f a i l u r e i s the
v i o l e n t release of energy causing the instantaneous fracture of
rock. Although the conditions associated with each may be very
d i f f e r e n t , both modes of f a i l u r e create serious d i f f i c u l t i e s for
mining.
This thesis w i l l describe and quantify progressive f a i l u r e .
Progressive f a i l u r e i s related to the i n s i t u rock properties of
the p i l l a r and mine, and the s t a t i c underground stress f i e l d .
12
Both of these factors are quantifiable with reasonable accuracy.
Bursting f a i l u r e i s also related to i n s i t u rock properties.
However, i t i s also dependent upon factors such as l o c a l stress
concentration, the energy released due to the mining and
changes i n the dynamic stress f i e l d . I t i s not intended to
investigate these factors as they are not quantifiable with
technology and budget available for t h i s study. For t h i s
reason, the thesis w i l l not attempt to describe or quantify
unstable f a i l u r e .
Although r i b p i l l a r f a i l u r e i n open stope mining i s not
uncommon, i t i s r a r e l y well documented. A reason for the lack
of documentation i s that v i s u a l observation and monitoring of
p i l l a r s i s d i f f i c u l t i n open stope mining and there i s no t
universal method to describe the c h a r a c t e r i s t i c s and e f f e c t s of
r i b p i l l a r f a i l u r e . Another pot e n t i a l reason for the absence of
documentation i s that the f a i l u r e of r i b p i l l a r s i s often not
considered an immediate problem, e s p e c i a l l y with open stope
mining methods using b a c k f i l l . In the primary mining, r i b
p i l l a r f a i l u r e often does not cause operational problems that
are serious enough to warrant changing the mining sequence.
Consequently, the operational e f f e c t s of r i b p i l l a r f a i l u r e may
not be experienced u n t i l p i l l a r mining s t a r t s . This f a i l u r e
often r e s u l t s i n low productivity, waste d i l u t i o n , higher mining
costs and possibly l o s t ore.
Several signs i n d i c a t i n g p i l l a r s t a b i l i t y problems i n open
stope r i b s have been i d e n t i f i e d . These signs of p i l l a r d i s t r e s s
13
are:
- cracking and s p a l l i n g of rock i n r i b p i l l a r development
and r a i s e s ,
- audible noise heard i n the p i l l a r s or microseismic events
located with monitoring systems,
- deformed or plugged d r i l l holes causing d r i l l rods to be
stuck and causing problems i n loading holes,
- overdraw from primary stopes with the "free" muck being
unblasted, oversize material from p i l l a r walls,
- stress r e d i s t r i b u t i o n from r i b p i l l a r s a f f e c t i n g nearby
p i l l a r s and hanging wall and footwall d r i f t s and raises,
- hourglassing and cracking of p i l l a r s seen from
development,
- major displacements and changes i n stress shown by
instrumented monitoring systems such as extensometers,
stress meters and sloughmeters.
No singl e sign necessarily denotes p i l l a r f a i l u r e , but these
signs are commonly reported during p i l l a r f a i l u r e .
Progressive p i l l a r f a i l u r e i s a gradual process. Problems
may be minor at f i r s t , but get worse with time. P i l l a r damage
and d e t e r i o r a t i o n can occur through i n t a c t rock and along
e x i s t i n g s t r u c t u r a l d i s c o n t i n u i t i e s . Although p u r e l y
s t r u c t u r a l l y c o n t r o l l e d f a i l u r e s occur i n p i l l a r s , the ov e r a l l
influence of geological structure i n open stope p i l l a r s i s not
predominant. Stress, p i l l a r loading and development of stress
r e l a t e d fractures appears to be predominant. Consequently, the
14
discussion of r i b p i l l a r f a i l u r e w i l l focus on rock fracturing,
p i l l a r loading, and the subsequent loss of p i l l a r load bearing
a b i l i t y .
2.1.1 Rock Fracturing
Rock f r a c t u r i n g i s a primary indicator of p i l l a r f a i l u r e and
i s the ultimate reason for the loss of load bearing a b i l i t y and
p i l l a r d i s i n t e g r a t i o n . Brady and Brown (1985) define
f r a c t u r i n g as " . . . the formation of planes of separation i n
the rock material. I t involves the breaking of bonds to form
new surfaces." Fracturing generally s t a r t s at the p i l l a r walls
where the rock mass i s weakest due to the lack of confinement of
p i l l a r material. As f a i l u r e progresses, fractures propagate and
develop i n the central parts of the p i l l a r and the s i z e and
i n t e n s i t y of e x i s t i n g fractures increases.
Krauland and Soder (1987) defined 6 stages to c l a s s i f y
p i l l a r f a i l u r e based on v i s u a l observation of p i l l a r f r a c t u r i n g
i n room and p i l l a r mines. The stages defined are:
"0) No fractures. 1) S l i g h t s p a l l i n g of p i l l a r corners and p i l l a r walls, with
short fracture lengths i n r e l a t i o n to p i l l a r height, subparallel to p i l l a r walls.
2) One or a few fractures near surface, d i s t i n c t s p a l l i n g . 3) Fractures appear also i n central parts of the p i l l a r . 4) One or a few fractures occur through central parts of the
p i l l a r , d i v i d i n g i t into two or several parts, with rock f a l l s from the p i l l a r . Fractures may be p a r a l l e l to p i l l a r walls or diagonal, i n d i c a t i n g emergence of an hour-glass-shaped p i l l a r .
5) Disintegration of the p i l l a r . Major blocks f a l l out and/or the p i l l a r i s cut o f f by well defined fractures. A l t e r n a t i v e l y , a well developed hour-glass shape may emerge, with central parts completely crushed."
15
Krauland and Soder also noted that although the appearance of
p i l l a r f a i l u r e was h i g h l y v a r i a b l e due to g e o l o g i c a l
inhomogeneities, the basic pattern of f a i l u r e propagation
remained constant for progressive f a i l u r e . This i s perhaps the
best documentation and d e f i n i t i o n of an actual mine p i l l a r
f a i l u r e mechanism. Use of the Krauland and Soder observational
approach to c l a s s i f y open stope p i l l a r s i s not generally
possible due to the lack of v i s u a l access. However, the mode of
f a i l u r e described above i s s i m i l a r to that seen by the author i n
several open stope mines and i s documented i n a few open stope
mines (Falmagne 1986; Bray 1967) where s u f f i c i e n t v i s u a l access
was av a i l a b l e . The only observation of Krauland and Soder that
t h i s author has not seen i n open stope mining i s the d i v i s i o n of
p i l l a r s into d i s t i n c t regions due to fr a c t u r i n g . This part of
the mechanism i s not l i k e l y to occur i n open stope p i l l a r s . The
pot e n t i a l for a fracture to completely sever a p i l l a r i s much
lower i n open stope mining than i n room and p i l l a r mining due to
the larger scale of open stope p i l l a r s . Fractures would have to
be very continuous, f l a t and planar to transect and divide open
stope p i l l a r s .
From personal observation and l i t e r a t u r e descriptions, some
of the most common types of fr a c t u r i n g found i n mine p i l l a r s
are:
i) surface fr a c t u r i n g and s p a l l i n g (figure 3a) i s usually
the f i r s t l o c a t i o n of fracture development (Krauland and Soder
1987) and often a r e s u l t of lack of p i l l a r wall confinement
original pillar surface
FIGURE 3a. P a r a l l e l f racturing and s p a l l i n g due to a lack of confinement at the p i l l a r walls (after Brady and Brown 1985).
-soft partings
- internal splitting
FIGURE 3b. Internal s p l i t t i n g and a x i a l cracking of a p i l l a r due to deformable p i l l a r layers or the propagation of p a r a l l e l wall fractures (af t e r Brady and Brown 1 9 8 5 ) .
FIGURE 3c. Diagonal crushing fractures may occur i n confined or massive p i l l a r s ( a f t e r Brady and Brown 1985)
17
(Fairhurst and Cook 1966).
i i ) i n t e r n a l a x i a l cracking (figure 3b) may be caused by
highly deformable layers between the p i l l a r and the adjacent
wall rock (Brady and Brown 1985) or may be p a r a l l e l surface
fractures that propagate or develop i n the centre of the p i l l a r
(Agapito 1974).
i i i ) diagonal crushing fractures (figure 3c) are often found
i n confined or massive p i l l a r s (Coates 1981).
2.1.2 P i l l a r Load-deformation Curve
P i l l a r loading can be hypothetically described using a load-
deformation (stress-strain) curve (see figure 4) . As a p i l l a r
i s loaded, i t compresses according to the l i n e OA. At a load pmax' t n e maximum p i l l a r load bearing capacity i s reached.
Beyond t h i s point, p o s t - f a i l u r e deformation of the p i l l a r w i l l
occur but at a reduced load. This peak load w i l l be taken as
the point of f a i l u r e i n a p i l l a r . Bieniawski (1987) states,
"... the ultimate strength i s a state at which the rock specimen
or the p i l l a r changes from a gradually increasing load-bearing
capacity to a constant or gradually decreasing load-bearing
capacity."
Determining the actual load-deformation c h a r a c t e r i s t i c s of a
hard rock mine p i l l a r i s not possible. Curves f o r small hard
rock laboratory specimens are e a s i l y determined and curves for
small i n s i t u coal p i l l a r s have been developed (Wagner 1974;
Bieniawski and Van Heerden 1975), but i t i s not experimentally
18
FIGURE 4 . A hypothetical load-deformation curve can be used to describe the s t r e s s - s t r a i n c h a r a c t e r i s t i c s of a p i l l a r . The p i l l a r e x h i b i t s l i n e a r e l a s t i c deformation (along l i n e OA) u n t i l the maximum load i s reached ( P m a x ) • P i l l a r deformation continues (along l i n e AB), but with a decreasing load bearing capacity (after S t a r f i e l d and Fairhurst 1968).
19
p r a c t i c a l to conduct load-deformation t e s t s on large samples of
j o i n t e d rock (Brady 1977). While t h i s leaves the load-
deformation curve of a hard rock mine p i l l a r as a t h e o r e t i c a l
concept, i t i s a convenient method to describe p i l l a r f a i l u r e
and the loss of p i l l a r load bearing capacity.
2.1.3 Loss of Load Bearing Capacity
Ultimately, rock f r a c t u r i n g i s the main reason for loss of
p i l l a r load bearing capacity. However, the onset of f r a c t u r i n g
does not necessarily s i g n i f y that the p i l l a r has f a i l e d .
Agapito (1974), i n h i s study of o i l shale p i l l a r s , found that
f r a c t u r i n g started as minor s p a l l i n g i n the p i l l a r perimeter and
occurred at stress l e v e l s well below the ultimate load capacity
of a p i l l a r . He also noted that as f r a c t u r i n g occurred i n the
outer s h e l l of the p i l l a r , monitoring showed that stress
concentrations b u i l t up i n the p i l l a r core. Wagner (1974)
monitored the i n s i t u stress d i s t r i b u t i o n i n more than 30
underground coal p i l l a r s using a s e r i e s of hydraulic jacks. He
found that at several stages of compression, the perimeter of
the p i l l a r c a r r i e d r e l a t i v e l y l i t t l e stress compared to the
central core of the p i l l a r (figure 5) . He noted that most of
the load bearing capacity of a p i l l a r i s found i n the core of
the p i l l a r and i s l a r g e l y dependent on the confinement provided
by the p i l l a r s h e l l .
A f t e r f a i l u r e of the p i l l a r (due to serious i n t e r n a l and
surface f r a c t u r i n g ) , Wagner (1974) found that a confined p i l l a r
Pillar compression (mm)
2
FIGURE 5 . Wagner (1974) did a series of in situ load-deformation tests on coal p i l l a r s using hydraulic jacks. For this case, 2 5 jacks were put in a 5X5 pattern in a square p i l l a r . The graph on the top shows the load-deformation characteristics of the p i l l a r in general. The oblique diagrams give the relative load on each of the 25 jacks at four stages of p i l l a r compression. The diagrams show that with increasing compression and increasing average p i l l a r stress, the core of the p i l l a r carries an increasing percentage of the load, while the unconfined periphery of the p i l l a r carries less load. Diagram four shows that the p i l l a r core carries a significant load despite the fact that the p i l l a r i s losing i t s overall load bearing capacity (redrawn from Wagner 1974).
core had a considerable load bearing capacity. Krauland and
Soder (1987) wrote that loss of load bearing capacity i n the
post f a i l u r e range of p i l l a r loading depends l a r g e l y upon the
slenderness of the p i l l a r s and the presence of f i l l . This i s
also supported by the laboratory t e s t i n g of rock specimens i n
" s t i f f - t e s t i n g " machines. S t a r f i e l d and Fairhurst (1968)
demonstrated that i f confining pressure on a sample i s
increased, the peak load capacity increases and the post f a i l u r e
load bearing capacity i s greatly enhanced (see figure 6).
The loss of load bearing capacity i n open stope r i b p i l l a r s
i s also highly dependent on confinement of the p i l l a r core.
However, i n open stope mining p i l l a r walls can be very large.
Once progressive f a i l u r e s t a r t s , the fractured wall material
w i l l peel o f f , preventing confinement of the p i l l a r core, and
f i n a l l y r e s u l t i n g i n complete p i l l a r d i s i n t e g r a t i o n . There are
methods to prevent fractured wall material from becoming
detached from the p i l l a r . These methods include the use of
b a c k f i l l , i n s t a l l a t i o n of a r t i f i c i a l support such as cable
b o l t s , and leaving open stopes f u l l of broken ore as long as
possible to provide some confinement to the p i l l a r walls. The
author has seen several examples of f a i l e d r i b p i l l a r s with a
considerable load bearing capacity. In these cases, the p i l l a r
core had remained confined because the fractured p i l l a r material
was confined by b a c k f i l l before i t had the opportunity to slough
from the p i l l a r walls.
22
FIGURE 6. The s t r e s s - s t r a i n curves for laboratory specimens loaded under increasing confining pressures show an increase i n peak load and an increase i n the post-peak load bearing capacity (a f t e r S t a r f i e l d and Fairhurst 1968) .
23
2.2 S i g n i f i c a n t Variables i n Open Stope P i l l a r S t a b i l i t y
Based on the f a i l u r e c h a r a c t e r i s t i c s described above, there
are several variables that could be important i n the design of
r i b p i l l a r s . This section w i l l describe the variables and t h e i r
p o t e n t i a l influence.
2.2.1 Intact Rock Strength
With rock f r a c t u r i n g playing a large r o l e i n the s t a b i l i t y
of p i l l a r s , the resistance of the p i l l a r material to fra c t u r i n g
and crushing i s an important factor i n p i l l a r strength. The
most common index for comparing the strength of d i f f e r e n t rock
types i s the u n i a x i a l compressive t e s t . The uni a x i a l
compressive s t r e n g t h (UCS) i s the maximum load that a
standardized diameter d r i l l core can sustain under un i a x i a l
loading conditions. The UCS i s variable upon specimen siz e , so
the sample diameter i s standardized to about 54 mm (NX size
d r i l l core). Further information about the u n i a x i a l t e s t can be
found i n a report by an International Commission on standard
i z a t i o n of laboratory t e s t s (ISRM Commission 1979).
2.2.2 P i l l a r Load
P i l l a r load i s a primary factor i n p i l l a r deformation, rock
f r a c t u r i n g and p i l l a r f a i l u r e . The d i s t r i b u t i o n of stress i n a
p i l l a r may have a s i g n i f i c a n t e f f e c t on the performance and
s t a b i l i t y of the p i l l a r . However, there i s no conclusive method
to determine stress i n a p i l l a r and there i s no single value
24
that can used to describe the complete loading condition of a
p i l l a r .
The state of stress i n a p i l l a r v a r i e s upon the stress
applied to the p i l l a r as well as the l o c a t i o n inside the p i l l a r .
The stress applied to a p i l l a r varies on the pre-mining stress
f i e l d and the s i z e and location of stopes, underground workings
and other p i l l a r s . The stress inside the p i l l a r i s dependent
upon areas of weakness such as geological d i s c o n t i n u i t i e s , the
proximity of excavations and the f r a c t u r i n g i n the p i l l a r . With
these points kept i n mind, determining the d i s t r i b u t i o n of
stress i n a p i l l a r with a high degree of p r e c i s i o n i s not
possible.
For t h i s thesis, i t was necessary to f i n d a value to
represent the load on a p i l l a r . The load was taken as the
average stress found at several points along the p i l l a r mid-
h e i g h t c e n t e r l i n e , determined u s i n g numerical modelling
techniques. The reason i s that t h i s l o c a t i o n has the highest
normal stresses i n the p i l l a r , and i s frequently observed as the
f i r s t area of f a i l u r e . This choice of stress analysis location
w i l l be discussed i n more d e t a i l i n Chapter 5.2.2.
2.2.3 P i l l a r Shape
Chapter 2.1.3 described the r o l e of confinement i n p i l l a r
s t a b i l i t y and the load bearing capacity. P i l l a r shape has a
huge influence on confinement of the p i l l a r core. I t a f f e c t s :
- the load-convergence c h a r a c t e r i s t i c s of p i l l a r s at f a i l u r e
25
(Hudson et a l . 1971; S t a r f i e l d and Fairhurst 1968),
- the p o s t - f a i l u r e deformation modulus of p i l l a r s (Hudson et
a l . 1971; Wagner 1974),
- the stress d i s t r i b u t i o n i n a p i l l a r ( S t a r f i e l d and Fairhurst
1968; Wagner 1974),
- and the e f f e c t of geological structure and f r a c t u r i n g on
p i l l a r s t i f f n e s s and f a i l u r e (Sarkka 1984).
This confirms that p i l l a r shape as a s i g n i f i c a n t variable i n
p i l l a r s t a b i l i t y .
2.2.4 Structural D i s c o n t i n u i t i e s i n P i l l a r s
The e f f e c t of geological structure on r i b p i l l a r s depends
upon whether the structure involves major d i s c o n t i n u i t i e s such
as f a u l t s and shear zones or minor d i s c o n t i n u i t i e s l i k e j o i n t
sets. P i l l a r s intersected by a major structure must be analyzed
based on the s p e c i f i c s i t u a t i o n . The or i e n t a t i o n and shear
strength of the major structure w i l l play a dominant r o l e i n
s t a b i l i t y . However, i n open stoping, i n t e r s e c t i o n of a major
structure i s not a common problem and design of such p i l l a r s i s
an exception rather than a regular occurrence. When possible,
r i b p i l l a r s are located to avoid i n t e r s e c t i o n by major
geological d i s c o n t i n u i t i e s .
Less prominent d i s c o n t i n u i t i e s such as j o i n t i n g and l o c a l
f r a c t u r i n g , are a much more common problem i n p i l l a r design.
The influence of minor d i s c o n t i n u i t i e s on r i b p i l l a r s depends
upon the orientation, continuity, frequency and shear strength
of the structures. At the p i l l a r central core, the e f f e c t of
minor d i s c o n t i n u i t i e s on p i l l a r s t a b i l i t y i s small because the
t r i a x i a l state of confinement prevents rock movement along the
j o i n t s . Geological d i s c o n t i n u i t i e s have a more s i g n i f i c a n t
e f f e c t on i n s t a b i l i t y i n unconfined regions of p i l l a r s . A l l c o t t
and A r c h i b a l d (1981), Page and Brennan (1981), and Von
Kimmelmann (1984) mention s t r u c t u r a l l y c o n t r o l l e d wedge f a i l u r e s
from p i l l a r walls. One would expect to f i n d l i t t l e or no
confinement of the rock near p i l l a r walls. Consequently, the
influence of structure i s best accounted for using wall
s t a b i l i t y analyses. An excellent method for wall s t a b i l i t y
analysis i s described by Potvin et a l . (1988a). The method
quantifies the influence of geological structure, mining induced
stress, and stope dimensions to predict the s t a b i l i t y of each
surface of an open stope. When the analysis predicts a stable
p i l l a r wall, the e f f e c t of minor structure on the s t a b i l i t y of
unfractured r i b p i l l a r s w i l l be small.
2.2.5 E f f e c t of P i l l a r Volume
P i l l a r s are made of blocks of i n t a c t rock separated by
natural and mining induced d i s c o n t i n u i t i e s . So the influence of
p i l l a r volume on s t a b i l i t y i s r e a l l y a function of two
v a r i a b l e s : the volume e f f e c t on the strength of i n t a c t rock,
and the influence of the number of s t r u c t u r a l defects i n the
p i l l a r .
Laboratory compressive t e s t i n g of small samples has shown an
influence of specimen s i z e on the compressive strength of int a c t
rock (see figure 7) . However, t e s t i n g of large i n t a c t rock
specimens has found that above a " c r i t i c a l " volume, the strength
does not decrease s i g n i f i c a n t l y (see figure 8). This concept of
asymptotic specimen strength i s reported by Bieniawski (1975) ,
Herget et a l . (1984), and Pratt et a l . (1972). These authors
found the c r i t i c a l volume to be less than one cubic metre. With
the volume of blocks i n open stope p i l l a r s usually being much
larger than t h i s c r i t i c a l volume, there i s a very limited
influence of the volume e f f e c t of i n t a c t rock.
The number of s t r u c t u r a l d i s c o n t i n u i t i e s i n a p i l l a r w i l l
depend upon the volume of the p i l l a r . Hoek and Brown (1980)
suggest that t h i s influence can be quantified through the use of
rock mass c l a s s i f i c a t i o n methods. Hardy and Agapito (1977),
Stephansson (1985), and other authors have suggested that
correction factors to account for p i l l a r volume be used i n
p i l l a r strength determination. Both of these ideas w i l l be
investigated with open stope r i b p i l l a r case h i s t o r i e s i n
Chapter 6.1.3.
2.2.6 E f f e c t of B a c k f i l l
The use of f i l l i s very important i n current open stope
mining methods. A survey by the Ontario Ministry of Labour
(Campbell 1987) found that almost a l l Ontario open stope mines
use cemented f i l l to a id i n p i l l a r recovery. The general
purpose of f i l l i s used to provide o v e r a l l mine s t a b i l i t y ,
0 . 3
Sp*>ol Book
O Harbta O Umastona V G r a n l t a A Basalt
Basa l t -andas l ta lava Cabbro ftarbla N o r i t a C r a n l t a Quartz d l o r l t a
T—t*d by
H 0 9 I ' " K o l f M n 1 " B u r e h a r t i at a l ' " K o l f a » n ' " N a l a k l d l a 1 " l l n l c k a y a 1 " l l n i c k a y a 1 " B l a n t a w t k l ' * 7
Hosklns t H o r l n o 1 7 0
Pratt at a l ' * '
( o e/«cS0) . ( 5 0 / d ) 0 - "
150 2 0 0 2 5 0
Specifwn d l a m t a r d
FIGURE 7. There i s a very large influence of specimen si z e on the strength of i n t a c t rock, for small specimen diameters (after Hoek and Brown 1980).
150
100
70
50
- Ix
c
, • r Johns (1966) Iron ore *
Oiorite
° Prott ̂ <J/(I972)
-•• Bieniowski (1967)
_L 0 5 I IS 2 2 5
Specimen side length, m
FIGURE 8. Strength t e s t i n g of samples of increasing specimen length shows a decreasing influence of s i z e . Beyond a " c r i t i c a l " length, there i s no s i g n i f i c a n t decrease i n specimen strength. This c r i t i c a l s i z e i s about 1 metre (after Bieniawski and Van Heerden 1975),
e s p e c i a l l y i n stope hanging walls and footwalls, by l i m i t i n g
spans to stable dimensions and to permit a high r a t i o of
extraction of the orebody with p o t e n t i a l l y minimal d i l u t i o n .
The r o l e of f i l l i n p i l l a r f a i l u r e i s much les s dramatic.
Singh (1976) finds that f i l l :
- provides l a t e r a l support to p i l l a r s to i n h i b i t s p a l l i n g and
prevent collapse,
- acts as a reta i n i n g media to contain fractured rock, thereby
retarding the development of f a i l u r e i n surrounding rock,
- and reduces energy release rates allowing rock to f a i l i n a
non-violent manner.
None of these e f f e c t s of f i l l i n g has a large influence on the
rock f r a c t u r i n g mode of f a i l u r e described above i n Chapter
2.1.1. F i l l does provide r e s t r a i n t and confinement to fractured
rock to prevent sloughing of p i l l a r material and consequently
enhances the p o s t - f a i l u r e load bearing capacity of p i l l a r s .
Thomas (1979) supports Singh's comments by wri t i n g that f i l l i s
not l i k e l y to provide stope wall support before u n r e a l i s t i c f i l l
deformation (approximately 20%) has occurred. He finds that
f i l l i s most b e n e f i c i a l to mining when i t provides rock
confinement causing the rock mass to support i t s e l f .
Consolidated and cemented f i l l s have been found more
e f f e c t i v e at aiding i n underground s t a b i l i t y (Bharti 1987) .
However, the main purpose of consolidated f i l l s i s to be s e l f -
supporting and free-standing during p i l l a r recovery operations.
3 0
f a i l u r e due to rock f r a c t u r i n g . I t does give support to f a i l e d
p i l l a r s to maintain t h e i r i n t e g r i t y and some load bearing
capacity. This aids i n o v e r a l l mine s t a b i l i t y and s i m p l i f i e s
p i l l a r recovery operations.
2.2.7 E f f e c t of Blasting
Blasting practices are very important i n the success of any
mining method. Poor b l a s t i n g practices can turn a stable and
e f f i c i e n t design into a very i n e f f i c i e n t design. Some of the
ef f e c t s of poor b l a s t i n g i n open stope mining include: poor
fragmentation, overbreak beyond stope l i m i t s , need f o r frequent
post-blast clean-up and development r e h a b i l i t a t i o n , development
of b l a s t induced fractures i n the rock mass, and rock mass
disturbance and i n s t a b i l i t y i n stope walls and p i l l a r s due to
excessive v i b r a t i o n s .
Quantifying poor b l a s t i n g i n an empirical method i s very
d i f f i c u l t . There i s no cl e a r d e f i n i t i o n of poor b l a s t i n g , and
the consequences are highly varied. The best solution i n
describing b l a s t i n g i s to l i s t some of the practices used to
minimize the e f f e c t of bl a s t i n g . These practices are often
re f e r r e d to as control b l a s t i n g , and include: minimizing the
charge weight per delay; using charge decking, decoupling,
and/or low density explosives; using e f f i c i e n t hole l o c a t i o n and
b l a s t sequencing; and b l a s t i n g to a free face.
Although the si g n i f i c a n c e of b l a s t i n g practices i s very
great i n mining, there are no c r i t e r i o n to quantify the e f f e c t s
31
of b l a s t i n g on mining. Consequently, b l a s t i n g w i l l not be
discussed as a design variable i n t h i s t h e s i s .
2.3 Chapter Summary
Progressive f a i l u r e of open stope r i b p i l l a r s i s d i f f i c u l t
to observe due to lack of v i s u a l access. Several i n d i r e c t signs
of p i l l a r d i s t r e s s have been documented. These signs are
d i r e c t l y associated with rock f r a c t u r i n g i n the p i l l a r .
Fracturing generally s t a r t s at the p i l l a r walls and propagates
or develops i n the p i l l a r core as p i l l a r d e t e r i o r a t i o n
progresses. Fractured rock loses some or a l l of i t s load
bearing capacity, depending on the confinement of the material.
P i l l a r f a i l u r e can be described as the state when a p i l l a r
changes from having an increasing load bearing capacity to a
constant or decreasing load bearing capacity. F a i l u r e can
hypothetically be described using a p i l l a r load-deformation
curve. The degree of confinement of a p i l l a r has a large
influence on the shape of that curve.
Open stope r i b p i l l a r design should be based on the
conditions that influence p i l l a r f a i l u r e and load bearing
capacity. These conditions are rock f r a c t u r i n g and p i l l a r
confinement. The conditions may be influenced by a number of
factors, including: the in t a c t strength of the p i l l a r material,
the p i l l a r load, the shape of the p i l l a r , the presence of
s t r u c t u r a l d i s c o n t i n u i t i e s , and the volume of the p i l l a r .
32
CHAPTER 3
REVIEW OF PILLAR DESIGN METHODS
There are two general approaches to current r i b p i l l a r
design: empirical methods, and numerical methods. Empirical
design i s based on observation of case h i s t o r i e s and previous
experience i n s i m i l a r geotechnical conditions. Numerical design
i s l a r g e l y based on measured parameters and material properties.
However, there i s not a cl e a r d i v i s i o n between the two
approaches. Some numerical procedures are occasionally used i n
e m p i r i c a l design and some experience and observational
information i s used i n numerical techniques.
This chapter w i l l discuss the two approaches as they are
applied to hard rock p i l l a r design. I t w i l l b r i e f l y describe
the background fundamentals i n each method, and give a short
discussion of t h e i r respective advantages, disadvantages and
l i m i t a t i o n s .
3.1 Empirical Design Methods
Empirical design methods are characterized by the fact that
they consider a p i l l a r as one unit. I t i s assumed that there i s
no v a r i a t i o n i n s t a b i l i t y within a p i l l a r . The s t a b i l i t y of
that p i l l a r i s interpreted based on three v a r i a b l e s :
i) p i l l a r load,
i i ) p i l l a r strength,
i i i ) and safety factor.
33
Methods o f c a l c u l a t i n g o r d e t e r m i n i n g each o f t h e s e p a r a m e t e r s
a r e b a s e d upon q u a n t i f y i n g u n d e r g r o u n d o b s e r v a t i o n s and p a s t
e x p e r i e n c e . T y p i c a l l y , p i l l a r l o a d i s d e t e r m i n e d u s i n g
e m p i r i c a l r u l e s o f thumb o r n u m e r i c a l t o o l s . P i l l a r s t r e n g t h
and an a p p r o p r i a t e s a f e t y f a c t o r a r e c a l i b r a t e d w i t h c a s e
h i s t o r i e s a n d / o r l a b o r a t o r y e x p e r i m e n t s .
The s a f e t y f a c t o r i s d e f i n e d a s :
S . F . = p i l l a r s t r e n g t h p i l l a r l o a d
I t has t h r e e b a s i c p u r p o s e s :
- t o expand t h e l o a d and s t r e n g t h d e t e r m i n a t i o n methods t o
d i f f e r e n t m i n i n g c o n d i t i o n s ,
- t o make a d e s i g n more c o n s e r v a t i v e
- and t o a c c o u n t f o r t h e i n a c c u r a c y i n t h e i n p u t p a r a m e t e r s .
F o r i n s t a n c e , a p i l l a r i n an e n t r y m i n i n g method w o u l d be
d e s i g n e d more c o n s e r v a t i v e l y t h a n a p i l l a r i n a n o n - e n t r y m i n i n g
m e t h o d . I n o r d e r t o use t h e same s t r e n g t h and l o a d
d e t e r m i n a t i o n p r o c e d u r e s f o r t h e d e s i g n o f b o t h s i t u a t i o n s , a
h i g h e r s a f e t y f a c t o r w o u l d be d e s i g n e d i n t h e e n t r y method
b e c a u s e t h e d e g r e e o f i n s t a b i l i t y a c c e p t a b l e i s l e s s . The
c h o i c e o f s a f e t y f a c t o r i s u s u a l l y b a s e d on e x p e r i e n c e w i t h t h e
s p e c i f i c d e s i g n method .
The f o l l o w i n g s u b - s e c t i o n s w i l l summar ize t h e t e c h n i q u e s
d e v e l o p e d f o r c a l c u l a t i n g p i l l a r s t r e n g t h and p i l l a r l o a d and
w i l l l i s t t h e s a f e t y f a c t o r s s u g g e s t e d f o r t h e s e d e s i g n
p r o c e d u r e s . Because t h e r e a r e a l a r g e number o f d i f f e r e n t
t e c h n i q u e s u s e d t o d e t e r m i n e p i l l a r l o a d and s t r e n g t h , emphas i s
w i l l be placed on those methods used f o r hard rock design. A
more complete discussion of the empirical design methods i s
documented by Potvin (1985).
3.1.1 P i l l a r Strength Determination
There are many factors that may influence the strength of a
mine p i l l a r . These factors include:
- s i z e and shape of the p i l l a r ,
- volume of the p i l l a r ,
- resistance of i n t a c t p i l l a r material to crushing,
- presence of d i s c o n t i n u i t i e s ,
- strength and orientation of the d i s c o n t i n u i t i e s ,
- confinement and t r i a x i a l strength of the p i l l a r rock
mass,
- and the presence of groundwater.
The number of p o t e n t i a l l y s i g n i f i c a n t variables makes p i l l a r
strength very d i f f i c u l t to determine a n a l y t i c a l l y . Some of
these variables are not s i g n i f i c a n t under selected mining
conditions. For such si t u a t i o n s , p i l l a r strength may be
estimated empirically. The most commonly used empirical p i l l a r
strength methods i n hard rock mining are:
- Salamon's formula,
- Hedley's formula,
- Obert and Duvall formula,
- and the Hoek and Brown p i l l a r strength curves.
The f i r s t three of these methods are v a r i a t i o n s of the empirical
s t r e n g t h formulas developed for underground coal mines.
Consequently, a b r i e f discussion of the empirical coal formulas
i s h e l p f u l , although they see very l i m i t e d use i n hard rock
p i l l a r design.
3.1.1.1 Empirical Strength Formulas
A major area of p i l l a r design research has been i n
underground coal mining. A basic premise of t h i s work was that
f u l l s i z e p i l l a r strength could be determined by extrapolating
the r e s u l t s from laboratory t e s t i n g of coal specimens. Two
forms of the empirical strength equation were developed:
- the s i z e e f f e c t formula,
- and the shape e f f e c t formula.
A) The s i z e e f f e c t formula i s defined as:
Op = K * (w a/h b) a f b
where:
<Tp = p i l l a r strength (psi) ,
K = u n i a x i a l compressive strength of one cubic foot of
p i l l a r material,
w = p i l l a r width,
h = p i l l a r height,
a,b = unequal empirically defined constants.
This formula i s based on the fact that rock strength i s
dependent on the s i z e of the sample. This i s due to the
presence of d i s c o n t i n u i t i e s (such as j o i n t s , f o l i a t i o n s ,
bedding, b l a s t fractures, and mineralogy). As rock samples of a
constant shape increase i n si z e , the strength of the sample
decreases. This si z e e f f e c t i s taken into account by giving a
d i f f e r e n t weighting to the c o e f f i c i e n t s for w and h i n a shape
e f f e c t formula. Table 1 gives the constants a and b proposed by
d i f f e r e n t authors.
Constants a and b used i n the s i z e e f f e c t formula: ap = K * wa /
SOURCE a b
Streat (1954) 0.5 1.00 Holland-Gaddy (1962) 0.5 1.00 Greenwald et a l . (1939) 0.5 0.833 Hedley and Grant (1972) 0.5 0.75 Salamon and Munro (1967) 0.46 0.66 Bieniawski (1968) 0.16 0.55
Table 1 (after Babcock, Morgan and Haramy 1981).
shape e f f e c t formula, which i s defined as:
K * [A + B * (w/h)]
K * (w a/h b) a = b
ap = p i l l a r strength ( p s i ) ,
K = u n i a x i a l compressive strength of one cubic foot of
p i l l a r material,
w = p i l l a r width,
h = p i l l a r height,
B) The
a P =
or
a B =
where:
A,B,a,b = empirically defined constants.
The shape e f f e c t formula denotes a difference i n strength for
p i l l a r s of d i f f e r e n t shape but equal cross-sectional area. The
greater the p i l l a r width to p i l l a r height r a t i o , the greater the
p i l l a r strength. A change i n mode of f a i l u r e i s one apparent
cause of the shape e f f e c t on p i l l a r strength. Slender p i l l a r s
tend to f a i l along s t r u c t u r a l d i s c o n t i n u i t i e s i n the rock mass.
While for wide p i l l a r s , f a i l u r e i s l i k e l y to be caused by
crushing of the p i l l a r material. Tables 2 and 3 give the
constants a,b,A,B proposed by d i f f e r e n t authors.
Constants a and b used i n the shape e f f e c t formula: oP = K * wa / h b
SOURCE a b
Zern (1926) Hazen and A r t i e r (1976) Holland (1956) Morrison et a l .
0.5 0.5 0.5 0.5
0.5 0.5 0.5 0.5
Table 2 (after Babcock, Morgan and Haramy 1981).
Constants A and B used i n the shape e f f e c t formula: Op = K * [ A + B * (w/h)]
SOURCE A B W / h
Bunting (1911) Obert et a l . (1960) Bieniawski (1968) Van Heerden (1973) Sorensen and Pariseau (1978)
0.700 0.778 0.556 0.704 0.693
0.300 0.222 0.444 0.296 0.307
0.5 - 1.0 0.5 - 2.0 1.0 - 3.1 1.14 - 3.4 0.5 - 2.0
Table 3 (after Babcock, Morgan and Haramy 1981).
38
The constants and c o e f f i c i e n t s i n each of these formulas
were based on p i l l a r case h i s t o r i e s and laboratory t e s t i n g of
scale p i l l a r s . Three of the most prominent empirical p i l l a r
design studies and surveys provided formulas commonly used i n
hard rock p i l l a r strength determination.
3.1.1.2 Salamon 1s Formula
In 1967, Salamon published a survey of stable and f a i l e d
square coal p i l l a r s i n South A f r i c a n mines. The study
investigated 98 stable and 27 collapsed p i l l a r areas. Using a
s i z e e f f e c t formula, and assuming the mean safety factor for a l l
the f a i l e d cases was 1.0, the c o e f f i c i e n t s K, a and b were
ca l i b r a t e d . This gave the formula:
strength = K * w 0- 4 6 / h 0 - 6 6
where:
strength = p i l l a r strength ( p s i ) ,
K = 1320 = strength of one cubic foot of p i l l a r
material,
w = p i l l a r width (feet),
h = p i l l a r height (feet).
The complete database i s commonly displayed i n a histogram (see
figure 9) . To determine a suitable safety factor for t h i s
strength formula i n entry mining methods, Salamon averaged the
safety factor of the most dense concentration of 50% of the
stable p i l l a r s to get an average of 1.57 (see figure 9). He
f e l t that t h i s safety factor was adequately conservative to
I 1 1 1 1 1 ' 2 2 • «> •* e» o
3DN3aarO00 JO ADN3nD3MJ
FIGURE 9. Histogram of the safety factors f o r stable and f a i l e d p i l l a r case h i s t o r i e s i n South A f r i c a n bord and p i l l a r coal mining. The range of safety factors for the most dense concentration of 50% of the stable cases i s between 1.31 and 1.88. Salamon chose the mean of t h i s range, 1.57, as adequately conservative to design stable, permanent p i l l a r s i n room and p i l l a r coal mining (after Salamon 1967).
40
ensure s t a b i l i t y f o r p i l l a r s i n room and p i l l a r coal mines.
Despite the fa c t that the study i s based on square p i l l a r s
i n bord and p i l l a r coal mining i n South A f r i c a , Salamon's
formula has been used for the design of hard rock open stope r i b
p i l l a r s . The factor to account f o r the strength of the p i l l a r
material i s adjusted to the strength of one cubic foot of int a c t
hard rock, but the c o e f f i c i e n t s and safety factor used are those
o r i g i n a l l y proposed by Salamon.
3.1.1.3 Hedley's Formula
Hedley and Grant (1972) proposed a p i l l a r strength formula
based on data from hard rock room and p i l l a r mining at E l l i o t
Lake. They empirically c a l i b r a t e d a s i z e e f f e c t formula s i m i l a r
to that proposed by Salamon (discussed above). The formula was
defined as:
Qu = k * w0-5 / h 0 - 7 5
where:
Qu = p i l l a r strength ( p s i ) ,
k = 26,000 = strength of one cubic foot of p i l l a r
material ( p s i ) ,
w = p i l l a r width (feet),
h = p i l l a r height (f e e t ) .
The data base to develop t h i s formula consisted of 2 3 stable
p i l l a r s , 2 p a r t i a l l y f a i l e d p i l l a r s and 3 crushed p i l l a r s . For
a p p l i c a t i o n of t h e i r p i l l a r strength formula, Hedley and Grant
suggested that p i l l a r s with a safety factor greater than 1.5 are
stable and p i l l a r s with a safety factor near 1.0 are crushed.
41
These safety factors are based on i n t e r p r e t a t i o n of the a
graphical p l o t of the data base (see figure 10).
This strength formula has been further confirmed for room
and p i l l a r mining, through studies by Von Kimmelmann et a l .
(1984), and Townsend (1982). I t i s the only p i l l a r strength
formula developed based on hard rock mining case h i s t o r i e s . So
although no published study has confirmed i t s use for open stope
p i l l a r s , i t i s widely used i n open stope p i l l a r design.
3.1.1.4 Obert and Duvall Shape E f f e c t Formula
Obert et a l . (1946) performed a series of compressive
strength t e s t s on specimen coal p i l l a r s with various shapes. I t
was determined that the shape e f f e c t of p i l l a r strength follows
the empirical r e l a t i o n s h i p :
o-p = a± * [0.778 + 0.222(w/h)]
where:
rjp = p i l l a r strength,
o"! = u n i a x i a l strength of a cubical p i l l a r specimen,
w = p i l l a r width,
h = p i l l a r height.
The formula d i d not include any factor to account for the size
e f f e c t on strength,, but instead suggested a safety factor
between 2 and 4 be used i n p i l l a r design.
In hard rock p i l l a r design, t h i s formula has been suggested
to account for shape e f f e c t by several authors (Krauland and
Soder 1987; Hedley et a l . 1979; Herget et a l . 1984). These
authors used additional methods to account f o r p i l l a r strength
rsxi ss*J)S JO/IM p>)Dwnsj}
FIGURE 10. The estimated stress and strength for case his t o r i e s of p i l l a r s in room and p i l l a r mining in the E l l i o t lake uranium mining d i s t r i c t . Safety factor lines have been drawn on the graph. The chart shows that a l l the case histories with a safety factor above 1.5 are stable (after Hedley and Grant 1972) .
43
si z e dependence.
3.1.1.5 Hoek and Brown P i l l a r Strength Curves
Hoek and Brown (1980) proposed a series of curves for the
estimation of p i l l a r strength (see figure 11). The curves were
developed based on numerical modelling and the d i s t r i b u t i o n of
f a i l e d rock inside p i l l a r s of d i f f e r e n t shapes and f o r a range
of rock mass q u a l i t i e s , using the empirical rock mass f a i l u r e
c r i t e r i a :
a p = a2 + ( m * a c * a 3 + s * a c2 ) ^
where:
a p = average p i l l a r strength,
a 3 = minimum p r i n c i p a l stress,
Oq = u n i a x i a l compressive strength of the i n t a c t
p i l l a r material,
m & s = empirical constants based on the rock mass
qua l i t y of the p i l l a r material.
Hoek and Brown proposed these p i l l a r design curves assuming that
a p i l l a r has f a i l e d when the stress across the centre of the
p i l l a r exceeds the strength of the rock mass. They stated that
a safety factor of 1.0 or less would imply that a p i l l a r i s
t h e o r e t i c a l l y unstable and that a safety factor i n excess of 1.5
should be used f o r permanent p i l l a r s . However, ' these
recommendations do not seem to be confirmed by case history
back-analysis.
Each curve can be considered a p i l l a r f a i l u r e c r i t e r i o n for
a s p e c i f i c rock mass qual i t y . Hoek and Brown proposed that the
Intact samples of fine grained igneous crystalline rock
m - 17, * - 1
Very good quality rock mas8
m • 8.5, s - 0.1
Good quality rock mass
m • 1.7, s » 0.00k
Fair quality rock mass m - 0.3^, s » 0.0001 Poor quality rock mass m - 0.09, s - 0.00001
1 2 3
Pi 1lar width/height Wp/h
FIGURE 11. Hoek and Brown (1980) proposed a series p i l l a r strength curves based on the theoretical d i s t r i b u t i o n of rock mass f a i l u r e i n a p i l l a r .
influence of p i l l a r volume and s t r u c t u r a l defects could be
quantified through the use of rock mass c l a s s i f i c a t i o n s .
Consequently, the m and s constants account for p i l l a r volume
and s t r u c t u r a l defects because they have been rel a t e d to the two
most common rock mass c l a s s i f i c a t i o n methods, CSIR by Bieniawski
(1973) and NGI by Barton et a l . (1974).
O r i g i n a l l y , the strength curves were not supported by case
h i s t o r i e s , however p r a c t i c a l a p p l i c a t i on by Potvin (1985) and
Page and Brennen (1982) has been successful f o r the good and
f a i r rock mass qu a l i t y curves.
3.1.2 P i l l a r Load
In underground mine design, i t i s d i f f i c u l t to determine the
actual load that w i l l be acting on a p i l l a r . For most safety
factor p i l l a r design methods, two procedures are currently used.
The f i r s t method, c a l l e d the Tributary Area Theory, uses a
s i m p l i f i e d approach to underground stress r e d i s t r i b u t i o n . The
other method, generally termed numerical modelling, involves the
use of the theory of e l a s t i c i t y to determine s t r e s s
r e d i s t r i b u t i o n . In contrast to the s i m p l i c i t y of the t r i b u t a r y
area theory, numerical modelling requires the use of a computer
due to the s o p h i s t i c a t i o n of the c a l c u l a t i o n process.
3.1.2.1 Tributary Area Theory
The Tributary Area Theory assumes that when stopes are
opened there i s an equal and symmetric stress r e d i s t r i b u t i o n
regardless of the s i z e and location of the p i l l a r s created. I t
i s often described using the analogy of a smooth flowing stream
obstructed by bridge piers (see figure 12) . To permit a
continuous flow rate i n the stream, streamlines are concentrated
between the pi e r s ( i e . between the stopes). This causes the
flow v e l o c i t y (stress) between the piers ( i n the p i l l a r s ) to
increase. The increase i n flow v e l o c i t y i s generally dependent
on the r a t i o of the width of the stream (width of the mining
area) to the sum of the distances unobstructed by the piers (sum
of the p i l l a r widths).
So i n a rock mechanics perspective, t h i s theory describes
the r e d i s t r i b u t i o n of p r i n c i p a l stress flowlines into p i l l a r s .
The average p i l l a r load thus depends on the r a t i o of the t o t a l
area extracted to the t o t a l area remaining i n the p i l l a r .
Figure 13 shows the application of the Tributary Area Theory to
several types of p i l l a r s (including r i b p i l l a r s ) .
Due to the s i m p l i c i t y of t h i s theory, some factors that
fundamentally influence stress i n p i l l a r s are ignored. These
factors are:
- the number of p i l l a r s i n the mining block (or the extent of
the mining area),
- the loc a t i o n of the p i l l a r i n the mining block,
- the r e d i s t r i b u t i o n of stress into the abutments,
- and the shape of the p i l l a r .
A study by Salamon (1974) d e t a i l s the f i r s t three problems
by comparing the average stress for a problem predicted by
4 7
FIGURE 12. The analogy of streamlines i n a smoothly flowing stream obstructed by bridge p i e r s i s often used to describe the concentration of stress i n p i l l a r s (after Hoek and Brown 1980).
U n i t l e n g t h
I-
£
RIB PILLARS - o B - Y z O + W ° / W )
1 • : • U I J .
1 H • E 3
SQUARE PILLARS - 0 p - yz(\ + w o / U p ) :
L i r -
i t i T
- P i l l a r a r e a
^ o / o
Rock column a r e a
o IRREGULAR PILLARS -
Rock column a r e a
RECTANGULAR PILLARS - 0 p - Y z ( l + W o / W p ) ( l + L o / L p ) P i l l a r a r e a
FIGURE 13. The tr i b u t a r y area theory, f o r average p i l l a r load c a l c u l a t i o n , applied to several d i f f e r e n t p i l l a r layouts (after Hoek and Brown 1980).
48
t r i b u t a r y area to those predicted by an e l e c t r i c analogue model.
The stress i n square room and p i l l a r panels of three, seven and
eleven square p i l l a r s (in each horizontal direction) were
investigated. The average p i l l a r load according to the
t r i b u t a r y area theory i s 4 Q 3 3 ( Q 3 3 i s the pre-mining stress
component). Figure 14 shows the analogue r e s u l t s of these
t e s t s . Stress r e d i s t r i b u t i o n into the abutments r e s u l t s i n the
analogue predicted stress always being lower than the t r i b u t a r y
area predicted load. As the panel widens (larger number of
p i l l a r s ) , the load predicted by the analogue approaches the
value of 4Q 3 3. I t i s also demonstrated by t h i s model that the
lo c a t i o n of the p i l l a r i n the panel has a s i g n i f i c a n t e f f e c t on
i t s load.
The influence of the shape of a p i l l a r i s documented i n an
in v e s t i g a t i o n of the Tributary Area Theory and two dimensional
boundary element modelling of r i b p i l l a r s (Potvin et a l . 1987).
Figure 15 shows that as a p i l l a r becomes more slender, the
average p i l l a r load predicted by modelling decreases. This
e f f e c t i s also discussed by Salamon (1974) and i s attributed to
decreasing p i l l a r s t i f f n e s s with increasing p i l l a r slenderness.
In summary, the Tributary Area Theory provides a very quick
s o l u t i o n for determining p i l l a r load. However, the accuracy of
the method i s diminished i f there are a small number of p i l l a r s ,
a small mining panel, or i f the p i l l a r s are slender i n shape.
B i e n i a w s k i (1983) comments t h a t i n c o a l mining, the
overestimation of p i l l a r load by t r i b u t a r y area may be as much
49
FIGURE 14. Using an e l e c t r i c analogue model, Salamon (1974) showed the v a r i a t i o n i n p i l l a r stress caused by increasing the number of p i l l a r s (N) i n a mining panel, a i s the p i l l a r stress, and Q 3 3 i s the premining stress. The tr i a n g u l a r symbols correspond to the three p i l l a r s i n panel (a), the c i r c u l a r symbols correspond to the seven p i l l a r s i n panel (b), and the diamond symbols correspond to the eleven p i l l a r s i n panel (c). The graph shows a d i s t i n c t influence of the location of a p i l l a r and the number of p i l l a r s on the stress induced.
A 4.0. _ tributary area
FIGURE 15. A study using two dimensional boundary element numerical modelling shows the influence of p i l l a r shape and the number of p i l l a r s on the average stress (a f t e r Potvin et a l . 1987).
as 40%, while the author has found that the Tributary Area
Theory may overestimate the load i n open stope r i b p i l l a r s by as
much as 100% (Hudyma 1988b).
3.1.2.2 Numerical Modelling
Several types of numerical models are a v a i l a b l e to aid i n
the c a l c u l a t i o n of p i l l a r load. Each of these models has
d i f f e r e n t c h a r a c t e r i s t i c s and a d i f f e r e n t means of c a l c u l a t i o n .
The models applicable to hard rock p i l l a r design w i l l be
discussed i n chapter 3.2.
When used i n empirical design methods, the c a p a b i l i t i e s of
numerical models include the a b i l i t y to:
- analyze complex mining geometries,
- account f o r any number of p i l l a r s and any s i z e of mining
seam,
- recognize p i l l a r l o c ation i n a mining block,
- determine loads i n i n d i v i d u a l p i l l a r s ,
- and account for variat i o n s i n p i l l a r shape.
Numerical modelling removes many of the problems associated with
t r i b u t a r y area and i s usually necessary to estimate the p i l l a r
load. However, the use of numerical modelling i s a s k i l l that
takes a degree of knowledge, experience and c a l i b r a t i o n to use
e f f i c i e n t l y i n p i l l a r design. These topics w i l l a l l be
discussed i n more depth i n Chapter 3.2 and Chapter 4.
3.1.3 Safety Factor
Hoek and Brown (1980) state that, "A safety factor of 1.0
52
implies that the p i l l a r i s t h e o r e t i c a l l y unstable and that the
f a i l u r e could propagate across the enti r e p i l l a r The
safety factors suggested for various empirical design procedures
i n entry mining methods are l i s t e d i n Table 4. The degree of
i n s t a b i l i t y acceptable i n entry methods i s much les s than that
i n open stope methods. So, although there seems to be an
agreement that a safety factor of about 1.5 i s s u f f i c i e n t for
p i l l a r design i n entry mining methods, t h i s has not been
v e r i f i e d for open stope mining.
SOURCE SAFETY FACTOR
Salamon (1967) Hedley (1972) Obert and Duvall (1967) Hoek and Brown (1980) Bieniawski (1983) Stacey and Page (1986)
1.6 1.5
2 - 4 1.5
1.5 - 2.0 1.5
Table 4. Safety factors suggested by various authors for p i l l a r design i n entry mining methods.
Stacey and Page (1986) state that for p i l l a r s i n non-entry
mining methods a minimum safety factor of 1.1 i s necessary and
to design p i l l a r s to y i e l d or f a i l , a safety factor of less than
0.5 should be used. However, no data are presented to
substantiate these values.
Ultimately, none of these formulas or safety factors i s
based on observation and experience i n open stope mining. Using
a factor of safety adds a conservative cushion against the
p o t e n t i a l error associated with empirical design methods.
However, a conservative design i s not necessarily the most cost
e f f e c t i v e design. Using the safety factors suggested for an
entry method p i l l a r s w i l l l i k e l y give a stable design, but
experience and c a l i b r a t i o n of an empirical design procedure w i l l
provide a better estimate of the safety factor needed.
3.2 Numerical Design Methods
In recent years, several .numerical (or computational)
methods have been developed s p e c i f i c a l l y f o r use i n underground
rock mechanics design. The program codes were created to permit
two dimensional or three dimensional stress and displacement
investigations around excavations i n rock.
In s i m p l i s t i c terms, numerical modelling can be described
with figure 16. A region (R) i s defined i n a medium and loading
conditions are applied to the region. Excavations (E) are then
created i n the medium. The p r i n c i p l e function of numerical
modelling i s to calculate the magnitude and orie n t a t i o n of the
stresses and displacements acting i n the v i c i n i t y of these
excavations. The r e d i s t r i b u t i o n of stresses may be based on
e l a s t i c and/or p l a s t i c behaviour of the medium.
3.2.1 Types of Numerical Methods
Individual computational methods were developed to analyze
problems with respect to s p e c i f i c properties of the medium.
Brown (1987) grouped these properties into three broad
categories:
FIGURE 16. An i d e a l i z e d sketch showing the p r i n c i p l e of numerical modelling of underground excavations a f t e r Potvin et a l . 1987).
- d i f f e r e n t i a l continuum methods,
- i n t e g r a l methods,
- and discontinuum methods.
D i f f e r e n t i a l continuum methods (also c a l l e d f i n i t e element
and f i n i t e difference methods) require d i s c r e t i z a t i o n of the
medium within the region of in t e r e s t , at the boundary of the
problem and at a long distance from the boundary of the problem
(also termed the f a r f i e l d ) . Continuum methods assume the
problem to be solved w i l l not be influenced by d i s c o n t i n u i t i e s
i n the rock mass (medium) . This means the rock mass contains
few or no s i g n i f i c a n t d i s c o n t i n u i t i e s , or the d i s c o n t i n u i t i e s
are so common and uniform that i n d i v i d u a l l y they have no e f f e c t
on stress r e d i s t r i b u t i o n . Consequently, for continuum methods,
i t i s assumed that the medium can be represented by "equivalent"
continuum rock mass material properties. D i f f e r e n t i a l continuum
methods permit analysis using e l a s t i c and p l a s t i c theory.
However, d i s c r e t i z a t i o n inaccuracies at the boundary and the far
f i e l d , extensive data preparation and high computing times make
f i n i t e element methods less appealing for rock mechanics design.
An extensive discussion of f i n i t e element methods i s presented
by Zienkiewicz (1977).
Integral methods (or boundary element methods) also use the
continuum approach but only r e q u i r e approximations or
d i s c r e t i z a t i o n at the problem boundary. This greatly reduces
the amount of data needed to describe the problem and
consequently the amount of computer time needed to complete the
computations. However, they are best suited to l i n e a r and
homogeneous (or piece-wise homogeneous) material behaviour. The
use of boundary element methods and t h e i r a p p l i c a t i o n i n rock
mechanics i s d e t a i l e d i n a book by Crouch and S t a r f i e l d (1983).
Discontinuum methods are a sp e c i a l type of d i f f e r e n t i a l
technique. They generally assume a rock mass can be modelled by
a f i n i t e number of discontinuous blocks. The most common
discontinuum approach i s c a l l e d the d i s t i n c t element method. I t
uses r i g i d blocks and the laws of motion to determine the forces
and displacements applied to the blocks. A good description of
the basis of d i s t i n c t element models and a general application
i n a rock mass i s given i n Cundall (1987).
The most appropriate numerical method for open stope p i l l a r
design depends on the i n s i t u medium conditions and the form of
stress response expected. As discussed i n Chapter 2, p i l l a r s
are not l i k e l y to be i n f l u e n c e d by i n d i v i d u a l minor
d i s c o n t i n u i t i e s and are loaded i n a b i a x i a l , e l a s t i c manner.
Consequently, the numerical method best suited to open stope
p i l l a r design i s a continuum approach using the theory of
e l a s t i c i t y . The most e f f i c i e n t approach for these conditions i s
the i n t e g r a l method. F i n i t e element methods could perform the
computations adequately, but are not as e f f i c i e n t as boundary
element methods i n e l a s t i c stress analysis. As a r e s u l t , a l l of
the numerical modelling i n t h i s thesis w i l l focus on the
a p p l i c a t i o n of boundary element methods.
57
3.2.2 Interpretation of Boundary Element Results i n Mining
The boundary element stress analysis technique has been
developed to approximate the stress d i s t r i b u t i o n around openings
with i r r e g u l a r shapes oriented i n a two dimensional or three
dimensional stress f i e l d . However, boundary element methods do
not d i r e c t l y determine f a i l u r e . The stress d i s t r i b u t i o n needs
to be interpreted to determine the e f f e c t on underground
s t a b i l i t y . Many types of f a i l u r e c r i t e r i o n have been applied i n
the analysis of stress d i s t r i b u t i o n s . This section w i l l outline
the common methods of boundary element i n t e r p r e t a t i o n used i n
p i l l a r design. The methods of int e r p r e t a t i o n include:
(i) post-processing f a i l u r e c r i t e r i o n ,
( i i ) i n t e r a c t i v e f a i l u r e c r i t e r i o n ,
( i i i ) and p r i n c i p a l stress magnitudes.
3.2.2.1 Post-Processing F a i l u r e C r i t e r i o n
Post processing f a i l u r e c r i t e r i a are applied to the solution
a f t e r the stress analysis i s complete. The f a i l u r e c r i t e r i o n
does not have any e f f e c t on the stress solution. Generally,
continuum material properties, such as i n t a c t rock strength,
rock mass strength, d i s c o n t i n u i t y shear strength, or rock mass
characterization parameters, are estimated f o r the rock mass
behaviour. The f a i l u r e c r i t e r i o n i s c a l i b r a t e d based on the
estimated material properties and experience i n s i m i l a r rock
conditions. Common f a i l u r e c r i t e r i a used i n post processing
were developed by:
- Murrell (1965) and Bieniawski (1974) fo r i n t a c t rock,
58
- Hoek and Brown (1980) for j o inted rock masses,
- and Coulomb (1776) for d i s c o n t i n u i t i e s .
The f a i l u r e c r i t e r i o n i s applied to stresses at many points i n a
p i l l a r . Based on the d i s t r i b u t i o n of t h e o r e t i c a l l y f a i l e d rock,
p i l l a r s t a b i l i t y i s determined and p o t e n t i a l mining problems are
delineated.
An example of the a p p l i c a t i o n of a post-processing f a i l u r e
c r i t e r i o n i s described by Brady (1977) i n the analysis of an
experimental open stope p i l l a r at the Mount Isa Mine in
Queensland, A u s t r a l i a . A c r i t e r i o n was c a l i b r a t e d for the
f a i l u r e of p i l l a r material based on a formula o r i g i n a l l y
proposed by Murrell (1965). From the observation of l o c a l rock
s p a l l i n g , the following formula was developed:
a x = 9.34a 30- 7 5 + 94.0
where,
c2_ = the major p r i n c i p a l stress at f a i l u r e (MPa) ,
0 3 = the minor p r i n c i p a l stress (MPa).
The f a i l u r e c r i t e r i o n was then applied to and a 3 stress
d i s t r i b u t i o n s for stable and f a i l e d open stope p i l l a r case
h i s t o r i e s f o r v e r i f i c a t i o n . Figure 17 shows the r e s u l t s of
applying the c r i t e r i o n to a stable p i l l a r . The points denoted
by "F" i n the figure representing the t h e o r e t i c a l zone of f a i l e d
rock i n the p i l l a r . The predicted zones of f a i l e d rock are
small and i s o l a t e d at the stope periphery, which corresponds
well with the stable assessment. Figure 18 shows the c r i t e r i o n
applied to the stress d i s t r i b u t i o n of a p i l l a r that f a i l e d . The
FIGURE 17. An empirical f a i l u r e c r i t e r i o n has been applied to the two dimensional stress d i s t r i b u t i o n of a stable open stope r i b p i l l a r . Points denoted by M F " represent the area of rock that has t h e o r e t i c a l l y f a i l e d . For t h i s p i l l a r , the f a i l u r e zones are small and i s o l a t e d at the periperhy of the p i l l a r . This corresponds to a generally stable assessment f o r the p i l l a r (after Brady 1977).
FIGURE 18. The t h e o r e t i c a l d i s t r i b u t i o n of f a i l e d rock i s much greater i n t h i s p i l l a r . The actual p i l l a r collapsed shortly a f t e r being reduced to t h i s s i z e (after Brady 1977).
zone of f a i l e d rock covers a s i g n i f i c a n t portion of the p i l l a r ,
which also agrees with the actual assessment.
Application of a f a i l u r e c r i t e r i o n to the t h e o r e t i c a l stress
d i s t r i b u t i o n around underground excavations i s very common for
the i n t e r p r e t a t i o n of boundary element solutions. However, i t
assumes that load i s e n t i r e l y c a r r i e d by the p i l l a r material and
that there i s no stress r e d i s t r i b u t i o n due to destressing of the
f a i l e d rock mass. This assumption may not be correct for highly
loaded p i l l a r s .
3.2.2.2 Interactive F a i l u r e C r i t e r i o n
An i n t e r a c t i v e f a i l u r e c r i t e r i o n works during the numerical
computations by adjusting the stress i n regions of the rock mass
that f a i l due to high stress. This requires a c r i t e r i o n to
determine the peak strength of the rock mass and the post
f a i l u r e rock mass c h a r a c t e r i s t i c s . C a l i b r a t i o n of t h i s type of
c r i t e r i o n i s very involved and has a fundamental e f f e c t on the
r e s u l t s .
Documentation of the use of an i n t e r a c t i v e f a i l u r e c r i t e r i o n
i s given by Maconachie et a l . (1981) at the C.S.A. mine, Cobar
Mines Pty., New South Wales. The displacement discontinuity
program "N-Fold" with an i n t e r a c t i v e f a i l u r e c r i t e r i o n was used
to investigate the stress condition of a s i l l p i l l a r . The
program considers non-linear deformation and b r i t t l e y i e l d i n g of
elements. The y i e l d point and post f a i l u r e deformation varies
based on the confinement of the element. Figure 60 shows that
for increasing confinement (increasing distance from a free
BRITTLENESS PEAK MOOULUS IMPol STRENGTH (MPol
a EXPOSED CORNER 12-5 72
b EXPOSED SIDE 8-3 90
c RE-ENTRANT CORNER 7-0 126
d ONE BEHIND FREE SIOE 6-3 1S6
FIGURE 19. The peak strength, deformation c h a r a c t e r i s t i c s , and e f f e c t of location used for investigating a p i l l a r case history with a displacement discontinuity program (after Maconachie et a l 1981).
| | ELASTIC
FIGURE 20. The normal stress and the f a i l e d regions estimated with the displacement discontinuity program for a s i l l p i l l a r case h i s t o r y (after Maconachie et a l 1981).
62
face), the peak strength increases and the post-peak load
bearing capacity of the rock improves. The c a l i b r a t i o n of the
f a i l u r e c r i t e r i o n was based on estimations of the i n s i t u rock
mass strength and laboratory material properties. The material
properties were subsequently v e r i f i e d based on observation and
monitoring of the s i l l p i l l a r .
When applied to a longitudinal section of the s i l l p i l l a r
(figure 20), the zones of f a i l e d , and y i e l d i n g rock were
outlined and the magnitude of the normal stresses f o r rock under
e l a s t i c deformation was determined. The f a i l u r e c r i t e r i o n
helped determine the best stope extraction sequence and
indicated the need of a pendant p i l l a r to maintain s t a b i l i t y i n
the s i l l p i l l a r .
While p o t e n t i a l l y very useful i n p i l l a r design, t h i s type of
f a i l u r e c r i t e r i o n needs a large amount of c a l i b r a t i o n and
v e r i f i c a t i o n before becoming a r e l i a b l e t o o l . Generally, the
more s o p h i s t i c a t e d and complex the program and f a i l u r e
c r i t e r i o n , the greater the number of assumptions introduced into
the s o l u t i o n .
3.2.2.3 P r i n c i p a l Stress Magnitude.
The most common and s i m p l i s t i c method of boundary element
in t e r p r e t a t i o n i s analysis of p r i n c i p a l stress magnitudes. In
p i l l a r s , stress d i s t r i b u t i o n s are plotted on mine plans or
sections to reveal areas of high or low p r i n c i p a l stress.
Potential mining problems are then estimated based on the stress
d i s t r i b u t i o n s .
A t y p i c a l example of the use of p r i n c i p a l stress magnitude
analysis i s given i n a paper by Bywater et a l . (1983) , at the
Mount Isa mine. I t was determined through experience that areas
with normal stress greater than 70 MN/m2 generally exhibit
s p a l l i n g and are prone to l o c a l rock f a i l u r e . A l i n e a r e l a s t i c
displacement d i s c o n t i n u i t y code was used to analyze the
p o t e n t i a l stress d i s t r i b u t i o n s i n a new mining block. Figure 21
shows two d i f f e r e n t extraction sequences for the mining block,
with the predicted stresses corresponding to the legend. The
analysis shows more overstressed areas being developed i n the
second sequence which would cause problems e a r l i e r i n the p i l l a r
recovery.
When the rock mass strength has not been estimated, stresses
are f r e q u e n t l y normalized a g a i n s t the i n t a c t u n i a x i a l
compressive strength of the rock. Mining problems are l i k e l y to
occur i f the normalized major p r i n c i p a l stress i s greater than
1/3 (Bawden et a l . 1988) to 1/2 (Mathews et a l . 1980).
3.2.3 Limitations of Boundary Element Modelling
While boundary element modelling i s a sophisticated design
t o o l , i t has several l i m i t a t i o n s and p o t e n t i a l sources of
inaccuracy i n applied rock mechanics. The l i m i t a t i o n s can be
grouped into two basic categories:
(i) l i m i t a t i o n s with respect to modelling a rock mass,
( i i ) and l i m i t a t i o n s due to computational assumptions.
3.2.3.1 Modelling a Rock Mass
NORMAL • +70 MN/m 2
STRESS £ S 60 - 69 MN/m'
/ £ ] 50 - 59 MN/m2
40 - 49 MN/m 2
FIGURE 21. The d i s t r i b u t i o n of normal stress i n a mining block was estimated f o r two d i f f e r e n t mining sequences to determine the best stope extraction sequence (after Bywater et a l . 1983).
A numerical modelling solution assumes the medium has
perfect material properties. In r e a l i t y , a rock mass i s not a
perfect material. A number of approximations and assumptions
are usually necessary for the estimation of the properties
describing the rock mass. The material properties of a rock
mass have to be estimated assuming the rock mass behaves as an
i s o t r o p i c continuum. This means that the rock mass eithe r has
no s i g n i f i c a n t d i s c o n t i n u i t i e s , or the d i s c o n t i n u i t i e s are
s u f f i c i e n t l y small, regular and frequent that they have no
e f f e c t on s t r e s s . For minor structure such as rock j o i n t s , t h i s
may not be a serious l i m i t a t i o n . However for major structure,
e s p e c i a l l y f a u l t s that have moved su b s t a n t i a l l y , the rock mass
may not act as an i s o t r o p i c continuum at a l l . This could
i n v a l i d a t e any numerical solution that did not e x p l i c i t l y model
the d i s c o n t i n u i t y .
Most boundary element methods give the rock mass l i n e a r
e l a s t i c deformational c h a r a c t e r i s t i c s . Laboratory measurements
have found that over a range of loading conditions, hard rock
samples exhi b i t some non-linear and p l a s t i c deformation. In
addition, the p o s t - f a i l u r e load bearing behaviour of an i n s i t u
rock mass i s dependent upon several variables that are not
r e l a t e d to the e l a s t i c c h a r a c t e r i s t i c s of the rock. For low to
medium loading conditions, the use of l i n e a r e l a s t i c i t y i s
generally acceptable, but for a discontinuum, highly loaded, or
f a i l e d rock mass, l i n e a r e l a s t i c behaviour i s a poor assumption.
Parametric studies using boundary element models have shown
a large influence of the pre-mining stress regime. This i s an
expensive and d i f f i c u l t parameter to measure. The actual i n
s i t u stress f i e l d varies with depth and can be profoundly
influenced by major s t r u c t u r a l d i s c o n t i n u i t i e s . Consequently,
the v i r g i n stress used i n numerical methods w i l l only be an
approximation of the actual conditions.
I t i s important to be aware of these l i m i t a t i o n s and t h e i r
possible e f f e c t on the numerical solution's a b i l i t y to describe
the condition of a stressed rock mass.
3.2.3.2 Computational Assumptions
Boundary element methods are numerical approximations of the
solut i o n to a boundary value problem. Only the simplest
excavation geometries can be solved a n a l y t i c a l l y , so for
complicated geometries, a solution i s determined through a
numerical i t e r a t i o n process. This necessitates d i s c r e t i z i n g the
boundary into segments and piecewise modelling of stresses and
displacements on each segment. The r e s u l t i s :
- the i n t e r i o r s o l u t i o n (stresses o f f the boundary) may not be
accurate very near the d i s c r e t i z e d boundary,
- and the numerical solution i s only an approximation because
the computation i s completed when a s p e c i f i e d convergence
c r i t e r i o n i s met.
Through the modelling of boundaries with known solutions, i t
has been found that the larger the number of elements on a
boundary, the greater the accuracy of the numerical model with
67
respect to the known closed form solution. The magnitude of the
difference between the numerical model and the closed form
solut i o n decreases with an increase i n the number of elements,
so there i s a p r a c t i c a l l i m i t to the influence of the number of
elements. Above t h i s l i m i t , the addition of extra elements does
l i t t l e or nothing to improve the accuracy of the solution.
In summary, reading too much d e t a i l i n a numerical solution
can be misleading. C a l i b r a t i o n of numerical models with
experience and case h i s t o r i e s can be as important as the type of
numerical model used or how the r e s u l t s are analyzed. I t should
be kept i n perspective that boundary element methods only
account for stress related f a i l u r e . S t r u c t u r a l l y controlled
f a i l u r e or f a i l u r e due to the combination of stress , and
structure may not be interpreted from numerical modelling stress
d i s t r i b u t i o n s .
68
CHAPTER 4
OPEN STOPE RIB PILLAR DATA BASE
The objective of t h i s chapter i s to present the r i b p i l l a r
data c o l l e c t e d during the Integrated Mine Design Study. This
w i l l be done by:
- d i s c u s s i n g some of the general c h a r a c t e r i s t i c s and
information of the p i l l a r case h i s t o r i e s ,
- presenting the background and physical information on each
case h i s t o r y ,
- defining the q u a l i t a t i v e scale used to give an assessment to
the case h i s t o r i e s ,
- and describing the signs of f a i l u r e f or a l l the case
h i s t o r i e s that experienced s t a b i l i t y problems.
4.1 General Data Base Information
The o r i g i n a l data used i n t h i s thesis has been c o l l e c t e d i n
Canadian open stope mines. The 47 case h i s t o r i e s are only a
f r a c t i o n of the t o t a l data c o l l e c t e d during the "Integrated Mine
Design Study". Some of the data was rejected because:
(i) geotechnical parameters including i n s i t u stress, i n t a c t
rock strength and the influence of geological structure
could not be estimated with confidence,
( i i ) the actual events of the case h i s t o r y could not be
v e r i f i e d ,
( i i i ) the stress conditions i n the case h i s t o r y were too complex
69
to be back-analyzed with the means ava i l a b l e at U.B.C.
Throughout the course of the study, several mines requested
that t h e i r name not appear d i r e c t l y associated with data. To
respect t h e i r anonymity, there i s no s p e c i f i c reference to the
s i t e of any unpublished data i n t h i s t h e s i s . S p e c i f i c
i n f o r m a t i o n about the mining environment, g e o t e c h n i c a l
parameters and case h i s t o r i e s i s presented through the use of
mine numbers.
The data base i s supplemented by information presented i n
U.B.C. theses that discuss open stope r i b p i l l a r s , by Goldbeck
(1985), Potvin (1985) and Pakalnis (1986).
A s i g n i f i c a n t feature of many of the p i l l a r s i n the data
base i s that they were stable at one time during the mining and
l a t e r f a i l e d . The f a i l u r e was caused by increased extraction
near the p i l l a r or mining portions of the p i l l a r . Among the 47
case h i s t o r i e s i n the data base, 30 originate from 13 p i l l a r s at
d i f f e r e n t stages of extraction. These " y i e l d i n g p i l l a r s " w i l l
be very important to the development of a r i b p i l l a r design
method.
4.2 Background Data
The background information concerning p i l l a r dimensions,
depth, mining environment including r a t i o of extraction and
b a c k f i l l , and an assessment of the p i l l a r condition i s given i n
Table 5. The dimensions and r a t i o of extraction are defined
70
PILLU KXNI PILLA1 PILL41 SBOMim lAcmix D t P T B EXTRACTION c s n t u c s ASSESSMENT NUKUt NUKBER MAKE ttLLA» sron flLLAI DIP (* mns (•) uno (•*) (MPl)
WIDTH { HEIGHT HEICHT ULCM) (•*) (MPl)
2 : 14-3-2/4 43 ! 3' 53 90 NO 820 3tX 62 2 0 0 STABLE 3 2 U-3-2 15 ! 34 49 90 NO 820 57X 62 2 0 0 PAILU1E 7 6 33-176/183 33 ! 50 20 90 12.1 T 1000 25X 64 121 STABLE 8 6 33-176 11 ! 50 20 90 12.1 T 1000 501 64 121 PAILUIX
15 8 23*7 12 ! 50 8 80 32:1 t 210 56Z 77 215 STABLE 16 2549 15 ! 50 7 80 32:1 1 210 571 77 215 STABLE 17 10 062 25 : too 27 65 20:1 1 360 SOX 60 70 SLOUCHINC IS 11 30-203 24 I M 11 90 NO 870 59Z 75 148 STABLE 19 11 30-205 3 5 i 100 12 90 NO (70 60Z 75 148 STABLE 20 16 77-90 15 ! 120 15 90 NO 300 71Z 71 176 SLOUGEDK 21 16 77-92 27 : 1 2 0 40 90 NO 300 SIX 71 176 STABLE 22 16 77-94 30 i 105 40 90 NO 300 49X 71 176 STABLE 23 16 77-92 27 ! 120 40 90 NO 300 68X 71 176 PAILUII 24 16 77-94 30 ! 105 40 90 NO 300 49X 71 176 STABLE 25 16 77-94 30 1 105 40 90 NO 300 84Z 71 176 PAILUU 26 16 80-78 21 ! 135 24 90 NO 210 671 71 176 STABLE 27 16 80-80 15 ! 135 12 90 NO 210 751 71 176 STABLE 28 16 80-82 15 ! '5 27 90 NO 210 71X 71 176 SLOUGHING 29 16 80-84 21 ! 75 39 90 NO. 210 63X 71 176 STABLE 30 16 80-82 15 ! " 27 90 NO 210 82Z 71 176 FAILURE 31 16 80-80 15 135 12 90 NO 210 87Z 71 176 STABLE 32 17 10-20 21 ! ISO 21 90 NO 215 55X 65 100 STABLE 33 17 10-21.5 ! 150 20 90 NO 215 74Z 65 100 FAILURE
17 10-23 15 ! 150 18 90 NO 215 60X 65 1 0 0 SLOUGHING 35 17 10-20 21 : 1 5 0 21 90 NO 215 66X 65 1 0 0 STABLE 36 17 10-20 15 ! 150 30 90 ROCXPILL 215 80Z 65 100 FAILURE 37 17 10-23 15 : i s o 18 90 NO 215 74X 65 100 FAILURE 42 19 LEVEL 11 #8 11 ! 55 23 90 30:1 T 620 501 78 316 FAILURE 43 19 Lll 16-8 33 ! 55 23 90 30.1 T 620 2SX 78 316 STABLE 44 19 Lll (14-16 33 ! 55 IS 90 30:1 T 620 2SX 78 316 STABLE 45 19 LEVEL 11 #14 11 ! 55 18 90 30:1 I 620 502 78 316 FAILURE 46 21 120-13D 32 ! 60 28 70 NO 340 37X 68 90 STABLE 47 21 12D-13S 25 ! 60 28 70 NO 340 46X 68 90 SLOUCHING 48 21 12D-13D 19 ! 60 28 70 NO 340 58X 68 90 FAILURE *9 21 12D-13D 14 ! 60 28 70 NO 340 70X 68 90 FAILURE
22 301 #15 17 ! 35 6 90 TAILINGS 320 66X 63 72 STABLE 51 22 301 116 21 ! 35 5 90 TAILINGS 320 67X 63 72 STABLE 52 22 301 #17 18 ! 35 4 90 TAILINGS 320 61Z 63 72 STABLE 53 22 330 #4-5 24 ! 58 18 90 TAILINGS 520 SIX 69 72 STABLE 54 23 341 VP 17 t 170 10 90 ROOJILL 290 ! 64Z 71 310 STABLE 55 2} 342 VP 20 170 8 90 R0CX7ILL 290 ; 67X 71 310 STABLE 56 31 448 27 I 110 46 90 NO 500 61X 75 26S SLOUGH 57 31 450 24 : n o 52 90 NO 500 : 38X : 75 265 STABLE 58 31 452 30 : n o 44 90 NO 500 ; 38X 75 265 STABLE 59 31 450 24 ; n o 52 90 NO 500 : 73X 75 265 SLOUGH 60 31 452 30 ! n o 44 90 NO 500 ; 75X 75 265 SLOUCH 61 30 2020 PILLAR 24 : n o 38 90 20:1 8 520 59X : 70 ; 160 SLOUGH
A r a t i o r a f a r s to a vasta to camant r a t i o T or TAILINGS naans tha b a c k f i l l i n g a a t a r l a l i a p r i m a r i l y c l a a a i f i a d m i l l t a i l l n f a . R or ROCKPILL aaana tha b a c k f i l l i n g a a t a r l a l l a p r l a v a r i l y vaata rock.
TABLE 5. Background data for a l l the p i l l a r case h i s t o r i e s .
71
according to figure 22. The dimensions presented are the design
dimensions. The actual dimensions may vary s l i g h t l y for most
f a i l e d , the actual dimensions (especially p i l l a r width) may be
s u b s t a n t i a l l y smaller than the design dimensions, due to
excessive sloughing. J u s t i f i c a t i o n for the assessment of the
condition of each sloughing and f a i l e d p i l l a r i s given i n
chapter 4.3.
S p e c i f i c information about the geological s e t t i n g of each
case h i s t o r y can be found i n the isometric sketch corresponding
to the mine number (see Appendix I ) . Each geological s e t t i n g i s
comprised of:
- the underground stress regime,
- the hanging wall, footwall and orebody material properties
and c h a r a c t e r i s t i c s including,
cases due to b l a s t induced damage. For p i l l a r s that have
- rock type,
- i n t a c t u n i a x i a l compressive strength,
- e l a s t i c modulus,
- poisson's r a t i o ,
- NGI rock mass c l a s s i f i c a t i o n ,
- the orebody shape and s i z e ,
- and the mining methods used i n various parts of the
orebody.
Several mines use very s i m i l a r stope and p i l l a r dimensions
throughout the mine. Inclusion of t h i s data would p o t e n t i a l l y
Lo1 = length of stope 1
Lo2 = length of stope 2
Wp = width of pillar
Hp = height of pillar, or stope breadth
Ho = stope height
FIGURE 22. This figure shows the geometrical d e f i n i t i o n for the stope and p i l l a r dimensions used i n t h i s t h e s i s .
double or t r i p l e the s i z e of the data base. However, using
several case h i s t o r i e s with the exact same information would not
broaden the c a p a b i l i t y of the data base to the develop a design
method. I t would create problems i n data presentation and
d i l u t e the influence of single case h i s t o r i e s . As a re s u l t ,
only unique cases are presented.
4 . 3 P i l l a r Assessment
The signs of r i b p i l l a r i n s t a b i l i t y are l i s t e d i n Chapter
2.1. Based on these signs, three q u a l i t a t i v e assessments have
been chosen to categorize the condition of the p i l l a r s i n the
data base.
A stable assessment i s given to p i l l a r s generally not
showing any signs of i n s t a b i l i t y . Any ground control problems
are too small to have an e f f e c t on mining near the p i l l a r .
A sloughing assessment i s given to p i l l a r s showing one or
more of the above signs, but the extent of de t e r i o r a t i o n i s not
severe and i s reported i n only a few areas of the p i l l a r . The
ground control problems associated with sloughing p i l l a r s have a
li m i t e d e f f e c t on mining, such as: d r i l l i n g problems, loss or
d i f f i c u l t y i n maintaining some d r i l l holes, the need for
development s c a l i n g and r e h a b i l i t a t i o n and some wall sloughing
and p i l l a r overbreak. The sloughing assessment i s also used to
describe p i l l a r s whose s t a b i l i t y problems are time dependent,
becoming more severe as mining continues. Several p i l l a r case
h i s t o r i e s have been assessed as sloughing, but have used quick
74
b a c k f i l l i n g to prevent complete p i l l a r f a i l u r e .
A f a i l e d assessment i s given to p i l l a r s showing large and
severe signs of i n s t a b i l i t y . Their e f f e c t s on mining, include:
- loss of ore,
- low p r o d u c t i v i t y due to oversize material and overbreak
created during mining, the need for frequent r e h a b i l i t a t i o n
of development or the use of cable b o l t s to prevent loss of
p i l l a r development,
- and severe cracking, j o i n t opening, and displacement often
needing immediate stope f i l l i n g to prevent complete p i l l a r
d i s i n t e g r a t i o n .
The assessment of p i l l a r s was based l a r g e l y on documentation
and d e s c r i p t i o n by on-site s t a f f and some observations by the
author. J u s t i f i c a t i o n of the assessment fo r a l l the sloughing
and f a i l e d p i l l a r s i s detailed below, by describing the most
serious signs of i n s t a b i l i t y f o r each case h i s t o r y :
CASE # 3 Assessment: F a i l u r e . P i l l a r Condition: Sloughing of large slabs from p i l l a r walls
into primary stope drawpoints, problems i n maintaining blastholes, wall sloughing intersected development i n the middle of the p i l l a r .
(reference: Falmagne 1986).
CASE # 8 Assessment: F a i l u r e . P i l l a r C o n d i t i o n : Severe a x i a l c r a c k i n g i n p i l l a r
development requiring cable b o l t i n g to maintain overcut and undercut s t a b i l i t y , several feet of overbreak beyond blastholes and hourglass sloughing i n the middle of p i l l a r walls.
75
CASE # 17 Assessment: Sloughing. P i l l a r Condition: Shears and j o i n t s opening i n p i l l a r s ,
sloughing of p i l l a r walls into primary stopes. Some problems i n d r i l l i n g and maintaining d r i l l holes.
(reference: Bawden 1988) .
CASE #20 Assessment: Sloughing. P i l l a r Condition: Progressive sloughing of p i l l a r walls into
adjacent stopes. (reference: A l l c o t t and Archibald 1981).
CASE #23 Assessment: F a i l u r e . P i l l a r Condition: Severe sloughing of p i l l a r walls into
adjacent stopes. (reference: A l l c o t t and Archibald 1981).
CASE #25 Assessment: F a i l u r e . P i l l a r Condition: Major shear displacement extending over
two l e v e l s 45 metres apart, sloughing of p i l l a r walls, (reference: A l l c o t t and Archibald 1981; Potvin 1984).
CASE #28 Assessment: Sloughing. P i l l a r C o n d i t i o n : Severe ground f r a c t u r i n g causes
abandonment of p i l l a r development, (reference: A l l c o t t and Archibald 1981).
CASE #30 Assessment: F a i l u r e . P i l l a r Condition: P i l l a r crushes v i o l e n t l y a f t e r nearby
p i l l a r i s recovered by bla s t i n g , (reference: A l l c o t t and Archibald 1981).
CASE #33 Assessment: F a i l u r e . P i l l a r Condition: Extensive cracking of p i l l a r , followed by
the sloughing of 2 rings of d r i l l holes and major collapse of the upper h a l f of the p i l l a r into adjacent stopes.
(reference: Bray 1967).
CASE #34 Assessment: Sloughing. P i l l a r Condition: Extensive cracking of the p i l l a r reported,
with some sloughing into nearby stopes. (reference: Bray 1967).
76 CASE #36
Assessment: F a i l u r e . P i l l a r Condition: West side of the p i l l a r sloughs into
adjacent stope causing breakthrough to a p i l l a r crosscut.
(reference: Bray 1967).
CASE #37 Assessment: F a i l u r e . P i l l a r Condition: Wall sloughing creates a hole completely
through the p i l l a r , (reference: Bray 1967).
CASE # 42,45 Assessment: F a i l u r e . P i l l a r Condition: Severe cracking, s p a l l i n g and j o i n t
opening i n p i l l a r development with wooden c r i b s and cable b o l t i n g needed to l i m i t development closure and collapse, heavy overbreak on production b l a s t s .
(reference: Bawden and Milne 1987; Chauvin 1986).
CASE #47 Assessment: Sloughing. P i l l a r Condition: One v i b r a t i n g wire stressmeter shows
decrease i n stress through p i l l a r , (reference: Goldbeck 1985).
CASE #48 Assessment: F a i l u r e . P i l l a r Condition: A l l v i b r a t i n g wire stressmeters show
decrease i n stress through p i l l a r , (reference: Goldbeck 1985).
CASE #49 Assessment: F a i l u r e . P i l l a r Condition: Sharp decrease i n p i l l a r stress shown by
v i b r a t i n g wire stressmeters. (reference: Goldbeck 1985).
CASE # 56 Assessment: Sloughing. P i l l a r Condition: Serious a x i a l cracking i n p i l l a r as stopes
retreated to p i l l a r .
CASE # 59 Assessment: Sloughing. P i l l a r Condition: A x i a l cracks i n p i l l a r develop and open
a f t e r recovery of a nearby p i l l a r .
77
CASE #60 Assessment: Sloughing. P i l l a r Condition: A x i a l cracks i n p i l l a r develop and open
a f t e r recovery of a nearby p i l l a r .
CASE # 61 Assessment: Sloughing. P i l l a r Condition: Sloughing of p i l l a r walls as f a r as centre
of p i l l a r , overbreak from p i l l a r s during primary mining and severe overbreak during secondary stope mining.
78
CHAPTER 5
BOUNDARY ELEMENT METHODS IN RIB PILLAR DESIGN
Boundary element numerical methods are an e f f e c t i v e way to
estimate the stress at any point i n a r i b p i l l a r (for reasons
described i n Chapter 3.2.3). For each of the case h i s t o r i e s
presented i n Chapter 4, a d i r e c t i n t e g r a l two dimensional
program (BITEM) and a pseudo-three dimensional displacement
d i s c o n t i n u i t y program (MINTAB) method w i l l be used to estimate
the average p i l l a r stress. For many r i b p i l l a r geometries,
these programs give adequate r e s u l t s . However, BITEM and MINTAB
have l i m i t a t i o n s that may cause serious inaccuracies when
applied to some three dimensional problems. Ideally, a three
dimensional method would be used to determine the stress
d i s t r i b u t i o n i n each case his t o r y . However, true three
dimensional analysis i s very new technology and the programs
have large setup and run times, need quite sophisticated
computing f a c i l i t i e s , and are li m i t e d i n program s i z e .
To better deine these l i m i t a t i o n s , a three dimensional
boundary element code (BEAP) and BITEM and MINTAB w i l l be used
to investigate the average stress i n t y p i c a l r i b p i l l a r
geometries. This comparison w i l l be used to approximate the
error associated with the application of the two dimensional and
displacement dis c o n t i n u i t y methods to 3D problems.
79
5.1 Boundary Element Methods Used
The following general description of the boundary element
methods and numerical codes involved i n the study i s taken
l a r g e l y from an unpublished paper written at U.B.C. (Hudyma
1988b).
5.1.1 BITEM
The 2D d i r e c t boundary i n t e g r a l model "BITEM" i s based on
the program "BITE" developed by P.C. R i c c a r d e l l a at the
Carnegie-Mellon u n i v e r s i t y i n 1973. I t was expanded to perform
p i e c e - w i s e homogeneous e l a s t i c i t y a n a l y s e s by CSIRO
(Commonwealth S c i e n t i f i c and I n d u s t r i a l Research Organization,
Australia) i n 1978. The program was subsequently modified for
the U.B.C. mainframe computer by R. Pakalnis i n 1983 and l a t e r
for an IBM compatible computer by CANMET under the program name
PCBEM (Pakalnis 1987).
The boundary i n t e g r a l technique i s designed for problems
that have one long dimension and a constant cross sectional
shape. I t requires the d i s c r e t i z a t i o n of a l l excavation
surfaces into segments connected by nodes (see figure 23) . An
e x p l i c i t s o l u t i o n i s selected to represent the medium's i n s i t u
stress conditions. These f i e l d stresses can be constant or can
vary l i n e a r l y with p o s i t i o n . When excavations are created, the
stress perpendicular to the boundary nodes becomes zero. BITEM
then calculates t r a c t i o n s and displacements at a l l the nodes of
a l l the boundaries. The boundary solution i s determined through
OPENING TO
FIGURE 23. Isometric view of an opening that i s long i n one d i r e c t i o n and the d i s c r e t i z a t i o n of the boundary used i n two dimensional modelling (after Hudyma 1988b).
81
an i t e r a t i v e procedure i n which the stress and displacement at
each node influences the stress and displacement of the other
nodes of the boundary. This procedure ends when the difference
between the l a s t two i t e r a t i o n s i s less than a user defined
convergence c r i t e r i o n . Once a boundary solu t i o n has been
determined, stresses and displacements i n t e r n a l to the problem
boundary can be determined using the boundary solu t i o n and
s t r e s s - s t r a i n r e l a t i o n s h i p s . A more det a i l e d d e s c r i p t i o n of the
boundary i n t e g r a l technique i s found i n Brady and Bray (1978).
5.1.2 MINTAB
Mintab i s a pseudo-three dimensional displacement
d i s c o n t i n u i t y boundary element program. The o r i g i n a l code was
written by Dr. S.L. Crouch i n South A f r i c a . The program has had
several major modifications r e s u l t i n g i n several d i f f e r e n t
program names, including: MINSIM, MINTAB, BESOL and N-FOLD.
Each v a r i a t i o n has special features such: as the i n c l u s i o n of
b a c k f i l l elements, use of a s e m i - i n f i n i t e domain (can account
for the surface of the earth), use of multiple en echelon seams,
f a u l t s and folds i n the seams and a program i n t e r a c t i v e f a i l u r e
c r i t e r i o n with p o s t - f a i l u r e rock mass c h a r a c t e r i s t i c s . The
version used f o r t h i s study i s CANMET's MINTAB version 4.0
(1983) which performs only l i n e a r e l a s t i c analysis of one planar
seam, i n an i n f i n i t e domain, and with no b u i l t i n f a i l u r e
c r i t e r i o n .
MINTAB uses the displacement di s c o n t i n u i t y method to solve
82
stresses, s t r a i n s and displacements i n three dimensions around
excavations i n tabular orebodies. In MINTAB, the orebody i s
d i s c r e t i z e d into a g r i d of square two dimensional elements (see
figure 24) . Each element represents mined or unmined area i n
the reef. The t h i r d dimension i s the width of the seam. To
give an accurate solution, the seam width must be small i n
r e l a t i o n to the o v e r a l l s i z e of the problem. The d e f i n i t i o n of
a small seam and the l i m i t a t i o n s of displacement d i s c o n t i n u i t y
modelling w i l l be discussed i n Chapter 5.4.
For p r a c t i c a l purposes, the reef can be considered as two
p a r a l l e l planes. Creating excavations i n the g r i d induces
movement of the planes. Relative movements between the two
planes are broken into two components. Ride components act
p a r a l l e l to the plane boundaries and closure components act
normal to the planes. The seam elements are subjected to a
three dimensional stress f i e l d (see figure 24) . Displacement
d i s c o n t i n u i t y components i n three dimensions are associated with
each element and represent r e l a t i v e displacement between the two
planes. I f the two planes do not come i n contact due to
displacement, the t r a c t i o n s o"zz, o"yZ, and a x z are a l l zero.
Displacements and stresses at unmined points i n the seam are
c a l c u l a t e d as a l i n e a r combination of the displacement
d i s c o n t i n u i t i e s of a l l the elements i n the seam. A more
det a i l e d description of the displacement d i s c o n t i n u i t y method i s
given by S t a r f i e l d and Crouch (1973).
24. Oblique view of the MINTAB seam geometry and the s applied l o c a l l y on each element i n the reef.
84
5.1.3 BEAP
BEAP i s a three dimensional boundary element program
developed by J.A.C. Diering as a PhD t h e s i s , at Pretoria
University (1987), i n conjunction with CANMET, INCO (Thompson
Division) and GEMCOM (Pty.) Limited. Version 1.0, used i n t h i s
project, i s due for public release i n the f a l l of 1988.
E x c a v a t i o n boundaries are g e n e r a l l y d i s c r e t i z e d by
q u a d r i l a t e r a l elements (see figure 25). The problem i s subject
to an a r b i t r a r i l y oriented stress f i e l d . The stress and
displacements on the boundary elements vary quadratically and
are non-conforming. This means displacements and t r a c t i o n s on
each element are assumed to vary according to a quadratic
polynomial, and the displacements between adjacent elements are
discontinuous. The r e s u l t i n g numerical model has some powerful
a b i l i t i e s i n mining related stress analysis, including:
- the need for fewer elements to d i s c r e t i z e an excavation than
other three dimensional boundary element models,
- the a b i l i t y to accommodate up to f i v e zones with d i f f e r e n t
material properties,
- the use of lumping to reduce data storage requirements,
- and the a b i l i t y to determine stresses and displacements very
close to an excavation boundary.
Further d e t a i l s about BEAP can be found i n Diering (1987) and
Diering and Stacey (1987).
5.2 Open Stope Rib P i l l a r Modelling
85
FIGURE 25. A t y p i c a l BEAP geometry showing the boundary of the excavations defined by two dimensional quadratic, non conforming elements in a three dimensional stress f i e l d (after Hudyma 1988b).
86
Boundary element numerical modelling of hard rock
excavations r e l i e s l a r g e l y on the problem geometry and the
magnitude and orientation of the pre-mining stress. This
section describes a consistent method to specify the stope and
p i l l a r dimensions and to determine the average load on r i b
p i l l a r s i n open stope mining.
5.2.1 Defining the Open Stope Geometry
In t h i s t h e s is, the dimensions of stopes and p i l l a r s w i l l be
defined according to figure 26. P i l l a r dimensions are defined
with respect to the d i r e c t i o n of the greatest induced stress.
The p i l l a r height i s t y p i c a l l y defined as p a r a l l e l to the
d i r e c t i o n of greatest induced load. Induced load, i n any
d i r e c t i o n , i s mostly a function of the s i z e and shape of the
excavation surface perpendicular to that load. For small
excavation surfaces, the stress r e d i s t r i b u t i o n i s small. For
large excavation surfaces, the stress r e d i s t r i b u t i o n w i l l be
much larger. In horizontal orebodies (where most of the
o r i g i n a l p i l l a r design research was done), the greatest induced
load i s v e r t i c a l and the p i l l a r height i s v e r t i c a l (see figure
27a). In steep dipping orebodies, the largest induced load i s
horizontal and the p i l l a r height i s horizontal (see figure 27b).
For i n c l i n e d orebodies, the p i l l a r height i s defined as the
d i r e c t i o n perpendicular to the orebody.
5.2.2 Defining the Average P i l l a r Stress
S t o p e 1
L o 1
Wp
S t o p e 2
L o 2
Lo1 = length of stope 1
Lo2 = length of stope 2
Wp = width of pillar
Hp = height of pillar, or stope breadth
FIGURE 26. This figure defines the dimensions for stopes and p i l l a r s , and the orientation f o r the in s i t u s t r e s s regime f o r t h i s thesis.
88
£p 0" = Ugh
| Hp
FIGURE 27a. A r i b p i l l a r i n a horizontal seam loaded by the weight of the overburden.
FIGURE 27b. The d i r e c t i o n of loading on a p i l l a r i n a v e r t i c a l orebody.
89
For an i d e a l i z e d open stope r i b p i l l a r i n a v e r t i c a l
orebody, the i n s i t u stress acts i n three basic d i r e c t i o n s : a x,
ay, and a 2 (see figure 28) . P i l l a r stress i s a r e s u l t of the
pre-mining stress that i s concentrated because of adjacent
excavations. Stress concentration i n a d i r e c t i o n i s generally
proportional to the s i z e and shape of the stope surfaces normal
to that stress d i r e c t i o n . In p i l l a r design, the d i r e c t i o n of
greatest importance i s usually the d i r e c t i o n that has the
highest s t r e s s .
Inside r i b p i l l a r s , the stress acting i n the a x d i r e c t i o n i s
the lowest because i t i s p a r a l l e l to the orebody s t r i k e which
causes i t to be shadowed by the open stopes. The induced load
i n the rjy d i r e c t i o n i s almost always larger than i n the a z
d i r e c t i o n , because the pre-mining stress i n the Oy d i r e c t i o n i s
t y p i c a l l y much greater than i n the a z d i r e c t i o n . In addition,
for s u b - v e r t i c a l l y dipping orebodies, the stope surface normal
to the Oy d i r e c t i o n i s much larger than those perpendicular to
the a2 d i r e c t i o n . This means the p i l l a r stress i n sub-vertical
orebodies i s almost always highest i n the Oy d i r e c t i o n .
There i s a large v a r i a t i o n i n the ay stress f i e l d i n a r i b
p i l l a r . The best location to determine the average ay stress i s
the p i l l a r c enterline at the middle of the stope height (also
c a l l e d the p i l l a r "mid-height c e n t e r l i n e " ) , see figure 28. The
reasons for t h i s l o c a t i o n are:
- i t i s the region of highest normal stress (ay d i r e c t i o n ) ,
- i t i s the region of lowest confining stress ( a x d i r e c t i o n ) ,
90
MID-HEIGHT CENTERLINE
MID-HEIGHT PLANE
FIGURE 28. The mid-height plane and centerline for t a l l open stope geometries.
- i t i s often observed to be one of the f i r s t areas of
i n s t a b i l i t y i n a p i l l a r ,
- the e f f e c t of the excavation corners and stope ends are at a
minimum,
- t h i s i s usually the plane of analysis when two dimensional
modelling (in plane strain) i s used.
However, there may be a large v a r i a t i o n i n the a v stress at
the mid-height centerline. Hoek and Brown (1980) show that as a
p i l l a r becomes more slender ( t a l l e r and narrower), the stress
d i s t r i b u t i o n across the mid-height of the p i l l a r becomes more
uniform. In a squat p i l l a r , the stress d i s t r i b u t i o n varies
s i g n i f i c a n t l y across the p i l l a r mid-height ce n t e r l i n e . They
suggest that the average p i l l a r stress should be the average
value of the maximum p r i n c i p a l stress (in the ay direction)
across the p i l l a r . So for t h i s thesis, the average p i l l a r
stress for open stope r i b p i l l a r s w i l l be calculated as the
average stress along the mid-height centerline of the p i l l a r .
5.3 2D Modelling of 3D Excavation Geometries
Numerical modelling of underground excavations with 3D
methods i s a time consuming and expensive procedure. Two
dimensional numerical modelling can be used e f f e c t i v e l y to
estimate the stress found i n some of the planes of a 3D p i l l a r
geometry, and at a much lower cost than 3D numerical methods.
One of these planes i s at the mid-height of t a l l open stopes,
which i s of primary concern i n open stope r i b p i l l a r design.
This sub-section w i l l discuss how 2D modelling can be used to
estimate the average p i l l a r stress i n open stope r i b p i l l a r s .
I t w i l l also estimate the difference between 2D and 3D numerical
modelling for various open stope mining geometries.
5.3.1 Plane S t r a i n Solution
To estimate the stress around open stopes, the plane s t r a i n
s o l u t i o n i s generally used. Plane s t r a i n conditions assume that
around an excavation a l l the mining induced displacements occur
i n the plane of the orebody cross-section and the displacements
are the same for a l l cross-sections. In a t y p i c a l geometry, a
stope i s modelled i n the xy plane (see figure 28) . The
assumption i s that i n the 3D s i t u a t i o n , the stope ends have no
influence on the cross-section plane. Brown (1985) notes that:
"For uniform excavation cross-sections, other than those with
extreme a x i a l r a t i o s , the plane s t r a i n boundary stresses
usually approximate the correct three-dimensional stress to
within l e s s than ten, and sometimes f i v e , per cent at
locations removed by at le a s t two excavation 'diameters' from
intersections, excavation ends or changes of cross-section."
In applying plane s t r a i n conditions to open stope r i b p i l l a r
design, the subject of i n t e r e s t i s the influence of the stope
ends on the stress at the mid-height centerline of the p i l l a r .
I f the mid-height plane i s not s u f f i c i e n t l y removed from the
stope ends, some of the mining induced stress r e d i s t r i b u t i o n
w i l l occur into the abutments at the stope ends, rather than
into the p i l l a r . This means that the stress at the mid-height
plane i s greatest when there i s no influence of the stope ends,
which i s the case for the 2D plane s t r a i n solution. This i s
confirmed i n work done by Watson and Cowling (1985) at Mt. Isa
and i s observed i n the r e s u l t s to be discussed i n Chapter 5.3.2.
5.3.2 Comparison of 2D and 3D Numerical Modelling Results
A comparison of several d i f f e r e n t stope geometries was done
with the 3D model BEAP, and the 2D model BITEM i n plane s t r a i n .
The objective was to investigate i n more depth the degree of
overestimation predicted by BITEM for d i f f e r e n t stope and p i l l a r
geometries.
The s i z e of the plane normal to the <7p stress (shaded plane,
figure 29) has the greatest influence on stress concentration at
the p i l l a r mid-height centerline. To check the influence of the
stope ends on the mid-height plane, the r a t i o of stope height to
stope length was varied. Four t e s t s , comprised of a t o t a l of 12
d i f f e r e n t stope geometries, were modelled with BITEM and BEAP.
The f i r s t t e s t checked the average p i l l a r stress as the height
was increased for stopes with a square cross-section. The
second t e s t checked the average p i l l a r stress for stopes with a
constant height and an increasing longitudinal stope length.
The t h i r d t e s t checked the average p i l l a r stress as the height
was increased for stopes with a constant longitudinal cross-
94
Op
H
L Wp FIGURE 29. The shaded plane has the greatest influence on
the mid-height a y stress.
TEST STOPE LENGTH
(D
STOPE BREADTH
(B)
STOPE HEIGHT
(H)
PILLAR WIDTH (Wp)
BEAP AVE.
PILLAR STRESS
INCREASE
BITEM H:L
RATIO
BITEM AVE.
PILLAR STRESS
INCREASE
SQUARE STOPE CROSS-
SECTION
10 10 10 10 1.25 1 : 1 1.8
SQUARE STOPE CROSS-
SECTION
10 10 20 10 1.A5 2 : 1 1.8 SQUARE STOPE CROSS-
SECTION 10 10 AO 10 1.65 A : 1 1.8
SQUARE STOPE CROSS-
SECTION 10 10 60 10 1.7 6 : 1 1.8
SQUARE STOPE CROSS-
SECTION
10 10 80 10 1.7 8 : 1 1.8
LONGITUDINAL STOPE CROSS-
SECTION
100 10 60 50 1.5 0.6 : 1 2.2 LONGIT
UDINAL STOPE CROSS-
SECTION
60 10 60 30 1.75 1 : 1 2.A5 LONGIT
UDINAL STOPE CROSS-
SECTION 30 10 60 15 2.05 2 : 1 2.5
LONGITUDINAL STOPE CROSS-
SECTION 10 10 60 10 1.7 6 : 1 1.8
LONGITUDINAL STOPE CROSS-
SECTION
30 10 30 15 1.65 1 : 1 2.5 LONGITUDINAL STOPE CROSS-
SECTION
30 10 60 15 2.05 2 : 1 2.5
LONGITUDINAL STOPE CROSS-
SECTION 30 10 120 15 2.3 A : 1 2.5
TRANSVERSE STOPE CROSS-
SECTION
10 10 AO 10 1.6 A : 1 1.8 TRANSVERSE STOPE CROSS-
SECTION
10 20 AO 10 l.A A : 1 1.6
TRANSVERSE STOPE CROSS-
SECTION 10 40 AO 10 1.2 A : 1 l.A
TABLE 6. Comparison of BEAP and BITEM for four sets of different orebody geometries.
section. The f i n a l t e s t checked the average p i l l a r stress as
stopes of a constant height and length were increased i n
breadth.
Table 6 shows the stope and p i l l a r dimensions f o r each run
(the dimensions are defined i n figure 29) . Table 6 also shows
the average p i l l a r stress increase for BEAP and BITEM and the
stope height:length r a t i o . The average p i l l a r stress increase
i s defined as the average p i l l a r stress divided by the pre-
mining stress i n that d i r e c t i o n ( i e . ay i n figure 28).
In a l l 12 cases, the average p i l l a r stress at the mid-height
centerline was higher for the 2D plane s t r a i n (BITEM) models
than the 3D BEAP models. The overestimation of BEAP by BITEM i s
shown for each geometry i n figure 30. The dashed l i n e on figure
3 0 i s an estimate of the maximum overestimation of BEAP by 2D
plane s t r a i n modelling for various stope height to stope length
r a t i o s . As the stope height to stope length r a t i o increases,
the average p i l l a r stress predicted by the 3D models i s closer
to the 2D plane s t r a i n solution. As the stope height to length
r a t i o increased over 4:1, the 3D stress induced i n the
horizontal plane e s s e n t i a l l y remained the same and converged to
l e v e l s s i m i l a r the stress predicted by plane s t r a i n modelling.
Brown's comment (above) that a stope cross-section needs to be
at l e a s t two excavation "diameters" from the stope end, f o r good
agreement between 2D plane s t r a i n and 3D modelling r e s u l t s ,
would correspond to a stope height to stope length r a t i o of 4:1.
His estimation of less than 10 % difference between 2D plane
aVCn H V n i d 30VH3AV JO NOLLVHI±S3a3AO
FIGURE 30. Overestimation of average p i l l a r load by the 2D "BITEM" boundary element method f o r the 12 runs i n the four t e s t s .
97
s t r a i n and 3D modelling agrees well with the r e s u l t s presented
i n figure 30.
5.4 Displacement Discontinuity Modelling of 3D Stope Geometries
For excavations with i r r e g u l a r cross-sections or small stope
length to stope height r a t i o s , the 2D plane s t r a i n method can
not e f f e c t i v e l y predict the average stress at the mid-height
centerline of a p i l l a r . The displacement d i s c o n t i n u i t y (DD)
boundary element method MINTAB may be useful i n these
conditions. The DD code can be used to predict three
dimensional s t r e s s r e d i s t r i b u t i o n around t h i n , t a b u l a r
orebodies. For MINTAB analysis, the orebody must be a single
seam with n e g l i g i b l e v a r i a t i o n i n s t r i k e , dip and thickness. In
addition, the thickness of the seam must be small compared to
the length of excavations made i n the seam. The following sub
sections w i l l investigate the e f f e c t of the seam thickness on '
MINTAB's a b i l i t y t o p r e d i c t stresses at the mid-height
centerline of open stope r i b p i l l a r s .
5.4.1 Seam Thickness Limitations
To help discuss the influence of the thickness of the reef,
the r a t i o of the shortest stope dimension to the seam thickness
i s defined as the "seam thickness r a t i o " . In open stope mining,
where stopes are t y p i c a l l y t a l l e r than they are long, the seam
thickness r a t i o w i l l usually be the r a t i o of stope length to
stope breadth (see figure 31). Other authors have discussed the
SEAM THICKNESS RATIO = J__ B
FIGURE 31. The dimensions and geometry of the MINTAB/BEAP comparison tests.
1 TEST STOPE
LENGTH (L)
STOPE BREADTH
(B)
STOPE HEIGHT
(H)
PILLAR WIDTH (Wp)
BEAP 1 MINTAB AVE. | SEAM PILLAR | THICK. STRESS I RATIO INCREASED
MINTABI AVE. PILLAR STRESS INCREASE
SQUARE STOPE CROSS-SECTION
10 10 10 10 1.25 1.0 1.25
SQUARE STOPE CROSS-SECTION
10 10 20 10 1.45 1.0 1.35 SQUARE STOPE CROSS-SECTION
10 10 40 10 1.65 1.0 1.5 J SQUARE STOPE CROSS-SECTION
10 10 60 10 1.7 | 1.0 1.65 fl
SQUARE STOPE CROSS-SECTION
10 10 80 10 1.7 | 1.0 1.6 |
LONGITUDINAL STOPE CROSS-SECTION
100 10 60 50 1.5 1 6.0 1.5 LONGITUDINAL STOPE CROSS-SECTION
60 10 60 30 1.75 | 6.0 1.7 LONGITUDINAL STOPE CROSS-SECTION
30 10 60 15 2.05 fi 3.0 1
2.0
LONGITUDINAL STOPE CROSS-SECTION
10 10 60 10 1.7 | 1.0 1.65
LONGITUDINAL STOPE CROSS-SECTION
30 10 30 15 1.65 B 3.0 1.65 LONGITUDINAL STOPE CROSS-SECTION
30 10 60 15 2.05 3.0 2.0
LONGITUDINAL STOPE CROSS-SECTION 30 10 120 15 2.3 | 3.0 2.2
TRANSVERSE STOPE CROSS-SECTION
10 10 40 10 1.6 1.0 1.5 TRANSVERSE STOPE CROSS-SECTION
10 20 40 10 1.4 0.5 1.45
TRANSVERSE STOPE CROSS-SECTION 10 40 40 10 | 1.2 | 0.25 1.45
TABLE 7. Comparison of BEAP and MINTAB for the four different tests.
influence of the seam thickness r a t i o . Crouch (1986) states
that 3D displacement disc o n t i n u i t y programs:
"...can be used to analyze any excavation that has a
breadth:thickness r a t i o of 3 or more."
When i n v e s t i g a t i n g s t r e s s d i s t r i b u t i o n s around d i f f e r e n t
e x c a v a t i o n geometries with the pseudo-3D displacement
d i s c o n t i n u i t y method, Brady (1978) was more conservative i n
finding that a,
"...comparison with r e s u l t s from independent t h r e e -
dimensional analyses of these excavation shapes, indicate
that the method i s s a t i s f a c t o r y for openings where the
span/height r a t i o i s greater than 5."
The influence of the seam thickness r a t i o on average p i l l a r
stress w i l l be checked through the use of the t e s t s described i n
Chapter 5.3.2.
5.4.2 Comparison of Displacement Discontinuity and 3D Numerical
Modelling
A comparison was made between the three dimensional average
p i l l a r stress r e s u l t s from the BEAP runs i n Chapter 5.3.2 and
the average p i l l a r stress predicted by MINTAB for the same stope
geometries. The goal was to determine the influence that the
seam thickness r a t i o has on the accuracy of displacement
d i s c o n t i n u i t y modelling. The 12 stope geometries f o r the four
t e s t s are summarized i n table 7. This table shows the stope and
p i l l a r dimensions, the seam thickness r a t i o f o r each geometry
100
and the average p i l l a r stress for each BEAP and MINTAB run
(average p i l l a r stress increase i s calculated as the r a t i o of
the average p i l l a r stress to the pre-mining s t r e s s ) .
The difference between the two models fo r the various seam
thickness r a t i o s i s given i n figure 32. A very rough estimate
of the maximum difference between MINTAB and BEAP i s shown i n
figure 32. This dashed envelope i s based on the absolute
magnitude of the difference (for a l l the points), and plotted as
a mirror image above and below the 0% l i n e . In the majority of
the t e s t s , there i s l i t t l e difference between the average p i l l a r
stresses predicted by BEAP and MINTAB. At a seam thickness of
1.0, there i s l e s s than 10% difference f o r a l l f i v e t e s t s .
There i s l e s s than a 5% difference for the f i v e t e s t s having a
seam thickness r a t i o equal to or greater than 3.0. Overall,
only one t e s t showed a difference of greater than 10%. However,
there are only two t e s t s with a seam thickness r a t i o of less
than one. Many more tests are needed before any conclusions can
be drawn about the a b i l i t y of MINTAB to model stope and p i l l a r
geometries with low seam thickness r a t i o s .
Considering the minimum seam thickness r a t i o s of 3 and 5
suggested by Crouch and Brady, the difference i n average p i l l a r
stress between BEAP and MINTAB i s much les s than expected.
Reasons why these authors suggest conservative seam thickness
r a t i o s may be:
- a high l e v e l of agreement between the DD and 3D solutions was
sought i n the analyses done by Crouch and Brady,
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COMPARISON: DD AND 3D NUMERICAL METHODS INFLUENCE OF THE SEAM THICKNESS RATIO
- 1 0 * H
- 2 0 * H
- 3 0 *
SEAM THICKNESS RATIO (LENGTH:BREADTH) • 3D TESTS
102
- using the average of several elements to determine the
average p i l l a r stress has the e f f e c t of "smoothing out" large
differences at i n d i v i d u a l elements i n the p i l l a r ,
- or the open stope r i b p i l l a r geometries analyzed i n the 12
t e s t s are much simpler and more amenable to DD numerical
modelling than the excavation geometries analyzed i n the
v e r i f i c a t i o n s by Crouch and Brady.
While complex mining geometries have not been investigated, the
r e s u l t s of the comparison suggest that using a seam thickness
r a t i o of three w i l l give very good agreement between MINTAB and
BEAP fo r open stope r i b p i l l a r s . Further checks of the
influence of the seam thickness r a t i o w i l l be done i n Chapter
5.5 using case h i s t o r i e s from the data base.
5.5 P i l l a r Load Calculations f o r the Open Stope Data Base
There i s no absolute method that can determine the average
stress or load i n a mine p i l l a r . As discussed above, and i n
Chapter 3, l i n e a r e l a s t i c numerical modelling can often give
consistent approximations of the p r e - f a i l u r e load i n hard rock
mine p i l l a r s . For p i l l a r s t h a t have a sloughing or
de t e r i o r a t i n g condition, load determined by l i n e a r e l a s t i c
numerical modelling may be a considerable overestimate. This
can be a t t r i b u t e d to the l o c a l loss of load bearing capacity due
to rock f r a c t u r i n g and p i l l a r deformation. For f a i l e d p i l l a r s ,
the l i n e a r e l a s t i c load w i l l not be representative of the stress
conditions. A f a i l e d p i l l a r w i l l have l o s t some, or nearly a l l
103
of i t s load bearing capacity, r e s u l t i n g i n stress r e d i s t r i b u t i o n
into nearby competent p i l l a r s or abutments. The i n a b i l i t y of
l i n e a r e l a s t i c modelling to determine an approximate load for
sloughing and e s p e c i a l l y f a i l e d p i l l a r s presents d i f f i c u l t i e s i n
developing a r e l i a b l e method of predicting p i l l a r f a i l u r e .
5.5.1 Assumptions
In order to set a consistent method for determining loading
conditions f o r a l l p i l l a r assessments, i t w i l l be assumed that
p i l l a r s a r e i n f i n i t e l y e l a s t i c i n t h e i r deformation
c h a r a c t e r i s t i c s . This means that p i l l a r s w i l l not loose t h e i r
load bearing capacity regardless of t h e i r physical condition.
While not being t e c h n i c a l l y accurate to the actual problem, t h i s
assumption w i l l permit the investigation of the stress and
geometrical conditions that existed before f a i l u r e and a
rudimentary look at the conditions that have resulted i n f a i l u r e
of open stope p i l l a r s . Ultimately, i t w i l l provide the basis
fo r p r e d i c t i n g conditions that are associated with p i l l a r
f a i l u r e .
5.5.2 P i l l a r Load Results
The a b i l i t y of BITEM and MINTAB to model each problem
geometry i n the data base was evaluated. I f a program could not
adequately account for the excavations a f f e c t i n g the stress
conditions of the p i l l a r , numerical analysis was not done. This
s i t u a t i o n occurred for BITEM when the geometries of a l l the
104
s i g n i f i c a n t excavations could not be included i n the plane of
the problem. MINTAB was not used to investigate a stope and
p i l l a r geometry when en-echelon stopes were part of the problem
geometry, or the orebody had s i g n i f i c a n t changes i n thickness or
s i g n i f i c a n t changes i n d i r e c t i o n . For each case h i s t o r y , Table
8 shows:
- the pre-mining stress normal to the orebody,
- the l i m i t i n g g e ometrical r a t i o s a s s o c i a t e d with the
a p p l i c a b i l i t y of MINTAB (the seam thickness rat i o ) and BITEM
(the stope height to length r a t i o ) ,
- the average stress predicted for the p i l l a r by each numerical
method and the best estimate of the average p i l l a r stress,
- the estimated error associated with the best load due to
assumptions associated with modelling three dimensional stope
and p i l l a r geometries with numerical methods that are not
three dimensional,
- the average p i l l a r load calculated using the t r i b u t a r y area
theory (chapter 3.1.2.1),
- and the error i n the t r i b u t a r y area load compared to the
numerically determined load.
The best estimate of the average p i l l a r load was chosen
based on the l i m i t i n g r a t i o s f o r BITEM and MINTAB. I f a case
h i s t o r y had a high stope length to stope width r a t i o , the BITEM
load was used. I f a case hi s t o r y had a high seam thickness
r a t i o , the MINTAB load was used. I f the stope geometry did not
105
• •" PUB- BITEM MINTAB ESTIMATED AVERAGE TRIBUTARY AREA 1 1 PILLAR MINING HEIGHT: SEAM ! PILLAR LOAD PILLAR LOAD
PILLAR j NUMBER STRESS LENGTH LOAD THICK, j LOAD j J ASSESSMENT | (MPa) RATIO (MPa) RATIO | (MPa)
(MPa) 1 Z ERROR (MPa) | Z ERROR
2 39 1.4 51 0.3 ; 47 51 ! 25-45Z 62 ! 22Z STABLE i 3 39 1.4 64 0.3 j 55 64 | 25-45Z 90 ; 40Z FAILURE | 7 46 4.5 55 0.6 | 60 55 ! <10Z 61 ; 12Z STABLE ! 8 46 4.5 69 0.6 | 83 69 ; <10Z 92 i 33Z FAILURE ! 15 14 2.6 28 1.5 | 24 28 ! 10-25Z 32 ! 15Z STABLE ! 16 14 1.8 , 29 1.7 ! 24 29 ! 25-45* 33 ! 12Z STABLE ! 17 16 4.0 29 0.9 ! 24 29 ! <10Z 32 ! 10Z SLOUGH ; 18 40 2.0 90 3.0 | 66 66 ! <10Z 98 ! 48Z STABLE ! 19 40 1.7 91 3.3 ! 63 63 | <10Z 99 i 57Z
STABLE 1 20 17 2.9 43 0.8 ! 41 *3 ! 10-25Z 58 ! 34Z SLOUGH | 21 17 4.0 28 0.7 j 28 28 | <10Z 35 ,' 24Z STABLE ! 22 17 3.5 29 0.7 j 26 29 i 10-25Z 33 J 14Z STABLE ! 23 17 1.4 38
0.7 1 31 38 ; 25-45Z 53 ! 39Z FAILURE i 24 17 3.5 33 0.7 | 27 33 ! 10-25Z 33 ! OZ STABLE ! 25 17 0.9 57 0.8 ! 30 57 ! >45Z 65 ! 15Z FAILURE ! 26 12 3.0 29 1.8 J 24 29 ! 10-25Z 37 ! 27Z STABLE ! 27 12 3.0 44 3.8 ! 33 33 ! <10Z 48 ! 45Z STABLE 28 12 N A N A 1.1 ! 28 28 | N A j NA SLOUGH ! 29 12 1.8 26 0.8 ; 21 26 ! 25-45Z 33 ! 27Z STABLE ! 30 12 N A N A 1.7 | 31 31 ! N A ; NA FAILURE ! 31 12 0.9 , 60 3.8 ! 37 37 ! <10Z 91 i 146Z STABLE ! 32 15 5.0 26 1.0 | 28 26 ! <10Z 33 ! 27Z , STABLE ,' 33 15 5.0 38 1.1 ! 38 38 i <10Z 57 ! 51Z ! FAILURE j 34 15 6.3 ! 31 1.2 ! 30 31 ! <10Z 38 ; 21Z SLOUGH | 35 15 2.5 31 i.o ! 30 31 ! 10-25Z 44 | 42Z STABLE ] 36 15 1.5 38 1.3 ! 32 38 25-45Z 58 ; 52Z j FAILURE ! 37 15 2.5 40 0.7 ', 35 40 j 10-25Z 57 ! 43Z ; FAILURE ! 42 55 5.0 99 0.5 | 78 99 ! <10Z no ; 11Z ! FAILURE | 43 55 5.0 75 0.5 j 60 75 ! <10Z 73 | -2Z ! STABLE ! 44 55 5.0 76 0.7 [ 59 76 ! <10Z 73 ! -4Z | STABLE ! 45 55 5.0 ! 102 0.6 ; 83 102 ! <10Z 110 | 8Z ! FAILURE ! 46 23 2.1 30 N A ; NA 30 | 10-25Z 36 ! 21Z ! STABLE ! 47 23 2.1 32 N A ! NA 32 j 10-25Z *2 ! 32Z | SLOUGH ! 48 23 1.5 41 N A ; NA 41 ! 25-45Z 55 ! 34Z ] FAILURE j 49 23 1.5 49 N A ; NA 49 i 25-45Z 71 ! 44Z ! FAILURE ! 50 15 N A N A 3-3 j 31 31 ! <10Z NA | NA ! STABLE i 51 15 N A N A 7.0 ! 39 39 ! <10Z NA | NA ! STABLE ! 52 15 N A N A 4.6 ! 48 48 | <10Z NA | NA ! STABLE ! 53 23 N A NA 0.7 ! 36 36 j NA ! NA ! STABLE | 54 18 5.6 43 3.0 ! 46 46 | <10Z 50 ; 8Z ! STABLE j 55 . 18 3.4 44 3.0 i 46 46 <10Z 54 ; 17Z ] STABLE ! 56 30 1.1 59 0.4 | 48 59 | 25-45Z 69 ! 17Z ! SLOUGH ! 57 30 5.8 ! 38 0.2 ] 46 38 ! <10Z 45 | i8z : STABLE ! 58 30 4.4 40 0.2 ! 45 40 ! <10Z 48 ! 20Z J STABLE ! 59 ! 30 0.8 72 0.2 ! 54 72 j >45Z 95 ! 31Z | SLOUGH ! 60 ! 30 0.6 82
0.7 1 53 82 | >45Z 119 ] 45Z ! SLOUGH | 61 35 5.0 70 N A ; NA 70 ! <10Z 88 j 25Z ! SLOUGH i
TABLE 8. P i l l a r load information f o r a l l the open stope r i b p i l l a r case h i s t o r i e s using BITEM, MINTAB and the Tributary Area Theory.
106
f i t e i t h e r l i m i t i n g r a t i o , the BITEM load was used. BITEM i s
used to estimate the average p i l l a r stress i n these situations
because i t accounts for the geometry of these problems better
than MINTAB, and the error associated with BITEM (from figure
30) , i s better understood than the error associated with MINTAB
(from figure 32).
The error associated with the best load i s based on the
comparisons of MINTAB and BITEM to a true three dimensional
numerical method presented i n chapters 5.3.2 and 5.4.2. The
r e s u l t s i n Table 8 show that stable case h i s t o r i e s and primary
stoping geometries tend to have a lower degree of error
associated with the predicted load. This i s because primary
stoping geometries are more regular than secondary and t e r t i a r y
geometries and consequently f i t the modelling constraints ( i e .
the l i m i t i n g ratios) better. The error i n the best p i l l a r load
i s an estimation of the maximum possible error based on figures
30 and 32. The actual error i s smaller for many of the p i l l a r s .
For t h i s reason, the load applied i n the development of a p i l l a r
design method w i l l not be adjusted for the estimated error.
Table 8 shows that the t r i b u t a r y area theory has highly
varied r e s u l t s compared to the best load estimated by numerical
modelling. I t can be assumed that t r i b u t a r y area overestimates
the average p i l l a r load. I t i s also apparent that the greater
the stope height:length r a t i o of the case h i s t o r y geometry, the
better the agreement between the t r i b u t a r y area theory load and
the load predicted by numerical modelling. In general, the
107
overestimation of the predicted stress makes the t r i b u t a r y area
theory very un r e l i a b l e i n the estimation of the average load i n
open stope r i b p i l l a r s .
5.5.3 Numerical Model Comparison Using the Case H i s t o r i e s
Chapters 5.3 and 5.4 gave a de t a i l e d comparison of two
dimensional and displacement d i s c o n t i n u i t y numerical modelling
against a three dimensional method. Analysis of the data base
case h i s t o r i e s provides further information f o r comparison.
Two case h i s t o r i e s f i t the MINTAB seam thickness r a t i o
l i m i t a t i o n of 3 or greater and also have a large height to
length r a t i o (greater than 4) making good BITEM cases. For both
of these case h i s t o r i e s , Table 9 shows the stope height to
length r a t i o , the seam thickness r a t i o , the average p i l l a r
stress predicted by BITEM and MINTAB and the difference i n the
predicted stress. This comparison shows good agreement between
the average p i l l a r load for the two methods when a stope and
p i l l a r geometry meets both of the l i m i t i n g r a t i o s .
CASE NUMBER
BITEM MINTAB PERCENT DIFFERENCE BETWEEN
BITEM AND MINTAB
CASE NUMBER HEIGHT:
LENGTH RATIO
AVERAGE PILLAR LOAD (MPa)
SEAM THICKNESS
RATIO
AVERAGE PILLAR LOAD (MPa)
PERCENT DIFFERENCE BETWEEN
BITEM AND MINTAB
54 5.6 43 3.0 46 - 7 %
55 3.4 44 3.0 46 - 5 %
Table 9. Comparison of MINTAB and BITEM r e s u l t s when both programs l i m i t a t i o n s are s a t i s f i e d .
108
Three case h i s t o r i e s s a t i s f y the MINTAB seam thickness
constraint, but do not have a large height to length r a t i o .
These are good MINTAB geometries, but not favorable for BITEM
modelling. BITEM w i l l overestimate the average p i l l a r load.
For each of these case h i s t o r i e s , Table 10 shows the stope
height to length r a t i o , the seam thickness r a t i o , the average
p i l l a r s t r e s s p r e d i c t e d by BITEM and MINTAB and the
overestimation by BITEM of the MINTAB predicted p i l l a r load.
When these three cases are compared against the BITEM
overestimation of BEAP graph developed i n Chapter 5.3.2, they
p l o t s l i g h t l y above the maximum over-estimation documented i n
chapter 5.3.2 (see figure 33). However, considering a pot e n t i a l
error of up to 10% for the MINTAB case h i s t o r i e s , the re s u l t s
are not very f a r above the l i m i t found i n Chapter 5.3.2.
CASE NUMBER
BITEM MINTAB PERCENT DIFFERENCE BETWEEN
BITEM AND MINTAB
CASE NUMBER HEIGHT:
LENGTH RATIO
AVERAGE PILLAR LOAD (MPa)
SEAM THICKNESS
RATIO
AVERAGE PILLAR LOAD (MPa)
PERCENT DIFFERENCE BETWEEN
BITEM AND MINTAB
18 2 . 0 90 3.0 66 + 36 %
19 1.7 91 3 . 3 63 + 44 %
31 0.9 60 3.8 37 + 62 %
Table 10. Comparison of BITEM and MINTAB, when the MINTAB l i m i t a t i o n i s met, but the BITEM l i m i t a t i o n i s not met. The overestimation by BITEM i s i n the range estimated i n Chapter 4.
70*
COMPARISON: 2D AND 3D NUMERICAL METHODS INFLUENCE OF STOPE HEIGHT:LENGTH RATIO
60* H
50* H
40* H
V \
30* H
20* • • \ \
i o * H §
OX
• 3D TESTS STOPE HEIGHT:L£NGTH RATIO
* DATA BASE t-1
o
110
Many of the case h i s t o r i e s investigated had a large stope
height to length r a t i o (making them good geometries for BITEM
modelling), but do not f i t the seam thickness c r i t e r i o n needed
for accurate MINTAB modelling. By using both numerical methods,
the e f f e c t of a low seam thickness r a t i o can be compared against
the s a t i s f a c t o r y p i l l a r load r e s u l t s given by BITEM. Table 11
shows the stope height to length r a t i o , the seam thickness
r a t i o , the BITEM and MINTAB average p i l l a r stress, and the
difference i n the average p i l l a r stress for t h i r t e e n d i f f e r e n t
geometries. The r e s u l t s of the MINTAB analysis vary up to
± 25 % with the BITEM r e s u l t s . For the geometries with larger
seam thickness r a t i o s (>1.0 but <3.0), the difference i n average
p i l l a r stress between the two methods i s l e s s . The maximum
difference i n p i l l a r load i s s l i g h t l y higher than the 12 runs i n
Chapter 5.4.2, when plotted on the graph of percent difference
i n p i l l a r stress versus seam thickness r a t i o (see figure 34) .
The envelope showing the maximum error has been redrawn i n
figure 34.
5.6 Chapter Summary
The three boundary element models (BITEM, MINTAB and BEAP),
used i n inve s t i g a t i n g open stope r i b p i l l a r load, have been
b r i e f l y described. Conventions for defining open stope r i b
p i l l a r geometries and determining the average p i l l a r stress have
been presented.
The use of three dimensional boundary element modelling i s
111
CASE NUMBER
BITEM MINTAB PERCENT DIFFERENCE BETWEEN MINTAB AND BITEM
CASE NUMBER HEIGHT:
LENGTH RATIO
AVERAGE PILLAR LOAD (MPa)
SEAM THICKNESS
RATIO
AVERAGE PILLAR LOAD (MPa)
PERCENT DIFFERENCE BETWEEN MINTAB AND BITEM
7 4.5 55 0.6 60 + 9 %
8 4.5 69 0.6 83 + 20 %
17 4.0 29 0.9 24 - 17 %
21 4.0 28 0.7 28 0 %
32 5.0 26 1.0 28 + 8 %
33 5.0 38 1.1 38 0 %
34 6.3 31 1.2 30 - 3 %
42 5.0 99 0.5 78 - 21 %
43 5.0 75 0.5 60 - 20 %
44 5.0 76 0.7 59 - 22 %
45 5.0 102 0.6 83 - 19 %
57 5.8 38 0.2 46 + 21 %
58 4.4 40 0.2 45 + 13 %
Table 11. Comparison between good BITEM and poor MINTAB geometries shows the average p i l l a r stress varying up to ± 25%.
BV1NIH A8 0310103yd 30N3y3JJIQ SS381S
FIGURE 34. The difference between the average p i l l a r stress predicted by MINTAB and the average p i l l a r stress predicted by BEAP for the comparison tests and 13 case h i s t o r i e s .
not possible for the case h i s t o r i e s i n the data base. This i s due
to: high program set up and run times, and program space
l i m i t a t i o n s . The 2D plane s t r a i n and pseudo-3D displacement
d i s c o n t i n u i t y (DD) methods have been used to estimate the load for
each p i l l a r case his t o r y . Both of these programs have geometrical
l i m i t a t i o n s that may introduce error into the average p i l l a r load.
The geometrical l i m i t a t i o n s have been described and the error
associated with 2D plane s t r a i n and DD methods has been quantified
using 12 t e s t runs and some case h i s t o r i e s from the data base.
Figure 33 shows the pote n t i a l error associated with 2D plane
s t r a i n modelling for open stope r i b p i l l a r geometries. Figure 34
shows the p o t e n t i a l error associated with the displacement
d i s c o n t i n u i t y method for open stope r i b p i l l a r geometries.
114
CHAPTER 6
DEVELOPMENT OF A PILLAR DESIGN METHOD
It was stated i n Chapter 3 that a design method for open
stope r i b p i l l a r s has not been developed or confirmed. Other
authors have shown that the best way to develop and v e r i f y a
design procedure i s to conduct a survey and confirm a method
with case h i s t o r i e s . There are many examples of p i l l a r design
studies, the most notable being: Salamon (1967) i n South African
coal mines, Hedley and Grant (1972) i n Canadian hard rock room
and p i l l a r mining, and Bieniawski (1983) i n United States coal
mines. Each of these studies used experience and c a l i b r a t i o n to
develop a method for mining s p e c i f i c conditions.
The number of mines v i s i t e d i n the "Integrated Mine Design
Study" has resulted i n the c o l l e c t i o n of a substantial amount of
data of stable and f a i l e d r i b p i l l a r s from Canadian open stope
mines. This data w i l l be used to develop an empirical design
method f o r r i b p i l l a r s i n open stope mining. In addition, a
wealth of data from hard rock room and p i l l a r mines has been
found i n l i t e r a t u r e to help confirm the new empirical method.
S p e c i f i c a l l y , the intention of t h i s chapter i s to:
- v e r i f y the variables s i g n i f i c a n t i n open stope r i b p i l l a r s
based on the data available,
- present a method that explains the r e s u l t s of the case
h i s t o r i e s i n the data base,
- use case h i s t o r i e s from l i t e r a t u r e (mostly from room and
115
p i l l a r mining), to v e r i f y the design concept and r e f i n e the
method,
- and compare the new method to some of the open stope design
procedures commonly used i n the past.
6.1 Choice of Variables
Chapter 2.3 discussed variables that may be s i g n i f i c a n t i n
the f a i l u r e of open stope r i b p i l l a r s . These variables were:
in t a c t rock strength, p i l l a r load, p i l l a r shape and confinement,
s t r u c t u r a l d i s c o n t i n u i t i e s , and p i l l a r volume. They w i l l be
quantified through the use of:
- u n i a x i a l compressive strength f o r i n t a c t rock strength,
- boundary element numerical modelling to determine p i l l a r
load,
- p i l l a r height and width to account for p i l l a r shape and
confinement,
- empirical rock mass c l a s s i f i c a t i o n methods to account for
s t r u c t u r a l d i s c o n t i n u i t i e s ,
- and the p i l l a r dimensions (from table 5, page 70) can be
used to determine the p i l l a r volume.
No attempt w i l l be made to quantify the e f f e c t of b a c k f i l l . In
Chapter 2, b a c k f i l l was not considered s i g n i f i c a n t i n preventing
the f a i l u r e of p i l l a r s , although i t s presence may have a large
influence i n preventing p i l l a r d i s i n t e g r a t i o n i f f a i l u r e occurs.
6.1.1 A p p l i c a b i l i t y of S t a t i s t i c a l Methods
116
Ideally, the data base presented i n Chapter 4.2 could be
used to t e s t the s i g n i f i c a n c e of each variable i n the s t a b i l i t y
of p i l l a r s . Some of the variables are obviously s i g n i f i c a n t .
P i l l a r load, p i l l a r width and the strength of the i n t a c t rock
are known to have a large influence on the s t a b i l i t y of a
p i l l a r . However, the influence of p i l l a r height, p i l l a r volume
and minor rock mass d i s c o n t i n u i t i e s (such as j o i n t s ) i n open
stope r i b p i l l a r s i s not obvious. The use of s t a t i s t i c s to t e s t
the s i g n i f i c a n c e of these three variables was considered, but
was l a t e r rejected for a couple of reasons.
The f i r s t reason i s the assessment of p i l l a r s t a b i l i t y can
not be quantified into a numerical value. The p i l l a r case
h i s t o r i e s were assessed with q u a l i t a t i v e categories of stable,
sloughing and f a i l e d . These categories l i m i t the use of
regression and f a c t o r i a l design methods, because the categories
can not be quantified numerically. A system of giving the
stable, sloughing and f a i l e d assessments an a r b i t r a r y numerical
value and using regression techniques on these values also would
not work well. The wide range of i n s t a b i l i t y signs and
c h a r a c t e r i s t i c s that are exhibited by the f a i l e d p i l l a r s can not
be quantified by a single a r b i t r a r y value and there i s no
s a t i s f a c t o r y c r i t e r i o n to determine a representative value for
f a i l e d p i l l a r s .
The second reason why the use of s t a t i s t i c s i s not f e a s i b l e
i s r e l a t e d to the y i e l d i n g p i l l a r case h i s t o r i e s . These are
p i l l a r s that were o r i g i n a l l y stable but eventually became
117
unstable due to stopes or p i l l a r s being mined i n the v i c i n i t y or
robbing of the p i l l a r . For the y i e l d i n g p i l l a r s , the u n i a x i a l
c o m p r e s s i v e s t r e n g t h (UCS) , p i l l a r h e i g h t , rock mass
charac t e r i z a t i o n and p i l l a r volume do not change s i g n i f i c a n t l y
from the stable to f a i l e d cases. Consequently, a s t a t i s t i c a l
method would f i n d that these variables have no s i g n i f i c a n t
influence of p i l l a r condition. The only variables that change
s i g n i f i c a n t l y for y i e l d i n g case h i s t o r i e s are the average p i l l a r
stress and the p i l l a r width. Removing the y i e l d i n g p i l l a r s from
the data base reduces the number of case h i s t o r i e s to 12 stable
p i l l a r s , 3 sloughing p i l l a r s , and 1 f a i l e d p i l l a r . This i s too
small a data base to reach confident s t a t i s t i c a l conclusions
about s i g n i f i c a n t variables.
The l a s t major problem with using s t a t i s t i c a l methods i n the
data base, i s the lack of p r e c i s i o n i n the estimation of some of
the data. Chapter 5.5 discusses the determination of average
p i l l a r load f o r each case his t o r y . The p o t e n t i a l error
associated with t h i s v a r i able varies from l e s s than 10% to
greater than 45% (see Table 8, page 105) and implies that a
large degree of accuracy should not be used. I t i s not a
precise v a r i a b l e and would present s i g n i f i c a n c e problems i f
included i n a s t a t i s t i c a l technique.
6.1.2 Design Variables
The most important variables i n open stope p i l l a r design are
p i l l a r width and the average p i l l a r load. There i s more
118
f l e x i b i l i t y i n choosing and designing these two variables than
any of the others. The i n t a c t rock u n i a x i a l compressive
strength, rock mass qual i t y and p i l l a r height (orebody width)
are a l l a function of the geological s e t t i n g and can not be
c o n t r o l l e d or changed. P i l l a r width has a large influence on
the l a t e r a l confinement of the p i l l a r core, the p i l l a r
s t i f f n e s s , and the modulus of deformation of f a i l i n g p i l l a r s .
The magnitude of p i l l a r load has a d i r e c t influence on the
degree of f r a c t u r i n g i n a p i l l a r . However, both of these
v a r i a b l e s need to be normalized before information from
d i f f e r e n t mining conditions can be compared. P i l l a r load i s
frequently normalized by comparing i t against the i n t a c t rock
strength (discussed i n Chapter 3.2.2.3). This gives a good
measure of the state of stress and f r a c t u r i n g i n a p i l l a r .
P i l l a r width i s t y p i c a l l y normalized through the use of the
r a t i o of the p i l l a r width/height. P i l l a r width/height i s used
by many authors to account for the e f f e c t s of p i l l a r shape (see
Chapter 3.1.1).
6.1.3 Discounted Variables
Two variables have been discounted for design. P i l l a r
volume and the influence of geological d i s c o n t i n u i t i e s may be
s i g n i f i c a n t i n general p i l l a r design, but t h e i r importance has
not been proven for open stope p i l l a r s . Using methods proposed
by other authors and information from the data base, i t w i l l be
shown that the two discounted variables have a r e l a t i v e l y small
119
v a r i a t i o n i n magnitude i n the open stope p i l l a r data base, and
consequently could only have a minor e f f e c t on p i l l a r s t a b i l i t y .
6.1.3.1 P i l l a r Volume
Several authors (Hoek and Brown 1980; Agapito and Hardy
1982; Stephansson 1985) have proposed the use of a factor to
account f o r the e f f e c t of p i l l a r volume. The reasoning was the
rock mass strength decreases with an increase i n p i l l a r volume,
due to a larger number of flaws and d i s c o n t i n u i t i e s i n the rock
mass. Consequently, the volume e f f e c t i s an i n d i r e c t means of
accounting f o r the e f f e c t of d i s c o n t i n u i t i e s .
Agapito and Hardy (1982) suggested the following equation to
r e l a t e the unconfined u n i a x i a l compressive strength from
laboratory t e s t i n g with i n s i t u unconfined compressive p i l l a r
strength:
°0 = aC ( v l / v l ) a
where,
OQ = unconfined compressive strength of the p i l l a r ,
OQ = average laboratory u n i a x i a l compressive strength,
V! = volume of the laboratory specimen,
Vj = volume of the p i l l a r ,
a = c o e f f i c i e n t of volume reduction,
= 0.12 f o r coal,
= 0.08 for o i l shale,
= 0.06 for good quality, hard quartzite.
Using the formula, we can compare the influence of the
v a r i a t i o n of p i l l a r volumes i n the data base. For t h i s data
120
base, the smallest open stope p i l l a r has a volume of about 2500
cubic metres, and the largest open stope p i l l a r has a volume of
about 150,000 cubic metres.
^2,500 _ °C (Vi / 2 5 0 0 ) 0 - 0 6 _ — — 1.2 o
^150,000 °C ( V l / 150000) 0' 0 6
So, f o r the f u l l range of p i l l a r volumes i n the data base, t h i s
formula shows only a small influence (less than 30%).
The lack of s e n s i t i v i t y of volume i s only part of the
problem with using t h i s c o e f f i c i e n t of volume reduction method.
Any method to account for the influence of flaws or discont
i n u i t i e s i n a rock mass should be based on an assessment of the
q u a l i t y of the rock mass. The frequency, orientation,
continuity and shear strength of d i s c o n t i n u i t i e s i n a rock mass
s h o u l d be c o n s i d e r e d when e s t i m a t i n g the e f f e c t of
d i s c o n t i n u i t i e s . This formula does not consider any rock mass
c h a r a c t e r i s t i c s and as a r e s u l t , i t does l i t t l e to account for
the influence of d i s c o n t i n u i t i e s i n p i l l a r strength.
6.1.3.2 Structural D i s c o n t i n u i t i e s
As mentioned above, to account for the influence of
g e o l o g i c a l d i s c o n t i n u i t i e s i n p i l l a r s t r e n g t h , the
c h a r a c t e r i s t i c s of the rock mass must be quantified. Currently,
the most e f f e c t i v e method of describing a rock mass i s with
empirical rock mass c l a s s i f i c a t i o n s . The two most common
c l a s s i f i c a t i o n s are the NGI system, developed by Barton, Lien
121 and Lunde of the Norwegian Geotechnical I n s t i t u t e (1974), and
the CSIR system, developed by Bieniawski of the South African
Council f o r S c i e n t i f i c and I n d u s t r i a l Research (1976).
Data for the CSIR rock mass c l a s s i f i c a t i o n was c o l l e c t e d i n
the "Integrated Mine Design Study." Herget et a l . (1984) and
Stacey and Page (1986) suggest using rock mass c l a s s i f i c a t i o n s
as strength reduction factors by applying them against the
u n i a x i a l compressive strength of rock. For instance, i f the i n
s i t u i n t a c t rock strength i s o0 and the rock mass has a CSIR
rock mass r a t i n g of 75%, then the i n s i t u rock mass strength i s
(0.75 * o 0 ) .
Table 5 (page 70) shows the CSIR geomechanics r a t i n g "RMR"
(acronym for rock mass rating) for the p i l l a r s i n the open stope
data base. The mean RMR i s 69.6, with a standard deviation of
4.8. This small range i n rock mass ratings i s not u n r e a l i s t i c
because the source of the majority of the information i n the
data base i s mines i n the Canadian s h i e l d . The c l a s s i f i c a t i o n
methods are designed to characterize a much wider range of rock
masses. With t h i s small a range of rock mass qua l i t y , however,
i t i s not possible to v e r i f y that the i n c l u s i o n of a rock mass
strength reduction factor would adequately account for any
influence of d i s c o n t i n u i t i e s i n the design of open stope r i b
p i l l a r s .
Using a strength reduction variable could be an e f f e c t i v e
method t o a c c o u n t f o r the i n f l u e n c e of s t r u c t u r a l
d i s c o n t i n u i t i e s i n a rock mass. However, the avai l a b l e data
122
could only prove t h i s over a small range of rock mass
conditions. Rather than include a variable whose influence can
not be e f f e c t i v e l y c a l i b r a t e d or v e r i f i e d , the e f f e c t of
s t r u c t u r a l d i s c o n t i n u i t i e s has been omitted. A large amount of
data from a much wider v a r i e t y of rock mass conditions i s needed
to confirm and c a l i b r a t e the s i g n i f i c a n c e of a strength
reduction factor.
6.2 P i l l a r S t a b i l i t y Graph
The methodology for the development of an open stope r i b
p i l l a r design c r i t e r i o n i s based on the graphical comparison of
the s i g n i f i c a n t variables discussed above and the assessment of
p i l l a r case h i s t o r i e s . The y-axis of the graph has been chosen
to represent the normalized p i l l a r load, while the x-axis i s
defined by the p i l l a r width to p i l l a r height r a t i o . Stable
p i l l a r s from the data base are plotted with square symbols,
sloughing p i l l a r s are represented by cross shaped symbols, and
f a i l e d p i l l a r s are located with diamond symbols (see figure 35).
By arranging the graph i n t h i s form (and not including
correction factors for volume and rock mass q u a l i t y ) , the graph
stays i n t u i t i v e l y simple. The influence of varying the design
variables i s clear-cut and e x p l i c i t . This graph w i l l be
referred to as the " p i l l a r s t a b i l i t y graph".
6.2.1 Graphical Data Analysis
Comparison of the shape and the loading condition of
o o CO
o m o d
o O O
d o o d
s o n / a v o i
FIGURE 35. The p i l l a r s t a b i l i t y graph showing the open stope r i b p i l l a r data base.
124
p i l l a r s , using the p i l l a r s t a b i l i t y graph, exposes a trend i n
r i b p i l l a r behaviour. The graph shows squat p i l l a r s under low
stress conditions as stable (bottom r i g h t region of the graph i n
figur e 35) . P i l l a r s become les s stable as t h e i r graphical
p o s i t i o n i s located more towards the upper l e f t corner of the
graph, which represents highly stressed, slender, and f a i l u r e
prone p i l l a r s .
The graph has be divided into two zones based on t h i s data
(see figure 36) . The upper l e f t side of the graph denotes
conditions i n which p i l l a r s have f a i l e d . The bottom r i g h t side
of the graph shows conditions i n which p i l l a r s have not suffered
any serious i n s t a b i l i t y . The two zones are separated by a
t r a n s i t i o n area. The location of t h i s area has been
approximated based on the graphical l o c a t i o n and physical
condition of the case h i s t o r i e s . No s t a t i s t i c a l methods have
been used to locate the t r a n s i t i o n area. The bottom l i n e of the
t r a n s i t i o n area corresponds to the region where major p i l l a r
s t a b i l i t y problems are f i r s t encountered. Only one sloughing
p i l l a r , no f a i l e d p i l l a r s , and a l l but four of the stable
p i l l a r s p l o t below t h i s l i n e . This bottom l i n e does not
necessarily s i g n i f y p i l l a r f a i l u r e , but rather the onset of
mining problems due to p i l l a r i n s t a b i l i t y . Sloughing or
de t e r i o r a t i n g p i l l a r s could carry an even greater load (as
reported by Goel and Page 1981) , but displacement, rock
f r a c t u r i n g and p i l l a r deformation w i l l increase. The top l i n e
roughly defines a c r i t e r i o n where p i l l a r f a i l u r e has been
H
3 G
H> 0) U> H-M • (D O.
N 3* O (D 3
10 K-M
0) H* 3 0) a it f t to 3* f t
cr f t H-*1 M JD |_u 3 f t to p -rtvQ H* ^ O B» 3 1 5
3* 0) ^ CO (D 3* 0> O • C
H-3 tQ f t 3" (D
to f t &»
tr M fO
o D \ Q < o _l
0.60
0.50
0.40 H
0.30 H
0.20 H
0.10 H
PILLAR STABILITY GRAPH OPEN STOPE RIB PILLAR DATA
•
0.00 - | 1 p
0.0 0.4 i 1 r
0.8 ' i i 1 1 1 r
1.2 1.6 2.0
• STABLE PILLAR WIDTH/PILLAR HEIGHT
+ SLOUGHING O FAILURE
126 observed i n the case h i s t o r i e s of the data base. No stable case
h i s t o r i e s , four of the nine sloughing p i l l a r s and a l l but three
of the f a i l e d p i l l a r s are found above t h i s l i n e . P i l l a r s
p l o t t i n g above t h i s l i n e generally have:
- started to lose load bearing capacity,
- suffered a large amount of frac t u r i n g ,
- experienced large displacements of rock,
- and had severe sloughing of p i l l a r walls (unless confined
by b a c k f i l l ) .
In regions of the graph where s u f f i c i e n t r i b p i l l a r data i s not
a v a i l a b l e to l o c a t e the t r a n s i t i o n zone, i t has been
approximated with dashed l i n e s .
6.2.2 Influence of P i l l a r Load Approximations
In Chapter 5.5.2, the maximum error i n the average p i l l a r
load was estimated for each case h i s t o r y . To check the
influence of t h i s error, the average p i l l a r load i s decreased by
the maximum amount of the error shown i n Table 8 (page 105) .
The reason f o r the decrease i s that the majority of p i l l a r loads
are estimated by BITEM, which overestimated the actual p i l l a r
load. Data i n which the error could not be reasonably estimated
were omitted. This occurred for 6 of the 47 data points.
Figure 37 i s a pl o t of the p i l l a r s t a b i l i t y graph using the
reduced average p i l l a r load with the o r i g i n a l t r a n s i t i o n area.
The modified data s t i l l f i t s the graph well, with only three
sloughing cases and one f a i l e d case below the t r a n s i t i o n zone.
son/avcn
128
I t should be kept i n mind that the adjusted load was decreased
by an estimate of the maximum error, and most cases w i l l have an
error smaller than the maximum.
We can conclude that the error i n the average p i l l a r load
does not s i g n i f i c a n t l y change the method proposed. I t also
demonstrates the fac t that the p i l l a r loading conditions has
less of an e f f e c t on p i l l a r s t a b i l i t y than the p i l l a r shape
(width/height r a t i o ) .
6.2.3 Importance of Yielding P i l l a r Case H i s t o r i e s
As discussed i n the data base description (Chapter 4.1),
there are 13 p i l l a r s that were stable and subsequently f a i l e d
due to mining. These p i l l a r s comprise 30 of the 47 case
h i s t o r i e s i n the open stope data base. The y i e l d i n g p i l l a r case
h i s t o r i e s are very useful i n developing a design method because
the stable and f a i l e d cases should p l o t i n t h e i r respective
zones separated by the t r a n s i t i o n area. Figure 38 i s a p l o t of
the e n t i r e data base with the stages of each y i e l d i n g p i l l a r
joined by a s o l i d l i n e . The y i e l d i n g p i l l a r endpoints
correspond well to the stable and f a i l e d zones which reinforces
the l o c a t i o n of the t r a n s i t i o n area. As a p i l l a r f a i l s , i t s
loc a t i o n moves from the stable zone, through the t r a n s i t i o n
area, and into the f a i l e d zone. The y i e l d i n g p i l l a r s also
demonstrate the s e n s i t i v i t y of the graph to predict p i l l a r
f a i l u r e .
s o n / a v o i
FIGURE 38. The p i l l a r s t a b i l i t y graph with a l l the case h i s t o r i e s of the 13 y i e l d i n g p i l l a r s joined by s o l i d l i n e s . This reinforces the l o c a t i o n of the t r a n s i t i o n zone and shows the s e n s i t i v i t y of the method to predict f a i l u r e .
130
6.2.4 Limitations of the P i l l a r S t a b i l i t y Graph
There are a few comments to be made concerning the l i m i t
ations of the p i l l a r s t a b i l i t y graph. F i r s t l y , the data i n and
near the t r a n s i t i o n zone shows a v a r i e t y of behaviour. This
suggests that a great degree of pre c i s i o n i s not inherent to the
graph. This lack of pr e c i s i o n i s a function of inaccuracy i n
the input data and the broad assessments used to categorize
p i l l a r s . The s i z e of the t r a n s i t i o n zone could be considered a
measure of the accuracy of the p i l l a r s t a b i l i t y graph.
I t should be emphasized that t h i s i s an empirically
developed r e l a t i o n s h i p and i s more r e l i a b l e when applied i n
conditions s i m i l a r to those i n the data base. S p e c i f i c a l l y , the
range of the various data i s :
70 MPA < UCS < 316 MPa,
9 metres < Wp < 45 metres,
60 < RMR < 78
where,
UCS = the i n t a c t rock u n i a x i a l compressive strength,
Wp = the p i l l a r width,
RMR = a measure of the rock mass competency using the
CSIR rock mass c l a s s i f i c a t i o n .
A f i n a l note about the p i l l a r s t a b i l i t y graph i s that there
are almost no stable p i l l a r s with an (average p i l l a r load/UCS)
r a t i o greater than 0.5, and very few stable p i l l a r s with an
(average load/UCS) r a t i o greater than 0.33. This suggests that
there i s a p r a c t i c a l l i m i t to the maximum normalized load for a
131
stable open stope r i b p i l l a r . These values correspond well with
suggestions by Mathews et a l . (1980) and Bawden et a l . (1988),
of the maximum normalized major p r i n c i p a l stress allowable
before stress related mining problems become excessive.
6.3 Data from L i t e r a t u r e
Very few open stope p i l l a r case h i s t o r i e s found i n
l i t e r a t u r e provide s u f f i c i e n t information that they can applied
to the p i l l a r s t a b i l i t y graph. F u l l y documented room and p i l l a r
mining case h i s t o r i e s are more common. Three studies of hard
rock p i l l a r design have been found which contain the p i l l a r
l o a d , u n i a x i a l compressive rock s t r e n g t h , p i l l a r shape
information and an assessment of the p i l l a r s t a b i l i t y . The two
largest studies deal with room and p i l l a r mining while the t h i r d
i s a smaller and more det a i l e d study that deals with open stope
r i b p i l l a r design.
6.3.1 Data from Canadian Room and P i l l a r Mining
In the 1960's, a major rock mechanics in v e s t i g a t i o n was
undertaken i n the E l l i o t Lake uranium mining d i s t r i c t to
determine stable stope and p i l l a r configurations. One of the
re s u l t s was a p i l l a r strength formula (described i n Chapters
3.1.1.3, and 6.4.1). The d e t a i l s of the formula development and
the data base were published by Hedley and Grant (1972). Their
data base consisted of 23 stable p i l l a r s , 2 p i l l a r s that were
p a r t i a l l y f a i l e d , and 3 p i l l a r s that were crushed. P i l l a r s i n
132
the uranium mines are very long i n one d i r e c t i o n which i s the
same shape as p i l l a r s i n open stope mines. However, the p i l l a r
dimensions and volume are s u b s t a n t i a l l y lower i n room and p i l l a r
mining.
Using the data i n the paper (Hedley and Grant 1972) , the
case h i s t o r i e s were plotted on the p i l l a r s t a b i l i t y graph (see
figure 39) . The E l l i o t Lake data f i t s the p i l l a r s t a b i l i t y
graph quite well with a l l of the stable p i l l a r s p l o t t i n g below
the t r a n s i t i o n area, and most of the p a r t i a l l y f a i l e d and
crushed p i l l a r s p l o t t i n g i n the t r a n s i t i o n area. Ideally, for
t h i s data, the t r a n s i t i o n zone would probably be s l i g h t l y lower.
This would give a better separation between the stable and
unstable p i l l a r s . However, there i s not s u f f i c i e n t data near
the t r a n s i t i o n zone to warrant adjusting i t s l o c a t i o n .
The rock mass qu a l i t y for the E l l i o t Lake mines i s s i m i l a r
to that found i n the "Integrated Mine Design Study". A
discussion on p i l l a r s t a b i l i t y at the Denison Mine (Townsend
1982), which i s one of the mines i n Hedley's study, gives the
p i l l a r s an NGI rock mass qu a l i t y of 45. This i s roughly
equivalent to a CSIR ra t i n g of 78, based on a r e l a t i o n s h i p
proposed by Bieniawski (1976). An RMR of 78 i s within the range
of the rock mass q u a l i t i e s found i n the open stope p i l l a r data
base. Due to the variable nature of a rock mass, i t i s wrong to
assume an RMR of 78 for a l l p i l l a r s i n the E l l i o t Lake data
base. However, i t can be concluded that the general rock mass
conditions between the two data bases are s i m i l a r .
s o n / a v c n
FIGURE 39. The p i l l a r s t a b i l i t y graph shoving the data from room and p i l l a r mining published by Hedley and Grant (1972) i n t h e i r study on the development of a p i l l a r strength formula.
134
An i n t e r e s t i n g observation can be made concerning the
influence of p i l l a r volume. The volume of an average p i l l a r i n
the E l l i o t Lake data base i s approximately 25 to 50 times
smaller than the average volume of the open stope data base
(« 1000 - 2000 m3 for room and p i l l a r , and » 50,000 m3 f o r open
stoping). A r e l a t i v e increase of p i l l a r strength due to the
smaller volume should r a i s e the r e l a t i v e p o s i t i o n of the
t r a n s i t i o n zone. This does not correspond with the cases of
p a r t i a l l y f a i l e d and crushed E l l i o t Lake p i l l a r s . According to
the Hedley data, the t r a n s i t i o n zone should probably be s l i g h t l y
lower. Based on t h i s observation, there appears to be l i t t l e
d i fference i n the influence of p i l l a r volume between p i l l a r s i n
open stope and room and p i l l a r mining.
6.3.2 Data from a Botswana Room and P i l l a r Mine
A paper by Von Kimmelmann et a l . (1984) discussed the
development of a p i l l a r design c r i t e r i o n at BCL Limited i n
Botswana. Back analysis of a large number of e x i s t i n g p i l l a r s
was performed using the pseudo-three dimensional displacement
d i s c o n t i n u i t y numerical method.
P i l l a r d e t e r i o r a t i o n was assessed with the following
c r i t e r i o n :
"Group A ( i n t a c t p i l l a r s ) d i s p l a y e d minor s p a l l i n g
p a r t i c u l a r l y associated with any overbreak into the hanging
wall or footwall gneisses. No j o i n t opening was observed.
Group B p i l l a r s exhibited prominent s p a l l i n g generally
135
associated with s t r u c t u r a l features. S l i g h t opening of the
j o i n t s into the p i l l a r was also noted.
Group C p i l l a r s displayed severe s p a l l i n g of i n t a c t rock,
pronounced opening of j o i n t s and deformation of d r i l l
holes."
The Group A assessment corresponds reasonably well with stable
p i l l a r s , Group B with sloughing p i l l a r s , and Group C with f a i l e d
p i l l a r s . Table 12 gives the p i l l a r c l a s s i f i c a t i o n , p i l l a r
shape, p i l l a r load, and remarks on the p i l l a r s t a b i l i t y for the
complete data base presented by Von Kimmelmann (1984).
Two d i f f e r e n t types of p i l l a r s were investigated. P i l l a r s
that were near square (when viewed i n plan) and p i l l a r s that
were very long i n one dimension (see figure 40) . The long
p i l l a r s were applied d i r e c t l y to the p i l l a r s t a b i l i t y graph (see
figure 41) . Using the t r a n s i t i o n zone for the open stope
p i l l a r s , one stable p i l l a r i s above the t r a n s i t i o n zone and f i v e
stable case h i s t o r i e s are i n the t r a n s i t i o n zone. These case
h i s t o r i e s suggest the t r a n s i t i o n zone could be located s l i g h t l y
h i g h e r making the current p i l l a r s t a b i l i t y graph a b i t
conservative f o r t h i s data.
The square p i l l a r s can not be d i r e c t l y applied to the p i l l a r
s t a b i l i t y graph. Several authors have noted that rectangular
p i l l a r s are s i g n i f i c a n t l y stronger than square p i l l a r s (Wagner
1974; Salamon 1983; Kersten 1984; Stacey and Page 1986). To
account f o r the difference during design, these authors have
suggested the use of an e f f e c t i v e p i l l a r width:
CLASSIFICATION OF SQUARE PILLARS 136 PILLAR NO. CLASSIFICATION W/H ESTIMATED
PILLAR STRESS (MPA) REMARKS
1 B 0,80 28 Opening of Joint* 2 A 1.70 26 Joints tight 3 A 1.70 30 Minor spalling 4 B 1.2* 34 Spalling i n gneiss 5 B 1.00 34 Spalling i n M.S. Joints tight 6 B 1.30 35 Fractured M.S. Assoc. with joi n t i n g 7 C 1,20 55 Sever* spalling 8 C 0,96 55 Severe spalling 9 c 1,00 58 Severe spalling
10 c 1.50 58 Severe spalling 4 opening of Joints 11 c 0,50 58 Failed p i l l a r 12 c 1,26 53 Marked hangingvall deterioration 13 B 1,40 48 Bangingvall deterioration 14 c 1,60 58 Severe spalling 15 c 1,40 55 Severe spalling 16 c 0,76 50 Slabbing Assoc. vitb fault 17 A 1,40 37 ) 18 B 1.74 40 )Spalling Assoc. with structural 19 A 2,50 35 )features 20 C 0,6"0 48 ) 21 C 0,90
0,60 0,60
48 .Severe spalling Assoc. with 22 C 0,90 0,60 0,60
48 .Severe spalling Assoc. with 23 C
0,90 0,60 0,60 48 ^deterioration of hangingvall
24 B/C 1.32 55 H/W i n s t a b i l i t y + deformed boreholes 25 B 1.50 47 Spalling 26 B 1.67 48 Joints opening 27 A 1,60 35 Minor spalling i n footvall gneiss 28 A 2,00 35 Minor spalling 29 C 1,00 59 Severe spalling 30 C 1,00 59 Assoc. with bad hangingvall conditions 31 C 1,00 59 Severe spalling 32 C 1,00 59 Failed 33 B 0,80 54 Large p i l l a r 34 B/C 0,92 55 Assoc. with bad hangingvall consitions 35 B/C 1.20 54 Severe spalling 36 C 1,00 55 Severe spalling 37 B 0,92 55 SpalfTng and local slabbing 38 C 0,60 60 Failed 39 B/C 1.30 56 Spalling of gneiss overbreak 40 C 2,27 60 Severe spalling 41 C 1.2C 63 Severe spalling 42 B/C 1.50 63 Severe spelling 43 C 2,00 59 Severe spalling 44 B 1,20 56 Spalling Assoc. with Joint opening 45 B/C 1,40 63 Prominent spalling in gneiss and M.S. 46 B 1,80 53 Spalling 47 A 2,60 60 Minor spalling
CLASSIFICATION OF LONG PILLARS (L»W)
PILLAR NO. CLASSIFICATION W/H ESTIMATED PILLAR STRESS (MPa) REMARKS
1 A 1,00 25 V. minor spalling 2 A 1,50 29 V. minor spalling 3 A 1,25 40 Joints opening 4 B 0,43 35 Spalling 5 B 0,40 50 Spalling 6 A 0,90 28 Minor spalling in M.S. 7 A 1,00 45 Slight movement on hangingvall contact
• 8 A 1.48 48 Minor spalling Assoc. with joints 9 A 1,30 50 No borehole deformation 10 A 1,20 47 Stable
TABLE 12. Data used by Von Kimmelmann et a l . (1984) i n the development of a p i l l a r f a i l u r e c r i t e r i o n .
137
FIGURE 40. A plan view of room and p i l l a r mining at BCL Limited, showing the use of long p i l l a r s and square p i l l a r s (after Von Kimmelmann 1984).
138
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139
W e f f = 4 * A C
where:
W eff = the e f f e c t i v e p i l l a r width,
A = p i l l a r cross sectional area,
C = p i l l a r circumference.
The reasoning i s that for very long p i l l a r s (and open stope r i b
p i l l a r s ) , a p i l l a r i s e f f e c t i v e l y exposed on only two walls and
consequently stronger than square p i l l a r s , which are exposed on
four walls. Using t h i s concept, square p i l l a r s have h a l f the
e f f e c t i v e width of a long p i l l a r having the same p i l l a r height
to width r a t i o . In figure 42, the square p i l l a r s at BCL Limited
have been plotted on the p i l l a r s t a b i l i t y graph using t h e i r
e f f e c t i v e p i l l a r width/ h e i g h t r a t i o ( i e . the a c t u a l
width/height r a t i o ) .
The adjusted square p i l l a r data agrees reasonably well with
the o r i g i n a l t r a n s i t i o n zone on the p i l l a r s t a b i l i t y graph.
Three stable square p i l l a r case h i s t o r i e s p l o t above the f a i l u r e
l i n e on the t r a n s i t i o n zone, while a l l the y i e l d i n g and f a i l e d
p i l l a r s p l o t above the t r a n s i t i o n area. The e f f e c t i v e width
adjustment for square p i l l a r s on the p i l l a r s t a b i l i t y graph
adequately explains the assessment for t h i s data. As with the
long p i l l a r s , the adjusted square p i l l a r data suggests the
t r a n s i t i o n zone could be located s l i g h t l y higher. However, t h i s
inaccuracy i s on the conservative side f o r stable p i l l a r design.
6.3.3 Data from an Australian Open Stope Mine
140
IN
O
M
son/avcn
FIGURE 42. The square p i l l a r Kimmelmann et a l . (1984) i s using an e f f e c t i v e width i n
data presented by Von plotted on the s t a b i l i t y graph the H/W r a t i o .
141
A t e s t open stoping block at Mt. Isa i s described i n depth
by Brady (1977). The objective of the t r i a l mining block was to
obtain information for r i b p i l l a r design and c a l i b r a t e a f a i l u r e
c r i t e r i o n f o r the rock mass. Figure 43 shows the t e s t broken
into f i v e stages.
Stage 1 (problem No. 1) shows the development of two s l o t
r a i s e s , and the S86 r a i s e to observe p i l l a r conditions.
Stage 2 contains the opening of the S85 stope.
Stage 3 shows the opening of S87 stope which creates the S86
p i l l a r .
Stage 4 i s the expansion of the S87 stope, with the S86 p i l l a r
remaining stable and i n t a c t .
Stage 5 shows the robbing of the S86 p i l l a r which resulted i n
f a i l u r e of the p i l l a r .
Brady presented s u f f i c i e n t information that stages 3, 4 and
5 could be modelled with BITEM to determine the average p i l l a r
load. The stope height:length r a t i o for a l l three cases i s
greater than 3, so less than 20% error i s expected i n the
average p i l l a r load determined by BITEM (the error i s estimated
using figure 33, page 109). The modelling r e s u l t s were i n good
agreement with a p r i n c i p a l stress contour diagram i n the
o r i g i n a l paper.
The rock mass, as described i n the paper by Brady, has
s i m i l a r c h a r a c t e r i s t i c s and qu a l i t y to the t y p i c a l rock mass
142
192 0
7 0/B MICAF
610
1 10-0
-1920
Problem No. 1
k -26-2 . ; 1 -
Boundary of S84 • pillar area
1 6 65
30-2
S85 slope
Problem No. 2
-I 1
i < i
SB7 Cut-off rais« (1 81 Dia.)
, Boundary of S86 < \ J pillar area
S86 raise
_ J
i | 15.1 '4-8 I —
n n
0— r — - S 87 stopt
Problem No 3
J
•1920 26.2
10-0
Problem No 4 1
1 6-65
i _
•34-4
SBS
6-7
S 6 6
O
1 r 1 37-8
! ses ; , 1
58b o
i S87 r 1
420
sen
Problem No. 5 Scole 10m
FIGURE 43. The f i v e stages of the S86 p i l l a r i n an open stope p i l l a r t e s t at Mt. Isa ( a f t e r Brady 1977).
143
found i n the data base. The volume of the A u s t r a l i a p i l l a r s i s
also s i m i l a r to that i n the data base. So, these two variables
are not l i k e l y to have a s i g n i f i c a n t influence i n p l o t t i n g the
data on the p i l l a r s t a b i l i t y graph.
The three stages are plotted on a p i l l a r s t a b i l i t y graph i n
figure 44. The S86 p i l l a r p l o t s i n the stable region for stages
3 and 4, and p l o t s i n the f a i l u r e zone a f t e r stage 5. This
agrees very well with Brady's description of the p i l l a r during
the t e s t .
6.3.4 Summary of A l l the Data
A p l o t of the open stope data and a l l the data from
l i t e r a t u r e i s given i n figure 45. The data from l i t e r a t u r e
helps confirm the location of the t r a n s i t i o n area over a greater
area. In the e n t i r e data base of 135 p i l l a r s , four stable case
h i s t o r i e s are found above the t r a n s i t i o n zone and one sloughing
p i l l a r i s found below the t r a n s i t i o n zone. Consequently, the
s o l i d design l i n e s f o r the t r a n s i t i o n zone have been extended.
The success of the p i l l a r s t a b i l i t y graph i n separating the
d i f f e r e n t p i l l a r assessments supports the decision to discount
the influence of p i l l a r volume and rock mass qu a l i t y as
i n s i g n i f i c a n t i n hard rock p i l l a r design.
6.4 Comparison Against Other Design Methods
A number of empirical design methods are frequently used for
r i b p i l l a r s . However, none of these methods was based on open
144
son/avon
FIGURE 4 4 . The t h i r d , fourth and f i f t h stages of the S86 open stope r i b p i l l a r , presented by Brady (1977), are shown on the p i l l a r s t a b i l i t y graph. The data agrees very well with the s t a b i l i t y graph.
• CD • 145
CM
son/avoT
F I sSL 4rib !m P i lh r l a b i l i t y graph showing the open
Hedlly M9?2J V o n a K ? t h e l i t e r a t ^ e data presented by tieaiey (1972), Von Kimmelmann (1984), and Brady (1977).
146
stope mining case h i s t o r i e s . The following comparison of the
methods a g a i n s t the p i l l a r s t a b i l i t y graph, shows the
a p p l i c a b i l i t y of the other methods to the design of open stope
r i b p i l l a r s . Any negative evaluation should not be taken as a
c r i t i c i s m of other methods, but rather i t serves to show the
l i m i t a t i o n s of these methods when applied to the design of open
stope r i b p i l l a r s .
6.4.1 Hedley's P i l l a r Strength Formula
The p i l l a r strength formula developed by Hedley and Grant
(1972) was based on data from room and p i l l a r mining at E l l i o t
Lake and has been discussed i n Chapters 3.1.1.3 and 6.3.1. The
formula i s defined as:
Qu = k * wa / h b
where:
Qu = p i l l a r strength
k = strength of 1 f t . cube (UCS 1 2)
w = p i l l a r width (ft)
h = p i l l a r height (ft)
a = empirical constant = 0.5
b = empirical constant = 0.75
To get UCS 1 2, several authors have used a s c a l i n g factor
from the compressive strength of a 2 inch diameter specimen
(UCS 2):
147
u c s 1 2 0.7 * UCS 2
This r e l a t i o n s h i p has been found i n works by Hedley and Grant
(1972), Hedley et a l . (1979), Hoek and Brown (1980), and Von
Kimmelmann et a l . (1984).
Hedley's formula i s a siz e e f f e c t formula, which means that
i t accounts f o r the actual dimensions of a p i l l a r and not just
the p i l l a r shape. To apply t h i s to open stope r i b p i l l a r s , the
s i z e of t y p i c a l open stope r i b p i l l a r s must be determined. The
range of r i b p i l l a r sizes seen i n 17 d i f f e r e n t Canadian open
stope mines i s presented i n figure 46. The dimensions of
permanent p i l l a r s are denoted by the symbol "P" and the
dimensions of p i l l a r s i n mining methods using b a c k f i l l and
temporary p i l l a r s are denoted by the symbol "B". The dashed
l i n e s give the upper and lower bound of p i l l a r dimensions used
i n the 17 Canadian open stope mines. For various p i l l a r width
to p i l l a r height r a t i o s ( i e . p i l l a r s t r i k e length to orebody
width r a t i o s ) , the minimum and maximum p i l l a r dimensions can be
determined and applied to Hedley's s i z e e f f e c t formula.
For a p p l i c a t i o n of t h e i r p i l l a r strength formula, Hedley and
Grant suggest that p i l l a r s with a safety factor greater than 1.5
are stable and p i l l a r s with a safety factor near 1.0 are
crushed. Rearrangement of the safety factor formula,
S.F. Qu 0.7 * UCS 2 * w a
c r p aP * h b
H rt»0 O O 3* ct> o» c
ft 3 0> W
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fl) fD o> o>
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< « 3* B O H * H * H * M> ft M 3 3* fl> fl> >1 f t f t • KT 3" 3* <t> fl) *0 w a> » M <o r t o»
f t H r )
~ fl) fl) f t O. f t
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M » a T J H - fl) 3 0 M 3 3 M O D. W • f t (!)
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45
40
35 -
30 -
25 -
20 -
15 -
10 -
5 -
PILLAR DIMENSIONS BASED ON 17 CANADIAN OPEN STOPE MINES
B B B
\ B B P P
B B
B
B
P P P B
B \ B
\
B
B
B
B
B
k B
\ B \
\
B = BACKFILLED
—] 1 1 1— 20 40
OREBODY WIDTH (m) P = PERMANENT
60
149
permits p l o t t i n g of safety factor l i n e s for 1.0 and 1.5, for the
maximum and minimum r i b p i l l a r sizes observed i n open stoping,
against the data base (figure 47). The upper shaded zone shows
the possible l o c a t i o n of open stope r i b p i l l a r s when designed
with a safety factor of 1.0. The lower zone shows the possible
l o c a t i o n of open stope r i b p i l l a r s when designed with a safety
factor of 1.5. Size e f f e c t formulas assume that smaller p i l l a r s
are stronger than large p i l l a r s . So, the upper l i n e of each
zone corresponds to the minimum p i l l a r sizes seen i n Canadian
open stope mines, while the lower l i n e of each zone corresponds
to the maximum p i l l a r sizes seen i n Canadian open stope mines.
The graph shows that, for open stope r i b p i l l a r design,
Hedley's formula i s conservative r e l a t i v e to the p i l l a r
s t a b i l i t y graph. In defense of Hedley's formula, i t was
designed f o r much smaller p i l l a r s and i t i s le s s conservative
when applied i n room and p i l l a r mining (due to the nature of the
s i z e e f f e c t formula).
Comparison of the p i l l a r s t a b i l i t y graph against Salamon's
formula (Chapter 3.1.1.2) would give a s i m i l a r conclusion.
Hedley and Salamon used the same method to determine the
strength v a r i a b l e "K" and Salamon has very s i m i l a r values for
the empirical constants (a=0.46 and b=0.66). Salamon's method
i s a c t u a l l y a b i t more conservative than Hedley's formula
because Salamon recommended the use of a safety factor of 1.6 to
ensure stable design and used a p i l l a r height c o e f f i c i e n t of
s o n / a v o n
FIGURE 47. Comparison of the p i l l a r s t a b i l i t y graph and Hedley 1s formula for two safety factors. Hedley's formula i s a s i z e e f f e c t formula, so there i s a range of p i l l a r strength f o r each safety f a c t o r based on the s i z e of open stope r i b p i l l a r s observed i n 17 Canadian mines.
b=0.66 compared to b=0.75 suggested by Hedley.
151
6.4.2 Hoek and Brown P i l l a r Strength Curves
Hoek and Brown (1980) proposed a serie s of curves (figure
11, page 44) for the estimation of p i l l a r strength. These
curves are discussed i n more depth i n Chapter 3.1.1.5. The
curves were developed based on numerical modelling, rock mass
f a i l u r e d i s t r i b u t i o n s inside p i l l a r s of d i f f e r e n t shapes, and
for a range of rock mass q u a l i t i e s , using the f a i l u r e c r i t e r i a :
°P = CT3 + ( m * aC * a3 + s * CTC2)!s
where:
ffp = average p i l l a r strength
o~3 = minimum p r i n c i p l e stress
a c = u n i a x i a l compressive strength of i n t a c t p i l l a r
material
m & s = empirical constants based on the rock mass
qua l i t y .
The m & s empirical constants have been rel a t e d to the NGI and
CSIR rock mass c l a s s i f i c a t i o n s .
Hoek and Brown proposed these p i l l a r design l i n e s assuming
that a p i l l a r i s f a i l e d when the stress across the centre of the
p i l l a r exceeds the strength of the rock mass. Each curve
corresponds to a f a i l u r e l i n e f or a d i f f e r e n t rock mass qual i t y .
152
Since Hoek and Brown used input parameters s i m i l a r to those
i n the p i l l a r s t a b i l i t y graph, i t was possible to reproduce some
of t h e i r design curves on the design chart (see figure 48). The
f i r s t observation i s that Hoek and Brown design l i n e f or good
rock mass qu a l i t y (RMR « 60 - 80) corresponds reasonably well
with the t r a n s i t i o n zone of the p i l l a r s t a b i l i t y graph. The
majority of p i l l a r s i n the open stope r i b data base have a good
rock mass qu a l i t y . However, Hoek and Brown suggest a safety
factor of 1.5 for permanent mine p i l l a r s . While t h i s safety
factor may be needed for the design of permanent p i l l a r s i n
entry mining methods, use of t h i s safety factor would make Hoek
and Brown curves quite conservative for open stope r i b p i l l a r
design.
Hoek and Brown suggest a very large influence of the rock
mass q u a l i t y on p i l l a r strength. The design curve for a f a i r
rock mass q u a l i t y i s well below the t r a n s i t i o n zone of the
p i l l a r s t a b i l i t y graph and the design curve for a very good rock
mass q u a l i t y i s f a r above the t r a n s i t i o n zone. There are very
few p i l l a r case h i s t o r i e s with f a i r or very good rock mass
q u a l i t i e s i n the data base, so the a p p l i c a b i l i t y of these curves
for p i l l a r design can not be v e r i f i e d . A substantial number of
case h i s t o r i e s of p i l l a r s i n f a i r and very good rock masses are
needed before these two curves could be used confidently i n open
stope r i b p i l l a r design.
6.4.3 P i l l a r Shape E f f e c t Formulas
son/avoi
FIGURE 48. Three of the Hoek and Brown (1980) p i l l a r strength curves plo t t e d on the p i l l a r s t a b i l i t y graph. The t r a n s i t i o n zone of the p i l l a r s t a b i l i t y graph and the good rock nass q u a l i t y curve are very close to each other.
154
There are several v a r i a t i o n s of the shape e f f e c t formula
(see Chapter 3.1.1.1). Two of the most common va r i a t i o n s were
developed by Obert and Duvall (1967) and Bieniawski (1983).
Obert and Duvall (1967) presented a formula to account for
the influence of p i l l a r shape. I t i s based on compressive
t e s t i n g of coal specimen p i l l a r s of various shape by Obert et
a l . (1946). The proposed re l a t i o n s h i p was:
dp = a 1 * [A + B * (w / h)]
where:
CTp = p i l l a r strength,
= u n i a x i a l strength of a cubical p i l l a r ,
w = p i l l a r width,
h = p i l l a r height,
A = empirical constant = 0.778
B = empirical constant = 0.222.
The formula has been used by several authors ( l i s t e d i n Chapter
3.1.1.4) to account for the shape e f f e c t i n hard rock p i l l a r
design.
The formula assumes that the strength of a cubical p i l l a r
(o~l) i s known. I f we assume the maximum cubical p i l l a r strength
on the p i l l a r s t a b i l i t y graph i s found at the i n t e r s e c t i o n of
w/h = 1 and the f a i l u r e l i n e (top of the t r a n s i t i o n zone) , the
Obert and Duvall formula can be compared to the p i l l a r s t a b i l i t y
graph and the data base. Figure 49 shows the Obert and Duvall
formula plotted on the p i l l a r s t a b i l i t y graph. I t does not
compare well with the p i l l a r data or the lo c a t i o n of the
155
son/avon
FIGURE 49. Comparison between the p i l l a r s t a b i l i t y graph and the Obert and Duvall (1967) shape e f f e c t formula applied with a safety factor of 1.0.
156
t r a n s i t i o n zone. The Obert and Duvall formula assumes a much
higher strength for slender p i l l a r s than that shown by the case
h i s t o r i e s and the p i l l a r s t a b i l i t y graph t r a n s i t i o n zone. There
are many f a i l e d and sloughing p i l l a r s below the f a i l u r e l i n e
proposed by Obert and Duvall. This formula i s not applicable to
the design of open stope r i b p i l l a r s .
A major coal p i l l a r design study was c a r r i e d out by
Bieniawski (1983) at Pennsylvania State University i n the la t e
1970's. One of the major r e s u l t s of the study was the
development of a shape e f f e c t p i l l a r strength formula.
Bieniawski used a formula s i m i l a r to that proposed by Obert and
Duvall. Bieniawski's formula i s :
(Tp = K * [ 0.64 + ( 0.36 * W )] H
where:
Op = the p i l l a r strength,
K = UCS 1 2 = the compressive strength of 1 cubic foot
of i n t a c t p i l l a r material,
W = p i l l a r width,
H = p i l l a r height.
Assuming UCS 1 2 ~ °' 7 * UCS 2 (shown i n Chapter 6.4.1), a
f a i l u r e l i n e can be plotted on the p i l l a r s t a b i l i t y graph.
Bieniawski's formula i s plotted i n figure 50, f o r a safety
f a c t o r of 1.0, 1.5 and 2.0. This formula does not compare well
with the p i l l a r data or the t r a n s i t i o n zone. For each safety
factor, there are many p i l l a r case h i s t o r i e s that can not be
157
son/avon FI?VoLf°* T h e s n a p e e f f e c t forumla proposed by Bieniawski
(1983) applied with three d i f f e r e n t safety factors i s compared against the p i l l a r s t a b i l i t y graph.
158
explained by Bieniawski's formula.
The conditions under which these formula were developed can
explain t h e i r inadequacy for open stope r i b p i l l a r design. Both
of the formulas i s more applicable f o r p i l l a r s with a
width/height r a t i o of much greater than one. For p i l l a r s with a
width/height r a t i o of l e s s than one, the shape e f f e c t formulas
w i l l overestimate p i l l a r strength by large amounts. Generally,
these formulas are not well suited to open stope r i b p i l l a r
design.
6.5 Chapter Summary
The variables that are s i g n i f i c a n t for open stope r i b p i l l a r
design are: the p i l l a r width and p i l l a r height (defined
according to figure 26, page 87), the compressive strength of
the i n t a c t rock material and the load induced on the p i l l a r .
The volume of a p i l l a r and the presence of geological
d i s c o n t i n u i t i e s do not appear to be s i g n i f i c a n t f o r open stope
r i b p i l l a r design, over the range observed for these variables
i n Canadian open stope mines.
A p i l l a r design chart has been developed based on open stope
r i b p i l l a r s and v e r i f i e d and refined based on hard rock room and
p i l l a r mining data found i n l i t e r a t u r e . The t o t a l data base
consists of 135 p i l l a r case h i s t o r i e s . The p i l l a r s t a b i l i t y
graph contains stable and f a i l e d design areas separated by a
t r a n s i t i o n zone, which shows a v a r i e t y of p i l l a r behaviour. The
159
t r a n s i t i o n zone i s represented by a s o l i d l i n e where i t s
l o c a t i o n i s well defined by data. The t r a n s i t i o n zone i s
represented by dashed l i n e s where i t s exact l o c a t i o n i s not
v e r i f i e d by the data.
The compatibility of a number of e x i s t i n g open stope r i b
p i l l a r design methods with the p i l l a r s t a b i l i t y graph and the
complete p i l l a r data base was checked. Hedley's s i z e e f f e c t
formula (1972) was found to be quite conservative f o r open stope
r i b p i l l a r design. The Hoek and Brown (1980) p i l l a r strength
curve for a good rock mass qu a l i t y agreed well with the p i l l a r
s t a b i l i t y graph. However, the a p p l i c a b i l i t y of the strength
curves f o r the other rock mass q u a l i t i e s could not be v e r i f i e d .
The p i l l a r shape e f f e c t formulas proposed by Obert and Duvall
(1967) and Bieniawski (1983) are not applicable to open stope
r i b p i l l a r design.
160
CHAPTER 7
DESIGNING RIB PILLARS FOR OPEN STOPE MINING
The design of r i b p i l l a r s depends on the duration of the
support to be provided. Rib p i l l a r s may be designed to give
permanent support to provide long-term s t a b i l i t y to open stopes,
to provide regional s t a b i l i t y to the ore block and to protect
access to the stopes. Conversely, r i b s may be designed to give
temporary support to a mining block u n t i l stope support i s
provided by b a c k f i l l . The p i l l a r i s then recovered.
The decision to use permanent or temporary p i l l a r s i s
l a r g e l y based on economics. In a r e l a t i v e l y low grade orebody,
a permanent p i l l a r may be the most economical form of support
because of the high costs associated with b a c k f i l l and p i l l a r
recovery methods. In higher grade orebodies, temporary p i l l a r s
are t y p i c a l l y used because the cost of b a c k f i l l i n g can be
j u s t i f i e d and the maximum extraction of the orebody i s desired.
This i s shown e x p l i c i t l y i n a comparison of the approximate
value of ore per ton found i n Canadian open stope mines using
permanent and temporary p i l l a r s (Table 13) . The average value
per tonne i n the mines using temporary p i l l a r s and f i l l i s
almost double that of the mines using permanent p i l l a r s .
Because permanent and temporary p i l l a r s have d i f f e r e n t
purposes, t h e i r designs can be quite d i f f e r e n t . The following
chapter w i l l discuss the design of permanent and temporary
161
MINES USING APPROXIMATE VALUE BACKFILL OF ORE
($US/ton)
NORITA $ 88 MATTAGAMI LAKE $ 60 MINES GASPE $ 68
WESMIN $ 128 CORBET $ 108
KIDD CREEK $ 125 KIENA $ 69 LOCKERBY $ 123
LAC SHORTT $ 69 GOLDEN GIANT $ 114 LYON LAKE $ 144 GECO $ 70
BRUNSWICK $ 125 CENTENNIAL $ 54
SELBAIE - ZONE B $ 100 FALCONBRIDGE $ 129
MEAN $ 98
MINES USING PERMANENT PILLARS
APPROXIMATE VALUE OF ORE ($US/ton)
RUTTAN $ 43 ALGOMA $ 25
HEATH STEELE $ 92 SELBAIE - ZONE A $ 47
MEAN $ 52
Table 13. Comparison of the value of ore ($US/ton) for mines using b a c k f i l l against mines using permanent p i l l a r s . The mine grades are from the 1987 Canadian Mines Handbook, and the pri c e of the metals i s from the January 1988 Engineering and Mining Journal (after Potvin et a l . 1988b).
162
p i l l a r s i n Canadian open stope mines and suggest some guidelines
for using the p i l l a r s t a b i l i t y graph method. An example of the
use of temporary p i l l a r s i s also given.
7.1 Permanent P i l l a r s
The maximum possible orebody extraction around permanent
p i l l a r s i s about 80%. Any remaining ore w i l l be l e f t i n place,
so i d e a l l y , permanent p i l l a r s should be located i n low grade ore
or waste. Oversize (conservative) p i l l a r dimensions are
permissible under these conditions. However, the design of
permanent p i l l a r s i n ore must be a compromise between
conservative dimensions, to maintain the s t a b i l i t y of the mining
blo c k f o r a long p e r i o d of time, and non-conservative
dimensions, to minimize the loss of ore i n the p i l l a r .
In a preliminary design, i t i s suggested that permanent
p i l l a r s should p l o t below the t r a n s i t i o n zone, i n the stable
area of the p i l l a r s t a b i l i t y graph. The distance below the
t r a n s i t i o n zone should be a function of the degree of confidence
i n the input data (especially the u n i a x i a l compressive strength
of the rock and the induced stress) . The les s confident the
input data, the further below the t r a n s i t i o n zone a p i l l a r
should p l o t .
Ultimately, the best design for permanent p i l l a r s i s
optimised according to mining experience i n the l o c a l ground
conditions. A good example of using l o c a l experience i n p i l l a r
design i s documented by Pakalnis (1986) at Ruttan. The r i b
163
p i l l a r s gradually f a i l as the longitudinal stopes are opened to
t h e i r planned l i m i t s . However) the p i l l a r s r e t a i n s u f f i c i e n t
rock mass competency that they remain r e l a t i v e l y i n t a c t , without
the use of b a c k f i l l , and continue to provide stope support and
regional mine support. In most mines, fr a c t u r i n g due to p i l l a r
f a i l u r e would combine with geological structure to cause severe
p i l l a r sloughing and eventually complete p i l l a r d i s i n t e g r a t i o n .
At Ruttan, sloughing of f a i l e d p i l l a r material i s not a problem,
so the r i b p i l l a r s can be designed to gradually f a i l because
they w i l l remain int a c t and s t i l l provide the necessary stope
support.
7.2 Temporary P i l l a r s
Temporary r i b p i l l a r s are used when i t i s intended to
recover the e n t i r e orebody. This type of open stope mining
involves the use of b a c k f i l l and the extraction of ore must be
c a r e f u l l y sequenced. An optimum mining sequence gives a high
rate of mining, while avoiding stope and p i l l a r i n s t a b i l i t y .
One of the primary concerns for the design of temporary
p i l l a r s i s the ease of recovery of the p i l l a r . Small p i l l a r s
are more d i f f i c u l t and more expensive to recover. Figure 51
shows the range of temporary p i l l a r dimensions used i n 14
Canadian open stope mines. Generally, temporary r i b p i l l a r s are
designed with a s t r i k e length of greater than 8-10 metres and
l e s s than 25 metres. P i l l a r height ( i e . orebody width) varies
from l e s s than 5 metres to 60 metres.
164
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FIGURE 51. The range of temporary r i b p i l l a r dimensions used i n 14 Canadian open stope mines. The maximum s t r i k e length ( p i l l a r width) i s about 25 metres, while the maximum orebody width ( p i l l a r height) i s about 60 metres.
165
The design of temporary p i l l a r s depends on whether the
p i l l a r i s intended to be stable or to f a i l . Both approaches are
used i n open stoping i n Canada, and there are d i f f e r e n t
recommendations that can be made i n the design of each type of
temporary p i l l a r .
7.2.1 Stable Temporary P i l l a r s
The majority of temporary r i b p i l l a r s are designed to be
stable. However, the mine operator's philosophy plays a large
r o l e i n determining the s i z e of temporary r i b p i l l a r s . P i l l a r s
may be designed larger than necessary, or t h e i r dimensions may
be minimized. Use of oversize r i b p i l l a r s permits easier p i l l a r
recovery. In addition, the s t a b i l i t y provided by the extra s i z e
means that the primary stopes may not need immediate f i l l i n g ,
leaving some f l e x i b i l i t y i n the f i l l i n g cycle. However,
minimizing temporary p i l l a r dimensions gives a higher primary
mining volume and a quicker payback on c a p i t a l and development
costs. Minimizing p i l l a r dimensions can become c o s t l y i f the
p i l l a r s f a i l unexpectedly or i f the p i l l a r s are d i f f i c u l t to
recover due to t h e i r small s i z e . The consequences of f a i l e d
temporary p i l l a r s may include:
- the loss of reserves,
- a high mining cost,
- the need for remedial s t a b i l i t y measures such as cable
b o l t i n g ,
- regional i n s t a b i l i t y such as hanging wall and back caving,
166
- and a low rate mining.
Cases of r i b p i l l a r i n s t a b i l i t y and recovery problems are
documented by many authors including Falmagne (1986), Brady
(1977) and Bray (1967).
7.2.2 F a i l e d Temporary P i l l a r s
A r e l a t i v e l y new concept i n open stoping i s to design the
r i b p i l l a r s to f a i l . The consequences of f a i l e d p i l l a r s
described above can often be minimized i f f a i l u r e i s planned.
The advantage i s that i n a high stress environment, the p i l l a r
w i l l not become overstressed and w i l l be easier to recover.
Designing r i b p i l l a r s to destress or f a i l has been documented at
INCO's Frood mine (Grace and Taylor 1985) and Falconbridge•s
Strathcona mine (Bharti 1987). To design a f a i l i n g p i l l a r with
the p i l l a r s t a b i l i t y graph, i t i s suggested that a p i l l a r p l o t
well above the t r a n s i t i o n area, have a low p i l l a r width to
height r a t i o while having a p i l l a r width large enough to permit
easy recover. Although there are no p i l l a r s designed to f a i l i n
the data base, several p i l l a r case h i s t o r i e s that were discarded
from the data base f i t the above design suggestions.
There are a few q u a l i t a t i v e recommendations and comments to
add to the design of f a i l i n g p i l l a r s :
- i t i s very important to f i l l the surrounding stopes as quickly
as possible. The f i l l w i l l provide l a t e r a l constraint on the
p i l l a r walls and w i l l reduce sloughing of the fractured p i l l a r
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material,
- control b l a s t i n g should be used near the p i l l a r walls to
minimize wall damage due to b l a s t v i b r a t i o n s ,
- development i n p i l l a r s w i l l l i k e l y need f u l l f r i c t i o n
a r t i f i c i a l support such as cable bol t s and grouted rebar, as
p i l l a r f r a c t u r i n g could s u b s t a n t i a l l y a f f e c t development
s t a b i l i t y ,
- and d r i l l hole closure and displacement could cause severe
problems f o r longhole (small diameter d r i l l hole) open stoping
methods. Large diameter blastholes w i l l l i k e l y be needed for
recovery of f a i l e d p i l l a r s .
7.3 Case Example: Transverse Rib P i l l a r s at Norita
7.3.1 Geology and Mining Method
The Norita mine i s located i n the Mattagami mining d i s t r i c t
i n north western Quebec. The geological s e t t i n g f o r the copper-
zinc orebody i s shown i n Mine #19 i n Appendix I. More d e t a i l
can be found i n papers by Bawden and Milne (1987) , Chauvin
(1986), and Goodier and Dube (1984). In recent years, the mine
has converted to a transverse blasthole open stoping method.
This case h i s t o r y w i l l focus on the transverse p i l l a r s i n the
open stoping between l e v e l s 9 and 11 of the orebody (figure 52).
The mining block was divided into two l e v e l s with 17 stopes
per l e v e l . The basic sequence of extraction for the mining
block i s shown by the roman numbers on figure 52. Primary
FIGURE 52. Isometric view of transverse blasthole open stoping at Norita. The basic sequence of stope extraction i s shown i n roman numbers.
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stopes were extracted every fourth stope. Stopes were f i l l e d
with a 30:1 r a t i o of m i l l t a i l i n g s and waste rock to cement.
Temporary p i l l a r s (composed of three consecutive unmined stopes)
are formed by the extraction of the primary stopes. S t a b i l i t y
problems were not reported during the primary mining and the
temporary p i l l a r s have been assessed as stable.
The next phase i n the mining was to extract the middle
(secondary) stope of the temporary p i l l a r s . The b l a s t i n g of the
secondary stopes was done c a r e f u l l y using control b l a s t i n g
methods. Explosives were decked with a maximum detonation per
delay of 90 kilograms. Afte r the stopes were emptied, they were
b a c k f i l l e d with a 30:1 r a t i o of m i l l t a i l i n g s and waste rock to
cement.
With the commencement of primary mining between l e v e l s 9 and
10 (stage IV) and t e r t i a r y stope mining between l e v e l s 10 and 11
(stage I I I ) , det e r i o r a t i o n of drawpoint p i l l a r s on l e v e l 10
necessitated frequent r e h a b i l i t a t i o n . Mining of the t e r t i a r y
stopes encountered heavy b l a s t overbreak (3.3 metre p u l l on 2
metre rounds) . The ore was described as badly broken and
fractured. This damage was induced by mining since the ground
was c l a s s i f i e d as very good (Q « 40 and RMR « 75) before mining
had started. With continued mining between l e v e l s 9 and 11
(stages I I I , IV, and V) , development d r i f t s i n the 8-8 s i l l
p i l l a r ( d i r e c t l y above l e v e l 9) deteriorated due to stress
shedding from the transverse mining area. This was confirmed by
s t r e s s c e l l s i n s t a l l e d near the t r a n s v e r s e p i l l a r s .
170
Extensometer monitoring of the 8-8 s i l l p i l l a r showed that the
de t e r i o r a t i o n was d i r e c t l y related to mining events i n the
t r a n s v e r s e mining block. Based on these observations
(documented by Bawden and Milne 1987), the t e r t i a r y p i l l a r s i n
the transverse mining area were assumed to have f a i l e d .
7.3.2 Back Analysis Using the P i l l a r S t a b i l i t y Graph
Back analysis w i l l focus on representative p i l l a r s i n the
mining block. A f t e r the primary mining between l e v e l s 10 and 11
was completed, stopes 10-5 and 10-9 had been extracted leaving a
stable temporary p i l l a r made of stopes 10-6, 10-7, and 10-8 (see
figure 53). The p i l l a r dimensions were: 55-60 metres i n (stope)
height, 33 metres i n ( p i l l a r ) width and 23 metres i n ( p i l l a r )
height (according to the convention i n figure 26, page 87). The
average load was estimated by two dimensional plane s t r a i n
modelling (BITEM) at 75 MPa (case 43 from Table 8, page 105).
The p i l l a r p l o t s well inside the stable zone of the p i l l a r
s t a b i l i t y graph (figure 54).
During secondary mining stope 10-7 was extracted leaving the
t e r t i a r y p i l l a r s 10-6 and 10-8 (figure 53) , which were given a
f a i l e d assessment. The p i l l a r dimensions were: 55-60 metres
(stope) height, 11 metres i n ( p i l l a r width) and 23 metres i n
( p i l l a r ) height. The t h e o r e t i c a l average p i l l a r load on the 10-
8 p i l l a r was estimated at 99 MPa (case 42 from Table 8, page
165) . This i s a t h e o r e t i c a l average p i l l a r load because i n
p r a c t i c e the p i l l a r has f a i l e d and destressed and therefore w i l l
FIGURE 53. A longitudinal section of the blasthole open s t o p i n g block at Norita showing the p i l l a r case h i s t o r i e s (10-6, 10-7, and 10-8) used i n t h i s case hist o r y analysis (after Goodier and Dube 1984).
172
S O n / Q V O T
F I o ? ^ f 4 \ K ? 6 P 4 l a r s t a b i l i t y graph showing the l o c a t i o n
173
have a much lower actual load (see Chapter 5.5.1 for a more
complete discussion of t h i s assumption). The p i l l a r p l o t s above
the t r a n s i t i o n zone i n the f a i l e d area (see figure 54) . This
agrees very well with the f a i l e d assessment f o r the t e r t i a r y
stopes.
7.3.3 Comments Concerning the P i l l a r Design
This y i e l d i n g p i l l a r case hi s t o r y i l l u s t r a t e s the use of
f a i l e d p i l l a r s i n open stope mining. There are several comments
and observations to make that are a consequence of the p i l l a r
design:
1 - Cable b o l t i n g of the t e r t i a r y stope backs was necessary, due
to severe cracking and j o i n t opening.
2 - Heavy overbreak during the p i l l a r ( t e r t i a r y stope) mining
was encountered.
3 - Blastholes (6h inch diameter) were used for the entire
mining block and were necessary to avoid the loss of d r i l l
holes due to crushing and f r a c t u r i n g during the t e r t i a r y
p i l l a r recovery.
4 - The stopes were f i l l e d quickly with waste rock and cemented
m i l l t a i l i n g s .
5 - The mining of the f a i l e d p i l l a r s was generally successful.
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CHAPTER 8
SUMMARY AND CONCLUSIONS
a.i summary
The purpose of t h i s study i s to investigate the s t a b i l i t y of
r i b p i l l a r s i n open stope mining and develop guidelines for the
optimization of r i b p i l l a r dimensions. This i s accomplished
through four major steps:
- d e s c r i p t i o n of the f a i l u r e mechanism i n open stope r i b
p i l l a r s ,
- i n v e s t i g a t i o n of the methods currently used i n open stope
r i b p i l l a r design,
- q u a n t i f i c a t i o n of the s i g n i f i c a n t design variables,
- and formulation and v e r i f i c a t i o n of a new method based on
open stope r i b p i l l a r data and case h i s t o r i e s .
8.1.1 Open Stope Rib P i l l a r F a i l u r e
There are two basic types of f a i l u r e i n hard rock p i l l a r s .
Progressive f a i l u r e r e f e r s to gradual d e t e r i o r a t i o n of a p i l l a r
i n a slow, non-violent manner. Bursting f a i l u r e i s character
ized by the v i o l e n t release of energy causing instantaneous
fracture of rock. This thesis only investigates progressive
f a i l u r e .
Open stope r i b p i l l a r i n s t a b i l i t y i s a progressive
mechanism. P i l l a r f a i l u r e i s defined as the point at which
progressive f a i l u r e causes a p i l l a r to s t a r t l o s i n g i t s load
175
bearing capacity. The decrease i n load bearing capacity i s
l a r g e l y due to f r a c t u r i n g of the rock mass i n the p i l l a r .
Several signs of increasing p i l l a r i n s t a b i l i t y have been
i d e n t i f i e d , including:
- cracking and s p a l l i n g of rock i n p i l l a r development,
- audible noise heard i n the p i l l a r s or microseismic events
detected with monitoring systems,
- deformed or plugged d r i l l holes,
- overdraw from stopes consisting of unblasted, oversize ore,
- stress r e d i s t r i b u t i o n from p i l l a r s a f f e c t i n g nearby p i l l a r s
or development,
- hourglassing and cracking of p i l l a r s ,
- and d i s p l a c e m e n t s or changes i n s t r e s s shown by
instrumentation.
8.1.2 Current P i l l a r Design Methods
Design methods used for open stope r i b p i l l a r s were based on
empirical p i l l a r design studies or the use of numerical
modelling and empirical f a i l u r e c r i t e r i o n . Empirical p i l l a r
design methods were developed based on laboratory t e s t i n g and/or
i n v e s t i g a t i o n of actual mine p i l l a r s . These methods were
developed for s p e c i f i c mining conditions and are not necessarily
applicable f o r open stope r i b p i l l a r design. Numerical methods
b a s i c a l l y assume e l a s t i c and/or p l a s t i c rock mass behaviour to
determine stress r e d i s t r i b u t i o n and rock mass displacement
around underground excavations. Empirical f a i l u r e c r i t e r i o n are
176
applied to the stress or displacement r e s u l t s to determine rock
mass f a i l u r e . However, i t i s d i f f i c u l t to v e r i f y an i n s i t u
rock mass f a i l u r e c r i t e r i o n . Consequently, numerical design
methods need extensive s i t e c a l i b r a t i o n before they can be used
e f f e c t i v e l y to design r i b p i l l a r s i n open stope mining.
The design methodology chosen for t h i s t h e s i s i s a
combination of numerical and empirical methods. Numerical
techniques are used to determine p i l l a r load, while p i l l a r
f a i l u r e i s determined from empirical back analysis of open stope
r i b p i l l a r case h i s t o r i e s .
8.1.3 I d e n t i f i c a t i o n and Quantification of the Design Variables
Based on the data and case h i s t o r i e s c o l l e c t e d i n the
Integrated Mine Design Project, the factors that are s i g n i f i c a n t
for open stope r i b p i l l a r design are:
- the compressive strength of i n t a c t p i l l a r material (UCS),
- the average p i l l a r stress (determined with boundary
element numerical modelling),
- the p i l l a r height,
- and the p i l l a r width.
Three factors were discounted as i n s i g n i f i c a n t i n r i b p i l l a r
f a i l u r e : the presence of minor geological d i s c o n t i n u i t i e s (such
as j o i n t s ) , the e f f e c t of p i l l a r volume, and the e f f e c t of
b a c k f i l l . The open stope r i b p i l l a r data and case h i s t o r i e s did
not prove these factors as being important i n p i l l a r f a i l u r e .
The background information for a l l the p i l l a r s i n the data base
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i s presented i n Table 5 (page 70) and the geological settings of
a l l of the p i l l a r case h i s t o r i e s are shown i n oblique orebody
diagrams i n Appendix I.
Three of the four design variables are quite easy to
quantify. The UCS can be determined by laboratory t e s t i n g of
i n t a c t rock samples or estimated with the point load t e s t . The
p i l l a r height and p i l l a r width are measured from mine plans.
The most d i f f i c u l t factor to quantify i s the average p i l l a r
s t r e s s . A method to determine average p i l l a r stress i s proposed
i n Chapter 5. The two dimensional boundary element code BITEM
and the pseudo-three dimensional displacement d i s c o n t i n u i t y
boundary element model "MINTAB" have been used to estimate the
p i l l a r load for a l l the p i l l a r s i n the data base. However,
these methods have l i m i t a t i o n s when modelling some p i l l a r
geometries. The major geometrical l i m i t a t i o n s associated with
two dimensional (2D) and displacement d i s c o n t i n u i t y (DD)
numerical modelling have been i d e n t i f i e d . In addition, a rough
error associated with these l i m i t a t i o n s i s given i n figure 33,
page 109 (for 2D modelling), and i n figure 34, page 112 (for DD
modelling). These error estimates are based on a comparison of
the 2D and DD models to 12 runs of the three dimensional
boundary element code "BEAP".
8.1.4 Development of the P i l l a r S t a b i l i t y Graph
The open stope r i b p i l l a r data c o l l e c t e d has been empir
i c a l l y analyzed and a p i l l a r design graph has been developed
178
(figure 36, page 125) . The design chart has been c a l l e d the
" P i l l a r S t a b i l i t y Graph". I t contains stable and f a i l e d design
areas separated by a t r a n s i t i o n zone. The p i l l a r s t a b i l i t y
graph has been v e r i f i e d and refined based on more than 80 hard
rock room and p i l l a r case h i s t o r i e s from l i t e r a t u r e . The
complete data base of about 135 p i l l a r s i s shown i n figure 45
(page 145). The design chart explains the s t a b i l i t y condition
of the data base case h i s t o r i e s very well and i s quite s e n s i t i v e
i n p r e d i c t i n g p i l l a r f a i l u r e .
Empirical design methods used for open stope r i b p i l l a r
design have been compared to the complete p i l l a r data base and
the p i l l a r s t a b i l i t y graph. The good rock mass q u a l i t y design
l i n e of the p i l l a r strength curves proposed by Hoek and Brown
(1980) agrees quite well with the data base and p i l l a r s t a b i l i t y
graph. However, the Hedley and Grant (1972) s i z e e f f e c t p i l l a r
strength formula and the shape e f f e c t p i l l a r strength formula's
by Obert and Duvall (1967) and Bieniawski (1983) do not compare
well with the p i l l a r data or the p i l l a r s t a b i l i t y graph.
Open stope r i b p i l l a r s may be designed to be permanent and
s t a b l e , temporary and stable, or temporary and f a i l i n g .
Guidelines have been suggested for the design of each type of
r i b p i l l a r using the p i l l a r s t a b i l i t y graph. A case history
discussing the use of stable and f a i l e d temporary r i b p i l l a r s i s
also presented.
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8.2 Conclusions
8.2.1 A p p l i c a b i l i t y of the Method
The p i l l a r s t a b i l i t y graph uses factors that are r e l a t i v e l y
easy to quantify data to predict the s t a b i l i t y of open stope r i b
p i l l a r s . The method i s most e f f e c t i v e when rough predictions of
s t a b i l i t y are required. Minor problems such as l o c a l f r a c t u r i n g
w i l l not be predicted, but gross changes i n p i l l a r s t a b i l i t y are
recognized. The method i s designed to predict f a i l u r e of open
stope r i b p i l l a r s , but can be applied to some other types of
p i l l a r s . I t should be applicable for the design of open stope
s i l l p i l l a r s , and r i b and s i l l p i l l a r s i n non-entry methods such
as V e r t i c a l Crater Retreat. The mechanism of p i l l a r f a i l u r e for
these types of p i l l a r s i s the same as the mechanism of f a i l u r e
i n open stope r i b p i l l a r s .
This design method has not been developed or confirmed for
p i l l a r s i n entry methods such as shrinkage and room and p i l l a r
mining. The p i l l a r s t a b i l i t y graph would l i k e l y need the
development of a safety factor before i t could be applied to
p i l l a r design i n entry mining methods.
8.2.2 Limitations of the Method
An empirical design method i s more r e l i a b l e when applied to
conditions s i m i l a r to those found i n the o r i g i n a l work.
Consequently, the following l i m i t a t i o n s are suggested f o r the
p i l l a r s t a b i l i t y graph:
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70 MPa < UCS < 316 MPa,
9 metres < Wp < 45 metres,
60 < RMR < 78,
(Average P i l l a r Load / UCS) < 0.5.
where,
UCS = the i n t a c t rock u n i a x i a l compressive strength,
Wp = the p i l l a r width,
RMR = a measure of the rock mass competency using the
CSIR rock mass c l a s s i f i c a t i o n ,
Average P i l l a r Load i s determined using two dimensional or
displacement dis c o n t i n u i t y boundary element numerical
modelling.
The p i l l a r s t a b i l i t y graph method may work s a t i s f a c t o r i l y
outside these l i m i t a t i o n s , but the current open stope data base
generally does not extend outside these l i m i t s .
F i n a l l y , i t should be kept i n perspective that t h i s i s a
preliminary design method. The assumptions and p o t e n t i a l error
associated with the variables and design chart l i m i t the
usefulness of the p i l l a r s t a b i l i t y graph for f i n a l design.
8.2.3 Design of Open Stope Rib P i l l a r s
The design of open stope r i b p i l l a r s i s dependent upon the
ro l e of that p i l l a r i n the s t a b i l i t y of the mine. Rib p i l l a r s
may be designed to be give permanent support to open stopes, or
they may be designed to give temporary stope support u n t i l
b a c k f i l l i s i n place. This decision i s l a r g e l y one of
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economics. Low grade orebodies cannot be mined using b a c k f i l l
and p i l l a r recovery methods due to the higher mining cost.
Medium and high grade mines can a f f o r d the cost of b a c k f i l l and
p i l l a r recovery, so temporary p i l l a r s can be designed. In some
instances, temporary p i l l a r s have been designed to f a i l to avoid
stress b u i l d up. There are a few consequences of designing
p i l l a r s to f a i l , including:
- the need f o r quick b a c k f i l l i n g a f t e r the stope i s extracted,
- the use of a r t i f i c i a l support i n p i l l a r development,
- and the use of large diameter d r i l l holes and control
b l a s t i n g p ractices.
8.3 Future Work
There i s a l i m i t to the value of c o l l e c t i n g further general
p i l l a r case h i s t o r i e s to r e f i n e the p i l l a r s t a b i l i t y graph.
More cases of open stope p i l l a r s are not l i k e l y to s i g n i f i c a n t l y
improve the accuracy of the e x i s t i n g graph or reduce the s i z e of
the t r a n s i t i o n area. This i s not to say that p i l l a r design at
s p e c i f i c s i t e s can not be aided by case h i s t o r i e s from that s i t e
or from s i m i l a r ground conditions. Past experience i s the best
way to r e f i n e p i l l a r design methods to l o c a l conditions.
The understanding of one of the possible design factors may
be improved by c o l l e c t i n g s p e c i f i c case h i s t o r i e s . The
influence of rock mass c h a r a c t e r i s t i c s was not found to be
s i g n i f i c a n t (Chapter 6.1.3.2), but varied over only a small
range of rock mass q u a l i t i e s . Analysis of p i l l a r case h i s t o r i e s
182
i n f a i r or very good q u a l i t y rock masses may show that the
qu a l i t y of the rock mass i s s i g n i f i c a n t i n open stope r i b p i l l a r
design. I f t h i s can be proven, a correction factor to the
ex i s t i n g p i l l a r s t a b i l i t y graph could be developed to account
for the e f f e c t of rock mass qual i t y .
Assessment of the p i l l a r s i n the data base was sometimes
d i f f i c u l t , and a substantial amount of data could not be applied
because a r e l i a b l e assessment could not be determined. A more
de t a i l e d i n v e s t i g a t i o n into p i l l a r f a i l u r e mechanisms and i n
s i t u rock mass f r a c t u r i n g could improve p i l l a r design methods.
A better d e f i n i t i o n of f a i l u r e can be developed through
systematic i n s i t u p i l l a r monitoring using v i s u a l techniques (as
shown by Krauland and Soder 1987) or through the use of
instrumentation such as stressmeters (as shown by Agapito 1974),
extensometers (as shown by A l l c o t t and Archibald 1981) or
microseismics. The use of microseismic systems f o r i n s i t u
m onitoring shows great p o t e n t i a l through quantifying the
decrease of rock mass qu a l i t y due to rock f r a c t u r i n g , and
monitoring the changes i n the load bearing condition of p i l l a r s .
Both of these topics can be investigated with the microseismic
technology currently available.
183
REFERENCES
Agapito, J.F.T. 1974. Rock mechanics applications to the design of o i l shape p i l l a r s . The Mining Engineer, no. 5, 20-25.
Agapito, J.F.T. and Hardy, M.P. 1982. Induced horizontal stress method of p i l l a r design i n o i l shale. Proc. 15th O i l Shale Symp. Golden: Colorado School of Mines, 179-191.
A l l c o t t , G.A. and Archibald, D.E. 1981. Description and p i l l a r behaviour at Heath Steele mines. Canadian I n s t i t u t e of Mining and Metallurgy B u l l e t i n . 74, October, 80-87.
Babcock, N., Morgan, T. and Haramy, K. 1981. Review of p i l l a r design equations including the e f f e c t s of constraint. 1st Conference on Ground Control i n Mining. Dept. of Mining Eng., West V i r g i n i a University, Morgantown, 23-34.
Barton, N., Lien, R. and Lunde, J . 1974. Engineering c l a s s i f i c a t i o n of rock masses for the design of tunnel support. Rock Mechanics. 6, No. 4, 189-236.
Bawden, W.F. and Milne, D. 1987. Geomechanical mine design approach at Noranda Minerals, Inc.
Bawden, W.F., Sa u r i o l , G., Milne, D. and Germain, P. 1988. P r a c t i c a l rock engineering stope design - case h i s t o r i e s from Noranda Minerals Inc. 90th CIM Annual General Meeting, Edmonton, Alberta.
Bharti, S., Udd, J.E. and Cornett, D.J. 1987. Ground Support at Strathcona Mine. Underground Support Systems, Special Volume 35. Montreal: Canadian I n s t i t u t e of Mining and Metallurgy, 13-26.
Bieniawski, Z.T. 1973. Engineering c l a s s i f i c a t i o n of jointed rock masses, Trans. S. Afr. Inst. C i v i l Engineers 15, No. 12, 335-344.
Bieniawski, Z.T. 1974. Estimating the strength of rock materials. J . S. Inst. Min. Metall. 74, No. 3, 312-320.
Bieniawski, Z.T. and Van Heerden, W.L. 1975. The s i g n i f i c a n c e of i n s i t u t ests on large rock specimens. Int. J . Rock Mech. Min. S c i . & Geomech. Abstr. 12, 101-113.
Bieniawski, Z.T. 1983. Improved design of room-and-pillar coal mines fo r U.S. conditions. F i r s t Int. Conf. on S t a b i l i t y i n Underground Mining. New York: AIME, 19-51.
184
Bieniawski, Z.T. 1987. Strata control i n mineral engineering. Rotterdam: A.A. Balkema.
Brady, B.H.G. 1977. An analysis of rock behaviour i n an experimental stoping block at the Mount Isa mine, Queensland, A u s t r a l i a . Int. J . Rock Mech. Min. S c i . & Geomech. Abstr. 14, 59-66.
Brady, B.H.G. 1978. A boundary element method for three-dimensional e l a s t i c analysis of tabular orebody extraction. Proc. 19th U.S. Sym. Rock Mech.. 431-438.
Brady, B.H.G. and Bray, J.W. 1978. The boundary element method for determining stresses and displacements around long openings i n a t r i a x i a l stress f i e l d . Int. J . Rock Mech. and Min. S c i . and Geomech. Abstrs. 15, 21-28.
Brady, B.H.G. 1981. Determination of s t a b i l i t y of underground structures. Design and Operation of Caving and Sublevel Open Stoping Mines. New York: AIME, 427-435.
Brady, B.H.G. and Brown, E.T. 1985. Rock Mechanics for Underground Mining. London: A l l e n & Unwin Ltd.
Bray, R.C.E. 1967. Control of Ground Movement at Geco Mine. Annual General Meeting, Noranda Mines. Geco Div., Geology Dept., Ottawa.
Brown, E.T. 1985. From theory to practice i n rock engineering. The Nineteenth S i r J u l i u s Wernher Memorial Lecture of the I n s t i t u t i o n of Mining and Metallurgy, Tunneling '85, Brighton, England.
Brown, E.T. 1987. Introduction i n A n a l y t i c a l and Computational Methods i n Engineering Rock Mechanics. London: A l l e n and Unwin, 1-27.
Bywater, S., Cowling, R. and Black, B.N. 1983. Stress measurement and analysis for mine planning. Proceedings of the Fourth Congress of the International Society of Rock Mechanics. D29-D37.
Campbell, P. 1987. B a c k f i l l Survey of Ontario Mines. 89th CIM Annual General Meeting, Toronto, Ontario.
Chauvin, J . 1986. A safer work place1 Ground control, monitoring and simulation to predict ground movement, Norita Mine, Mattagami Lake, Quebec. Noranda F a l l Engineering Seminar, unpublished report.
Coates, D.F. 1981. Rock mechanics p r i n c i p l e s .
185
Cook, N.G.W. 1967. Contributions to discussion. J . S. Afr. Inst. Min. Metall. 67, No. 11, 192-195.
Coulomb, C.A. 1776. Essaie sur une app l i c a t i o n des regies de maximis et mininis a quelques problemes de statique, r e l a t i f s a 1 1 architecture. Memories de Mathematicrue et de Physique, l'Academie Royale des Sciences. 7, 343-382.
Crotty, J.M. and Wardle, L.J. 1980. User's Manual for Program BITEM - Two-dimensional E l a s t i c Stress Analysis for Piecewise Homogeneous Solids. CSIRO Di v i s i o n of Applied Geomechanics, Geomechanics program No.3.
Crouch, S.L. and S t a r f i e l d , A.M. 1983. Boundary Element Methods i n S o l i d Mechanics. London: A l l e n and Unwin.
Crouch, S.L. 1986. The Besol System: Boundary Element Solutions for Rock Mechanics Problems. Part I I . Three-dimensional programs. User's guide, version 1.15.
Cundall, P.A. 1987. D i s t i n c t element methods of rock and s o i l structure. In A n a l y t i c a l and Computational Methods i n Engineering Rock Mechanics. London: A l l e n and Unwin, 129-162.
Diering, J.A.C. 1987. Advanced e l a s t i c analysis of complex mine excavations using the three-dimensional boundary element technique. PhD. Thesis, Pretoria University, South A f r i c a .
Diering, J.A.C. and Stacey, T.R. 1987. Three-dimensional stress analysis: a p r a c t i c a l planning t o o l for mining problems. APCOM 87. Proceedings of the Twentieth International Symposium on the Application of Computers and Mathematics i n the Mineral Industries. Volume 1: Mining. Johannesburg: SAIMM, 33-42.
Fairhurst, C. and Cook, N.G.W. 1966. The phenomenon of rock s p l i t t i n g p a r a l l e l to the d i r e c t i o n of maximum compression i n the neighborhood of a surface. Proceedings. 1st International Congress on Rock Mechanics. Lisbon, Vol. 1, 687-692.
Falmagne, V. 1986. Recuperation des p i l i e r s de l a l e n t i l l e #3 a l a mine Corbet.
Goel, S.C. and Page, C.H. 1981. Regional support p i l l a r s f or improving working conditions i n open stoping. Design and Operation of Caving and Sublevel Stoping Mines. New York: AIME, 459-470.
Goldbeck, B. 1985. Analysis of stress changes at S h e r r i t t Gordon's Ruttan Mine. Bachelor's Thesis, University of B r i t i s h Columbia.
186
Goodier, A. and Dube, R. 1984. Changes i n mining methods to overcome ground conditions at the Norita mine. 86th CIM Annual General Meeting, Ottawa.
Grace, M. and Taylor, D. 1985. Remnant p i l l a r recovery at Frood Mine - INCO Limited. Seventh Underground Operators Conference, Feb. 1985, Bathurst, New Brunswick.
Hardy, M.P. and Agapito, J.F.T. 1977. P i l l a r design i n underground o i l shale mines. 16th U.S. Symp. on Rock Mechanics. 257-266.
Hedley, D.G.F. and Grant, F. 1972. Stope-and-pillar design for the E l l i o t Lake uranium mines. Trans. Can. Inst. Min. Met. No. 7, 37-44.
Hedley, D.G.F., Herget, G., Miles, P. and Yu, Y.S. 1979. CANMET's Rock Mechanics Research at the Kidd Creek Mine. CANMET Report 79-11.
Herget, G., Oliver, P., Gyenge, M. and Yu, Y.S. 1984. Strength of a mine p i l l a r at copper c l i f f south mine. Mining Science Technology. 2, 1-16.
Hoek, E. and Brown, E.T. 1980. Underground Excavations i n Rock, London: I n s t i t u t e of Mining and Metallurgy.
Hudson, J.A., Brown, E.T., and Fairhurst, C. 1971. Shape of the complete s t r e s s - s t r a i n curve f o r rock. Proc. 13th Symp. Rock Mech.. Urbana. 111.
Hudyma, M.R. 1988a. Open stope mining i n Canada. Unpublished UBC report.
Hudyma, M.R. 1988b. Comparison of two and three dimensional boundary element numerical methods. Unpublished UBC report.
International Society for Rock Mechanics. 1979. Commission of standardization of laboratory and f i e l d t e s t s . Int. J . Rock Mech. Min. S c i . 16, No. 2, 137-140.
Kersten, R.W.O. 1984. The design of p i l l a r s i n the shrinkage stoping of a South A f r i c a n gold mine, J . S. Inst. Min. Metall. 84, No. 11, 365-368.
Krauland, N. and Soder, P. 1987. Determining p i l l a r strength from p i l l a r f a i l u r e observation. Engineering and Mining Journal 188, No. 8, 34-40.
Maconochie, D.J., Friday, R.G., Palmer, W.T. and Thompson, I.R.R. 1981. An application of monitoring and numerical
187
modelling i n open stope mining. Proceedings of the Fourth Australian Tunnelling Conference, Melbourne. A u s t r a l i a . 157-170.
Mathews, K.E., Hoek, E., Wyllie, D.C. and Stewart, S.B.V. 1980. Prediction of Stable Excavations for Mining at Depths Below 1000 Metres i n Hard Rock. CANMET Report 802-1571.
Murrell, S.A.F. 1965. The e f f e c t of t r i a x i a l stress systems on the strength of rock at atmospheric temperatures. Geophvs. J. R. Astr. Soc. 10, 231-281.
Obert, L., Windes, S.L. and Duvall, W.I. 1946. Standardization t e s t s for determining the physical properties of mine rock. U.S. Bureau of Mines Report of Investigations, 3891.
Obert, L. and Duvall, W.I. 1967. Rock Mechanics and the Design of Structures i n Rock. New York: John Wiley & Sons.
Page, C.H. and Brennen, R.G. 1982. S t a b i l i t y of large open stopes i n weak rock. F i r s t Int. Conf. on S t a b i l i t y i n Underground Mining. New York: AIME, 336-356.
Pakalnis, R.C.T. 1986. Empirical stope design at the Ruttan mine, S h e r r i t t Gordon Limited. PhD. Thesis, University of B r i t i s h Columbia.
Pakalnis, R.C.T. 1987. PCBEM User's Manual. Canada/Manitoba Mineral Development Agreement, CANMET Project No. 4^-9147-1, Energy, Mines and Resources Canada, Ottawa.
Potvin, Y. 1985. Investigation of underground excavation mine p i l l a r design procedures. Master's Thesis, University of B r i t i s h Columbia.
Potvin, Y., Hudyma, M.R. and M i l l e r , H.D.S. 1987. Progress report of the integrated mine design project. Unpublished report.
Potvin, Y., Hudyma, M.R. and M i l l e r , H.D.S. 1988a. The s t a b i l i t y graph method for open stope design. 90th CIM Annual General Meeting, Edmonton, Alberta.
Potvin, Y., Hudyma, M.R. and M i l l e r , H.D.S. 1988b. F i n a l report of the integrated mine design project. To be published.
Pratt, H.R., Black, A.D., Brown, W.S. and Brace, W.R. 1972. The e f f e c t of specimen si z e on the mechanical properties of unjointed d i o r i t e . Int. J . Rock Mech. Min. S c i . Vol. 9, 513-529.
188
Sarkka, P.S. 1984. The in t e r a c t i v e dimensioning of p i l l a r s i n Finnish Mines. S t a b i l i t y i n Underground Mining I I . New York: AIME, 71-84.
Salamon, M.D.G. 1967. A method of designing bord and p i l l a r workings. J . S. Inst. Min. Metall. 68, No. 9, 68-78.
Salamon, M.D.G. 1974. Rock mechanics of underground excavations. Advances i n Rock Mechanics - Proceedings of the Third Congress of the International Society of Rock Mechanics. Volume IB. Washington: National Academy of Sciences, 951-1099.
Salamon, M.D.G. 1983. The ro l e of p i l l a r s i n mining. In Rock Mechanics i n Mining Practice. Ed. S. Budavari. Johannesburg: SAIMM, 173-200.
Stacey, T.R. and Page, C.H. 1986. P r a c t i c a l Handbook for Underground Rock Mechanics. C l a u s t h a l - Z e l l e r f e l d : Trans Tech Publications.
S t a r f i e l d , A.M. and Fairhurst, C. 1968. How high-speed computers advance design of p r a c t i c a l mine p i l l a r systems. Engineering and Mining Journal. 169, No. 5, 78-84.
S t a r f i e l d , A.M. and Crouch, S.L. 1973. E l a s t i c analysis of single seam extraction. New Horizons i n Rock Mechanics. H.R. Hardy, and R. Stefanko (eds), New York: Am. Soc. C i v i l Eng., 421-439.
Stephansson, 0. 1985. P i l l a r design for large hole open stoping. Proceedings of the International Symposium on Large Scale Underground Mining. Lulea: Centek publishers, 185-194.
Thomas, E.G., Nantel, J.H. and Notley, K.R. 1979. F i l l Technology i n Underground Metalliferous Mines. Kingston: International Academic Services.
Townsend, P. 1982. P i l l a r s t a b i l i t y at E l l i o t Lake - A comparison of empirical and a n a l y t i c a l methods of prediction. Rock Breaking and Mechanical Excavation. Special Volume 30. Montreal: Canadian I n s t i t u t e of Mining and Metallurgy, 133-137.
Von Kimmelmann, M.R., Hyde, B. and Madgwick, R.J. 1984. The use of computer applications at BCL Limited i n planning p i l l a r e xtraction and the design of mining layouts. Design and Performance of Underground Excavations: Design. Cambridge: International Society of Rock Mechanics, 53-63.
Wagner, H. 1974. Determination of the complete load-deformation c h a r a c t e r i s t i c s of coal p i l l a r s . Advances i n Rock
189 Mechanics - Proceedings of the Third Congress of the International Society of Rock Mechanics. Volume IIB. Washington: National Academy of Sciences, 1076-1081.
Watson, J.O. and Cowling, R. 1985. Application of three-dimensional boundary element methods to modelling of large mining excavations at depth. Proceedings of the 5th International Conference on Numerical Methods i n Geomechanics. 1901-1910.
Yu, Y.S., Toews, N.A. and Wong, A.S. 1983. MINTAB user's guide -a mining simulator for determining the e l a s t i c response of st r a t a surrounding tabular mining excavations (version 4.0, 1982). D i v i s i o n report MRP/MRL 83-25 (TR), Mining Research Laboratories, CANMET, Energy, Mines and Resources Canada, Ottawa.
Zienkiewicz, O.C. 1977. The F i n i t e Element Method. London: McGraw-Hill.
190
APPENDIX I
S p e c i f i c information about the geological s e t t i n g of each
case h i s t o r y can be found i n the isometric sketch corresponding
to the mine number. Each geological s e t t i n g i s comprised of:
- the underground stress regime,
- the hanging wall, footwall and orebody material properties
and c h a r a c t e r i s t i c s including (when a v a i l a b l e ) :
- rock type,
- i n t a c t u n i a x i a l compressive strength,
- e l a s t i c modulus,
- poisson's r a t i o ,
- NGI rock mass c l a s s i f i c a t i o n ,
- stereonet of the major j o i n t sets,
- the orebody shape and siz e ,
- and the mining methods used i n various parts of the
orebody.
Mine #22 does not have an isometric orebody sketch due to the
complexity of the orebody and the v a r i a b i l i t y of the material
properties and stress f i e l d .
MINE No. 2 ORE (LENS 2 * 3 )
Rock Type:
1 = °c = E = V = Q' =
Massive Sulphide
4.2 t/m3
200 MPa 61.0 GPa 0.3
HANGING WALL t, ROOF (LENS 2)
Rock Type: Andes i t e
y
E v Q"
o»=ifh
om=2.3yt\ 70m
01,2=2. 2th
2.9 t/m3
109 MPa 63.0 GPa 0.25 4
LENS 2
-H5m
LONGITUDINAL OPEN STOPE
A*
0
0*
HANGING WALL t ROOF (LENS 3)
Rock Type: A l t e r e d A n d e s i t e
Y = 3.0 t/m3
o c = 87 MPa E - 84.0 GPa v = 0.28
192
MINE No. 6
ORE
Rock Type: Breccia 4 Massive Sulphide
T • 2 e : V • Q' -
3.1 t/m3
125 MPa 94.0 GPa 0.22 9
WORTH WALL
Rock Type: Norite
T -*: V • Q' •
2.9 t/m3
113 MPa S6.0 GPa 0.17 9
SOOTH WALL
T
V
2.7 t/m3
184 MPa 73.0 GPa 0.23 25
ISOm
Rock Type: Granite
274 m
Depth 1050 m
MINE No. 8
N
MINE No. 11
MINED OUT (No Backfill)
200m
r MINED OUT !
T
(No Backfill)
PERMANENT PILLAR (No Grodo)
71 LONGITUDINAL
LONGH<SLE STOPE
• 30m-H
62m
LONGITUDINAL LONGHO
STOPE OOm
/ /
LONGITUDINAL LONGHOLE
STOPE
4*
-33m — 2O0m
-62m
_Dtplh 925m
ORE Rock Type: Porphyry
7 - 2.72 t/«3
o, - 148 MPa Z » 18.S GPa v • 0.20 Q* - 30
0,'1.15-rh
' » e«»1.5Yh
o.a-1.7th
MINE No. 16
ORB Rock Typei Kaaalva Sulphlda
Surfoca
y -°c -8 • v • 0* -
4.6 t/«' 176 MPa 119.0 CP* 0.24 20
HANGING HALL Book Type• Quarta Porphyry
y - 2.9 t/aj1
o c - 91 MPa B - 68.7 GPa v - 0.19 0' - 42
080m
FOOT WALL Rook Typai Chlorlta Tuff
Y - 2.9 t/m1
o e - 84 MPa E - 68.5 GPa v - 0.2S 0 ' - 40
MINE No. 17
870m LONGITUDINAL LONOHOLE
OPEN STOPING
-1600m-
ORg WALL Rock Typai Maaelva Sulphide Rock Typei Cnalaa
y - S.3 t/«* y - 2.7 t/m1
o t - 100 MPa ot - 52 MPa E - 103 CPa E - 105 GPa v - 0.31 v - 0.20 0' - 19 Q" - 18
o,-th
2.6th*
foraula by Berget
MINE No. 19 o s - » h 1
30m
MINED OUT a BACKFILLED TO SURFACE
•MI-3-3YI»
420m
70m LONOITUDINAL SUB-LEVEL RETREAT
30m
• 180m •
LONOITUDINAL SUB-LEVEL RETREAT
2-18 m
110m
ORB Rock Typoi Maaalva Bulphlda
Oapih 780m
WORTH WALL (10»)
o, - 316 MP* E - 232.2 GPa v - 0.16 0' - 44 N
Rock Typos Baaaltlo Tuff
o c - 11B MPa B - 95.0 GPa v - 0.26 0* - 4.0 N
SOUTH WALL ISO*)
Rook Typai Rhyolltio Tuff
o c - 98 MPa B - 67.9 GPa v - 0.15 0 * -
MINE No. 21 199
TYPICAL MINE CROSS SECTION
LONGHOLE tc BLASTHOLE LONGITUDINAL OPEN STOPING
ORE Rock Type: Massive Sulphide 0*c = 100 MPa E = 88 GPa V = 0.20 Q' = 10-20
HANGING WALL & FOOTWALL Rock Type: Quartz Meta
Sediments CTC = 50-135 MPa E = 50-75 GPa V = 0.12-0.34 Q' = 0.1-50
= 2.5 0"v
MINE No. 23
200
Rock Type: Massive Sulphide
UCS =310 MPa Q' = 20
FOOTWALL & HANGING WALL
Rock Type: Argy1ite
UCS =75 MPa Q' = 0.6
MINE No. 30
ORE Rock Type: Massive Sulphide Y = C c = E = V = Q' =
3.3 t / m ' 160 MPa 80 GPa 0.21 22
TYPICAL MINE CROSS SECTION
TRANSVERSE BLASTHOLE OPEN STOPING
1500m
HANGING WALL Rock Y = 0"c = E = V = Q' =
Type: Rhyolite 2.7 t / m s
120-150 MPa 80 GPa 0.14 13-30
FOOTWAa Rock Type: Andesite/Diorite
(TV=YH
0\ = 6+O.055H(m)
Y
E V Q'
3.0 t / m ' 160 MPa 85 GPa 0.23 14
0"j = 0.80",
2 0 2
MINE No. 31