DEVELOPMENT OF EMPIRICA RIL PILLAB R DESIGN … H82.pdf · 1.2.1 Definition of Open Stoping 3 1.2.2...

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 .

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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

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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

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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

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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




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


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


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,


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


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


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



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


SECTION 10 10 60 10 1.7 6 : 1 1.8


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


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


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


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


10 10 60 10 1.7 | 1.0 1.65


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


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


SEAM THICKNESS

RATIO


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


SEAM THICKNESS

RATIO


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

son/avcn

139

W e f f = 4 * A C

where:

W eff = the e f f e c t i v e p i l l a r width,

A = p i l l a r cross sectional area,

C = p i l l a r circumference.

The reasoning i s that for very long p i l l a r s (and open stope r i b

p i l l a r s ) , a p i l l a r i s e f f e c t i v e l y exposed on only two walls and

consequently stronger than square p i l l a r s , which are exposed on

four walls. Using t h i s concept, square p i l l a r s have h a l f the

e f f e c t i v e width of a long p i l l a r having the same p i l l a r height

to width r a t i o . In figure 42, the square p i l l a r s at BCL Limited

have been plotted on the p i l l a r s t a b i l i t y graph using t h e i r

e f f e c t i v e p i l l a r width/ h e i g h t r a t i o ( i e . the a c t u a l

width/height r a t i o ) .

The adjusted square p i l l a r data agrees reasonably well with

the o r i g i n a l t r a n s i t i o n zone on the p i l l a r s t a b i l i t y graph.

Three stable square p i l l a r case h i s t o r i e s p l o t above the f a i l u r e

l i n e on the t r a n s i t i o n zone, while a l l the y i e l d i n g and f a i l e d

p i l l a r s p l o t above the t r a n s i t i o n area. The e f f e c t i v e width

adjustment for square p i l l a r s on the p i l l a r s t a b i l i t y graph

adequately explains the assessment for t h i s data. As with the

long p i l l a r s , the adjusted square p i l l a r data suggests the

t r a n s i t i o n zone could be located s l i g h t l y higher. However, t h i s

inaccuracy i s on the conservative side f o r stable p i l l a r design.

6.3.3 Data from an Australian Open Stope Mine

140

IN

O

M

son/avcn

FIGURE 42. The square p i l l a r Kimmelmann et a l . (1984) i s using an e f f e c t i v e width i n

data presented by Von plotted on the s t a b i l i t y graph the H/W r a t i o .

141

A t e s t open stoping block at Mt. Isa i s described i n depth

by Brady (1977). The objective of the t r i a l mining block was to

obtain information for r i b p i l l a r design and c a l i b r a t e a f a i l u r e

c r i t e r i o n f o r the rock mass. Figure 43 shows the t e s t broken

into f i v e stages.

Stage 1 (problem No. 1) shows the development of two s l o t

r a i s e s , and the S86 r a i s e to observe p i l l a r conditions.

Stage 2 contains the opening of the S85 stope.

Stage 3 shows the opening of S87 stope which creates the S86

p i l l a r .

Stage 4 i s the expansion of the S87 stope, with the S86 p i l l a r

remaining stable and i n t a c t .

Stage 5 shows the robbing of the S86 p i l l a r which resulted i n

f a i l u r e of the p i l l a r .

Brady presented s u f f i c i e n t information that stages 3, 4 and

5 could be modelled with BITEM to determine the average p i l l a r

load. The stope height:length r a t i o for a l l three cases i s

greater than 3, so less than 20% error i s expected i n the

average p i l l a r load determined by BITEM (the error i s estimated

using figure 33, page 109). The modelling r e s u l t s were i n good

agreement with a p r i n c i p a l stress contour diagram i n the

o r i g i n a l paper.

The rock mass, as described i n the paper by Brady, has

s i m i l a r c h a r a c t e r i s t i c s and qu a l i t y to the t y p i c a l rock mass

142

192 0

7 0/B MICAF

610

1 10-0

-1920

Problem No. 1

k -26-2 . ; 1 -

Boundary of S84 • pillar area

1 6 65

30-2

S85 slope

Problem No. 2

-I 1

i < i

SB7 Cut-off rais« (1 81 Dia.)

, Boundary of S86 < \ J pillar area

S86 raise

_ J

i | 15.1 '4-8 I —

n n

0— r — - S 87 stopt

Problem No 3

J

•1920 26.2

10-0

Problem No 4 1

1 6-65

i _

•34-4

SBS

6-7

S 6 6

O

1 r 1 37-8

! ses ; , 1

58b o

i S87 r 1

420

sen

Problem No. 5 Scole 10m

FIGURE 43. The f i v e stages of the S86 p i l l a r i n an open stope p i l l a r t e s t at Mt. Isa ( a f t e r Brady 1977).

143

found i n the data base. The volume of the A u s t r a l i a p i l l a r s i s

also s i m i l a r to that i n the data base. So, these two variables

are not l i k e l y to have a s i g n i f i c a n t influence i n p l o t t i n g the

data on the p i l l a r s t a b i l i t y graph.

The three stages are plotted on a p i l l a r s t a b i l i t y graph i n

figure 44. The S86 p i l l a r p l o t s i n the stable region for stages

3 and 4, and p l o t s i n the f a i l u r e zone a f t e r stage 5. This

agrees very well with Brady's description of the p i l l a r during

the t e s t .

6.3.4 Summary of A l l the Data

A p l o t of the open stope data and a l l the data from

l i t e r a t u r e i s given i n figure 45. The data from l i t e r a t u r e

helps confirm the location of the t r a n s i t i o n area over a greater

area. In the e n t i r e data base of 135 p i l l a r s , four stable case

h i s t o r i e s are found above the t r a n s i t i o n zone and one sloughing

p i l l a r i s found below the t r a n s i t i o n zone. Consequently, the

s o l i d design l i n e s f o r the t r a n s i t i o n zone have been extended.

The success of the p i l l a r s t a b i l i t y graph i n separating the

d i f f e r e n t p i l l a r assessments supports the decision to discount

the influence of p i l l a r volume and rock mass qu a l i t y as

i n s i g n i f i c a n t i n hard rock p i l l a r design.

6.4 Comparison Against Other Design Methods

A number of empirical design methods are frequently used for

r i b p i l l a r s . However, none of these methods was based on open

144

son/avon

FIGURE 4 4 . The t h i r d , fourth and f i f t h stages of the S86 open stope r i b p i l l a r , presented by Brady (1977), are shown on the p i l l a r s t a b i l i t y graph. The data agrees very well with the s t a b i l i t y graph.

• CD • 145

CM

son/avoT

F I sSL 4rib !m P i lh r l a b i l i t y graph showing the open

Hedlly M9?2J V o n a K ? t h e l i t e r a t ^ e data presented by tieaiey (1972), Von Kimmelmann (1984), and Brady (1977).

146

stope mining case h i s t o r i e s . The following comparison of the

methods a g a i n s t the p i l l a r s t a b i l i t y graph, shows the

a p p l i c a b i l i t y of the other methods to the design of open stope

r i b p i l l a r s . Any negative evaluation should not be taken as a

c r i t i c i s m of other methods, but rather i t serves to show the

l i m i t a t i o n s of these methods when applied to the design of open

stope r i b p i l l a r s .

6.4.1 Hedley's P i l l a r Strength Formula

The p i l l a r strength formula developed by Hedley and Grant

(1972) was based on data from room and p i l l a r mining at E l l i o t

Lake and has been discussed i n Chapters 3.1.1.3 and 6.3.1. The

formula i s defined as:

Qu = k * wa / h b

where:

Qu = p i l l a r strength

k = strength of 1 f t . cube (UCS 1 2)

w = p i l l a r width (ft)

h = p i l l a r height (ft)

a = empirical constant = 0.5

b = empirical constant = 0.75

To get UCS 1 2, several authors have used a s c a l i n g factor

from the compressive strength of a 2 inch diameter specimen

(UCS 2):

147

u c s 1 2 0.7 * UCS 2

This r e l a t i o n s h i p has been found i n works by Hedley and Grant

(1972), Hedley et a l . (1979), Hoek and Brown (1980), and Von

Kimmelmann et a l . (1984).

Hedley's formula i s a siz e e f f e c t formula, which means that

i t accounts f o r the actual dimensions of a p i l l a r and not just

the p i l l a r shape. To apply t h i s to open stope r i b p i l l a r s , the

s i z e of t y p i c a l open stope r i b p i l l a r s must be determined. The

range of r i b p i l l a r sizes seen i n 17 d i f f e r e n t Canadian open

stope mines i s presented i n figure 46. The dimensions of

permanent p i l l a r s are denoted by the symbol "P" and the

dimensions of p i l l a r s i n mining methods using b a c k f i l l and

temporary p i l l a r s are denoted by the symbol "B". The dashed

l i n e s give the upper and lower bound of p i l l a r dimensions used

i n the 17 Canadian open stope mines. For various p i l l a r width

to p i l l a r height r a t i o s ( i e . p i l l a r s t r i k e length to orebody

width r a t i o s ) , the minimum and maximum p i l l a r dimensions can be

determined and applied to Hedley's s i z e e f f e c t formula.

For a p p l i c a t i o n of t h e i r p i l l a r strength formula, Hedley and

Grant suggest that p i l l a r s with a safety factor greater than 1.5

are stable and p i l l a r s with a safety factor near 1.0 are

crushed. Rearrangement of the safety factor formula,

S.F. Qu 0.7 * UCS 2 * w a

c r p aP * h b

H rt»0 O O 3* ct> o» c

ft 3 0> W

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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»

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PILLAR DIMENSIONS BASED ON 17 CANADIAN OPEN STOPE MINES

B B B

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B \ B

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B

k B

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—] 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 ,



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.

174

CHAPTER 8

SUMMARY AND CONCLUSIONS

a.i summary

The purpose of t h i s study i s to investigate the s t a b i l i t y of

r i b p i l l a r s i n open stope mining and develop guidelines for the

optimization of r i b p i l l a r dimensions. This i s accomplished

through four major steps:

- d e s c r i p t i o n of the f a i l u r e mechanism i n open stope r i b

p i l l a r s ,

- i n v e s t i g a t i o n of the methods currently used i n open stope

r i b p i l l a r design,

- q u a n t i f i c a t i o n of the s i g n i f i c a n t design variables,

- and formulation and v e r i f i c a t i o n of a new method based on

open stope r i b p i l l a r data and case h i s t o r i e s .

8.1.1 Open Stope Rib P i l l a r F a i l u r e

There are two basic types of f a i l u r e i n hard rock p i l l a r s .

Progressive f a i l u r e r e f e r s to gradual d e t e r i o r a t i o n of a p i l l a r

i n a slow, non-violent manner. Bursting f a i l u r e i s character

ized by the v i o l e n t release of energy causing instantaneous

fracture of rock. This thesis only investigates progressive

f a i l u r e .

Open stope r i b p i l l a r i n s t a b i l i t y i s a progressive

mechanism. P i l l a r f a i l u r e i s defined as the point at which

progressive f a i l u r e causes a p i l l a r to s t a r t l o s i n g i t s load

175

bearing capacity. The decrease i n load bearing capacity i s

l a r g e l y due to f r a c t u r i n g of the rock mass i n the p i l l a r .

Several signs of increasing p i l l a r i n s t a b i l i t y have been

i d e n t i f i e d , including:

- cracking and s p a l l i n g of rock i n p i l l a r development,

- audible noise heard i n the p i l l a r s or microseismic events

detected with monitoring systems,

- deformed or plugged d r i l l holes,

- overdraw from stopes consisting of unblasted, oversize ore,

- stress r e d i s t r i b u t i o n from p i l l a r s a f f e c t i n g nearby p i l l a r s

or development,

- hourglassing and cracking of p i l l a r s ,

- and d i s p l a c e m e n t s or changes i n s t r e s s shown by

instrumentation.

8.1.2 Current P i l l a r Design Methods

Design methods used for open stope r i b p i l l a r s were based on

empirical p i l l a r design studies or the use of numerical

modelling and empirical f a i l u r e c r i t e r i o n . Empirical p i l l a r

design methods were developed based on laboratory t e s t i n g and/or

i n v e s t i g a t i o n of actual mine p i l l a r s . These methods were

developed for s p e c i f i c mining conditions and are not necessarily

applicable f o r open stope r i b p i l l a r design. Numerical methods

b a s i c a l l y assume e l a s t i c and/or p l a s t i c rock mass behaviour to

determine stress r e d i s t r i b u t i o n and rock mass displacement

around underground excavations. Empirical f a i l u r e c r i t e r i o n are

176

applied to the stress or displacement r e s u l t s to determine rock

mass f a i l u r e . However, i t i s d i f f i c u l t to v e r i f y an i n s i t u

rock mass f a i l u r e c r i t e r i o n . Consequently, numerical design

methods need extensive s i t e c a l i b r a t i o n before they can be used

e f f e c t i v e l y to design r i b p i l l a r s i n open stope mining.

The design methodology chosen for t h i s t h e s i s i s a

combination of numerical and empirical methods. Numerical

techniques are used to determine p i l l a r load, while p i l l a r

f a i l u r e i s determined from empirical back analysis of open stope

r i b p i l l a r case h i s t o r i e s .

8.1.3 I d e n t i f i c a t i o n and Quantification of the Design Variables

Based on the data and case h i s t o r i e s c o l l e c t e d i n the

Integrated Mine Design Project, the factors that are s i g n i f i c a n t

for open stope r i b p i l l a r design are:

- the compressive strength of i n t a c t p i l l a r material (UCS),

- the average p i l l a r stress (determined with boundary

element numerical modelling),

- the p i l l a r height,

- and the p i l l a r width.

Three factors were discounted as i n s i g n i f i c a n t i n r i b p i l l a r

f a i l u r e : the presence of minor geological d i s c o n t i n u i t i e s (such

as j o i n t s ) , the e f f e c t of p i l l a r volume, and the e f f e c t of

b a c k f i l l . The open stope r i b p i l l a r data and case h i s t o r i e s did

not prove these factors as being important i n p i l l a r f a i l u r e .

The background information for a l l the p i l l a r s i n the data base

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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

181

economics. Low grade orebodies cannot be mined using b a c k f i l l

and p i l l a r recovery methods due to the higher mining cost.

Medium and high grade mines can a f f o r d the cost of b a c k f i l l and

p i l l a r recovery, so temporary p i l l a r s can be designed. In some

instances, temporary p i l l a r s have been designed to f a i l to avoid

stress b u i l d up. There are a few consequences of designing

p i l l a r s to f a i l , including:

- the need f o r quick b a c k f i l l i n g a f t e r the stope i s extracted,

- the use of a r t i f i c i a l support i n p i l l a r development,

- and the use of large diameter d r i l l holes and control

b l a s t i n g p ractices.

8.3 Future Work

There i s a l i m i t to the value of c o l l e c t i n g further general

p i l l a r case h i s t o r i e s to r e f i n e the p i l l a r s t a b i l i t y graph.

More cases of open stope p i l l a r s are not l i k e l y to s i g n i f i c a n t l y

improve the accuracy of the e x i s t i n g graph or reduce the s i z e of

the t r a n s i t i o n area. This i s not to say that p i l l a r design at

s p e c i f i c s i t e s can not be aided by case h i s t o r i e s from that s i t e

or from s i m i l a r ground conditions. Past experience i s the best

way to r e f i n e p i l l a r design methods to l o c a l conditions.

The understanding of one of the possible design factors may

be improved by c o l l e c t i n g s p e c i f i c case h i s t o r i e s . The

influence of rock mass c h a r a c t e r i s t i c s was not found to be

s i g n i f i c a n t (Chapter 6.1.3.2), but varied over only a small

range of rock mass q u a l i t i e s . Analysis of p i l l a r case h i s t o r i e s

182

i n f a i r or very good q u a l i t y rock masses may show that the

qu a l i t y of the rock mass i s s i g n i f i c a n t i n open stope r i b p i l l a r

design. I f t h i s can be proven, a correction factor to the

ex i s t i n g p i l l a r s t a b i l i t y graph could be developed to account

for the e f f e c t of rock mass qual i t y .

Assessment of the p i l l a r s i n the data base was sometimes

d i f f i c u l t , and a substantial amount of data could not be applied

because a r e l i a b l e assessment could not be determined. A more

de t a i l e d i n v e s t i g a t i o n into p i l l a r f a i l u r e mechanisms and i n

s i t u rock mass f r a c t u r i n g could improve p i l l a r design methods.

A better d e f i n i t i o n of f a i l u r e can be developed through

systematic i n s i t u p i l l a r monitoring using v i s u a l techniques (as

shown by Krauland and Soder 1987) or through the use of

instrumentation such as stressmeters (as shown by Agapito 1974),

extensometers (as shown by A l l c o t t and Archibald 1981) or

microseismics. The use of microseismic systems f o r i n s i t u

m onitoring shows great p o t e n t i a l through quantifying the

decrease of rock mass qu a l i t y due to rock f r a c t u r i n g , and

monitoring the changes i n the load bearing condition of p i l l a r s .

Both of these topics can be investigated with the microseismic

technology currently available.

183

REFERENCES

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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.

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190

APPENDIX I

S p e c i f i c information about the geological s e t t i n g of each

case h i s t o r y can be found i n the isometric sketch corresponding

to the mine number. Each geological s e t t i n g i s comprised of:

- the underground stress regime,

- the hanging wall, footwall and orebody material properties

and c h a r a c t e r i s t i c s including (when a v a i l a b l e ) :

- rock type,

- i n t a c t u n i a x i a l compressive strength,

- e l a s t i c modulus,

- poisson's r a t i o ,

- NGI rock mass c l a s s i f i c a t i o n ,

- stereonet of the major j o i n t sets,

- the orebody shape and siz e ,

- and the mining methods used i n various parts of the

orebody.

Mine #22 does not have an isometric orebody sketch due to the

complexity of the orebody and the v a r i a b i l i t y of the material

properties and stress f i e l d .

MINE No. 2 ORE (LENS 2 * 3 )

Rock Type:

1 = °c = E = V = Q' =

Massive Sulphide

4.2 t/m3

200 MPa 61.0 GPa 0.3

HANGING WALL t, ROOF (LENS 2)

Rock Type: Andes i t e

y

E v Q"

o»=ifh

om=2.3yt\ 70m

01,2=2. 2th

2.9 t/m3

109 MPa 63.0 GPa 0.25 4

LENS 2

-H5m

LONGITUDINAL OPEN STOPE

A*

0

0*

HANGING WALL t ROOF (LENS 3)

Rock Type: A l t e r e d A n d e s i t e

Y = 3.0 t/m3

o c = 87 MPa E - 84.0 GPa v = 0.28

192

MINE No. 6

ORE

Rock Type: Breccia 4 Massive Sulphide

T • 2 e : V • Q' -

3.1 t/m3

125 MPa 94.0 GPa 0.22 9

WORTH WALL

Rock Type: Norite

T -*: V • Q' •

2.9 t/m3

113 MPa S6.0 GPa 0.17 9

SOOTH WALL

T

V

2.7 t/m3

184 MPa 73.0 GPa 0.23 25

ISOm

Rock Type: Granite

274 m

Depth 1050 m

MINE No. 8

N

MINE No. 11

MINED OUT (No Backfill)

200m

r MINED OUT !

T

(No Backfill)

PERMANENT PILLAR (No Grodo)

71 LONGITUDINAL

LONGH<SLE STOPE

• 30m-H

62m

LONGITUDINAL LONGHO

STOPE OOm

/ /

LONGITUDINAL LONGHOLE

STOPE

4*

-33m — 2O0m

-62m

_Dtplh 925m

ORE Rock Type: Porphyry

7 - 2.72 t/«3

o, - 148 MPa Z » 18.S GPa v • 0.20 Q* - 30

0,'1.15-rh

' » e«»1.5Yh

o.a-1.7th

MINE No. 16

ORB Rock Typei Kaaalva Sulphlda

Surfoca

y -°c -8 • v • 0* -

4.6 t/«' 176 MPa 119.0 CP* 0.24 20

HANGING HALL Book Type• Quarta Porphyry

y - 2.9 t/aj1

o c - 91 MPa B - 68.7 GPa v - 0.19 0' - 42

080m

FOOT WALL Rook Typai Chlorlta Tuff

Y - 2.9 t/m1

o e - 84 MPa E - 68.5 GPa v - 0.2S 0 ' - 40

MINE No. 17

870m LONGITUDINAL LONOHOLE

OPEN STOPING

-1600m-

ORg WALL Rock Typai Maaelva Sulphide Rock Typei Cnalaa

y - S.3 t/«* y - 2.7 t/m1

o t - 100 MPa ot - 52 MPa E - 103 CPa E - 105 GPa v - 0.31 v - 0.20 0' - 19 Q" - 18

o,-th

2.6th*

foraula by Berget

MINE No. 19 o s - » h 1

30m

MINED OUT a BACKFILLED TO SURFACE

•MI-3-3YI»

420m

70m LONOITUDINAL SUB-LEVEL RETREAT

30m

• 180m •

LONOITUDINAL SUB-LEVEL RETREAT

2-18 m

110m

ORB Rock Typoi Maaalva Bulphlda

Oapih 780m

WORTH WALL (10»)

o, - 316 MP* E - 232.2 GPa v - 0.16 0' - 44 N

Rock Typos Baaaltlo Tuff

o c - 11B MPa B - 95.0 GPa v - 0.26 0* - 4.0 N

SOUTH WALL ISO*)

Rook Typai Rhyolltio Tuff

o c - 98 MPa B - 67.9 GPa v - 0.15 0 * -

MINE No. 21 199

TYPICAL MINE CROSS SECTION

LONGHOLE tc BLASTHOLE LONGITUDINAL OPEN STOPING

ORE Rock Type: Massive Sulphide 0*c = 100 MPa E = 88 GPa V = 0.20 Q' = 10-20

HANGING WALL & FOOTWALL Rock Type: Quartz Meta

Sediments CTC = 50-135 MPa E = 50-75 GPa V = 0.12-0.34 Q' = 0.1-50

= 2.5 0"v

MINE No. 23

200

Rock Type: Massive Sulphide

UCS =310 MPa Q' = 20

FOOTWALL & HANGING WALL

Rock Type: Argy1ite

UCS =75 MPa Q' = 0.6

MINE No. 30

ORE Rock Type: Massive Sulphide Y = C c = E = V = Q' =

3.3 t / m ' 160 MPa 80 GPa 0.21 22

TYPICAL MINE CROSS SECTION

TRANSVERSE BLASTHOLE OPEN STOPING

1500m

HANGING WALL Rock Y = 0"c = E = V = Q' =

Type: Rhyolite 2.7 t / m s

120-150 MPa 80 GPa 0.14 13-30

FOOTWAa Rock Type: Andesite/Diorite

(TV=YH

0\ = 6+O.055H(m)

Y

E V Q'

3.0 t / m ' 160 MPa 85 GPa 0.23 14

0"j = 0.80",

2 0 2

MINE No. 31

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