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Numerical modelling of large scale toppling Pritchard, Mark Anderson 1989

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NUMERICAL MODELLING OF LARGE SCALE TOPPLING by MARK ANDERSON PRITCHARD .A.Sc., The U n i v e r s i t y of B r i t i s h Columbia, 19 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of G e o l o g i c a l S c i e n c e s The U n i v e r s i t y of B r i t i s h Columbia We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September 1989 © Mark Anderson P r i t c h a r d 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 of &<Jl&(o The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT The p r i n c i p l e purpose of t h i s research i s to resolve the mode of f a i l u r e of the Heather H i l l landslide, one of several well defined f a i l u r e s i n the Beaver Valley, Glacier National Park, B r i t i s h Columbia. F i e l d work led to the preliminary conclusion that some type of toppling process contributed to the f a i l u r e . A l i t e r a t u r e review of toppling revealed that large scale topples have never been qu a n t i t a t i v e l y assessed, and that currently used a n a l y t i c a l techniques are not adequate. Consideration of al t e r n a t i v e numerical techniques resulted i n the d i s t i n c t element method being selected as the best technique f o r modelling toppling. The Universal D i s t i n c t Element Code (UDEC) was purchased and i t s s u i t a b i l i t y demonstrated by reevaluating examples of toppling analysis reported i n the l i t e r a t u r e , and evaluating a large scale engineered slope at Brenda mine where toppling i s known to occur. UDEC i s used to examine and c l a s s i f y the mode of f a i l u r e of the Heather H i l l s l i d e . This research leads to very important general conclusions on toppling and s p e c i f i c conclusions r e l a t i n g to the Heather H i l l l a n d s l i d e : UDEC i s suitable f o r modelling a l l types of topples. The program can be used to back analyze rock mass strength parameters and determine the shape and location of the f i n a l f a i l u r e surface i n f l e x u r a l toppling. A quantitative assessment with UDEC confirms that the base of f a i l u r e i n f l e x u r a l t o p p l i n g may be p l a n a r or c u r v i l i n e a r , and t h a t pore p r e s s u r e s s i g n i f i c a n t l y a f f e c t s t a b i l i t y . The Heather H i l l l a n d s l i d e f a i l e d by f l e x u r a l t o p p l i n g l i m i t i n g t o a c u r v i l i n e a r f a i l u r e s u r f a c e , and the s l o p e immediately n o r t h of the Heather H i l l l a n d s l i d e i s deformed by f l e x u r a l t o p p l i n g . The l o c a t i o n s o f l a n d s l i d e s i n the Beaver V a l l e y correspond w i t h the occurrence of f o l i a t e d p e l i t i c rocks i n the lower s l o p e s and the boundary between these rocks and s t r o n g e r g r i t s i s the up s l o p e l i m i t . The kinematic t e s t of t o p p l i n g p o t e n t i a l i s v i o l a t e d by the Heather H i l l l a n d s l i d e . T h i s t e s t i s shown t o o n l y a p p l y t o s m a l l s c a l e d r a i n e d s l o p e s . i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i i i LIST OF FIGURES i x ACKNOWLEDGEMENTS x i i QUOTE x i i i PART I CHAPTER 1. INTRODUCTION 1 1.1 R a t i o n a l f o r Research 1 1.2 Research Procedure 2 1.3 T h e s i s S t r u c t u r e 3 CHAPTER 2. LITERATURE REVIEW 5 2 .1 I n t r o d u c t i o n 5 2.2 General D e f i n i t i o n and H i s t o r i c a l P e r s p e c t i v e 5 2.3 Types of Topples 9 2.4 Methods of A n a l y s i s 11 2.4.1 P h y s i c a l Models 11 2.4.2 Kinematic A n a l y s i s 12 2.4.3 L i m i t E q u i l i b r i u m Method 14 2.4.4 F i n i t e Element Method 18 2.4.5 D i s t i n c t Element Method 2 0 2.4.6 Comparative Assessment of A n a l y t i c a l Methods 22 2.5 Parameters C o n t r o l l i n g T o p p l i n g : D i s c u s s i o n 24 2.5.1 I n f l u e n c e of S t r u c t u r e and Rock Type 24 i v 2.5.2 Shear S t r e n g t h of D i s c o n t i n u i t i e s 2 6 2.5.3 Groundwater 28 2.6 Summary of Areas Needing F u r t h e r Work 29 2.6.1 F a i l u r e Plane P r e d i c t i o n 29 2.6.2 I n f l u e n c e of C o n f i n i n g S t r e s s 3 0 2.6.3 T o p p l i n g i n Mixed Rock Types 3 0 2.6.4 Time Dependent Deformation 31 2.6.5 Large Slopes and Weak Rock 31 2.6.6 Groundwater 32 PART I I CHAPTER 3. DISTINCT ELEMENT METHOD 3 3 3 .1 I n t r o d u c t i o n 33 3.2 Theory of D i s t i n c t Element Method 34 3.2.1 E x p l i c i t S o l u t i o n Procedure 34 3.2.2 Equations o f Motion and System Damping 36 3.3 Features of UDEC 40 3.3.1 Block I n t e r f a c e C o n s t i t u t i v e R e l a t i o n s 40 3.3.2 Block D e f o r m a b i l i t y and C o n s t i t u t i v e R e l a t i o n s . 44 3.4 L i m i t a t i o n s o f UDEC 49 CHAPTER 4. MODELLING TOPPLING WITH UDEC 51 4.1 I n t r o d u c t i o n 51 4.2 R i g i d B l o c k / F l e x u r a l T o p p l i n g Example 52 4.3 F l e x u r a l T o p p l i n g Examples 60 4.3.1 Base F r i c t i o n Model 60 4.3.2 Brenda Mine 68 4.4 Conclusi o n s 82 v 4.4.1 Recommendations f o r Slope Design with UDEC 85 PART I I I CHAPTER 5. SITE CHARACTERIZATION 87 5.1 I n t r o d u c t i o n 87 5.2 Regional Geology 89 5.2.1 Bedrock Geology 89 5.2.2 Geomorphic Development of Beaver V a l l e y 93 5.3 C h a r a c t e r i s t i c s of Beaver V a l l e y Slope Movements... 94 5.4 Previo u s L a n d s l i d e S t u d i e s i n the Beaver V a l l e y . . . . 9 6 5.5 F i e l d Program 97 5.5.1 I n t r o d u c t i o n 97 5.5.2 L o c a l Geology 97 5.5.3 Evidence o f Deformation 101 CHAPTER 6. MODELLING HEATHER HILL LANDSLIDE DEVELOPMENT..106 6.1 I n t r o d u c t i o n 106 6.2 Pr e v i o u s A n a l y s i s of the Heather H i l l L a n d s l i d e 106 6.3 C h a r a c t e r i s t i c s of the UDEC Model 107 6.3.1 Pore Pressure 113 6.4 C h a r a c t e r i z a t i o n of Rock Mass 113 6.5 E v o l u t i o n of Model 116 6.6 R e s u l t s of UDEC M o d e l l i n g . . . 117 6.7 L i m i t a t i o n s of A n a l y s i s 121 6.8 Conclus i o n s 124 6.8.1 Heather H i l l L a n d s l i d e 124 6.8.2 Kinematic T e s t For T o p p l i n g 125 CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS 134 v i 7.1 PART I: Conclus i o n s of L i t e r a t u r e Review 134 7.2 PART I I : F l e x u r a l T o p p l i n g : C o n c l u s i o n s of Research 13 5 7.3 PART I I I : Beaver V a l l e y : C o n c l u s i o n s and Recommendations 136 7.3.1 Heather H i l l Study Area 13 6 7.3.2 S t a b i l i t y of Slopes i n Beaver V a l l e y 137 7.3.3 E n g i n e e r i n g Design I m p l i c a t i o n s and Recommendations 138 7.4 F l e x u r a l T o p p l i n g : Recommendations f o r Fu r t h e r Work 140 7.4.1 C u r v i l i n e a r F a i l u r e S u r f a c e i n F l e x u r a l Topples 140 7.4.2 I n f l u e n c e of D i l a t i o n on T o p p l i n g 141 7.4.3 I n f l u e n c e of G l a c i a l Events on T o p p l i n g . . . . 141 7.4.4 Mountain S c a l e Deformation 142 7.4.5 A p p l i c a t i o n of UDEC t o Slope Design 142 7.4.6 Geometric S e n s i t i v i t y S t u d i e s 143 REFERENCES 144 APPENDIX 1 151 APPENDIX 2 158 APPENDIX 3 175 MAP 1A MAP IB v i i LIST OF TABLES Table T i t l e Page 4.1 Range of L i m i t i n g F r i c t i o n Angle f o r Block Toppling..60 4.2 Geometry of Base F r i c t i o n Model and UDEC Model 63 4.3 Values of UDEC Parameters f o r Base F r i c t i o n Model....65 4.4 UDEC Parameters f o r Brenda Mine Model: Pure F l e x u r a l T o p p l i n g 73 4.5 UDEC Parameters f o r Brenda Mine Model: "Graben" Topple 79 5.1 S t r u c t u r a l Data Summary i n Heather H i l l Study Area..100 6.1 UDEC St r e n g t h Parameters f o r Heather H i l l Model 119 6.2 I n v e s t i g a t e d V a r i a t i o n i n Strength Parameters 121 v i i i LIST OF FIGURES F i g u r e T i t l e Page 2.1a F l e x u r a l T o p p l i n g 11 2.1b Block T o p p l i n g 11 2.1c B l o c k / F l e x u r a l T o p p l i n g 11 2.2a Kinematic T e s t o f T o p p l i n g P o t e n t i a l Using S t e r e o p l o t 14 2.2b S t r e s s O r i e n t a t i o n s on Slope and D i r e c t i o n of Shear on D i s c o n t i n u i t i e s 14 2.2c C o n d i t i o n f o r I n t e r l a y e r s l i p 14 2.3 T y p i c a l Slope C o n f i g u r a t i o n Assumed i n L i m i t E q u i l i b r i u m Method A n a l y s i s 16 3.1a Nature of D i s t i n c t Element Model 35 3.1b D i s t i n c t Element Model C a l c u l a t i o n C y c l e 35 3.2a Mechanical R e p r e s e n t a t i o n o f I n t e r f a c e s i n D i s t i n c t Element Model 42 3.2b Edge t o Edge Contact 42 3.2c Contact Length f o r F u l l y Deformable Blocks 42 3.3a E l a s t i c - P l a s t i c J o i n t Model 45 3.3b T y p i c a l J o i n t Behaviour 45 4.1 Geometry of UDEC Model f o r Block T o p p l i n g 54 4.2a H o r i z o n t a l V e l o c i t y v s . Mechanical Time a t HI, S t a b l e Slope 55 4.2b H o r i z o n t a l V e l o c i t y v s . Mechanical Time a t HI, F a i l i n g Slope 56 4.3 P a t t e r n of Deformation f o r F a i l i n g Slope 58 4.4 Geometry of Base F r i c t i o n Model and UDEC Model 62 4.5a Base F r i c t i o n Model Deformation 66 4.5b UDEC S i m u l a t i o n o f Base F r i c t i o n Model Deformation..67 i x 4.6a Brenda Mine: Zoned Block Geometry P r i o r t o F a i l u r e . 7 1 4.6b Brenda Mine: Block Geometry and Water Table Used i n UDEC Model 72 4.7a Brenda Mine: Pure F l e x u r a l T o p p l i n g Deformation w i t h G r i d P o i n t V e l o c i t i e s (Dry Slope) 74 4.7b Brenda Mine: Pure F l e x u r a l T o p p l i n g Deformation w i t h H o r i z o n t a l Displacement Contours (Dry Slope)...75 4.8a Brenda Mine: "Graben" T o p p l i n g Deformation w i t h G r i d P o i n t V e l o c i t i e s (Dry Slope) 77 4.8b Brenda Mine: "Graben" T o p p l i n g Deformation w i t h H o r i z o n t a l Displacement Contours (Dry Slope)...78 4.9a Moment Driven Deformation w i t h A c t i v e and P a s s i v e Wedges 81 4.9b S i m i l a r i t y of "Graben" T o p p l i n g t o Example of Moment D r i v e n Deformation Described by Ni e t o , 1987 ( F i g u r e 4 . 9a) 83 5.1 Topographic map of the Beaver R i v e r V a l l e y Showing L o c a t i o n s of Deep Seated L a n d s l i d e s 88 5.2 R e g i o n a l Geology map of the Beaver R i v e r V a l l e y 90 5.3 G e o l o g i c a l Cross S e c t i o n Number 1, Beaver R i v e r V a l l e y 91 5.4 S t r u c t u r a l Geology Summary f o r Study Area 100 5.5 Topographic P r o f i l e S e c t i o n A-A', and Gradient of Creek B 103 5.6 Topographic P r o f i l e South of Creek A, S e c t i o n B-B' 105 6.1 C i r c u l a r A n a l y s i s o f Heather H i l l L a n d s l i d e ; Assumed Slope Geometry and F a i l u r e S u r f a c e 108 6.2 Heather H i l l : Assumed P r e - S l i d e Topography 109 6.3 Heather H i l l : I n i t i a l Block Geometry of UDEC Model 110 6.4 Heather H i l l : F i r s t G l a c i a l E x c a v a t i o n 112 6.5 Heather H i l l UDEC Model: D i s t r i b u t i o n o f Rock Types 118 x 6.6a Heather H i l l UDEC Model: V e l o c i t i e s of G r i d P o i n t s 120 6.6b Heather H i l l UDEC Model: H o r i z o n t a l Displacement..122 6.7a Kinematic T e s t : Toe of Slope i n UDEC Model 12 6 6.7b Kinematic T e s t : E l e v a t i o n o f Change i n Slope i n UDEC Model 126 6.8 Heather H i l l UDEC Model: P r i n c i p l e S t r e s s e s 12 8 6.9 Heather H i l l UDEC Model: V a r i a t i o n o f E f f e c t i v e F r i c t i o n Angle Along an SO F o l i a t i o n 129 6.10 Heather H i l l UDEC Model: V a r i a t i o n i n F a c t o r of S a f e t y Along SO F o l i a t i o n 131 6.11a Normal and Shear S t r e s s e s on Dry J o i n t 132 6.11b E f f e c t i v e Normal and Shear S t r e s s e s When Pore Pres s u r e a c t s on J o i n t 132 x i ACKNOWLEDGEMENTS T h i s r e s e a r c h would not have been p o s s i b l e without a s s i s t a n c e from many i n d i v i d u a l s and o r g a n i z a t i o n s . I wish t o express my g r a t i t u d e t o my s u p e r v i s o r , Dr. K.W. Savigny, who suggested t h e t o p i c and never f a i l e d t o p r o v i d e support, encouragement and guidance. I would l i k e t o thank R. von Sacken and P. Buchanan f o r t h e i r f i e l d a s s i s t a n c e . The author i s a l s o i ndebted t o T. S p e r l i n g , B. James, and Dr. R.A. Freeze of the UBC Groundwater Group f o r the use of t h e i r computer hardware. Thanks are a l s o extended to J . Hammack and M. Keep who p r o v i d e d f i e l d equipment. I would e s p e c i a l l y l i k e t o thank Dr. P. Byrne, Dr. S. Evans, Mr. D. M a r t i n , and Dr. L. Smith whose guidance and comments g r e a t l y enhanced t h e q u a l i t y of t h i s t h e s i s . L o g i s t i c a l support was s u p p l i e d by Environment Canada Parks and the T e r r a i n S c i e n c e s D i v i s i o n , G e o l o g i c a l Survey o f Canada. Mr. E. R i n d t , a t the Western R e g i o n a l O f f i c e ( T r a n s p o r t a t i o n D i v i s i o n ) o f Environment Canada Parks, was of gr e a t a s s i s t a n c e , as were R. Beardmore, Park Superintendent and J . T u r n b u l l , C h i e f Park Warden, Mount R e v e l s t o k e and G l a c i e r N a t i o n a l Parks (MRGNP). Thanks are a l s o extended t o the MRGNP s t a f f f o r t h e i r h o s p i t a l i t y and support; i n p a r t i c u l a r , K. Webb and M. McMahon from the MRGNP I n t e r p r e t a t i o n Department s t a f f . L a s t l y , I extend a s p e c i a l thanks t o V. W i l k i n s o n whose p a t i e n c e and encouragement made i t p o s s i b l e f o r t h i s r e s e a r c h t o be completed. F i e l d work was funded under NSERC Op e r a t i n g Grant No. A1923. Computer hardware and software purchases were funded under S c i e n c e C o u n c i l o f B r i t i s h Columbia Grant No. 57(RC-18) and UBC Grant No. 5-56492 t o which the f o l l o w i n g agencies made c o n t r i b u t i o n s : B.C. Hydro and Power A u t h o r i t y , B.C. M i n i s t r y of T r a n s p o r t a t i o n and Highways, C.N. R a i l , CP R a i l , Regional D i s t r i c t o f F r a s e r and Cheam, Trans Mountain Pipe L i n e Co. Ltd . , and Westcoast Energy Inc. Funding f o r the maps c r e a t e d f o r t h i s r e s e a r c h was p r o v i d e d by the G e o l o g i c a l Survey o f Canada, T e r r a i n S c i e n c e s D i v i s i o n . x i i "Theory and c a l c u l a t i o n are not s u b s t i t u t e s f o r judgment, but are the bases f o r sounder judgment. A t h e o r e t i c a l framework i n t o which the known e m p i r i c a l o b s e r v a t i o n s and f a c t s can be accommodated p e r m i t s us e x t r a p o l a t e t o new c o n d i t i o n s w i t h f a r g r e a t e r c o n f i d e n c e than we c o u l d j u s t i f y by e m p i r i c i s m a l o n e " . R. Peck, 1969 x i i i 1.0 I n t r o d u c t i o n 1.1 R a t i o n a l e f o r Research The r e s e a r c h d e s c r i b e d i n t h i s t h e s i s was undertaken t o i n v e s t i g a t e l a r g e s c a l e n a t u r a l s l o p e movements i n the Beaver V a l l e y , G l a c i e r N a t i o n a l Park, B r i t i s h Columbia. The Beaver V a l l e y forms the e a s t e r n p a r t o f a major t r a n s p o r t a t i o n c o r r i d o r t h a t t r a v e r s e s the S e l k i r k Mountains a t Rogers Pass. T h i s c o r r i d o r i s u t i l i z e d by the Trans Canada Highway and a twinned s e c t i o n o f the CP R a i l main l i n e . A lthough the economic importance of the Beaver R i v e r V a l l e y as the e a s t e r n approach t o the Rogers Pass r o u t e has l o n g been r e c o g n i z e d , the d i s t r i b u t i o n o f l a r g e mass movement hazards al o n g the v a l l e y s l o p e s has o n l y r e c e n t l y been documented ( P r i t c h a r d e t . a l . , 1988). The Heather H i l l l a n d s l i d e , one of s e v e r a l w e l l d e f i n e d f a i l u r e s i n t h e v a l l e y , i s s e l e c t e d as a r e p r e s e n t a t i v e example f o r d e t a i l e d study. The primary o b j e c t i v e i s t o determine the mode of f a i l u r e o f t h i s l a n d s l i d e . T h i s knowledge w i l l enable o t h e r s t o more e f f e c t i v e l y a s sess r i s k s a s s o c i a t e d w i t h i t and oth e r mass movements. 1 1.2 Research Procedure F i e l d work a t the Heather H i l l l a n d s l i d e was undertaken d u r i n g the summer of 1988. T h i s l e d t o the p r e l i m i n a r y c o n c l u s i o n t h a t a t o p p l i n g p r o c e s s (Goodman and Bray, 1976) c o n t r i b u t e d t o the f a i l u r e a t Heather H i l l and a d j a c e n t areas of deep-seated i n s t a b i l i t y . Moreover, the same pro c e s s appears t o be a f f e c t i n g o t h e r s l o p e s nearby which p r e s e n t l y show no i n d i c a t i o n of deep-seated f a i l u r e . T h i s p r e l i m i n a r y c o n c l u s i o n meant t h a t any technique of s t a b i l i t y a n a l y s i s used t o examine the Heather H i l l f a i l u r e must be a b l e t o model l a r g e s c a l e t o p p l i n g i n n a t u r a l s l o p e s , but should not be unduly b i a s e d towards a t o p p l i n g mode of f a i l u r e . The l i t e r a t u r e survey of t o p p l i n g r e p o r t e d i n Chapter 2 was undertaken a t t h i s p o i n t . T h i s review r e v e a l s t h a t v e r y l i t t l e i s known about t o p p l i n g i n l a r g e n a t u r a l s l o p e s , and t h a t c u r r e n t l y used a n a l y t i c a l t e c h n i q u e s are inadequate f o r t h e s e s l o p e s . To e x p l a i n the mechanism of the Heather H i l l f a i l u r e a method of a n a l y s i s capable o f m o d e l l i n g t o p p l i n g , but not r e s t r i c t e d t o t h i s mode of f a i l u r e , i s r e q u i r e d . A c o n c l u s i o n o f the l i t e r a t u r e review i s t h a t a numerical package known as the U n i v e r s a l D i s t i n c t Element Code (UDEC) i s the most s u i t a b l e program. The s u i t a b i l i t y of UDEC f o r a n a l y s i s o f a l l types of t o p p l e s i s demonstrated. The program i s then used t o examine and 2 c l a s s i f y the mode of f a i l u r e o f the Heather H i l l l a n d s l i d e , i l l u s t r a t i n g the a b i l i t y o f the d i s t i n c t element method t o model rock mass deformation i n the s l o p e s o f the Beaver V a l l e y . T h i s a n a l y s i s a l s o demonstrates t h a t UDEC p r o v i d e s an important framework f o r e n g i n e e r i n g d e s i g n and f o r e x p l a i n i n g the geomorphic f e a t u r e s a s s o c i a t e d w i t h the e v o l u t i o n o f n a t u r a l s l o p e s . 1.3 T h e s i s S t r u c t u r e T h i s r e s e a r c h i s r e p o r t e d i n t h r e e p a r t s . P a r t I c o n t a i n s t h i s i n t r o d u c t o r y chapter, and the l i t e r a t u r e review (Chapter 2 ) . P a r t I I i s concerned w i t h the d e s c r i p t i o n and use of UDEC. Chapter 3 i n t r o d u c e s the program, o u t l i n i n g the th e o r y o f the d i s t i n c t element method and the c a p a b i l i t i e s and l i m i t a t i o n s o f UDEC. Chapter 4 demonstrates t h a t the d i s t i n c t element method can be used t o model a l l types o f t o p p l i n g f a i l u r e s . T h i s i s done by u s i n g UDEC t o r e e v a l u a t e examples of t o p p l i n g a n a l y s i s r e p o r t e d i n the l i t e r a t u r e o r known t o the author. In P a r t I I I the mechanism of f a i l u r e o f the Heather H i l l l a n d s l i d e i s e v a l u a t e d . Chapter 5 i s a c h a r a c t e r i z a t i o n o f the study area. T h i s chapter i n c l u d e s the r e g i o n a l geology 3 and geomorphic development of the Beaver V a l l e y , p r e v i o u s work on the s l o p e movements, and the r e s u l t s o f the 1988 f i e l d program. In Chapter 6 the Heather H i l l l a n d s l i d e development i s modelled u s i n g UDEC. Chapter 7 c o n t a i n s the c o n c l u s i o n s o f t h i s r e s e a r c h , and g i v e s recommendations f o r f u r t h e r work. 4 2. L i t e r a t u r e Review 2.1 I n t r o d u c t i o n The aims o f t h i s review are t o summarize the s t a t e - o f - t h e - a r t i n t o p p l i n g and t o i d e n t i f y d e f i c i e n c i e s . T o p p l i n g i s d e f i n e d and an h i s t o r i c a l review i s p r o v i d e d i n the f i r s t s e c t i o n . In subsequent s e c t i o n s the h i s t o r y o f t o p p l i n g r e s e a r c h i s o u t l i n e d , the development and c a p a b i l i t i e s o f p h y s i c a l and numerical models of t o p p l i n g are reviewed, and some o f the p h y s i c a l and mechanical parameters t h a t i n f l u e n c e t o p p l i n g are d i s c u s s e d . A summary of gaps i n the understanding o f t o p p l i n g and s u g g e s t i o n s f o r f u r t h e r r e s e a r c h are i n c l u d e d a t the end of the review. 2.2 General D e f i n i t i o n and H i s t o r i c a l P e r s p e c t i v e T o p p l i n g f a i l u r e i s g e n e r a l l y d e f i n e d as the down-slope o v e r t u r n i n g , e i t h e r through r o t a t i o n o r f l e x u r e , o f i n t e r a c t i n g columns or b l o c k s o f rock (Goodman and Bray, 1976). T h i s mode o f f a i l u r e can develop i n s l o p e s which c o n t a i n w e l l developed d i s c o n t i n u i t i e s o r a p e r v a s i v e f o l i a t i o n d i p p i n g s t e e p l y i n t o the s l o p e . In a d d i t i o n , the d i s c o n t i n u i t i e s or f o l i a t i o n should s t r i k e p a r a l l e l o r s u b p a r a l l e l (plus o r minus 20 degrees) t o the s l o p e c r e s t , and 5 l a t e r a l r e l e a s e should be p o s s i b l e due t o the topography of the s l o p e o r down-slope t r e n d i n g d i s c o n t i n u i t i e s . T o p p l i n g f a i l u r e s have o n l y been d e s c r i b e d i n l i t e r a t u r e w i t h i n the l a s t twenty f i v e y e a r s , and attempts t o model t o p p l i n g have on l y been undertaken i n the l a s t twenty y e a r s . As a r e s u l t o f the b r i e f p e r i o d t h a t t h i s mechanism of f a i l u r e has been r e c o g n i z e d , r e f e r e n c e s on t o p p l i n g are spar s e . One o f the f i r s t r e f e r e n c e s d e s c r i b i n g the motion of t h i s type o f f a i l u r e as t o p p l i n g i s M u l l e r (1968). P h y s i c a l model s t u d i e s were c a r r i e d out under M u l l e r ' s d i r e c t i o n by Hofmann (1972). S i g n i f i c a n t s t u d i e s on the mechanics of t o p p l i n g were undertaken from 1970 t o 1974 a t Im p e r i a l C o l l e g e by Ashby (1971) and C u n d a l l (1971). Ashby p r o v i d e d a comprehensive a n a l y s i s o f the s l i d i n g and o v e r t u r n i n g components of t o p p l i n g . H i s work, which e x p l a i n e d the k i n e m a t i c s o f t o p p l i n g and examined the i n f l u e n c e o f p h y s i c a l and mechanical parameters, l a t e r became the fou n d a t i o n f o r l i m i t e q u i l i b r i u m methods o f t o p p l i n g a n a l y s i s (Sec. 2.4.3). C u n d a l l (1971) made one o f the e a r l i e s t attempts t o study t o p p l i n g n u m e r i c a l l y u s i n g the d i s t i n c t element method (Sec. 2.4.5). During the same p e r i o d , r e s e a r c h e r s a t James Cook U n i v e r s i t y made s i g n i f i c a n t c o n t r i b u t i o n s t o the understanding o f 6 t o p p l i n g i n j o i n t e d rock mass behaviour. Burman (1974) i n t r o d u c e d r o t a t i o n i n t o numerical s i m u l a t i o n s of b l o c k rock systems, and d i s c u s s e d the i n f l u e n c e o f b l o c k r o t a t i o n on p l a n a r f a i l u r e s . One of the f i r s t q u a l i t a t i v e papers d e s c r i b i n g f i e l d examples o f t o p p l i n g f a i l u r e s was p u b l i s h e d by de F r i e t a s and Watters (1973). T h i s paper i s p a r t i c u l a r l y s i g n i f i c a n t as i t c o n v i n c i n g l y demonstrates t h a t t o p p l i n g f a i l u r e " ... r e q u i r e s n e i t h e r unusual g e o l o g i c a l c o n d i t i o n s , nor unusual g e o l o g i c a l m a t e r i a l s i n order t o develop; i n f a c t the r e v e r s e would seem t o be t r u e . " As w e l l , t h e i r paper p r o v i d e d much needed f i e l d e vidence of t o p p l i n g f a i l u r e s and demonstrated t h a t t o p p l e s occur a t a l l s c a l e s and i n c o n t r a s t i n g s t r u c t u r a l s e t t i n g s . T h e i r work was p i v o t a l i n persuading the g e o t e c h n i c a l community t o accept t o p p l i n g as a s i g n i f i c a n t and d i s t i n c t mode of f a i l u r e . With the r e c o g n i t i o n of t o p p l i n g came the development of t e c h n i q u e s t o a ssess the s t a b i l i t y of s l o p e s prone t o t o p p l i n g . The b e s t known technique f o r a n a l y z i n g t o p p l i n g s t a b i l i t y i s the l i m i t e q u i l i b r i u m method (Goodman and Bray, 1976). T h i s method i s based on an e v a l u a t i o n o f s t a t i c f o r c e s and moments of a system of b l o c k s r e p r e s e n t i n g the s l o p e . Goodman and Bray a l s o d e f i n e d the v a r i o u s types of t o p p l e s and t h e i r occurrence, and proposed a k i n e m a t i c t e s t o f the p o t e n t i a l f o r t o p p l i n g (Sees. 2.3, 2.4.2). Both the kinematic 7 t e s t and the l i m i t e q u i l i b r i u m a n a l y s i s have become accepted t e c h n i q u e s f o r p r e d i c t i n g and a n a l y z i n g b l o c k t o p p l i n g f a i l u r e s (Choquet and Tanon, 1985). Simultaneously, but p r i m a r i l y s e p a r a t e l y , f i n i t e element m o d e l l i n g of j o i n t e d rock mass was d e v e l o p i n g (Sec. 2.4.4). Many f i n i t e element programs d e s c r i b e d i n the l i t e r a t u r e owe t h e i r o r i g i n s t o work by Duncan and Goodman (1968) who o u t l i n e d a f i n i t e element technique f o r j o i n t e d rock. K a l k a n i (1977) and H i t t i n g e r (1978) completed important f i n i t e element s t u d i e s of j o i n t e d rock; K a l k a n i w i t h w e l l j o i n t e d r o c k s l o p e s and H i t t i n g e r w i t h t o p p l i n g . A l s o s i m u l t a n e o u s l y , C u n d a l l was c o n t i n u i n g a n a l y t i c a l work on the deformation o f j o i n t e d rock u s i n g the d i s t i n c t element method. C u n d a l l e t a l . (1978) modelled an example of t o p p l i n g p u b l i s h e d by Goodman and Bray (1976) as a v a l i d a t i o n of the method. From the l a t e s e v e n t i e s t o p r e s e n t work on t o p p l i n g has d e a l t mainly w i t h case h i s t o r i e s , u s i n g both the l i m i t e q u i l i b r i u m ( W y l l i e , 1980; P i t e a u and M a r t i n , 1981; P i t e a u e t a l . , 1981), and the f i n i t e element (Brown e t a l . , 1980; Brown , 1982; Evans e t a l . , 1981) methods of a n a l y s i s . One post-1980 p u b l i c a t i o n uses the d i s t i n c t element method t o a n a l y z e a t o p p l i n g s l o p e ( I s h i d a e t a l . , 1987). Many papers s i n c e the l a t e s e v e n t i e s d i s c u s s refinements t o the l i m i t e q u i l i b r i u m 8 technique, o r p r o v i d e nomograms t o f a c i l i t a t e use o f the l i m i t e q u i l i b r i u m method ( P i t e a u and M a r t i n , 1981; P i t e a u e t a l . , 1981; Teme and West, 1983; Zanbak, 1983; Choquet and Tanon, 1985; Sagaseta, 1986). 2.3 Types of Topples The g e n e r a l l y accepted d e f i n i t i o n s o f the p r o c e s s and types o f t o p p l i n g a re g i v e n by Goodman and Bray (1976) and Hoek and Bray (1977). T o p p l i n g f a i l u r e as d e f i n e d by Goodman and Bray (1976) can be comprised o f t h r e e types o f motion: F l e x u r a l T o p p l i n g : Continuous columns of rock bend down-slope, e v e n t u a l l y b r e a k i n g i n t e n s i o n a t depth. P r i o r t o f r a c t u r e , displacement i s accommodated by i n t e r n a l deformation o f i the i n t a c t rock columns and f l e x u r a l s l i p a l o n g the s e p a r a t i o n s between columns ( F i g . 2.1a) Block T o p p l i n g : Columns of rock, d i v i d e d by c r o s s j o i n t s , o v e r t u r n down-s l o p e . The f a i l u r e s u r f a c e s t e p s as r e q u i r e d a l o n g j o i n t s , but no s l i d i n g o ccurs on c r o s s j o i n t s . ( F i g . 2.1b). 9 B l o c k / F l e x u r a l T o p p l i n g : Columns of rock o v e r t u r n down-slope by r o t a t i o n and s l i d i n g on c r o s s j o i n t s . The motion i s s i m i l a r t o b l o c k t o p p l i n g , but u n l i k e b l o c k t o p p l i n g s l i d i n g on c r o s s j o i n t s i s s i g n i f i c a n t ( F i g . 2.1c). These d e f i n i t i o n s a c c u r a t e l y d e s c r i b e the types o f deformation behaviour t h a t can occur d u r i n g t o p p l i n g . However, the mode of t o p p l i n g t h a t occurs i n r e a l s l o p e s i s o f t e n a complicated mix o f the modes d e f i n e d above. 2.4 Methods o f A n a l y s i s 2.4.1 P h y s i c a l Models Some o f the e a r l i e s t m o d e l l i n g attempts u t i l i z e d the f r i c t i o n t a b l e o r t i l t t a b l e . Ashby (1971), Soto (1974), and Whyte (1973) examined b l o c k and b l o c k / f l e x u r a l t o p p l i n g , Kuykendall (1975), experimented w i t h f l e x u r a l t o p p l i n g models, and Hofman (1973) c o n s i d e r e d mixed modes of b l o c k / f l e x u r e and f l e x u r a l t o p p l i n g . The l i m i t e q u i l i b r i u m method and numerical methods q u i c k l y became more popul a r p r i m a r i l y due t o t h e i r f l e x i b i l i t y . 10 F i g u r e 2 . 1 a F l e x u r a l T o p p l i n g ( a f t e r Goodman and B r a y , 1976) F i g u r e 2 . 1 c B l o c k / F l e x u r a l T o p p l i n g ( a f t e r Goodman and B r a y , 1976) 11 2.4.2 Kinematic A n a l y s i s P r e d i c t i o n o f t o p p l i n g p o t e n t i a l u s i n g a k i n e m a t i c a n a l y s i s was proposed by Goodman and Bray (1976). For t o p p l i n g t o be p o s s i b l e the p o l e t o the r e g u l a r d i s c o n t i n u i t y s e t d i p p i n g i n t o the s l o p e must l i e o u t s i d e a g r e a t c i r c l e whose d i p i s the s l o p e f a c e angle p l u s the f r i c t i o n angle o f the d i s c o n t i n u i t y . T h i s t e s t can be q u i c k l y done u s i n g a s t e r e o n e t p l o t ( F i g . 2.2a). The t e s t i s based on two l i m i t i n g s t r e s s c o n d i t i o n s of t o p p l i n g a t the p o i n t where f l e x u r a l s l i p a l o n g d i s c o n t i n u i t i e s o c c u r s . The f i r s t c o n d i t i o n r e s u l t s from s t r e s s e q u i l i b r i u m requirements and a p p l i e s a t the f r e e s u r f a c e o f the s l o p e ( s l o p e f a c e ) . Along the s l o p e f a c e the maximum ( a l ) and median (a2) s t r e s s d i r e c t i o n s must l i e i n the plane o f the s l o p e . The minimum s t r e s s (a3) i s o r i e n t e d normal t o the s l o p e face and has zero magnitude. I t i s assumed t h a t the median s t r e s s a c t s p a r a l l e l t o the t r e n d of the s l o p e and the maximum p e r p e n d i c u l a r ( F i g 2.2b). The second c o n d i t i o n comes from the requirements f o r shear a l o n g the d i s c o n t i n u i t i e s near the s l o p e f a c e . Given t h a t a 3 i s zero, f o r shear ( i n the a l , a3 plane) t o be p o s s i b l e along the d i s c o n t i n u i t y the maximum p r i n c i p a l s t r e s s must a c t a t an angle t o the p o l e of the d i s c o n t i n u i t y equal o r g r e a t e r than the f r i c t i o n angle of the d i s c o n t i n u i t y . U s i n g these two 12 f a i l u r e c r i t e r i a , t h a t the maximum p r i n c i p a l s t r e s s d i r e c t i o n i s a l i g n e d w i t h the s l o p e face ($) and must be i n c l i n e d by a t l e a s t the f r i c t i o n angle (</>) t o the d i s c o n t i n u i t y , i t i s p o s s i b l e t o determine the l i m i t i n g c o n d i t i o n s f o r s t a b i l i t y ; t h a t 6<(4>+a) (Goodman and Bray, 1976) ( F i g . 2.2c). T h i s t e s t has gained acceptance s i n c e i t was proposed. However, i t can o n l y p r e d i c t whether t o p p l i n g f a i l u r e i s k i n e m a t i c a l l y p o s s i b l e ; i t cannot p r e d i c t whether or not a g i v e n s l o p e w i l l t o p p l e . Choquet and Tanon (1985) suggest a minor a l t e r a t i o n of t h i s t e s t t o i n c l u d e a l i m i t i n g c o n d i t i o n of t o p p l i n g t h a t occurs when the f a i l u r e plane becomes so steep t h a t the columns w i l l f a i l p u r e l y by s l i d i n g a l o n g j o i n t s . 2.4.3 L i m i t E q u i l i b r i u m Method By f a r the most p o p u l a r a n a l y t i c a l technique t o p r e d i c t whether a s l o p e w i l l t o p p l e i s the l i m i t e q u i l i b r i u m method developed by Goodman and Bray (1976). T h i s t e c h n i q u e i s based on the k i n e m a t i c s developed by Ashby (1971) and can be used t o c a l c u l a t e a f a c t o r of s a f e t y f o r a s l o p e prone t o t o p p l i n g . As the t e c h n i q u e i s d e s c r i b e d i n d e t a i l by Hoek and Bray (1977) and by Goodman and Bray (1976), t h i s review w i l l p r o v i d e o n l y a b r i e f summary of the method c o n c e n t r a t i n g on the c a p a b i l i t i e s and l i m i t a t i o n s of the t e c h nique. 13 T o p p l i n g p o s s i b l e f o r p o l e s l y i n g w i t h i n r u l e d r e g i o n . F i g u r e 2 . 2 a K i n e m a t i c T e s t o f T o p p l i n g P o t e n t i a l u s i n g S t e r e o p l o t . ( a f t e r Goodman and B r a y , 1976) F i g u r e 2 . 2 b S t r e s s O r i e n t a t i o n s on S l o p e and D i r e c t i o n o f S h e a r on D i s c o n t i n u i t i e s ( a f t e r Goodman and B r a y , 1 9 7 6 ) . F i g u r e 2 . 2 c C o n d i t i o n f o r I n t e r l a y e r S l i p ( a f t e r Goodman and B r a y , 1 9 7 6 ) . 14 The l i m i t e q u i l i b r i u m s o l u t i o n i s formed by approximating the s l o p e as a s e r i e s o f columns r e s t i n g on a stepped base ( F i g . 2.3). The s o l u t i o n begins by r e s o l v i n g the f o r c e s a c t i n g on the uppermost column i n the s l o p e i n t o f o r c e s normal ( y 1 ) and p a r a l l e l (x') t o the base of the b l o c k . The f a i l u r e mode f o r the b l o c k i s determined by s o l v i n g two s t a t i c s problems, one assuming b l o c k s l i d i n g and one assuming b l o c k t o p p l i n g . The r e s u l t a n t x* f o r c e s from each p o t e n t i a l mode o f f a i l u r e a re compared, and the s o l u t i o n producing the l a r g e s t r e s u l t a n t i n the x' d i r e c t i o n i s taken t o be the mode of f a i l u r e o f the b l o c k . T h i s r e s u l t a n t x' f o r c e i s then a p p l i e d t o the next b l o c k i n the s l o p e and the a n a l y s i s i s repeated. The a n a l y s i s p r o g r e s s e s from b l o c k t o b l o c k down the s l o p e t o the toe bl o c k . The f i n a l r e s u l t a n t f o r c e a t the toe b l o c k i s the f o r c e r e q u i r e d t o m a i n t a i n the s t a b i l i t y o f the s l o p e . A F a c t o r o f s a f e t y can be c a l c u l a t e d from the r a t i o o f the c o e f f i c i e n t o f f r i c t i o n o f the l a s t b l o c k without support t o the c o e f f i c i e n t o f f r i c t i o n w i t h support. There are s e v e r a l l i m i t i n g assumptions t o t h i s a n a l y s i s . 1. No b l o c k can be both t o p p l i n g and s l i d i n g . 2. The method o n l y a p p l i e s t o b l o c k t o p p l i n g o f continuous columns. Columns may be j o i n t e d , but s l i p on j o i n t s o r o v e r t u r n i n g o f i n d i v i d u a l b l o c k s d e f i n e d by j o i n t s w i t h i n a column i s not allowed. 15 F i g u r e 2.3 T y p i c a l Slope C o n f i g u r a t i o n Assumed i n L i m i t E q u i l i b r i u m Method of A n a l y s i s . ( a f t e r Goodman and Bray, 1976) 16 3. The columns are r i g i d . The a n a l y z e t o p p l i n g w i t h l a r g e 4. The l o c a t i o n and i n c l i n a t i o : must be assumed. technique cannot a c c u r a t e l y i n t e r n a l column deformations. , of the stepped f a i l u r e plane 5. The a n a l y s i s i s by d e f i n i t i o n a s t a t i c balance of f o r c e s . T o p p l i n g f a i l u r e of a s l o p e i s a dynamic p r o c e s s , and deformation a f f e c t s s t r e n g t h parameters. A l i m i t e q u i l i b r i u m a n a l y s i s of t o p p l i n g does not a l l o w e v a l u a t i o n of m o b i l i z e d s t r e n g t h of j o i n t s , which depends not o n l y on normal s t r e s s , but a l s o on t a n g e n t i a l displacement. In o t h e r words, the a n a l y s i s cannot i n c o r p o r a t e n o n - l i n e a r s t r e s s - d i s p l a c e m e n t s j o i n t r e l a t i o n s h i p s . 6. C u r r e n t programs r e s t r i c t the s l o p e geometry t o a uniform s t e p and b l o c k width. Even w i t h t h e s e l i m i t a t i o n s , the l i m i t e q u i l i b r i u m method has proven u s e f u l f o r examining t o p p l i n g . The s i m p l i c i t y o f the s o l u t i o n and the output of r e q u i r e d r e t a i n i n g f o r c e o r f a c t o r of s a f e t y have l e a d t o the s u c c e s s f u l use of the technique f o r e n g i n e e r i n g d e s i g n ( P i t e a u e t a l . , 1981). 17 2.4.4 F i n i t e Element Method The f i n i t e element method has been used w i t h moderate success t o model t o p p l i n g s l o p e s as a d i s c r e t i z e d continuum c o n t a i n i n g j o i n t elements. T h i s s e c t i o n w i l l g i v e a b r i e f h i s t o r y o f the a p p l i c a t i o n of the f i n i t e element method t o t o p p l i n g f a i l u r e s f o l l o w e d by the c a p a b i l i t i e s and l i m i t a t i o n s o f the technique and i t s use i n p r a c t i c e . F i n i t e element models owe t h e i r development t o many workers who each improved the technique f o r m o d e l l i n g j o i n t e d rock mass (Duncan and Goodman, 1968; Goodman e t a l . , 1968; Goodman and Dubois, 1971; Burman, 1974). Although f i n i t e element methods f o r j o i n t e d rock have been used e x t e n s i v e l y i n a l l areas o f rock mechanics, t h e r e are few a p p l i c a t i o n s o f the method t o t o p p l i n g (Burman e t a l . , 1975; K a l k a n i and P i t e a u , 1976; and H i t t i n g e r , 1978). F i n i t e element methods are capable of m o d e l l i n g t o p p l e s more r e a l i s t i c a l l y than the l i m i t e q u i l i b r i u m method. The c o n s t i t u t i v e r e l a t i o n s h i p s of the i n t a c t rock mass and the j o i n t s can be more r e a l i s t i c a l l y modelled, pore p r e s s u r e s can be i n t r o d u c e d , and any geometry, geology, and l o a d i n g h i s t o r i e s can be used. However, the f i n i t e element method i s not without problems. I t has a l i m i t e d a b i l i t y t o model j o i n t e d rock mass because of 18 i t s continuum f o r m u l a t i o n . To o b t a i n the approximate s o l u t i o n of d isplacements and s t r e s s e s i n the problem domain, l a r g e m a t r i c e s must be formulated and s o l v e d from the governing equations a t the g r i d p o i n t s . Whenever s i g n i f i c a n t displacement occurs a t a g r i d p o i n t t h i s g l o b a l s t i f f n e s s m a t r i x must be reformed. Thus, problems w i t h l a r g e d i splacements are time consuming and d i f f i c u l t t o s o l v e . The method i s a l s o not a dynamic technique. I t can p r e d i c t s t r e s s e s and displacements, but i f a s l o p e i s u n s t a b l e i t cannot be used t o study how a f a i l u r e p r o g r e s s e s . The s t a t e - o f - t h e - a r t i n f i n i t e element a n a l y s i s of t o p p l i n g appears t o be the program developed by H i t t i n g e r ( H i t t i n g e r , 1978). A case h i s t o r y by Brown e t a l . (1980) a p p l i e s t h i s program t o a n a l y z e a r e a l s l o p e . Evans e t a l . (1981) r e p o r t s what appears t o be the most r e c e n t attempt t o a pply f i n i t e element a n a l y s i s t o t o p p l i n g . The l a c k o f use of the f i n i t e element method i n t o p p l i n g a n a l y s i s i s l i k e l y a r e s u l t of the complexity of the t e c h n i q u e . Except f o r l a r g e problems t h a t j u s t i f y the time i n v o l v e d i n a more d e t a i l e d a n a l y s i s , p r a c t i t i o n e r s p r e f e r the s i m p l e r l i m i t e q u i l i b r i u m technique. 19 2.4.5 D i s t i n c t Element Method The d i s t i n c t element method has a much more c l e a r l y d e f i n e d h i s t o r y than the f i n i t e element method. The f i n i t e element method a p p l i e d t o j o i n t e d rock and s p e c i f i c a l l y t o t o p p l e s owes i t s development t o a l a r g e number of r e s e a r c h e r s , but the development o f the d i s t i n c t element method can be t r a c e d t o one r e s e a r c h e r , Dr. P.A. C u n d a l l . The o r i g i n a l paper d e s c r i b i n g the method was p u b l i s h e d i n 1971 ( C u n d a l l , 1971). S i n c e t h i s p u b l i c a t i o n , C u n d a l l , and o t h e r s have co n t i n u e d t o develop t h e method. T h i s s e c t i o n p r o v i d e s a b r i e f h i s t o r y of the development of the d i s t i n c t element method as i t r e l a t e s t o t o p p l i n g f a i l u r e . The c a p a b i l i t i e s and l i m i t a t i o n s o f the method al o n g w i t h i t s use i n p r a c t i c e w i l l be d i s c u s s e d . The t e c h n i q u e a p p l i e s an e x p l i c i t , f i n i t e d i f f e r e n c e method of s o l u t i o n t o model l a r g e displacements and r o t a t i o n s o f b l o c k systems. The rock mass i s r e p r e s e n t e d by an assemblage of b l o c k s , and the d i s c o n t i n u i t i e s d i v i d i n g the b l o c k s a c t as boundary i n t e r a c t i o n s w i t h a p r e s c r i b e d j o i n t behaviour. S i n c e i t was f i r s t d e s c r i b e d i n 1971, the method has evolved i n t o a h i g h l y f l e x i b l e computer package. The o r i g i n a l program c o n s i d e r e d the b l o c k s t o be r i g i d and a p p l i e d a s i m p l i s t i c j o i n t r e l a t i o n s h i p . By the mid e i g h t i e s the o r i g i n a l program had been m o d i f i e d i n t o s e v e r a l v e r s i o n s t h a t i n c l u d e d such c a p a b i l i t i e s as b l o c k deformation and s p l i t t i n g ( C undall e t 20 a l . , 1978; C u n d a l l and M a r t i , 1979), a j o i n t g e n e r a t o r capable of c r e a t i n g d i s c o n t i n u o u s j o i n t s by s e t s ( C u n d a l l , 1983), t r a n s i e n t f l u i d p r e s s u r e and flow u t i l i z i n g j o i n t p e r m e a b i l i t y l i n k e d t o mechanical deformation, and v a r i o u s j o i n t c o n s t i t u t i v e models ( C u n d a l l , 1985; C u n d a l l and Lemos, 1988). In a d d i t i o n the d i s t i n c t element method has been l i n k e d t o a boundary element code a l l o w i n g s i g n i f i c a n t r e d u c t i o n of the computational s i z e o f some problems (Lemos and Brady, 1983). By 1985 the s e and o t h e r f e a t u r e s had been u n i f i e d i n t o a two dim e n s i o n a l program known as the u n i v e r s a l d i s t i n c t element code (UDEC). A t h r e e dimensional v e r s i o n of t h i s program i s known as 3DEC. A l l the advantages noted i n S e c t i o n 2.4.4 f o r the f i n i t e element method a l s o apply t o the d i s t i n c t element method, however the d i s t i n c t element method has a d d i t i o n a l advantages over the f i n i t e element method. A p a r t i c u l a r advantage of the f i n i t e d i f f e r e n c e technique i s i t s computational s i m p l i c i t y . Because the method i s an e x p l i c i t f i n i t e d i f f e r e n c e approach, s o l v e d u s i n g dynamic r e l a x a t i o n , i t does not form l a r g e m a t r i c e s and makes l i m i t e d demands on computer memory requirements. The f o r m u l a t i o n of the problem as a c o l l e c t i o n of i n t e r a c t i n g b l o c k s a l s o has advantages over the continuum method used by f i n i t e element t e c h n i q u e s . The making and b r e a k i n g of c o n t a c t s between b l o c k s and l a r g e displacements and r o t a t i o n s of b l o c k s are more e a s i l y accommodated. 21 Disadvantages o f the method i n c l u d e the o f t e n s m a l l time step, and c o r r e s p o n d i n g l o n g run time, r e q u i r e d t o ensure numerical s t a b i l i t y . T h i s disadvantage has become much l e s s s i g n i f i c a n t i n the l a s t few years as desk top computers have become cheaper and more powerful. 2.4.6 Comparative Assessment of A n a l y t i c a l Methods By f a r the most p o p u l a r method r e p o r t e d i n the l i t e r a t u r e t o model t o p p l i n g i s the l i m i t e q u i l i b r i u m method. However, the method cannot a c c u r a t e l y p r e d i c t the s t a b i l i t y o f t o p p l e s t h a t undergo i n t e r n a l deformation ( f l e x u r e ) p r i o r t o f a i l u r e , o r when the c o n s t i t u t i v e r e l a t i o n s h i p s o f the i n t a c t rock or j o i n t s v a r y i n a n o n - l i n e a r manner w i t h s t r e s s l e v e l or displacement. Although s e r i o u s , these problems are o f t e n overshadowed by problems w i t h the fundamental assumptions of the method l i s t e d i n S e c t i o n 2.4.3. As d i s c u s s e d i n S e c t i o n 2.4.4, f i n i t e element methods overcome most of the l i m i t a t i o n s of the l i m i t e q u i l i b r i u m method, but they have been used much l e s s f r e q u e n t l y t o model t o p p l i n g . Most o f the f i n i t e element work wi t h t o p p l i n g s l o p e s i s r e s t r i c t e d t o hard, s t i f f rock. T h i s i s done e i t h e r t o f a c i l i t a t e comparison of f i n i t e element r e s u l t s t o r e a l rock s l o p e s (Brown e t a l . , 1980; K a l k a n i and P i t e a u , 1976; Evans e t a l . , 1981), the l i m i t e q u i l i b r i u m method, or p h y s i c a l models ( H i t t i n g e r , 1978). When hard rock i s modelled i t deforms 22 l i t t l e , and most of the s t r e s s dependent deformation i s d e r i v e d from the j o i n t s . The p r e f e r e n c e f o r hard rock t o p p l e s i s p a r t i a l l y a r e s u l t of r e s e a r c h b e i n g d i r e c t e d toward s m a l l s c a l e t o p p l e s where low i n s i t u s t r e s s c o n d i t i o n s support r i g i d b l o c k behaviour. As a r e s u l t o f t h i s p r e f e r e n c e f o r s m a l l s l o p e s w i t h r i g i d column behaviour, l a r g e s l o p e s w i t h h i g h e r i n s i t u s t r e s s e s and c o r r e s p o n d i n g l a r g e r column deformations, have not been s t u d i e d . D i s t i n c t element methods have been a p p l i e d t o b l o c k t o p p l e s both as a v a l i d a t i o n of the d i s t i n c t element method and as a m o d e l l i n g technique f o r examining b l o c k t o p p l i n g . C u n d a l l (1971), C u n d a l l e t a l . (1977), and C u n d a l l e t a l . (1978) a l l use b l o c k t o p p l i n g examples t o v a l i d a t e the d i s t i n c t element method. A s i d e from these b r i e f uses of t o p p l i n g as examples of d i s t i n c t element method v a l i d a t i o n , t h e r e are v e r y few examples i n the l i t e r a t u r e of the d i s t i n c t element method b e i n g used t o model e i t h e r h y p o t h e t i c a l o r r e a l t o p p l i n g s l o p e s . Hocking (1978) used a r i g i d b l o c k d i s t i n c t element program t o examine t o p p l i n g s l i d i n g f a i l u r e modes of h y p o t h e t i c a l b l o c k y s l o p e s . More r e c e n t l y I s h i d a e t a l . (1987) a p p l i e d a r i g i d b l o c k v e r s i o n of the d i s t i n c t element method t o a r e a l example of b l o c k t o p p l i n g . The v e r s i o n o f the d i s t i n c t element method used by I s h i d a e t a l . (1987) i s , however, outdated compared t o o t h e r a v a i l a b l e programs. The d i s t i n c t element method does not 23 appear t o have been used t o model the more complex f l e x u r a l and composite modes of t o p p l i n g . In summary, t o p p l i n g r e s e a r c h has been l a r g e l y d i r e c t e d towards the l i m i t e q u i l i b r i u m method. T h i s method cannot r e a l i s t i c a l l y be used when rock or j o i n t s t r e n g t h s v a r y non-l i n e a r l y w i t h s t r e s s or i n any manner wit h displacement. F i n i t e element methods can p r e d i c t t o p p l i n g s l o p e deformation more a c c u r a t e l y than the l i m i t e q u i l i b r i u m method, but have not been used as e x t e n s i v e l y . A l s o , the f i n i t e element method i s f o rmulated as a continuum and cannot accommodate l a r g e d i splacements as w e l l as the d i s t i n c t element method. The d i s t i n c t element method i s designed t o model l a r g e d eformations, but i t s f o r m u l a t i o n r e q u i r e s l o n g computer runs. There are v e r y few a p p l i c a t i o n s o f the d i s t i n c t element method t o b l o c k t o p p l i n g , and none t o f l e x u r a l t o p p l i n g . 2.5 Parameters C o n t r o l l i n g T o p p l i n g : D i s c u s s i o n 2.5.1 I n f l u e n c e of S t r u c t u r e and Rock Type A l l r o c k types are s u s c e p t i b l e t o t o p p l i n g i f the r e q u i s i t e geometry and s t r u c t u r e are p r e s e n t (de F r i e t a s and Watters, 1973; Goodman and Bray, 1976). S t r u c t u r e p r o v i d e s d i s t i n c t p l a n e s of weakness w i t h i n the rock mass, and l i t h o l o g y 24 c o n t r o l s the s t r e n g t h and deformation c h a r a c t e r i s t i c s o f the i n t a c t rock. The i n f l u e n c e o f j o i n t i n g i s fundamental, as e v i d e n t i n the d e f i n i t i o n s of t o p p l e types. F l e x u r a l t o p p l i n g occurs i n columns w i t h no c r o s s - f r a c t u r e s , b l o c k t o p p l i n g occurs by s e p a r a t i o n a l o n g p r e - e x i s t i n g j o i n t s , and b l o c k - f l e x u r a l t o p p l i n g r e q u i r e s a p e r v a s i v e c r o s s - j o i n t i n g . The primary s t r e n g t h c h a r a c t e r i s t i c s of i n t a c t rock t h a t i n f l u e n c e t o p p l i n g s l o p e f a i l u r e s are shear and t e n s i l e s t r e n g t h , 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 , and, perhaps, rheology. These p r o p e r t i e s are dependent on rock type. A t low t o moderate c o n f i n i n g p r e s s u r e s , s t r o n g rock w i l l have a h i g h e l a s t i c modulus and e x h i b i t low s t r a i n t o a b r i t t l e f a i l u r e . Weak rock w i l l have an lower e l a s t i c modulus and a n o n - l i n e a r s t r e s s s t r a i n r e l a t i o n s h i p a l l o w i n g l a r g e deformations f o r s t r e s s l e v e l s c l o s e t o u l t i m a t e f a i l u r e . There i s n o t h i n g q u a n t i t a t i v e i n the l i t e r a t u r e c o n c e r n i n g the i n f l u e n c e o f these rock s t r e n g t h c h a r a c t e r i s t i c s on t o p p l e s . T h i s seems t o be an i n a d v e r t e n t r e s u l t o f the d i r e c t i o n t o p p l i n g r e s e a r c h has taken. Research has c o n c e n t r a t e d on the l i m i t e q u i l i b r i u m method, wi t h a s m a l l amount of work on the f i n i t e element method. The l i m i t e q u i l i b r i u m method has i n h e r e n t r e s t r i c t i o n s on the deformation behaviour o f i n t a c t r o c k and j o i n t s . The f i n i t e element method does not have 25 t h e s e r e s t r i c t i o n s , but i t has a l s o been used v e r y l i t t l e f o r m o d e l l i n g t o p p l i n g . 2.5.2 Shear S t r e n g t h of D i s c o n t i n u i t i e s . I t i s important t o note t h a t t o p p l i n g f a i l u r e i s o f t e n c o n t r o l l e d by the behaviour of d i s c o n t i n u i t i e s , not by the s t r e s s - s t r a i n p r o p e r t i e s of i n t a c t rock. T h i s i s e s p e c i a l l y t r u e i n s m a l l s c a l e t o p p l e s where low i n s i t u s t r e s s e s cause l i t t l e d eformation t o i n t a c t rock. The i n t a c t rock i s e s s e n t i a l l y r i g i d and the mechanical behaviour o f d i s c o n t i n u i t i e s i s of paramount importance. D i s c o n t i n u i t i e s p r o v i d e a d e f i n e d s u r f a c e of f a i l u r e i n the rock mass, and can have complicated n o n - l i n e a r s t r e s s -displacement behaviour t h a t i n c l u d e s peak and/or r e s i d u a l s t r e n g t h , creep deformation p r o p e r t i e s , cohesion, and s e p a r a t i o n i n t e n s i o n . Shear s t r e n g t h of a d i s c o n t i n u i t y depends on the normal s t r e s s , the i n c l i n a t i o n and s t r e n g t h of i r r e g u l a r i t i e s on the s u r f a c e (Patton, 1966; Ladanyi and Archambault, 1969), and on displacement. S u r f a c e i r r e g u l a r i t i e s cause a d i s c o n t i n u i t y t o d i l a t e when t e s t e d under con s t a n t normal s t r e s s . I f a d i l a t i v e d i s c o n t i n u i t y i s c o n f i n e d d u r i n g shear the normal s t r e s s on the d i s c o n t i n u i t y w i l l i n c r e a s e , i n c r e a s i n g the shear s t r e n g t h . Consequently, i n a r e a l s l o p e w i t h d i l a t i v e 26 j o i n t s f i n i t e or d i s t i n c t element models w i l l be s i m u l a t i n g c o n s e r v a t i v e behaviour i f d i l a t i o n i s not i n c l u d e d i n the j o i n t behaviour o f the model (Barton, 1986) . D i l a t i o n o f j o i n t s i s l i m i t e d by the shear s t r e n g t h o f a s p e r i t i e s on the j o i n t s u r f a c e . Ladanyi and Archambault (1969) observed the s t r e s s l e v e l a t which s h e a r i n g o f a s p e r i t i e s o c c u r s t o be approximately 9.5 x 106N/m2. Above t h i s l e v e l , d i l a t i o n o f j o i n t s w i l l not occur. Depending on the rock d e n s i t y and s t r e s s h i s t o r y , t h i s i s ro u g h l y e q u i v a l e n t t o the s t r e s s l e v e l a t a 300 t o 450m depth. T h e o r e t i c a l l y a l l but the l a r g e s t s l o p e s should d i s p l a y some degree o f d i l a t a n t j o i n t behaviour. The above d i s c u s s i o n on deformation c h a r a c t e r i s t i c s o f i n t a c t rock and j o i n t s l e a d s i n t o a d i s c u s s i o n o f s c a l e i n f l u e n c e s on t o p p l e s . The most fundamental d i f f e r e n c e between a s m a l l s l o p e (<100m high) and a l a r g e s l o p e i s the i n s i t u s t r e s s c o n d i t i o n . As d e s c r i b e d above, t h i s confinement a c t s t o i n c r e a s e the s t r e n g t h o f d i l a t i v e j o i n t s undergoing shear. Hence, the shear s t r e n g t h o f d i l a t i v e d i s c o n t i n u i t i e s w i l l i n c r e a s e w i t h confinement i n h i g h e r s l o p e s . Bovis (1982), suggested d i l a t i o n o f d i s c o n t i n u i t i e s c o u l d e x p l a i n the a r r e s t e d development of some t o p p l i n g f a i l u r e s . 27 2.5.3 Groundwater Few r e s e a r c h e r s have g i v e n more than s i m p l i s t i c treatment t o the i n f l u e n c e o f groundwater on t o p p l i n g . L i k e the i n f l u e n c e of rock s t r e n g t h c h a r a c t e r i s t i c s d i s c u s s e d e a r l i e r , t h i s i s a r e s u l t o f the d i r e c t i o n t o p p l i n g r e s e a r c h has taken. Much of the r e s e a r c h t h a t has been done i s aimed a t s o l v i n g e n g i n e e r i n g problems r e l a t e d t o mining or s l o p e e x c a v a t i o n . Because of the s m a l l s c a l e of these f a i l u r e s and the d i l a t e d n a ture of the rock, the s l o p e s are o f t e n assumed t o be d r a i n e d w i t h no pore p r e s s u r e (Choquet and Tanon, 1985). Even when pore p r e s s u r e s are i n c l u d e d i n the a n a l y s i s , the assumptions used f o r t h e water t a b l e and flow are o f t e n s i m p l i s t i c ( H i t t i n g e r , 1978; P i t e a u e t a l . , 1981; Brown, 1982). The most common assumption f o r the water t a b l e i s a s t r a i g h t l i n e from the t o e o f the s l o p e up t o a p o i n t d i r e c t l y below the c r e s t of the s l o p e . From t h i s p o i n t the water t a b l e i s assumed t o be h o r i z o n t a l back i n t o the s l o p e . The assumption of no pore p r e s s u r e s or an approximate water t a b l e may be adequate f o r the a n a l y s i s of road c u t s and p i t s l o p e s , but t o p p l e s i n l a r g e r s l o p e s may r e q u i r e a more a c c u r a t e c o n s i d e r a t i o n of pore p r e s s u r e . L a r g e r s l o p e s are p a r t of a r e g i o n a l flow system and, except i n the most a r i d r e g i o n s , w i l l have a water t a b l e . In o r d e r f o r the i n f l u e n c e of pore p r e s s u r e s t o be c o r r e c t l y modelled, the 28 groundwater flow system i n the s l o p e must be a c c u r a t e l y q u a n t i f i e d . 2.6 Summary of Areas Needing F u r t h e r Work 2.6.1 F a i l u r e Plane P r e d i c t i o n One of the problems w i t h the commonly used l i m i t e q u i l i b r i u m method f o r t o p p l i n g a n a l y s i s developed by Goodman and Bray (1976) i s t h a t i t cannot p r e d i c t the shape and l o c a t i o n o f the f a i l u r e p l a n e . The us e r must apply a t r i a l and e r r o r approach, s e l e c t i n g d i f f e r e n t p l a n a r f a i l u r e s u r f a c e s t o determine the s u r f a c e w i t h the lowest f a c t o r o f s a f e t y . A l s o , t h i s l i m i t e q u i l i b r i u m method assumes t h a t the f a i l u r e s u r f a c e i s p l a n a r , but i t i s not known i f t h i s i s always t r u e . F u r t h e r r e s e a r c h i n t o the form a t i o n and shape of the f a i l u r e s u r f a c e i n a l l types o f t o p p l e s i s r e q u i r e d . The d i s t i n c t element method i s capable o f p r e d i c t i n g a f a i l u r e s u r f a c e c o n f i g u r a t i o n by m o d e l l i n g both i n t a c t rock and j o i n t d eformations u s i n g r e a l i s t i c c o n s t i t u t i v e r e l a t i o n s h i p s . U s i n g t h i s method t o model t o p p l i n g deformation o f h y p o t h e t i c a l s l o p e s having v a r i a b l e m a t e r i a l p r o p e r t i e s and geometry s h o u l d l e a d t o a b e t t e r understanding o f the development and geometry of f l e x u r a l t o p p l i n g f a i l u r e s . 29 2.6.2 I n f l u e n c e o f C o n f i n i n g S t r e s s The i n f l u e n c e of i n s i t u s t r e s s e s on rock s t r e n g t h i s w e l l understood and can be i n c o r p o r a t e d i n the c o n s t i t u t i v e s t r e s s -s t r a i n laws f o r i n t a c t rock and j o i n t s . One o f the flaws of the l i m i t e q u i l i b r i u m approach t o t o p p l i n g a n a l y s i s i s t h a t i t does not i n c o r p o r a t e r e a l i s t i c i n s i t u s t r e s s e s . Although both the f i n i t e element and f i n i t e d i f f e r e n c e methods u t i l i z e more r e a l i s t i c s t r e s s e s , n e i t h e r has been used t o i n v e s t i g a t e the i n f l u e n c e of s t r e s s c o n d i t i o n s on t o p p l i n g s l o p e s . T h i s can be done w i t h the d i s t i n c t element method u s i n g l a r g e s c a l e s l o p e s and deformable b l o c k s . 2.6.3 T o p p l i n g i n Mixed Rock Types No attempt has been made t o n u m e r i c a l l y model t o p p l i n g s l o p e s of mixed rock t y p e s . Large s l o p e s c o n s i s t i n g of l a y e r e d hard and s o f t u n i t s ( i e : sandstone and s h a l e , or q u a r t z i t e and p h y l l i t e ) t h a t undergo s i g n i f i c a n t o v e r t u r n i n g and f l e x u r e p r i o r t o f a i l u r e cannot be a c c u r a t e l y modelled w i t h the l i m i t e q u i l i b r i u m method. A r e s e a r c h program c o u l d use the d i s t i n c t element method t o compare the behaviour of mixed rock type s l o p e s t o s l o p e s of one m a t e r i a l . The primary g o a l would be t o n u m e r i c a l l y reproduce the deformation observed i n these s l o p e s . 30 2.6.4 Time Dependent Deformation Most o f the r e s e a r c h on t o p p l i n g i n the l i t e r a t u r e c o n c e n t r a t e s on s m a l l r a p i d l y excavated s l o p e s . Creep deformations i n these s l o p e s are l i k e l y i n s i g n i f i c a n t compared t o deformations from s t r e s s changes. In l a r g e r n a t u r a l s l o p e s excavated by f l u v i a l and/or g l a c i a l e r o s i o n o r oversteepened by mass wasting or t e c t o n i c u p l i f t , creep i n f l u e n c e s may be much more s i g n i f i c a n t . I t may be p o s s i b l e t o use f i n i t e d i f f e r e n c e t e c h n i q u e s a p p l i e d t o a d i s c r e t i z e d continuum (such as the program FLAC, d e s c r i b e d by C u n d a l l and Board, 1988), or f i n i t e element tec h n i q u e s t o model t h i s type o f deformation. 2.6.5 Large Slopes and Weak Rock Most t o p p l i n g r e s e a r c h has d e a l t w i t h e n g i n e e r i n g o r mining e x c a v a t i o n s . At the s c a l e of these s m a l l e x c a v a t i o n s , deformation of the i n t a c t rock i s much l e s s s i g n i f i c a n t than deformation a l o n g d i s c o n t i n u i t i e s i n the rock. In l a r g e s l o p e s , the s t r e n g t h and deformation c h a r a c t e r i s t i c s o f both the rock m a t e r i a l and rock mass w i l l c o n t r i b u t e t o s t a b i l i t y . In a d d i t i o n , i n c r e a s e d c o n f i n i n g s t r e s s e s w i l l i n c r e a s e the s t r e n g t h of d i l a t i v e j o i n t s . Although t h e r e are s e v e r a l q u a l i t a t i v e d e s c r i p t i o n s of l a r g e s c a l e t o p p l e s i n the l i t e r a t u r e (Tabor, 1971; de F r i e t a s and Watters, 1973; Bovis, 1982; Holmes and J a r v i s , 1985; Evans, 1987; P r i t c h a r d e t . a l . , 31 1988), no a n a l y s i s o f these s l o p e s t h a t i n c o r p o r a t e s the i n f l u e n c e o f the rock m a t e r i a l o r rock mass s t r e n g t h has y e t been attempted. 2.6.6 Groundwater To date, no r e s e a r c h e r working on t o p p l i n g s l o p e s has c o n s i d e r e d the heterogeneous, a n i s o t r o p i c nature o f h y d r a u l i c c o n d u c t i v i t y i n bedded d e p o s i t s . A more d e t a i l e d treatment of the groundwater flow may not be necessary i n s m a l l e r t o p p l i n g s l o p e s , but i t may be r e q u i r e d f o r r e a l i s t i c m o d e l l i n g o f l a r g e r mountain s c a l e t o p p l e s . 32 3. D i s t i n c t Element Method 3.1 I n t r o d u c t i o n : UDEC The u n i v e r s a l d i s t i n c t element code (UDEC) marketed by I t a s c a C o n s u l t a n t s was purchased f o r t h i s r e s e a r c h program. The h i s t o r i c development and c a p a b i l i t i e s o f t h i s program and i t s p a r t i c u l a r advantages f o r m o d e l l i n g j o i n t e d rock systems are reviewed i n s e c t i o n 2.4.5. The remainder o f t h i s chapter d i s c u s s e s the theory, f e a t u r e s , and l i m i t a t i o n s of the program. UDEC i s a ve r y comprehensive m o d e l l i n g package w i t h many f e a t u r e s . Only the f e a t u r e s used i n t h i s r e s e a r c h program are d i s c u s s e d i n t h i s chapter. Readers i n t e r e s t e d i n a more complete g e n e r a l d e s c r i p t i o n of the program are r e f e r r e d t o Lemos e t a l . (1985). The g e n e r a l r e f e r e n c e s used i n the f o l l o w i n g d i s c u s s i o n are: C u n d a l l (1987), I t a s c a (1989), L o r i g (1984), and Cu n d a l l e t a l . (1978). UDEC i s w r i t t e n i n FORTRAN77 and i s a v a i l a b l e i n source code or executable form. T h i s r e s e a r c h uses UDEC v e r s i o n 1.5 r e l e a s e d March, 1989. I t i s compiled f o r o p e r a t i o n on an 80386-based microcomputer running D0S3.X, u s i n g SVS FORTRAN 386, the PHARLAP l i n k e r , and ICG X-AM DOS extender ( I t a s c a , 1989) . Screen g r a p h i c s support i s handled through a FORTRAN-l i n k a b l e l i b r a r y (SCITECH p l o t t i n g package) ( I t a s c a , 1989). The v e r s i o n used f o r t h i s r e s e a r c h was compiled t o u t i l i z e approximately f o u r megabytes of RAM, and a math cop r o c e s s o r . 33 With t h i s amount of memory a problem s i z e o f approximately 2500 r i g i d b l o c k s or 1000 f u l l y deformable b l o c k s can be used. 3.2 Theory of D i s t i n c t Element Method The d i s t i n c t element method i s based on a discontinuum approach t o rock mass m o d e l l i n g t h a t a l l o w s a j o i n t e d rock mass t o be re p r e s e n t e d by d i s t i n c t b l o c k s t h a t i n t e r a c t along t h e i r boundaries. In a d d i t i o n t o the discontinuum m o d e l l i n g of the b l o c k i n t e r a c t i o n , each b l o c k can be allowed t o deform as a continuum modelled by f i n i t e d i f f e r e n c e s ( F i g . 3.1a). 3.2.1 E x p l i c i t S o l u t i o n Procedure Deformation i s determined by u s i n g an e x p l i c i t s o l u t i o n procedure time s t e p p i n g a l g o r i t h m . In an e x p l i c i t method, a l l q u a n t i t i e s on one s i d e of a l l equations are known and a simple c a l c u l a t i o n produces the q u a n t i t y a t the next time s t e p . In UDEC the q u a n t i t i e s c a l c u l a t e d are incremental displacements or s t r a i n s . The technique r e l i e s on the f a c t t h a t i t takes a f i n i t e time f o r a displacement t o pass through the system of b l o c k s . I f the time step i s s m a l l enough such t h a t a displacement cannot propagate from one b l o c k t o an ad j a c e n t b l o c k i n one time step, then the equations of motion f o r a l l b l o c k s become uncoupled and the numerical procedure i s s t a b l e . When continuum f i n i t e d i f f e r e n c e zones are a p p l i e d w i t h i n the 34 D i s t i n c t E l e m e n t M o d e l F i g u r e 3 . 1 a N a t u r e o f D i s t i n c t E l e m e n t M o d e l ( a f t e r I t a s c a , 1989) C o n s t i t u t i v e R e l a t i o n S t r e s s D i s p l a c e m e n t o r S t r a i n Law o f M o t i o n u — F o r c e Mass u i n t e g r a t e d t w i c e F i g u r e 3 . 1 b D i s t i n c t E l e m e n t M o d e l C a l c u l a t i o n C y c l e ( a f t e r C u n d a l l e t . a l . , 1977) 35 b l o c k s , the time step a l s o becomes dependent on the p r o p a g a t i o n of i n f o r m a t i o n between adjacent zones w i t h i n the b l o c k . Determination of the r e q u i r e d time step i s based on the mass and m a t e r i a l s t i f f n e s s of b l o c k s or zones. The main disadvantage of t h i s method of s o l u t i o n i s the s m a l l time step r e q u i r e d . The program i t e r a t e s by u s i n g f o r c e displacement laws t o determine the net f o r c e on each b l o c k r e s u l t i n g from the i n f l u e n c e of surrounding b l o c k s and a b l o c k s own weight. I t then uses these f o r c e s and the time step t o determine b l o c k a c c e l e r a t i o n s and displacements. The c y c l e r e p e a t s i t s e l f when the increment of displacement i s used t o r e e v a l u a t e the f o r c e s on each b l o c k . T h i s procedure i s d i a g r a m m a t i c a l l y i l l u s t r a t e d i n F i g u r e 3.1b. The user i s r e s p o n s i b l e f o r d e t e r m i n i n g when the problem e i t h e r s t a b i l i z e s or f a i l s . T h i s i s achieved by m o n i t o r i n g time h i s t o r i e s of displacements, v e l o c i t i e s , or any of s e v e r a l other parameters s e l e c t e d by the user w i t h i n the problem. 3.2.2 Equations of Motion and System Damping The s o l u t i o n process d e s c r i b e d i n the p r e v i o u s s e c t i o n i s known as dynamic r e l a x a t i o n and was f i r s t d e s c r i b e d by O t t e r e l . a l . (1966). In dynamic r e l a x a t i o n the b l o c k s are moved a c c o r d i n g t o Newton's second law of motion, which i s j u s t i f i e d 36 on p h y s i c a l grounds (Cundall, 1987). T h i s law can be w r i t t e n i n the form: <3u = Z [1] dt m where F= f o r c e m= mass u= v e l o c i t y t= time U s i n g c e n t r a l d i f f e r e n c e theory we can w r i t e the above equation as: u ( t + At/2) = - u ( t - At/2) + £ t ) A t [ 2 ] m W r i t t e n f o r a b l o c k w i t h g r a v i t y (g^) i n c l u d e d t h i s e quation becomes: A (t + At/2) = u (t - At/2) + ( fiE^t) + A t X X HI «- J where i denotes a d i r e c t i o n a l index u^= the v e l o c i t y o f the c e n t e r of mass and g x= o Note t h a t t h i s c e n t r a l d i f f e r e n c e i n t e g r a t i o n assumes t h a t a c c e l e r a t i o n i s constant over a time increment from (t - At/2) t o (t + A t / 2 ) . By i n t e g r a t i n g the e x p r e s s i o n f o r v e l o c i t y a t the h a l f time st e p over the i n t e r v a l (t) t o (t + A t ) , i n cremental 37 displacement (u^) of the b l o c k i s determined. T h i s i s then used t o o b t a i n the new b l o c k l o c a t i o n ( x ^ ) : x . ( t + At) = x . ( t ) + ^ . ( t + At/2) A t [ 4 ] The development i s s i m i l a r f o r r o t a t i o n a l motions of the b l o c k s . R o t a t i o n a l v e l o c i t i e s a t the h a l f timestep are g i v e n by: 0 ( t + At/2) = 0 ( t - At/2) + s M ( t ) A t [ 5 ] I where 0 = angular v e l o c i t y of b l o c k about i t s c e n t r o i d I = moment of i n e r t i a of b l o c k about i t s c e n t r o i d EM = sum of the moments about the b l o c k c e n t r o i d R o t a t i o n a l displacements are g i v e n by: 0 . ( t + At) = e . ( t ) + e . . ( t + At/2) A t [ 6 ] For s t a t i c s o l u t i o n s , some form of energy d i s s i p a t i o n or damping must be i n c l u d e d t o prevent the system from o s c i l l a t i n g i n d e f i n i t e l y . UDEC uses e i t h e r mass p r o p o r t i o n a l or s t i f f n e s s p r o p o r t i o n a l damping. Each of these s i m u l a t e v i s c o u s dashpots at t a c h e d t o the system. Mass p r o p o r t i o n a l dampens the system t o an a b s o l u t e frame of r e f e r e n c e , and i s a k i n t o immersing the whole system i n a v i s c o u s f l u i d . S t i f f n e s s p r o p o r t i o n a l damping i s a r e l a t i v e damping technique t h a t a p p l i e s dashpots o n l y a c r o s s c o n t a c t s between b l o c k s . Only mass p r o p o r t i o n a l damping i s used i n t h i s r e s e a r c h program. * 38 In mass p r o p o r t i o n a l damping, the dashpots generate a f o r c e t h a t opposes the b l o c k s v e l o c i t y and i s p r o p o r t i o n a l t o the b l o c k v e l o c i t y and mass. The equation of motion i s m o d i f i e d as f o l l o w s t o i n c l u d e v i s c o u s damping. — = — - cm + g [7] dt m ^ where a i s the damping f a c t o r In f i n i t e d i f f e r e n c e n o t a t i o n centered a t time t v e l o c i t y a t the h a l f time step becomes: u ( t + A t / 2 ) = { { l ( t - A t / 2 ) ( 1 _ a A t ) + ( F _ + g ) A t } / ( l + «At/2) [8] 2 m R o t a t i o n s are damped i n a s i m i l a r manner ( I t a s c a , 1989). T h i s scheme of damping i s not without d i f f i c u l t i e s . A p p l y i n g v e l o c i t y p r o p o r t i o n a l damping t o b l o c k s t h a t are moving a t a constant v e l o c i t y generates erroneous body f o r c e s opposing the d i r e c t i o n of motion of the b l o c k . These s p u r i o u s body f o r c e s may a f f e c t the s o l u t i o n (Cundall, 1987). UDEC p a r t i a l l y overcomes t h i s problem by a d j u s t i n g the damping f a c t o r based on the sum of the change i n k i n e t i c energy i n the system i n a time ste p . The damping f a c t o r i s a d j u s t e d each time s t e p t o m a i n t a i n a p r e s c r i b e d r a t i o (R) of power adsorbed by damping i n the system t o t o t a l change i n k i n e t i c energy i n the system. As the a c c e l e r a t i o n of a system of b l o c k s reduces 39 t o zero, the damping f a c t o r a l s o reduces t o zero. Experience has shown t h a t a d j u s t i n g the damping f a c t o r t o m a i n t a i n R a t approximately 0.5 produces a damping e f f e c t t h a t approaches c r i t i c a l damping ( L o r i g , 1984). In p r a c t i c e t h i s i s onl y a p a r t i a l s o l u t i o n . In systems with a s i g n i f i c a n t v a r i a t i o n i n b l o c k s i z e o r motion, l a r g e a c c e l e r a t i n g b l o c k s w i l l have a d i s p r o p o r t i o n a t e a f f e c t on the sum of the k i n e t i c energy term, and the damping f a c t o r w i l l be weighted t o these b l o c k s . In such a system, s m a l l b l o c k s moving a t a constant v e l o c i t y w i l l s t i l l e x perience s p u r i o u s body f o r c e s . 0 Manual damping i s a l s o a v a i l a b l e f o r dynamic s i m u l a t i o n s . A d e s c r i p t i o n o f how the damping f a c t o r can be determined manually f o r mass or s t i f f n e s s p r o p o r t i o n a l damping i s g i v e n by C u n d a l l e t a l . (1978) and L o r i g (1984). 3.3 Features of UDEC 3.3.1 Block I n t e r f a c e C o n s t i t u t i v e R e l a t i o n s UDEC has two b u i l t i n i n t e r f a c e , o r j o i n t c o n s t i t u t i v e r e l a t i o n s h i p s . The o r i g i n a l j o i n t r e l a t i o n s h i p i s l i n e a r e l a s t i c - p l a s t i c . A c o n t i n u o u s l y y i e l d i n g j o i n t model t h a t i s capable of m o d e l l i n g p r o g r e s s i v e damage of the j o i n t due t o s h e a r i n g has a l s o been i n c o r p o r a t e d i n the program (Cundall 40 and Lemos, 1988). Only the o r i g i n a l j o i n t r e l a t i o n s h i p i s used i n t h i s r e s e a r c h . In the o r i g i n a l j o i n t r e l a t i o n s h i p , the d e f o r m a b i l i t y and f r i c t i o n a l c h a r a c t e r i s t i c s of b l o c k i n t e r f a c e s are rep r e s e n t e d by s p r i n g - s l i d e r systems l o c a t e d a t the c o n t a c t p o i n t s between b l o c k s . Incremental normal and shear f o r c e s ( A F n , A F S) are r e l a t e d t o the incremental r e l a t i v e displacement ( A u n, Au s) u s i n g l i n e a r f o r c e displacement laws: A F n = K n A u n [9] A F S = K s A u s [10] where K n and K s are the c o n t a c t normal and shear s t i f f n e s s e s . A mechanical r e p r e s e n t a t i o n of t h i s model i s shown i n F i g u r e 3 . 2a. Edge t o edge j o i n t c o n t a c t s are rep r e s e n t e d by two co r n e r t o edge c o n t a c t s , w i t h the f o r c e a p p l i e d a t each c o r n e r d i s t r i b u t e d over a c o n t a c t l e n g t h L as shown i n F i g u r e s 3.2b and 3.2c. The normal and shear s t r e s s a c r o s s each c o n t a c t (Acr n , A C T s ) are r e l a t e d t o displacement i n the same manner as f o r c e a c r o s s a s i n g l e c o n t a c t above: A a n = k n A u n [11] A C T s = k s A u s [12] where k n and k s are the normal and shear s t i f f n e s s e s expressed i n s t r e s s / l e n g t h r a t h e r than f o r c e / l e n g t h . 41 J2VW-1 Ks I l H >JJ K I I I Normal I n t e r a c t i o n Shear I n t e r a c t i o n c ) \ / \ / \ / \ /c 3 , — \ -—< C4 / / 1 / / 1 / / 1 / 1 I — * M F i g u r e 3 . 2 a ) M e c h a n i c a l R e p r e s e n t a t i o n o f I n t e r f a c e s i n D i s t i n c t E l e m e n t M o d e l b ) Edge t o Edge C o n t a c t c ) C o n t a c t L e n g t h f o r F u l l y D e f o r m a b l e B l o c k s ( a f t e r I t a s c a , 1989) 42 F i g u r e 3.2c a l s o i l l u s t r a t e s how e x t e r i o r g r i d p o i n t s on b l o c k s r e s u l t i n g from i n t e r n a l d i s c r e t i z a t i o n are modelled. These g r i d p o i n t s are t r e a t e d as new c o r n e r s , and the e x p r e s s i o n s d i s c u s s e d above are a p p l i e d . M e c h a n i c a l l y , the o v e r l a p of two b l o c k s i s p r o p o r t i o n a l t o the normal f o r c e or s t r e s s on the c o n t a c t . In the i t e r a t i v e c y c l e of the program, a change i n o v e r l a p i s used t o update the c o n t a c t f o r c e s or s t r e s s e s , which are then used t o determine new b l o c k a c c e l e r a t i o n s . The main d i f f e r e n c e between normal and shear behaviour of the j o i n t s i s the i n c o r p o r a t i o n of a peak e l a s t i c s t r e n g t h i n shear. The peak s t r e n g t h of the j o i n t i s l i m i t e d by a Mohr-Coulomb f r i c t i o n law: |CTs| < c + c r n t a n 4> [ 1 3 ] where c and <f> are the j o i n t cohesion and f r i c t i o n angle. T e n s i l e s t r e n g t h normal t o the j o i n t can be i n c l u d e d , and d i l a t i o n can be added as an increment t o the j o i n t f r i c t i o n angle. The b i l i n e a r e l a s t i c - p l a s t i c model behaviour d e s c r i b e d above i s a s i m p l i f i c a t i o n of r e a l j o i n t behaviour and has l i m i t a t i o n s . In r e a l i t y both shear and normal s t i f f n e s s i n c r e a s e w i t h the c o n f i n i n g s t r e s s on a j o i n t , and r e a l j o i n t s u s u a l l y do not d i s p l a y instantaneous p l a s t i c shear a t the peak 4 3 s t r e n g t h . In r e a l j o i n t s , p l a s t i c displacement begins t o accumulate b e f o r e the peak shear s t r e n g t h i s reached, and the shear s t r e s s r e q u i r e d f o r continuous p l a s t i c shear i s o f t e n c o n s i d e r a b l y l e s s than the peak shear s t r e n g t h . F i g u r e s 3.3a and 3.3b i l l u s t r a t e how the model d i f f e r s from r e a l j o i n t behaviour. The c o n t i n u o u s l y y i e l d i n g j o i n t model mentioned a t the beg i n n i n g of t h i s s e c t i o n i s designed t o more r e a l i s t i c a l l y model j o i n t behaviour. L i k e the o r i g i n a l model, normal and shear s t r e s s e s are r e l a t e d through j o i n t s t i f f n e s s e s t o displacements. In the c o n t i n u o u s l y y i e l d i n g model the normal and shear s t i f f n e s s e s i n c r e a s e w i t h c o n f i n i n g s t r e s s , and the continuous accumulation of p l a s t i c shear begins b e f o r e the peak shear s t r e n g t h i s reached. The model a l s o a l l o w s the shear s t r e s s i n the post peak p l a s t i c r e g i o n t o drop below the peak shear s t r e s s . (Cundall e t a l . , 1978; C u n d a l l and Hart, 1984; C u n d a l l and Lemos, 1988; and I t a s c a , 1989) 3.3.2 Block D e f o r m a b i l i t y and C o n s t i t u t i v e R e l a t i o n s Three types of b l o c k d e f o r m a b i l i t y are a v a i l a b l e i n UDEC: r i g i d , simply deformable, and f u l l y deformable. In a system comprised of r i g i d b l o c k s , a l l the deformation i s accommodated by normal and shear displacement on the j o i n t s . The b l o c k s have two t r a n s l a t i o n a l and one r o t a t i o n a l degrees of freedom, but the geometry of the b l o c k s does not change. 44 Figure 3.3a) E l a s t i c - P l a s t i c J o i n t Model b) T y p i c a l J o i n t Behaviour T h i s type of a n a l y s i s i s a p p r o p r i a t e when the i n t a c t rocks e l a s t i c deformation i s n e g l i g i b l e compared t o deformation on d i s c o n t i n u i t i e s . Simply deformable b l o c k s add t h r e e more i n t e r n a l degrees of freedom corresponding t o t h r e e s t r a i n s i n two dimensions ( e x x , e y y e x y + e y x ) ' a n < ^ i n c o r p o r a t e the a b i l i t y t o f r a c t u r e based on G r i f f i t h ' s t heory (Cundall e t a l . , 1978; C u n d a l l and M a r t i , 1979; and W i l l i a m s and Mustoe, 1987). The aim of t h i s f o r m u l a t i o n i s t o i n c o r p o r a t e b l o c k deformation, but a v o i d computer i n t e n s i v e f u l l y deformable b l o c k s . Because t h i s type of b l o c k i s c o n s t r a i n e d t o the combined degrees of freedom o u t l i n e d above, they are not as a c c u r a t e as f u l l y deformable b l o c k s and are not used i n t h i s r e s e a r c h . F u l l y deformable b l o c k s are a p p r o p r i a t e when c o n f i n i n g s t r e s s e s or t r a n s i e n t loads are h i g h enough t h a t i n t e r n a l b l o c k deformation i s s i g n i f i c a n t r e l a t i v e t o b l o c k displacements and j o i n t deformations. In t h i s f o r m u l a t i o n i n d i v i d u a l b l o c k s are d i s c r e t i z e d i n t o t r i a n g u l a r f i n i t e d i f f e r e n c e zones and modelled as a continuum. The s o l u t i o n method i s e x p l i c i t , d i f f e r e n c e s are ce n t e r e d i n time and space, and plane s t r a i n c o n d i t i o n s are assumed (Cundall e t a l . , 1978). The g e n e r a l s o l u t i o n sequence f o r a g r i d p o i n t formed by the t r i a n g u l a r zoning i s as f o l l o w s . In each time step, s t r e s s e s 46 are i n t e g r a t e d about the g r i d p o i n t t o determine a r e s u l t a n t f o r c e from surrounding zones. To t h i s i s added the t o t a l of any e x t e r n a l f o r c e s from b l o c k c o n t a c t s or otherwise. Net a c c e l e r a t i o n i s obtained by d i v i d i n g the net f o r c e by the lumped mass a t the g r i d p o i n t and adding g r a v i t a t i o n a l a c c e l e r a t i o n . The equation of motion can be w r i t t e n as f o l l o w s : 5Uj a t j d s + F i [14] m where s= the s u r f a c e e n c l o s i n g the mass m lumped a t a g r i d p o i n t nj= the u n i t normal t o s, F^= the r e s u l t a n t of a l l e x t e r n a l f o r c e s a p p l i e d t o the g r i d p o i n t g^= g r a v i t a t i o n a l a c c e l e r a t i o n , and i and j are d i r e c t i o n a l i n d i c e s . In a s i m i l a r manner t o the equation of motion f o r b l o c k s , c e n t r a l d i f f e r e n c e s are a p p l i e d t o the a c c e l e r a t i o n s of g r i d p o i n t s t o determine v e l o c i t i e s and r e l a t i v e d i s p l a c e m e n t s . The b a s i c d e f i n i t i o n s of two dimensional s t r a i n a re used t o r e l a t e zone s t r a i n s and r o t a t i o n s t o nodal displacements as f o l l o w s : i j = 2 ( d i , J + d J , i } [15] 0 i j = 2 ( ^ < 3 " i J » i ) [16] 47 where u= r e l a t i v e displacement i and j are d i r e c t i o n a l i n d i c e s comma i or j ( i e : , i or ,j) denotes a p a r t i a l d e r i v a t i v e with r e s p e c t t o i or j , and the dots are time d e r i v a t i v e s . A d e t a i l e d d e s c r i p t i o n of how the s t r a i n components f o r the constant s t r a i n elements are determined from the displacement of the surrounding nodes i s g i v e n by C u n d a l l e t a l . (1978). The s t r a i n components i n a zone are used t o determine zone s t r e s s e s by the b l o c k c o n s t i t u t i v e r e l a t i o n s . The standard s t r e s s - s t r a i n f o r m u l a t i o n f o r a l i n e a r homogeneous i s o t r o p i c m a t e r i a l i s used. The r e l a t i o n s h i p i s used i n an incremental form and r e s t r i c t e d t o plane s t r a i n c o n d i t i o n s . The equation i s : e A r ^ j = A A e v 5 ^ j + 2/iAe^j [17] where A,/z are the Lame consta n t s , e A r ^ j are the e l a s t i c increments o f the s t r e s s t e n s o r , A s ^ j are the incremental s t r a i n s , A s v = the increment of v o l u m e t r i c s t r a i n ( A e - ^ + A t ^ ) S J L J = Kronecker d e l t a f u n c t i o n . In UDEC, two c o n s t i t u t i v e r e l a t i o n s h i p s f o r f u l l y deformable b l o c k s are a v a i l a b l e . Both use the above s t r e s s - s t r a i n r e l a t i o n s h i p , but one i n c o r p o r a t e s s t r e n g t h l i m i t s i n the rock d e f i n e d by a Mohr-Coulomb envelope. With t h i s f o r m u l a t i o n , 48 the rock deforms e l a s t i c a l l y up t o the s t r e n g t h l i m i t and p l a s t i c a l l y p a s t t h i s p o i n t . The user d e f i n e s the envelope by s e l e c t i n g the rock i n t e r n a l f r i c t i o n angle, cohesion, t e n s i l e s t r e n g t h , and d i l a t i o n angle. The s t r e s s increments determined i n Eq. [17] are used t o update s t r e s s e s i n the elements, and the c y c l e r e p e a t s i t s e l f when these element s t r e s s e s are used i n Eq. [14] t o determine nodal a c c e l e r a t i o n s . 3.4 L i m i t a t i o n s of UDEC There are a few l i m i t a t i o n s b u i l t i n t o the r e l a t i o n s h i p s used i n UDEC. At the moment the c o n s t i t u t i v e r e l a t i o n s h i p f o r the i n t a c t rock i s l i m i t e d t o a l i n e a r e l a s t i c - p l a s t i c a n a l y s i s of homogeneous i s o t r o p i c b l o c k s . In models wi t h l a r g e and sm a l l b l o c k s undergoing d i f f e r e n t a c c e l e r a t i o n s , the v e l o c i t y p r o p o r t i o n a l damping used i n UDEC can c r e a t e s p u r i o u s f o r c e s i n the system (Sec. 3.2.2). These a r t i f i c i a l f o r c e s can a f f e c t the s o l u t i o n of the problem i n some systems. 49 With v e r y l a r g e problems e x e c u t i o n time i s s t i l l a l i m i t i n g f a c t o r . The s i z e of problem t h a t can be run i s not l i m i t e d by computer memory as much as by computational speed. Probably the two f a c t o r s t h a t have the most impact on the e f f e c t i v e n e s s o f UDEC are the accuracy of i n p u t parameters, and the u s e r s ' a b i l i t y t o i n t e r p r e t the r e s u l t s o f the a n a l y s i s . U sing the f u l l c a p a b i l i t i e s of UDEC t o a c c u r a t e l y s o l v e a rock mechanics problem o f t e n r e q u i r e s complete knowledge of the rock and j o i n t s t r e n g t h s and e l a s t i c p r o p e r t i e s . With most e n g i n e e r i n g problems, economics p r e c l u d e the s i t e c h a r a c t e r i z a t i o n r e q u i r e d t o a c c u r a t e l y determine these parameters. UDEC i s an i n t e r a c t i v e program t h a t r e l i e s on the user t o assess the performance of the model. I t i s d e c e p t i v e l y easy t o use, but the w e l l developed i n t e r a c t i v e g r a p h i c s and program output can i n s t i l l a f a l s e sense o f c o n f i d e n c e i n an u n s k i l l e d user. The user must be f a m i l i a r w i t h rock mechanics, e l a s t i c theory, and the c a p a b i l i t i e s and l i m i t a t i o n s o f the d i s t i n c t element method t o c o r r e c t l y assess the performance of a model. Without a thorough understanding of a l l o f these areas, i t i s p o s s i b l e t o s e r i o u s l y m i s i n t e r p r e t the program output. 50 4.0 M o d e l l i n g T o p p l i n g w i t h UDEC 4.1 I n t r o d u c t i o n The l i t e r a t u r e review i n chapter 2 shows t h a t a d i s t i n c t element program such as UDEC has been used t o model b l o c k t o p p l i n g , and concludes t h a t i t should be a b l e t o model both b l o c k and f l e x u r a l modes of t o p p l i n g . The unique combination of discontinuum and continuum methods of s o l u t i o n i n UDEC should make the program w e l l s u i t e d f o r m o d e l l i n g f l e x u r a l modes of t o p p l i n g . The t h e o r e t i c a l b a s i s o f UDEC has been tho r o u g h l y v a l i d a t e d a g a i n s t exact a n a l y t i c a l s o l u t i o n s by e a r l i e r r e s e a r c h e r s ( C u n d a l l , 1971; Cu n d a l l e t a l . , 1978; C u n d a l l , 1983; C u n d a l l , 1985; C u n d a l l and Lemos, 1988). The aim of t h i s c h apter i s t o demonstrate t h a t UDEC can be used t o a c c u r a t e l y model both b l o c k and f l e x u r a l types of t o p p l i n g a f f e c t i n g engineered s l o p e s . Block t o p p l i n g i s modelled by r e p e a t i n g an example of the l i m i t e q u i l i b r i u m method of a n a l y s i s f i r s t r e p o r t e d i n Goodman and Bray (1976). T h i s example has a l s o been e v a l u a t e d u s i n g a pre d e c e s s o r of UDEC (Cundall e t a l . , 1978). UDEC i s a p p l i e d t o t h i s example and the r e s u l t s compared wi t h the e a r l i e r a n a l y s e s . 51 Examples of f l e x u r a l t o p p l i n g are not as common as b l o c k t o p p l i n g i n the l i t e r a t u r e . The few examples r e p o r t e d e i t h e r i n v o l v e u n d e s i r a b l e c o m p l i c a t i o n s , o r do not r e p o r t the rock s t r e n g t h o r geometric parameters necessary t o a c c u r a t e l y formulate the problem i n a d i s t i n c t element model. For these reasons the examples s e l e c t e d and modelled w i t h UDEC i n S e c t i o n 4.3 are not d e f i n i t i v e . These models demonstrate t h a t UDEC i s ab l e t o reproduce the deformations observed i n the example s l o p e s u s i n g reasonable e s t i m a t e s of mechanical and geometric parameters. T h i s v e r i f i c a t i o n i s necessary b e f o r e proceeding w i t h the a n a l y s i s of t o p p l i n g i n n a t u r a l s l o p e s where measurement of mechanical p r o p e r t i e s of rock m a t e r i a l and rock mass, and the a b i l i t y t o observe deformation p a t t e r n s are n e c e s s a r i l y compromised. 4.2 R i g i d B l o c k / F l e x u r a l T o p p l i n g Example A simple, h y p o t h e t i c a l example of b l o c k / f l e x u r a l t o p p l i n g was r e p o r t e d Goodman and Bray (1976) who a l s o a n alyzed i t u s i n g the l i m i t e q u i l i b r i u m method. C u n d a l l e t a l . (1978), used a pre d e c e s s o r o f UDEC t o analyze the same model. These s t u d i e s r e p o r t the f r i c t i o n angle along the s i d e s and base of the b l o c k s necessary t o ma i n t a i n s t a b i l i t y . T h i s s e c t i o n compares 52 these v a l u e s w i t h the l i m i t i n g f r i c t i o n angle f o r s t a b i l i t y determined w i t h UDEC. The model geometry and s c a l e are shown i n F i g u r e 4.1. The s i m p l i f i c a t i o n s and r e s t r i c t i o n s t h a t apply i n the l i m i t e q u i l i b r i u m method are simulated w i t h t h i s UDEC model. The r i g i d b l o c k model and the o r i g i n a l j o i n t model (Sec. 3.3.1) are used. The j o i n t s are assumed t o have no cohesion or t e n s i l e s t r e n g t h . G r a v i t y i s a p p l i e d t o the b l o c k s w h i l e the toe b l o c k i s h e l d f i x e d . Once the s l o p e i s s t a b l e under g r a v i t y , the toe b l o c k i s removed. The f r i c t i o n angle on the j o i n t s i s then changed i n an i t e r a t i v e manner t o i d e n t i f y the v a l u e a t which the s l o p e becomes u n s t a b l e . S t a b i l i t y of the s l o p e i s assessed by m o n i t o r i n g mechanical time h i s t o r i e s of the v e l o c i t i e s and displacements of the b l o c k s . F i g u r e s 4.2a and 4.2b are h i s t o r y p l o t s of mechanical time v e r s u s h o r i z o n t a l v e l o c i t y f o r the b l o c k c o r n e r l a b e l l e d HI i n F i g u r e 4.1. Note t h a t the o r d i n a t e s c a l e i n F i g u r e 4.2b i s d i f f e r e n t than i n F i g u r e 4.2a. F i g u r e 4.2a i s f o r a t r i a l t h a t d i d not f a i l . C h a r a c t e r i s t i c s of the h i s t o r y i n c l u d e i n i t i a l movement due t o toe b l o c k e x c a v a t i o n , and s t a b i l i t y shown by v e l o c i t i e s r e t u r n i n g t o 53 UDEC (Version 1.50J legend H i \ \ \ • 31/05/1989 15: 38 cycle 0 -1.565E+01 < x < 1.3B1E+02 -1.232E+02 < y < 3.051E+01 block plot l i n i i i m l n m m i l 0 2e 1 A^- Toe B l o c k Univ. of B r i t i s h Columbia F i g u r e 4 . 1 Geomet ry o f UDEC mode l f o r B l o c k T o p p l i n g Dept. of Geological Science UDEC (Version 1.50J legend 31/05/1989 16: 1 1 cycle 4000 -5.33E-03 <hiat 1> 1.01E-05 Ul UI Univ. of B r i t i s h Columbia Dept. of Geological Science (M0MK-3) UDEC (Version 1.50J legend 31/05/1989 IB: 50 cycle 17010 -4.76E-01 <hlst 1> 3.B0E-05 Univ. of B r i t i s h Columbia Dept. of Geological Science 1.0 2.0 3.0 -4.0 5.0 Figure 4.2b Horizontal V e l o c i t y vs. Mechanical Time at H^, F a i l i n g Slope ( H I O X H 0) zero. I n i t i a l movement wh i l e the problem was loaded under g r a v i t y w i t h the toe b l o c k i s not i n c l u d e d . F i g u r e 4.2b i s f o r a t r i a l t h a t d i d f a i l . Note t h a t the v e l o c i t i e s do not r e t u r n t o zero, but con t i n u e t o o s c i l l a t e i n d e f i n i t e l y . T h i s type o f o s c i l l a t i o n i s a t y p i c a l i n d i c a t i o n o f f a i l u r e f o r these t r i a l s . F i g u r e 4.3 demonstrates the deformation o f a f a i l i n g s l o p e a t a much l a t e r stage. Table 4.1 l i s t s the l i m i t i n g range o f v a l u e s f o r j o i n t f r i c t i o n angle determined w i t h UDEC, by Goodman and Bray (1976) and by Cu n d a l l e t a l . (1978). Note t h a t the l i m i t e q u i l i b r i u m a n a l y s i s produces one f r i c t i o n v a l u e , but due t o the nature o f the s o l u t i o n procedure, the d i s t i n c t element method produces a range of v a l u e s . T h i s range can be narrowed by f u r t h e r i t e r a t i o n . In these t r i a l s the range o f l i m i t i n g f r i c t i o n angle r e p o r t e d was i t e r a t e d t o w i t h i n 0.05 degrees. When rounded t o the f i r s t decimal p l a c e t h i s range can be expressed as a s i n g l e v a l u e (Table 4.1). The f r i c t i o n angle v a l u e s determined w i t h UDEC l i e w i t h i n the range determined by C u n d a l l e t a l . (1978), but do not correspond e x a c t l y t o the v a l u e determined w i t h the l i m i t e q u i l i b r i u m a n a l y s i s . One reason f o r t h i s s l i g h t d i f f e r e n c e i s the b l o c k geometry used i n the UDEC a n a l y s i s . 57 UDEC (Version 1.50) legend 7/06/1989 13: 27 c y c l e 127030 -1.5B5E+01 < X < -1.H32E+02 < y < 1.381E+02 3.0S1E+01 block p l o t I i i i n i n i l 0 2e 1 (Jl 03 v e l o c i t y v e c t o r s maximum - 9.458E-02 5e -1 U n i v . of B r i t i s h Columbia Dept . o f G e o l o g i c a l S c i e n c e Figure 4.3 Pattern of Deformation f o r F a i l i n g Slope In UDEC the corn e r s of b l o c k s are rounded t o f a c i l i t a t e the a n a l y s i s of b l o c k i n t e r a c t i o n mechanics. The b l o c k c o r n e r s are rounded w i t h a c i r c l e tangent t o each s i d e o f the corner, and the use r s e l e c t s the r a d i u s of the c i r c l e t o be used. Rounding the b l o c k c o r n e r s e f f e c t i v e l y reduces the width of the b l o c k s where they are i n c o n t a c t w i t h the f a i l u r e p lane. T h i s i n c r e a s e s the o v e r t u r n i n g moment, d e c r e a s i n g the s t a b i l i t y o f the bl o c k . As a r e s u l t , somewhat h i g h e r f r i c t i o n a ngles are r e q u i r e d along the s i d e s of the b l o c k t o m a i n t a i n s t a b i l i t y . The r e s u l t s from two s e t s o f t r i a l s w i t h UDEC u s i n g a rounding r a d i u s o f 0.1m and 0.01m are r e p o r t e d i n Table 4.1. A comparison o f the l i m i t i n g f r i c t i o n angle f o r each rounding l e n g t h v e r i f i e s t h a t when a s m a l l e r rounding l e n g t h i s used the b l o c k s are s t a b l e a t a lower f r i c t i o n angle. As a r e s u l t of the i n f l u e n c e of rounded c o r n e r s , the l i m i t i n g f r i c t i o n angle f o r s t a b i l i t y determined with UDEC i s s l i g h t l y more c o n s e r v a t i v e than the f r i c t i o n angle determined w i t h the l i m i t e q u i l i b r i u m method. 59 Table 4.1: Range of L i m i t i n g F r i c t i o n Angle f o r Block T o p p l i n g . F r i c t i o n angle range (deg.) Goodman and Bray (1976) C u n d a l l e t a l . (1978) UDEC (Round=.lm) UDEC (Round=.01m) 38.2 37.6 t o 38.7 38.4 38.3 The UDEC i n p u t f i l e used t o c r e a t e t h i s model i s g i v e n i n Appendix 1. 4.3 F l e x u r a l T o p p l i n g Examples A v a i l a b l e examples of f l e x u r a l t o p p l i n g are not w e l l enough d e f i n e d t o be used f o r a d e f i n i t i v e a n a l y s i s . For t h i s reason, the examples used i n t h i s s e c t i o n are onl y intended as a demonstration of the a b i l i t y of UDEC t o model f l e x u r a l t o p p l e s . The examples were chosen f o r t h e i r r e l a t i v e s i m p l i c i t y . Both are examples of p u r e l y f l e x u r a l t o p p l i n g u s i n g a simple s l o p e p r o f i l e , one rock type, and columns of a uniform width. 4.3.1 Base F r i c t i o n Model T h i s example of f l e x u r a l t o p p l i n g i s taken from a s e r i e s of model s t u d i e s w i t h a base f r i c t i o n t a b l e r e p o r t e d i n Kuykendall (1975) and H i t t i n g e r (1978). The base f r i c t i o n t a b l e i s comprised of a continuous sand paper b e l t d r i v e n a t a 60 c o n s t a n t v e l o c i t y . The model r e s t s on t h i s b e l t and i s c o n s t r a i n e d from moving wi t h the b e l t by a f i x e d b a r r i e r . When the b e l t i s i n motion, f r i c t i o n between the model and the sandpaper s i m u l a t e s body f o r c e s i n the model. For the s e r i e s of s t u d i e s r e p o r t e d i n Kuykendall (1975) and H i t t i n g e r (1978) a t h i n s l a b o f a sand, o i l , and f l o u r mixture was spread on the base f r i c t i o n t a b l e t o form the model. An i n i t i a l l y l a r g e r , r e c t a n g u l a r model was formed and " c o n s o l i d a t e d " by t u r n i n g on the machine. The machine was turned o f f w h i l e the sl o p e and d i s c o n t i n u i t i e s were cut, and turned back on f o r the t e s t ( H i t t i n g e r , 1978). The model s e l e c t e d f o r e v a l u a t i o n with UDEC i s shown i n F i g u r e 4.4. T h i s p a r t i c u l a r model was s e l e c t e d f o r study w i t h UDEC because i t f a i l e d along a w e l l developed f a i l u r e s u r f a c e w i t h s i g n i f i c a n t b l o c k r o t a t i o n . The geometry of t h i s model c o u l d not be reproduced a t the same s c a l e w i t h UDEC due t o problems with decimal p r e c i s i o n when d e s i g n a t i n g the b l o c k rounding l e n g t h . The model c r e a t e d with UDEC i s 100 times l a r g e r than the base f r i c t i o n model, but wi t h the same geometry ( F i g . 4.4). The dimensions o f the base f r i c t i o n model and the UDEC model are d e f i n e d i n Tab l e 4.2. 61 UDEC (Version 1.50) legend 14/06/1989 15: 16 c y c l e 2000 -3.B10E+00 < x < 8.001E+01 -6.015E+01 < y < H.367E+01 block p l o t 1 1 1 1 1 i 1 1 1 i 1 1 1 1 1 1 1 1 1 1 I 0 2a 1 Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science Figure 4.4 Geometry of Base F r i c t i o n Model and UDEC Model Table 4 . 2 : Geometry of Base F r i c t i o n Model and UDEC Model Parameter Base F r i c t i o n Model UDEC Model Slope Height (H) 1 2 inches 3 0 . 5 m Slope Face Angle (6) \ 7 8 degrees 7 8 degrees J o i n t I n c l i n a t i o n (from v e r t i c a l ) (a) 3 0 degrees 3 0 degrees Column Width (w) 2 inches 5 . 0 8 m The m o d e l l i n g procedure i s as f o l l o w s . A r e c t a n g u l a r b l o c k bounded by f i x e d support b l o c k s i s c r e a t e d . T h i s c e n t e r b l o c k i s then d i v i d e d by the 6 0 degree d i p p i n g j o i n t s e t and by a cr a c k t h a t i s used t o simulate the s l o p e f a c e . The angled b l o c k s t h a t form the sl o p e are d i v i d e d i n t o f i n i t e d i f f e r e n c e zones, and m a t e r i a l p r o p e r t i e s are a p p l i e d t o the zoned b l o c k s and the j o i n t s . I n i t i a l i n s i t u s t r e s s e s a t K Q = 1 . 0 are a p p l i e d i n the f u l l y deformable b l o c k s , and the system i s allowed t o come t o e q u i l i b r i u m under g r a v i t y . The s l o p e i s then excavated, and g r a v i t y i s a p p l i e d u n t i l s t a b i l i t y o r f a i l u r e i s achieved. The o n l y p h y s i c a l p r o p e r t y of the model m a t e r i a l r e p o r t e d i n H i t t i n g e r ( 1 9 7 8 ) i s the f r i c t i o n angle o f a c o h e s i o n l e s s j o i n t , which i s 3 9 degrees. T h i s j o i n t f r i c t i o n angle i s used i n the UDEC model. I t i s assumed t h a t the j o i n t s have no cohesion, t e n s i l e s t r e n g t h , or d i l a t i o n . 6 3 A l l o t h e r r e q u i r e d parameters i n the UDEC model are assumed. The e l a s t i c parameters used are i n the range of a t y p i c a l sandstone (Hunt, 1986). I n i t i a l l y the i n t a c t rock f r i c t i o n angle, cohesion and t e n s i l e s t r e n g t h are s e t l a r g e enough t h a t the excavated s l o p e w i l l be s t a b l e . The cohesion and t e n s i l e s t r e n g t h are then p r o g r e s s i v e l y lowered t o determine the l i m i t i n g v a l u e s f o r s t a b i l i t y . The i n t e r n a l f r i c t i o n angle i s f i x e d a t 39 degrees and d i l a t i o n equals zero. The range of v a l u e s t h a t w i l l produce the approximate f a i l u r e geometry of the base f r i c t i o n model i s r e p o r t e d i n T a b l e 4.3. At a cohesion of 0.09 MPa and a t e n s i l e s t r e n g t h of 0.10 MPa the s l o p e becomes u n s t a b l e . At these v a l u e s the f a i l u r e s u r f a c e e x i t s j u s t above the toe b l o c k and i s s l i g h t l y s t e e p e r than i n the base f r i c t i o n model. When cohesion and t e n s i l e s t r e n g t h are reduced f u r t h e r t o 0.06 and 0.075 MPa r e s p e c t i v e l y , the f a i l u r e s u r f a c e moves lower i n the s l o p e and b e t t e r approximates the base f r i c t i o n model f a i l u r e . 64 Table 4.3: Values o f UDEC Parameters f o r Base F r i c t i o n Model. M a t e r i a l Number | Parameter | Value Block Mat 1 Density (kg/m 3) Bulk Modulus (MPa) Shear Modulus (MPa) Cohesion (MPa) T e n s i l e S t r e n g t h (MPa) F r i c t i o n Angle (deg.) D i l a t i o n (deg.) 2600 10500 10000 0. 09 0.10 39 0 J o i n t Mat 1 F r i c t i o n Angle (deg.) Cohesion (MPa) T e n s i l e S t r e n g t h (MPa) D i l a t i o n (deg.) Normal S t i f f n e s s (MPa/m) Shear S t i f f n e s s (MPa/m) 39 0 0 0 15000 10000 F i g u r e s 4.5a and 4.5b compare the base f r i c t i o n model deformation t o the deformation produced by UDEC u s i n g the p h y s i c a l parameters l i s t e d i n Table 4.3 (cohesion and t e n s i l e s t r e n g t h reduced t o 0.06 and 0.075 MPa, r e s p e c t i v e l y ) . The magnitude and p a t t e r n of deformation i n the UDEC model are i l l u s t r a t e d i n F i g u r e 4.5b by contours o f h o r i z o n t a l displacement. R o t a t i o n i s accommodated a t the l o c a t i o n s where the columns f a i l forming a f a i l u r e plane t h a t has n e a r l y the same angle and p o s i t i o n as the f a i l u r e plane i n the p h y s i c a l model. The f a i l u r e c o n d i t i o n i n the UDEC model i s i n f e r r e d from time h i s t o r i e s of v e l o c i t i e s a t s e v e r a l l o c a t i o n s along the s l o p e f a c e , from the p a t t e r n and magnitude of v e l o c i t i e s i n the model, and from the a c t u a l deformation of the model. 65 UDEC (Version 1.50) l e g e n d 15/06/1989 09: 26 c y c l e 34250 2.000E+01 < x < 6.000E+01 -3.500E+01 < y < 5.000E+00 block p l o t I—i—i—i—i i i i i i I 0 l e 1 x- d l s p contours contour I n t e r v a l - 1.000E-01 number of c o n t o u r s / c o l o r - 2 min—1.100E+00 max—1.000E-01 -1.100E+00 -1.000E+00 -9.000E-01 -8.000E-01 -7.000E-01 -6.000E-01 -5.000E-01 -4.000E-01 -3.000E-01 -2.000E-01 -1.000E-01 -1.000E-01 c: k: -9.000E-01 -1.000E-01 Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science F i g u r e 4 . 5 b UDEC S i m u l a t i o n of Base F r i c t i o n Model D e f o r m a t i o n 4.3.2 Brenda Mine The p r e v i o u s example demonstrates the a b i l i t y o f UDEC t o reproduce the geometry of f a i l u r e seen i n a base f r i c t i o n model of f l e x u r a l t o p p l i n g . In t h i s s e c t i o n a l a r g e r , engineered s l o p e t h a t i s known t o be s u s c e p t i b l e t o t o p p l i n g i s modelled u s i n g UDEC. The purpose of t h i s model i s t o demonstrate t h a t UDEC can sim u l a t e f l e x u r a l t o p p l i n g i n a r e a l s l o p e u s i n g reasonable rock and j o i n t s t r e n g t h parameters, and t o i l l u s t r a t e t h a t l a r g e r s c a l e t o p p l e s behave d i f f e r e n t l y than s m a l l e r t o p p l e s . The s l o p e chosen f o r t h i s study i s the east/west t r e n d i n g south w a l l o f the Brenda Mine i n Peachland, B r i t i s h Columbia. The o r i g i n a l s l o p e experienced s i g n i f i c a n t t o p p l i n g deformation when mined a t 4 0 degrees t o a depth of approximately 200 meters. Water p r e s s u r e i s c o n s i d e r e d t o be a s i g n i f i c a n t f a c t o r i n the s t a b i l i t y o f t h i s s l o p e ( P i t e a u and Assoc., 1988). T h i s s l o p e i s c u r r e n t l y b e i n g d e p r e s s u r i z e d , s e t back and re-benched a t an o v e r a l l s l o p e angle o f 4 5 degrees. The rock forming the s l o p e i s hard, f r a c t u r e d quartz d i o r i t e w i t h t h r e e major d i s c o n t i n u i t y s e t s . Set A d i s c o n t i n u i t i e s are continuous gouge f i l l e d f a u l t s t h a t t r e n d approximately 68 east/west, d i p from 7 0 t o 80 degrees south, and have an estimated s p a c i n g of 15 t o 27 meters i n the v i c i n i t y of the south w a l l . Set B c o n s i s t s of j o i n t s and f a u l t s which s t r i k e approximately north/south and d i p moderately t o s t e e p l y t o the n o r t h e a s t . Set C are east/west t r e n d i n g j o i n t s t h a t d i p from 23 t o 50 degrees t o the n o r t h ( P i t e a u and Assoc., 1988) T o p p l i n g motion of the o r i g i n a l w a l l i s accommodated by f l e x u r a l s l i p along the gouge f i l l e d , east-west t r e n d i n g f a u l t s of Set A. I t i s a l s o b e l i e v e d t h a t these f a u l t s a c t as low p e r m e a b i l i t y b a r r i e r s t o groundwater ( P i t e a u and Assoc., 1988). The UDEC s i m u l a t i o n c o n s i d e r s the s t a b i l i t y of the new 45 degree s l o p e . I t i s assumed t h a t the Set A f a u l t s d i v i d e the s l o p e i n t o i n c l i n e d columns ( P i t e a u and Assoc., 1988). Although a r e a l s l o p e i s used, a l l of the rock and j o i n t s t r e n g t h parameters i n t h i s a n a l y s i s are i n i t i a l l y unknown. The procedure i s s i m i l a r t o t h a t used f o r the p h y s i c a l model i n the p r e v i o u s s e c t i o n . The model i s c r e a t e d by d i v i d i n g a l a r g e r e c t a n g u l a r domain i n t o i n c l i n e d b l o c k s , d e f i n e d by the Set A f a u l t s . A d i p of 80 degrees and s p a c i n g of 27 meters are chosen f o r these f a u l t s . These b l o c k s are f u r t h e r d i v i d e d f o r l a t e r e x c a v a t i o n of the s l o p e f a c e . The b l o c k s are zoned and m a t e r i a l p r o p e r t i e s are a p p l i e d t o the zoned b l o c k s and j o i n t s . The boundaries of the domain are f i x e d and g r a v i t y i s 69 a p p l i e d t o s t r e s s the domain. Once the s t r e s s e s i n the domain have come t o e q u i l i b r i u m , the s l o p e i s excavated two benches at a time t o the f i n a l depth. The s t r e s s e s i n the s l o p e are allowed t o come t o e q u i l i b r i u m between e x c a v a t i o n s . I n i t i a l l y the j o i n t f r i c t i o n angle i s s e t a t a v a l u e t h a t ensures the s l o p e w i l l be s t a b l e a t the f i n a l e x c a v a t i o n l e v e l . Once a t the f i n a l e x c a v a t i o n l e v e l , the j o i n t f r i c t i o n angle i s i t e r a t e d t o determine the l i m i t i n g v a l u e . The UDEC in p u t f i l e f o r t h i s model i s g i v e n i n Appendix 1. The zoned b l o c k geometry p r i o r t o f a i l u r e i s shown i n F i g u r e 4.6a. Note t h a t the i n c l i n e d j o i n t deep i n the s l o p e i s c r e a t e d t o f a c i l i t a t e the f i n i t e d i f f e r e n c e zoning. T h i s j o i n t i s f i x e d and does not i n f l u e n c e the model. To study the i n f l u e n c e of groundwater an a n a l y s i s i s done u s i n g a b i l i n e a r water t a b l e t h a t approximates the c o n d i t i o n s i n the r e a l s l o p e ( F i g . 4.6b). T h i s a n a l y s i s a p p l i e s pore p r e s s u r e s along the f a u l t s based on t h i s water t a b l e . Two modes of t o p p l i n g f a i l u r e are i d e n t i f i e d f o r t h i s s l o p e . The f i r s t mode of f a i l u r e i s a p u r e l y f l e x u r a l t o p p l e and the second mode i s a more complicated movement h e r e i n r e f e r r e d t o as a "graben" t o p p l e . 70 UDEC (Version 1.50) legend 14/06/1989 15: 23 cycle 31000 -4.000E+01 < x < 8.400E+02 -S.900E+02 < y < 2.900E+02 zones plotted In fdef blocks block plot 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2e 2 Univ. of B r i t i s h Columble Dept. of Beologlcal Science F i g u r e 4.6a B r e n d a M i n e : Zoned B l o c k Geomet ry P r i o r t o F a i l u r e The l i m i t i n g j o i n t f r i c t i o n angle and other f i x e d parameter v a l u e s f o r pure f l e x u r a l t o p p l i n g are g i v e n i n Table 4.4. The i n i t i a l v a l u e and l i m i t i n g range of j o i n t f r i c t i o n are g i v e n f o r both the dry and s a t u r a t e d t r i a l s . Note t h a t T a b l e 4.4 r e p o r t s o n l y the l i m i t i n g f r i c t i o n angle f o r the p a r t i c u l a r rock s t r e n g t h s used. I t i s expected t h a t t h e r e are many combinations of rock and j o i n t parameters t h a t w i l l a l l o w f l e x u r a l t o p p l i n g i n t h i s model. Tab l e 4.4: UDEC Parameters f o r Brenda Mine Model: Pure F l e x u r a l T o p p l i n g . M a t e r i a l Number | Parameter | Value Block Mat 1 Dens i t y (kg/m 3) Bulk Modulus (MPa) Shear Modulus (MPa) Cohesion (MPa) T e n s i l e S t r e n g t h (MPa) F r i c t i o n Angle (deg.) D i l a t i o n (deg.) 2700 33333 20000 0.15 0.21 35 0 J o i n t Mat 1 I n i t i a l L i m i t i n g Range Dry L i m i t i n g Range Wet F r i c t i o n Angle (deg.) F r i c t i o n Angle (deg.) F r i c t i o n Angle (deg.) Cohesion (MPa) T e n s i l e S t r e n g t h (MPa) D i l a t i o n (deg.) Normal S t i f f n e s s (MPa/m) Shear S t i f f n e s s (MPa/m) 25 18.75 t o 20.0 21.25 t o 23.75 0 0 0 40000 20000 F i g u r e s 4.7a and 4.7b i l l u s t r a t e the deformation t h a t r e s u l t s f o r the dry s l o p e . F i g u r e 4.7a i l l u s t r a t e s the deformation of the b l o c k s and v e l o c i t y o f the g r i d p o i n t s d u r i n g f a i l u r e . F i g u r e 4.7b i l l u s t r a t e s the deformation of the b l o c k s g i v i n g 73 75 contours of h o r i z o n t a l displacement of the g r i d p o i n t s . Note t h a t shear along the Set A f a u l t s i s i n d i c a t e d by d i f f e r e n t g r i d p o i n t v e l o c i t y d i r e c t i o n s on o p p o s i t e s i d e s of the f a u l t s , and t h a t g r i d p o i n t v e l o c i t i e s a t t e n u a t e w i t h depth as expected i n t o p p l i n g . The geometry of the f a i l u r e i n d i c a t e s t h a t o v e r t u r n i n g i s being accommodated at a d e f i n e d depth i n each b l o c k . One of the most s i g n i f i c a n t c h a r a c t e r i s t i c s of t h i s s i m u l a t i o n i s the c i r c u l a r nature of the f a i l u r e s u r f a c e d e f i n e d by the b l o c k o v e r t u r n i n g . T h i s i s most c l e a r l y i l l u s t r a t e d by the h o r i z o n t a l displacement contours i n F i g u r e 4.7b. The a d d i t i o n of pore p r e s s u r e s as d e f i n e d i n F i g u r e 4.6b does not a f f e c t the shape of the f a i l u r e s u r f a c e . The l i m i t i n g j o i n t f r i c t i o n angle range with these buoyant f o r c e s i s g i v e n i n Table 4.4. A second model of f a i l u r e , r e f e r r e d t o as a "graben" t o p p l e , i s a l s o i d e n t i f i e d . T h i s mode of f a i l u r e i s shown i n F i g u r e s 4.8a and 4.8b and i s c h a r a c t e r i z e d by a wedge shaped b l o c k dropping down behind the top of the s l o p e w h i l e the lower p o r t i o n of the s l o p e f a i l s by f l e x u r a l t o p p l i n g . The p h y s i c a l parameters i n t h i s example are s i m i l a r t o those t h a t produced pure f l e x u r a l t o p p l i n g (Table 4.5). The d i f f e r e n c e i s a s m a l l i n c r e a s e i n the b l o c k i n t e r n a l f r i c t i o n 76 angle, and a decrease i n cohesion and t e n s i l e s t r e n g t h by two t h i r d s . The procedure i s the same as f o r the p r e v i o u s example. The b l o c k f r i c t i o n angle, cohesion and t e n s i l e s t r e n g t h are f i x e d , and t r i a l s with d i f f e r e n t j o i n t f r i c t i o n angles are run t o determine the l i m i t i n g v a l u e f o r s t a b i l i t y . T h i s a n a l y s i s i s not done wi t h pore p r e s s u r e s . Table 4.5: UDEC Parameters f o r Brenda Mine Model: "Graben" Topple M a t e r i a l Number | Parameter | Value Block Mat 1 Density (kg/m 3) Bulk Modulus (MPa) Shear Modulus (MPa) Cohesion (MPa) T e n s i l e S t r e n g t h (MPa) F r i c t i o n Angle (deg.) D i l a t i o n (deg.) 2700 33333 20000 0. 05 0. 05 40 0 J o i n t Mat 1 F l e x u r a l T o p p l i n g "Graben" T o p p l i n g F r i c t i o n Angle (deg.) F r i c t i o n Angle (deg.) F r i c t i o n Angle (deg.) Cohesion (MPa) T e n s i l e S t r e n g t h (MPa) D i l a t i o n (deg.) Normal S t i f f n e s s (MPa/m) Shear S t i f f n e s s (MPa/m) 25 21.25 t o 22.5 18.75 t o 20.0 0 0 0 40000 20000 When the j o i n t f r i c t i o n angle i s lowered t o between 21.25 and 22.5 degrees, pure f l e x u r a l t o p p l i n g develops. The geometry of t h i s f a i l u r e i s s i m i l a r t o the f a i l u r e shown i n F i g u r e 4.7, but o n l y i n v o l v e s the s l o p e down t o the top of the f i f t h bench. When the f r i c t i o n angle i s lowered f u r t h e r t o between 79 18.75 and 20 degrees the "graben" t o p p l e shown i n F i g u r e 4.8 develops. I n i t i a l l y t h i s "graben" t o p p l e i s a pure f l e x u r a l t o p p l e . A f t e r some r o t a t i o n , the b l o c k s t h a t form the "graben" stop f a i l i n g by o v e r t u r n i n g and begin t o f a i l by s l i d i n g . The s l i d i n g s u r f a c e develops through the p o i n t o f bending i n each column formed by the i n i t i a l t o p p l i n g . The v e l o c i t y v e c t o r s i n F i g u r e 4.9a show t h a t w i t h i n the "graben", b l o c k s on e i t h e r s i d e o f a f a u l t are moving i n the same d i r e c t i o n . T h i s i n d i c a t e s t h a t shear i s no lon g e r o c c u r r i n g along the f a u l t . The lower p a r t o f the s l o p e c o n t i n u e s t o f a i l by f l e x u r a l t o p p l i n g . T h i s mode of f a i l u r e i s very s i m i l a r t o a f a i l u r e d e s c r i b e d as a type of moment d r i v e n deformation by N i e t o (1987). In t h i s example, N i e t o d e s c r i b e s a mine s l o p e t h a t i s f a i l i n g by moment d r i v e n deformation ( f l e x u r a l t o p p l i n g ) and a c t i v e and p a s s i v e wedges ( F i g . 4.9a). i n t h i s example, f a v o r a b l y o r i e n t e d j o i n t s e t s a l l o w the upper, a c t i v e , and lower, p a s s i v e , wedges t o form w h i l e the middle p o r t i o n o f the sl o p e f a i l s by b l o c k t o p p l i n g . The p a s s i v e wedge i s d r i v e n by the combined l o a d i n g of the o v e r t u r n i n g p o r t i o n of the s l o p e and the a c t i v e wedge. The "graben" t o p p l e demonstrated by UDEC has many of the same c h a r a c t e r i s t i c s as t h i s example of moment d r i v e n deformation 80 Figure 4.9a Moment Driven Deformation with Active and Passive Wedges (after Nieto, 1987) d e s c r i b e d by N i e t o ( F i g . 4.9b). The "graben" i s an a c t i v e wedge t h a t loads the t o p p l i n g b l o c k s below, and the geometry of the t o p p l i n g b l o c k s i n the lower p a r t o f the s l o p e i s s i m i l a r t o the p a s s i v e wedge i n F i g u r e 4.9a. 4.4 Co n c l u s i o n s The b l o c k t o p p l i n g s i m u l a t i o n v e r i f i e s t h a t UDEC can be used t o model b l o c k t o p p l i n g , but because of the i n f l u e n c e o f b l o c k rounding i s s l i g h t l y more c o n s e r v a t i v e . Although the f l e x u r a l t o p p l i n g examples r e p o r t e d i n t h i s s e c t i o n are intended as demonstrations, s e v e r a l c o n c l u s i o n s can be drawn from them. In both examples, f l e x u r a l t o p p l i n g f a i l u r e o ccurs u s i n g reasonable e s t i m a t e s o f rock and j o i n t p r o p e r t i e s . T h i s confirms t h a t UDEC can sim u l a t e f l e x u r a l types o f t o p p l i n g f a i l u r e . In the s i m u l a t i o n of the base f r i c t i o n model, the rock s t r e n g t h parameters are a d j u s t e d t o f i n d the v a l u e s t h a t produce the base f r i c t i o n model f a i l u r e geometry. T h i s s i m u l a t i o n demonstrates t h a t UDEC can be used t o back analyze a f l e x u r a l t o p p l i n g f a i l u r e t o o b t a i n s t r e n g t h v a l u e s a t f a i l u r e . 82 00 t>0 c4 O ft JL / ~7 Z 8 3 F l e x u r a l t o p p l i n g r e s e a r c h u s i n g p h y s i c a l or f i n i t e element models has onl y produced p l a n a r f a i l u r e s u r f a c e s . The s i m u l a t i o n s i n t h i s s e c t i o n i n d i c a t e t h a t the f a i l u r e s u r f a c e generated i n f l e x u r a l t o p p l i n g may be p l a n a r or c u r v i l i n e a r . In the UDEC s i m u l a t i o n o f the base f r i c t i o n model w i t h a sl o p e h e i g h t o f approximately 3 0 meters, the f a i l u r e s u r f a c e i s p l a n a r , but i n the 180 meter h i g h Brenda Mine s l o p e the f a i l u r e s u r f a c e i s c u r v i l i n e a r . I t i s suspected t h a t the t r a n s i t i o n from a p l a n a r t o a c u r v i l i n e a r f a i l u r e s u r f a c e i s i n p a r t c o n t r o l l e d by the s i z e of the s l o p e , the d e n s i t y of back d i p p i n g d i s c o n t i n u i t i e s , and i s a l s o dependent on the va l u e s of b l o c k cohesion and t e n s i l e s t r e n g t h . The geometry and l o c a t i o n o f the f a i l u r e s u r f a c e i n l a r g e r s l o p e s i s dependent on the combination o f b l o c k cohesion, b l o c k t e n s i l e s t r e n g t h , and the j o i n t f r i c t i o n angle. When cohesion and t e n s i l e s t r e n g t h are s e t a t .15 MPa i n the Brenda Mine s l o p e , o n l y pure f l e x u r a l t o p p l i n g w i t h a c u r v i l i n e a r f a i l u r e s u r f a c e occurs f o r the range of j o i n t f r i c t i o n angle t e s t e d (25 t o 15 degrees). When cohesion and t e n s i l e s t r e n g t h are s e t a t .05 MPa, both c u r v i l i n e a r , f l e x u r a l t o p p l i n g and "graben" t o p p l i n g can occur depending on the j o i n t f r i c t i o n angle. The UDEC "graben" t o p p l i n g s i m u l a t i o n demonstrates t h a t f l e x u r a l t o p p l i n g can r e s u l t i n deformation s i m i l a r t o the 84 mode of moment d r i v e n deformation d e s c r i b e d by N i e t o (1987). In a d d i t i o n , the UDEC s i m u l a t i o n suggests t h a t the c h a r a c t e r i s t i c a c t i v e and p a s s i v e wedges formed i n t h i s mode of f a i l u r e do not n e c e s s a r i l y r e q u i r e f a v o r a b l y o r i e n t e d j o i n t s e t s t o occur. Pore p r e s s u r e s i g n i f i c a n t l y a f f e c t s the s t a b i l i t y o f s l o p e s s u s c e p t i b l e t o f l e x u r a l t o p p l i n g . I n c l u d i n g pore p r e s s u r e s i n the Brenda Mine model ( F i g . 4.6b) r e q u i r e s an i n c r e a s e i n the j o i n t f r i c t i o n angle of 13 t o 26 percent (2.5 t o 5 degrees) t o ma i n t a i n s t a b i l i t y (Table 4.4). 4.4.1 Recommendations f o r Slope Design w i t h UDEC I t i s p o s s i b l e t o use UDEC t o de s i g n s l o p e s i n a rock mass s u s c e p t i b l e t o t o p p l i n g . However, the accuracy o f the de s i g n i s dependent on the accuracy of the rock mass s t r e n g t h parameters used i n the model. The b e s t way t o determine these parameters i s by back a n a l y s i s o f a l a r g e number of known t o p p l i n g f a i l u r e s i n s i m i l a r rock types, which has not y e t been done. Even without a c c u r a t e knowledge of rock mass s t r e n g t h parameters, i t i s s t i l l p o s s i b l e t o apply UDEC t o examine the mode of t o p p l i n g p o s s i b l e i n a sl o p e and t o develop a c o n s e r v a t i v e d e s i g n . T h i s can be done by f i x i n g the rock and j o i n t s t r e n g t h parameters, the water t a b l e , and the j o i n t 85 i n c l i n a t i o n and s p a c i n g a t c o n s e r v a t i v e v a l u e s , and v a r y i n g the s l o p e f a c e angle and h e i g h t . Such an a n a l y s i s a l l o w s the d e s i g n e r t o determine the maximum sl o p e h e i g h t and f a c e angle f o r l a r g e s l o p e s s u s c e p t i b l e t o t o p p l i n g . In a d d i t i o n , the a n a l y s i s y i e l d s the p o t e n t i a l f a i l u r e geometry, and can be used t o assess the e f f e c t of d i f f e r e n t dewatering schemes and o t h e r s t a b i l i z a t i o n methods. 86 5.0 S i t e C h a r a c t e r i z a t i o n 5.1 I n t r o d u c t i o n The Beaver R i v e r V a l l e y i s s i t u a t e d i n G l a c i e r N a t i o n a l Park between Golden and Revelstoke, B r i t i s h Columbia ( F i g . 5.1), and forms the e a s t e r n p a r t o f a narrow t r a n s p o r t a t i o n c o r r i d o r which t r a v e r s e s the rugged P u r c e l l and S e l k i r k Mountains. The rout e was f i r s t d i s c o v e r e d and u t i l i z e d by the Canadian P a c i f i c Railway (now CP R a i l ) i n the l a t e 19th century. The Trans Canada Highway was c o n s t r u c t e d along the c o r r i d o r i n the e a r l y 1960's and a second CP R a i l l i n e has r e c e n t l y been completed. Both CP R a i l alignments e n t e r the no r t h e r n end of the Beaver V a l l e y along the v a l l e y bottom and climb the western s l o p e s . The highway a l s o e n t e r s from the nor t h , but h i g h on the e a s t e r n s l o p e . I t then descends t o the v a l l e y f l o o r , c r o s s e s the Beaver R i v e r , and climbs a g a i n along the western s l o p e ( F i g . 5.1). Although the economic importance of the Beaver R i v e r V a l l e y as the e a s t e r n approach t o the Rogers Pass ro u t e has l o n g been r e c o g n i z e d , l a r g e , deep-seated mass movement hazards along the v a l l e y s l o p e s have on l y r e c e n t l y been documented ( P r i t c h a r d e t a l . , 1988). 87 CO co Deep Seated Landslides (from P r i t c h a r d e t . a l . , 1988) F i e l d work d u r i n g the summer of 1988 c o n c e n t r a t e d on an area of the e a s t s l o p e of the Beaver R i v e r V a l l e y i n c l u d i n g the Heather H i l l l a n d s l i d e and adjacent s l o p e s t o the n o r t h ( F i g . 5.1). T h i s s i t e was s e l e c t e d f o r d e t a i l e d study because i t c o n t a i n s a w e l l developed and w e l l d e f i n e d , deep-seated l a n d s l i d e , and the o p p o r t u n i t y t o study s l o p e s immediately a d j a c e n t which show l e s s e r degrees of deformation and no apparent deep-seated i n s t a b i l i t y . The r e g i o n a l geology and s l o p e deformation i n the Beaver V a l l e y , and the geology of the Heather H i l l study area are d i s c u s s e d i n t h i s chapter. 5.2 R e g i o n a l Geology 5.2.1 Bedrock Geology The Beaver V a l l e y i s s i t u a t e d i n the Omineca T e c t o n i c B e l t of B r i t i s h Columbia. The northwest t r e n d i n g v a l l e y i s f l a n k e d on the e a s t by the P r a i r i e H i l l s of the P u r c e l l Mountains and on the west by the Hermit and S i r Donald Ranges of the S e l k i r k Mountains. The r e g i o n a l geology i s shown i n F i g u r e 5.2, and F i g u r e 5.3. The v a l l e y i s formed i n rocks of two groups: the Hadrynian 89 L E G E N D | H | Hamill Group UC SP SL GR Horsethief Creek Group Upper Clastic division Carbonate division Semipeite Amphibolite unit Slate division Grit division | Normal fault Thrust fault Overturned Thrust fault • Garnet Isograd Geologic Contact defined, assumed CP Rail — — — Trans Canada Hwy. Glacier National Park Boundary (GNP) Contour interval 400m Topography from: Energy Mines and Resources Canada, Map MCR 219 Geology after: Poulton and S'mony, 1980 ( 100km t 61* 20' RwaMofce Figure 5.2 Regional Geology map of the Beaver River V a l l e y ( a f t e r Poulton and Simony, 1980) C r o s s - S e c t i o n 1 No V.E. F i g u r e 5 . 3 G e o l o g i c a l C r o s s S e c t i o n Number 1, B e a v e r R i v e r V a l l e y . See L e g e n d F i g . 5 . 2 . ( a f t e r S imony and W i n d , 1970 ; P o u l t o n and S imony 1980) 91 (Late Precambrian) H o r s e t h i e f Creek Group, and the Lower Cambrian H a m i l l Group (Wheeler, 1963; Simony and Wind, 1970). The H o r s e t h i e f Creek Group i n c l u d e s a lower g r i t d i v i s i o n s u c c e s s i v e l y o v e r l a i n by a s l a t e d i v i s i o n , a carbonate d i v i s i o n , and an upper c l a s t i c d i v i s i o n . The s l a t e d i v i s i o n i s f u r t h e r d i v i d e d i n t o a s e m i p e l i t e a m p h i b o l i t e u n i t i n the Beaver V a l l e y . The H a m i l l Group c o n s i s t s of Upper, Middle and Lower Members of which o n l y the dominantly q u a r t z i t e Lower Member i s pr e s e n t i n the Beaver V a l l e y (Simony and Wind, 1970). The e a s t s l o p e o f the Beaver V a l l e y c o n s i s t s o f a s e r i e s of i m b r i c a t e t h r u s t sheets, w i t h the s l o p e s formed p r i m a r i l y i n the overturned g r i t and s l a t e d i v i s i o n s o f the H o r s e t h i e f Creek Group. On the west v a l l e y s l o p e s , o n l y one west-dipping t h r u s t f a u l t i n t e r r u p t s the u p r i g h t s t r a t i g r a p h i c sequence of g r i t through upper c l a s t i c d i v i s i o n s , o v e r l a i n by Lower H a m i l l q u a r t z i t e s (Poulton and Simony, 1980). In the Beaver V a l l e y , the rocks are complexly f o l d e d e x h i b i t i n g p l a n a r bedding (SO) on the s c a l e o f outcrop. P e n e t r a t i v e f o l i a t i o n (SI) t h a t i s a x i a l p l a n a r t o the f i r s t phase of f o l d i n g i s v i r t u a l l y o b l i t e r a t e d on both s i d e s o f the Beaver R i v e r by i n t e n s e c r e n u l a t i o n cleavage (S2) (Rickard, 1961; Simony and Wind, 1970). The SO bedding t r e n d s dominantly northwestward throughout the area, d i p p i n g s t e e p l y 92 e a s t on the e a s t s i d e o f the v a l l e y and s t e e p l y west on the o p p o s i t e s i d e (Simony and Wind, 1970)• 5.2.2 Geomorphic Development of Beaver V a l l e y The geomorphic development of the Beaver V a l l e y i s dominated by s e v e r a l p e r i o d s o f g l a c i a l advance and r e t r e a t . These g l a c i a l p e r i o d s have been t e n t a t i v e l y grouped i n t o t h r e e events (VanBuskirk, 1987). The f i r s t g l a c i a l event reached an e l e v a t i o n of a t l e a s t 2950 meters (Thurber C o n s u l t a n t s L t d . , 198 3a) and c r e a t e d the broad U-shaped Beaver V a l l e y w i t h a s l o p e angle o f between 2 0 and 2 5 degrees. The second g l a c i a l event reached an e l e v a t i o n o f approximately 1100 meters and oversteepened the lower v a l l e y s l o p e s . T h i s oversteepening i s evidenced by t r u n c a t e d spurs and s t e e p e r s l o p e angles o f 30 t o 45 degrees. These g l a c i a l events were probably complete by approximately 9000 years B.P., but a minor readvance o c c u r r e d p r i o r t o approximately 7500 years B.P. (Thurber C o n s u l t a n t s L t d . , 1983a). During t h i s t h i r d event i c e readvanced down the Beaver V a l l e y t o approximately the l o c a t i o n of the east p o r t a l o f the Mt. Macdonald t u n n e l . Drainage o f the Beaver V a l l e y was p e r i o d i c a l l y b l o c k e d d u r i n g t h i s time by a con c u r r e n t readvance down the Cupola Creek V a l l e y 1 . T h i s blockage formed a l a k e t o an approximate e l e v a t i o n o f 990 meters i n the v a l l e y •'•Cupola Creek V a l l e y i s j u s t o f f the n o r t h edge of F i g u r e 5.1, on the west s i d e of the Beaver V a l l e y 93 c a u s i n g d e l t a s t o develop a t the mouths of major t r i b u t a r y streams (Thurber C o n s u l t a n t s L t d . , 1983a). S i n c e the t h i r d g l a c i a l event, the sediment supply r e s u l t i n g from the reworking of these d e l t a s i n t o modern a l l u v i a l fans, and the a d d i t i o n o f sediment t o the a l l u v i a l fans r e s u l t i n g from d e b r i s t o r r e n t s has c r e a t e d a s e r i e s o f l o c a l base l e v e l s a long the Beaver R i v e r , c a u s i n g the f l o o d p l a i n t o aggrade. 5.3 C h a r a c t e r i s t i c s of Beaver V a l l e y Slope Movements The l a r g e l a n d s l i d e s shown i n F i g u r e 5.1 are l o c a t e d on the lower v a l l e y s l o p e s i n the g r i t and s l a t e d i v i s i o n s o f the H o r s e t h i e f Creek Group. The lower g r i t d i v i s i o n c o n s i s t s mainly of coarse and f i n e - g r a i n e d g r i t t y , f e l d s p a t h i c and micaceous sandstone w i t h s l a t e i n t e r b e d s (Simony and Wind, 197 0); p l a n a r bedding and graded beds on the s c a l e o f outcrop are common (Poulton and Simony, 1980). The s l a t e d i v i s i o n c o n s i s t s o f p e l i t i c rocks, w i t h minor c o a r s e r c l a s t i c and carbonate i n t e r b e d s t r a n s i t i o n a l w i t h adjacent u n i t s . The exact age of the f a i l u r e s i s unknown. I t i s b e l i e v e d t h a t the i n i t i a l G r i f f i t h s l i d e ( F i g . 5.1) predates the l a s t g l a c i a t i o n (Thurber C o n s u l t a n t s L t d . , 1979), and t h a t a l l show evidence of post g l a c i a l movement. 94 The e l e v a t i o n of the f l o o r of the v a l l e y a t the end of the f i n a l p e r i o d of g l a c i a t i o n i s unknown. However, d r i l l i n v e s t i g a t i o n s of the v a l l e y f l o o r f o r the new CP R a i l l i n e went t o an e l e v a t i o n of 755 meters and d i d not encounter bedrock (Thurber C o n s u l t a n t s L t d . , 1983b). N a t u r a l s l o p e angles i n the v a l l e y v a r y from 20 t o 45 degrees. The h e i g h t of the l a n d s l i d e s , measured from the l e v e l of the f l o o d p l a i n (approximate e l e v a t i o n of 825 meters) t o the top of the headscarps, v a r i e s from 450 t o 1250 meters. The volume of the s l o p e movements v a r i e s from approximately 5 t o 30 x l 0 6 m 3 . I t i s p o s s i b l e t h a t these f a i l u r e s extend below the c u r r e n t f l o o d p l a i n l e v e l . For t h i s reason, the estimated maximum r e l i e f and volume of these f a i l u r e s may be c o n s e r v a t i v e . P r o g r e s s i v e deformations have been measured a t the G r i f f i t h s l i d e ( F i g . 5.1) where continuous movement of the d e b r i s has caused displacement of the c u r r e n t CP R a i l l i n e throughout i t s l i f e , n e c e s s i t a t i n g d e t a i l e d g e o t e c h n i c a l s t u d i e s and m i t i g a t i v e works. M o n i t o r i n g of s l o p e i n d i c a t o r s shows deformations of up t o approximately 30 mm over a one month m o n i t o r i n g p e r i o d (Thurber C o n s u l t a n t s L t d . , 1979). Whether or not o t h e r deep seated mass movements are moving, and t h e i r r a t e of movement are not y e t known. 95 5.4 Pr e v i o u s L a n d s l i d e S t u d i e s i n the Beaver V a l l e y P r e v i o u s unpublished work d e s c r i b e s and q u a n t i f i e s the mode of f a i l u r e o f the s l o p e s . In a r e p o r t t o CP R a i l , EBA E n g i n e e r i n g C o n s u l t a n t s L t d . (1976) o u t l i n e d the l o c a t i o n of many s l o p e movements i n the v a l l e y . Based on the geometry of the bedrock s l i d e s carps and rubble , EBA suggested t h a t the modes of the f a i l u r e are c i r c u l a r . In a l a t e r r e p o r t f o r Environment Canada Parks, EBA E n g i n e e r i n g C o n s u l t a n t s L t d . (1978) e v a l u a t e d the s t a b i l i t y o f the Heather H i l l l a n d s l i d e as a deep-seated r o t a t i o n a l f a i l u r e . P i t e a u and A s s o c i a t e s L t d . (1982), i n work f o r CP R a i l on the west v a l l e y s l o p e near the entrance t o Rogers Pass, observed s e v e r a l l o c a l i t i e s where p r e e x i s t i n g t o p p l i n g f a i l u r e s (Goodman and Bray, 1976) are exposed by r a i l w a y or creek c u t s . Rapp (1987), u s i n g the nomograms developed by Brown (1982), confirmed t h a t l a r g e s c a l e t o p p l i n g f a i l u r e i s p o s s i b l e i n the v a l l e y s l o p e s ; furthermore, Rapp p o s t u l a t e d t h a t s l i d e s such as the G r i f f i t h and Unnamed s l i d e r e p r e s e n t the f i n a l stages o f e a r l i e r massive t o p p l i n g f a i l u r e s . 96 5.5 F i e l d Program 5.5.1 I n t r o d u c t i o n . F i e l d i n v e s t i g a t i o n of the study area shown i n F i g u r e 5.1 was undertaken d u r i n g the summer of 1988. T h i s work i n v o l v e d s t r u c t u r a l mapping along the creek g u l l i e s and the highway back s l o p e . Temporary benchmarks were e s t a b l i s h e d along the highway and a t the base of each creek u s i n g an AGA model 14A o E l e c t r o n i c D i s t a n c e Meter (EDM) and a W i l d T2 t h e o d o l i t e . T r a v e r s e s were s t a r t e d from these benchmarks and c a r r i e d up the creeks and around the s l i d e headscarp u s i n g a h i p c h a i n and hand h e l d c l i n o m e t e r f o r c o n t r o l . These t r a v e r s e s were l a t e r t r a n s f e r r e d t o a 1 t o 2500 s c a l e 5 meter contour i n t e r v a l t o p o g r a p h i c map of the study area (Maps 1A and IB, Map Pocket). 5.5.2 L o c a l Geology The geology o f the study area c o n s i s t s o f the lower g r i t and s l a t e d i v i s i o n s o f the H o r s e t h i e f Creek Group ( F i g . 5.2). P e l i t i c rocks o f the s l a t e d i v i s i o n occupy the base of the s l o p e , and t r a v e r s e s upslope p e r p e n d i c u l a r t o the s t r i k e of the SO bedding encounter a g r a d a t i o n a l change t o g r i t d i v i s i o n r o c k s . SO bedding t h i c k n e s s v a r i e s from m i l l i m e t e r s t o tens of meters, but the most common t h i c k n e s s i s i n the range of 0.1m t o 3m. 97 A n a l y s i s of the f i e l d data i n d i c a t e s s e v e r a l dominant s t r u c t u r a l f e a t u r e s : SO p l a n a r bedding f o l i a t i o n , S2 c r e n u l a t i o n cleavage, and a t l e a s t two j o i n t s e t s ( J l , J 2 ) . SI a x i a l p l a n a r f o l i a t i o n e x i s t s , and appears t o be s u b p a r a l l e l t o the SO f o l i a t i o n , however the o r i e n t a t i o n of SI f o l i a t i o n i s d i f f i c u l t t o q u a n t i f y due t o the e f f e c t of S2 c r e n u l a t i o n cleavage. The J l j o i n t s e t t r e n d s n o r t h w e s t e r l y , s u b - p a r a l l e l t o the SO f o l i a t i o n , but d i p s downslope p e r p e n d i c u l a r t o i t . The J2 j o i n t s e t i s o r i e n t e d p e r p e n d i c u l a r t o both the SO f o l i a t i o n and the J l s e t . These j o i n t s e t s occur most commonly i n the more competent g r i t t y beds, and combine wi t h the SO f o l i a t i o n t o break the rock mass i n t o l a r g e b l o c k y fragments. S l a t y beds c o n t a i n v e r y few of the J l or J2 j o i n t s but d i s p l a y i n t e n s e c r e n u l a t i o n cleavage. S t r u c t u r a l data were obtained from t r a v e r s e s up the t h r e e creek g u l l i e s , around the base of the Heather H i l l l a n d s l i d e headscarp, and along the highway c u t . Equal area s t e r e o n e t p l o t s of the s t r u c t u r e i n each creek are g i v e n i n Appendix 2. Three p l o t s are shown f o r each t r a v e r s e ; the p o l e s t o the SO and S2 d i s c o n t i n u i t i e s , a contour p l o t of the SO and S2 p o l e s , and a p l o t of the p o l e s t o a l l j o i n t s . In a d d i t i o n , a p l o t of p o l e s t o a l l the j o i n t s measured i n the creeks and a contour p l o t of these p o l e s are g i v e n . 98 The average o r i e n t a t i o n f o r the SO and S2 d i s c o n t i n u i t y s e t s from each t r a v e r s e and the estimated average j o i n t o r i e n t a t i o n s f o r a l l the creeks i n the study area are summarized i n Table 5.1 and p l o t t e d i n F i g u r e 5.4. The creek t r a v e r s e s are used t o c a t e g o r i z e the s t r u c t u r e a l o n g the s l o p e . The average s t r u c t u r a l o r i e n t a t i o n s from the t r a v e r s e around the base of the Heather H i l l l a n d s l i d e headscarp are a l s o shown i n F i g u r e 5.4 t o i l l u s t r a t e the t o p p l i n g o f the rock mass. Tabl e 5.1: S t r u c t u r a l Data Summary i n Study Area T r a v e r s e SO Bedding S2 Cleavage | J l J o i n t J2 J o i n t Creek A 333\66 005\62 N\A 2 N\A 2 Creek B 338\47 023\56 N\A 2 N\A 2 Creek C 338\46 024\51 N\A 2 N\A 2 A l l Creek Data N\A 2 N\A 2 140\33 t o 204\54 247\90 HeadScarp 346\21 043\42 163\73 t o 212\79 N\A 2 The s t r u c t u r a l r e l a t i o n s h i p between the SO bedding and the S2 cleavage i s c o n s i s t e n t i n the study area, but the SO and S2 zFor the creek t r a v e r s e s , N\A i n d i c a t e s t h a t the data cannot be c o r r e l a t e d as one data s e t . For the j o i n t data, N\A i n d i c a t e s t h a t the data d i d not c o r r e l a t e w e l l enough t o make an estimate of average o r i e n t a t i o n f o r the creek or headscarp t r a v e r s e s . 99 AVE. STRUCTURAL ORIENTATIONS: CREEKS A,B,C, SCARP N o r t h EQUAL AREA PROJECTION Symbol CREEK A AVERAGE SO AND S2 ORIENTATION 2 P o i n t s • CREEK B AVERAGE SO AND S2 ORIENTATION 2 P o i n t s A CREEK C AVERAGE SO AND S2 ORIENTATION 2 P o i n t s + SCARP TRAVERSE AVERAGE SO AND S2 ORIENTATION 2 P o i n t s 0 ALL CREEKS AND SCARP: EST. RANGE OF J l ORIENTATION 4 P o i n t s X ALL CREEKSi ESTIMATED AVERAGE ORIENTATION OF J2 1 P o i n t s o 13 P o i n t s T o t a l F i g u r e 5.4 S t r u c t u r a l Geology Summary f o r Study Area 100 o r i e n t a t i o n s v a r y s l i g h t l y as i n d i c a t e d i n F i g u r e 5.4. The s t r i k e s o f these s t r u c t u r e s do not va r y s i g n i f i c a n t l y , but the d i p s of both SO and S2 are g r e a t e r i n Creek A than i n Creeks B and C. The j o i n t data from each creek i s much more s c a t t e r e d than the SO or S2 data, and no s t a t i s t i c a l averages o f the j o i n t o r i e n t a t i o n s c o u l d be determined. However, the contour p l o t of the data i n Appendix 2 i l l u s t r a t e s the dominant J l and J2 j o i n t s e t s and i s used t o estimate the average o r i e n t a t i o n of these j o i n t s e t s i n the study area (Table 5.1). 5.5.3 Evidence of Deformation The decrease i n the d i p of SO and S2 from n o r t h t o south i n the study area i s i n d i c a t e d by comparing the d i p shown from Creek A wi t h Creek B, and Creek B w i t h Creek C i n F i g u r e 5.4. T h i s can be e x p l a i n e d as a n a t u r a l s t r u c t u r a l v a r i a t i o n , or as an i n c r e a s e i n the degree of t o p p l i n g i n the southern and middle p a r t o f the study area. There i s evidence t h a t suggests the decrease i s a t l e a s t p a r t i a l l y a r e s u l t of t o p p l i n g . T o p p l i n g of SO bedding i s v i s i b l e i n the hi g h , near v e r t i c a l c u t s (60m) of the creek v a l l e y s . In these creek cuts t o p p l i n g and d i l a t i o n are seen t o i n c r e a s e updip. I n v e s t i g a t i o n of the s l o p e j u s t t o the n o r t h of Creek B upslope of a cut backslope along Highway 1 r e v e a l e d obsequent s c a r p s w i t h t o r n s u r f i c i a l s o i l and r o o t s and r e l i e f of up t o 101 1.5 meters (Map 1A). Obsequent scarps are g e n e r a l l y viewed as an i n d i c a t i o n o f t o p p l i n g (Goodman and Bray, 1976). The t r a v e r s e around the base of the headscarp supports the v i s i b l e evidence of t o p p l i n g c i t e d above. The average s t r u c t u r a l o r i e n t a t i o n s from t h i s t r a v e r s e i n d i c a t e the t o p p l e d nature of the rock mass i n the headscarp r e l a t i v e t o t h a t o f the creek t r a v e r s e s . The data from t h i s t r a v e r s e are b e l i e v e d t o be from d i s t u r b e d zones of rock and not r e p r e s e n t a t i v e of the i n t a c t s t r u c t u r e . I t i s b e l i e v e d t h a t the rock above the headscarp, which has an average bedding f o l i a t i o n d i p approximately 5 degrees lower than i n Creek C, i s more r e p r e s e n t a t i v e of the extent o f t o p p l i n g p r i o r t o dep-seated f a i l u r e . S t r u c t u r a l data o b t a i n e d from above the headscarp were too few t o o b t a i n a more a c c u r a t e estimate of s t r u c t u r a l o r i e n t a t i o n s . I t i s p o s s i b l e t h a t the t o p p l i n g d e s c r i b e d above extends below the e l e v a t i o n of Creeks B and C. F i g u r e 5.5 i s a topo g r a p h i c c r o s s s e c t i o n o f the s l o p e j u s t n o r t h o f the Heather H i l l l a n d s l i d e . The c r o s s s e c t i o n a l s o i n c l u d e s the g r a d i e n t p r o f i l e o f Creek B and the p r o j e c t e d p o s i t i o n of the back sca r p of the Heather H i l l s l i d e . T h i s f i g u r e i l l u s t r a t e s t h a t the c r e e k s are not deeply i n c i s e d i n t o the s l o p e r e l a t i v e t o the Heather H i l l l a n d s l i d e . For t h i s reason, s t r u c t u r a l data from Creeks B and C may be from zones of d i s t u r b e d rock and not r e p r e s e n t a t i v e o f the i n t a c t s t r u c t u r e . 102 o 1600- , 1400 — 1200 c o 5 1 0 0 0 -Q) 8 0 0 -TOPOGRAPHIC PROFILE SECTION A - A ' , AND GRADIENT OF CREEK B 600 Section A—A' Approximate Elevation of Glacial Lake Impoundment ^ Gradient, Creek B (projected into line of cross section) Heather Hill Slide Scarp and Projected Failure Surface (projected into line of cross section) Estimated Bedrock Profile i i i i i i i 1 1 1 1 1 1 1 1 1— - 1 0 0 100 300 500 700 900 1100 1300 1500 H. dist.(m) From East bank of Beaver River 1700 Figure 5.5 Topographic P r o f i l e Section A-A' and Gradient of Creek B V i s i b l e d i s t u r b a n c e of the s l o p e s i n the study area i s g r e a t e s t i n the v i c i n i t y of the Heather H i l l s l i d e and i n the v i c i n i t y o f Creek B, and decreases towards Creek A. The d e c r e a s i n g d i s t u r b a n c e of the s l o p e s towards the n o r t h of the study area i s supported by the f l a t t e r s l o p e p r o f i l e i n the v i c i n i t y o f Creek A ( F i g . 5.6). For these reasons i t i s b e l i e v e d t h a t the s t r u c t u r a l data from Creek A are the most r e p r e s e n t a t i v e of the i n t a c t rock c o n d i t i o n . 104 TOPOGRAPHIC PROFILE SOUTH OF CREEK A SECTION B - B ' u 1 1 I i I i i 1 1 1 1 1 1 1 j 1 j 1 1 - 1 0 0 100 300 500 700 900 1100 1300 1500 1700 H. dist.(rn) From East bank of Beaver River Figure 5.6 Topographic P r o f i l e South of Creek A, Section B-B' 6.0 M o d e l l i n g Heather H i l l L a n d s l i d e Development 6.1 I n t r o d u c t i o n The mode of f a i l u r e of the Heather H i l l l a n d s l i d e i s examined wit h UDEC i n t h i s chapter. The g o a l s o f t h i s a n a l y s i s are t o determine the mode of f a i l u r e o f the s l i d e , and t o examine the c h a r a c t e r i s t i c s o f the f a i l u r e . There are s e v e r a l f a c t o r s t h a t make t h i s a n a l y s i s unique. F i r s t , the Heather H i l l l a n d s l i d e i s a l a r g e f a i l u r e i n a n a t u r a l s l o p e where f i e l d evidence i n d i c a t e s t o p p l i n g i s w e l l advanced. P o t e n t i a l t o p p l i n g f a i l u r e s o f t h i s s i z e have never been q u a n t i t a t i v e l y assessed. Second, the l i t h o l o g y o f the study area i s h i g h l y v a r i a b l e and grades from dominantly quartz b i o t i t e s c h i s t a t the base of the s l o p e t o dominantly f e l d s p a t h i c g r i t above the headscarp o f the s l i d e . The i n f l u e n c e o f mixed l i t h o l o g y on t o p p l i n g development has not been q u a n t i t a t i v e l y assessed. 6.2 P r e v i o u s A n a l y s i s o f the Heather H i l l L a n d s l i d e The o n l y p r e v i o u s m o d e l l i n g on the Heather H i l l l a n d s l i d e i s by EBA E n g i n e e r i n g C o n s u l t a n t s L t d . (1978) who used the S i m p l i f i e d Bishop method of s l i c e s t o assess the s l i d e as a 106 deep seated r o t a t i o n a l f a i l u r e . The assumed o r i g i n a l s l o p e geometry and s l i p s u r f a c e are shown i n F i g u r e 6.1. A f a c t o r of s a f e t y o f 0.64 was obtained f o r the f u l l y s a t u r a t e d s l o p e . The rock s t r e n g t h parameters used f o r t h i s a n a l y s i s are not gi v e n . 6.3 C h a r a c t e r i s t i c s of the UDEC Model The geometry o f the model i s s i m p l i f i e d from the r e a l s i t e c o n d i t i o n s . The t o p o g r a p h i c c r o s s s e c t i o n A-A' (Map 1A) l o c a t e d immediately n o r t h o f the s l i d e i s used t o approximate the sl o p e p r o f i l e p r i o r t o the l a n d s l i d e . F i g u r e 6.2 i l l u s t r a t e s t h i s p r o f i l e superimposed on a topo g r a p h i c p r o f i l e through the approximate c e n t e r o f the s l i d e s c a r p . The dashed l i n e i n F i g u r e 6.2 i s the assumed p r e - s l i d e topography used i n the UDEC model. Note t h a t t h i s topography c o n t i n u e s below the modern f l o o d p l a i n l e v e l t o the minimum e l e v a t i o n o f g l a c i a l e x c a v a t i o n estimated i n S e c t i o n 5.2.2. F i g u r e 6.3 - i l l u s t r a t e s s e v e r a l f e a t u r e s o f the UDEC model. The l e f t (west) boundary o f the model i s a t the c e n t e r o f the v a l l e y , and the symmetry of the v a l l e y i s invoked t o c o n s t r a i n t h i s boundary from moving h o r i z o n t a l l y . The base o f the model 107 o CO Distance From Beaver River (m) F i g u r e 6.1 C i r c u l a r A n a l y s i s o f Heather H i l l L a n d s l i d e ; Assumed Slope Geometry and F a i l u r e S u r f a c e (from EBA Engin e e r i n g C o n s u l t a n t s L t d . , 1978) 1600 1400 ^ 1 2 0 0 H c o ° 1000 0) 800-TOPOGRAPHIC PROFILE SECTIONS A-A' AND C - C , MAP 1A Section A—A' Section C—C *—Assumed Pre—slide Topography Used in UDEC Model 600 T T T T 100 300 500 700 900 ' 1100 ' 1300 ' 1500 H. dist.(m) From East bank of Beaver River V700 -100 Figure 6.2 Heather H i l l : Assumed Pre-Slide Topography UDEC (Version 1.50) legend Univ. of B r i t i s h Columbia Dept. of Geological Science F i g u r e 6 . 3 H e a t h e r H i l l : I n i t i a l B l o c k Geomet ry o f UDEC M o d e l i s f i x e d , and a constant i n s i t u s t r e s s a t K 0=0.5 i s a p p l i e d a t the r i g h t boundary. The domain i n the model i s d i v i d e d i n t o 65 degree d i p p i n g columns. T h i s d i s c o n t i n u i t y i s designed t o s i m u l a t e the combined i n f l u e n c e of SO f o l i a t i o n and S2 cleavage on the rock mass. An i n c l i n a t i o n of 65 degrees i s chosen based on what i s b e l i e v e d t o be the i n t a c t rock s t r u c t u r e i n the study area (Sec. 5.5.3). The e x c a v a t i o n of the s l o p e i n the model i s designed t o s i m u l a t e the r e a l g l a c i a l e x c a v a t i o n of the s l o p e . I n i t i a l s t r e s s e s of K n=1.0 are a p p l i e d i n the domain shown i n F i g u r e 6.3 and g r a v i t y i s a p p l i e d u n t i l the s t r e s s e s are a t e q u i l i b r i u m . The f i r s t g l a c i a l e x c a v a t i o n of the v a l l e y i s modelled by s e q u e n t i a l l y removing the b l o c k s t h a t p a r a l l e l the upper s l o p e f a c e , b e g i n n i n g w i t h the b l o c k i n the top l e f t c o r n e r of the domain. The geometry of the s l o p e a t the end of t h i s e x c a v a t i o n i s shown i n F i g u r e 6.4. I t i s assumed t h a t the s l o p e f a i l s when i t i s oversteepened by the second g l a c i a l e x c a v a t i o n . T h i s i s simulated by removing the remaining t h r e e b l o c k s i n F i g u r e 6.4. The s t r e s s e s i n the s l o p e are allowed t o come t o e q u i l i b r i u m a f t e r the e x c a v a t i o n of each b l o c k . I l l UDEC (Version 1.50) legend 21/07/19B9 IB: 05 cycle 0 -1.0B0E+02 < x < 2.268E+03 -1.83BE+03 < y < 5.3B0E+02 block plot I I I I I I 0 5e 2 Univ. of B r i t i s h Columbia Dept. of Geological Science Figure 6.4 Heather H i l l : F i r s t G l a c i a l Excavation 6.3.1 Pore Pressure Pore p r e s s u r e s based on a f u l l y s a t u r a t e d s l o p e are i n c l u d e d i n the model. P i t e a u and A s s o c i a t e s L t d . (1982) r e p o r t s t h a t the c u r r e n t water t a b l e e l e v a t i o n i n the west v a l l e y s l o p e c l o s e t o the entrance t o Rogers Pass i s near the s u r f a c e . When d r i l l i n g from an e l e v a t i o n of 1040m, P i t e a u encountered the water t a b l e approximately 15m below the s u r f a c e a t the c o n t a c t between s u r f i c i a l m a t e r i a l s and bedrock. In a d d i t i o n , i t i s c o n s i d e r e d t h a t the m i l d c l i m a t e d u r i n g downwasting of the second g l a c i a t i o n may have c o n t r i b u t e d t o h i g h pore p r e s s u r e s i n the s l o p e (Mathewes and Heusser, 1981). For these reasons, i t i s reasonable t o assume t h a t the water t a b l e i n the s l o p e a t the end of the second g l a c i a t i o n was as l e a s t as h i g h as i t i s c u r r e n t l y , and may w e l l have been s l i g h t l y h i g h e r . 6.4 C h a r a c t e r i z a t i o n of Rock Mass The rock mass i n the v i c i n i t y of the Heather H i l l l a n d s l i d e i s d i f f i c u l t t o c h a r a c t e r i z e . The main d i s c o n t i n u i t y s e t t h a t weakens the rock mass i s the SO f o l i a t i o n . These s u r f a c e s d i v i d e the rock mass i n t o long t h i n columns t h a t are c e n t i m e t e r s t o s e v e r a l meters t h i c k . The S2 cleavage f u r t h e r d i v i d e s the s o f t e r p e l i t i c beds, and the harder g r i t beds are broken by the J l and J2 c r o s s j o i n t s . At the s c a l e of the 113 Heather H i l l l a n d s l i d e most of these d i s c o n t i n u i t i e s are too f i n e l y spaced t o be e x p l i c i t l y i n c o r p o r a t e d i n a UDEC model. Although m o d e l l i n g the s t r u c t u r e of the study area completely as a discontinuum i s not p r a c t i c a l , i t i s e s s e n t i a l t o i n c o r p o r a t e the a f f e c t of the d i s c o n t i n u i t i e s . T h i s i s done by m o d e l l i n g a coarse approximation of the SO f o l i a t i o n e x p l i c i t l y , and the f o l i a t e d and j o i n t e d " i n t a c t " m a t e r i a l between the coarse SO f o l i a t i o n s as a continuum w i t h a lower s t r e n g t h than competent rock. A minimum SO f o l i a t i o n s p a c i n g of 2 5 meters i s used i n the model. T h i s approximates the minimum s e p a r a t i o n of obsequent scarps l o c a t e d n o r t h of Creek B (Map 1A) . In the v i c i n i t y of the Heather H i l l l a n d s l i d e the rock changes g r a d a t i o n a l l y from dominantly f o l i a t e d p e l i t i c rock a t the base of the s l o p e t o dominantly j o i n t e d f e l d s p a t h i c g r i t above the s l i d e . T h i s change i n rock mass i s i n c o r p o r a t e d i n the model by a l l o w i n g the j o i n t and rock mass s t r e n g t h p r o p e r t i e s , and the SO f o l i a t i o n s p a c i n g t o i n c r e a s e approximately l i n e a r l y from the bottom of the s l o p e t o above the headscarp. The program uses a Mohr-Coulomb f a i l u r e c r i t e r i o n d e f i n e d by an i n t e r n a l f r i c t i o n angle, cohesion i n t e r c e p t and t e n s i l e s t r e n g t h t o c h a r a c t e r i z e the s t r e n g t h of the rock mass. Although these parameters c o u l d e a s i l y be determined i n the l a b o r a t o r y f o r s m a l l , i n t a c t rock samples from the study area, 114 t h e r e i s no a c c u r a t e way, s h o r t of l a r g e s c a l e t e s t i n g , t o determine these parameters f o r the f o l i a t e d and j o i n t e d i n s i t u rock mass. There are s e v e r a l i n d i r e c t methods of a s s e s s i n g the i n s i t u rock mass s t r e n g t h (Hoek and Brown, 1980). These techn i q u e s are a l l e m p i r i c a l and use measurements of c h a r a c t e r i s t i c s of the rock mass t o determine a f a i l u r e c r i t e r i o n . Many of these f a i l u r e c r i t e r i a are q u a l i t a t i v e , but some such as the Hoek Brown s t r e n g t h c r i t e r i o n can be used t o c a l c u l a t e a f a i l u r e envelope f o r the rock mass. U n f o r t u n a t e l y , i n h e a v i l y j o i n t e d rock masses t h i s technique s t i l l r e q u i r e s a g r e a t d e a l of judgement (Hoek and Brown, 1980). Because of the l a r g e u n c e r t a i n t y i n v o l v e d i n e s t i m a t i n g the rock mass s t r e n g t h parameters e m p i r i c a l l y , a d e t e r m i n i s t i c a n a l y s i s based on a s i n g l e , estimated s e t of parameters i s not attempted. In t h i s UDEC model, the rock mass s t r e n g t h parameters are determined by back a n a l y s i s . The procedure i s s i m i l a r t o the examples i n Chapter 4. I n i t i a l l y , the rock s t r e n g t h parameters are s e t h i g h enough t o ensure t h a t the s l o p e w i l l be s t a b l e when f u l l y excavated. Once excavated, the parameters are g r a d u a l l y lowered t o determine the p o i n t a t which the s l o p e becomes u n s t a b l e . T h i s i s d i s c u s s e d f u r t h e r i n S e c t i o n 6.6. 115 6.5 E v o l u t i o n o f Model The g r a d a t i o n a l treatment of the SO sp a c i n g and the rock mass p r o p e r t i e s was adopted a f t e r s i m p l e r approximations f a i l e d t o generate the Heather H i l l s l i d e geometry. E a r l y m o d e l l i n g attempts used a SO sp a c i n g o f 25 or 50 meters and one rock type f o r the e n t i r e s l o p e . At a 50 meter spac i n g , u n r e a l i s t i c a l l y weak rock mass and j o i n t p r o p e r t i e s were r e q u i r e d t o o b t a i n f a i l u r e . More r e a l i s t i c p r o p e r t i e s r e s u l t e d when a uniform 25 meter s p a c i n g was used. However, the geometry of the f a i l u r e was p l a n a r , extending p a r a l l e l t o the upper s l o p e from the toe of the s l o p e t o the e a s t boundary of the model. Changing the rock mass p r o p e r t i e s from one rock type t o a g r a d a t i o n a l i n c r e a s e i n s t r e n g t h up s l o p e r e s u l t e d i n some cu r v a t u r e , but the l i m i t o f the model l a n d s l i d e s t i l l exceeded the i n s i t u l a n d s l i d e . T h i s prompted the i n c l u s i o n o f i n c r e a s i n g SO s p a c i n g i n the model. With t h i s change, the Heather H i l l l a n d s l i d e geometry can be approximated u s i n g reasonable rock mass p r o p e r t i e s . 116 6.6 R e s u l t s of UDEC M o d e l l i n g UDEC i s l i m i t e d t o 10 d i f f e r e n t m a t e r i a l p r o p e r t i e s . One of these m a t e r i a l s i s used t o f i x the a r t i f i c i a l j o i n t t h a t i s c r e a t e d t o f a c i l i t a t e b l o c k zoning, and the remaining nine are used t o si m u l a t e the g r a d a t i o n a l change from f o l i a t e d p e l i t i c rock a t the base of the sl o p e t o dominantly f e l d s p a t h i c g r i t above the headscarp. F i g u r e 6.5 i l l u s t r a t e s how the rock s t r e n g t h parameters are assign e d t o the s l o p e . Four SO spacings are used: 25m, 3 3m, 41m, and 49m. T h i s s p a c i n g a r b i t r a r i l y i n c r e a s e s i n increments o f 8 meters from 25 meters a t the base of the s l o p e t o 49 meters above the headscarp as i l l u s t r a t e d i n F i g u r e 6.4. The a n a l y s i s begins w i t h the s l o p e excavated t o the l e v e l o f the second g l a c i a t i o n , f u l l y s a t u r a t e d , and s t a b l e . Note t h a t the f l o o r o f the v a l l e y i n t h i s a n a l y s i s i s approximately 70 meters below the c u r r e n t f l o o d p l a i n l e v e l . From t h i s p o i n t the i n t e r n a l f r i c t i o n angle of the rock mass i s lowered i n sma l l increments u n t i l f a i l u r e develops. The s t r e n g t h p r o p e r t i e s o f the rock mass a t f a i l u r e are r e p o r t e d i n Table 6.1. For s i m p l i c i t y the e l a s t i c p r o p e r t i e s are not r e p o r t e d i n t h i s t a b l e , but are i n c l u d e d i n the i n i t i a l data i n p u t f i l e i n Appendix 3. In these t r i a l s j o i n t s 117 UDEC (Version i.50j legend are assumed t o have no cohesion, t e n s i o n or d i l a t i o n , and the rock mass i s assumed t o have no d i l a t i o n . T able 6.1 UDEC Str e n g t h Parameters f o r Heather H i l l Model Rock Mass J o i n t M a t e r i a l F r i c t i o n T e n s i l e F r i c t i o n Angle Cohesion S t r e n g t h Angle (deg.) (MPa) (MPa) (deg.) 1 31.0 .100 .050 22 2 33.0 .150 .075 25 3 35.5 .200 . 100 28 4 38.0 .250 . 125 31 5 40.5 .300 . 150 35 6 43 . 0 . 350 . 175 39 7 46.0 .400 .225 44 8 49. 0 .450 .250 47 9 52.0 . 500 .300 50 The geometry of the f a i l u r e t h a t r e s u l t s a t these s t r e n g t h parameters i s shown i n F i g u r e s 6.6a, and 6.6b. Note t h a t the p a r t of the model d e p i c t e d i n each f i g u r e i s shown i n the top l e f t c o r n e r . T h i s i s necessary due t o the d e n s i t y of the j o i n t s and g r i d p o i n t s . F i g u r e 6.6a i s a p l o t of g r i d p o i n t v e l o c i t i e s . Note t h a t i n the same manner as the Brenda Mine example ( F i g . 4.7a), d i f f e r e n t v e l o c i t i e s on e i t h e r s i d e of an SO f o l i a t i o n i n d i c a t e shear i s o c c u r r i n g along the f o l i a t i o n s , and t h a t v e l o c i t i e s a t t e n u a t e w i t h depth. Both of these f e a t u r e s are t y p i c a l of f l e x u r a l t o p p l i n g f a i l u r e . 119 UDEC (Version 1.50) legend 23/07/1989 09: 31 c y c l e 38500 4.500E+02 < x < 7.500E+02 -8.500E+02 < y < -5.500E+02 block p l o t 1 I I I I I 0 5e 1 v e l o c i t y v e c t o r s maximum - 4.368E-01 11 i i i i i i i i I i i i i i i i i i I 0 2e 0 Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science Figure 6.6a Heather H i l l UDEC Model: V e l o c i t i e s of Gri d Points F i g u r e 6.6b i s a contour p l o t of h o r i z o n t a l displacement and i l l u s t r a t e s the geometry of the f a i l u r e . The shape of the f a i l u r e s u r f a c e and the extent o f the f a i l u r e i n the UDEC model approximate the observed f a i l u r e geometry and headscarp l o c a t i o n . There are many combinations o f the s t r e n g t h parameters t h a t w i l l cause f a i l u r e i n the model. However, the parameter v a l u e s r e p o r t e d i n Table 6.1 a l l o w a f a i l u r e t o develop i n the model t h a t b e s t approximates the observed geometry and extent of the Heather H i l l l a n d s l i d e . The v a r i a t i o n i n the v a l u e s i n v e s t i g a t e d f o r t h i s model are l i s t e d i n Tab l e 6.2. The minimum and maximum v a l u e s f o r both m a t e r i a l 1 and m a t e r i a l 9 are g i v e n . The remaining m a t e r i a l v a l u e s range i n an approximately l i n e a r manner between these two end members. Tabl e 6.2 I n v e s t i g a t e d V a r i a t i o n i n Parameters M a t e r i a l Range of Values F r i c t i o n T e n s i l e F r i c t i o n Angle Cohesion S t r e n g t h Angle (deg.) (MPa) (MPa) (deg.) 1 30 - 35 .025-.150 .010-.075 22 9 45 - 52 .100-.500 .065-.300 35 - 50 6.7 L i m i t a t i o n s of A n a l y s i s The r e s u l t s of the a n a l y s i s r e p o r t e d i n the p r e v i o u s s e c t i o n are l i m i t e d by the approximations i n the model. For example, 121 F i g u r e 6 . 6 b Heather H i l l UDEC Model: H o r i z o n t a l Displacement i n t h i s model the SO f o l i a t i o n s p a c i n g i s v a r i e d from 25 t o 49 meters. The c h o i c e of 25 meters as a minimum s p a c i n g of shear s u r f a c e s i n the s l o p e i s supported by the f i e l d evidence o f obsequent s c a r p s n o r t h o f Creek B (Map 1A). However the c h o i c e o f the maximum spac i n g o f 49 meters i s a r b i t r a r y . I f the maximum sp a c i n g i s a l t e r e d a d i f f e r e n t s e t of rock s t r e n g t h parameters a t f a i l u r e and a d i f f e r e n t geometry of f a i l u r e w i l l r e s u l t . Other approximations i n the model i n c l u d e the estimated maximum depth o f g l a c i a l e x c a v a t i o n and the approximation of the rock mass as homogeneous and i s o t r o p i c between the SO f o l i a t i o n s . The r e s u l t s o f the a n a l y s i s are dependent on the pore p r e s s u r e s i n the s l o p e . In r e a l i t y , the l e v e l o f the water t a b l e i n the f a i l i n g rock would d e c l i n e as the rock mass becomes i n c r e a s i n g l y broken and d i l a t e d . As the v a r i a t i o n of the water t a b l e d u r i n g f a i l u r e i s not known, i t i s c o n s e r v a t i v e l y assumed i n t h i s model t h a t pore p r e s s u r e s c o r r e s p o n d i n g t o a f u l l y s a t u r a t e d s l o p e apply a t a l l times. T h i s pore p r e s s u r e assumption has the e f f e c t of pr o p a g a t i n g the f a i l u r e . In r e a l i t y , the combination o f a d e c l i n e i n pore p r e s s u r e and i n c r e a s e d j o i n t s t r e n g t h due t o j o i n t d i l a t i o n may cause a f a i l i n g s l o p e t o s t a b i l i z e . . The i m p l i c a t i o n s of t h i s p o s s i b i l i t y f o r the s t a b i l i t y o f s l o p e s i n the Beaver V a l l e y and f o r e n g i n e e r i n g d e s i g n i n these s l o p e s are d i s c u s s e d i n S e c t i o n s 7.2.2 and 7.2.3 r e s p e c t i v e l y . 123 6.8 Co n c l u s i o n s 6.8.1 Heather H i l l L a n d s l i d e Due t o the approximation of the r e a l g e o l o g i c c o n d i t i o n s d i s c u s s e d i n the p r e v i o u s s e c t i o n , a d e f i n i t i v e s t a b i l i t y a n a l y s i s i s not p o s s i b l e . Even w i t h these approximations, the UDEC model f a i l s by f l e x u r a l t o p p l i n g l i m i t i n g t o a c u r v i l i n e a r f a i l u r e s u r f a c e . T h i s model i n d i c a t e s t h a t the most l i k e l y mode of f a i l u r e o f the Heather H i l l l a n d s l i d e i s f l e x u r a l t o p p l i n g . Experience w i t h the UDEC model of the Heather H i l l f a i l u r e i n d i c a t e s the importance o f i n c l u d i n g the up s l o p e i n c r e a s e i n rock mass s t r e n g t h due t o v a r i a t i o n i n rock type. I t was found i n the model t h a t the l i m i t o f the f a i l u r e i s r e l a t e d t o the g r a d a t i o n a l change i n rock type from f o l i a t e d p e l i t i c rock a t the base of the sl o p e t o f e l d s p a t h i c g r i t above the headscarp o f the Heather H i l l l a n d s l i d e . T h i s r e l a t i o n s h i p i s supported by the o v e r a l l d i s t r i b u t i o n of l a n d s l i d e s i n the Beaver V a l l e y ( F i g . 5.1). Most of the i d e n t i f i e d l a n d s l i d e s i n the v a l l e y occur i n the S l a t e d i v i s i o n rocks and, wit h the ex c e p t i o n o f the l a r g e l a n d s l i d e south o f the study area, are 124 roughly l i m i t e d up s l o p e by the occurrence o f the G r i t d i v i s i o n rocks ( F i g . 5.2). 6.8.2 Kinematic T e s t For T o p p l i n g The k i n e m a t i c t e s t f o r t o p p l i n g p o t e n t i a l (Goodman and Bray, 197 6; and Sec. 2.4.2) i s wid e l y accepted as a c o n s e r v a t i v e means t o estimate t o p p l i n g p o t e n t i a l . One of the most i n t e r e s t i n g c o n c l u s i o n s o f t h i s chapter i s t h a t the geometry of the Heather H i l l l a n d s l i d e does not s a t i s f y t h i s t e s t . For t o p p l i n g t o be p o s s i b l e , the kinemat i c t e s t r e q u i r e s t h a t the s l o p e f a c e angle (6) be g r e a t e r than the sum of the j o i n t f r i c t i o n angle (<f>) and the i n c l i n a t i o n from v e r t i c a l (a) of the back d i p p i n g d i s c o n t i n u i t y s e t ( i e : 6 > <j> + a) ( F i g . 2.2a). When a p p l i e d t o the Heather H i l l model d i s c u s s e d i n S e c t i o n 6.6 t h i s t e s t i n d i c a t e s t h a t t o p p l i n g i s not k i n e m a t i c a l l y p o s s i b l e . The t e s t i s not s a t i s f i e d by a margin o f 5 degrees a t the base of the s l o p e ( i e : 42 < 22 + 25) t o 15 degrees j u s t below the e l e v a t i o n of the change i n s l o p e ( i e : 41 < 31 + 25). T h i s i s i l l u s t r a t e d i n F i g u r e s 6.7a and 6.7b. There are a t l e a s t two reasons why t h i s t e s t i s not s a t i s f i e d . The k i n e m a t i c t e s t i s based on two c r i t e r i a . For shear on a j o i n t t o occur the net s t r e s s a c t i n g on the j o i n t must be a l i g n e d w i t h the sl o p e f a c e and i n c l i n e d by a t l e a s t cj> t o the normal of the j o i n t (Sec. 2.4.2). When t h i s t e s t i s used t o 125 N F i g u r e 6.7a Kinematic T e s t : Toe of Slope i n UDEC Model. N T F i g u r e 6.7b Kinematic T e s t : E l e v a t i o n of Change i n Slope i n UDEC Model 126 assess the t o p p l i n g p o t e n t i a l of a s l o p e , i t i s assumed t h a t the o r i e n t a t i o n o f the net s t r e s s d e f i n e d by the s l o p e face angle a t the s u r f a c e a p p l i e s a t depth a l o n g the j o i n t . T h i s may be a re a s o n a b l e assumption i n s m a l l s c a l e s l o p e s , but i s not v a l i d i n l a r g e r s l o p e s . In l a r g e r s l o p e s the p r i n c i p a l s t r e s s d i r e c t i o n s along a j o i n t , and hence the net s t r e s s d i r e c t i o n , change with depth i n the s l o p e . F i g u r e 6.8 i s taken from the model r e p o r t e d i n S e c t i o n 6.6 a t a stage when the s l o p e i s s t a b l e . T h i s f i g u r e i s a p l o t o f p r i n c i p a l s t r e s s e s a t the g r i d p o i n t s i n the model and i l l u s t r a t e s how the p r i n c i p a l s t r e s s d i r e c t i o n s change al o n g the j o i n t s . Note t h a t t h i s f i g u r e o n l y d e p i c t s the p o r t i o n o f the model shown i n the top l e f t c o r n e r . F i g u r e 6.9 i s a p l o t o f t a n - 1 ( s h e a r s t r e s s / n o r m a l s t r e s s ) v s . l e n g t h between A and A' along a j o i n t shown i n F i g u r e 6.8. T h i s p l o t i l l u s t r a t e s how the m o b i l i z e d f r i c t i o n angle on a j o i n t v a r i e s w i t h depth i n the s l o p e . Note t h a t the m o b i l i z e d f r i c t i o n angle i s lowest near the s l o p e f a c e and i n c r e a s e s w i t h depth. The c h a r a c t e r i s t i c s of s t r e s s e s along the j o i n t s i l l u s t r a t e d i n F i g u r e s 6.8 and 6.9 i n d i c a t e t h a t i n l a r g e s l o p e s , the assumption t h a t net s t r e s s on a j o i n t i s p a r a l l e l t o the s l o p e face a t depth i n the sl o p e i s not v a l i d . F u r t h e r , when a p p l i e d t o a ki n e m a t i c assessment of t o p p l i n g p o t e n t i a l t h i s 127 H t o 03 UDEC fVersion 1.50) l e g e n d 23/07/1989 12: 39 c y c l e 26500 5.000E+02 < x < 7.000E+02 -8.000E+02 < y < -6.000E+02 block p l o t I L J I 5e 1 p r i n c i p a l s t r e s s e s maximum - -1.510E-01 minimum - -1.141E+01 I I I L o -I I 5e 1 Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science Figure 6.6b Figure 6.'ea Figure 6.8 Heather H i l l UDEC Model: P r i n c i p l e Stresses 29 Change in Eff. Fr ict ion Angle 28 -24 -23 20 A 40 F i g u r e 6.9 60 ~ r ~ 80 100 120 Distance Along Joint: A—A' Heather H i l l UDEC Model: V a r i a t i o n o f E f f e c t i v e F r i c t i o n Angle Along an SO F o l i a t i o n 140 A' assumption i s not c o n s e r v a t i v e . F i g u r e 6.10 i s a p l o t o f f a c t o r o f s a f e t y (shear s t r e n g t h / s h e a r s t r e s s ) along the same j o i n t l e n g t h as i n F i g u r e 6.9. T h i s f i g u r e i n d i c a t e s t h a t f a i l u r e a l o n g j o i n t s d u r i n g t o p p l i n g f a i l u r e may a c t u a l l y b e g i n a t depth, and progresses t o the s u r f a c e as f a i l i n g s e c t i o n s o f a j o i n t t r a n s f e r t h e i r l o a d t o adjacent up d i p s e c t i o n s . the UDEC model of the Heather H i l l l a n d s l i d e a l s o does not s a t i s f y a second assumption of the ki n e m a t i c t e s t . I t i s assumed i n the kinema t i c t e s t t h a t no pore p r e s s u r e s a c t along the j o i n t s . When pore p r e s s u r e s a re c o n s i d e r e d the normal s t r e s s (cr n ) i s reduced by the magnitude of the pore p r e s s u r e (a n *= a n - u ) , wh i l e the shear s t r e s s (r) i s not a f f e c t e d . In t h i s s i t u a t i o n the f a i l u r e o f the j o i n t occurs when the e f f e c t i v e m o b i l i z e d j o i n t f r i c t i o n angle ( t a n - 1 [shear s t r e s s / e f f e c t i v e normal s t r e s s ] ) i s g r e a t e r than or equal t o the j o i n t f r i c t i o n angle (<t>m,> 4>) • The net e f f e c t o f pore p r e s s u r e i s t o a l l o w the j o i n t t o shear a t a lower angle o f a p p l i e d t o t a l s t r e s s . T h i s i s i l l u s t r a t e d i n F i g u r e s 6.11a and 6.11b. I t s h o u l d be r e a l i z e d t h a t the k i n e m a t i c t e s t i s a t e s t o f t o p p l i n g p o t e n t i a l . I t i s not in t e n d e d t o t e s t the s t a b i l i t y o f a s l o p e w i t h r e s p e c t t o t o p p l i n g , i t simply i n d i c a t e s i f shear on a j o i n t i s k i n e m a t i c a l l y p o s s i b l e . W i t h i n the l i m i t s imposed by the assumptions of the t e s t , i t p r o v i d e s a 130 Factor of Safety Along Joint 1.28 -1.26 -1.24 -1.22 -1.2 -1.18 -1.08 -1.06 -1.04 -1.02 -1 H 1 1 1 1 1 1 1 1 1 I I 20 40 60 80 100 120 140 A Distance Along Joint: A—A' F i g u r e 6.10 Heather H i l l UDEC Model: V a r i a t i o n i n F a c t o r of Saf e t y Along SO F o l i a t i o n JOINT 6. l i a <t> - J o i n t F r i c t i o n Angle <*>m At F a i l u r e Dry <t>m = Mobilized J o i n t F r i c t i o n Angle 6.11b JOINT <p = J o i n t F r i c t i o n Angle At F a i l u r e Wet 0 < 4> 4>m> <t> Qm- E f f e c t i v e Mobilized J o i n t F r i c t i o n Angle F i g u r e 6.11a) Normal and Shear S t r e s s e s on Dry J o i n t 6.11b) E f f e c t i v e Normal and Shear S t r e s s e s When Pore Pressure a c t s on J o i n t 132 c o n s e r v a t i v e i n d i c a t i o n o f t o p p l i n g p o t e n t i a l . The above d i s c u s s i o n demonstrates t h a t when the assumptions r e g a r d i n g the o r i e n t a t i o n o f t o t a l s t r e s s and pore p r e s s u r e s along a j o i n t are not s a t i s f i e d the t e s t i s not a c o n s e r v a t i v e estimate of t o p p l i n g p o t e n t i a l . I t i s recommended t h a t the ki n e m a t i c t e s t of t o p p l i n g p o t e n t i a l be q u a l i f i e d . The t e s t should o n l y be a p p l i e d t o sm a l l s c a l e d r a i n e d s l o p e s i n which the t o t a l s t r e s s o r i e n t a t i o n along the j o i n t s i s a reasonable approximation of the kin e m a t i c t e s t requirements. 133 7.0 C o n c l u s i o n s and Recommendations 7.1 PART I : Co n c l u s i o n s of L i t e r a t u r e Review S e v e r a l c o n c l u s i o n s r e s u l t from the l i t e r a t u r e review on t o p p l i n g i n Chapter 2, and are summarized below. 1. Large s c a l e f l e x u r a l t o p p l e s , and the i n f l u e n c e o f j o i n t d i l a t i o n , rock m a t e r i a l and rock mass s t r e n g t h on t o p p l i n g , have never been q u a n t i t a t i v e l y assessed. 2. The l i m i t e q u i l i b r i u m technique, f i n i t e element method, and d i s t i n c t element method have a l l been used t o model t o p p l i n g . The l i m i t e q u i l i b r i u m technique i s by f a r the most p o p u l a r . 3. The l i m i t e q u i l i b r i u m technique has i n h e r e n t r e s t r i c t i o n s however, t h a t make i t u n s u i t a b l e f o r m o d e l l i n g l a r g e s c a l e f l e x u r a l modes of t o p p l i n g . 4. F i n i t e element methods overcome the r e s t r i c t i o n s o f the l i m i t e q u i l i b r i u m technique, but have a l i m i t e d a b i l i t y t o model l a r g e deformations i n j o i n t e d r o c k mass due t o t h e i r continuum f o r m u l a t i o n . 5. The d i s t i n c t element method overcomes the d i f f i c u l t i e s w i t h the f i n i t e element method. The making and b r e a k i n g 134 of j o i n t c o n t a c t s , l a r g e displacements, and r o t a t i o n s o f d i s c r e t e b l o c k s and deformation of the b l o c k s are a l l e a s i l y accommodated. 7.2 PART I I : F l e x u r a l T o p p l i n g : C o n c l u s i o n s o f Research There are s e v e r a l c o n c l u s i o n s on f l e x u r a l t o p p l i n g t h a t r e s u l t from the example models i n Chapter 4. 1. The r e s u l t s from the b l o c k and f l e x u r a l t o p p l i n g examples r e p o r t e d i n Chapter 4 c o n f i r m t h a t UDEC can simulate a l l t y p e s o f t o p p l e s . These examples a l s o demonstrate t h a t UDEC can be used t o back analyze rock mass s t r e n g t h parameters, and determine the shape and l o c a t i o n o f the f i n a l f a i l u r e s u r f a c e i n f l e x u r a l t o p p l i n g . 2. The geometry of the f a i l u r e s u r f a c e formed d u r i n g f l e x u r a l t o p p l i n g f a i l u r e may be p l a n a r o r c u r v i l i n e a r . T h i s has never be f o r e been q u a n t i t a t i v e l y confirmed. 3. Two modes of f l e x u r a l t o p p l i n g f a i l u r e appear t o be p o s s i b l e : pure f l e x u r a l t o p p l i n g , and "graben" t o p p l i n g . The development of "graben" t o p p l i n g i s l a r g e l y c o n t r o l l e d by the i n t e r n a l f r i c t i o n angle o f the rock mass. 135 4. Pore p r e s s u r e s i g n i f i c a n t l y a f f e c t s the s t a b i l i t y of sl o p e s s u s c e p t i b l e t o f l e x u r a l t o p p l i n g . 7.3 PART I I I : Beaver V a l l e y : C o n c l u s i o n s and Recommendations 7.3.1 Heather H i l l Study Area The UDEC model of the Heather H i l l f a i l u r e demonstrates t h a t the most l i k e l y mechanism of f a i l u r e i n v o l v e s l a r g e s c a l e f l e x u r a l t o p p l i n g t h a t l i m i t s t o a c u r v i l i n e a r f a i l u r e s u r f a c e . F a i l u r e begins i n the toe of the s l o p e as hig h s t r e s s e s cause f a i l u r e o f the rock mass and s h e a r i n g on the SO f o l i a t i o n s . In the study area n o r t h o f the Heather H i l l l a n d s l i d e , f i e l d o b s e r v a t i o n s r e v e a l evidence of r e c e n t deep-seated movement i n slo p e s t h a t were i n i t i a l l y b e l i e v e d t o be s t a b l e . Both the f i e l d evidence and the UDEC model of the Heather H i l l l a n d s l i d e i n d i c a t e t h a t t h i s movement i n v o l v e s f l e x u r a l t o p p l i n g . F u r t h e r n o r t h i n t h e v i c i n i t y of Creek A (Map IB) the sl o p e s are b e l i e v e d t o be more s t a b l e due t o the lower s l o p e angle. The UDEC model o f the Heather H i l l l a n d s l i d e demonstrates t h a t the up s l o p e l i m i t of the f a i l u r e i s r e l a t e d t o the 136 g r a d a t i o n a l change i n r o ck type from f o l i a t e d p e l i t i c rock a t the base of the s l o p e t o f e l d s p a t h i c g r i t above the headscarp of the Heather H i l l l a n d s l i d e . T h i s i s supported by the d i s t r i b u t i o n of l a n d s l i d e s i n the Beaver V a l l e y . The k i n e m a t i c t e s t f o r t o p p l i n g p o t e n t i a l proposed by Goodman and Bray (1976) i s v i o l a t e d by the Heather H i l l l a n d s l i d e model. C o n s i d e r a t i o n of the mechanics of l a r g e s c a l e t o p p l i n g f a i l u r e s i n d i c a t e s t h a t the kinematic t e s t s h o u l d be q u a l i f i e d . The t e s t should o n l y be a p p l i e d t o s m a l l s c a l e d r a i n e d s l o p e s i n which the t o t a l s t r e s s o r i e n t a t i o n a l o n g the j o i n t s i s a reasonable approximation of the k i n e m a t i c t e s t requirements. 7.3.2 S t a b i l i t y of Slopes i n Beaver V a l l e y The evidence of modern movement d i s c o v e r e d n o r t h of the Heather H i l l l a n d s l i d e where no i n s t a b i l i t y was p r e v i o u s l y s uspected r a i s e s d i s t u r b i n g q u e s t i o n s about the s t a b i l i t y of s i m i l a r s l o p e s throughout the Beaver V a l l e y . Large t o p p l i n g f a i l u r e s are g e n e r a l l y c o n s i d e r e d slow f a i l u r e s (de F r i e t a s and Watters, 1973), which accommodate a l a r g e degree o f deformation p r i o r t o c o l l a p s e and are o f t e n s e l f s t a b i l i z i n g (Goodman and Bray, 1976; N i e t o , 1987). I t has been suggested t h a t t o p p l i n g f a i l u r e s s e l f s t a b i l i z e due t o 137 j o i n t d i l a t i o n which causes a d e c l i n e i n the water t a b l e and an i n c r e a s e i n j o i n t s t r e n g t h i n the f a i l i n g rock mass (Bovis, 1982) . I t i s p o s s i b l e t h a t the s l o p e n o r t h of the Heather H i l l l a n d s l i d e and o t h e r a p p a r e n t l y s t a b l e s l o p e s i n the Beaver V a l l e y are l o c a t i o n s where t o p p l i n g i s w e l l advanced, or i n the e a r l y stages of deep seated t o p p l i n g f a i l u r e , and have undergone some d i l a t i o n and d e g r a d a t i o n of rock mass s t r e n g t h . The i m p l i c a t i o n s of t h i s s t a b i l i t y c o n d i t i o n f o r e n g i n e e r i n g d e s i g n are d i s c u s s e d i n the next s e c t i o n . I t i s recommended t h a t s l o p e s i n the Beaver V a l l e y t h a t have undergone some degree o f deformation be i d e n t i f i e d . T h i s can be done by f i r s t c a t e g o r i z i n g h i g h r i s k areas o f the s l o p e s on the b a s i s of degree of g l a c i a l o v e r s t e e p e n i n g of the t o e , rock type, and p r o x i m i t y t o e x i s t i n g l a n d s l i d e s . High r i s k areas can then be i n s p e c t e d u s i n g low l e v e l a i r photographs and on the ground. Such an assessment can be used t o p l a n more d e t a i l e d g e o t e c h n i c a l i n v e s t i g a t i o n s f o r e n g i n e e r i n g works. 7.3.3 E n g i n e e r i n g Design I m p l i c a t i o n s and Recommendations I f the s t a b i l i t y of p r e v i o u s l y d i s t u r b e d s l o p e s i s not c o n s i d e r e d d u r i n g the d e s i g n and c o n s t r u c t i o n of e n g i n e e r i n g works, c o s t l y d e s i g n e r r o r s o r m i t i g a t i v e works may r e s u l t . An e n g i n e e r must c o n s i d e r the e f f e c t of an engineered s t r u c t u r e such as a cut or t u n n e l on the s t a b i l i t y of the 138 whole s l o p e , and, a l s o , how the p r e v i o u s d i s t u r b a n c e of the rock mass i n f l u e n c e s the d e s i g n . The impact o f an e n g i n e e r i n g s t r u c t u r e on the s t a b i l i t y of a p r e v i o u s l y d i s t u r b e d s l o p e can be assessed w i t h a UDEC model s i m i l a r t o the one used i n Chapter 6. The e x i s t i n g s l o p e can be developed, the s t r u c t u r e i n t r o d u c e d , and the e f f e c t on s t a b i l i t y s t u d i e d . I t i s a r e l a t i v e l y s t r a i g h t forward e x e r c i s e t o i n c l u d e the rock mass and s t r e s s c o n d i t i o n s r e s u l t i n g from p r e v i o u s t o p p l i n g d i s t u r b a n c e i n the d e s i g n of s u r f a c e or s u b - s u r f a c e engineered s t r u c t u r e s . T h i s can be done by d e v e l o p i n g a second s t a b i l i t y model f o r the area o f i n t e r e s t i n the l a r g e r model. Due t o t h e s m a l l e r area, t h i s model c o u l d u t i l i z e much more d e t a i l e d i n f o r m a t i o n on the SO bedding f o l i a t i o n s p a c i n g , j o i n t s p a c i n g , and rock type v a r i a t i o n . T h i s i n f o r m a t i o n can be o b t a i n e d d i r e c t l y from l i n e mapping of the s l o p e . The i n i t i a l s t r e s s c o n d i t i o n s f o r t h i s model can be determined from the l a r g e r model of the whole s l o p e , and d i s c o n t i n u i t i e s can be a s s i g n e d s t r e n g t h s based on the degree of deformation of the n a t u r a l s l o p e . There are two recommendations t h a t can be made by c o n s i d e r i n g the f a c t o r s t h a t c o n t r o l the s t a b i l i t y of rock s l o p e s i n which t o p p l i n g has o c c u r r e d . The toe area i s c r i t i c a l t o the s t a b i l i t y of these s l o p e s and i t i s recommended t h a t major 139 e x c a v a t i o n s not be undertaken i n t h i s a r ea. In a d d i t i o n , the groundwater flow system should not be a l t e r e d i n a way t h a t would cause i n c r e a s e d pore p r e s s u r e s . 7.4 F l e x u r a l T o p p l i n g : Recommendations f o r F u r t h e r Work 7.4.1 C u r v i l i n e a r F a i l u r e Surface i n F l e x u r a l Topples. The geometry of the f a i l u r e s u r f a c e formed d u r i n g f l e x u r a l t o p p l i n g f a i l u r e may be p l a n a r or c u r v i l i n e a r . I t i s recommended t h a t f u r t h e r r e s e a r c h be done t o i n v e s t i g a t e what f a c t o r s c o n t r o l the shape of the f a i l u r e s u r f a c e . T h i s work should i n v o l v e s e n s i t i v i t y s t u d i e s w i t h t h e s t r e n g t h parameters f o r the i n t a c t rock ( i n t e r n a l f r i c t i o n angle, cohesion, and t e n s i l e s t r e n g t h ) , and s h o u l d be conducted on s m a l l (<100m) and l a r g e s c a l e s l o p e s . In both the Brenda Mine and Heather H i l l models the f a i l u r e s u r f a c e i s approximately c i r c u l a r . There may be a r e l a t i o n s h i p between c i r c u l a r f a i l u r e s u r f a c e s i n f l e x u r a l t o p p l i n g and c i r c u l a r f a i l u r e s u r f a c e s i n homogeneous, i s o t r o p i c rock s l o p e s . I t may be p o s s i b l e t o develop a r e l a t i o n s h i p t h a t uses accepted nomograms f o r c i r c u l a r f a i l u r e p o t e n t i a l t o a s s e s s the s t a b i l i t y of f l e x u r a l t o p p l e s t h a t l i m i t t o a c i r c u l a r f a i l u r e s u r f a c e . 140 7.4.2 I n f l u e n c e o f D i l a t i o n on T o p p l i n g I t i s w e l l known t h a t d i l a t i o n d u r i n g shear can s i g n i f i c a n t l y i n c r e a s e the s t r e n g t h o f a j o i n t . Consequently, numerical models t h a t do not i n c l u d e j o i n t d i l a t i o n w i l l be s i m u l a t i n g c o n s e r v a t i v e behaviour (Barton, 1986). I t i s p o s s i b l e t o use UDEC t o i n v e s t i g a t e the i n f l u e n c e o f d i f f e r e n t degrees of d i l a t i o n on the s t a b i l i t y o f t o p p l i n g s l o p e s . As the i n c r e a s e i n s t r e n g t h of a j o i n t due t o d i l a t i o n i s dependent on the c o n f i n i n g s t r e s s , i t i s important t h a t such a study be done on both s m a l l and l a r g e s c a l e s l o p e s . 7.4.3 I n f l u e n c e o f G l a c i a l Events on T o p p l i n g S e v e r a l authors have suggested t h a t s l o p e deformations are i n i t i a t e d e i t h e r d u r i n g g l a c i a l u n d e r c u t t i n g o f s l o p e s o r d u r i n g g l a c i a l r e t r e a t ( M o l l a r d , 1977; Radbruch-Hall e t a l . , 1976; Tabor, 1971; T e r z a g h i , 1962). Bovis (1982), Patton and Hendron (1974), and de F r i e t a s and Watters (1973) suggest t h i s s p e c i f i c a l l y i n r e f e r e n c e t o t o p p l e s . I t i s p o s s i b l e t o use UDEC t o model the e f f e c t of repeated g l a c i a l events on the rock mass and j o i n t s o f a s l o p e s u s c e p t i b l e t o t o p p l i n g . Such an a n a l y s i s would use the c o n t i n u o u s l y y i e l d i n g j o i n t model which a l l o w s p r o g r e s s i v e damage and weakening of the j o i n t s due t o sequences of g l a c i a l e x c a v a t i o n and c y c l i c l o a d i n g . 141 7.4.4 Mountain S c a l e Deformation Sakung i s a g e n e r a l term used t o d e s c r i b e the g r a v i t y d e f o r m a t i o n of v e r y l a r g e s l o p e s . T h i s r e s e a r c h has not p r e v i o u s l y d i s c u s s e d sakung because i t i s d e f i n e d as creep on a mountain s c a l e or g r a v i t a t i o n a l sagging (Varnes, 1978). I t i s b e l i e v e d t h a t many mountain s c a l e movements r e p o r t e d and termed sakung or simply creep deformation i n the l i t e r a t u r e (Tabor, 1971; Nemcok, 1972) may be more a c c u r a t e l y d e s c r i b e d as l a r g e s c a l e t o p p l e s . I t may be p o s s i b l e t o e v a l u a t e the t o p p l i n g p o t e n t i a l and deformation of very l a r g e s l o p e s u s i n g UDEC. 7.4.5 A p p l i c a t i o n of UDEC t o Slope Design The examples i n Chapter 4 and the Heather H i l l model demonstrate t h a t UDEC can be used f o r s l o p e d e s i g n i n a rock mass s u s c e p t i b l e t o t o p p l i n g . However, the accuracy of the d e s i g n i s dependent on the accuracy of the rock mass s t r e n g t h parameters used i n the model. The bes t way t o determine these parameters i s by back a n a l y s i s o f a l a r g e number of known t o p p l i n g f a i l u r e s i n s i m i l a r rock types, which has not y e t been done. I t i s recommended t h a t UDEC be used t o back analyze known f l e x u r a l t o p p l i n g f a i l u r e s t o develop a volume of case h i s t o r i e s c h a r a c t e r i z i n g rock mass s t r e n g t h . T h i s i n f o r m a t i o n 142 w i l l a l l o w more accurate e n g i n e e r i n g d e s i g n i n a rock mass s u s c e p t i b l e t o t o p p l i n g . 7.4.6 Geometric S e n s i t i v i t y S t u d i e s For each example of t o p p l i n g i n t h i s r e s e a r c h , one geometry was chosen f o r a n a l y s i s . A g r e a t d e a l more can be l e a r n e d about what c o n t r o l s f l e x u r a l t o p p l i n g by v a r y i n g the geometric parameters of the s l o p e . T h i s r e s e a r c h should be performed on small and l a r g e s c a l e h y p o t h e t i c a l s l o p e s u t i l i z i n g v a r i a t i o n i n the s l o p e face angle, column t h i c k n e s s and column i n c l i n a t i o n . 143 REFERENCES Ashby, J . , 1971: S l i d i n g and T o p p l i n g Modes of F a i l u r e i n Model and J o i n t e d Rock Slopes, MSc. t h e s i s , I mperial C o l l e g e , Royal School of Mines, London. Barton, N.R., 1986: Deformation Phenomena i n J o i n t e d Rock. Geotechnique, V o l . 36, No. 2, pp. 147-167. Bovis, M.J., 1982, U p h i l l - F a c i n g ( A n t i s l o p e ) Scarps i n the Coast Mountains, Southwest B r i t i s h Columbia, G e o l o g i c a l S o c i e t y o f America B u l l e t i n , v.93, pp. 804—812. Brown, A., 1982: T o p p l i n g Induced Movements i n Large, R e l a t i v e l y F l a t Rock Slopes: P r o c , 23rd U.S. Symposium on Rock Mechanics, Berkeley, C a l i f o r n i a , pp. 1035. Brown, I . , H i t t i n g e r , M., and Goodman, R.E., 1980: F i n i t e Element Study of the Nevis B l u f f (New Zealand) Rock Slope F a i l u r e . Rock Mechanics, V o l . 12, pp. 231-245. Burman, B.C., 1974: Development of a Numerical Model f o r D i s c o n t i n u a . A u s t r a l i a n Geomechanics J o u r n a l , 1974. pp. 1-10. Burman, B.C., T r o l l o p e , D.H., and P h i l i p , M.G., 1975: The Behaviour o f Excavated Slopes i n J o i n t e d Rock, A u s t r a l i a n Geomechanics J o u r n a l , 1975, pp.26-31. Choquet, P., Tanon, D.D.B., 1985: Nomograms f o r the Assessment of T o p p l i n g F a i l u r e i n Rock Slopes. P r o c , 26'th U.S. Symposium on Rock Mechanics, Rapid C i t y , pp. 19-30. C u n d a l l , P.A., 1971: A Computer Model f o r S i m u l a t i n g P r o g r e s s i v e , L a r g e - s c a l e Movements i n Blocky Rock Systems, Proc. I n t e r n a t i o n a l Symposium on Rock F r a c t u r e s , Nancy, France, paper I I - 8 . C u n d a l l , P.A., 1983: Numerical Modeling of Water Flow i n Rock Masses., P r o j e c t PECD 7/9/22, Department of the Environment, U n i t e d Kingdom. C u n d a l l , P.A., 1985: A Simple J o i n t Model That Embodies Continuous Y i e l d i n g , presented a t the 1985 I n t e r n a t i o n a l Symposium on the fundamentals of Rock J o i n t s . C u n d a l l , P.A, 1987: D i s t i n c t Element Models of Rock and S o i l S t r u c t u r e , i n A n a l y t i c a l and Computational Methods i n E n g i n e e r i n g Rock Mechanics, pp. 129-163. E.T. Brown, E d i t o r , George A l l e n and Unwin, London. 144 C u n d a l l , P.A., and Board, M.P., 1988: A Microcomputer Program f o r Modeling L a r g e - S t r a i n P l a s t i c i t y Problems, prepared f o r : 6'th I n t e r n a t i o n a l Conference on Numerical Methods i n Geomechanics, Innsbruck, A u s t r i a . C u n d a l l , P.A. and Hart, R.D., 1984: A n a l y s i s o f Block T e s t No. 1 I n e l a s t i c Rock Mass Behaviour: Phase 2 - A C h a r a c t e r i z a t i o n o f J o i n t Behavior ( F i n a l R e p o r t ) . I t a s c a C o n s u l t i n g Group, Subcontract SA-957, Rockwell Hanford Operations, R i c h l a n d , Washington, March 1984. C u n d a l l , P.A., and Lemos, J.V., 1988: Numerical S i m u l a t i o n of F a u l t I n s t a b i l i t i e s w i t h the C o n t i n u o u s l y - Y i e l d i n g J o i n t Model, Second I n t e r n a t i o n a l Symposium of Rock b u r s t s and S e i s m i c i t y i n Mines, U n i v e r s i t y of Minnesota, June, 1988. C u n d a l l , P.A., M a r t i , J . , B e r e s f o r d , P.J., L a s t , N.C. and Asgian, M.I., 1978: Computer M o d e l l i n g of J o i n t e d Rock Masses, U.S. Army Engineer Waterways Experiment S t a t i o n , T e c h n i c a l Report No. N-78-4, 399p. C u n d a l l , P.A., and M a r t i , J . , 1979: Some new Developments i n D i s c r e t e Numerical Methods f o r Dynamic M o d e l l i n g o f J o i n t e d Rock Masses, Proc. o f the Rapid E x c a v a t i o n and T u n n e l l i n g Conference, A t l a n t a , Georgia. C u n d a l l , P.A., Voegele, M., F a i r h u r s t , C., 1977: Computerized Design of Rock Slopes u s i n g I n t e r a c t i v e G r a p h i c s f o r the Input and Output o f Geometrical Data, Proc. 16'th Symposium on Rock Mechanics, Univ. of Minnesota, M i n n e a p o l i s , pp. 5-14. de F r i e t a s , M.H., and Watters, R.J., 1973: Some F i e l d Examples o f T o p p l i n g F a i l u r e , Geotechnique, V o l 23, no. 4, pp. 495-514. Duncan, J.M., and Goodman, R.E., 1968: F i n i t e Element A n a l y s e s of Slopes i n J o i n t e d Rock, C o n t r a c t Report S-68-3, U.S. Army Eng. Waterways Exper. S t a t i o n , Corps o f Engineers, V i c k s b u r g , Miss., 271 pp. EBA E n g i n e e r i n g C o n s u l t a n t s L t d . 1976: CPR - Rogers Pass, G e o t e c h n i c a l E v a l u a t i o n of A l t e r n a t e Routes, Report t o Canadian P a c i f i c Railways, J u l y 1976. EBA E n g i n e e r i n g C o n s u l t a n t s L t d . 1978: Heather H i l l L a n d s l i d e , G l a c i e r N a t i o n a l Park. Report t o Parks Canada, F i l e 36-0267, Feb., 1978. Evans, S.G., 1987: Su r f a c e Displacements and Massive T o p p l i n g on the Northeast Ridge of Mount C u r r i e , B r i t i s h Columbia, C u r r e n t Research, P a r t A, G e o l o g i c a l Survey o f Canada, Paper 87-1A, pp. 181-189. 145 Evans, R., V a l l i a p p a n , S., McGuckin, D., and Raja Sekar, H.L., 1981: S t a b i l i t y A n a l y s i s of a Rock Slope A g a i n s t T o p p l i n g F a i l u r e . Proc., 3rd I n t e r n a t i o n a l Symposium on Weak Rock, Tokyo., pp. 665-670. Goodman, R.E., and Bray, J.W., 1976: T o p p l i n g of Rock Slopes, Proc. of ASCE S p e c i a l t y Conference, Rock E n g i n e e r i n g f o r Foundations and Slopes, V o l . 2, Boulder, Colorado, pp. 201-234. Goodman, R.E., and Dubois, J . , 1971: D u p l i c a t i o n of D i l i t a n t Behaviour i n the A n a l y s i s of J o i n t e d Rocks. U.S. Army, Corps of Engineers, Rept., Omaha. Goodman, R.E., T a y l o r , R.L., Brekke, T.L., 1968: A Model f o r the Mechanics of J o i n t e d Rock. J o u r n a l of the S o i l Mechanics and Foundation D i v i s i o n , ASCE, May, 1968, SM 3, pp. 637-658. H i t t i n g e r , M., 1978: Numerical A n a l y s i s of T o p p l i n g F a i l u r e s i n J o i n t e d Rock: Ph.D t h e s i s , U n i v e r s i t y of C a l i f o r n i a , B e r k e l e y . Hocking, G., 1978: A n a l y s i s of T o p p l i n g - S l i d i n g Mechanisms f o r Rock Slopes: P r o c , 19'th Symposium on Rock Mechanics, pp. 288. Hoek, E., and Brown, E.T., 1980: Underground E x c a v a t i o n s i n Rock, The I n s t i t u t e of M i n i n g and M e t a l l u r g y , London. Hoek, E., and Bray, J . , 1977: Rock Slope E n g i n e e r i n g (2nd e d i t i o n ) , The I n s t i t u t e of M i ning and M e t a l l u r g y , London. Hofmann, H., 1972: Kinematische M o d e l l s t u d i e n zum Boschungsproblem i n r e g e l m a s s i g g e k l u f t e t e n Medien. V e r o f f e n t l i c h u n g e n des I n s t i t u t e s f u r Bodenmechanik und Felsmechanik, K a r l s r u h e , H e f t 54. Hofman, K. von, 1973: Modellversuche zur H a n g e l t e k t o n i c G e o l . Rdsch. 62, No. 1, pp.16-29. Holmes, G., and J a r v i s , J . J . , 1985: Large S c a l e T o p p l i n g W i t h i n a Sackung type Deformation a t Ben Attow, S c o t l a n d , Q u a r t e r l y J o u r n a l of E n g i n e e r i n g Geology, London, V o l 18, pp. 287-289. Hunt R.E., 1986: G e o t e c h n i c a l E n g i n e e r i n g A n a l y s i s and E v a l u a t i o n . McGraw H i l l Inc., 1986, p.134. I s h i d a , T., C h i g i r a , M., and H i b i n o , S., 1987: A p p l i c a t i o n of the D i s t i n c t Element Method f o r A n a l y s i s of T o p p l i n g Observed on a F i s s u r e d Rock Slope, Rock Mechanics and Rock E n g i n e e r i n g 20, pp. 277-283. 146 I t a s c a , 1989: U n i v e r s a l D i s t i n c t Element Code: Manual, V e r s i o n ICG1.5, I t a s c a C o n s u l t i n g Group, Inc., M i n n e a p o l i s , Minnesota. K a l k a n i , E.C., 1977: Two Dimensional F i n i t e Element A n a l y s i s f o r the Design of Rock Slopes. 16'th Symposium on Rock Mechanics, U n i v e r s i t y of Minnesota, M i n n e a p o l i s , U.S.A., pp. 15-24. K a l k a n i , E.C., and P i t e a u , D.R., 1976: F i n i t e Element A n a l y s i s o f T o p p l i n g F a i l u r e a t H e l l ' s Gate B l u f f s , B r i t i s h Columbia. B u l l , assoc. Eng. Geol., 13, pp. 315-327. K u y k e n d a l l , L. , 1975: Kinematic Study of T o p p l i n g F a i l u r e Mode and P r a c t i c a l Aspects of Using the Base F r i c t i o n M o d e l l i n g Machine. I n t e r n a l Report, U n i v e r s i t y o f C a l i f o r n i a , Berkeley, Department of C i v i l E n g i n e e r i n g . Ladanyi, B., and Archambault, G., 1969: S i m u l a t i o n o f Shear Behaviour o f a J o i n t e d Rock Mass. 11'th Symposium on Rock Mechanics, Berkeley, C a l i f o r n i a , pp. 105-125. Lemos J.V., and Brady B.H.G., 1983: S t r e s s D i s t r i b u t i o n i n a J o i n t e d and F r a c t u r e d Medium, 24'th U.S. Symposium on Rock Mechanics, June, 1983, pp. 53-59. Lemos, J.V., Hart, R.D., and C u n d a l l , P.A., 1985: A G e n e r a l i z e d D i s t i n c t Element Program f o r M o d e l l i n g J o i n t e d Rock Mass, Proc. I n t . Symp. on Fundamentals o f Rock J o i n t s , B j o r k l i d e n , Sweden, pp. 335-343. L o r i g , L . J . , 1984: A Hy b r i d Computational Model f o r E x c a v a t i o n and Support Design i n J o i n t e d Media, Ph.D. T h e s i s , U n i v e r s i t y of Minnesota, 1984. Mathewes, R.W., and Heusser, L.E., 1981: A 12,000 Year P a l y n o l o g i c a l Record of Temperature and P r e c i p i t a i o n Trends i n Southwestern B r i t i s h Columbia. Canadian J o u r n a l of Botany, V o l . 59, pp. 707-710. M o l l a r d , J.D., 1977: Regiona l L a n d s l i d e Types i n Canada, i n Reviews i n E n g i n e e r i n g Geology, V o l . 3: L a n d s l i d e s . Boulder, Colorado, G e o l o g i c a l s o c i e t y of America, pp. 29-56. M u l l e r , L., 1968: New c o n s i d e r a t i o n s on the Vajont S l i d e , Felsmechanik und I n g e n i e u r g e o l o g i e , V o l . 6, no. 1, pp. 1-91. Nemcock, A., 1972: G r a v i t a t i o n a l Slope Deformation i n High Mountains. Proceedings, 24'th I n t e r n a t i o n a l G e o l o g i c a l Congress, Sec. 1, pp. 132-141. 147 N i e t o A.S., 1987: I n f l u e n c e of G e o l o g i c a l D e t a i l s on the F i e l d Behavior of S o i l s and Rocks: Some Case H i s t o r i e s , i n R.B. Peck Symposium Volume: The A r t and Science of G e o t e c h n i c a l E n g i n e e r i n g a t the Dawning of the Twenty-F i r s t Century. W.T. H a l l , E d i t o r , P r e n t i c e - H a l l Inc., Englewood C l i f f s , New J e r s e y . O t t e r , J.R.H., C a s s e l l , A . C , Hobbs, R.E., 1966: Dynamic R e l a x a t i o n , Proc. I n s t , of C i v i l Eng., V o l . 35, D e c , 1966, pp. 633-656. Patton, F.D. and Hendron A.J., 1974: Mass Movements - General Report, Theme V. 2nd I n t e r n a t i o n a l Congress of E n g i n e e r i n g Geology, Sao Paulo, pp. 1-57. Patton, F.D., 1966: M u l t i p l e Modes of Shear F a i l u r e i n Rock and R e l a t e d M a t e r i a l s . Ph.D t h e s i s , U n i v e r s i t y of I l l i n o i s a t Urbana. P i t e a u and A s s o c i a t e s L t d . , 1988: P r e l i m i n a r y G e o t e c h n i c a l Assessment o f South Wall Slope S t a b i l i t y Problems, u n p u b l i s h e d r e p o r t t o Brenda Mines L t d . , Oct. 6, 1988 P i t e a u and A s s o c i a t e s L t d . , 1982: E n g i n e e r i n g Geology and Rock Mechanics Assessments f o r E s t i m a t i n g Support Requirements f o r the Proposed Rogers Pass Short Tunnel. Report t o CPR. P r o j e c t 81-340, March 1982 P i t e a u , D.R., and M a r t i n , D.C., 1981: Mechanics of Rock Slope F a i l u r e . 3rd I n t . Conference on S t a b i l i t y i n Surface Mining, C O . Brawner ed. , pp. 113. P i t e a u , D.R. , Stewart, A.F., and M a r t i n , D.C, 1981: Design Examples of Open p i t Slopes S u s c e p t i b l e t o T o p p l i n g . P r o c T h i r d I n t e r n a t i o n a l Conference on S t a b i l i t y i n S u r f a c e Mining, Soc. of Min. Eng. of AIME, Vancouver, pp. 679-712. Poulton, T.P., and Simony, P.S. 1980: S t r a t i g r a p h y , sedimentology, and r e g i o n a l c o r r e l a t i o n of the H o r s e t h i e f Creek Group (Hadrynian, Late Precambrian) i n the northern P u r c e l l and S e l k i r k Mountains, B r i t i s h Columbia. Canadian J o u r n a l of E a r t h S c i e n c e s v.17, pp. 1708-1724. P r i t c h a r d M.A., Savigny K.W., and Evans S.G., 1988: Deep-Seated Slope Movements i n the Beaver R i v e r V a l l e y , G l a c i e r N a t i o n a l Park, B.C.. G e o l o g i c a l Survey of Canada, Open F i l e 2011. Radbruch-Hall, D.H., Varnes, D.J., and Savage, W.Z., 1976: G r a v i t a t i o n a l Spreading of Steep-Sided Ridges ("sakung") i n Western U n i t e d S t a t e s . I n t . A s s o c of Eng. Geology, B u l l . No. 14, pp. 23-35. 148 Rapp, P.A. 1987: Rock T o p p l i n g and Massive Slope I n s t a b i l i t y i n the Beaver V a l l e y , B r i t i s h Columbia., unpub. B.A.Sc t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, V a n e , B.C. R i c k a r d M.J. 1961: A note on cleavages i n c r e n u l a t e d rocks. Geol. Mag., v.98 no.4, pp. 324-332. Sagaseta C., 1986: On the Modes of I n s t a b i l i t y of a R i g i d Block on an I n c l i n e d Plane, Rock Mechanics and Rock E n g i n e e r i n g 19, pp. 261-266. Simony, P.S., and Wind, G. 1970: S t r u c t u r e of the Dogtooth Range and a d j a c e n t p o r t i o n s of the Rocky Mountain Trench, i n S t r u c t u r e s of the Canadian C o r d i l l e r a . G e o l o g i c a l A s s o c i a t i o n of Canada, S p e c i a l Paper 6, pp. 41-51. Soto, C , 1974, A Comparative Study of Slope M o d e l l i n g Techniques f o r F r a c t u r e d Ground, MSc. t h e s i s , I m p e r i a l C o l l e g e , Royal School of Mines, London. Tabor, R.W., 1971, O r i g i n of Ridge-Top Depressions by Large-s c a l e Creep i n the Olympic Mountains, Washington. G e o l o g i c a l S o c i e t y o f America B u l l e t i n , v.82, pp. 1811-1822. Teme S . C , and West T.R., 1983: Some Secondary T o p p l i n g F a i l u r e Mechanisms i n Discontinuous Rock Slopes, 24'th U.S. Symposium on Rock Mechanics, June, 1983. T e r z a g h i , K., 1962: S t a b i l i t y o f Steep Slopes on Hard Unweathered rock. Geotechnique, V o l . 12, pp. 251-270. Thurber C o n s u l t a n t s L t d . , 1983a: Rogers Pass R e v i s i o n , Volume 1: Geology, Geomorphology and Hydrology. Report t o CP R a i l S p e c i a l P r o j e c t s , F i l e 17-6-58 Thurber C o n s u l t a n t s L t d . , 1983b: Rogers Pass R e v i s i o n , Volume 5: Beaver V a l l e y Grade 1982 Route I n v e s t i g a t i o n , P a r t 3. Report t o CP R a i l S p e c i a l P r o j e c t s , F i l e 17-6-58 Thurber C o n s u l t a n t s L t d . 1979: Assessment of G r i f f i t h L a n d s l i d e s f o r Proposed Rogers Pass Grade R e v i s i o n , M i l e 72.2 t o 73.1 Mountain S u b d i v i s i o n , Report t o CP R a i l S p e c i a l P r o j e c t s . F i l e 17-6-31, December, 1979. VanBuskirk, CD., 1987: Reassessment of the G r i f f i t h L a n d s l i d e , Rogers Pass, B r i t i s h Columbia, unpub. B.A.Sc. t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, V a n e , B.C. Varnes, D.J., 1978: Slope Movements Types and Processes, i n L a n d s l i d e s , A n a l y s i s and C o n t r o l , T r a n s p o r t Research Board S p e c i a l Report 176, Schuster R.L. and Raymond J.K., e d i t o r s , N a t i o n a l Academy of Scien c e s , Washington, D.C. 149 Wheeler, J.O. 1963: Rogers Pass map area, B r i t i s h Columbia and A l b e r t a (82N Wl/2). G e o l o g i c a l Survey of Canada, Paper 62-32. W i l l i a m s J.R., and Mustoe, G.W, 1987: Modal Methods f o r the A n a l y s i s of D i s c r e t e Systems, Computers and Geotechnics, 4, pp.1-19. Whyte, R.J., 1973, A Study of P r o g r e s s i v e Hanging Wall Caving a t Chambishi Coppermine i n Zambia Using the Base F r i c t i o n Model Concept, M.Sc. t h e s i s , I mperial c o l l e g e , Royal School of Mines, London. W y l l i e , D.C., 1980: T o p p l i n g Rock Slope F a i l u r e s ; Examples of A n a l y s i s and S t a b i l i z a t i o n . Rock Mechanics, V o l . 13, pp. 89-98. Zanbak C., 1983: Design Charts f o r Rock Slopes S u s c e p t i b l e t o T o p p l i n g , J o u r n a l of G e o t e c h n i c a l E n g i n e e r i n g , ASCE, V.109, pp. 1039-1061. 150 APPENDIX 1 UDEC Input Data F i l e s f o r : — Goodman and Bray Block Topple, S e c t i o n 4.2 — Base F r i c t i o n Model, S e c t i o n 4.3.1 — Brenda Mine Model, S e c t i o n 4.4 151 **Goodman and Bray Block Topple** START ROUND .1 BLOCK -8.66025 -97.5 56.02241 0.46634 -97.5 SAVE GB1 *CRACK FOLIATION FOR BLOCKS 10-16 131.0641 4.9706 131.0641 CRACK 82.10254 -34.7057 61.60254 0 CRACK 90.26279 -28.8397 72.76279 1 CRACK 98.42304 -22.9737 83.92304 2 CRACK 106.5833 -17.1076 95.08330 2 CRACK 114.7435 -11.2416 106.2435 3 CRACK 122.9038 -5.37564 117.4038 4 CRACK 131.0640 0.490381 128.5640 4 *CRACK FOLIATION FOR BLOCKS 1-10 .801270 .471143 .141016 .810889 .480762 .150635 .820508 CRACK 0 -92.5 -2.5 -88 .1698 CRACK 8 . 660254 -87.5 3.660254 -78 .8397 CRACK 16. 82050 -81 . 6339 9.820508 -69 .5096 CRACK 24. 98076 -75 .7679 15.98076 -60 .1794 CRACK 33. 14101 -69 .9019 22.14101 -50 .8493 CRACK 41. 30127 -64 . 0358 28.30127 -41 .5192 CRACK 49. 46152 -58 . 1698 34.46152 -32 .1891 CRACK 57. 62177 -52 .3038 40.62177 -22 .8589 CRACK 65. 78203 -46 .4378 46.78203 -13 . 5288 CRACK 73 . 94228 -40 . 5717 52.94228 -4. 19872 SAVE GB2 *CRACK BASE OF BLOCKS CRACK 0 -92.5 8.660254 -87.5 CRACK 8.160254 -86 .6339 16.82050 -81 .6339 CRACK 16. 32050 -80 .7679 24.98076 -75 .7679 CRACK 24. 48076 -74 .9019 33.14101 -69 .9019 CRACK 32. 64101 -69 . 0358 41.30127 -64 . 0358 CRACK 40. 80127 -63 . 1698 49.46152 -58 .1698 CRACK 48. 96152 -57 .3038 57.62177 -52 .3038 CRACK 57. 12177 -51 .4378 65.78203 -46 .4378 CRACK 65. 28203 -45 .5717 73.94228 -40 .5717 CRACK 73. 44228 -39 .7057 82.10254 -34 .7057 CRACK 81. 60254 -33 .8397 90.26279 -28 .8397 CRACK 89. 76279 -27 .9737 98.42304 -22 .9737 CRACK 97. 92304 -22 . 1076 106.5833 -17 . 1076 CRACK 106 .0833 -16 .2416 114.7435 -11 .2416 CRACK 114 .2435 -10 .3756 122.9038 -5. 37564 CRACK 122 .4038 -4. 50961 131.0640 0.490381 SAVE GB3 * CRACK OFF TOP OF BLOCKS CRACK 6.160254 -83.1698 -2.5 CRACK 12.32050 -73.8397 3.660254 CRACK 18.48076 -64.5096 9.820508 CRACK 24.64101 -55.1794 15.98076 CRACK 30.80127 -45.8493 22.14101 CRACK 36.96152 -36.5192 28.30127 •88.1698 -78.8397 -69.5096 -60.1794 -50.8493 -41.5192 152 CRACK 43 . 12177 -27.1891 34 . 46152 -32 .1891 CRACK 49. 28203 -17.8589 40. 62177 -22 .8589 CRACK 55. 44228 -8.52885 46. 78203 -13 .5288 CRACK 61. 60254 0.801270 52. 94228 -4. 19872 CRACK 72. 76279 1.471143 64. 10254 -3 . 52885 CRACK 83 . 92304 2.141016 75. 26279 -2 . 85898 CRACK 95. 08330 2.810889 86. 42304 -2. 18911 CRACK 106 .2435 3 .480762 97. 58330 -1. 51923 CRACK 117 .4038 4.150635 108 .7435 -0. 84936 CRACK 128 .5640 4.820508 119 .9038 -0. 17949 SAVE GB4 *DELETE SMALL BLOCKS LEFT ON SLOPE DEL 0,133 -100,10 26 **CRACK BASE BLOCK CRACK -8.660254,-97.5 0,-92.5 SAVE GB5 **PROPERTIES FOR MATERIAL 1 (AREA CONTACT):CONS=l, JCONS=2 PROP MAT=1 DENS=.0025484 BULK=26974 G=25554 JKN=25000 PROP MAT=1 JKS=25000 JCOH=0 JTEN=0 JDIL=0 JFRIC=.80 SAVE GB6 **ASSIGN MATERIAL NUMBER, CONSTITUTIVE LAW CHANGE MAT=1 CONS=l JCONS=2 SAVE GB7 **SET BOUNDARY CONDITIONS: FIX BOTTOM AND END BLOCK FIX 60 100 -80 -40 FIX -10 0 -100 -90 *SET HISTORIES HIST XVEL 52,-4 YVEL 52,-4 XDIS 52,-4 YDIS 52,-4 XVEL 96 -2.5 HIST YVEL 96 -2.5 XDIS 96 -2.5 YDIS 96 -2.5 HIST DAMP **APPLY GRAVITY TO BLOCKS GRAVITY 0 -9.81 SAVE GB8 FRAC=.1 DAMP AUTO CYCLE=0 SAVE GB9 cycle=5000 save gblO d e l -10 0 -100 -90 g r a v i t y 0 -9.81 save gblOa STOP 153 **DATA FILE FOR KUK. FIG 4-13 **FDEF BLOCKS* **100 times l a r g e r than base f r i c t i o n modeL ************************************* START ROUND .3 **CREATE CENTER AND SUPPORT BLOCKS** BLOCK 0,0 76.2,0 76.2,-36.48 0,-36.48 CRACK -1,-30.48 77.2,-30.48 CRACK 73.15,1 73.15,-30.5 CRACK 3.048,0 3.048,-30.5 SAVE F l **FIX VELOCITIES OF BOUNDARY SUPPORT BLOCKS** FIX 0,76.2 -36.5,-30.5 FIX 73.2,76 -30.5,0 FIX 0 3.0 -30,0 **CREATE CENTER BLOCK PROPERTIES** PROP MAT=1 DEN=.0026 BULK=10500 G=5700 COH=.15 FRIC=1 JKN=15000 + JKS=10000 PROP MAT=1 TENS=.l JCOH=0 JTENS=0 JFRIC=.81 DIL=0 PROP MAT=3 DEN=.0026 BULK=10000 G=10000 JKS=10000 JKN=15000 + JFRIC=.81 PROP MAT=3 FRIC=1 COH=l TENS=.l DIL=0 **CREATE JOINTS** JREGION 1.5,0 73.15,0 73.15,-30.5 4,-30.5 JSET -60,0 80,0 0,0 5.08,0 21.33,-30.48 **CRACK FOR LATER EXCAVATION** CRACK 21.33,-30.48 28.017,-978 **ASSIGN BLOCK AND JOINT PROPERTIES TO FDEF ZONE AND SUPPORT** CHANGE 3.046,73.16 -30.5,0 MAT=1 Cons=3 JCons=2 JMat=l GENER REG 21.33,-30.5 27.8,0 73.1,0 73.1,-30.5 QUAD 2.2 GENER REG 21.33,-30.5 27.8,0 73.1,0 73.1,-30.5 EDGE 3.6 GENER REG 3.048,0 27,0 21,-30 3.048,-30 EDGE 10 **STIFFEN SUPPORT BLOCKS ALLOWING MAT=1 JOINT ON BOUNDARIES** CHANGE 0,77 -3 6,-29 MAT=3 JMAT=1 CONS=l CHANGE 0,4.0 -3 0.5,0 MAT=3 JMAT=1 CONS=l CHANGE 72 77 -30,0 MAT=3 JMAT=1 CONS=l **ASSIGN HISTORIES ON FACE AT TOP BOTTOM AND MIDDLE** HIST XVEL 27.8,-1.5 YVEL 27.8,-1.5 XDIS 27.8,-1.5 YDIS 27.8,-1.5 HIST XVEL 21.35,-30.47 YVEL 21.35,-30.47 XDIS 21.35,-30.47 HIST YDIS 21.35,-30.47 DAMP TYPE 9 HIST XVEL 24.49,-15.63 YVEL 24.49 -15.63 XDIS 24.49 -15.63 HIST YDIS 24.49 -15.63 HIST TYPE 1 ••CONSOLIDATE CENTER BLOCKS** INSITU 3,73 -30.5 0 STR 0,0,0 YGRAD .0265, 0, .0265 GRAVITY 0,-9.81 FRAC=.2 DAMP AUTO save F2 CYC 0 154 SAVE F2 CYC 2000 SAVE F3 **EXCAVATE SLOPE** DEL 0,21.33 -30.48,0 DEL 21.33 27.80 -20 0 **RESET RECORDS RESET DISP HIST JDISP TIME ROTA **RE-ASSIGN HISTORIES ON FACE AT TOP MIDDLE AND BOTTOM** HIST XVEL 29,-2 YVEL 29,-2 XDIS 29,-2 YDIS 29,-2 HIST XVEL 21.35,-30.47 YVEL 21.35,-30.47 XDIS 21.35,-30.47 HIST YDIS 21.35,-30.47 DAMP TYPE 9 HIST XVEL 24.49,-15.63 YVEL 24.49 -15.63 XDIS 24.49 -15.63 HIST YDIS 24.49 -15.63 HIST TYPE 1 frac=.2 **APPLY GRAVITY TO SLOPE** g r a v i t y 0 -9.81 HIST NCYC 50 SAVE F4 STOP **(From t h i s p o i n t reduce s t r e n g t h o f rock and j o i n t s t o f a i l u r e ) 155 * * DATA FILE FOR BRENDA MINES SLOPE, **FDEF BLOCKS* ************************************* START ROUND 1. **CREATE CENTER AND SUPPORT BLOCKS** BLOCK 0 ,0 800,0 800, -300 0,-300 **BENCH FACE CRACKS CRACK 440.000 0 .000 459.0498 -30. 4798 CRACK 470.480 -30 .480 489.5298 -60. 9593 CRACK 500.960 -60 .960 520.0099 -91. 4389 CRACK 531.440 -91 .439 550.4900 -121 .918 CRACK 561.919 -121 .919 580.9701 -152 .398 CRACK 592.399 -152 .399 611.4502 -182 .877 CRACK 622.879 -182 .879 641.9303 -213 .357 **BENCH LEVEL CRACKS CRACK 459.0498 -30. 4798 800.000 -30 .480 CRACK 489.5298 -60. 9593 800.000 -60 .960 CRACK 520.0099 -91. 4389 800.000 -91 .439 CRACK 550.4900 -121 .918 800.000 -121 .919 CRACK 580.9701 -152 .398 800.000 -152 . 399 CRACK 611.4502 -182 .877 800.000 -182 .879 CRACK 641.9303 -213 .357 800.000 -213 .357 **CREATE CENTER BLOCK PROPERTIES** PROP MAT=1 DEN=.0027 BULK=33333 G=20000 COH=.15 FRIC=.70 + JKN=40000 JKS=20000 PROP MAT=1 TENS=.21 JCOH=0 JTENS=0 JFRIC=.4 66 DIL=0 PROP JMAT=2 JKN=40000 JKS=20000 JCOH=3 JTENS=5 JFRIC=.84 **CRACK TO DIVIDE FDEF ZONES** CRACK 0,-150 626.653,-300 **CREATE JOINT SET** JREGION 0,0 800,0 800,-300 0,-300 JSET 80,0 400,0 0,0 27.43,0 641.9303,-213.357 SAVE BR1 **ASSIGN BLOCK AND JOINT PROPERTIES TO FDEF ZONES* CHANGE MAT=1 Cons=3 JCons=2 JMat=l **BASE BLOCK GENER REG 0,-300 0,-150 626.6,-299 626.6,-301 EDGE 90 **TOE REGION GENER REG 641.9,-213.3 800,-213.3 800,-300 626.6,-300 EDGE 60 **MATERIAL TO BE EXCAVATED CLOSE TO FACE GENER REG 440,0 500,0 800,-213.4 641.9,-213.4 EDGE 60 **MATERIAL TO BE EXCAVATED FAR FROM FACE GENER REG 500,-1 500,1 800,0 800,-213.358 EDGE 90 **MAIN SLOPE GENER REG 216.8,-188.2 250,0 641.9,-213.3 633.4,-261.67 EDGE 32 GENER REG 0,0 250,0 216.8,-188.2 0,-150 EDGE 90 **FIX ARTIFICIAL CRACK AND EXCAVATION LEVEL CRACKS** CHANGE ANGLE -15,1 JMAT=2 **ASSIGN HISTORIES ON FACE AT TOP MIDDLE AND BOTTOM** **TOP OF BENCH 1 HIST XVEL 440.000,0.000 YVEL 440,0 XDIS 440,0 YDIS 440,0 156 **TOP OF BENCH 2 HIST XVEL 470.48,-30.48 YVEL 470.48,-30.48 HIST XDIS 470.48,-30.48 YDIS 470.48,-30.48 **TOP OF BENCH 3 HIST XVEL 500.96,-60.96 YVEL 500.96,-60.96 HIST XDIS 500.96,-60.96 YDIS 500.96,-60.96 **TOP OF BENCH 4 HIST XVEL 531.44,-91.44 YVEL 531.44,-91.44 HIST XDIS 531.44,-91.44 YDIS 531.44,-91.44 **TOP OF BENCH 5 HIST XVEL 561.92,-121.92 YVEL 561.92,-121.92 HIST XDIS 561.92,-121.92 YDIS 561.92,-121.92 **TOP OF BENCH 6 HIST XVEL 592.40 -152.40 YVEL 592.40,-152.40 HIST XDIS 592.40 -152.40 YDIS 592.40,-152.40 **TOP OF BENCH 7 HIST XVEL 622.88 -182.88 YVEL 622.88,-182.88 HIST XDIS 622.88 -182.88 YDIS 622.88,-182.88 **BASE OF SLOPE HIST XVEL 641.9,-213.4 YVEL 641.9,-213.4 HIST XDIS 641.9,-213.4 YDIS 641.9,-213.4 HIST DAMP TYPE 9 **ASSIGN BOUNDARY CONDITIONS** BOUND 0,800 -301,-299 YVEL=0 BOUND -1,1 -3 00,0 XVEL=0 BOUND 799,801 -300,0 XVEL=0 ••CONSOLIDATE STABLE PROBLEM** GRAVITY 0,-9.81 FRAC=.1 DAMP AUTO save BR2 CYC 0 SAVE BR3 CYC 7500 SAVE BR4 **EXCAVATE FIRST TWO BENCHES DEL 440,800 -60,0 AREA=1000 **APPLY GRAVITY TO SLOPE** CYC 5000 SAVE BR5 **EXCAVATE NEXT TWO BENCHES DEL 440,800 -121,0 AREA=1000 CYC 5000 SAVE BR6 DEL 440,800 -183,0 AREA=1000 CYC 5000 SAVE BR7 DEL 440,800 -213,0 AREA=1000 CYC 5000 SAVE BR8 STOP **(Continue by l o w e r i n g j o i n t f r i c t i o n angle t o f a i l u r e ) 157 APPENDIX 2 S t r u c t u r a l Data from Heather H i l l Study Area 158 The s t e r e o g r a p h i c p r o j e c t i o n s c o n t a i n e d i n t h i s appendix are equal area p r o j e c t i o n s (Schmidt n e t ) , and were processed u s i n g software a v a i l a b l e i n the Geology Department at UBC. 159 CREEK A SO BEDDING AND S2 CLEAVAGE North _ I _ T EQUAL AREA PROJECTION Symbol SO B e d d i n g F o l i a t i o n , Creek A 30 P o i n t s • FOLIATIONS, LOWER PART CRKA, SEPT 23,1988 22 P o i n t s • CRENULATION CLEAVAGES IN CREEK "A" 17 P o i n t s A CREN., CLEAVAGE, LOWER PART CRKA, SEPT 23, 1988 12 P o i n t s A 81 P o i n t s T o t a l 160 CREEK A SO BEDDING AND S 2 CLEAVAGE: CONTOUR PLOT N o r t h - _ I _ + LEGEND ( f o r f i r s t 9 I n t e r v a l s ) m B m 15 9 22 1- 7 8- 14 21 28 29- 35 0 3 6 -43-5 0 -5 7 -42 49 5 6 6 3 81 P o i n t s C o n t o u r Method: C o u n t i n g A r e a : C o n t o u r I n t e r v a l : Maximum c o n t o u r : S c h m i d t (1925) 0 . 0 1 0 7% P o i n t s per 1% Area 2 1 NOTE: C o n t o u r P a t t e r n s Repeat E v e r y 9 I n t e r v a l s 1 6 1 CREEK A: JOINT PLOT N o r t h I 54 P o i n t s T o t a l 162 CREEK B BEDDING AND S2 CLEAVAGE N o r t h I EQUAL AREA PROJECTION Symbol SO B e d d i n g F o l i a t i o n , Creek B 34 P o i n t s • SO B e d d i n g F o l i a t i o n , Creek B, S e p t . 11,12 1988 14 P o i n t s • S2 C l e a v a g e F o l i a t i o n , Creek B 30 P o i n t s A S2 C l e a v a g e F o l i a t i o n , Creek B, S e p t . 1988 6 P o i n t s A 84 P o i n t s T o t a l 1 6 3 CREEK B SO BEDDING AND S2 CLEAVAGE: CONTOUR PLOT N o r t h LEGEND ( f o r f i r s t m B B 10- 18 19- 27 28-37-36 45 9 i n t e r v a l s ) H 46- 54 B 55- 63 a 64-• 73-84 P o i n t s 72 81 C o n t o u r Method: C o u n t i n g A r e a : C o n t o u r I n t e r v a l : Max1BUB c o n t o u r : S c h a i d t (1925) 0.010 9% P o i n t s per 1* A r e a 18 N O T E : C o n t o u r P a t t e r n s Repeat E v e r y 9 I n t e r v a l s 164 CREEK B: JOINT PLOT N o r t h I 32 P o i n t s T o t a l 165 CREEK C SO BEDDING AND S 2 CLEAVAGE N o r t h I _ EQUAL AREA PROJECTION Symbol SO B e d d i n g F o l i a t i o n Creek C 38 P o i n t s • 32 C l e a v a g e F o l i a t i o n , Creek C 32 P o i n t s A 70 P o i n t s T o t a l 166 CREEK C SO BEDDING AND S 2 CLEAVAGE: CONTOUR PLOT N o r t h I + LEGEND (Cor f i r s t m 5 s 1- 6 7- 12 13- 18 19 2 5 24 30 9 I n t e r v a l s ) S 31- 36 37- 42 43- 48 49- 54 70 P o i n t s 0 C o n t o u r Method: C o u n t i n g A r e a : C o n t o u r I n t e r v a l : Maximum C o n t o u r : Schmidt (1925) 0.010 6% P o i n t s p e r 1% A r e a 24 NOTE: Contour P a t t e r n s R e p e a t E v e r y 9 I n t e r v a l s 167 J o i n t O r i e n t a t i o n s , Creek C N o r t h 29 P o i n t s T o t a l 168 JOINT PLOT FOR CREEK A, B, AND C N o r t h I EQUAL AREA PROJECTION Symbol J o i n t R e a d i n g s , Creek A, Aug. 4,5 1988 21 P o i n t s + J o i n t R e a d i n g s , Creek A, S e p t . 23 33 P o i n t s + J o i n t Measurements i n Creek B 31 P o i n t s A J o i n t Measurements i n Creek B, S e p t . 23, 1988 1 P o i n t s A J o i n t O r i e n t a t i o n s , Creek C 29 P o i n t s • 11S. P o i n t s T o t a l 169 COUNTOUR P L O T " OF POLES TO A L L JOINTS N o r t h I 115 P o i n t s LEGEND ( f o r f i r s t 9 i n t e r v a l s ) m 1- 3 S3 16- 18 Contour Method: Schmidt (1925) a 4- 6 19- 21 C o u n t i n g A r e a : 0.010 EB 7- 9 22- 24 C o n t o u r I n t e r v a l : 3% P o i n t s per 1% 9 10- 12 • 25- 27 Maximum Contour: 9 E9 13- 15 NOTE: Co n t o u r P a t t e r n s Repeat E v e r y 9 I n t e r v a l s 170 SCARP TRAVERSE SO BEDDING AND S2 CLEAVAGE N o r t h EQUAL AREA PROJECTION Symbo SO BEDDING FOLIATION, SCARP, AUG. 10,11,13 54 P o i n t s • SO BEDDING FOLIATION UP SCARP FROM STA.137, AUG 11 4 P o i n t s • S2 CRENULATION CLEAVAGE, SCARP, AUG. 10,11,13 41 P o i n t s A S2 CRENULATION CLEAVAGE UP SCARP FROM STA. 137 3 P o i n t s A 102 P o i n t s T o t a l 171 SCARP TRAV. SO BEDDING, S2 CLEAVAGE: CONTOUR PLOT N o r t h I 95 P o i n t s LEGEND ( f o r f i r s t 9 i n t e r v a l s ) CD 1- 7 S 36- 42 C o n t o u r Method: Schmidt (1925) B 8 - 1 4 0 43- 49 C o u n t i n g A r e a : 0.010 ffl 15- 21 IS 50- 56 Contour I n t e r v a l : 1% P o i n t s per 1% A r e a BE 22- 28 • 57- 63 Maximum C o n t o u r : 21 29- 35 NOTE: Contour P a t t e r n s Repeat E v e r y 9 I n t e r v a l s 172 JOINTS ON SCARP TRAVERSE, AUGUST 10, 11, 13, 1988 No r t h I I EQUAL AREA PROJECTION Symbol JOINTS ON SCARP TRAVERSE, AUGUST 10, 11, 13, 1988 71 P o i n t s + 71 P o i n t s T o t a l 173 JOINTS ON SCARP TRAVERSE, AUGUST 10 , 11 , 13 , 1988 N o r t h LEGEND ( f o r f i r s t 9 i n t e r v a l s ) m B EB EB 1-6-11-16- 20 21- 25 5 10 15 26- 30 31- 35 36- 40 41- 45 71 P o i n t s Contour Method: Schmidt (1925) C o u n t i n g A r e a : 0.010 Contour I n t e r v a l : 5% P o i n t s per 1% Maximum C o n t o u r : 10 NOTE: Contour P a t t e r n s Repeat E v e r y 9 I n t e r v a l s 174 APPENDIX 3 Data Input F i l e f o r UDEC Model of Heather H i l l L a n d s l i d e . 175 * * DATA FILE FOR HEATHER HILL BASE **FDEF BLOCKS* **New Data Deck, with changing sp a c i n g **PRIMARY DISCONTINUITY DIP 65 DEG., PURE FLEXURE * *GRADATIONAL ROCK PROPERTIES ************************************* START ROUND 2.0 **CREATE CENTER AND SUPPORT BLOCKS** BLOCK 0,0 2160,0 2160,-1300 0,-1300 **CRACK OFF CORNERS CRACK 1890,20 2170,-600 CRACK 2200,-560 580,-1310 **FINAL SLOPE PROFILE CRACKS CRACK 0,-870 340,-855 CRACK 340,-855 390,-840 CRACK 390,-840 450,-790 CRACK 450,-790 750,-530 CRACK 750,-530 1895,0 **FIRST LEVEL GLACIAL EXCAVATION CRACK AND VALLEY BOTTOM CRACK 0,-790 450,-790 CRACK 350,-700 565,-700 CRACK 190,-790 750,-530 **INITIAL EXCAVATION LEVEL CRACKS CRACK 0 -200 500,0 CRACK 0 -400 900 0 CRACK 0 -600 1300 0 CRACK 0 -750 1600 0 **DELETE CORNERS DEL 1900,2200 -600,0 DEL 1400,2200 -1300,-900 * * * * * * * * * * * * * * * **CREATE INITIAL GRADATIONAL ROCK PROPERTIES** **MAT=1** PROP MAT=1 DEN=.0027 BULK=9500 G=8700 COH=.100 FRIC=.649 PROP MAT=1 JKN=1200 JKS=600 PROP MAT=1 TENS=.050 JCOH=0 JTENS=0 JFRIC=.404 JDIL=0 **MAT=2** PROP MAT=2 DEN=.00269 BULK=9650 G=9100 JKS=1275 JKN=2550 JFRIC=.466 PROP MAT=2 FRIC=.687 COH=.150 TENS=.075 DIL=0 JTENS=0 JDIL=0 JCOH=0 **MAT=3** PROP MAT=3 DEN=.00268 BULK=9800 G=9400 JKS=1800 JKN=3600 JFRIC=.532 PROP MAT=3 FRIC=.726 COH=.200 TENS=.100 DIL=0 JTENS=0 JDIL=0 JCOH=0 **MAT=4** PROP MAT=4 DEN=.00267 BULK=9950 G=9750 JKS=2400 JKN=4800 JFRIC=.601 PROP MAT=4 FRIC=.781 COH=.250 TENS=.125 DIL=0 JTENS=0 JDIL=0 JCOH=0 **MAT=5** PROP MAT=5 DEN=.00266 BULK=10100 G=10100 JKS=3000 JKN=6000 PROP MAT=5 JFRIC=.700 PROP MAT=5 FRIC=.854 COH=.300 TENS=.150 DIL=0 JTENS=0 JDIL=0 JCOH=0 **MAT=6** PROP MAT=6 DEN=.00265 BULK=10250 G=10450 JKS=3600 JKN=7200 PROP MAT=6 JFRIC=.810 PROP MAT=6 FRIC=.933 COH=.350 TENS=.175 DIL=0 JTENS=0 JDIL=0 JCOH=0 176 **MAT=7** PROP MAT=7 DEN=.00264 BULK=10400 G=10800 JKS=4200 JKN=8400 PROP MAT=7 JFRIC=.965 JCOH=0 PROP MAT=7 FRIC=1.036 COH=.400 TENS=.200 DIL=0 JTENS=0 JDIL=0 **MAT=8** PROP MAT=8 DEN=.00263 BULK=10550 G=11150 JKS=4800 JKN=9600 PROP MAT=8 JFRIC=1.072 JCOH=0 PROP MAT=8 FRIC=1.150 COH=.450 TENS=.225 DIL=0 JTENS=0 JDIL=0 **MAT=9** PROP MAT=9 DEN=.00262 BULK=10700 G=11500 JKS=5400 JKN=10800 PROP MAT=9 JFRIC=1.192 JCOH=0 PROP MAT=9 FRIC=1.280 COH=.500 TENS=.250 DIL=0 JTENS=0 JDIL=0 *************************** **CREATE PROPERTIES TO FIX LOWER BOUND CRACK** PROP JMAT=10 JKN=1200 JKS=600 JFRIC=1. JCOH=l JTEN=.3 ************* **CREATE PRIMARY JOINT SET** JREGION 0,-1300 0,-870 390,-840 600,-1300 JSET -65,0 700,0 0,0 25,0 0,-1300 JREGION 600,-1300 390,-840 750,-530 1016,-1110 JSET -65,0 700,0 0,0 25,0 0,-1300 JREGION 1016,-1110 750,-530 1111,-363 1375 -944.4 JSET -65,0 720,0 0,0 33,0 1015,-1110 JREGION 1375,-944.4 1111,-363 1483.3,-191.2 1747.2,-772.2 JSET -65,0 700,0 0,0 41,0 1374,-944 JREGION 1747.2,-772.2 1483.3,-191.2 1870,-10 2137,-590 JSET -65,0 700,0 0,0 49,0 1746,-773 * * * * * * * * * * * * * * * **GENERATE FDEF ZONES** **CREATE ARTIFICIAL CRACK TO FACILITATE ZONING CRACK 419,-1162 1719,-561 **AREA OF INTEREST ZONING GENER REG 432,-1151 298,-854 720,-555 886,-942 EDGE 50 GENER REG 886,-942 720,-555 1434.5,-214 1694,-796 EDGE 50 **MAIN SLOPE GENER REG 600,-1300 0,-1300 0,-870 390,-840 EDGE 100 GENER REG 390,-840 750,-530 1015,-1110 600,-1300 EDGE 100 GENER REG 750,-530 1895,0 2160,-580 1015,-1110 EDGE 100 **MATERIAL TO BE EXCAVATED FROM FACE GENER REG 0,0 1500,0 350,-840 0,-840 EDGE 300 **ASSIGN A MATERIAL AND CONSTIT. REL'NS TO DOMAIN* CHANGE MAT=5 Cons=3 JCons=2 JMat=5 *************************** **ASSIGN GRADATIONAL INCREASE IN STRENGTH UPSLOPE** CHANGE REG 0,-870 472,-773 689,-1250 0,-1400 MAT=1 JMAT=1 CHANGE REG 472,-773 588,-675 831,-1190 689,-1250 MAT=2 JMAT=2 CHANGE REG 588,-675 709,-568 965,-1130 831,-1190 MAT=3 JMAT=3 CHANGE REG 709,-568 838,-493 1100,-1060 965,-1130 MAT=4 JMAT=4 CHANGE REG 838,-493 965,-425 1243,-996 1100,-1060 MAT=5 JMAT=5 CHANGE REG 965,-425 1100,-364 1378,-935 1243,-996 MAT=6 JMAT=6 CHANGE REG 1100,-364 1250,-297 1513,-876 1378,-935 MAT=7 JMAT=7 CHANGE REG 1250,-297 1385,-236 1648,-816 1513,-876 MAT=8 JMAT=8 CHANGE REG 1385,-236 1895,0 2160,-580 1648,-816 MAT=9 JMAT=9 177 **FIX ARTIFICIAL CRACK CHANGE ANGLE 10 35 JMAT=10 *CHANGE REG 419,-1170 419,-1150 1710,-557 1710,-577 JMAT=10 ****************** **DELETE BOTTOM LEFT CORNER (2 BLOCKS) DEL 0 75 -1300 -1150 **ASSIGN BOUNDARY CONDITIONS** BOUND CORNER 524 135 STR 0,0,0 YGRAD .01325, 0, .0265 BOUND CORNER 135 2928 XVEL=0 YVEL=0 BOUND CORNER 3132 24 XVEL=0 **ASSIGN HISTORIES ON UPPER FINAL SLOPE** HIST XVEL 1500,-200 YVEL 1500,-200 XDIS 1500,-200 YDIS 1500,-200 **UPPER SLOPE IN SLIDE HIST XVEL 1050,-400 YVEL 1050,-400 HIST XDIS 1050,-400 YDIS 1050,-400 **TRIM LINE HIST XVEL 750,-550 YVEL 750,-550 HIST XDIS 750,-550 YVEL 750,-550 **GLACIER MID HEIGHT HIST XVEL 550,-720 YVEL 550,-720 HIST XDIS 550,-720 YDIS 550,-720 **TOE OF SLOPE HIST XVEL 360,-860 YVEL 360,-860 HIST XDIS 360,-860 YDIS 360,-860 HIST DAMP TYPE 9 **SET INITIAL STRESSES, Ko=l INSITU 0 2200 -1300 0 STR 0,0,0 YGRAD .0265, 0, .0265 *CONSOLIDATE STABLE PROBLEM** GRAVITY 0,-9.81 FRAC=.5 DAMP AUTO SAVE HN265S.2 CYC 0 SAVE HN265S.3 STOP *********** *********** **CONTINUE WITH EXCAVATION** REST HN2 65S.3 CYC 1000 SAVE HN2 65S.4 CYC 3000 SAVE HN2 65S.4 DEL 0 250 -150 0 RESET DISP JDISP ROTA TIME RESET HIST **ASSIGN HISTORIES ON UPPER FINAL SLOPE** HIST XVEL 1500,-200 YVEL 1500,-200 XDIS 1500,-200 YDIS 1500,-200 **UPPER SLOPE IN SLIDE HIST XVEL 1050,-400 YVEL 1050,-400 HIST XDIS 1050,-400 YDIS 1050,-400 **TRIM LINE HIST XVEL 750,-550 YVEL 750,-550 HIST XDIS 750,-550 YVEL 750,-550 . 178 **GLACIER MID HEIGHT HIST XVEL 550,-720 YVEL 550,-720 HIST XDIS 550,-720 YDIS 550,-720 **TOE OF SLOPE HIST XVEL 360,-860 YVEL 360,-860 HIST XDIS 360,-860 YDIS 360,-860 HIST DAMP TYPE 13 ************ HIST NCYC 7 5 FRAC=.5 CYC 2000 SAVE HN265S.5 DEL 0 500 -200 0 CYC 2000 SAVE HN2 65S.5 DEL 0 650 -350 0 CYC 2500 SAVE HN265S.5 DEL 0 800 -450 0 CYC 2500 SAVE HN2 65S.5 DEL 0 1100 -500 0 CYC 3000 SAVE HN2 65S.5 ***************** ***ADD WATER TABLE PFIX REG 0,-870 390,-840 600,-1300 0,-1300 P=-8.7 X=0 Y=-.01 PFIX REG 390,-840 750,-530 1015,-1110 600,-1300 P=-11.76 X=.00861 +Y=-.01 PFIX REG 750,-530 1895,0 2160,-580 1015,-1110 P=-8.77 X=.00463 + Y=-.01 ********* CYC 2500 SAVE HN265SW.6 DEL 0 500 -700 0 CYC 2000 SAVE HN265SW.6 DEL 0 600 -800 0 CYC 2000 DEL 0 400 -870 0 CYC 3500 SAVE HN265SW.7 STOP 179 

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