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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,  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE Department o f G e o l o g i c a l The  University  We a c c e p t t h i s  of British  thesis  to the required  STUDIES Sciences Columbia  as c o n f o r m i n g standard  THE UNIVERSITY OF BRITISH COLUMBIA September 1989 ©  Mark A n d e r s o n  Pritchard  19  In  presenting this  degree at the  thesis  in  partial  University of  fulfilment  of  of  department  this thesis for or  by  his  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  her  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be  or  for  It  is  granted  by the  understood  that  head of copying  my 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 o f t h i s r e s e a r c h  mode o f f a i l u r e o f t h e Heather H i l l well defined Park, B r i t i s h  i s t o resolve the  l a n d s l i d e , one o f s e v e r a l  f a i l u r e s i n t h e Beaver V a l l e y , G l a c i e r N a t i o n a l Columbia.  F i e l d work l e d t o t h e 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 some type o f t o p p l i n g process  contributed t o the f a i l u r e .  A  l i t e r a t u r e review o f t o p p l i n g r e v e a l e d t h a t l a r g e s c a l e t o p p l e s have never been q u a n t i t a t i v e l y assessed, c u r r e n t l y used a n a l y t i c a l techniques Consideration  technique f o r modelling The and  a r e not adequate.  o f a l t e r n a t i v e numerical  the d i s t i n c t element method being  and t h a t  techniques  resulted i n  s e l e c t e d as t h e b e s t  toppling.  U n i v e r s a l D i s t i n c t Element Code (UDEC) was purchased  i t s s u i t a b i l i t y demonstrated by r e e v a l u a t i n g examples o f  toppling a n a l y s i s reported  i n t h e l i t e r a t u r e , and e v a l u a t i n g a  l a r g e s c a l e engineered s l o p e a t Brenda mine where t o p p l i n g i s known t o o c c u r .  UDEC i s used t o examine and c l a s s i f y t h e mode  of f a i l u r e o f t h e Heather H i l l This research  slide.  leads t o very  important g e n e r a l  on t o p p l i n g and s p e c i f i c c o n c l u s i o n s Hill  landslide:  topples.  conclusions  r e l a t i n g t o t h e Heather  UDEC i s s u i t a b l e f o r m o d e l l i n g  a l l types o f  The program can be used t o back analyze  rock mass  s t r e n g t h parameters and determine t h e 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 surface i n f l e x u r a l toppling.  q u a n t i t a t i v e assessment with UDEC confirms  A  t h a t t h e base o f  failure  in flexural  that pore pressures The limiting  Valley rocks and of  significantly  Heather H i l l  north  toppling.  correspond i n the  of the The with  drained  This test  planar  affect by  or c u r v i l i n e a r ,  flexural the  toppling slope  l a n d s l i d e i s deformed  l o c a t i o n s of l a n d s l i d e s i n the the occurrence  of  foliated  is violated  by  the  The  pelitic  i s shown t o o n l y a p p l y  slopes.  iii  kinematic  Heather  by  Beaver  the boundary between t h e s e slope l i m i t .  and  stability.  s u r f a c e , and  Heather H i l l  i s t h e up  toppling potential  landslide.  failure  l o w e r s l o p e s and  stronger g r i t s  be  landslide failed  to a curvilinear  immediately flexural  t o p p l i n g may  rocks test  Hill  to small  scale  TABLE OF CONTENTS Page  ABSTRACT  i i  TABLE OF CONTENTS  iv  L I S T OF TABLES  viii  L I S T OF FIGURES  ix  ACKNOWLEDGEMENTS  x i i  QUOTE  xiii  PART I CHAPTER 1.  INTRODUCTION  1  1.1  Rational  1.2  Research Procedure  2  1.3  Thesis  3  CHAPTER 2.  f o r Research  1  Structure  LITERATURE REVIEW  5  2 .1  Introduction  2.2  General D e f i n i t i o n  2.3  Types o f T o p p l e s  2.4  Methods o f 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 Analysis  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  Finite  18  2.4.5  Distinct  2.4.6  5 and H i s t o r i c a l  Perspective  9  E l e m e n t Method E l e m e n t Method  20  Comparative Assessment o f A n a l y t i c a l Methods  2.5  22  Parameters C o n t r o l l i n g Toppling: 2.5.1  5  Influence  of Structure iv  Discussion  24  a n d R o c k Type  24  2.6  2.5.2  Shear S t r e n g t h  2.5.3  Groundwater  of Discontinuities  26 28  Summary o f A r e a s N e e d i n g 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  Influence  30  2.6.3  Toppling  2.6.4  Time Dependent D e f o r m a t i o n  31  2.6.5  L a r g e S l o p e s and Weak Rock  31  2.6.6  Groundwater  32  of Confining  Stress  i n M i x e d Rock T y p e s  30  PART I I CHAPTER 3.  DISTINCT ELEMENT METHOD  3 .1  Introduction  3.2  Theory o f D i s t i n c t  3.3  3.4  33 33  E l e m e n t Method  3.2.1  Explicit  3.2.2  E q u a t i o n s o f M o t i o n and S y s t e m Damping  Features  S o l u t i o n Procedure  o f UDEC  Block  3.3.2  Block D e f o r m a b i l i t y Relations.  Interface Constitutive Relations  36  40  and C o n s t i t u t i v e 44  L i m i t a t i o n s o f UDEC  49  CHAPTER 4. MODELLING TOPPLING WITH UDEC 4.1 I n t r o d u c t i o n  51 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  4.3.1  34  40  3.3.1  4.3 F l e x u r a l T o p p l i n g  34  Example  52  Examples  60  Base F r i c t i o n M o d e l  60  4.3.2 B r e n d a M i n e  68  4.4 C o n c l u s i o n s  82  v  4.4.1  Recommendations f o r S l o p e with  Design  UDEC  85  PART I I I CHAPTER 5.  S I T E CHARACTERIZATION  87  5.1  Introduction  87  5.2  Regional  89  Geology  5.2.1  Bedrock Geology  89  5.2.2  Geomorphic Development o f 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 o f Beaver V a l l e y Slope  5.4  Previous  5.5  Field  Landslide  i n t h e Beaver  Program  Valley....96 97  5.5.1  Introduction  97  5.5.2  L o c a l Geology  97  5.5.3  Evidence o f Deformation  CHAPTER 6.  101  MODELLING HEATHER H I L L LANDSLIDE DEVELOPMENT..106  6.1  Introduction  6.2  Previous  6.3  Studies  Movements... 94  106  A n a l y s i s o f t h e Heather  Hill  Landslide  106  C h a r a c t e r i s t i c s o f t h e UDEC M o d e l  107  6.3.1  113  Pore Pressure  6.4  C h a r a c t e r i z a t i o n o f Rock Mass  113  6.5  E v o l u t i o n o f Model  116  6.6  Results  117  6.7  Limitations of Analysis  121  6.8  Conclusions  124  o f UDEC M o d e l l i n g . . .  6.8.1  Heather H i l l  6.8.2  Kinematic  CHAPTER 7.  Landslide  Test  For Toppling  CONCLUSIONS AND RECOMMENDATIONS  vi  124 125 134  7.1  PART I :  7.2  PART I I :  7.3  Conclusions  PART I I I :  Flexural Toppling: Research Beaver V a l l e y : and  7.3.1 7.3.2 7.3.3 7.4  134  Conclusions of 13 5  Conclusions  Recommendations  Heather H i l l  136  Study Area  13 6  S t a b i l i t y o f Slopes i n Beaver V a l l e y E n g i n e e r i n g D e s i g n I m p l i c a t i o n s and Recommendations  Flexural 7.4.1  o f L i t e r a t u r e Review  T o p p l i n g : Recommendations f o r F u r t h e r Work  C u r v i l i n e a r Failure Surface Topples  137 138 140  i n Flexural 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  7.4.3  I n f l u e n c e o f G l a c i a l E v e n t s on T o p p l i n g . . . . 141  7.4.4  Mountain Scale Deformation  7.4.5  Application  7.4.6  Geometric S e n s i t i v i t y Studies  o f UDEC t o S l o p e  141  142 Design  142 143  REFERENCES  144  APPENDIX 1  151  APPENDIX 2  158  APPENDIX 3  175  MAP 1A MAP IB  vii  L I S T OF TABLES Table  Title  4.1  Range o f L i m i t i n g  4.2  Geometry o f B a s e F r i c t i o n  Model  4.3  V a l u e s o f UDEC P a r a m e t e r s  f o r Base F r i c t i o n  4.4  UDEC P a r a m e t e r s f o r B r e n d a Mine Pure F l e x u r a l T o p p l i n g  Model:  UDEC P a r a m e t e r s  Model:  4.5  "Graben"  Friction  Page  Angle f o r Block Toppling..60  f o r Brenda Mine  a n d UDEC M o d e l  63  Model....65  73  Topple  79  5.1  Structural  D a t a Summary i n H e a t h e r H i l l  6.1  UDEC S t r e n g t h P a r a m e t e r s  6.2  Investigated Variation  Study  f o r Heather H i l l  Model  i n Strength Parameters  viii  Area..100 119 121  L I S T OF FIGURES  Figure  Title  Page  2.1a  Flexural Toppling  11  2.1b  Block  11  2.1c  Block/Flexural Toppling  2.2a  Kinematic Test o f Toppling Using Stereoplot  2.2b  Toppling  Stress Orientations  11 Potential 14  on S l o p e a n d 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  14  2.2c  Condition  14  2.3  T y p i c a l S l o p e C o n f i g u r a t i o n Assumed i n  f o rInterlayer slip  L i m i t E q u i l i b r i u m Method 3.1a  Nature of D i s t i n c t  3.1b  Distinct  3.2a  Mechanical Representation Distinct  Analysis  16  Element Model  35  Element Model C a l c u l a t i o n C y c l e  35  of Interfaces i n  Element Model  42  3.2b  Edge t o Edge C o n t a c t  3.2c  Contact Length f o r F u l l y  3.3a  Elastic-Plastic  3.3b  T y p i c a l J o i n t Behaviour  4.1  Geometry  4.2a  H o r i z o n t a l V e l o c i t y v s . M e c h a n i c a l Time a t H I , Stable Slope H o r i z o n t a l V e l o c i t y v s . M e c h a n i c a l Time a t HI,  55  Failing  Slope  56  4.3  Pattern  of Deformation f o r F a i l i n g  4.4  Geometry  4.5a  Base F r i c t i o n M o d e l D e f o r m a t i o n  4.5b  UDEC S i m u l a t i o n  4.2b  42 Deformable Blocks  J o i n t Model  o f UDEC M o d e l  42 45 45  f o r Block  Toppling  Slope  o f Base F r i c t i o n M o d e l a n d UDEC M o d e l  54  58 62 66  o f Base F r i c t i o n Model Deformation..67 ix  4.6a  Brenda Mine:  Zoned  4.6b  Brenda Mine:  B l o c k Geometry and W a t e r T a b l e U s e d i n UDEC M o d e l  4.7a  B l o c k Geometry P r i o r t o F a i l u r e . 7 1  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)  72 74  4.7b  Brenda Mine: Pure F l e x u r a l T o p p l i n g D e f o r m a t i o n w i t h H o r i z o n t a l D i s p l a c e m e n t C o n t o u r s (Dry S l o p e ) . . . 7 5  4.8a  Brenda Mine: "Graben" T o p p l i n g D e f o r m a t i o n 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 D e f o r m a t i o n w i t h H o r i z o n t a l D i s p l a c e m e n t C o n t o u r s (Dry S l o p e ) . . . 7 8  4.9a  Moment D r i v e n D e f o r m a t i o n w i t h A c t i v e a n d P a s s i v e Wedges  81  4.9b  S i m i l a r i t y o f " G r a b e n " T o p p l i n g t o Example o f Moment D r i v e n D e f o r m a t i o n D e s c r i b e d b y N i e t o , 1987 ( F i g u r e 4 . 9a) 83  5.1  T o p o g r a p h i c map o f t h e B e a v e r R i v e r V a l l e y L o c a t i o n s o f Deep S e a t e d L a n d s l i d e s  Showing 88  5.2  R e g i o n a l G e o l o g y map o f t h e B e a v e r R i v e r V a l l e y  90  5.3  Geological Valley  C r o s s S e c t i o n Number 1, B e a v e r  91  5.4  Structural  G e o l o g y Summary f o r S t u d y A r e a  5.5  Topographic P r o f i l e of Creek B  S e c t i o n A-A', and G r a d i e n t  Topographic P r o f i l e S e c t i o n B-B'  S o u t h o f C r e e k A,  5.6 6.1  River 100 103 105  C i r c u l a r A n a l y s i s o f Heather H i l l Landslide; Assumed S l o p e Geometry a n d 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 T o p o g r a p h y  109  6.3  Heather H i l l :  Initial  B l o c k Geometry o f UDEC  Model 6.4  Heather H i l l :  6.5  Heather H i l l  First  110 Glacial  UDEC M o d e l :  x  Excavation  D i s t r i b u t i o n o f Rock Types  112  118  6.6a  Heather H i l l  UDEC M o d e l :  Velocities 6.6b  Heather H i l l  6.7a  Kinematic Test:  6.7b  Kinematic Test:  of Grid Points  UDEC M o d e l :  Horizontal  120 Displacement..122  Toe o f S l o p e i n UDEC M o d e l  12 6  6.8  Heather H i l l  E l e v a t i o n o f Change i n S l o p e i n UDEC M o d e l UDEC M o d e l : Principle Stresses  126 12 8  6.9  H e a t h e r H i l l UDEC M o d e l : Variation of Effective F r i c t i o n A n g l e A l o n g an SO F o l i a t i o n  129  H e a t h e r H i l l UDEC M o d e l : Variation i n Factor of S a f e t y A l o n g SO F o l i a t i o n  131  6.11a  Normal  132  6.11b  E f f e c t i v e Normal and S h e a r S t r e s s e s When P r e s s u r e a c t s on J o i n t  6.10  and Shear S t r e s s e s  xi  on D r y J o i n t Pore  132  ACKNOWLEDGEMENTS  T h i s r e s e a r c h would n o t have been p o s s i b l e w i t h o u t f r o m many i n d i v i d u a l s a n d o r g a n i z a t i o n s .  assistance  I w i s h t o e x p r e s s my g r a t i t u d e t o my s u p e r v i s o r , D r . K.W. S a v i g n y , who s u g g e s t e d t h e t o p i c a n d n e v e r f a i l e d t o p r o v i d e support, encouragement and guidance. I w o u l d l i k e t o t h a n k R. v o n S a c k e n a n d P. B u c h a n a n f o r t h e i r f i e l d assistance. T h e a u t h o r i s a l s o i n d e b t e d t o T. S p e r l i n g , B. James, a n d D r . R.A. F r e e z e o f t h e UBC G r o u n d w a t e r Group f o r the u s e o f t h e i r computer hardware. Thanks a r e a l s o extended t o J . Hammack a n d M. Keep who p r o v i d e d f i e l d equipment. I w o u l d e s p e c i a l l y l i k e t o t h a n k Dr. P. B y r n e , D r . S. E v a n s , Mr. D. M a r t i n , a n d D r . L . S m i t h whose g u i d a n c e a n d comments g r e a t l y enhanced t h e q u a l i t y o f t h i s t h e s i s . L o g i s t i c a l s u p p o r t was s u p p l i e d b y E n v i r o n m e n t Canada P a r k s and t h e 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 S u r v e y o f Canada. Mr. E . R i n d t , a t t h e W e s t e r n 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 E n v i r o n m e n t Canada P a r k s , was o f g r e a t a s s i s t a n c e , a s w e r e R. Beardmore, P a r k S u p e r i n t e n d e n t and J . T u r n b u l l , C h i e f P a r k Warden, Mount R e v e l s t o k e a n d G l a c i e r N a t i o n a l P a r k s (MRGNP). T h a n k s a r e a l s o e x t e n d e d t o t h e 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 a n d s u p p o r t ; i n p a r t i c u l a r , K. Webb a n d M. McMahon f r o m t h e 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 e x t e n d a s p e c i a l t h a n k s t o V. W i l k i n s o n whose p a t i e n c e a n d e n c o u r a g e m e n t 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 to be completed. F i e l d work was f u n d e d u n d e r NSERC O p e r a t i n g G r a n t No. A1923. Computer h a r d w a r e a n d s o f t w a r e p u r c h a s e s were f u n d e d u n d e r S c i e n c e C o u n c i l o f B r i t i s h C o l u m b i a G r a n t No. 57(RC-18) a n d UBC G r a n t No. 5-56492 t o w h i c h t h e f o l l o w i n g a g e n c i e s made contributions: B.C. H y d r o a n d Power A u t h o r i t y , B.C. M i n i s t r y o f T r a n s p o r t a t i o n a n d H i g h w a y s , C.N. R a i l , CP R a i l , R e g i o n a l D i s t r i c t o f F r a s e r a n d Cheam, T r a n s M o u n t a i n P i p e L i n e Co. Ltd., and Westcoast Energy Inc. F u n d i n g f o r t h e 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 b y t h e G e o l o g i c a l S u r v e y 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 .  xii  " T h e o r y and c a l c u l a t i o n a r e n o t s u b s t i t u t e s f o r judgment, b u t a r e t h e b a s e s f o r sounder judgment. A t h e o r e t i c a l framework i n t o w h i c h t h e 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 c a n be accommodated p e r m i t s u s 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 t h a n we c o u l d j u s t i f y b y e m p i r i c i s m a l o n e " . R.  xiii  Peck,  1969  1.0  Introduction  1.1  The  Rationale  research  investigate Valley, Valley  described  in this  t h e s i s was u n d e r t a k e n t o  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 t h e B e a v e r  Glacier National  Park, B r i t i s h  Columbia.  The Beaver  forms t h e 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  corridor This  f o r Research  t h a t t r a v e r s e s t h e S e l k i r k Mountains a t Rogers  corridor i s utilized  Pass.  by t h e T r a n s Canada Highway a n d a  t w i n n e d s e c t i o n o f t h e CP R a i l m a i n  line.  A l t h o u g h t h e economic importance o f t h e Beaver R i v e r V a l l e y as the  eastern  recognized, along  the d i s t r i b u t i o n  the valley  (Pritchard  The  approach t o t h e Rogers Pass route  Heather H i l l  failures  hazards  documented  l a n d s l i d e , one o f s e v e r a l w e l l  defined  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 s t u d y . d e t e r m i n e t h e mode o f f a i l u r e  associated with  r e c e n t l y been  been  1988).  i n the valley,  knowledge w i l l  o f l a r g e mass movement  s l o p e s has only  et.al.,  has long  enable others  The p r i m a r y o b j e c t i v e i s t o of this  landslide.  t o more e f f e c t i v e l y  i t a n d o t h e r mass movements.  1  This assess  risks  1.2  Research  Field the  work a t t h e  summer o f  that  Procedure  Heather H i l l  1988.  This  a t o p p l i n g process  t o the  failure  seated  instability.  affecting  l a n d s l i d e was  l e d to the  (Goodman and  at Heather H i l l  other  and  Moreover, the  slopes  undertaken  during  preliminary  conclusion  Bray,  contributed  1976)  adjacent  areas of  same p r o c e s s  nearby which p r e s e n t l y  appears t o  show  be  no  indication  of deep-seated  failure.  conclusion  meant t h a t  t e c h n i q u e of s t a b i l i t y a n a l y s i s used  t o examine t h e large  Heather H i l l  literature  little  preliminary  must be  slopes,  but  t o w a r d s a t o p p l i n g mode o f  point.  This  able to should  these slopes.  To  review reveals that  techniques  e x p l a i n the  are  mechanism o f t h e  restricted  conclusion  of the  literature  failure,  Distinct  E l e m e n t Code  The  s u i t a b i l i t y o f UDEC f o r a n a l y s i s o f a l l t y p e s o f The  program  i s t h e n u s e d t o examine  2  Hill  A  numerical  most s u i t a b l e p r o g r a m .  demonstrated.  for  toppling,  the  is  and  i s required.  review i s t h a t a  p a c k a g e known a s t h e U n i v e r s a l  very  Heather  but  mode o f  was  inadequate  a method o f a n a l y s i s c a p a b l e o f m o d e l l i n g to this  be  slopes,  failure not  not  i n Chapter 2  i s known a b o u t t o p p l i n g i n l a r g e n a t u r a l  c u r r e n t l y used a n a l y t i c a l  model  failure.  survey of t o p p l i n g reported  undertaken at t h i s  that  failure  scale toppling in natural  unduly biased  The  any  This  deep-  (UDEC) i s  topples and  classify  t h e mode o f f a i l u r e o f t h e H e a t h e r H i l l  illustrating model r o c k Valley.  o f t h e Beaver  design  associated with  This  research  Part  I contains  and f o r e x p l a i n i n g  the evolution of  Structure  i s reported  this  i n three  parts.  introductory chapter,  and t h e l i t e r a t u r e  (Chapter 2 ) .  I I i s concerned with  Chapter 3 introduces distinct  t h e d e s c r i p t i o n a n d u s e o f UDEC.  t h e program, o u t l i n i n g  e l e m e n t method a n d t h e c a p a b i l i t i e s  o f UDEC.  the theory  Chapter 4 demonstrates t h a t t h e d i s t i n c t  i s done b y u s i n g UDEC t o r e e v a l u a t e  analysis  In Part  reported  I I I t h e mechanism o f f a i l u r e  landslide the  i n the literature  i s evaluated.  study area.  This  of the  and l i m i t a t i o n s  method c a n b e u s e d t o model a l l t y p e s o f t o p p l i n g This  an  slopes.  Thesis  Part  i n the slopes  framework f o r e n g i n e e r i n g  1.3  review  e l e m e n t method t o  a n a l y s i s a l s o d e m o n s t r a t e s t h a t UDEC p r o v i d e s  geomorphic f e a t u r e s  natural  of the distinct  mass d e f o r m a t i o n  This  important the  the a b i l i t y  landslide,  element failures.  examples o f t o p p l i n g  o r known t o t h e a u t h o r .  o f the Heather  Hill  Chapter 5 i s a c h a r a c t e r i z a t i o n o f  chapter  includes the regional  3  geology  and geomorphic  development  o f t h e Beaver V a l l e y , p r e v i o u s  work  on t h e s l o p e movements, a n d t h e r e s u l t s  o f t h e 1988  program.  l a n d s l i d e development  In Chapter 6 the Heather H i l l  field  i s m o d e l l e d u s i n g UDEC.  Chapter 7 contains the conclusions of t h i s recommendations  f o r f u r t h e r work.  4  research,  and g i v e s  2.  2.1  The  L i t e r a t u r e Review  Introduction  aims o f t h i s  r e v i e w a r e t o summarize t h e 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 and  an h i s t o r i c a l  deficiencies.  review i s provided  Toppling  i n the f i r s t  i s defined  section.  In  subsequent s e c t i o n s t h e h i s t o r y o f t o p p l i n g research i s outlined,  t h e d e v e l o p m e n t and c a p a b i l i t i e s  numerical  m o d e l s o f t o p p l i n g a r e r e v i e w e d , a n d some o f t h e  physical  and m e c h a n i c a l p a r a m e t e r s t h a t  discussed. and  o f p h y s i c a l and  influence toppling are  A summary o f g a p s i n t h e u n d e r s t a n d i n g o f t o p p l i n g  suggestions  f o r further research  are included  a t t h e end  of the review.  2.2  General  Toppling  D e f i n i t i o n and H i s t o r i c a l  failure  overturning, interacting  i s generally defined  Perspective  as t h e down-slope  e i t h e r through r o t a t i o n or f l e x u r e , of columns o r b l o c k s  1 9 7 6 ) . T h i s mode o f f a i l u r e  of rock  (Goodman a n d B r a y ,  can develop  i n slopes  contain w e l l developed d i s c o n t i n u i t i e s or a foliation  dipping  discontinuities subparallel  steeply  into the slope.  or f o l i a t i o n  should  which  pervasive In addition, the  strike parallel or  ( p l u s o r m i n u s 20 d e g r e e s ) t o t h e s l o p e  5  c r e s t , and  lateral the  r e l e a s e should  slope  Toppling within  b e p o s s i b l e due t o t h e t o p o g r a p h y o f  o r down-slope t r e n d i n g  discontinuities.  f a i l u r e s have o n l y been d e s c r i b e d  t h e l a s t twenty f i v e years,  i n literature  a n d a t t e m p t s t o model  t o p p l i n g have o n l y been u n d e r t a k e n i n t h e l a s t twenty As  a result  of the brief  has  been r e c o g n i z e d ,  One  of the f i r s t  of  p e r i o d t h a t t h i s mechanism o f f a i l u r e  references  references  on t o p p l i n g a r e s p a r s e .  d e s c r i b i n g t h e motion o f t h i s  f a i l u r e as t o p p l i n g i s M u l l e r  s t u d i e s were c a r r i e d  years.  (1968).  out under M u l l e r ' s  type  P h y s i c a l model direction  b y Hofmann  (1972).  Significant undertaken  s t u d i e s on t h e m e c h a n i c s o f t o p p l i n g were from  1970 t o 1974 a t I m p e r i a l  (1971) a n d C u n d a l l analysis  H i s work, w h i c h e x p l a i n e d  a comprehensive  components o f  the kinematics  of  and examined t h e i n f l u e n c e o f p h y s i c a l and m e c h a n i c a l  parameters,  l a t e r became t h e f o u n d a t i o n  methods o f t o p p l i n g a n a l y s i s made one o f t h e e a r l i e s t numerically  During  Ashby p r o v i d e d  o f t h e s l i d i n g and o v e r t u r n i n g  toppling. toppling  (1971).  C o l l e g e by Ashby  using  2.4.3).  Cundall  attempts t o study  toppling  t h e d i s t i n c t e l e m e n t method  t h e same p e r i o d ,  made s i g n i f i c a n t  (Sec.  f o rlimit equilibrium  researchers  (Sec.  2.4.5).  a t James Cook U n i v e r s i t y  c o n t r i b u t i o n s t o the understanding  6  (1971)  of  toppling  i n j o i n t e d r o c k mass b e h a v i o u r .  introduced systems, planar  One  r o t a t i o n into numerical simulations  and  discussed  the  influence of block  first  of toppling (1973).  This  published  by  paper i s p a r t i c u l a r l y  materials  demonstrates t h a t  i n order  true."  As  failures  rock on  mode o f  examples Watters  as i t  failure  "  ...  requires  nor  unusual  geological  i n f a c t the  reverse  w o u l d seem  and  much n e e d e d  demonstrated t h a t  in contrasting  field  topples  structural settings.  p i v o t a l i n persuading the  community t o a c c e p t t o p p l i n g as  field  F r i e t a s and  w e l l , t h e i r paper provided  o c c u r a t a l l s c a l e s and T h e i r work was  de  toppling  to develop;  evidence of t o p p l i n g  geotechnical  a significant  and  distinct  failure.  With the  r e c o g n i t i o n o f t o p p l i n g came t h e  techniques to assess the toppling. stability  The  best  i s the  stability  limit  Bray a l s o d e f i n e d  occurrence,  potential  slopes  e q u i l i b r i u m method  T h i s method i s b a s e d on  Goodman and  of  development prone  known t e c h n i q u e f o r a n a l y z i n g  an  moments o f a s y s t e m o f b l o c k s  their  rotation  significant  n e i t h e r unusual g e o l o g i c a l conditions,  and  of block  q u a l i t a t i v e papers d e s c r i b i n g  f a i l u r e s was  convincingly  1976).  (1974)  failures.  of the  t o be  Burman  and  for toppling  the  toppling  representing  of  static  the  7  2.4.2).  Bray, forces  slope.  types of topples  proposed a kinematic t e s t of ( S e e s . 2.3,  to  (Goodman and  evaluation  various  of  and  the  Both the  kinematic  test  and  the l i m i t  techniques failures  equilibrium  for predicting  ( C h o q u e t and  Simultaneously,  their  toppling  separately, f i n i t e developing  Duncan and  element technique  Hittinger  Goodman  (Sec.  (1968)  important  finite  element  toppling.  the deformation method.  of jointed  Goodman and  rock  rock using the d i s t i n c t  Bray  slopes  c o n t i n u i n g a n a l y t i c a l work  C u n d a l l e t a l . (1978) m o d e l l e d  p u b l i s h e d by  who Kalkani  and  C u n d a l l was  owe  rock.  rock; Kalkani with w e l l j o i n t e d  Also simultaneously,  2.4.4).  literature  for jointed  (1978) c o m p l e t e d  element  studies of j o i n t e d H i t t i n g e r with  accepted  1985).  r o c k mass was  t o work by  a finite  (1977) and  analyzing block  element programs d e s c r i b e d i n t h e  origins  outlined  Tanon,  but p r i m a r i l y  modelling of j o i n t e d Many f i n i t e  and  a n a l y s i s h a v e become  on  element  an example o f  (1976) a s a v a l i d a t i o n  toppling of  the  method.  From t h e mainly  s e v e n t i e s t o p r e s e n t work on  with case h i s t o r i e s ,  (Wyllie, and  late  the  1980; finite  P i t e a u and element  E v a n s e t a l . , 1981)  using both  Martin,  late  slope  the  1981;  limit  methods o f a n a l y s i s .  equilibrium  Brown  One  ,  1982;  post-1980  e l e m e n t method t o a n a l y z e  ( I s h i d a e t a l . , 1987).  seventies discuss refinements  8  dealt  P i t e a u e t a l . , 1981),  (Brown e t a l . , 1980;  p u b l i c a t i o n uses the d i s t i n c t toppling  t o p p l i n g has  Many  to the  papers  limit  a  s i n c e the  equilibrium  technique,  o r p r o v i d e nomograms t o f a c i l i t a t e  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 ,  use o f the l i m i t  1981; P i t e a u e t a l . ,  1981;  Teme a n d West, 1983; Zanbak, 1983; C h o q u e t a n d Tanon,  1985;  Sagaseta,  1986).  2.3  Types o f Topples  The  g e n e r a l l y accepted  definitions  of the process  t o p p l i n g a r e g i v e n b y Goodman a n d B r a y Bray  (1977).  Toppling  (1976) c a n b e c o m p r i s e d  Flexural  failure  and t y p e s o f  (1976) a n d Hoek a n d  a s d e f i n e d b y Goodman a n d B r a y  of three types  o f motion:  Toppling:  C o n t i n u o u s columns o f r o c k bend down-slope, e v e n t u a l l y breaking  i n t e n s i o n a t depth.  displacement  Prior to fracture,  i s accommodated b y i n t e r n a l  deformation  of  i  the  intact  r o c k columns and f l e x u r a l  s e p a r a t i o n s between columns Block  slip  along the  ( F i g . 2.1a)  Toppling:  Columns o f r o c k ,  d i v i d e d by c r o s s j o i n t s ,  slope.  The f a i l u r e  joints,  b u t no s l i d i n g  overturn  s u r f a c e steps as r e q u i r e d occurs  2.1b).  9  down-  along  on c r o s s j o i n t s . ( F i g .  Block/Flexural Toppling:  Columns o f r o c k o v e r t u r n d o w n - s l o p e b y r o t a t i o n a n d sliding  on c r o s s j o i n t s .  toppling, joints  but unlike block toppling  i s significant  These d e f i n i t i o n s behaviour  that  i s similar t o block sliding  on c r o s s  ( F i g . 2.1c).  accurately describe the types o f deformation  can occur during toppling.  of toppling that mix  The m o t i o n  occurs  i n real  However, t h e mode  slopes i s often a complicated  o f t h e modes d e f i n e d a b o v e .  2.4  Methods o f A n a l y s i s  2.4.1  Physical  Models  Some o f t h e e a r l i e s t table  or t i l t  table.  m o d e l l i n g attempts Ashby  (1971),  Soto  (1973) e x a m i n e d b l o c k a n d b l o c k / f l e x u r a l (1975),  experimented  with  flexural  utilized (1974),  the f r i c t i o n a n d Whyte  toppling,  Kuykendall  t o p p l i n g m o d e l s , a n d Hofman  (1973) c o n s i d e r e d m i x e d modes o f b l o c k / f l e x u r e a n d f l e x u r a l toppling.  The l i m i t  e q u i l i b r i u m method a n d n u m e r i c a l  q u i c k l y became more p o p u l a r p r i m a r i l y flexibility.  10  due t o t h e i r  methods  Figure  Figure  2.1a  2.1c  Flexural Toppling ( a f t e r Goodman a n d B r a y , 1976)  Block/Flexural Toppling ( a f t e r Goodman a n d B r a y ,  11  1976)  2.4.2  Kinematic  Prediction  Analysis  of toppling potential using  was p r o p o s e d b y Goodman and B r a y  a kinematic  (1976).  analysis  F o r t o p p l i n g t o be  possible the pole to the regular d i s c o n t i n u i t y set dipping i n t o t h e s l o p e must l i e o u t s i d e the  slope  face angle  discontinuity. stereonet  plot  a great  plus the f r i c t i o n  This test  toppling  a t t h e p o i n t where f l e x u r a l occurs.  maximum  and  The f i r s t  of the slope.  (a2)  the  the  from  Along the slope  (a3)  f o r shear  to the trend  friction  angle  of the slope  ( F i g 2.2b).  from t h e r e q u i r e m e n t s face.  f o r shear Given that a 3  ( i n t h e a l , a3 p l a n e ) t o be p o s s i b l e  d i s c o n t i n u i t y t h e maximum p r i n c i p a l t o the pole  i s oriented  f a c e and h a s z e r o m a g n i t u d e . I t i s assumed  the d i s c o n t i n u i t i e s near the slope  zero,  face the  s t r e s s d i r e c t i o n s must l i e i n t h e  t h e maximum p e r p e n d i c u l a r  angle  along  condition results  t h e median s t r e s s a c t s p a r a l l e l  along  slip  The minimum s t r e s s  The s e c o n d c o n d i t i o n comes  is  stress conditions of  (slope face).  ( a l ) and m e d i a n  normal t o t h e s l o p e that  a  e q u i l i b r i u m r e q u i r e m e n t s and a p p l i e s a t t h e f r e e  surface of the slope  plane  of the  ( F i g . 2.2a).  i s b a s e d on two l i m i t i n g  stress  angle  whose d i p i s  c a n be q u i c k l y done u s i n g  The t e s t  discontinuities  circle  s t r e s s must a c t a t an  of the d i s c o n t i n u i t y equal of the d i s c o n t i n u i t y .  12  along  or greater  Using  these  than  two  failure is  criteria,  aligned  least  the  possible  that  with the friction  the  slope angle  6<(4>+a) (Goodman and  This  t e s t has  kinematically slope  ($)  and  limiting Bray,  only  conditions  1976)  i n c l i n e d by  for  i t is stability;  i t was  proposed. failure  is  i t cannot p r e d i c t whether or not  topple.  C h o q u e t and  Tanon  include  of t o p p l i n g  f a i l u r e p l a n e becomes  steep that  the  o c c u r s when t h e  columns w i l l  fail  purely  a  by  a  (1985) s u g g e s t  minor a l t e r a t i o n of t h i s t e s t to that  at  ( F i g . 2.2c).  p r e d i c t whether t o p p l i n g  possible;  will  must be  discontinuity,  gained acceptance since  However, i t c a n  given  face  (</>) t o t h e  t o determine the  that  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  limiting  sliding  a  condition so  along  joints.  2.4.3  By  Limit Equilibrium  f a r the  most p o p u l a r a n a l y t i c a l t e c h n i q u e t o  whether a s l o p e d e v e l o p e d by on  the  the  topple  Goodman and  a  f a c t o r of  technique  (1977) and  by  provide only the  will  i s the  Bray  safety  Ashby  Bray  be  used  Bray will  method c o n c e n t r a t i n g  l i m i t a t i o n s of the  13  i s based  toppling.  Hoek and  (1976), t h i s r e v i e w  a b r i e f summary o f t h e  c a p a b i l i t i e s and  can  prone to by  method  technique  (1971) and  in detail  predict  equilibrium  This  for a slope  i s described  Goodman and  limit  (1976).  k i n e m a t i c s d e v e l o p e d by  calculate As  Method  technique.  on  to  Toppling  possible  within ruled  Figure  2.2a  Kinematic Test of Toppling P o t e n t i a l ( a f t e r Goodman a n d B r a y , 1976)  for  poles  region.  using  Stereoplot.  Figure  2.2b  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 Shear on D i s c o n t i n u i t i e s ( a f t e r Goodman a n d B r a y , 1 9 7 6 ) .  Figure  2.2c  Condition  for Interlayer Slip ( a f t e r Goodman a n d B r a y ,  14  1976).  lying  The  limit  equilibrium  s o l u t i o n i s formed by a p p r o x i m a t i n g t h e  slope  a s a s e r i e s o f c o l u m n s r e s t i n g on a s t e p p e d b a s e  2.3).  The s o l u t i o n b e g i n s by r e s o l v i n g t h e f o r c e s  the  uppermost column i n t h e s l o p e  parallel the  into forces  (x') t o t h e b a s e o f t h e b l o c k .  block  a c t i n g on  normal  (y ) 1  and  T h e f a i l u r e mode f o r  i s d e t e r m i n e d b y s o l v i n g two s t a t i c s p r o b l e m s , one  assuming b l o c k resultant  (Fig.  sliding  x* f o r c e s  a n d one a s s u m i n g b l o c k  toppling.  The  f r o m e a c h p o t e n t i a l mode o f f a i l u r e a r e  compared, a n d t h e s o l u t i o n p r o d u c i n g t h e 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 t a k e n t o b e t h e mode o f f a i l u r e  block. block  This  i n the slope  progresses block. force  The f i n a l  t o block  resultant  of the last  coefficient of friction  There a r e s e v e r a l  limiting  1.  No b l o c k  2.  T h e method o n l y  to the toe  of the slope.  from t h e r a t i o block  i s the A  ofthe  without support t o  support.  assumptions t o t h i s a n a l y s i s .  c a n be b o t h t o p p l i n g  applies  and s l i d i n g .  t o block  toppling  o f continuous  Columns may be j o i n t e d , b u t s l i p  overturning a  with  The a n a l y s i s  a t the toe block  c a n be c a l c u l a t e d  of friction  columns.  down t h e s l o p e  force  t o t h e next  i s repeated.  t o maintain the s t a b i l i t y  of safety  coefficient  i s then applied  and t h e a n a l y s i s  from b l o c k  required  Factor  the  r e s u l t a n t x' f o r c e  ofthe  of i n d i v i d u a l blocks  column i s n o t a l l o w e d .  15  defined  on j o i n t s o r  by j o i n t s  within  Figure  2.3  T y p i c a l S l o p e 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 o f A n a l y s i s . ( a f t e r Goodman and B r a y , 1976)  16  3.  The  columns a r e  large internal  analyze toppling with  4.  The  l o c a t i o n and  must be  5.  The  The t e c h n i q u e c a n n o t  rigid.  i n c l i n a t i o : , of the  stepped  deformations.  failure  plane  assumed.  analysis  Toppling  i s by  failure  definition  of a slope  equilibrium evaluation only  on  analysis  strength  normal s t r e s s , but  A  does not of  forces. and  limit  allow  joints,  a l s o on  I n o t h e r words, t h e  non-linear  balance of  parameters.  of t o p p l i n g  of mobilized  displacement. incorporate  a static  i s a dynamic p r o c e s s ,  deformation a f f e c t s strength  not  column  accurately  which  depends  tangential  analysis  stress-displacements  cannot joint  relationships.  6.  C u r r e n t programs r e s t r i c t step  and  block  the  solution of  and  output of  s a f e t y have l e a d t o the  engineering  limit  f o r examining t o p p l i n g . the  design  geometry t o  a  uniform  width.  Even w i t h t h e s e l i m i t a t i o n s , the proven u s e f u l  slope  (Piteau  required  equilibrium The  simplicity  of  r e t a i n i n g force or  successful  use  e t a l . , 1981).  17  method  of the  has  the factor  technique  for  2.4.4  The to  Finite  finite model  joint  Element  Method  e l e m e n t method h a s b e e n u s e d w i t h m o d e r a t e  toppling  elements.  application  s l o p e s as a d i s c r e t i z e d This section w i l l  of the f i n i t e  give a b r i e f  containing  history  e l e m e n t method t o t o p p l i n g  f o l l o w e d by t h e c a p a b i l i t i e s and  continuum  and l i m i t a t i o n s  success  of the  failures  of the technique  i t s use i n p r a c t i c e .  Finite who  element models  owe  t h e i r development  t o many w o r k e r s  each improved t h e t e c h n i q u e f o r m o d e l l i n g j o i n t e d  mass  (Duncan and Goodman, 1968;  and D u b o i s , 1971;  Goodman e t a l . ,  Burman, 1 9 7 4 ) .  methods f o r j o i n t e d  1968;  Although f i n i t e  rock Goodman  element  r o c k have been used e x t e n s i v e l y  in a l l  a r e a s o f r o c k m e c h a n i c s , t h e r e a r e few a p p l i c a t i o n s o f t h e method t o t o p p l i n g 1976;  Finite  and H i t t i n g e r ,  constitutive  be  K a l k a n i and  Piteau,  1978).  than the l i m i t relationships  e q u i l i b r i u m method.  of the i n t a c t  c a n be more r e a l i s t i c a l l y  introduced,  histories  and any g e o m e t r y ,  The  r o c k mass and t h e  modelled, pore pressures g e o l o g y , and  can  loading  c a n be u s e d .  However, t h e f i n i t e It  1975;  e l e m e n t methods a r e c a p a b l e o f m o d e l l i n g t o p p l e s more  realistically  joints  (Burman e t a l . ,  has a l i m i t e d  e l e m e n t method i s n o t w i t h o u t p r o b l e m s .  ability  t o model  18  jointed  r o c k mass b e c a u s e o f  its  continuum  formulation.  o f d i s p l a c e m e n t s and  To  stresses  obtain i n the  m a t r i c e s must be  f o r m u l a t e d and  equations at the  grid points.  reformed.  displacements are  stresses  and  c a n n o t be  The  state-of-the-art  a p p e a r s t o be 1978).  A  the  l a c k o f use  involved simpler  Except  predict  progresses.  Hittinger  of  toppling  (Hittinger,  Brown e t a l . (1980) a p p l i e s  most r e c e n t  E v a n s e t a l . (1981) attempt t o apply  this reports  finite  finite  e l e m e n t method i n  a r e s u l t of the  complexity  f o r l a r g e problems t h a t  of  toppling the  justify  the  time  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 limit  The  toppling.  of the  is likely  technique.  the  solve.  i s unstable i t  element a n a l y s i s  analyze a r e a l slope.  element a n a l y s i s t o  analysis  failure  to  I t can  i f a slope  p r o g r a m d e v e l o p e d by  what a p p e a r s t o be  The  in finite  c a s e h i s t o r y by  program t o  a  governing  large  difficult  a dynamic t e c h n i q u e .  s t u d y how  large  this global stiffness  Thus, problems w i t h  displacements, but  used to  from the  solution  Whenever s i g n i f i c a n t  t i m e c o n s u m i n g and  method i s a l s o n o t  approximate  p r o b l e m domain,  solved  displacement occurs at a g r i d point m a t r i x must be  the  equilibrium  technique.  19  the  2.4.5  Distinct  Element  Method  The d i s t i n c t  e l e m e n t method h a s a much more c l e a r l y  defined  history  the f i n i t e  element  than  e l e m e n t method.  method a p p l i e d t o j o i n t e d owes i t s d e v e l o p m e n t development one  r o c k and s p e c i f i c a l l y  of the d i s t i n c t  publication,  t h e method.  the development  systems. blocks, boundary  Since into  The c a p a b i l i t i e s  relationship.  had been m o d i f i e d capabilities  be  computer  of the  discussed.  b y an a s s e m b l a g e  of  t h e b l o c k s a c t as behaviour.  t h e method h a s  p a c k a g e . The  original  and a p p l i e d a  evolved program  simplistic  By t h e m i d e i g h t i e s t h e o r i g i n a l  into  program  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  as b l o c k d e f o r m a t i o n  20  of  d i f f e r e n c e method o f  a prescribed joint  d e s c r i b e d i n 1971,  a highly flexible  history  to  and r o t a t i o n s o f b l o c k  and t h e d i s c o n t i n u i t i e s d i v i d i n g  c o n s i d e r e d t h e b l o c k s t o be r i g i d joint  finite  large displacements  first  continued  and l i m i t a t i o n s  i t s use i n p r a c t i c e w i l l  interactions with  1971).  e l e m e n t method a s i t r e l a t e s  The r o c k mass i s r e p r e s e n t e d  i t was  (Cundall,  C u n d a l l , and o t h e r s h a v e  a p p l i e s an e x p l i c i t ,  s o l u t i o n t o model  paper  This section provides a b r i e f  to toppling f a i l u r e .  The t e c h n i q u e  The o r i g i n a l  p u b l i s h e d i n 1971  of the d i s t i n c t  method a l o n g w i t h  to topples  e l e m e n t method c a n be t r a c e d t o  Cundall.  d e s c r i b i n g t h e method was  develop  finite  t o a l a r g e number o f r e s e a r c h e r s , b u t t h e  r e s e a r c h e r , D r . P.A.  Since t h i s  The  and s p l i t t i n g  (Cundall et  al., of  1978;  C u n d a l l and M a r t i , 1 9 7 9 ) , a j o i n t  creating discontinuous  transient linked  fluid  pressure  In a d d i t i o n the d i s t i n c t boundary  size  By 1985  and o t h e r  these  dimensional  program  (UDEC).  joint  e l e m e n t method h a s b e e n  o f some p r o b l e m s  permeability  C u n d a l l and Lemos,  element code a l l o w i n g s i g n i f i c a n t  computational  joint  and v a r i o u s  ( C u n d a l l , 1985;  1988).  linked  to a  reduction of the  (Lemos and B r a d y ,  f e a t u r e s had been u n i f i e d  1983).  into a  known a s t h e u n i v e r s a l d i s t i n c t  A three dimensional  capable  ( C u n d a l l , 1983),  and f l o w u t i l i z i n g  t o mechanical deformation,  c o n s t i t u t i v e models  code  j o i n t s by s e t s  generator  two  element  v e r s i o n o f t h i s program i s  known a s 3DEC.  All  the advantages noted  i n S e c t i o n 2.4.4  f o r the  e l e m e n t method a l s o a p p l y t o t h e d i s t i n c t however t h e d i s t i n c t over  the f i n i t e  finite  d i f f e r e n c e technique  requirements. of  relaxation,  and makes l i m i t e d The  A particular  finite  breaking  simplicity.  d i f f e r e n c e approach,  i t does n o t form l a r g e  demands on c o m p u t e r  memory  f o r m u l a t i o n o f t h e problem as a  i n t e r a c t i n g b l o c k s a l s o has advantages over  method u s e d by  finite  element t e c h n i q u e s .  o f c o n t a c t s between  a n d r o t a t i o n s o f b l o c k s a r e more e a s i l y  collection  t h e continuum  The m a k i n g  b l o c k s and l a r g e  21  advantages  advantage o f the  i s i t s computational  B e c a u s e t h e method i s an e x p l i c i t  matrices  e l e m e n t method,  e l e m e n t method h a s a d d i t i o n a l  e l e m e n t method.  s o l v e d u s i n g dynamic  finite  and  displacements  accommodated.  Disadvantages and  o f t h e method i n c l u d e t h e o f t e n s m a l l t i m e  corresponding long run time,  stability.  This disadvantage  i n the l a s t  few  cheaper  more p o w e r f u l .  2.4.6  By  and  has  r e q u i r e d to ensure  numerical  become much l e s s  significant  y e a r s a s d e s k t o p c o m p u t e r s h a v e become  Comparative  Assessment o f A n a l y t i c a l  Methods  f a r t h e most p o p u l a r method r e p o r t e d i n t h e l i t e r a t u r e  model t o p p l i n g method c a n n o t  i s the l i m i t  deformation  when t h e c o n s t i t u t i v e joints vary  e q u i l i b r i u m method.  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  undergo i n t e r n a l  (flexure)  prior  r e l a t i o n s h i p s of the  Although  serious,  to failure,  intact  most o f t h e l i m i t a t i o n s t h e y have been used finite  facilitate  comparison  stiff  1981), t h e l i m i t 1978).  or  assumptions  of  e q u i l i b r i u m method,  f r e q u e n t l y t o model  of f i n i t e  slopes i s  element r e s u l t s  K a l k a n i and  to  to real  P i t e a u , 1976;  e q u i l i b r i u m method, o r p h y s i c a l  When h a r d  rock i s modelled  22  but  toppling.  r o c k . T h i s i s done e i t h e r  (Brown e t a l . , 1980;  (Hittinger,  level  or  e l e m e n t methods overcome  e l e m e n t work w i t h t o p p l i n g  t o hard,  al.,  of the l i m i t  much l e s s  restricted  slopes  rock  or  i n S e c t i o n 2.4.3.  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  Most o f t h e  the  these problems are o f t e n  o v e r s h a d o w e d by p r o b l e m s w i t h t h e f u n d a m e n t a l t h e method l i s t e d  However,  to  of topples that  i n a n o n - l i n e a r manner w i t h s t r e s s  displacement.  As  step,  rock  Evans e t models  i t deforms  little,  and  most o f t h e  derived  from the  s t r e s s dependent d e f o r m a t i o n  joints.  is partially a result  The  preference  of research being  f o r hard  i n situ stress conditions  rigid  block behaviour.  As  small  slopes with  higher  deformations,  Distinct both  use  preference  technique  of the d i s t i n c t  larger  with  column  and  topples  e l e m e n t method and  f o r examining b l o c k t o p p l i n g .  C u n d a l l e t a l . (1977),  Aside  distinct  for  large slopes  from t h e s e  brief  literature  a  C u n d a l l e t a l . (1978) a l l  uses o f t o p p l i n g as  e l e m e n t method v a l i d a t i o n ,  examples i n t h e  as  Cundall  b l o c k t o p p l i n g examples t o v a l i d a t e t h e d i s t i n c t  method. of  corresponding  small  support  e l e m e n t methods h a v e b e e n a p p l i e d t o b l o c k  modelling  topples  have not been s t u d i e d .  as a v a l i d a t i o n  (1971),  of t h i s  r i g i d column b e h a v i o u r ,  i n s i t u s t r e s s e s and  rock  d i r e c t e d toward  s c a l e t o p p l e s where low  a result  is  element examples  there are very  of the d i s t i n c t  few  e l e m e n t method  b e i n g u s e d 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  toppling  slopes.  Hocking  (1978) u s e d a r i g i d b l o c k d i s t i n c t  examine t o p p l i n g s l i d i n g slopes.  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  block toppling.  u s e d by  The  to  f a i l u r e modes o f h y p o t h e t i c a l b l o c k y  block v e r s i o n of the d i s t i n c t of  element program  e l e m e n t method t o a r e a l  v e r s i o n of the d i s t i n c t  distinct  23  example  e l e m e n t method  I s h i d a e t a l . (1987) i s , however, o u t d a t e d  o t h e r a v a i l a b l e p r o g r a m s . The  rigid  compared  e l e m e n t method d o e s  to not  appear t o have been u s e d t o model t h e and  In  c o m p o s i t e modes o f  summary, t o p p l i n g  towards the  limit  realistically  be  research  not is  2.5.1  All  strengths  very  Also,  slope  the  distinct  finite  toppling,  requires  and  none t o  flexural  Parameters C o n t r o l l i n g Toppling:  Influence  of Structure  rock types are  susceptible  structure  Goodman and  and  Bray,  are  1976).  p l a n e s o f weakness w i t h i n  the  The  long  computer  runs.  e l e m e n t method  toppling.  Discussion  Rock T y p e  (de  i f the  F r i e t a s and  Structure  provides  r o c k mass, and  24  large  large  distinct  to toppling  present  have  e l e m e n t method  e l e m e n t method.  a p p l i c a t i o n s of the  non-  deformation  c a n n o t accommodate  i t s formulation  few  vary  displacement.  e l e m e n t method i s d e s i g n e d t o model  g e o m e t r y and 1973;  the  cannot  e q u i l i b r i u m method, b u t  a c o n t i n u u m and  deformations, but  to block  joint  predict toppling  limit  as  T h i s method  manner w i t h  extensively.  d i s p l a c e m e n t s as w e l l  2.5  i n any  than the  f o r m u l a t e d as  There are  been l a r g e l y d i r e c t e d  u s e d when r o c k o r  b e e n u s e d as  distinct  has  e q u i l i b r i u m method.  e l e m e n t methods c a n  more a c c u r a t e l y  flexural  toppling.  l i n e a r l y with s t r e s s or Finite  more c o m p l e x  requisite Watters, distinct  lithology  c o n t r o l s t h e s t r e n g t h and intact  The  deformation  characteristics  influence of j o i n t i n g  i s fundamental,  of topple types.  c o l u m n s w i t h no  Flexural  cross-fractures,  as e v i d e n t i n t h e  toppling  occurs  in  block toppling  occurs  by  separation along pre-existing  joints,  toppling  cross-jointing.  requires a pervasive  primary  strength characteristics  influence toppling strength,  slope f a i l u r e s  stress-strain  and  block-flexural  of i n t a c t  are shear  relationships,  T h e s e p r o p e r t i e s a r e d e p e n d e n t on  rock that  and  and,  e l a s t i c m o d u l u s and Weak r o c k w i l l  exhibit  h a v e an  low  rock type.  lower  At  strain  relationship  stress  levels  close to ultimate  toppling  finite  to a b r i t t l e  i n the l i t e r a t u r e  inadvertent result  r e s e a r c h has  to high  failure.  a non-linear  taken.  for  failure.  rock strength c h a r a c t e r i s t i c s  an  low  allowing l a r g e deformations  There i s nothing q u a n t i t a t i v e  T h i s seems t o be  rheology.  have a  e l a s t i c m o d u l u s and  stress  influence of these  strain  tensile  perhaps,  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 r o c k w i l l  limit  the  rock.  definitions  The  of  Research  of the has  concerning  on t o p p l e s .  direction  concentrated  on  e q u i l i b r i u m method, w i t h a s m a l l amount o f work on e l e m e n t method. The  limit  e q u i l i b r i u m method  inherent  restrictions  on t h e d e f o r m a t i o n  r o c k and  joints.  finite  The  behaviour  the  the  has of  e l e m e n t method d o e s n o t  25  the  intact have  these r e s t r i c t i o n s , modelling  2.5.2  It  but  i t has  a l s o been used v e r y  of D i s c o n t i n u i t i e s .  i s important to note t h a t t o p p l i n g f a i l u r e  c o n t r o l l e d by  the  intact  true  where low  i n small  scale topples  deformation to  essentially  rigid  discontinuities  and  intact the  can  in  stresses  intact  rock  the  a defined  surface  have c o m p l i c a t e d  inclination  surface  (Patton,  displacement.  is  of  of  failure  non-linear  in  the  stress-  i n c l u d e s peak and/or r e s i d u a l  1966;  Surface  and  strength  L a d a n y i and  and  shear strength.  Consequently,  irregularities  on  the  1 9 6 9 ) , and  on  cause a d i s c o n t i n u i t y to  during  increase,  in a real  26  normal  normal s t r e s s .  d i s c o n t i n u i t y i s confined discontinuity will  of  the  Archambault,  irregularities  d i l a t e when t e s t e d u n d e r c o n s t a n t  the  cause  importance.  o f a d i s c o n t i n u i t y d e p e n d s on  stress,  on  The  the  tension.  Shear s t r e n g t h  stress  in situ  by  is especially  creep deformation p r o p e r t i e s , cohesion,  separation  dilative  This  mechanical behaviour  displacement behaviour that strength,  rock.  rock.  i s o f paramount  D i s c o n t i n u i t i e s provide mass, and  i s often  behaviour of d i s c o n t i n u i t i e s , not  s t r e s s - s t r a i n p r o p e r t i e s of  rock  for  toppling.  Shear Strength  little  little  If a  shear the  normal  increasing  slope with  the  dilative  joints  finite  conservative joint  or d i s t i n c t  element models w i l l  behaviour i f d i l a t i o n  b e h a v i o u r o f t h e model  Dilation  of joints  asperities  this the  level, rock  equivalent  surface.  L a d a n y i and Archambault a t which s h e a r i n g o f  of joints w i l l  not occur.  and s t r e s s h i s t o r y , t h i s  Above  joint  D e p e n d i n g on  i s roughly  a t a 300 t o 450m  a l l but the largest slopes  degree o f d i l a t a n t  The  1986) .  6  to the stress level  Theoretically  i nthe  t o be a p p r o x i m a t e l y 9.5 x 10 N/m2.  dilation  density  i s not included  (Barton,  (1969) o b s e r v e d t h e s t r e s s l e v e l occurs  simulating  i s l i m i t e d by t h e shear s t r e n g t h o f  on t h e j o i n t  asperities  be  should  depth. d i s p l a y some  behaviour.  a b o v e d i s c u s s i o n on d e f o r m a t i o n c h a r a c t e r i s t i c s o f i n t a c t  rock  and j o i n t s  topples. slope  leads  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  The most fundamental d i f f e r e n c e between a  (<100m h i g h ) and a l a r g e s l o p e  condition. increase  As d e s c r i b e d  the strength  increase with  of dilative  slopes.  d e v e l o p m e n t o f some t o p p l i n g  shear.  discontinuities will  of d i s c o n t i n u i t i e s could  27  stress  confinement acts t o  j o i n t s undergoing  confinement i n higher  suggested d i l a t i o n arrested  above, t h i s  of dilative  Hence, t h e s h e a r s t r e n g t h  i s the i n s i t u  small  Bovis  (1982),  explain the  failures.  2.5.3  Groundwater  Few  r e s e a r c h e r s h a v e g i v e n more t h a n  the  i n f l u e n c e o f g r o u n d w a t e r on  of rock result the  of the d i r e c t i o n  engineering  of the  no  small rock,  are  1978;  common a s s u m p t i o n the toe of the the  the  slope.  slopes, accurate part  is a  Much o f  failures  excavation.  and  Tanon, 1985).  included i n the flow  a n a l y s i s , the are often  P i t e a u e t a l . , 1981;  the  s l o p e up  dilated  assumptions  simplistic  Brown, 1 9 8 2 ) .  to a point d i r e c t l y  drained  E v e n when  f o r the water t a b l e i s a s t r a i g h t  The line  below the  be  but  crest  pore pressures  o r an  a n a l y s i s of road  i n l a r g e r s l o p e s may  o f a r e g i o n a l f l o w s y s t e m and, have a water t a b l e .  of pore pressures  t o be  be  approximate water  Larger  except In order  c o r r e c t l y modelled,  28  c u t s and p i t  r e q u i r e a more  c o n s i d e r a t i o n of pore pressure.  regions, w i l l  of  slope.  adequate f o r the topples  most from  From t h i s p o i n t t h e w a t e r t a b l e i s assumed t o  a s s u m p t i o n o f no  t a b l e may  this  taken.  to mining or slope  ( C h o q u e t and  h o r i z o n t a l back i n t o the  The  influence  s l o p e s a r e o f t e n assumed t o be  f o r t h e w a t e r t a b l e and  (Hittinger,  to  b e e n done i s a i m e d a t s o l v i n g  s c a l e of these  pore pressure  pore pressures used  Like the  t o p p l i n g r e s e a r c h has  problems r e l a t e d  Because of the  with  toppling.  treatment  strength characteristics discussed earlier,  r e s e a r c h t h a t has  nature  simplistic  slopes  i n t h e most f o r the the  are arid  influence  groundwater flow system i n t h e slope  must b e  accurately  quantified.  2.6  Summary  2.6.1  o f Areas Needing Further  F a i l u r e Plane  Prediction  One o f t h e p r o b l e m s w i t h t h e commonly method  f o rtoppling  (1976) i s t h a t  limit  i s planar,  limit  T h e u s e r must a p p l y a t r i a l  selecting d i f f e r e n t planar  equilibrium  and e r r o r  failure  with the lowest  surfaces  method assumes t h a t  Further  research  surface  i n a l l types o f topples  e l e m e n t method  the f a i l u r e  Also, surface  true.  i n t o t h e f o r m a t i o n and shape o f t h e f a i l u r e i s required.  The d i s t i n c t  i s capable of p r e d i c t i n g a f a i l u r e  surface  by m o d e l l i n g b o t h i n t a c t r o c k and j o i n t  deformations using  realistic  constitutive relationships.  U s i n g t h i s method t o model t o p p l i n g hypothetical  to  factor of safety.  b u t i t i s n o t known i f t h i s i s a l w a y s  configuration  equilibrium  a n a l y s i s d e v e l o p e d b y Goodman a n d B r a y  determine the surface this  used  i t cannot p r e d i c t t h e shape and l o c a t i o n o f t h e  f a i l u r e plane. approach,  Work  slopes  geometry s h o u l d  deformation of  having v a r i a b l e material  lead to a better  understanding of the  development and geometry o f f l e x u r a l t o p p l i n g  29  p r o p e r t i e s and  failures.  2.6.2  The  Influence  i n f l u e n c e of  u n d e r s t o o d and strain the  of Confining  in situ  can  be  s t r e s s e s on  incorporated  laws f o r i n t a c t  limit  Stress  rock  and  incorporate  both the  f i n i t e e l e m e n t and  more r e a l i s t i c  joints.  realistic  in situ  s t r e s s e s , n e i t h e r has  i n f l u e n c e of s t r e s s conditions  can  be  done w i t h  slopes  and  2.6.3  Toppling  of mixed rock units  phyllite) prior  to  constitutive stressOne  of the  flaws  of  compare t h e  Although  distinct  utilize  investigate  toppling slopes.  e l e m e n t method u s i n g  This  large  scale  blocks.  i n M i x e d Rock T y p e s  b e e n made t o n u m e r i c a l l y types.  Large slopes  ( i e : s a n d s t o n e and  failure  A research  stresses.  been used t o  on  c a n n o t be  model t o p p l i n g  c o n s i s t i n g of shale,  t h a t undergo s i g n i f i c a n t  equilibrium  one  the  deformable  attempt has  soft  i s well  f i n i t e d i f f e r e n c e methods  the  and  i n the  strength  e q u i l i b r i u m approach to 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  No  rock  layered  or q u a r t z i t e  overturning  slopes  and  accurately modelled with  hard  and  flexure the  limit  method.  program c o u l d use  the  distinct  b e h a v i o u r o f mixed r o c k  material.  reproduce the  The  primary goal  30  type slopes  w o u l d be  deformation observed  e l e m e n t method  to  i n these  to  slopes  numerically slopes.  to of  2.6.4  Time Dependent  Deformation  M o s t o f t h e r e s e a r c h on t o p p l i n g c o n c e n t r a t e s on deformations to  excavated  i n these slopes are l i k e l y  deformations  excavated  small rapidly  i n the  by  from  s t r e s s changes.  fluvial  by mass w a s t i n g  and/or g l a c i a l  or tectonic u p l i f t ,  much more s i g n i f i c a n t . difference techniques  I t may  literature slopes.  insignificant  erosion or creep  i n f l u e n c e s may  C u n d a l l and  finite  Board,  e l e m e n t t e c h n i q u e s t o model t h i s t y p e o f  2.6.5  Large  Weak Rock  excavations.  At the s c a l e of these small excavations, intact  dealt with engineering or  deformation  of the  deformation  along d i s c o n t i n u i t i e s  r o c k i s much l e s s  In  l a r g e s l o p e s , t h e s t r e n g t h and  of  b o t h t h e r o c k m a t e r i a l and  literature 1982;  (Tabor,  Holmes and  Jarvis,  de  deformation  joints.  and  Evans,  31  characteristics contribute to stresses  Although  will  there  are  of l a r g e s c a l e t o p p l e s i n the  Frietas  1985;  than  rock.  increased confining  descriptions 1971;  i n the  mining  significant  r o c k mass w i l l  increase the strength of d i l a t i v e qualitative  or  deformation.  r e s e a r c h has  several  (such  1988),  Most t o p p l i n g  In a d d i t i o n ,  be  continuum  finite  stability.  slopes  oversteepened  be p o s s i b l e t o u s e  a s t h e p r o g r a m FLAC, d e s c r i b e d by  compared  In l a r g e r n a t u r a l  applied to a discretized  S l o p e s and  Creep  Watters,  1987;  1973;  Pritchard  Bovis, et.al.,  1 9 8 8 ) , no a n a l y s i s influence been  of the rock material  incorporates  o r r o c k mass s t r e n g t h  the has y e t  Groundwater  date,  no r e s e a r c h e r  considered  w o r k i n g on t o p p l i n g  the heterogeneous,  conductivity the  that  attempted.  2.6.6  To  of these slopes  i n bedded d e p o s i t s .  b u t i t may be r e q u i r e d  l a r g e r mountain s c a l e  has  anisotropic nature of hydraulic A more d e t a i l e d t r e a t m e n t o f  g r o u n d w a t e r f l o w may n o t be n e c e s s a r y  slopes,  slopes  i n smaller  for realistic  topples.  32  toppling  modelling of  3.  Distinct  3.1  E l e m e n t Method  I n t r o d u c t i o n : UDEC  The  universal  distinct  element code  C o n s u l t a n t s was p u r c h a s e d historic  advantages  i n section  for modelling  2.4.5.  discusses the theory, program.  r e s e a r c h program.  development and c a p a b i l i t i e s  particular reviewed  f o rt h i s  (UDEC) m a r k e t e d b y I t a s c a  Only  jointed  The r e m a i n d e r  t h e f e a t u r e s used  t o Lemos e t a l . ( 1 9 8 5 ) .  the following  (1989),  Lorig  form.  r e l e a s e d March,  Cundall  T h i s r e s e a r c h uses I t i s compiled  80386-based microcomputer r u n n i n g 386,  t h e PHARLAP l i n k e r ,  1989) . linkable The  Screen  library  v e r s i o n used  (1987),  approximately  Itasca  i n source  code  UDEC v e r s i o n 1.5  f o r o p e r a t i o n on an  D0S3.X, u s i n g SVS FORTRAN  package)  through  f o u r m e g a b y t e s o f RAM,  (Itasca, a FORTRAN-  (Itasca,  r e s e a r c h was c o m p i l e d  33  used  (1978).  i s handled  (SCITECH p l o t t i n g f o rthis  research  a n d ICG X-AM DOS e x t e n d e r  graphics support  with  o f t h e program a r e  and C u n d a l l e t a l .  1989.  of the  Readers i n t e r e s t e d i n  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 or executable  chapter  The g e n e r a l r e f e r e n c e s  d i s c u s s i o n are:  (1984),  systems a r e  of this  i n this  chapter.  a more c o m p l e t e g e n e r a l d e s c r i p t i o n  in  rock  comprehensive m o d e l l i n g package  program a r e d i s c u s s e d i n t h i s  referred  program and i t s  f e a t u r e s , and l i m i t a t i o n s  UDEC i s a v e r y  many f e a t u r e s .  of this  The  a n d a math  1989).  to utilize coprocessor.  With  this  amount o f memory a p r o b l e m  2500 r i g i d  b l o c k s o r 1000 f u l l y  3.2  Theory  The  distinct  approach  of Distinct  element  deformable  Element  method i s b a s e d  mass t o be r e p r e s e n t e d by d i s t i n c t  3.2.1  Explicit  Deformation  calculation  finite  time  blocks.  m o d e l l e d by f i n i t e  Solution  rock  interact  along  differences  ( F i g . 3.1a).  Procedure  i s determined  by u s i n g an e x p l i c i t  solution  I n an e x p l i c i t  method,  a l l  on one s i d e o f a l l e q u a t i o n s a r e known a n d a s i m p l e produces  the q u a n t i t y a t the next time s t e p .  In  are incremental displacements  The t e c h n i q u e r e l i e s  on t h e f a c t  that  i t takes a  f o r a displacement t o pass through t h e system o f  I f t h e t i m e s t e p i s s m a l l enough s u c h t h a t  displacement cannot propagate block  allows a jointed  e a c h b l o c k c a n be a l l o w e d t o d e f o r m  UDEC t h e q u a n t i t i e s c a l c u l a t e d or s t r a i n s .  on a d i s c o n t i n u u m  blocks that  procedure time stepping algorithm. quantities  b l o c k s c a n be u s e d .  In a d d i t i o n t o the discontinuum modelling  of the block i n t e r a c t i o n , as a continuum  of approximately  Method  t o r o c k mass m o d e l l i n g t h a t  t h e i r boundaries.  size  f r o m one b l o c k t o an a d j a c e n t  i n one t i m e s t e p , t h e n t h e e q u a t i o n s o f m o t i o n  b l o c k s become u n c o u p l e d When c o n t i n u u m  finite  a  and t h e n u m e r i c a l p r o c e d u r e  difference  34  zones  for a l l i s stable.  are applied within the  Distinct  Figure  3.1a  Nature  of  Element  Model  D i s t i n c t Element Model ( a f t e r I t a s c a , 1989)  Constitutive Relation  Stress  Displacement or S t r a i n  Law  u —  of  Motion  Force Mass  u integrated  Figure  3.1b  twice  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 ( a f t e r C u n d a l l e t . a l . , 1977)  35  blocks,  the time  propagation block.  s t e p a l s o becomes d e p e n d e n t on  o f i n f o r m a t i o n between a d j a c e n t  Determination  of the  r e q u i r e d time  t h e mass and  material stiffness  disadvantage  o f t h i s method o f s o l u t i o n  the  zones w i t h i n step  i s based  of b l o c k s or zones. i s the  The  the on main  s m a l l time  step  required.  The  program  i t e r a t e s by u s i n g  determine the net  f o r c e on  i n f l u e n c e of surrounding then  uses these  accelerations when t h e f o r c e s on  each b l o c k r e s u l t i n g  b l o c k s and  f o r c e s and  and  force displacement  the time  displacements.  increment  each b l o c k .  i n F i g u r e 3.1b.  determining  when t h e p r o b l e m e i t h e r  is  by m o n i t o r i n g  achieved  velocities,  o r any  user w i t h i n the  3.2.2  The  Equations  time  weight.  cycle repeats  block  itself  i s used t o r e e v a l u a t e  user  is  It  the  diagrammatically  i s responsible for  stabilizes  histories  of  or f a i l s .  This  displacements, the  problem.  o f M o t i o n and  System  Damping  described i n the previous  known a s d y n a m i c r e l a x a t i o n (1966).  the  o f s e v e r a l o t h e r p a r a m e t e r s s e l e c t e d by  s o l u t i o n process  el.al.  The  to  step to determine  This procedure  illustrated  from  a b l o c k s own  The  of displacement  laws  and  was  section i s  f i r s t d e s c r i b e d by  Otter  I n dynamic r e l a x a t i o n t h e b l o c k s a r e moved  a c c o r d i n g t o Newton's s e c o n d law  36  of motion, which i s  justified  on  physical  grounds  (Cundall,  1987).  This  l a w c a n be  written  i n t h e form: <3u = Z dt m where  F=  force  m=  mass  [1]  u= v e l o c i t y t=  time  Using central difference  t h e o r y we c a n w r i t e  t h e above  equation as:  u  (t  + At/2)  =  - ( t - At/2) u  +  £t)  A  t  [  2  ]  m Written  f o r a block with gravity  (g^) i n c l u d e d  this  equation  becomes: A  (t + At/2) X  =  u  ( t - At/2)  +  (  fiE^t)  +  A  t  HI  X  «-  J  where i d e n o t e s a d i r e c t i o n a l i n d e x u^= t h e v e l o c i t y o f t h e c e n t e r o f mass a n d g = x  Note t h a t  o  this central difference  acceleration  integration  i s constant over a time increment  to  (t +  By  integrating  assumes from  that  ( t - At/2)  At/2).  the expression f o r v e l o c i t y at the h a l f  step over the i n t e r v a l  (t) t o (t + A t ) ,  37  incremental  time  displacement  (u^) o f t h e b l o c k i s d e t e r m i n e d .  u s e d t o o b t a i n t h e new b l o c k l o c a t i o n  x  The  .(t  + At)  =  x  .(t)  development i s s i m i l a r  blocks.  (x^):  ^ . ( t + At/2)  +  A  t  forrotational  Rotational velocities  T h i s i s then  at the half  [  4  ]  motions o f t h e timestep  are given  by:  0  (t  + At/2)  =  0  ( t - At/2)  sM(t)  +  A t  [  5  ]  I where  0 =  angular v e l o c i t y  I =  moment o f i n e r t i a  EM = Rotational  static  o f b l o c k about  displacements  solutions,  =  a r e g i v e n by:  e  .(t)  +  e  . . ( t + At/2)  A  t  [  6  ]  some f o r m o f e n e r g y d i s s i p a t i o n o r  damping must be i n c l u d e d t o p r e v e n t oscillating  i t s centroid  sum o f t h e moments a b o u t t h e b l o c k c e n t r o i d  0.(t + At)  For  o f b l o c k about i t s c e n t r o i d  indefinitely.  t h e system  from  UDEC u s e s e i t h e r mass p r o p o r t i o n a l  o r s t i f f n e s s p r o p o r t i o n a l damping.  Each o f these  v i s c o u s dashpots a t t a c h e d t o t h e system. dampens t h e s y s t e m t o an a b s o l u t e  simulate  Mass p r o p o r t i o n a l  frame o f r e f e r e n c e , and i s  a k i n t o immersing t h e whole system i n a v i s c o u s  fluid.  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  that  a p p l i e s d a s h p o t s 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 u s e d  program.  *  38  i n this  research  I n mass p r o p o r t i o n a l that  opposes  block  damping, t h e d a s h p o t s g e n e r a t e a  the blocks  v e l o c i t y and  v e l o c i t y and mass.  as f o l l o w s  The  to include viscous  —  dt  where a i s t h e damping  In  finite  the  u  (t  + At/2)  Rotations  This  =  { { l  equation of motion  modified  damping.  [7]  factor  centered  a t time t v e l o c i t y at  becomes:  (t- At/2)  ( 1  _ aAt 2  )+  (  F_  +  g)  A t  } / ( l + «At/2)  a r e damped i n a s i m i l a r manner  (Itasca,  1989).  scheme o f damping i s n o t w i t h o u t d i f f i c u l t i e s . proportional  constant  v e l o c i t y g e n e r a t e s e r r o n e o u s body f o r c e s  direction  damping t o b l o c k s  of motion of the block.  a f f e c t the s o l u t i o n  UDEC p a r t i a l l y  (Cundall,  These  that  Applying  a r e moving a t a  spurious  opposing the body  t h e damping  f a c t o r b a s e d on t h e sum  o f t h e change i n k i n e t i c e n e r g y  system  The  time step by damping the  damping f a c t o r i s a d j u s t e d  to maintain a prescribed  system.  i n the system t o t o t a l  ratio  i n the each  (R) o f power a d s o r b e d  change i n k i n e t i c energy i n  As t h e a c c e l e r a t i o n o f a s y s t e m o f b l o c k s  39  forces  1987).  o v e r c o m e s t h i s p r o b l e m by a d j u s t i n g  i n a time step.  [8]  m  velocity  may  is  to the  = — - cm + g m ^  difference notation  h a l f time step  i s proportional  force  reduces  to  zero,  has  t h e damping  shown t h a t  approximately critical  In a  adjusting  also  reduces t o zero.  t h e damping f a c t o r  (Lorig,  accelerating  approaches  1984).  t h i s i s only a p a r t i a l solution.  significant variation  Experience  to maintain R at  0.5 p r o d u c e s a damping e f f e c t t h a t  damping  practice  factor  In systems  i n b l o c k s i z e o r motion,  blocks w i l l  large  h a v e a d i s p r o p o r t i o n a t e a f f e c t on t h e  sum o f t h e k i n e t i c e n e r g y t e r m , and t h e damping f a c t o r weighted t o these blocks.  I n such a system,  moving a t a c o n s t a n t v e l o c i t y w i l l body  with  still  small  experience  will  be  blocks spurious  forces. 0  M a n u a l damping i s a l s o description manually by  3.3.1  f o r dynamic s i m u l a t i o n s .  o f how t h e damping f a c t o r  et a l .  (1978) and L o r i g  A  c a n be d e t e r m i n e d  f o r mass o r s t i f f n e s s p r o p o r t i o n a l  Cundall  3.3  available  damping  i s given  (1984).  F e a t u r e s o f UDEC Block Interface  UDEC h a s two b u i l t relationships.  Constitutive  i n interface,  Relations  or joint  constitutive  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  elastic-plastic.  A continuously yielding  i s linear  j o i n t model t h a t i s  c a p a b l e o f m o d e l l i n g p r o g r e s s i v e damage o f t h e 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  40  i n t h e program  (Cundall  and  Lemos,  used  1988).  in this  by  joint  between b l o c k s . n  AF )  displacement  where K  interfaces are  systems l o c a t e d a t t h e c o n t a c t  I n c r e m e n t a l n o r m a l and s h e a r  (Au , Au ) n  and K  n  of block  are r e l a t e d t o the incremental  S  relationship i s  r e l a t i o n s h i p , t h e d e f o r m a b i l i t y and  characteristics  spring - slider  (AF ,  joint  research.  In t h e o r i g i n a l frictional  Only t h e o r i g i n a l  s  using  s  linear  represented points  forces  relative  force displacement  laws:  AF  n  = K  n  Au  n  [9]  AF  S  = K  s  Au  s  [10]  are the contact  n o r m a l and s h e a r  stiffnesses.  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 t h i s model i s shown  i n Figure  3 . 2a.  Edge t o edge j o i n t edge c o n t a c t s , distributed and  3.2c.  (Acr , n  ACT ) s  in  n  are represented  by two c o r n e r t o  t h e f o r c e a p p l i e d a t each  over a contact  l e n g t h L a s shown  The n o r m a l and s h e a r s t r e s s a c r o s s are r e l a t e d t o displacement  force across  where k  with  contacts  a single contact  and k  s  Aa  n  ACT  s  = k =  k  s  n  corner i n Figures each  contact  i n t h e same manner a s  above: Au Au  n  s  a r e t h e n o r m a l and s h e a r s t i f f n e s s e s  s t r e s s / l e n g t h rather than  3.2b  force/length.  41  [11] [12]  expressed  J2VW-  1  I  Normal I n t e r a c t i o n  >JJ  Ks  K II  I  Shear I n t e r a c t i o n  \  / \  / \  , —  l H  / \ /c  \  3  -—<  C  4  / /  c) /  /  Figure  3.2a) b) c)  1  /  1  1 1I  /  /  —*M  Mechanical Representation of I n t e r f a c e s i n D i s t i n c t Element Model Edge t o Edge C o n t a c t Contact Length f o r F u l l y Deformable B l o c k s ( a f t e r I t a s c a , 1989)  42  Figure  3.2c  blocks  resulting  These g r i d  a l s o i l l u s t r a t e s how from i n t e r n a l  discretization  p o i n t s a r e t r e a t e d a s new  expressions  discussed  Mechanically,  the  above a r e  overlap  n o r m a l f o r c e o r s t r e s s on of the  exterior grid  blocks  modelled.  and  the  In the  iterative  i s used t o update  f o r c e s or s t r e s s e s , which are then used t o  new  block accelerations.  The  m a i n d i f f e r e n c e between n o r m a l and  joints  are  i s proportional to  contact.  p r o g r a m , a change i n o v e r l a p  contact  i s the The  peak s t r e n g t h o f t h e  Coulomb  friction  s  Tensile dilation  <f> a r e t h e  be  determine  strength  i s limited  by  the  in  a Mohr-  joint  t a n 4>  n  cohesion  s t r e n g t h normal t o the can  the  law:  |CT | < c + c r where c and  joint  the  cycle  shear behaviour of  i n c o r p o r a t i o n o f a peak e l a s t i c  shear.  on  applied.  o f two the  corners,  points  added a s  an  joint  [13]  and  can  friction  be  increment to the  angle.  included, joint  and  friction  angle.  The is  bilinear  e l a s t i c - p l a s t i c model b e h a v i o u r d e s c r i b e d  a simplification  limitations. increase with usually  do  not  of r e a l  j o i n t b e h a v i o u r and  I n r e a l i t y b o t h s h e a r and the  c o n f i n i n g s t r e s s on  d i s p l a y instantaneous  43  normal  a joint, plastic  above  has stiffness and  real  joints  shear at the  peak  strength.  In r e a l  joints,  plastic  displacement begins t o  accumulate  b e f o r e t h e peak s h e a r s t r e n g t h i s r e a c h e d ,  shear s t r e s s  required  considerably  l e s s t h a n t h e peak s h e a r s t r e n g t h .  and  f o r continuous p l a s t i c  3.3b i l l u s t r a t e how t h e model d i f f e r s  shear  from  and t h e  i s often  F i g u r e s 3.3a  real  joint  behaviour.  The  continuously yielding  beginning of t h i s model j o i n t  section  behaviour.  and  i s d e s i g n e d t o more  through  joint  peak shear s t r e n g t h i s reached.  Three rigid,  (Cundall et a l . ,  r e g i o n t o drop below t h e 1978; C u n d a l l a n d H a r t , 1989)  B l o c k 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  types of block deformability simply deformable,  comprised  accommodated by n o r m a l  of  and t h e  The model a l s o a l l o w s t h e  C u n d a l l and Lemos, 1988; and I t a s c a ,  In a system  The  stress,  shear begins before the  i n t h e p o s t peak p l a s t i c  peak s h e a r s t r e s s .  3.3.2  and  stiffnesses to  increase with confining  continuous accumulation of p l a s t i c  1984;  realistically  I n t h e c o n t i n u o u s l y y i e l d i n g model t h e n o r m a l  shear s t i f f n e s s e s  shear s t r e s s  at the  L i k e t h e o r i g i n a l model, normal  shear s t r e s s e s are r e l a t e d displacements.  j o i n t model m e n t i o n e d  are available  and f u l l y  of r i g i d  i n UDEC:  deformable.  blocks, a l l the deformation i s  and s h e a r d i s p l a c e m e n t on t h e j o i n t s .  b l o c k s h a v e two t r a n s l a t i o n a l  a n d one r o t a t i o n a l  degrees  freedom, b u t t h e geometry o f t h e b l o c k s does n o t change.  44  F i g u r e 3.3a) b)  E l a s t i c - P l a s t i c J o i n t Model T y p i c a l J o i n t Behaviour  This type elastic  o f a n a l y s i s i s a p p r o p r i a t e when t h e i n t a c t  deformation  i s negligible  rocks  compared t o d e f o r m a t i o n  on  discontinuities.  Simply  d e f o r m a b l e b l o c k s a d d t h r e e more i n t e r n a l  freedom c o r r e s p o n d i n g e  yy  e  xy  + e  yx) '  Griffith's 1979;  a n <  to three strains  1987).  and M a r t i ,  deformable b l o c k s .  but avoid  Because t h i s  of block  i s c o n s t r a i n e d t o t h e combined d e g r e e s o f f r e e d o m  outlined  above, t h e y  a r e not as a c c u r a t e  b l o c k s and a r e n o t u s e d  Fully  i n this  block deformation displacements  deformable  research.  l o a d s a r e h i g h enough t h a t  i s significant  and j o i n t  blocks are discretized  difference  z o n e s and m o d e l l e d  method i s e x p l i c i t , space,  and p l a n e  relative  deformations.  individual  The  as f u l l y  type  d e f o r m a b l e b l o c k s a r e a p p r o p r i a t e when c o n f i n i n g  stresses or transient  al.,  ,  The a i m o f t h i s  i s t o incorporate block deformation,  computer i n t e n s i v e f u l l y  x x  t o f r a c t u r e b a s e d on  ( C u n d a l l e t a l . , 1978; C u n d a l l  and W i l l i a m s and Mustoe,  formulation  i n two d i m e n s i o n s ( e  ^ incorporate the a b i l i t y  theory  degrees of  to block  In t h i s  formulation  into triangular  as a continuum.  differences are centered  strain  internal  finite  The s o l u t i o n i n t i m e and  c o n d i t i o n s a r e assumed  (Cundall e t  1978).  general  triangular  solution zoning  sequence f o r a g r i d  i s as f o l l o w s .  46  p o i n t formed by t h e  I n each time  step, stresses  are  integrated  force any  about t h e g r i d p o i n t  from s u r r o u n d i n g  external  forces  acceleration  t o determine a  z o n e s . To t h i s i s a d d e d t h e t o t a l o f  from b l o c k c o n t a c t s o r o t h e r w i s e . Net  i s o b t a i n e d by d i v i d i n g t h e n e t f o r c e  lumped mass a t t h e g r i d p o i n t acceleration.  resultant  by t h e  and a d d i n g g r a v i t a t i o n a l  The e q u a t i o n o f m o t i o n c a n be w r i t t e n  as  follows: j  5Uj  at  where  s= nj=  d  s  +  F  i  [14]  m  the surface gridpoint the unit  enclosing  t h e mass m lumped a t a  n o r m a l t o s,  F^= t h e r e s u l t a n t o f a l l e x t e r n a l 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 , i  In  points  and j a r e d i r e c t i o n a l i n d i c e s .  differences  are applied  f o r blocks,  to the accelerations  of grid  t o d e t e r m i n e 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 .  basic  relate  applied to  and  a s i m i l a r manner t o t h e e q u a t i o n o f m o t i o n  central  The  forces  d e f i n i t i o n s o f two d i m e n s i o n a l  zone s t r a i n s and r o t a t i o n s  s t r a i n a r e used t o  t o nodal d i s p l a c e m e n t s as  follows:  ij = 2 i , J ( d  +  J,i  d  0i j = 2 ^ < 3 " J » i (  i  47  [15]  }  )  [16]  where  u= r e l a t i v e i  displacement  and j a r e d i r e c t i o n a l  indices  comma i o r j ( i e : , i o r , j ) d e n o t e s a p a r t i a l derivative time  A detailed constant of  The  with  r e s p e c t t o i o r j , and t h e d o t s a r e  derivatives.  description  o f how t h e s t r a i n components f o r t h e  s t r a i n elements a r e determined  the surrounding  from t h e d i s p l a c e m e n t  n o d e s i s g i v e n by C u n d a l l e t a l .  s t r a i n components i n a zone a r e u s e d t o d e t e r m i n e  stresses  by t h e b l o c k c o n s t i t u t i v e  stress-strain material  relations.  (1978).  zone  The s t a n d a r d  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  i s used.  The r e l a t i o n s h i p  form and r e s t r i c t e d t o p l a n e  i s used  i n an i n c r e m e n t a l  strain conditions.  The e q u a t i o n  is: e Ar^j  where  = AAe 5^j v  +  2/iAe^j  [17]  A,/z a r e t h e Lame c o n s t a n t s , e Ar^j  a r e t h e e l a s t i c increments  As^j  are the incremental  As  v  SJLJ  = t h e increment  blocks are available. relationship,  tensor,  strains,  of volumetric s t r a i n  = Kronecker d e l t a  I n UDEC, two c o n s t i t u t i v e  of the stress  (Ae-^+ A t ^ )  function.  relationships  forfully  deformable  B o t h u s e t h e above s t r e s s - s t r a i n  b u t 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 t h e r o c k  d e f i n e d b y a Mohr-Coulomb e n v e l o p e .  48  With t h i s  formulation,  the  rock deforms e l a s t i c a l l y  plastically  up t o t h e s t r e n g t h  past t h i s point.  The u s e r d e f i n e s  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 strength,  The  stress  and d i l a t i o n  i n t h e elements,  when t h e s e e l e m e n t s t r e s s e s nodal  3.4  t h e e n v e l o p e by  cohesion,  tensile  angle.  increments determined  update s t r e s s e s  angle,  l i m i t and  i n E q . [17] a r e u s e d t o and t h e c y c l e  a r e used  repeats  itself  i n E q . [14] t o d e t e r m i n e  accelerations.  Limitations  o f UDEC  T h e r e a r e a few l i m i t a t i o n s b u i l t  into the relationships  used  i n UDEC.  At  t h e moment t h e c o n s t i t u t i v e r e l a t i o n s h i p  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 homogeneous i s o t r o p i c  In models w i t h l a r g e accelerations, can  create  artificial  forces  analysis of  blocks.  and s m a l l  blocks undergoing d i f f e r e n t  the v e l o c i t y proportional  spurious  f o rthe intact  forces  i n t h e system  damping u s e d (Sec.  3.2.2).  i n UDEC These  can a f f e c t t h e s o l u t i o n o f t h e problem i n  some s y s t e m s .  49  With very factor.  l a r g e problems e x e c u t i o n time  isstill  speed.  t h e two f a c t o r s t h a t h a v e t h e most i m p a c t  e f f e c t i v e n e s s o f UDEC a r e t h e a c c u r a c y and  limiting  The s i z e o f p r o b l e m t h a t c a n b e r u n i s n o t l i m i t e d by  c o m p u t e r memory a s much a s b y c o m p u t a t i o n a l  Probably  a  the users' a b i l i t y  to interpret  of input  the results  on t h e  parameters, of the  analysis.  Using the f u l l  capabilities  o f UDEC t o a c c u r a t e l y s o l v e a r o c k  mechanics problem o f t e n r e q u i r e s complete knowledge o f t h e r o c k and j o i n t  s t r e n g t h s and e l a s t i c  properties.  W i t h most  e n g i n e e r i n g problems, economics p r e c l u d e t h e s i t e characterization  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 p r o g r a m t h a t r e l i e s a s s e s s t h e performance o f t h e model. to  use, but t h e w e l l developed  program output unskilled  user.  mechanics,  can i n s t i l l  theory,  of the d i s t i n c t  t h e p e r f o r m a n c e o f a model. of  a l l o f these areas,  misinterpret  I t i s d e c e p t i v e l y easy  i n t e r a c t i v e g r a p h i c s and  a false  sense  of confidence  The u s e r must be f a m i l i a r w i t h  elastic  limitations  on t h e u s e r t o  rock  and t h e c a p a b i l i t i e s and e l e m e n t method t o c o r r e c t l y Without a thorough  output.  50  assess  understanding  i ti s possible to seriously  t h e program  i n an  4.0 M o d e l l i n g  Toppling with  UDEC  4.1 I n t r o d u c t i o n  The  literature  review  i n chapter  2 shows t h a t a d i s t i n c t  e l e m e n t p r o g r a m s u c h a s UDEC h a s b e e n u s e d t o model toppling, block  and c o n c l u d e s  that i t should  a n d f l e x u r a l modes o f t o p p l i n g .  of discontinuum should  block  b e a b l e t o model The u n i q u e  a n d c o n t i n u u m methods o f s o l u t i o n  make t h e p r o g r a m w e l l s u i t e d f o r m o d e l l i n g  both  combination i n UDEC flexural  modes o f t o p p l i n g .  The  theoretical  against exact (Cundall, 1985;  b a s i s o f UDEC h a s b e e n t h o r o u g h l y  analytical  1971; C u n d a l l  Cundall  s o l u t i o n s by e a r l i e r  researchers  e t a l . , 1978; C u n d a l l ,  a n d Lemos, 1 9 8 8 ) .  validated  1983; C u n d a l l ,  The a i m o f t h i s  chapter  d e m o n s t r a t e t h a t UDEC c a n be u s e d t o a c c u r a t e l y model block  and f l e x u r a l  types  of toppling affecting  i s to  both  engineered  slopes.  Block  t o p p l i n g i s m o d e l l e d b y r e p e a t i n g a n example o f t h e  limit  e q u i l i b r i u m method o f a n a l y s i s f i r s t  and  Bray  (1976).  predecessor to t h i s  reported  i n Goodman  T h i s example h a s a l s o b e e n e v a l u a t e d  o f UDEC  ( C u n d a l l e t a l . , 1978).  example a n d t h e r e s u l t s  analyses.  51  compared w i t h  using a  UDEC i s a p p l i e d the e a r l i e r  Examples o f f l e x u r a l toppling  t o p p l i n g a r e n o t a s common a s b l o c k  i n the literature.  The few e x a m p l e s r e p o r t e d  either  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 n o t r e p o r t t h e r o c k strength o r geometric  parameters necessary  formulate t h e problem  i n a distinct  to accurately  element model.  reasons  t h e examples s e l e c t e d and m o d e l l e d  Section  4.3 a r e n o t d e f i n i t i v e .  F o r these  w i t h UDEC i n  T h e s e m o d e l s d e m o n s t r a t e t h a t UDEC i s a b l e t o r e p r o d u c e t h e deformations estimates  toppling  properties observe  i n t h e example s l o p e s u s i n g  o f mechanical  verification of  observed  and g e o m e t r i c  i s necessary  parameters.  before proceeding  This  with the analysis  i n n a t u r a l s l o p e s where measurement o f m e c h a n i c a l o f r o c k m a t e r i a l a n d r o c k mass, a n d t h e a b i l i t y t o  deformation  patterns are necessarily  compromised.  4.2 R i g i d  Block/Flexural Toppling  A simple,  h y p o t h e t i c a l example o f b l o c k / f l e x u r a l  r e p o r t e d Goodman a n d B r a y the  reasonable  blocks necessary  i t using  C u n d a l l e t a l . (1978),  o f UDEC t o a n a l y z e t h e same m o d e l .  r e p o r t t h e f r i c t i o n angle  t o p p l i n g was  (1976) who a l s o a n a l y z e d  l i m i t e q u i l i b r i u m method.  predecessor  Example  used  a  These s t u d i e s  a l o n g t h e s i d e s and base o f t h e  t o maintain  stability.  52  This section  compares  these values with the l i m i t i n g determined  f r i c t i o n angle  for stability  w i t h UDEC.  The model g e o m e t r y and s c a l e a r e shown i n F i g u r e 4.1. simplifications  and r e s t r i c t i o n s  e q u i l i b r i u m method rigid  that apply  are simulated with t h i s  b l o c k model and t h e o r i g i n a l  are used.  The j o i n t s  i n the l i m i t UDEC m o d e l .  j o i n t model  a r e assumed t o h a v e no c o h e s i o n  strength.  Gravity  i s applied to the blocks while the toe block  fixed.  Once t h e s l o p e i s s t a b l e u n d e r g r a v i t y ,  is  removed.  The f r i c t i o n a n g l e  in  an i t e r a t i v e manner t o i d e n t i f y  monitoring  unstable.  mechanical  displacements  Figures versus  Figure of  time  histories  i s then  changed  a t which the  of the v e l o c i t i e s  are h i s t o r y plots  i n Figure  by  and  of mechanical  f o r the block corner  time  labelled  HI i n  4.2a.  i s for a trial  the history  excavation,  the toe block  N o t e t h a t t h e 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  than  4.2a  i s held  S t a b i l i t y of the slope i s assessed  horizontal velocity  different  the value  or  of the blocks.  4.2a and 4.2b  F i g u r e 4.1.  on t h e j o i n t s  The  ( S e c . 3.3.1)  tensile  s l o p e becomes  The  that d i d not f a i l .  include i n i t i a l  movement due t o t o e b l o c k  and s t a b i l i t y shown by v e l o c i t i e s  53  Characteristics  returning to  UDEC (Version 1.50J  legend 31/05/1989 15: 38 cycle 0 -1.565E+01 < x < -1.232E+02 < y <  H  i  \  \  \  1.3B1E+02 3.051E+01  block p l o t liniiimlnmmil  0  2e  1  A^-  Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science  Figure  Toe  4.1  Block  Geometry of  UDEC m o d e l  for  Block  Toppling  •  UDEC (Version  1.50J (M0MK-3)  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 G e o l o g i c a l Science  UDEC (Version  1.50J  legend 31/05/1989 cycle  IB: 50  17010  -4.76E-01 <hlst  1> 3.B0E-05  1.0 Univ. of B r i t i s h Columbia Dept. of Geological Science  F i g u r e 4.2b  2.0  3.0  -4.0  5.0  H o r i z o n t a l V e l o c i t y v s . M e c h a n i c a l Time a t H^, F a i l i n g Slope  (HIOXH  0)  zero.  Initial  movement w h i l e t h e p r o b l e m  was l o a d e d  under  g r a v i t y with the toe block i s not included.  F i g u r e 4.2b i s f o r a t r i a l velocities  indication  T h i s type o f o s c i l l a t i o n  of failure  f o r these  F i g u r e 4.3 d e m o n s t r a t e s a much l a t e r  the limiting  range  w i t h UDEC, by Goodman a n d B r a y  a n a l y s i s produces  Note t h a t t h e l i m i t  one f r i c t i o n v a l u e , b u t due t o  the nature o f the s o l u t i o n procedure, method p r o d u c e s  friction  a range  iteration.  angle  of values.  The  r e p o r t e d was i t e r a t e d  determined  equilibrium  range  degrees. c a n be  (Table 4.1).  w i t h UDEC l i e w i t h i n t h e  e x a c t l y t o the value determined One r e a s o n  t h e b l o c k geometry used  of limiting  t o w i t h i n 0.05  by C u n d a l l e t a l . (1978),  analysis.  element  c a n be narrowed  t h e range  decimal place t h i s  as a s i n g l e v a l u e  correspond  is  T h i s range  f r i c t i o n angle values determined  range  the d i s t i n c t  In these t r i a l s  When r o u n d e d t o t h e f i r s t expressed  of a f a i l i n g slope at  of values f o r j o i n t  (1976) and b y C u n d a l l e t a l . ( 1 9 7 8 ) .  further  typical  trials.  the deformation  angle determined  equilibrium  is a  stage.  T a b l e 4.1 l i s t s  by  Note t h a t t h e  do n o t r e t u r n t o z e r o , b u t c o n t i n u e t o o s c i l l a t e  indefinitely.  friction  that d i d f a i l .  f o rthis  i n t h e UDEC  57  b u t do n o t with the l i m i t slight  analysis.  difference  UDEC  (Version  1.50)  legend 7/06/1989 13: 27 c y c l e 127030 -1.5B5E+01 < X < -1.H32E+02 < y < block  1.381E+02 3.0S1E+01  plot Iiiininil  0 (Jl 03  2e  1  velocity vectors maximum -  9.458E-02  5e  Univ. Dept.  -1  of B r i t i s h Columbia of Geological Science  F i g u r e 4.3  P a t t e r n o f Deformation f o r F a i l i n g  Slope  I n UDEC t h e c o r n e r s analysis  of block  are rounded w i t h and  the user  o f b l o c k s a r e rounded t o f a c i l i t a t e t h e  i n t e r a c t i o n mechanics. a circle  tangent  selects the radius of the c i r c l e  t h e b l o c k s where t h e y  corners  t o each s i d e o f t h e corner,  Rounding t h e b l o c k c o r n e r s e f f e c t i v e l y  This  The b l o c k  t o be used.  reduces  the width of  are i n contact with the f a i l u r e  plane.  i n c r e a s e s t h e o v e r t u r n i n g moment, d e c r e a s i n g t h e  stability angles  of the block.  As a r e s u l t ,  somewhat h i g h e r  friction  are required along the sides of the block t o maintain  stability.  The  results  f r o m two s e t s o f t r i a l s w i t h UDEC u s i n g a  r a d i u s o f 0.1m a n d 0.01m a r e r e p o r t e d i n T a b l e comparison o f t h e l i m i t i n g length v e r i f i e s  friction  friction  t h e i n f l u e n c e o f rounded c o r n e r s ,  angle  f o rstability  conservative than equilibrium  f o r each  t h a t when a s m a l l e r r o u n d i n g  the b l o c k s a r e s t a b l e a t a lower of  angle  determined  the f r i c t i o n  method.  59  4.1.  rounding  A rounding  l e n g t h i s used  angle.  As a r e s u l t  the limiting  friction  w i t h UDEC i s s l i g h t l y  more  angle  the limit  determined  with  T a b l e 4.1:  Range o f L i m i t i n g Block Toppling.  F r i c t i o n Angle f o r  Friction Goodman a n d B r a y (1976) C u n d a l l e t a l . (1978) UDEC (Round=.lm) UDEC (Round=.01m) The UDEC i n p u t f i l e i n A p p e n d i x 1.  4.3 F l e x u r a l  Available  37.6  a n g l e r a n g e (deg.)  38.2 t o 38.7 38.4 38.3  u s e d t o c r e a t e t h i s model  Toppling  i s given  Examples  examples o f f l e x u r a l  toppling are not well  defined  t o be u s e d f o r a d e f i n i t i v e a n a l y s i s .  reason,  t h e examples u s e d i n t h i s  a demonstration of the a b i l i t y  section  enough  For this  are only  o f UDEC t o model  i n t e n d e d as  flexural  topples.  The e x a m p l e s were c h o s e n f o r t h e i r are  examples o f p u r e l y  profile,  4.3.1  flexural  one r o c k t y p e ,  toppling using  a simple  and columns o f a u n i f o r m  toppling  s t u d i e s w i t h a base f r i c t i o n  Kuykendall table  simplicity.  Both slope  width.  Base F r i c t i o n Model  T h i s example o f f l e x u r a l model  relative  (1975) a n d H i t t i n g e r  i s taken from a s e r i e s o f table reported i n  (1978).  The b a s e  i s comprised o f a c o n t i n u o u s sand paper b e l t  60  friction driven at a  constant v e l o c i t y . constrained  The model r e s t s  on t h i s b e l t  from moving w i t h t h e b e l t by a f i x e d  When t h e b e l t  i s i n motion, f r i c t i o n  and i s barrier.  b e t w e e n t h e model a n d t h e  s a n d p a p e r s i m u l a t e s body f o r c e s i n t h e m o d e l .  For the s e r i e s of studies reported i n Kuykendall Hittinger  (1978) a t h i n  s l a b o f a sand, o i l , and f l o u r  was s p r e a d on t h e b a s e f r i c t i o n initially  larger,  (1975) a n d mixture  t a b l e t o form t h e model.  An  r e c t a n g u l a r model was f o r m e d a n d  " c o n s o l i d a t e d " b y t u r n i n g on t h e m a c h i n e .  The m a c h i n e was  t u r n e d o f f w h i l e t h e s l o p e a n d d i s c o n t i n u i t i e s were c u t , a n d t u r n e d b a c k on f o r t h e t e s t  The model s e l e c t e d 4.4.  (Hittinger,  f o r e v a l u a t i o n w i t h UDEC i s shown i n F i g u r e  T h i s p a r t i c u l a r model was s e l e c t e d  because i t f a i l e d  along a well developed  significant  rotation.  block  1978).  f o r s t u d y w i t h UDEC failure  surface with  The g e o m e t r y o f t h i s model c o u l d n o t be r e p r o d u c e d  a t t h e same  s c a l e w i t h UDEC due t o p r o b l e m s w i t h d e c i m a l p r e c i s i o n when designating the block rounding UDEC i s 100 t i m e s  The model c r e a t e d w i t h  l a r g e r than t h e base f r i c t i o n model, b u t  w i t h t h e same g e o m e t r y friction  length.  ( F i g . 4.4).  The d i m e n s i o n s o f t h e b a s e  model a n d t h e UDEC model a r e d e f i n e d i n T a b l e 4.2.  61  UDEC  (Version  1.50)  legend 14/06/1989 15: 16 cycle 2000 -3.B10E+00 < x < -6.015E+01 < y < block 11111  8.001E+01 H.367E+01  plot i 111  i 1 1 1 1 1 1 1 1 1 1  0  I  2a  1  F i g u r e 4.4 Univ. of B r i t i s h  Columbia  Dept. o f G e o l o g i c a l  Science  Geometry  o f Base F r i c t i o n Model and UDEC Model  Table  4 . 2 :  Parameter  Base F r i c t i o n 12  Slope  Height  (H)  Slope  Face Angle  (6)  78  \  Joint Inclination ( f r o m v e r t i c a l ) (a) Column W i d t h  The  modelling  Model  2  inches  78  degrees  that  blocks  i s used t o simulate  that  form t h e s l o p e  m  5.08  A rectangular  i s created.  t h e n d i v i d e d by t h e 6 0 d e g r e e d i p p i n g  crack  degrees  3 0 degrees  inches  blocks  m  30.5  procedure i s as f o l l o w s . support  UDEC M o d e l  UDEC M o d e l  3 0 degrees  (w)  bounded by f i x e d is  M o d e l and  Geometry o f Base F r i c t i o n  the slope  block  This center  joint  s e t and by a  face.  The a n g l e d  are divided into f i n i t e  difference  zones, and m a t e r i a l p r o p e r t i e s a r e a p p l i e d t o t h e zoned and  the joints.  Initial  in situ  stresses at  KQ=1.0  applied  i n the f u l l y  allowed  t o come t o e q u i l i b r i u m u n d e r g r a v i t y .  then excavated, failure  The  deformable blocks,  blocks  are  and t h e system i s  and g r a v i t y i s a p p l i e d u n t i l  The s l o p e i s stability or  i s achieved.  only physical property  Hittinger joint,  block  (1978)  i s the f r i c t i o n  which i s 3 9 degrees.  i n t h e UDEC m o d e l . cohesion,  tensile  o f t h e model m a t e r i a l angle  of a  This j o i n t  reported i n  cohesionless  friction  angle  i s used  I t i s assumed t h a t t h e j o i n t s h a v e no strength,  or dilation.  63  All  o t h e r r e q u i r e d p a r a m e t e r s i n t h e UDEC model a r e  The  e l a s t i c parameters used  sandstone angle,  (Hunt,  cohesion  the excavated  1986). and  are  i n the range of a  I n i t i a l l y the  tensile  s l o p e w i l l be  intact  fixed  The  values  a t 39  stable.  for stability.  degrees  and  typical  rock  friction  s t r e n g t h a r e s e t l a r g e enough t h a t The  s t r e n g t h are then p r o g r e s s i v e l y lowered limiting  assumed.  The  dilation  cohesion  tensile  t o determine  internal  equals  and  the  f r i c t i o n angle i s  zero.  range of v a l u e s t h a t w i l l produce the approximate  failure  g e o m e t r y o f t h e b a s e 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  MPa  a cohesion  the  MPa  and  s l o p e becomes u n s t a b l e .  surface exits than  o f 0.09  just  a tensile  At these values the  above t h e t o e b l o c k and  i n t h e base f r i c t i o n model.  s t r e n g t h are reduced respectively,  the  b e t t e r approximates  s t r e n g t h o f 0.10  failure  is slightly  When c o h e s i o n  f u r t h e r t o 0.06  and  0.075  s u r f a c e moves l o w e r  t h e b a s e f r i c t i o n model  64  failure  and  steeper  tensile  MPa i n the  failure.  slope  and  T a b l e 4.3: Material  V a l u e s o f UDEC P a r a m e t e r s Model.  Number  |  f o r Base  Parameter  Friction |  Value  B l o c k Mat 1  D e n s i t y (kg/m ) B u l k M o d u l u s (MPa) S h e a r M o d u l u s (MPa) C o h e s i o n (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 A n g l e (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 A n g l e (deg.) C o h e s i o n (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  Figures  3  4.5a a n d 4.5b compare t h e b a s e f r i c t i o n  deformation physical  t o the deformation  parameters  s t r e n g t h reduced  listed  produced  i n T a b l e 4.3  b y UDEC u s i n g t h e ( c o h e s i o n and t e n s i l e  t o 0.06 a n d 0.075 MPa, r e s p e c t i v e l y ) .  magnitude and p a t t e r n o f d e f o r m a t i o n illustrated  model  The  i n t h e UDEC model a r e  i n F i g u r e 4.5b b y c o n t o u r s 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 t h e l o c a t i o n s  t h e columns f a i l  where  forming a f a i l u r e plane t h a t has n e a r l y t h e  same a n g l e a n d p o s i t i o n  as t h e f a i l u r e plane  i n the physical  model.  The  failure  histories face,  from  condition  i n t h e UDEC model i s i n f e r r e d  of velocities  at several  locations  the actual deformation  65  time  along the slope  t h e p a t t e r n and magnitude o f v e l o c i t i e s  model, and from  from  i n the  o f t h e model.  UDEC (Version 1.50)  legend 15/06/1989 09: 26 cycle 34250 2.000E+01 < x < -3.500E+01 < y < block  6.000E+01 5.000E+00  plot  I—i—i—i—i  i  i  0  i  i  i  I  le  1  x-dlsp contours contour I n t e r v a l 1.000E-01 number o f 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:  -9.000E-01  k:  -1.000E-01  Univ. o f 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 4.5b  UDEC S i m u l a t i o n o f Base F r i c t i o n Model Deformation  4.3.2 B r e n d a M i n e  The  previous  example d e m o n s t r a t e s t h e a b i l i t y  o f UDEC t o  r e p r o d u c e t h e geometry o f f a i l u r e seen i n a base model o f f l e x u r a l engineered  toppling.  slope that  In t h i s  friction  section a larger,  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 m o d e l l e d u s i n g UDEC.  The  p u r p o s e o f t h i s model i s t o d e m o n s t r a t e t h a t UDEC c a n  simulate rock  and j o i n t  larger  The  toppling i n a real  s t r e n g t h parameters,  slope using  chosen f o r t h i s  study  deformation  i s the east/west  slope  experienced  significant  200 m e t e r s .  a significant  factor i n the s t a b i l i t y  Assoc.,  1988).  depressurized, angle  The with are  of 45  rock  that topples.  trending  British  Columbia.  toppling  when mined a t 4 0 d e g r e e s t o a d e p t h o f  approximately  and  than smaller  w a l l o f t h e Brenda Mine i n Peachland,  original  reasonable  and t o i l l u s t r a t e  s c a l e t o p p l e s behave d i f f e r e n t l y  slope  south The  flexural  Water p r e s s u r e  This slope  i s considered  of this  i s currently  slope  t o be  (Piteau  being  s e t back and re-benched a t an o v e r a l l  slope  degrees.  forming  the slope  i s hard,  f r a c t u r e d quartz  t h r e e major d i s c o n t i n u i t y s e t s . continuous  gouge f i l l e d  faults  68  Set A  that trend  diorite  discontinuities approximately  east/west, d i p estimated  f r o m 7 0 t o 80  spacing  south w a l l .  Set  of  15  t o 27  23  to  50  Set  C are  Toppling  motion of the  flexural  slip  faults low  along  o f S e t A.  and  and  north  an  vicinity  of  f a u l t s which  wall  Assoc.,  strike  gouge f i l l e d ,  east-west  b a r r i e r s t o groundwater  the  from  1988)  i s accommodated  by  trending  I t i s also believed that these  permeability  the  joints that dip  ( P i t e a u and  original  the  have  dip moderately to steeply to  east/west trending  degrees to the  and  meters i n the  B c o n s i s t s of j o i n t s  approximately north/south northeast.  degrees south,  faults  ( P i t e a u and  act  as  Assoc.,  1988).  The  UDEC s i m u l a t i o n  degree slope. slope  Although a r e a l  The in  the  stability  I t i s assumed t h a t t h e  into inclined  strength  considers  columns  slope  ( P i t e a u and  parameters i n t h i s  previous  section.  a n a l y s i s are  large rectangular faults.  The  A  are  chosen f o r these  faults.  for  later  A d i p o f 80  of the  and  m a t e r i a l p r o p e r t i e s are  excavation  The  faults  divide  rock  spacing  These b l o c k s slope  face.  a p p l i e d to the  boundaries of the  69  domain a r e  are  The  unknown.  p h y s i c a l model  model i s c r e a t e d  d e g r e e s and  the  joint  initially  f o r the  45  1988). and  domain i n t o i n c l i n e d b l o c k s ,  Set  joints.  new  Assoc.,  i s used, a l l of the  procedure i s s i m i l a r to t h a t used the  Set A  of the  by  dividing a  defined of  27  the  meters  further divided  blocks  are  zoned b l o c k s fixed  by  and  zoned and  gravity is  a p p l i e d t o s t r e s s the  domain.  Once t h e  h a v e come t o e q u i l i b r i u m , t h e at  a time t o the  allowed  final  the  ensures the level.  joint  s l o p e w i l l be  angle  i s iterated  input  file  to  geometry p r i o r  study  the  and  real  pressures  i n Appendix  i n f l u e n c e the  ( F i g . 4.6b).  the  faults  b a s e d on  The  first  mode o f  failure  The  topple.  70  UDEC  1.  i s shown i n slope  Figure is This  model.  a n a l y s i s i s done conditions  t h i s water t a b l e .  identified  i s a purely  s e c o n d mode i s a more c o m p l i c a t e d "graben"  friction  This a n a l y s i s a p p l i e s pore  modes o f t o p p l i n g f a i l u r e a r e  a  joint  j o i n t deep i n t h e  Two  as  the  l i m i t i n g value.  failure  that  f i n i t e d i f f e r e n c e zoning.  does not  are  excavation  water t a b l e t h a t approximates the  slope  along  final  level,  i n f l u e n c e o f g r o u n d w a t e r an  a bilinear  the  inclined  to  slope  excavations.  s t a b l e at the excavation  domain  benches  i s set at a value  to determine the  f a c i l i t a t e the  i s fixed  using in  final  Note t h a t the  created  To  s t r e s s e s i n the  f o r t h i s model i s g i v e n  zoned b l o c k  joint  The  f r i c t i o n angle  Once a t t h e  4.6a.  depth.  i s e x c a v a t e d two  t o come t o e q u i l i b r i u m between  Initially  The  slope  s t r e s s e s i n the  for this  flexural  topple  movement h e r e i n  slope. and  the  referred to  UDEC  (Version  1.50)  legend 14/06/1989 15: 23 c y c l e 31000 -4.000E+01 < x < -S.900E+02 < y <  8.400E+02 2.900E+02  zones p l o t t e d In fdef blocks block p l o t 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  0  2e  2  Figure  4.6a  Brenda Mine:  Zoned B l o c k Prior  Univ. of B r i t i s h Columble Dept. of B e o l o g l c a l Science  to  Geometry  Failure  The  limiting  values  joint  friction  f o r pure f l e x u r a l  initial  s t r e n g t h s used.  combinations flexural  Table  friction  angle  I t i s expected  o f r o c k and j o i n t  toppling i n this  4.4:  fixed  parameter  i n Table  friction  4.4.  The  are given  Note t h a t T a b l e  4.4  f o r the particular  t h a t t h e r e a r e many  parameters t h a t w i l l  allow  model.  UDEC P a r a m e t e r s f o r B r e n d a M i n e M o d e l : 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 B l o c k Mat 1  J o i n t Mat 1 Initial L i m i t i n g Range D r y L i m i t i n g Range Wet  Figures  range o f j o i n t  t h e d r y and s a t u r a t e d t r i a l s .  reports only the l i m i t i n g rock  and o t h e r  toppling are given  v a l u e and l i m i t i n g  f o r both  angle  |  Parameter Dens i t y (kg/m ) B u l k M o d u l u s (MPa) S h e a r M o d u l u s (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 A n g l e (deg.) D i l a t i o n (deg.)  Value 2700 33333 20000 0.15 0.21 35 0  3  F r i c t i o n A n g l e (deg.) 25 F r i c t i o n A n g l e (deg.) 18.75 t o 20.0 F r i c t i o n A n g l e (deg.) 21.25 t o 23.75 C o h e s i o n (MPa) 0 T e n s i l e S t r e n g t h (MPa) 0 D i l a t i o n (deg.) 0 Normal S t i f f n e s s (MPa/m) 40000 Shear S t i f f n e s s (MPa/m) 20000  4.7a and 4.7b i l l u s t r a t e  for the dry slope.  |  the deformation  F i g u r e 4.7a i l l u s t r a t e s  of the grid points during  Figure  the deformation  73  results  the deformation  t h e b l o c k s and v e l o c i t y 4.7b i l l u s t r a t e s  that  of  failure.  of the blocks  giving  75  contours  of h o r i z o n t a l displacement  that  shear along  grid  point velocity  faults,  and  expected  each  block.  faults  d i r e c t i o n s on  The  i s being  block  circular  nature  overturning.  horizontal  This  i s most c l e a r l y contours  not  affect  i n Table  shape o f t h e angle  and  dropping portion  The  depth  as  failure indicates  of t h i s  simulation  i l l u s t r a t e d by  i n Figure  as d e f i n e d  range with  these  the the  4.7b.  i n Figure  f a i l u r e surface.  The  buoyant  f a i l u r e , r e f e r r e d t o as  also identified.  4.8a  with  4.6b  does  limiting  forces i s  given  4.4.  A s e c o n d model o f is  the  f a i l u r e s u r f a c e d e f i n e d by  a d d i t i o n of pore pressures  friction  attenuate  Note  different  sides of  characteristics  The  joint  points.  accommodated a t a d e f i n e d d e p t h i n  of the  displacement  the  opposite  geometry o f the  o f t h e most s i g n i f i c a n t the  grid  i s i n d i c a t e d by  point velocities  in toppling.  overturning  is  Set A  that grid  that  One  the  of the  4.8b  and  i s c h a r a c t e r i z e d by  down b e h i n d of the  T h i s mode o f f a i l u r e  slope  the  top  fails  of the  by  t h a t produced pure f l e x u r a l difference  i s a small  increase  76  topple,  i s shown i n  slope while  the  Figures block  lower  toppling.  example a r e  toppling  "graben"  a wedge s h a p e d  flexural  p h y s i c a l parameters i n t h i s  a  similar  (Table 4.5).  i n the block  internal  to  those  The friction  angle,  and a d e c r e a s e  thirds.  The p r o c e d u r e  example.  Table  and t r i a l s  a r e r u n t o determine  This analysis  4.5:  and t e n s i l e  the limiting  value  |  Parameter D e n s i t y (kg/m ) B u l k M o d u l u s (MPa) S h e a r M o d u l u s (MPa) C o h e s i o n (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 A n g l e (deg.) Dilation (deg.)  but  Value 2700 33333 20000 0. 05 0. 05 40 0  3  Mat 1 Friction  Angle  (deg.)  Friction  Angle  (deg.)  25  Toppling  When t h e j o i n t degrees,  this  f o rs t a b i l i t y .  |  21.25  F r i c t i o n A n g l e (deg.) C o h e s i o n (MPa) T e n s i l e S t r e n g t h (MPa) Dilation (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)  of  friction  pressures.  "Graben" T o p p l i n g  22.5  joint  UDEC P a r a m e t e r s f o r B r e n d a M i n e M o d e l : "Graben" T o p p l e  B l o c k Mat 1  Flexural  cohesion  with d i f f e r e n t  i s n o t done w i t h p o r e  M a t e r i a l Number  Joint  s t r e n g t h b y two  i s t h e same a s f o r t h e p r e v i o u s  The b l o c k f r i c t i o n a n g l e ,  strength are fixed, angles  i n c o h e s i o n and t e n s i l e  f r i c t i o n angle pure f l e x u r a l  failure  i s similar  i s lowered  t o 22.5  18.75  t o 20.0 0 0 0 40000 20000  t o b e t w e e n 21.25 a n d  toppling develops. to the failure  The g e o m e t r y  shown i n F i g u r e 4.7,  o n l y i n v o l v e s t h e s l o p e down t o t h e t o p o f t h e f i f t h  bench.  When t h e f r i c t i o n a n g l e  79  i s lowered  f u r t h e r t o between  18.75  a n d 20 d e g r e e s t h e " g r a b e n " t o p p l e  shown i n F i g u r e  4.8  develops.  Initially After  this  "graben" t o p p l e  i s a pure f l e x u r a l  some r o t a t i o n , t h e b l o c k s  that  and b e g i n  topple.  form t h e "graben"  failing  by o v e r t u r n i n g  sliding  surface develops through the p o i n t o f bending  column formed by t h e i n i t i a l in  Figure  toppling.  by s l i d i n g .  The v e l o c i t y  4.9a show t h a t w i t h i n t h e " g r a b e n " , b l o c k s  side of a fault  a r e m o v i n g i n t h e same d i r e c t i o n .  i n d i c a t e s t h a t s h e a r i s no l o n g e r The  to fail  occurring along  lower p a r t o f t h e slope continues  to fail  by  stop The i n each  vectors on e i t h e r  This the fault. flexural  toppling.  T h i s mode o f f a i l u r e a type  i s very  similar to a failure  o f moment d r i v e n d e f o r m a t i o n  example, N i e t o  describes  by N i e t o  a mine s l o p e t h a t  moment d r i v e n d e f o r m a t i o n  (flexural  (1987).  In t h i s  i s f a i l i n g by  toppling)  ( F i g . 4.9a).  oriented  joint  s e t s a l l o w t h e upper, a c t i v e , and lower,  passive,  wedges t o f o r m w h i l e  by b l o c k  combined  toppling.  example,  and a c t i v e and  p a s s i v e wedges  fails  i n this  d e s c r i b e d as  favorably  the middle p o r t i o n o f the slope  The p a s s i v e wedge i s d r i v e n by t h e  loading of the overturning  p o r t i o n o f t h e s l o p e and  the  a c t i v e wedge.  The  " g r a b e n " t o p p l e d e m o n s t r a t e d b y UDEC h a s many o f t h e same  characteristics  as t h i s  example o f moment d r i v e n  80  deformation  F i g u r e 4.9a  Moment D r i v e n Deformation w i t h A c t i v e and P a s s i v e Wedges ( a f t e r N i e t o , 1987)  d e s c r i b e d by N i e t o  ( F i g . 4.9b).  The " g r a b e n " i s a n a c t i v e  wedge t h a t l o a d s t h e t o p p l i n g b l o c k s b e l o w , a n d t h e g e o m e t r y of  the toppling blocks  i n t h e lower  part of the slope i s  s i m i l a r t o t h e p a s s i v e wedge i n F i g u r e 4.9a.  4.4  The to  Conclusions  block toppling simulation v e r i f i e s  t h a t UDEC c a n b e u s e d  model b l o c k t o p p l i n g , b u t b e c a u s e o f t h e 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 flexural  section are intended  t o p p l i n g examples r e p o r t e d i n t h i s as demonstrations,  several conclusions  c a n be drawn f r o m them.  In both  examples,  reasonable confirms  flexural  estimates  toppling failure  o f r o c k and j o i n t  t h a t UDEC c a n s i m u l a t e  occurs  properties.  flexural  types  using This  of toppling  failure.  In t h e s i m u l a t i o n o f t h e base f r i c t i o n model, t h e r o c k s t r e n g t h parameters a r e adjusted t o f i n d p r o d u c e t h e b a s e f r i c t i o n model f a i l u r e  the values geometry.  that This  s i m u l a t i o n d e m o n s t r a t e s t h a t UDEC c a n be u s e d t o b a c k a flexural  analyze  toppling f a i l u r e t o obtain strength values at  failure.  82  c4  00  O ft  t>0  JL  Z  /  ~7  83  Flexural toppling research  using physical or f i n i t e  models has o n l y produced p l a n a r simulations generated  i n this  failure  surfaces.  element The  section indicate that the f a i l u r e  i n flexural  t o p p l i n g may be p l a n a r  surface  or curvilinear.  I n t h e UDEC s i m u l a t i o n o f t h e b a s e f r i c t i o n model w i t h height  o f approximately  3 0 meters, t h e f a i l u r e  planar,  b u t i n t h e 180 m e t e r h i g h  failure  surface  transition  i s curvilinear.  from a p l a n a r  back d i p p i n g d i s c o n t i n u i t i e s , values  The  of block  block  cohesion  and t e n s i l e  Mine s l o p e , failure tested  strength,  that the  failure  of the slope,  surface i s  the density of  a n d i s a l s o d e p e n d e n t on t h e  and t e n s i l e  strength.  surface  i s d e p e n d e n t on t h e c o m b i n a t i o n o f b l o c k tensile  surface i s  I t i s suspected  geometry and l o c a t i o n o f t h e f a i l u r e  slopes  are  cohesion  slope  Brenda Mine s l o p e t h e  to a curvilinear  i n p a r t c o n t r o l l e d by t h e s i z e  a  and t h e j o i n t  friction  i n larger cohesion,  angle.  When  s t r e n g t h a r e s e t a t .15 MPa i n t h e B r e n d a  only pure f l e x u r a l  surface occurs  toppling with  a curvilinear  f o r t h e range o f j o i n t  (25 t o 15 d e g r e e s ) .  When c o h e s i o n  s e t a t .05 MPa, b o t h c u r v i l i n e a r ,  "graben" t o p p l i n g can occur  friction  and t e n s i l e  flexural  angle  strength  t o p p l i n g and  d e p e n d i n g on t h e j o i n t  friction  angle.  The  UDEC " g r a b e n " t o p p l i n g s i m u l a t i o n d e m o n s t r a t e s  flexural  t o p p l i n g can r e s u l t  i n deformation  84  that  similar tothe  mode o f moment d r i v e n d e f o r m a t i o n In  addition,  t h e UDEC s i m u l a t i o n s u g g e s t s  characteristic of  failure  d e s c r i b e d by N i e t o that the  a c t i v e a n d p a s s i v e wedges f o r m e d  do n o t n e c e s s a r i l y  (1987).  i n this  mode  require favorably oriented  joint  sets 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 susceptible to flexural the  B r e n d a M i n e model  joint  f r i c t i o n angle  maintain  4.4.1  It  stability  toppling.  I n c l u d i n g pore  pressures i n  ( F i g . 4.6b) r e q u i r e s a n i n c r e a s e i n t h e o f 13 t o 26 p e r c e n t  (2.5 t o 5 d e g r e e s ) t o  (Table 4.4).  Recommendations f o r S l o p e  Design  w i t h UDEC  i s p o s s i b l e t o u s e UDEC t o d e s i g n s l o p e s i n a r o c k mass  susceptible to toppling. is  affects the s t a b i l i t y of slopes  However, t h e a c c u r a c y  d e p e n d e n t on t h e a c c u r a c y  parameters used  of the design  o f t h e r o c k mass s t r e n g t h  i n t h e model.  The b e s t way t o d e t e r m i n e  these  p a r a m e t e r s i s b y b a c k a n a l y s i s o f a l a r g e number o f known toppling  failures  i n similar  rock types, which has n o t y e t  b e e n done.  Even w i t h o u t parameters,  a c c u r a t e k n o w l e d g e o f r o c k mass s t r e n g t h i ti s s t i l l  p o s s i b l e t o a p p l y UDEC t o examine t h e  mode o f t o p p l i n g p o s s i b l e i n a s l o p e a n d t o d e v e l o p conservative design. joint  T h i s c a n be done b y f i x i n g  s t r e n g t h parameters,  t h e water t a b l e ,  85  a  t h e r o c k and  and t h e j o i n t  inclination the  slope  designer for  and  spacing  face angle  and  height.  values,  S u c h an  susceptible to toppling.  a n a l y s i s y i e l d s the used t o assess  the  stabilization  potential failure effect  of d i f f e r e n t  methods.  86  and  varying  a n a l y s i s allows  t o d e t e r m i n e t h e maximum s l o p e h e i g h t  large slopes  other  at conservative  and  face  In a d d i t i o n ,  g e o m e t r y , and  can  the  angle the be  d e w a t e r i n g schemes  and  5.0  Site Characterization  5.1  Introduction  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  between G o l d e n and R e v e l s t o k e , and  British  Columbia  Park  ( F i g . 5.1),  forms t h e 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 t h e rugged P u r c e l l r o u t e was f i r s t  discovered  Pacific  (now CP R a i l )  Railway  and S e l k i r k M o u n t a i n s .  and u t i l i z e d  early  by t h e C a n a d i a n  i n the late  T r a n s Canada Highway was c o n s t r u c t e d 1960's a n d a s e c o n d CP R a i l  The  19th century.  along  The  the c o r r i d o r i n the  l i n e has r e c e n t l y been  completed.  B o t h CP R a i l  alignments enter  Valley  t h e v a l l e y bottom and c l i m b  The  highway a l s o e n t e r s  eastern the  along  slope.  the northern  from t h e n o r t h ,  end o f t h e Beaver  the western but high  I t then descends t o t h e v a l l e y  Beaver R i v e r ,  and c l i m b s  again  along  slopes.  on t h e  floor,  the western  crosses slope  (Fig. 5.1).  A l t h o u g h t h e economic importance o f t h e Beaver R i v e r V a l l e y as the  eastern  recognized, valley al.,  approach t o t h e Rogers Pass r o u t e  has l o n g  been  l a r g e , d e e p - s e a t e d mass movement h a z a r d s a l o n g t h e  s l o p e s h a v e o n l y r e c e n t l y b e e n documented  1988).  87  (Pritchard et  CO  co  Deep Seated L a n d s l i d e s  (from P r i t c h a r d e t . a l . ,  1988)  Field of  work d u r i n g t h e  the  east  slope of the  Heather H i l l 5.1).  summer o f  adjacent  and  the  adjacent  and  opportunity t o study  The  and  r e g i o n a l geology and  discussed  an  area  (Fig.  deep-seated  slopes  slope deformation  north  immediately  i n the  of the Heather H i l l  study  and  no  Beaver area  are  chapter.  Geology  Bedrock  Geology  B e a v e r V a l l e y i s s i t u a t e d i n t h e Omineca T e c t o n i c B e l t  British the  geology  in this  Regional  5.2.1  The  the  on  because i t  w h i c h show l e s s e r d e g r e e s o f d e f o r m a t i o n instability.  5.2  study  well defined,  apparent deep-seated  Valley,  slopes t o the  selected for detailed  contains a w e l l developed landslide,  concentrated  Beaver R i v e r V a l l e y i n c l u d i n g the  l a n d s l i d e and  T h i s s i t e was  1988  Columbia.  e a s t by  t h e w e s t by  the  The  northwest t r e n d i n g v a l l e y  P r a i r i e H i l l s of the  t h e H e r m i t and  of  i s flanked  P u r c e l l M o u n t a i n s and  S i r D o n a l d Ranges o f t h e  on on  Selkirk  Mountains.  The  r e g i o n a l geology  The  valley  i s shown i n F i g u r e 5.2,  i s formed i n r o c k s  o f two  89  and  groups: the  Figure  5.3.  Hadrynian  LEGEND | H |  Hamill  Group  Horsethief C r e e k  Group  Upper Clastic division  UC  Carbonate division  SP  Semipeite Amphibolite unit  SL  Slate division  GR  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  F i g u r e 5.2  R e g i o n a l Geology map o f the Beaver R i v e r ( a f t e r P o u l t o n and Simony, 1980)  Valley  Cross-Section 1 No V.E.  Figure  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 Valley. See L e g e n d F i g . 5 . 2 . ( a f t e r Simony and W i n d , 1970; P o u l t o n and Simony 1980)  91  (Late Precambrian) H o r s e t h i e f Cambrian H a m i l l The  Horsethief  successively division, is  Group  C r e e k Group, a n d t h e Lower  (Wheeler,  1963; Simony a n d Wind,  C r e e k Group i n c l u d e s a l o w e r g r i t  o v e r l a i n by a s l a t e d i v i s i o n ,  and an u p p e r c l a s t i c  division.  The H a m i l l  division  a carbonate The s l a t e  further divided into a semipelite amphibolite  Beaver V a l l e y .  1970).  division  unit i n the  Group c o n s i s t s o f U p p e r , M i d d l e and  Lower Members o f w h i c h o n l y t h e d o m i n a n t l y q u a r t z i t e Lower Member i s p r e s e n t  i n t h e Beaver V a l l e y  (Simony a n d Wind,  1970).  The  east  slope  imbricate the  t h r u s t sheets,  overturned  Creek Group. thrust grit  o f t h e Beaver V a l l e y c o n s i s t s o f a s e r i e s o f  fault  grit  with  and s l a t e d i v i s i o n s  On t h e w e s t v a l l e y  (Poulton  and Simony,  exhibiting planar  bedding  foliation  phase o f f o l d i n g  formed p r i m a r i l y i n of the Horsethief only  i s virtually  Hamill  1980).  are complexly  folded  (SO) on t h e s c a l e o f  (SI) t h a t  west-dipping  o v e r l a i n b y Lower  outcrop.  i s axial planar  to the f i r s t  o b l i t e r a t e d on b o t h s i d e s o f t h e  B e a v e r R i v e r by i n t e n s e c r e n u l a t i o n c l e a v a g e 1961;  one  s t r a t i g r a p h i c sequence o f  divisions,  In t h e Beaver V a l l e y , t h e rocks  Penetrative  slopes,  interrupts the upright  through upper c l a s t i c  quartzites  the slopes  Simony a n d Wind, 1 9 7 0 ) .  The SO b e d d i n g  dominantly northwestward throughout t h e area,  92  (S2) ( R i c k a r d , trends dipping  steeply  e a s t on t h e e a s t s i d e o f t h e v a l l e y opposite side  5.2.2  The by  (Simony and Wind,  a n d s t e e p l y w e s t on t h e  1970)•  Geomorphic Development o f Beaver  Valley  geomorphic development o f t h e Beaver V a l l e y several periods of g l a c i a l  glacial events  The  first  meters  a d v a n c e and r e t r e a t .  p e r i o d s have been t e n t a t i v e l y (VanBuskirk,  glacial  i s dominated  grouped  into  These three  1987).  event  reached  an e l e v a t i o n o f a t l e a s t  ( T h u r b e r C o n s u l t a n t s L t d . , 198 3a)  2950  and c r e a t e d t h e broad  U-shaped Beaver V a l l e y w i t h a s l o p e a n g l e o f between 2 0 and 2 5 degrees.  The second  approximately slopes. and  glacial  event  an e l e v a t i o n o f  1100 m e t e r s and o v e r s t e e p e n e d  This oversteepening  t h e lower  s t e e p e r s l o p e a n g l e s o f 30 t o 45 d e g r e e s .  b u t a minor readvance  by a p p r o x i m a t e l y  occurred p r i o r  These  event  approximately  the location  Macdonald t u n n e l . periodically readvance  i c e readvanced  down t h e C u p o l a  a l a k e t o an approximate  During  down t h e B e a v e r V a l l e y t o o f t h e Mt.  o f t h e Beaver V a l l e y  blocked during t h i s  glacial  t o approximately  of the east portal  Drainage  spurs  9000 y e a r s  7500 y e a r s B.P. ( T h u r b e r C o n s u l t a n t s L t d . , 1 9 8 3 a ) . this third  valley  i s e v i d e n c e d by t r u n c a t e d  e v e n t s were p r o b a b l y c o m p l e t e B.P.,  reached  was  time by a c o n c u r r e n t  Creek V a l l e y . 1  This blockage  formed  e l e v a t i o n o f 990 m e t e r s i n t h e v a l l e y  •'•Cupola C r e e k V a l l e y i s j u s t o f f t h e n o r t h edge o f F i g u r e 5.1, on t h e w e s t s i d e o f t h e B e a v e r V a l l e y  93  causing d e l t a s t o develop streams  (Thurber  Since the t h i r d from and  Consultants Ltd.,  glacial  the reworking the addition  from  a t t h e mouths o f m a j o r  event,  1983a).  the sediment supply  o f sediment t o t h e a l l u v i a l  fans  5.3  Characteristics  The  large landslides  o f Beaver V a l l e y  slopes i n the g r i t  with  197 0 ) ; p l a n a r b e d d i n g a r e common consists  The l o w e r  grit  slate  Movements  division  interbeds  and g r a d e d  (Simony a n d Wind,  The s l a t e  The  exact  age o f t h e f a i l u r e s  the  initial  evidence  (Thurber  division  rocks, w i t h minor c o a r s e r c l a s t i c  interbeds t r a n s i t i o n a l with adjacent  glaciation  consists  f e l d s p a t h i c and  carbonate  Griffith  of the  b e d s on t h e s c a l e o f o u t c r o p  ( P o u l t o n and Simony, 1 9 8 0 ) .  of p e l i t i c  levels  t o aggrade.  and s l a t e d i v i s i o n s  o f c o a r s e and f i n e - g r a i n e d g r i t t y ,  micaceous sandstone  base  shown i n F i g u r e 5.1 a r e l o c a t e d on t h e  H o r s e t h i e f Creek Group. mainly  Slope  fans,  resulting  of local  along t h e Beaver R i v e r , c a u s i n g t h e f l o o d p l a i n  valley  resulting  o f t h e s e d e l t a s i n t o modern a l l u v i a l  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  lower  tributary  slide  i s unknown.  and  units.  I t i s believed that  ( F i g . 5.1) p r e d a t e s  the l a s t  C o n s u l t a n t s L t d . , 1979), a n d t h a t a l l show  of post g l a c i a l  movement.  94  The  elevation  final  period  of the f l o o r of the v a l l e y of g l a c i a t i o n  investigations  i s unknown.  of the v a l l e y  went t o an e l e v a t i o n o f 755  floor  a t t h e end However,  f o r t h e new  m e t e r s and  d i d not  bedrock  (Thurber C o n s u l t a n t s L t d . , 1983b).  Natural  s l o p e a n g l e s i n t h e v a l l e y v a r y from  The  height of the l a n d s l i d e s ,  floodplain  (approximate  the headscarps,  varies  t h e s l o p e movements v a r i e s It  450 from  t o 1250  floodplain relief  level.  For t h i s  CP R a i l  t o 45  caused life,  meters.  The  of  volume o f xl0 m . 6  3  be c o n s e r v a t i v e .  Griffith  where c o n t i n u o u s movement o f t h e d e b r i s h a s  necessitating detailed  line  throughout i t s  geotechnical studies  m i t i g a t i v e works.  Monitoring of slope indicators  deformations  to approximately  or  the  r e a s o n , t h e e s t i m a t e d maximum  d i s p l a c e m e n t o f t h e c u r r e n t CP R a i l  o f up  monitoring period  of  extend below t h e c u r r e n t  and v o l u m e o f t h e s e f a i l u r e s may  ( F i g . 5.1)  degrees.  meters) t o the top  P r o g r e s s i v e d e f o r m a t i o n s have been measured a t t h e slide  line  encounter  a p p r o x i m a t e l y 5 t o 30  i s possible that these f a i l u r e s  the  drill  measured from t h e l e v e l  e l e v a t i o n o f 825 from  20  of  30 mm  and shows  o v e r a one  (Thurber C o n s u l t a n t s L t d . , 1979).  month Whether  n o t o t h e r deep s e a t e d mass movements a r e m o v i n g , and  r a t e o f movement a r e n o t y e t known.  95  their  5.4  Previous  Previous failure  Landslide  unpublished  Studies  work d e s c r i b e s  of the slopes.  Engineering  i n t h e Beaver V a l l e y  a n d q u a n t i f i e s t h e mode o f  I n a r e p o r t t o CP R a i l ,  Consultants  EBA  L t d . (1976) o u t l i n e d t h e l o c a t i o n o f  many s l o p e movements i n t h e v a l l e y .  B a s e d on t h e g e o m e t r y o f  the  EBA s u g g e s t e d t h a t t h e  bedrock s l i d e  scarps  modes o f t h e f a i l u r e  and r u b b l e ,  are circular.  E n v i r o n m e n t Canada P a r k s , (1978) e v a l u a t e d as  the  EBA E n g i n e e r i n g  the s t a b i l i t y  a deep-seated r o t a t i o n a l  Ltd.  (1982), entrance  i n work f o r CP R a i l  Consultants Ltd. landslide  P i t e a u and A s s o c i a t e s  on t h e w e s t v a l l e y  slope  t o Rogers Pass, observed s e v e r a l l o c a l i t i e s  e x p o s e d by r a i l w a y  or creek  nomograms d e v e l o p e d by Brown scale toppling failure  and  report f o r  o f the Heather H i l l  failure.  preexisting toppling failures  furthermore,  In a l a t e r  (Goodman a n d B r a y ,  cuts.  Rapp  Unnamed s l i d e  massive t o p p l i n g  the f i n a l  failures.  96  1976) a r e  that  i s possible i n the valley  represent  where  (1987), u s i n g t h e  (1982), c o n f i r m e d  Rapp p o s t u l a t e d t h a t s l i d e s  near  large  slopes;  such as t h e G r i f f i t h  stages  of earlier  5.5  Field  5.5.1  Program  Introduction.  Field  i n v e s t i g a t i o n o f t h e study  undertaken during structural  t h e summer o f 1988.  mapping a l o n g  back s l o p e .  area  the creek  Traverses  Distance  and  hand h e l d  Map  (EDM) a n d a W i l d  and around t h e s l i d e clinometer  using  a n AGA m o d e l 14A T2 t h e o d o l i t e .  b e n c h m a r k s a n d c a r r i e d up  headscarp using  forcontrol.  topographic  map o f t h e s t u d y  a h i p chain  T h e s e t r a v e r s e s were  area  contour  (Maps 1A a n d I B ,  Pocket).  Local  Geology  geology o f t h e study  slate  divisions  Pelitic slope, the  involved  and t h e highway  t r a n s f e r r e d t o a 1 t o 2500 s c a l e 5 m e t e r  5.5.2  The  Meter  were s t a r t e d f r o m t h e s e  creeks  interval  5.1 was  T e m p o r a r y b e n c h m a r k s were e s t a b l i s h e d a l o n g t h e  the  later  T h i s work  gullies  highway and a t t h e base o f each c r e e k oElectronic  shown i n F i g u r e  rocks  area  c o n s i s t s o f t h e lower g r i t and  of the Horsethief  C r e e k Group  of the slate division  ( F i g . 5.2).  occupy t h e base o f t h e  and t r a v e r s e s u p s l o p e p e r p e n d i c u l a r  to the strike of  SO b e d d i n g e n c o u n t e r a g r a d a t i o n a l c h a n g e t o g r i t  rocks.  division  SO b e d d i n g t h i c k n e s s v a r i e s f r o m m i l l i m e t e r s t o t e n s  o f m e t e r s , b u t t h e most common t h i c k n e s s 0.1m t o 3m.  97  i s i n t h e range o f  Analysis  of the  structural  field  data  features:  SO  c r e n u l a t i o n cleavage, SI a x i a l  planar  subparallel foliation  planar bedding  and  at least  foliation  t o t h e SO  i n d i c a t e s s e v e r a l dominant  exists,  foliation,  is difficult  sub-parallel  foliation,  SO  J l joint  perpendicular to i t .  The  p e r p e n d i c u l a r t o both  t h e SO  combine w i t h t h e SO  large blocky  t h e J l o r J2  Structural creek  fragments.  j o i n t s but  be  effect  of  d a t a were o b t a i n e d  gullies, and  Equal  area  stereonet plots  given  i n A p p e n d i x 2.  SO  and  S2  creeks  and  downslope  and  the J l s e t .  foliation  These  gritty  to break the  r o c k mass  S l a t y beds c o n t a i n v e r y  few  of  f r o m t r a v e r s e s up  the  three landslide  cut.  of the  s t r u c t u r e i n each creek  are  T h r e e p l o t s a r e shown f o r e a c h t r a v e r s e ; and  S2  p o l e s , and  a contour  S2  set i s oriented  foliation  a l o n g t h e highway  In a d d i t i o n , a p l o t  SI  northwesterly,  around the base of the Heather H i l l  t h e p o l e s t o t h e SO  of  d i s p l a y intense c r e n u l a t i o n cleavage.  headscarp,  the  joint  t o the  dips  ( J l , J2).  orientation  set trends  but  S2  s e t s o c c u r most commonly i n t h e more c o m p e t e n t  b e d s , and into  J2  sets  appears t o  t o q u a n t i f y due The  joint  and  joint  however t h e  c r e n u l a t i o n cleavage. t o the  two  foliation,  discontinuities,  a plot  of these  98  plot  of  of the poles to a l l j o i n t s .  of poles to a l l the plot  a contour  j o i n t s measured i n the  poles are  given.  The  average o r i e n t a t i o n  from each t r a v e r s e orientations summarized traverses slope.  f o r t h e SO a n d S2 d i s c o n t i n u i t y  and t h e e s t i m a t e d a v e r a g e  joint  f o r a l l the creeks i n the study area are  i n T a b l e 5.1 a n d p l o t t e d a r e used t o c a t e g o r i z e  i n F i g u r e 5.4.  the structure  The average s t r u c t u r a l o r i e n t a t i o n s  around t h e base o f t h e Heather H i l l also  sets  The c r e e k  along the  from t h e t r a v e r s e  l a n d s l i d e headscarp are  shown i n F i g u r e 5.4 t o i l l u s t r a t e  the toppling  of the  r o c k mass.  T a b l e 5.1:  Structural  D a t a Summary i n S t u d y  Traverse  SO B e d d i n g  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 HeadScarp  The  N\A  2  346\21  S2 C l e a v a g e  Area  N\A  2  043\42  | J l Joint  140\33 t o 204\54 163\73 t o 212\79  J2  Joint  247\90 N\A  2  s t r u c t u r a l r e l a t i o n s h i p between t h e SO b e d d i n g a n d t h e S2  cleavage  i s consistent  i n t h e s t u d y a r e a , b u t t h e SO and S2  For t h e c r e e k t r a v e r s e s , N\A i n d i c a t e s t h a t t h e d a t a c a n n o t be c o r r e l a t e d a s one d a t a s e t . F o r t h e j o i n t d a t a , N\A i n d i c a t e s t h a t t h e d a t a d i d n o t c o r r e l a t e w e l l enough t o make an e s t i m a t e o f a v e r a g e o r i e n t a t i o n f o r t h e c r e e k o r h e a d s c a r p traverses. z  99  AVE.  EQUAL  AREA  STRUCTURAL  ORIENTATIONS: North  CREEKS  A,B,C,  SCARP  PROJECTION  Symbol  C R E E K A AVERAGE SO AND S 2 O R I E N T A T I O N C R E E K B AVERAGE SO AND S 2 O R I E N T A T I O N C R E E K C AVERAGE SO AND S 2 O R I E N T A T I O N SCARP T R A V E R S E A V E R A G E SO AND S 2 O R I E N T A T I O N A L L C R E E K S AND S C A R P : E S T . RANGE OF J l O R I E N T A T I O N ALL C R E E K S i ESTIMATED AVERAGE O R I E N T A T I O N OF J 2  13  F i g u r e 5.4  Structural  Geology  100  • A  2 Points 2 Points 2 Points 2 Points 4 Points 1 Points Points  + 0 X o Total  Summary f o r S t u d y  Area  orientations vary s l i g h t l y strikes  as i n d i c a t e d  i n F i g u r e 5.4.  o f t h e s e s t r u c t u r e s do n o t v a r y s i g n i f i c a n t l y ,  d i p s o f b o t h SO and S2 a r e g r e a t e r i n C r e e k and  C.  The  joint  d a t a from each  o r i e n t a t i o n s c o u l d be d e t e r m i n e d .  s e t s and i s used  these j o i n t  5.5.3  The  sets  decrease  the study  part  orientation of  (Table 5.1).  a r e a i s i n d i c a t e d by c o m p a r i n g B, a n d C r e e k  i n c r e a s e i n t h e degree  cuts  toppling  and d i l a t i o n  Investigation  (60m)  from  C i n F i g u r e 5.4.  structural variation,  There  o r as  i n t h e s o u t h e r n and i s evidence  i s at least p a r t i a l l y  T o p p l i n g o f SO b e d d i n g  vertical  t h e d i p shown  B w i t h Creek  of toppling  of the study area.  suggests the decrease toppling.  t h e d o m i n a n t J l a n d J2  Deformation  T h i s c a n be e x p l a i n e d a s a n a t u r a l  middle  plot  i n t h e d i p o f SO and S2 f r o m n o r t h t o s o u t h i n  Creek A w i t h Creek  an  B  of the j o i n t  t o estimate the average  i n the study area  Evidence of  i n Creeks  However, t h e c o n t o u r  t h e data i n Appendix 2 i l l u s t r a t e s  joint  A than  but the  c r e e k i s much more s c a t t e r e d t h a n t h e  SO o r S2 d a t a , a n d no s t a t i s t i c a l a v e r a g e s  of  The  a result of  i s visible  of the creek v a l l e y s .  that  i n the high,  near  In these creek cuts  a r e seen t o i n c r e a s e updip.  o f the s l o p e j u s t t o the n o r t h o f Creek  u p s l o p e o f a c u t b a c k s l o p e a l o n g Highway 1 r e v e a l e d scarps with torn s u r f i c i a l s o i l  101  B obsequent  a n d r o o t s and r e l i e f o f up t o  1.5 m e t e r s an  The  (Map 1 A ) .  Obsequent s c a r p s  indication of toppling  traverse  visible  (Goodman a n d B r a y ,  toppled  o r i e n t a t i o n s from t h i s  nature o f the rock  above.  The a v e r a g e  traverse  indicate the  mass i n t h e h e a d s c a r p r e l a t i v e t o  that of the creek traverses.  The d a t a  believed  zones o f r o c k  t o be f r o m d i s t u r b e d  representative the  rock  of the intact  structure.  and n o t  I t i s believed  that  bedding  d i p a p p r o x i m a t e l y 5 d e g r e e s l o w e r t h a n i n C r e e k C,  more r e p r e s e n t a t i v e  seated  from t h i s t r a v e r s e a r e  above t h e h e a d s c a r p , which has an a v e r a g e  foliation is  1976).  around t h e base o f t h e headscarp supports t h e  evidence of t o p p l i n g c i t e d  structural  a r e g e n e r a l l y viewed as  failure.  of the extent  S t r u c t u r a l data  h e a d s c a r p were t o o few t o o b t a i n  o f t o p p l i n g p r i o r t o dep-  obtained  from above t h e  a more a c c u r a t e  estimate  of  structural orientations.  It the  i s possible that the toppling described e l e v a t i o n o f C r e e k s B and C.  cross  section of the slope  landslide. profile scarp  The c r o s s  Figure  just north  of t h e Heather H i l l  creeks  the  Heather H i l l  5.5 i s a  topographic  o f the Heather  are not deeply  slide.  p o s i t i o n o f t h e back  This  figure illustrates  i n c i s e d into the slope  landslide.  For t h i s  reason,  representative  of the intact  102  structure.  that  relative to  s t r u c t u r a l data  f r o m C r e e k s B and C may be f r o m z o n e s o f d i s t u r b e d not  Hill  section also includes the gradient  o f Creek B and t h e p r o j e c t e d  the  above e x t e n d s below  r o c k and  TOPOGRAPHIC PROFILE SECTION A - A ' , AND GRADIENT OF CREEK B  1600-,  Section A—A'  1400  — 1200  Approximate Elevation of Glacial Lake Impoundment ^  Gradient, Creek B (projected into line of cross section)  c  o o  5 1000-  Heather Hill Slide Scarp and Projected Failure Surface (projected into line of cross section)  Q)  800Estimated Bedrock 600 -100  i  i  100  i  i  300  i  i  500  Profile i  1  700  1  1  900  1  1  1  1100  1  1300  1—  1  1500  H. dist.(m) From East bank of Beaver River F i g u r e 5.5  Topographic P r o f i l e S e c t i o n and G r a d i e n t o f Creek B  A-A'  1700  Visible  disturbance of the  slopes i n the  study  greatest  i n the v i c i n i t y  of the Heather H i l l  vicinity  o f C r e e k B,  decreases  and  decreasing disturbance of the study  area  i s supported  vicinity  of Creek A  believed  that the  by  intact  and  t o w a r d s C r e e k A.  flatter  ( F i g . 5.6).  r e p r e s e n t a t i v e of the  slide  is i n the The  s l o p e s towards the n o r t h of  the  structural  area  data  slope p r o f i l e  For these  reasons  104  i n the  i t is  from Creek A a r e the  rock c o n d i t i o n .  the  most  TOPOGRAPHIC PROFILE SOUTH OF CREEK A SECTION B - B '  u  1  -100  1  I  100  i  I  300  i  i  500  1  1  700  1  1  900  1  1  H. dist.(rn) From East bank of F i g u r e 5.6  1  1100  j  1  1300  Beaver  Topographic P r o f i l e South o f Creek A, S e c t i o n  j  1500  River  B-B'  1  1  1700  6.0 M o d e l l i n g  Heather H i l l  6.1  Introduction  The  mode o f f a i l u r e  Landslide  o f t h e Heather H i l l  w i t h UDEC i n t h i s c h a p t e r .  The g o a l s  d e t e r m i n e t h e mode o f f a i l u r e characteristics  slope  advanced.  where f i e l d  failures  ina i s well  o f t h i s s i z e have  never  Second, t h e l i t h o l o g y o f t h e dominantly  s c h i s t a t t h e base o f t h e s l o p e  feldspathic grit  unique.  failure  i s h i g h l y v a r i a b l e and g r a d e s from  quartz b i o t i t e  areto  a n d t o examine t h e  evidence i n d i c a t e s t o p p l i n g  been q u a n t i t a t i v e l y a s s e s s e d .  influence  of the slide,  landslide i s a large  Potential toppling  study area  of this analysis  f a c t o r s t h a t make t h i s a n a l y s i s  t h e Heather H i l l  natural  l a n d s l i d e i s examined  of the failure.  There a r e s e v e r a l First,  Development  t o dominantly  above t h e h e a d s c a r p o f t h e s l i d e .  o f m i x e d l i t h o l o g y on t o p p l i n g  The  development has n o t  been q u a n t i t a t i v e l y a s s e s s e d .  6.2  The by  Previous Analysis  only  o f t h e Heather H i l l  Landslide  p r e v i o u s m o d e l l i n g on t h e H e a t h e r H i l l  EBA E n g i n e e r i n g  Simplified  Consultants Ltd.  B i s h o p method o f s l i c e s  106  landslide i s  (1978) who u s e d t h e t o assess the s l i d e  as a  deep s e a t e d geometry  rotational  and s l i p  failure.  s u r f a c e a r e shown i n F i g u r e  o f s a f e t y o f 0.64 was o b t a i n e d The  rock  The assumed o r i g i n a l  f o r the f u l l y  s t r e n g t h parameters used  for this  6.1.  slope  A factor  saturated  slope.  analysis are not  given.  6.3  The  C h a r a c t e r i s t i c s o f t h e UDEC  geometry  Model  o f t h e model i s s i m p l i f i e d  from t h e r e a l  site  conditions.  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 north slope p r o f i l e this profile approximate Figure  of the slide  prior t o the landslide. superimposed  center  excavation  this  scarp.  6.2  illustrates  profile  through the  The d a s h e d  Note t h a t t h i s topography c o n t i n u e s  estimated  line i n  5.2.2.  s e v e r a l f e a t u r e s o f t h e UDEC  (west) b o u n d a r y  model.  o f t h e model i s a t t h e c e n t e r  a n d t h e symmetry o f t h e v a l l e y  boundary  below t h e  t o t h e minimum e l e v a t i o n o f g l a c i a l  i n Section  6.3 - i l l u s t r a t e s  left  valley,  on a t o p o g r a p h i c  of the slide  modern f l o o d p l a i n l e v e l  The  Figure  6.2 i s t h e assumed p r e - s l i d e t o p o g r a p h y u s e d i n t h e  UDEC m o d e l .  Figure  i s used t o approximate t h e  i s invoked  from moving h o r i z o n t a l l y .  107  of the  to constrain  The b a s e o f t h e model  o CO  Distance From Beaver River (m) Figure  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 S l o p e Geometry a n d F a i l u r e S u r f a c e (from 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)  TOPOGRAPHIC PROFILE SECTIONS A - A ' AND C - C , MAP 1A  1600  1400 Section A—A'  ^1200H  Section C—C  c o ° 1000 0)  800* — A s s u m e d Pre—slide Topography Used in UDEC Model 600 -100  T  100  T  300  500  H. dist.(m) F i g u r e 6.2  T  700  T  900  ' 1100  ' 1300  '  1500  From East bank of Beaver River  Heather H i l l :  Assumed P r e - S l i d e  Topography  V700  UDEC  (Version  1.50)  legend  Figure Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science  6.3  Heather  Hill:  I n i t i a l B l o c k Geometry Model  o f UDEC  is  fixed,  at  the  The  and  right  a constant  in situ  s t r e s s a t K =0.5 i s a p p l i e d 0  boundary.  domain i n t h e model i s d i v i d e d i n t o  columns.  This discontinuity  combined mass.  An  believed (Sec.  The  i n f l u e n c e o f SO inclination t o be  the  65  i s designed  foliation  and  degree d i p p i n g  to simulate  S2  cleavage  the  on  the  rock  o f 65 d e g r e e s i s c h o s e n b a s e d on what i s  intact  rock s t r u c t u r e i n the  study  area  5.5.3).  excavation  simulate the  of the  real  s l o p e i n t h e model i s d e s i g n e d  glacial  excavation of the  slope.  to Initial  s t r e s s e s o f K =1.0 a r e a p p l i e d i n t h e domain shown i n F i g u r e n  6.3  and  gravity  equilibrium. modelled  by  i s applied until  The  first  glacial  this the  o f t h e domain.  excavation slope f a i l s  excavation. blocks to  s t r e s s e s are  excavation  at  of the v a l l e y  is  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  upper s l o p e face, beginning corner  the  The  with the block geometry o f t h e  i n the top  left  slope at the  end  i s shown i n F i g u r e 6.4.  I t i s assumed t h a t  when i t i s o v e r s t e e p e n e d  by  T h i s i s s i m u l a t e d by  i n F i g u r e 6.4.  The  removing the  s t r e s s e s i n the  come t o e q u i l i b r i u m a f t e r t h e  Ill  the  excavation  second  of each  of  glacial  remaining  slope are  the  three  allowed block.  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 p l o t I  0  I  I  I  I  I  5e  2  Univ. of B r i t i s h Columbia Dept. of G e o l o g i c a l Science  Figure  6.4  Heather H i l l :  First  Glacial  Excavation  6.3.1  Pore  Pressure  Pore p r e s s u r e s  b a s e d on  in  P i t e a u and  the  the model.  a fully  saturated  Associates  slope  Ltd.  are  included  (1982) r e p o r t s  c u r r e n t water t a b l e e l e v a t i o n i n t h e west v a l l e y  c l o s e t o the  that  slope  entrance  t o Rogers Pass i s near the  surface.  When d r i l l i n g f r o m an  e l e v a t i o n o f 1040m, P i t e a u  encountered  the water t a b l e approximately contact it the  pressures  i n the  reasons,  slope  as  bedrock.  (Mathewes and  end  of the  Heusser,  downwasting  of  pore  1981).  For  t o assume t h a t t h e w a t e r t a b l e s e c o n d g l a c i a t i o n was  i t i s c u r r e n t l y , and  the  In a d d i t i o n ,  have c o n t r i b u t e d t o h i g h  i t i s reasonable  slope at the  as h i g h  surface at  t h a t the m i l d c l i m a t e during  s e c o n d g l a c i a t i o n may  i n the  below the  b e t w e e n s u r f i c i a l m a t e r i a l s and  i s considered  these  15m  may  w e l l have been  as  least  slightly  higher.  6.4  The  C h a r a c t e r i z a t i o n o f Rock Mass  rock  mass i n t h e v i c i n i t y  difficult  to characterize.  weakens t h e d i v i d e the  r o c k mass i s t h e  of the  The SO  foliation.  r o c k mass i n t o l o n g t h i n t o s e v e r a l meters t h i c k .  d i v i d e s the  s o f t e r p e l i t i c b e d s , and  the  J l and  J2  These  columns t h a t  cross joints.  113  landslide is  main d i s c o n t i n u i t y s e t  centimeters  b r o k e n by  Heather H i l l  The the At  S2  the  surfaces are  cleavage  harder  that  grit  further beds  scale of  the  are  Heather  Hill  finely  spaced  Although  l a n d s l i d e most o f t h e s e d i s c o n t i n u i t i e s t o be  explicitly  i s not p r a c t i c a l ,  incorporate the a f f e c t  and  the f o l i a t e d  between t h e c o a r s e SO  and  foliations  s t r e n g t h t h a n competent r o c k . of  2 5 meters i s used  completely  i t i s essential  of the d i s c o n t i n u i t i e s .  by m o d e l l i n g a c o a r s e a p p r o x i m a t i o n explicitly,  o f t h e SO  jointed  to  T h i s i s done foliation  "intact" material  as a continuum w i t h a  A minimum SO  i n t h e model.  foliation  lower spacing  T h i s approximates  the  minimum s e p a r a t i o n o f o b s e q u e n t s c a r p s l o c a t e d n o r t h o f B  (Map  In  the v i c i n i t y  of the Heather  from  dominantly  Hill  the s l i d e . model by  linearly  an  foliation  from  rock at  the  feldspathic grit  and  above  r o c k mass s t r e n g t h p r o p e r t i e s ,  spacing to increase approximately  t h e bottom o f t h e s l o p e t o above t h e  program uses internal  jointed  pelitic  changes  T h i s c h a n g e i n r o c k mass i s i n c o r p o r a t e d i n t h e  allowing the j o i n t  t h e SO  l a n d s l i d e the rock  foliated  base o f the s l o p e t o dominantly  The  Creek  1A) .  gradationally  and  too  i n c o r p o r a t e d i n a UDEC m o d e l .  modelling the s t r u c t u r e of the study area  as a d i s c o n t i n u u m  are  a Mohr-Coulomb f a i l u r e  friction  criterion  angle, cohesion i n t e r c e p t  and  headscarp.  d e f i n e d by tensile  s t r e n g t h t o c h a r a c t e r i z e t h e s t r e n g t h o f t h e r o c k mass. Although  these parameters  laboratory  c o u l d e a s i l y be  for small, intact  determined  r o c k samples from  114  i n the  the study  area,  there  i s no  accurate  way,  short  of  determine these parameters f o r the situ  rock  There are rock  large scale testing, to foliated  several  i n d i r e c t methods o f a s s e s s i n g (Hoek and  a l l e m p i r i c a l and  the  r o c k mass t o d e t e r m i n e a f a i l u r e criteria  Brown s t r e n g t h  are  use  Brown, 1 9 8 0 ) .  are  qualitative,  criterion  can  rock  technique s t i l l  (Hoek and  uncertainty  involved  mass.  be  rock  masses t h i s  the  These  in  situ  techniques  measurements o f c h a r a c t e r i s t i c s o f  envelope f o r the  judgement  jointed in  mass.  mass s t r e n g t h  failure  and  criterion.  but  Many o f  some s u c h as t h e  used t o c a l c u l a t e a  Unfortunately, requires  Brown, 1 9 8 0 ) .  the  Hoek  failure  in heavily jointed  a great  Because o f the  i n estimating  these  r o c k mass  deal  of  large strength  p a r a m e t e r s 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 b a s e d on single,  estimated  s e t of parameters i s not  I n t h i s UDEC m o d e l , t h e d e t e r m i n e d by  r o c k mass s t r e n g t h  back a n a l y s i s .  The  attempted.  parameters  e x a m p l e s i n C h a p t e r 4.  Initially,  parameters are  enough t o e n s u r e t h a t t h e  be  s t a b l e when f u l l y  parameters are which the in  set high  Section  slope  excavated.  gradually  rock  Once e x c a v a t e d ,  6.6.  115  This  the  strength  lowered to determine the  becomes u n s t a b l e .  are  procedure i s s i m i l a r to the  a  slope  will  the point  i s discussed  at  further  6.5  The  E v o l u t i o n o f Model  gradational  t r e a t m e n t o f t h e SO s p a c i n g  p r o p e r t i e s was a d o p t e d a f t e r s i m p l e r generate t h e Heather H i l l  Early modelling and  one r o c k  spacing,  slide  approximations  type f o r the e n t i r e slope. weak r o c k failure.  r e s u l t e d when a u n i f o r m  25 m e t e r s p a c i n g  geometry o f t h e f a i l u r e  the  upper slope  failed to  o f 25 o r 50 m e t e r s  A t a 50 m e t e r  mass a n d j o i n t  were r e q u i r e d t o o b t a i n  the  mass  geometry.  a t t e m p t s u s e d a SO s p a c i n g  unrealistically  and t h e r o c k  properties  More r e a l i s t i c p r o p e r t i e s  was p l a n a r ,  was u s e d . extending  from t h e t o e o f t h e s l o p e  However, parallel to  t o the east  boundary  o f t h e model.  Changing t h e rock gradational curvature, the  mass p r o p e r t i e s  increase  i n strength  but the l i m i t  f r o m one r o c k up s l o p e  type t o a  r e s u l t e d i n some  o f t h e model l a n d s l i d e s t i l l  i n situ landslide.  T h i s p r o m p t e d t h e 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 model. can  exceeded  With t h i s  change, t h e H e a t h e r H i l l  be a p p r o x i m a t e d u s i n g  reasonable  116  rock  i n the  l a n d s l i d e geometry mass p r o p e r t i e s .  6.6  Results  o f UDEC  Modelling  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 .  these materials  i s used t o f i x t h e a r t i f i c i a l  created  to facilitate  used t o simulate rock  block  zoning,  the gradational  a t t h e base o f t h e slope  above t h e h e a d s c a r p . strength  change from  6.5 i l l u s t r a t e s  increases  foliated  pelitic  feldspathic grit how t h e r o c k  to the slope.  a r e u s e d : 25m, 3 3m,  arbitrarily  that i s  and t h e r e m a i n i n g n i n e a r e  t o dominantly  parameters a r e assigned  F o u r SO s p a c i n g s spacing  Figure  joint  One o f  41m, a n d 49m.  This  i n increments o f 8 meters  from  25 m e t e r s a t t h e b a s e o f t h e s l o p e  t o 49 m e t e r s a b o v e t h e  headscarp as i l l u s t r a t e d  i n Figure  6.4.  The  analysis begins with  the slope  excavated t o the l e v e l o f  the  second g l a c i a t i o n ,  the  floor  fully  of the valley i n this  meters below t h e c u r r e n t the  internal  small  The  are  friction  strength  not reported  initial  data  floodplain level.  failure  6.1.  From t h i s  file  point  develops.  mass a t f a i l u r e a r e  For simplicity  i n A p p e n d i x 3.  117  that  mass i s l o w e r e d i n  the e l a s t i c  i n this table, but are included  input  Note  a n a l y s i s i s a p p r o x i m a t e l y 70  p r o p e r t i e s o f t h e rock  i n Table  and s t a b l e .  angle of the rock  increments u n t i l  reported  saturated,  properties  i n the  In these t r i a l s  joints  UDEC  (Version  legend  i.50j  are  assumed t o h a v e no  r o c k mass i s  Table  6.1  cohesion,  assumed t o h a v e  UDEC S t r e n g t h  tension  or d i l a t i o n ,  Friction Angle (deg.)  1 2 3 4 5 6 7 8 9  Parameters f o r Heather H i l l  The  Tensile Strength (MPa)  .100 .150 .200 .250 .300 . 350 .400 .450 . 500  geometry of the  failure  part  of the  left  corner.  joints  and  Figure  6.6a  the  model d e p i c t e d This  grid  that  indicate  r e s u l t s at these  6.6a,  and  6.6b.  strength  Note t h a t  the  i n e a c h f i g u r e i s shown i n t h e  top  i s n e c e s s a r y due  i s a p l o t of g r i d the  velocities  to the  density  on  velocities  attenuate  typical  flexural  point velocities.  B r e n d a M i n e example e i t h e r side of  shear i s occurring  of  22 25 28 31 35 39 44 47 50  of  the  points.  same manner as  different  Friction Angle (deg.)  .050 .075 . 100 . 125 . 150 . 175 .225 .250 .300  p a r a m e t e r s i s shown i n F i g u r e s  Model  Joint  Cohesion (MPa)  31.0 33.0 35.5 38.0 40.5 43 . 0 46.0 49. 0 52.0  the  no d i l a t i o n .  Rock Mass Material  and  along  with depth. toppling  the  in  ( F i g . 4.7a), SO  foliation  foliations,  Both of these  failure.  119  an  Note t h a t  and  that  features  are  UDEC  (Version  1.50)  legend 23/07/1989 09: 31 cycle 38500 4.500E+02 < x < 7.500E+02 -8.500E+02 < y < -5.500E+02 block 1 0  I  plot  I I I I 5e  1  velocity vectors maximum 11  4.368E-01  iiiiiii iIiiiiiiiii I  0  2e  Univ. of B r i t i s h  0  Columbia  Dept. o f G e o l o g i c a l  Science  F i g u r e 6.6a  Heather H i l l UDEC Model:  Velocities of Grid  Points  Figure  6.6b i s a c o n t o u r p l o t  o f h o r i z o n t a l d i s p l a c e m e n t and  i l l u s t r a t e s t h e geometry o f t h e f a i l u r e . failure  The s h a p e o f t h e  s u r f a c e and t h e e x t e n t o f t h e f a i l u r e  model a p p r o x i m a t e  the observed  failure  i n t h e UDEC  geometry and headscarp  location.  There will  a r e many c o m b i n a t i o n s cause  failure  o f t h e s t r e n g t h parameters  i n t h e model.  However, t h e p a r a m e t e r  v a l u e s r e p o r t e d i n T a b l e 6.1 a l l o w a f a i l u r e model t h a t b e s t a p p r o x i m a t e s of  t h e Heather  investigated  Hill  the observed  landslide.  given.  The v a r i a t i o n  6.2  i n an  l i n e a r manner between t h e s e two e n d members.  Investigated Variation  i n Parameters  Range o f V a l u e s Friction Angle (deg.)  6.7  The  1 and m a t e r i a l 9  The r e m a i n i n g m a t e r i a l v a l u e s r a n g e  Material  1 9  i n the  i n the values  f o r t h i s model a r e l i s t e d i n T a b l e 6.2.  approximately  Table  t o develop  geometry and e x t e n t  minimum a n d maximum v a l u e s f o r b o t h m a t e r i a l are  that  30 45  - 35 - 52  Cohesion (MPa)  Tensile Strength (MPa)  .025-.150 .100-.500  .010-.075 .065-.300  Friction Angle (deg.) 35  22 - 50  Limitations of Analysis  The  results  of the analysis reported i n the previous  are  l i m i t e d by t h e a p p r o x i m a t i o n s  121  i n t h e model.  section  F o r example,  Figure 6.6b  Heather H i l l  UDEC M o d e l :  Horizontal  Displacement  in this  model t h e SO f o l i a t i o n  spacing  i s v a r i e d f r o m 25 t o 49  meters.  The c h o i c e o f 25 m e t e r s a s a minimum s p a c i n g o f s h e a r  surfaces  i n t h e slope i s supported  by t h e f i e l d  o b s e q u e n t s c a r p s n o r t h o f C r e e k B (Map 1 A ) .  evidence o f  However t h e  c h o i c e o f t h e maximum s p a c i n g o f 49 m e t e r s i s a r b i t r a r y . t h e maximum s p a c i n g  i s altered  s t r e n g t h parameters a t f a i l u r e failure  will  result.  include the estimated the approximation isotropic  The  pressures table  s e t o f rock  and a d i f f e r e n t  Other approximations  geometry o f  i n t h e model  maximum d e p t h o f g l a c i a l  e x c a v a t i o n and  o f t h e r o c k mass a s homogeneous a n d  b e t w e e n t h e SO  results  a different  foliations.  o f t h e a n a l y s i s a r e d e p e n d e n t on t h e p o r e  i n the slope.  In r e a l i t y ,  the level  o f t h e water  i n t h e f a i l i n g r o c k would d e c l i n e as t h e r o c k  becomes i n c r e a s i n g l y b r o k e n a n d d i l a t e d .  mass  As t h e v a r i a t i o n o f  the water t a b l e d u r i n g f a i l u r e  i s n o t known, i t i s  conservatively  model t h a t p o r e  corresponding  assumed i n t h i s  t o a f u l l y saturated slope apply  T h i s pore pressure the  failure.  pressure  assumption has t h e e f f e c t  In r e a l i t y ,  the combination  and i n c r e a s e d j o i n t  possibility  Valley  a t a l l times.  of propagating  o f a d e c l i n e i n pore dilation  . The i m p l i c a t i o n s o f  f o r t h e s t a b i l i t y o f s l o p e s i n t h e Beaver  and f o r e n g i n e e r i n g d e s i g n  discussed  pressures  s t r e n g t h due t o j o i n t  may c a u s e a f a i l i n g s l o p e t o s t a b i l i z e . this  If  i n these  slopes are  i n S e c t i o n s 7.2.2 a n d 7.2.3 r e s p e c t i v e l y .  123  6.8  Conclusions  6.8.1  Heather H i l l  Landslide  Due t o t h e a p p r o x i m a t i o n discussed analysis  i n the previous section,  approximations,  toppling  T h i s model  a definitive  Experience  limiting  landslide  t h e UDEC model  to a curvilinear  fails  failure  i s flexural  by surface.  toppling.  w i t h t h e UDEC model o f t h e H e a t h e r H i l l  i n d i c a t e s t h e importance  i n t h e model t h a t t h e l i m i t  i n rock type.  of the failure  t h e g r a d a t i o n a l change i n r o c k t y p e  from  foliated  t h e base o f t h e s l o p e t o f e l d s p a t h i c g r i t  headscarp  o f t h e Heather H i l l  supported  by t h e o v e r a l l  landslide.  distribution  occur  i n the Slate d i v i s i o n  124  pelitic  of landslides  in  south  i s related to rock  This relationship i s  ( F i g . 5 . 1 ) . Most o f t h e i d e n t i f i e d  exception of the large landslide  I t was  above t h e  Beaver V a l l e y the valley  failure  o f i n c l u d i n g t h e up s l o p e i n c r e a s e i n  r o c k mass s t r e n g t h due t o v a r i a t i o n  at  stability  i n d i c a t e s t h a t t h e most l i k e l y mode o f f a i l u r e o f  the Heather H i l l  found  geologic conditions  i s not possible.  Even w i t h t h e s e flexural  of the real  i n the  landslides  r o c k s and, w i t h t h e  o f t h e study  area, are  roughly  limited  division  6.8.2  The  up s l o p e b y t h e o c c u r r e n c e  rocks  (Fig.  Kinematic  kinematic  197 6;  and Sec.  For Toppling  f o r t o p p l i n g p o t e n t i a l (Goodman a n d B r a y ,  2.4.2) i s w i d e l y  means t o e s t i m a t e interesting  5.2).  Test  test  accepted  toppling potential.  conclusions  of t h e Heather H i l l  of this  as a  chapter  i s t h a t t h e geometry  l a n d s l i d e does n o t s a t i s f y t h i s  t o p p l i n g t o be p o s s i b l e , t h e k i n e m a t i c  the  slope  face angle angle  6.6 t h i s possible.  test  (<f>) a n d t h e i n c l i n a t i o n  requires  from v e r t i c a l  model d i s c u s s e d  The t e s t  two r e a s o n s why t h i s  kinematic  test  t o occur  aligned with  ( F i g . 2.2a).  i n Section  ( i e : 42 < 22 + 25) t o 15 d e g r e e s  i s i l l u s t r a t e d i n Figures  joint  (a) o f  i s n o t s a t i s f i e d by a margin o f 5 degrees  b e l o w t h e e l e v a t i o n o f t h e change i n s l o p e  least  that  indicates that toppling i s not kinematically  t h e base o f t h e slope  This  test.  (6) be g r e a t e r t h a n t h e sum o f t h e j o i n t  When a p p l i e d t o t h e H e a t h e r H i l l  The  test  b a c k 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)  the  at  conservative  One o f t h e most  For  friction  of the Grit  test  just  ( i e : 41 < 31 + 2 5 ) .  6.7a a n d 6.7b.  There a r e a t  i s not s a t i s f i e d .  i s b a s e d on two c r i t e r i a .  F o r s h e a r on a  t h e n e t s t r e s s a c t i n g on t h e j o i n t must b e  the slope  normal o f t h e j o i n t  f a c e and i n c l i n e d  (Sec.  2.4.2).  125  by a t l e a s t  When t h i s t e s t  cj> t o t h e  i s used t o  N  Figure  6.7a  Kinematic  Test:  Toe o f S l o p e  i n UDEC M o d e l .  N  T  Figure  6.7b  Kinematic Test: UDEC M o d e l  E l e v a t i o n o f Change i n S l o p e i n  126  assess the  the toppling potential of a slope,  o r i e n t a t i o n of the net s t r e s s defined  angle  not v a l i d  Section  the p r i n c i p a l  Figure  6.8  6.6 a t a s t a g e  a plot  of principal  model a n d i l l u s t r a t e s change a l o n g the  6.9  This plot  i s a plot  angle  - 1  (shear  This  points  depicts  corner.  stress/normal  a joint  figure  i n the  f i g u r e only  shown i n t h e t o p l e f t  of tan  stress) vs.  shown i n F i g u r e  how t h e m o b i l i z e d  i s lowest  depth  stress directions  Note t h a t t h i s  depth i n the slope.  friction  6.8.  angle  on a  Note t h a t t h e m o b i l i z e d  near t h e s l o p e  f a c e and  increases  depth.  The c h a r a c t e r i s t i c s in  i s stable.  how t h e p r i n c i p a l  illustrates  a  change w i t h  stresses at the g r i d  the joints.  j o i n t v a r i e s with  with  but i s  i s t a k e n f r o m t h e model r e p o r t e d i n  l e n g t h b e t w e e n A a n d A' a l o n g  friction  This  s t r e s s d i r e c t i o n s along  when t h e s l o p e  p o r t i o n o f t h e model  Figure  the joint.  scale slopes,  and hence t h e n e t s t r e s s d i r e c t i o n ,  in the slope.  is  i n small  face  i n larger slopes.  larger slopes  joint,  assumption  that  by t h e s l o p e  a t t h e s u r f a c e a p p l i e s a t depth along  may be a r e a s o n a b l e  In  i t i s assumed  Figures  6.8  of stresses along  a n d 6.9  illustrated  indicate that i n large slopes, the  a s s u m p t i o n t h a t n e t s t r e s s on a j o i n t face a t depth i n the slope applied t o a kinematic  the joints  i s parallel  i s not v a l i d .  Further,  to the slope when  assessment o f t o p p l i n g p o t e n t i a l t h i s  127  UDEC  fVersion  1.50)  Figure 6.6b Figure 6.'ea  legend 23/07/1989 cycle  12: 39  26500  5.000E+02 < x <  7.000E+02  -8.000E+02 < y <  -6.000E+02  block  I  plot  L  J  I 5e  H to 03  principal  stresses  maximum minimum I  o  I  I  1  L  -I  -1.510E-01 -1.141E+01  I 5e  1  Univ. o f 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  F i g u r e 6.8  Heather H i l l UDEC Model:  Principle  Stresses  C h a n g e in Eff. Friction Angle 29  28  -  24  -  23 20  40  A  60  ~r~ 80  100  120  A'  Distance Along Joint: A—A' Figure  6.9  H e a t h e r H i l l UDEC M o d e l : Variation of F r i c t i o n A n g l e A l o n g an SO F o l i a t i o n  140  Effective  assumption factor joint  i s not conservative.  of safety  F i g u r e 6.10 i s a p l o t o f  (shear s t r e n g t h / s h e a r  l e n g t h a s i n F i g u r e 6.9.  failure begin  along  This  s t r e s s ) a l o n g t h e same  figure  indicates that  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 t depth,  and p r o g r e s s e s  sections of a joint  t o t h e s u r f a c e as  transfer their  actually failing  load t o adjacent  up d i p  sections.  t h e UDEC m o d e l o f t h e H e a t h e r H i l l satisfy  a second assumption o f t h e kinematic  assumed i n t h e k i n e m a t i c the  joints. n  n  this  situation  the f a i l u r e  stress/effective joint  pressure applied and  It  angle  (r)  of the joint friction  angle  (<t> > 4>) • ,  i s t o allow the j o i n t total  stress  m  stress.  a c t along  a r e c o n s i d e r e d t h e normal  In  o c c u r s when t h e (tan  [shear  - 1  or equal t o  The n e t e f f e c t  t o shear  pressure  i s not a f f e c t e d .  normal s t r e s s ] ) i s g r e a t e r than  friction  I ti s  t h a t no p o r e p r e s s u r e s  - u ) , while the shear  n  test.  by t h e m a g n i t u d e o f t h e p o r e  effective mobilized joint  the  test  When p o r e p r e s s u r e s  (cr ) i s reduced  stress (a *= a  l a n d s l i d e a l s o does n o t  a t a lower  This i s i l l u s t r a t e d  o f pore angle of  i n F i g u r e s 6.11a  6.11b.  s h o u l d be r e a l i z e d  toppling potential. of a slope with shear  on a j o i n t  that the kinematic I t i s not intended  test  i s a test of  to test  respect t o t o p p l i n g , i t simply i s kinematically possible.  imposed by t h e assumptions o f t h e t e s t ,  130  the s t a b i l i t y indicates i f  Within  the l i m i t s  i tprovides a  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  20  1 40  1  1 60  1  1  1  80  1  1  100  I  I  120  Distance Along Joint: A—A'  A  Figure  6.10  H e a t h e r H i l l UDEC M o d e l : Variation S a f e t y A l o n g SO F o l i a t i o n  i n Factor of  140  JOINT  <t> - J o i n t  F r i c t i o n Angle  6. l i a  At F a i l u r e  <*>  Dry  m  <t>m = M o b i l i z e d J o i n t F r i c t i o n Angle  JOINT  <p =  J o i n t F r i c t i o n Angle  6.11b  At F a i l u r e  Wet  0 < 4> 4>m> <t>  Qm-  Figure  6.11a) 6.11b)  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  N o r m a l and S h e a r S t r e s s e s on D r y J o i n t E f f e c t i v e N o r m a l and S h e a r S t r e s s e s When P o r e P r e s s u r e a c t s on J o i n t  132  conservative  indication  of toppling potential.  The a b o v e  d i s c u s s i o n d e m o n s t r a t e s t h a t when t h e a s s u m p t i o n s the o r i e n t a t i o n joint  are not s a t i s f i e d  estimate  It  of total  of toppling  i s recommended  potential small  stress  and p o r e  the test  pressures along a  i s not a conservative  potential.  that the kinematic  be q u a l i f i e d .  The t e s t  test  of toppling  s h o u l d o n l y be a p p l i e d t o  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  orientation  along the j o i n t s  the kinematic  test  regarding  i s a reasonable  requirements.  133  stress approximation  of  7.0  Conclusions  7.1  PART I :  Several  2.  i n Chapter  Large  scale  from  Review  the literature  2, a n d a r e s u m m a r i z e d  flexural  review  on  below.  t o p p l e s , and t h e i n f l u e n c e o f j o i n t  dilation,  r o c k m a t e r i a l a n d r o c k mass s t r e n g t h on  toppling,  have never  The l i m i t e q u i l i b r i u m and  distinct  toppling. most  3.  Conclusions of Literature  conclusions result  toppling  1.  and Recommendations  been q u a n t i t a t i v e l y  technique,  assessed.  f i n i t e e l e m e n t method,  e l e m e n t method h a v e a l l b e e n u s e d  The l i m i t e q u i l i b r i u m  technique  t o model  i s by f a r t h e  popular.  The l i m i t e q u i l i b r i u m t e c h n i q u e  has i n h e r e n t  restrictions  h o w e v e r , 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 scale  4.  Finite limit to  modes o f t o p p l i n g .  e l e m e n t methods overcome t h e r e s t r i c t i o n s equilibrium  technique,  model l a r g e deformations  their  5.  flexural  i n jointed  ability  r o c k mass due t o  continuum f o r m u l a t i o n .  The d i s t i n c t with  b u t have a l i m i t e d  of the  e l e m e n t method o v e r c o m e s t h e d i f f i c u l t i e s  t h e f i n i t e e l e m e n t method.  134  The m a k i n g a n d b r e a k i n g  of  joint  discrete easily  7.2  contacts, blocks  large displacements,  and r o t a t i o n s o f  and d e f o r m a t i o n o f t h e b l o c k s  area l l  accommodated.  PART I I :  Flexural Toppling:  There a r e s e v e r a l conclusions  Conclusions  on f l e x u r a l  o f Research  toppling that  result  f r o m t h e example m o d e l s i n C h a p t e r 4.  1.  The r e s u l t s from t h e b l o c k reported  and f l e x u r a l  i n Chapter 4 confirm  types of topples.  final  2.  These examples a l s o demonstrate  3.  rock  mass  that  strength  and d e t e r m i n e t h e s h a p e a n d l o c a t i o n o f t h e  failure  surface  i n flexural  The geometry o f t h e f a i l u r e flexural  examples  t h a t UDEC c a n s i m u l a t e a l l  UDEC c a n b e u s e d t o b a c k a n a l y z e parameters,  toppling  toppling.  surface  formed  t o p p l i n g f a i l u r e may be p l a n a r  during  or curvilinear.  T h i s has never before  been q u a n t i t a t i v e l y c o n f i r m e d .  Two modes o f f l e x u r a l  toppling failure  possible: The  pure f l e x u r a l  a p p e a r t o be  t o p p l i n g , and "graben" t o p p l i n g .  development o f "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 t h e i n t e r n a l mass.  135  friction  angle o f the rock  4.  Pore p r e s s u r e slopes  7.3  a f f e c t s the s t a b i l i t y of  susceptible to flexural  PART I I I :  7.3.1  significantly  Beaver V a l l e y : Recommendations  Heather H i l l  Conclusions  most l i k e l y  flexural  mechanism  toppling that  surface.  and  Study Area  The UDEC model o f t h e H e a t h e r H i l l the  toppling.  failure  of f a i l u r e  limits  demonstrates  involves  large  cause f a i l u r e  scale  to a curvilinear failure  F a i l u r e begins i n the toe of the slope  stresses  that  as high  o f t h e r o c k mass a n d s h e a r i n g  on t h e SO  foliations.  In t h e study area observations slopes field  north  reveal  t h a t were  o f t h e Heather H i l l  evidence of recent  initially  believed  landslide,  d e e p - s e a t e d movement i n  t o be s t a b l e .  e v i d e n c e a n d t h e UDEC model o f t h e H e a t h e r  landslide  indicate that  t h i s movement  field  involves  Both t h e Hill  flexural  toppling.  Further are  north  believed  i n the v i c i n i t y  o f Creek A  t o be more s t a b l e due t o t h e l o w e r s l o p e  The UDEC m o d e l o f t h e H e a t h e r H i l l the  up s l o p e  (Map IB) t h e s l o p e s  limit  of the f a i l u r e  136  angle.  l a n d s l i d e demonstrates i s related to the  that  gradational  change i n r o c k t y p e  the  the  of  base of the  slope  Heather H i l l  distribution  of  kinematic t e s t  and  Bray  This  i n the  for toppling  Consideration indicates  qualified.  joints  landslide.  (1976) i s v i o l a t e d by  failures  drained  feldspathic grit  landslides  The  model.  to  The  slopes  from f o l i a t e d  of  that  the the  pelitic  above t h e  Beaver  the  Valley.  p o t e n t i a l p r o p o s e d by the  Heather H i l l  mechanics of  t e s t should only  be  total  to  Goodman  landslide  large  applied  stress  at  headscarp  i s s u p p o r t e d by  scale  kinematic t e s t should  i n which the  rock  toppling  be  small  scale  orientation  along  i s a reasonable approximation of the  kinematic  the  test  requirements.  7.3.2  The  Stability  Slopes  i n Beaver  Valley  e v i d e n c e o f modern movement d i s c o v e r e d  Heather H i l l suspected similar  l a n d s l i d e where no  raises disturbing  slopes  Large t o p p l i n g (de  of  F r i e t a s and  degree of  Watters,  i n s t a b i l i t y was  q u e s t i o n s about the  throughout the  f a i l u r e s are  Beaver  generally  (Goodman and  been suggested t h a t  previously stability  considered  toppling  1976;  and  Nieto,  failures self  137  of  slow f a i l u r e s  1 9 7 3 ) , w h i c h accommodate a  Bray,  the  Valley.  deformation p r i o r to collapse  stabilizing  north of  are  large  often  1987). stabilize  self  It due  has to  joint an  dilation  which causes a d e c l i n e i n the water t a b l e  increase in joint  strength  i n the  failing  r o c k mass  and  (Bovis,  1982) .  It  i s p o s s i b l e t h a t the  landslide Valley the  and  are  other  slope north  apparently  o f deep s e a t e d  u n d e r g o n e some d i l a t i o n  and  i m p l i c a t i o n s of t h i s  design that  are discussed  slopes  i n the  of degree of g l a c i a l  be  low  risk  level be  If  stability  structure  areas  T h i s can  of the  engineering  be  of the toe,  Implications  on  s u c h as a c u t o r t u n n e l  138  on  basis  can  and  then  ground.  detailed works.  and  c o n s t r u c t i o n of  effect  the  the  i s not engineering  e r r o r s o r m i t i g a t i v e w o r k s may  must c o n s i d e r t h e  by  rock type,  High r i s k areas  u s e d t o p l a n more  and  done  s l o p e s on  a i r p h o t o g r a p h s and  during the design  engineer  have  I t i s recommended  of p r e v i o u s l y d i s t u r b e d slopes  works, c o s t l y d e s i g n An  section.  investigations for engineering  E n g i n e e r i n g Design Recommendations  considered  and  in  o f r o c k mass s t r e n g t h .  condition for  identified.  7.3.3  the  next  landslides.  assessment can  geotechnical  degradation  oversteepening  to existing  inspected using S u c h an  Beaver  B e a v e r V a l l e y t h a t h a v e u n d e r g o n e some  c a t e g o r i z i n g high  proximity  i n the  toppling failure,  stability  i n the  degree of deformation first  stable slopes  Hill  l o c a t i o n s where t o p p l i n g i s w e l l a d v a n c e d , o r  e a r l y stages  The  of the Heather  o f an the  result.  engineered  stability  of  the  be  whole s l o p e ,  and,  a l s o , how  r o c k mass i n f l u e n c e s t h e  The  impact  o f an  previously  developed,  stability  It  the  can  be  of the  smaller area,  and  and  of  a  a UDEC model  existing  slope  the e f f e c t  from  can  on  be  done by of  natural  a  i n the l a r g e r  t h i s model c o u l d u t i l i z e  t h e SO  bedding  foliation  This  s t r e n g t h s b a s e d on  the  slope. be  and  much  spacing,  information  from l i n e mapping o f t h e  can  The  determined  discontinuities  degree of  deformation  be made by  considering  slope.  recommendations t h a t can  f a c t o r s t h a t c o n t r o l the  t o p p l i n g has  sub-surface  developing  interest  l a r g e r model o f t h e w h o l e s l o p e ,  assigned  the  previous  of surface or  s t r e s s c o n d i t i o n s f o r t h i s model c a n  stability  stability  with  The  rock type v a r i a t i o n .  directly  T h e r e a r e two the  T h i s can  i n f o r m a t i o n on  spacing,  from t h e  the  exercise to include  model f o r t h e a r e a  to the  more d e t a i l e d  obtained  forward  i n the design  structures.  Due  initial  the  assessed  stress conditions resulting  second s t a b i l i t y  joint  be  i n C h a p t e r 6.  straight  disturbance  engineered  model.  s t r u c t u r e on  structure introduced,  is a relatively  toppling  used  of  studied.  r o c k mass and  be  engineering  one  disturbance  design.  d i s t u r b e d s l o p e can  s i m i l a r to the be  the previous  occurred.  of these  The  stability toe  s l o p e s and  area  of rock  slopes  is critical  to  i n which  the  i t i s recommended t h a t m a j o r  139  excavations  not  be  groundwater flow  undertaken  system should  would cause i n c r e a s e d  7.4  The  pore  Flexural Toppling:  7.4.1  in this not  be  toppling  recommended t h a t  parameters f o r the cohesion, small  planar  and  tensile  (<100m) and  In both the surface  intact  formed d u r i n g  be  done t o  failure  studies with rock  large scale  B r e n d a M i n e and  circular.  t o p p l i n g and  surfaces  rock  relationship potential limit  slopes.  I t may  be  t h a t uses accepted  to assess  to a c i r c u l a r  the  T h i s work  strength  friction be  angle,  conducted  on  surfaces  be in  failure  a flexural  i n homogeneous,  nomograms f o r c i r c u l a r  surface.  140  models the  p o s s i b l e to develop  s t a b i l i t y of  failure  It is  T h e r e may  failure  isotropic  flexural  slopes.  Heather H i l l  failure  Work  surface.  should  r e l a t i o n s h i p between c i r c u l a r circular  that  i n v e s t i g a t e what  the  (internal  s t r e n g t h ) , and  i s approximately  the  Topples.  or c u r v i l i n e a r .  shape o f t h e  involve sensitivity  in Flexural  surface  further research  f a c t o r s c o n t r o l the should  be  a l t e r e d i n a way  Recommendations f o r F u r t h e r  failure  f a i l u r e may  In a d d i t i o n ,  pressures.  C u r v i l i n e a r F a i l u r e Surface  geometry of t h e  area.  flexural  topples  a failure that  7.4.2  It  Influence  of Dilation  on T o p p l i n g  i s w e l l known t h a t d i l a t i o n  increase the strength  during  of a joint.  m o d e l s t h a t do n o t i n c l u d e j o i n t conservative  behaviour  (Barton,  shear can s i g n i f i c a n t l y  Consequently, dilation will  1986).  numerical  be s i m u l a t i n g  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 t h e i n f l u e n c e o f d i f f e r e n t  degrees of  dilation  As t h e i n c r e a s e  in  on t h e s t a b i l i t y  strength  confining both small  7.4.3  and l a r g e s c a l e  authors  initiated during  Tabor,  E v e n t s on T o p p l i n g  glacial  r e t r e a t (Mollard,  1971; T e r z a g h i ,  undercutting  i n reference  Bovis  t o topples. of repeated  ( 1 9 8 2 ) , P a t t o n and (1973) s u g g e s t  this  I t i s p o s s i b l e t o use glacial  e v e n t s on t h e  susceptible to toppling.  a n a l y s i s would use t h e c o n t i n u o u s l y progressive  of slopes or  1977; R a d b r u c h - H a l l e t a l . ,  1962).  r o c k mass and j o i n t s o f a s l o p e  which allows  be done on  have s u g g e s t e d t h a t s l o p e d e f o r m a t i o n s a r e  UDEC t o model t h e e f f e c t  due  t h a t such a study  ( 1 9 7 4 ) , a n d de F r i e t a s and W a t t e r s  specifically  an  i s d e p e n d e n t on t h e  slopes.  of Glacial  either during  glacial  Hendron  due t o d i l a t i o n  s t r e s s , i t i s important  Influence  Several  1976;  of a j o i n t  of toppling slopes.  yielding  joint  Such  model  damage a n d w e a k e n i n g o f t h e j o i n t s  t o sequences o f g l a c i a l  excavation  141  and c y c l i c  loading.  7.4.4  Mountain Scale  Deformation  Sakung i s a g e n e r a l term deformation previously  of very  used  large  to describe the gravity  slopes.  d i s c u s s e d sakung because  a mountain s c a l e o r g r a v i t a t i o n a l is  T h i s r e s e a r c h has n o t  believed  i t i s d e f i n e d a s c r e e p on  sagging  as  1971; Nemcok,  large  toppling  1978).  It  t h a t many m o u n t a i n s c a l e movements r e p o r t e d a n d  termed sakung o r simply creep deformation (Tabor,  (Varnes,  1972)  scale topples . potential  i n the literature  may be more a c c u r a t e l y d e s c r i b e d  I t may be p o s s i b l e t o e v a l u a t e t h e  and d e f o r m a t i o n  of very large  slopes using  UDEC.  7.4.5  The  Application  examples  demonstrate  o f UDEC t o S l o p e  i n Chapter  4 and t h e Heather  t h a t UDEC c a n be u s e d  mass s u s c e p t i b l e t o t o p p l i n g . design  Design  Hill  model  f o r slope design i n a rock  However, t h e a c c u r a c y o f t h e  i s d e p e n d e n t on t h e a c c u r a c y o f t h e r o c k mass s t r e n g t h  parameters  used  parameters  i s by b a c k a n a l y s i s  toppling  i n t h e model.  failures  i n similar  The b e s t way t o d e t e r m i n e  these  o f a l a r g e number o f known  rock types, which has n o t y e t  been done.  It  i s recommended t h a t UDEC be u s e d  flexural histories  toppling  failures  characterizing  t o back a n a l y z e  t o develop  a volume o f c a s e  r o c k mass s t r e n g t h .  142  known  This information  will  a l l o w more a c c u r a t e  engineering  design  i n a rock  mass  susceptible to toppling.  7.4.6  For  Geometric S e n s i t i v i t y  each example o f t o p p l i n g i n t h i s  was c h o s e n  f o r analysis.  A great  a b o u t what c o n t r o l s f l e x u r a l parameters small in  Studies  of the slope.  research,  d e a l more c a n be  t o p p l i n g by v a r y i n g  This research  should  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  the slope  face angle,  one  column  inclination.  143  thickness  geometry learned  the geometric  be p e r f o r m e d on  utilizing and  column  variation  REFERENCES Ashby, J . , 1971: S l i d i n g and T o p p l i n g Modes o f F a i l u r e i n M o d e l a n d J o i n t e d Rock S l o p e s , MSc. t h e s i s , I m p e r i a l C o l l e g e , R o y a l S c h o o l o f Mines, London. B a r t o n , N.R., 1986: D e f o r m a t i o n Phenomena i n J o i n t e d G e o t e c h n i q u e , V o l . 36, No. 2, pp. 147-167.  Rock.  B o v i s , M.J., 1982, U p h i l l - F a c i n g ( A n t i s l o p e ) S c a r p s i n t h e 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 A m e r i c a B u l l e t i n , v . 9 3 , pp. 8 0 4 — 8 1 2 . Brown, A., 1982: T o p p l i n g I n d u c e d Movements i n L a r g e , R e l a t i v e l y F l a t Rock S l o p e s : P r o c , 2 3 r d U.S. Symposium on Rock M e c h a n i c s , B e r k e l e y , 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: Finite E l e m e n t S t u d y o f t h e N e v i s B l u f f (New Z e a l a n d ) Rock S l o p e Failure. R o c k M e c h a n i c s , V o l . 12, p p . 231-245. Burman, B.C., 1974: Development o f a N u m e r i c a l Model f o r Discontinua. A u s t r a l i a n G e o m e c h a n i c s 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 B e h a v i o u r o f E x c a v a t e d S l o p e s i n J o i n t e d Rock, A u s t r a l i a n G e o m e c h a n i c s J o u r n a l , 1975, pp.26-31. C h o q u e t , P., T a n o n , D.D.B., 1985: Nomograms f o r t h e A s s e s s m e n t o f T o p p l i n g F a i l u r e i n Rock S l o p e s . Proc, 2 6 ' t h U.S. Symposium on Rock M e c h a n i c s , R a p i d C i t y , pp. 19-30. C u n d a l l , P.A., 1971: A Computer M o d e l 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 B l o c k y Rock S y s t e m s , P r o c . 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, F r a n c e , p a p e r I I - 8 . C u n d a l l , P.A., 1983: N u m e r i c a l M o d e l i n g o f W a t e r F l o w i n Rock M a s s e s . , P r o j e c t PECD 7/9/22, D e p a r t m e n t o f t h e E n v i r o n m e n t , U n i t e d Kingdom. C u n d a l l , P.A., 1985: A S i m p l e J o i n t M o d e l T h a t Embodies C o n t i n u o u s Y i e l d i n g , p r e s e n t e d a t t h e 1985 I n t e r n a t i o n a l Symposium on t h e f u n d a m e n t a l s o f 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 E l e m e n t M o d e l s o f 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 C o m p u t a t i o n a l Methods i n E n g i n e e r i n g Rock M e c h a n i c s , pp. 129-163. E.T. Brown, E d i t o r , G e o r g e A l l e n and Unwin, L o n d o n .  144  C u n d a l l , P.A., a n d B o a r d , M.P., 1988: A M i c r o c o m p u t e r 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, p r e p a r e d f o r : 6 ' t h I n t e r n a t i o n a l C o n f e r e n c e on N u m e r i c a l Methods i n Geomechanics, Innsbruck, A u s t r i a . C u n d a l l , P.A. a n d H a r t , R.D., 1984: A n a l y s i s o f B l o c k T e s t No. 1 I n e l a s t i c Rock Mass B e h a v i o u r : 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 (Final Report). I t a s c a C o n s u l t i n g Group, S u b c o n t r a c t SA-957, R o c k w e l l H a n f o r d O p e r a t i o n s , R i c h l a n d , W a s h i n g t o n , M a r c h 1984. C u n d a l l , P.A., a n d Lemos, J.V., 1988: N u m e r i c a l S i m u l a t i o n o f Fault I n s t a b i l i t i e s with the Continuously-Yielding Joint M o d e l , S e c o n d I n t e r n a t i o n a l Symposium o f R o c k b u r s t s a n d S e i s m i c i t y i n M i n e s , U n i v e r s i t y o f M i n n e s o t a , J u n e , 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. a n d A s g i a n , M.I., 1978: Computer M o d e l l i n g o f J o i n t e d Rock M a s s e s , U.S. Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , T e c h n i c a l R e p o r t No. N-78-4, 399p. C u n d a l l , P.A., a n d M a r t i , J . , 1979: Some new D e v e l o p m e n t s i n D i s c r e t e N u m e r i c a l M e t h o d s f o r Dynamic M o d e l l i n g o f J o i n t e d Rock M a s s e s , P r o c . o f t h e R a p i d E x c a v a t i o n a n d 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., V o e g e l e , M., F a i r h u r s t , C., 1977: C o m p u t e r i z e d D e s i g n o f Rock S l o p e s 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 t h e I n p u t and Output o f G e o m e t r i c a l Data, P r o c . 1 6 ' t h Symposium o n R o c k M e c h a n i c s , U n i v . o f M i n n e s o t a , M i n n e a p o l i s , p p . 5-14. de F r i e t a s , M.H., a n d W a t t e r s , R . J . , 1973: Some F i e l d E x a m p l e s o f T o p p l i n g F a i l u r e , G e o t e c h n i q u e , V o l 23, no. 4, p p . 495-514. Duncan, J.M., a n d Goodman, R.E., 1968: F i n i t e E l e m e n t A n a l y s e s o f S l o p e s i n J o i n t e d Rock, C o n t r a c t R e p o r t S-683, U.S. Army E n g . Waterways E x p e r . S t a t i o n , C o r p s o f E n g i n e e r s , V i c k s b u r g , M i s s . , 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 - R o g e r s P a s s , G e o t e c h n i c a l E v a l u a t i o n o f A l t e r n a t e Routes, Report t o C a n a d i a n P a c i f i c R a i l w a y s , 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: H e a t h e r 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 C a n a d a , F i l e 36-0267, F e b . , 1978.  E v a n s , S.G., 1987: S u r f a c e D i s p l a c e m e n t s a n d M a s s i v e T o p p l i n g on t h e N o r t h e a s t R i d g e o f Mount C u r r i e , B r i t i s h C o l u m b i a , C u r r e n t R e s e a r c h , P a r t A, G e o l o g i c a l S u r v e y o f Canada, P a p e r 87-1A, p p . 181-189.  145  E v a n s , R., V a l l i a p p a n , S., M c G u c k i n , D., and R a j a S e k a r , H.L., 1981: S t a b i l i t y A n a l y s i s o f a Rock S l o p e A g a i n s t Toppling Failure. P r o c . , 3 r d 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 B r a y , J.W., 1976: T o p p l i n g o f Rock S l o p e s , P r o c . o f ASCE S p e c i a l t y C o n f e r e n c e , Rock E n g i n e e r i n g f o r F o u n d a t i o n s and S l o p e s , V o l . 2, B o u l d e r , C o l o r a d o , pp. 201-234. Goodman, R.E., and D u b o i s , J . , 1971: Duplication of D i l i t a n t Behaviour i n the A n a l y s i s o f J o i n t e d Rocks. U.S. Army, C o r p s o f E n g i n e e r s , R e p t . , Omaha. Goodman, R.E., T a y l o r , R.L., B r e k k e , T.L., 1968: A Model f o r t h e M e c h a n i c s o f J o i n t e d Rock. Journal of the S o i l M e c h a n i c s and F o u n d a t i o n 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 Toppling 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 o f C a l i f o r n i a , Berkeley. H o c k i n g , G., 1978: A n a l y s i s o f T o p p l i n g - S l i d i n g Mechanisms f o r Rock S l o p e s : P r o c , 1 9 ' t h Symposium on Rock M e c h a n i c s , 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 o f M i n i n g and M e t a l l u r g y , London. Hoek, E., and B r a y , J . , 1977: Rock S l o p e 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 o f M i n i n g and M e t a l l u r g y , London. Hofmann, H., 1972: K i n e m a t i s c h e 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 d e s I n s t i t u t e s f u r Bodenmechanik Felsmechanik, K a r l s r u h e , H e f t 54. Hofman, K. von, 1973: G e o l . R d s c h . 62,  Modellversuche zur No. 1, pp.16-29.  und  Hangeltektonic  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 S a c k u n g t y p e D e f o r m a t i o n a t Ben A t t o w , S c o t l a n d , Q u a r t e r l y J o u r n a l o f E n g i n e e r i n g G e o l o g y , London, V o l 18, pp. 287-289. H u n t R.E., 1986: Evaluation.  Geotechnical Engineering Analysis McGraw H i l l I n c . , 1986, p.134.  and  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 t h e D i s t i n c t Element Method f o r A n a l y s i s o f T o p p l i n g O b s e r v e d on a F i s s u r e d R o c k S l o p e , Rock M e c h a n i c s 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 E l e m e n t Code: M a n u a l , 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, I n c . , Minneapolis, Minnesota. K a l k a n i , E.C., 1977: Two D i m e n s i o n a l F i n i t e E l e m e n t A n a l y s i s f o r t h e D e s i g n o f Rock S l o p e s . 1 6 ' t h Symposium on Rock M e c h a n i c s , U n i v e r s i t y o f M i n n e s o t a , 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., a n d P i t e a u , D.R., 1976: F i n i t e E l e m e n t 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 , a s s o c . E n g . G e o l . , 13, p p . 315327. K u y k e n d a l l , L. , 1975: K i n e m a t i c S t u d y o f T o p p l i n g F a i l u r e Mode a n d P r a c t i c a l A s p e c t s o f U s i n g t h e 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 , B e r k e l e y , Department o f C i v i l E n g i n e e r i n g . L a d a n y i , B., a n d A r c h a m b a u l t , G., 1969: S i m u l a t i o n o f S h e a r B e h a v i o u r o f a J o i n t e d Rock Mass. 1 1 ' t h Symposium on R o c k M e c h a n i c s , B e r k e l e y , C a l i f o r n i a , pp. 105-125. Lemos J . V . , a n d B r a d y 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 a n d F r a c t u r e d Medium, 2 4 ' t h U.S. Symposium on R o c k M e c h a n i c s , J u n e , 1983, p p . 53-59. Lemos, J . V . , H a r t , 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 E l e m e n t Program f o r M o d e l l i n g J o i n t e d Rock Mass, P r o c . I n t . Symp. on F u n d a m e n t a l s R o c k J o i n t s , B j o r k l i d e n , Sweden, p p . 335-343.  of  L o r i g , L . J . , 1984: A H y b r i d C o m p u t a t i o n a l Model f o r E x c a v a t i o n a n d S u p p o r t D e s i g n i n J o i n t e d M e d i a , Ph.D. T h e s i s , U n i v e r s i t y o f M i n n e s o t a , 1984. Mathewes, R.W., a n d H e u s s e r , L . E . , 1981: A 12,000 Y e a r P a l y n o l o g i c a l R e c o r d o f T e m p e r a t u r e 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 o f B o t a n y , V o l . 59, p p . 707-710. M o l l a r d , J.D., 1977: R e g i o n a l L a n d s l i d e T y p e s i n Canada, i n R e v i e w s i n E n g i n e e r i n g G e o l o g y , V o l . 3: L a n d s l i d e s . B o u l d e r , C o l o r a d o , G e o l o g i c a l s o c i e t y o f A m e r i c a , p p . 2956. M u l l e r , L . , 1968: New c o n s i d e r a t i o n s on t h e V a j o n t S l i d e , F e l s m e c h a n i k u n d I n g e n i e u r g e o l o g i e , V o l . 6, no. 1, p p . 191. Nemcock, A., 1972: G r a v i t a t i o n a l S l o p e D e f o r m a t i o n i n H i g h 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 C o n g r e s s , S e c . 1, pp. 132-141.  147  N i e t o A.S., 1987: I n f l u e n c e o f G e o l o g i c a l D e t a i l s on t h e F i e l d B e h a v i o r o f S o i l s and R o c k s : Some C a s e H i s t o r i e s , i n R.B. P e c k Symposium Volume: The A r t and S c i e n c e o f 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 t h e Dawning o f t h e TwentyF 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., E n g l e w o o d C l i f f s , New Jersey. 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 , P r o c . I n s t , o f C i v i l Eng., V o l . 35, Dec, 1966, pp. 633-656. P a t t o n , F.D. and H e n d r o n A . J . , 1974: Mass Movements R e p o r t , Theme V. 2nd I n t e r n a t i o n a l C o n g r e s s o f E n g i n e e r i n g G e o l o g y , Sao P a u l o , pp. 1-57.  General  P a t t o n , F.D., 1966: M u l t i p l e Modes o f S h e a r 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 o f 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: Preliminary Geotechnical 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 B r e n d a M i n e s L t d . , O c t . 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 G e o l o g y and Rock M e c h a n i c s A s s e s s m e n t s f o r E s t i m a t i n g S u p p o r t Requirements f o r the Proposed Rogers Pass Short Tunnel. R e p o r t t o CPR. P r o j e c t 81-340, M a r c h 1982 P i t e a u , D.R., and M a r t i n , D.C., 1981: M e c h a n i c s o f Rock S l o p e Failure. 3 r d I n t . C o n f e r e n c e on S t a b i l i t y i n S u r f a c e Mining, CO. Brawner e d . , pp. 113. P i t e a u , D.R. , S t e w a r t , A.F., and M a r t i n , D . C , 1981: Design E x a m p l e s o f Open p i t 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 . P r o c T h i r d I n t e r n a t i o n a l C o n f e r e n c e on S t a b i l i t y i n S u r f a c e M i n i n g , S o c . o f M i n . Eng. o f AIME, V a n c o u v e r , pp. 679-712. P o u l t o n , T.P., and Simony, P.S. 1980: Stratigraphy, s e d i m e n t o l o g y , and r e g i o n a l c o r r e l a t i o n o f t h e H o r s e t h i e f Creek Group (Hadrynian, L a t e Precambrian) i n t h e n o r t h e r n P u r c e l l and S e l k i r k M o u n t a i n s , B r i t i s h C o l u m b i a . C a n a d i a n J o u r n a l o f 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., S a v i g n y K.W., and E v a n s S.G., 1988: DeepS e a t e d S l o p e Movements i n t h e B e a v e r 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 P a r k , B.C.. G e o l o g i c a l S u r v e y o f Canada, Open F i l e 2011. Radbruch-Hall, D.H., V a r n e s , D.J., and S a v a g e , W.Z., 1976: G r a v i t a t i o n a l S p r e a d i n g o f S t e e p - S i d e d R i d g e s ("sakung") i n Western United S t a t e s . I n t . A s s o c o f Eng. G e o l o g y , B u l l . No. 14, pp. 23-35.  148  Rapp, P.A. 1987: Rock T o p p l i n g and M a s s i v e S l o p e I n s t a b i l i t y i n t h e B e a v e r V a l l e y , B r i t i s h C o l u m b i a . , unpub. B.A.Sc t h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n e , B.C. Rickard M.J. 1961: A n o t e on c l e a v a g e s i n c r e n u l a t e d G e o l . Mag., v.98 no.4, pp. 324-332.  rocks.  S a g a s e t a C., 1986: On t h e Modes o f I n s t a b i l i t y o f a R i g i d B l o c k on an I n c l i n e d P l a n e , Rock M e c h a n i c s 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 o f the Dogtooth Range and a d j a c e n t p o r t i o n s o f t h e R o c k y M o u n t a i n T r e n c h , 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 o f Canada, S p e c i a l P a p e r 6, pp. 41-51. Soto,  C , 1974, A C o m p a r a t i v e S t u d y o f S l o p e M o d e l l i n g T e c h n i q u e s 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 , R o y a l S c h o o l o f M i n e s , London.  T a b o r , R.W., 1971, O r i g i n o f R i d g e - T o p D e p r e s s i o n s by L a r g e 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 A m e r i c a B u l l e t i n , v.82, pp. 18111822. Teme S . C , and West T.R., 1983: Some S e c o n d a r y T o p p l i n g F a i l u r e M e c h a n i s m s i n D i s c o n t i n u o u s Rock S l o p e s , 2 4 ' t h U.S. Symposium on R o c k M e c h a n i c s , J u n e , 1983. T e r z a g h i , K., 1962: S t a b i l i t y o f S t e e p S l o p e s on H a r d Unweathered r o c k . G e o t e c h n i q u e , V o l . 12, pp. 251-270. T h u r b e r C o n s u l t a n t s L t d . , 1983a: R o g e r s P a s s R e v i s i o n , Volume 1: G e o l o g y , G e o m o r p h o l o g y and H y d r o l o g y . R e p o r t 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 T h u r b e r C o n s u l t a n t s L t d . , 1983b: R o g e r s P a s s R e v i s i o n , Volume 5: B e a v e r V a l l e y G r a d e 1982 R o u t e I n v e s t i g a t i o n , P a r t 3. R e p o r t 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 T h u r b e r C o n s u l t a n t s L t d . 1979: Assessment o f 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 M o u n t a i n S u b d i v i s i o n , R e p o r t t o CP R a i l Special Projects. F i l e 17-6-31, December, 1979. VanBuskirk, CD., 1987: Reassessment o f t h e G r i f f i t h L a n d s l i d e , R o g e r s P a s s , B r i t i s h C o l u m b i a , unpub. B.A.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n e , B.C. V a r n e s , D.J., 1978: S l o p e Movements T y p e s and P r o c e s s e s , 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 R e s e a r c h B o a r d S p e c i a l R e p o r t 176, S c h u s t e r R.L. and Raymond J.K., e d i t o r s , N a t i o n a l Academy o f S c i e n c e s , W a s h i n g t o n , D.C.  149  W h e e l e r , J.O. 1963: R o g e r s P a s s map a r e a , B r i t i s h C o l u m b i a and A l b e r t a (82N W l / 2 ) . G e o l o g i c a l S u r v e y o f C a n a d a , P a p e r 62-32. W i l l i a m s J.R., and Mustoe, G.W, 1987: Modal Methods f o r t h e A n a l y s i s o f D i s c r e t e S y s t e m s , Computers and G e o t e c h n i c s , 4, pp.1-19. Whyte, R . J . , 1973, A S t u d y o f P r o g r e s s i v e H a n g i n g W a l l C a v i n g a t C h a m b i s h i C o p p e r m i n e i n Zambia U s i n g t h e B a s e F r i c t i o n M o d e l C o n c e p t , M.Sc. t h e s i s , I m p e r i a l c o l l e g e , R o y a l S c h o o l o f Mines, London. W y l l i e , D.C., Analysis 89-98.  1980: T o p p l i n g Rock S l o p e F a i l u r e s ; E x a m p l e s o f and S t a b i l i z a t i o n . Rock M e c h a n i c s , V o l . 13, pp.  Zanbak C., 1983: D e s i g n C h a r t s f o r Rock 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 , J o u r n a l o f 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 I n p u t D a t a F i l e s f o r : — — —  Goodman and B r a y B l o c k T o p p l e , S e c t i o n Base F r i c t i o n M o d e l , S e c t i o n 4.3.1 B r e n d a M i n e M o d e l , S e c t i o n 4.4  151  4.2  **Goodman a n d B r a y B l o c k T o p p l e * * START ROUND .1 BLOCK -8.66025 -97.5 56.02241 0.46634 131.0641 4.9706 131.0641 -97.5 SAVE GB1 *CRACK FOLIATION FOR BLOCKS 10-16 CRACK 82.10254 -34.7057 61.60254 0 .801270 CRACK 90.26279 -28.8397 72.76279 1 .471143 CRACK 98.42304 -22.9737 83.92304 2 .141016 CRACK 106.5833 -17.1076 95.08330 2 .810889 CRACK 114.7435 -11.2416 106.2435 3 .480762 CRACK 122.9038 -5.37564 117.4038 4 .150635 CRACK 131.0640 0.490381 128.5640 4 .820508 *CRACK FOLIATION FOR BLOCKS 1-10 -2.5 -88 .1698 CRACK 0 -92.5 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 •88.1698 CRACK 12.32050 -73.8397 3.660254 -78.8397 CRACK 18.48076 -64.5096 9.820508 -69.5096 CRACK 24.64101 -55.1794 15.98076 -60.1794 CRACK 30.80127 -45.8493 22.14101 -50.8493 CRACK 36.96152 -36.5192 28.30127 -41.5192  152  43 .12177 -27.1891 34 .46152 -32 .1891 CRACK CRACK 49. 28203 -17.8589 40. 62177 -22 .8589 55. 44228 -8.52885 46. 78203 -13 .5288 CRACK 61. 60254 0.801270 52. 94228 -4. 19872 CRACK CRACK 72. 76279 1.471143 64. 10254 -3 .52885 83 .92304 2.141016 75. 26279 -2 .85898 CRACK 95. 08330 2.810889 86. 42304 -2. 18911 CRACK CRACK 106 .2435 3 .480762 97. 58330 -1. 51923 117 .4038 4.150635 108 .7435 -0. 84936 CRACK CRACK 128 .5640 4.820508 119 .9038 -0. 17949 SAVE GB4 *DELETE SMALL BLOCKS L E F T 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: F I X BOTTOM AND END BLOCK F I X 60 100 -80 -40 F I X -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 F I L E FOR KUK. F I G 4-13 **FDEF BLOCKS* **100 t i m e s l a r g e r t h a n b a s e 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 * * F I X V E L O C I T I E S OF BOUNDARY SUPPORT BLOCKS** F I X 0,76.2 -36.5,-30.5 F I X 73.2,76 -30.5,0 F I X 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 T E N S = . l DIL=0 **CREATE JOINTS** JREGION 1.5,0 73.15,0 73.15,-30.5 4,-30.5 J S E T -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 J M a t = 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 * * S T I F F E N 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 s a v e 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 J D I S P 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 * * ( F r o m t h i s p o i n t r e d u c e s t r e n g t h o f r o c k and j o i n t s t o failure)  155  * * DATA F I L E 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 0 .000 459.0498 -30. 4798 CRACK 440.000 -30 .480 489.5298 -60. 9593 CRACK 470.480 -60 .960 520.0099 -91. 4389 CRACK 500.960 CRACK 531.440 -91 .439 550.4900 -121 .918 CRACK 561.919 -121 .919 580.9701 -152 .398 592.399 -152 .399 611.4502 -182 .877 CRACK CRACK 622.879 -182 .879 641.9303 -213 .357 **BENCH L E V E L CRACKS 800.000 -30 .480 CRACK 459.0498 -30. 4798 800.000 -60 .960 489.5298 -60. 9593 CRACK 800.000 CRACK 520.0099 -91. 4389 -91 .439 800.000 -121 .919 CRACK 550.4900 -121 .918 800.000 -152 . 399 CRACK 580.9701 -152 .398 CRACK 611.4502 -182 .877 800.000 -182 .879 800.000 -213 .357 CRACK 641.9303 -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 J O I N T SET** JREGION 0,0 800,0 800,-300 0,-300 J S E T 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 J M a t = 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 * * F I X A R T I F I C I A L CRACK AND EXCAVATION L E V E L 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 s a v e BR2 CYC 0 SAVE BR3 CYC 7500 SAVE BR4 **EXCAVATE F I R S T 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 Structural  Data  from Heather H i l l  158  Study  Area  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 a p p e n d i x a r e e q u a l a r e a p r o j e c t i o n s ( S c h m i d t n e t ) , and were p r o c e s s e d u s i n g s o f t w a r e a v a i l a b l e i n t h e G e o l o g y D e p a r t m e n t a t UBC.  159  CREEK  A SO BEDDING AND S2 C L E A V A G E North _  I  _  T EQUAL  AREA  PROJECTION  Symbol  SO B e d d i n g F o l i a t i o n , C r e e k A F O L I A T I O N S , LOWER PART CRKA, S E P T 23,1988 C R E N U L A T I O N C L E A V A G E S I N CREEK "A" CREN., C L E A V A G E , LOWER PART CRKA, S E P T 2 3 , 1 9 8 8  160  30 22 17 12  Points Points Points Points  81  Points  • • A A Total  CREEK  A SO BEDDING -  AND _  S 2 C L E A V A G E : CONTOUR North I  PLOT  _  +  81 P o i n t s ( f o rf i r s t 9 Intervals) 17 3 6 - 42 Contour Method: Schmidt (1925) 0 8- 14 43- 49 Counting Area: 0 . 0 1 0 15 21 5 0 - 56 Contour I n t e r v a l : 7% P o i n t s p e r 1% A r e a 22 Maximum c o n t o u r : 28 57- 63 21 29- 3 5 NOTE: C o n t o u r 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  LEGEND  m  B m 9  161  CREEK  A:  J O I N T PLOT North  I  54  162  Points  Total  CREEK  B BEDDING AND North  S2  CLEAVAGE  I  EQUAL SO SO S2 S2  AREA  PROJECTION  Symbol  B e d d i n g F o l i a t i o n , Creek B B e d d i n g F o l i a t i o n , C r e e k B, S e p t . 1 1 , 1 2 1 9 8 8 C l e a v a g e F o l i a t i o n , Creek B C l e a v a g e F o l i a t i o n , C r e e k B, S e p t . 1 9 8 8  34 14 30 6  Points Points Points Points  84 P o i n t s  163  • • A A Total  CREEK B SO BEDDING AND S2 CLEAVAGE: CONTOUR PLOT North  LEGEND  m B B  (for first 9  10192837-  18 27 36 45  intervals) H 4 6 - 54 B 5 5 - 63 a 6 4 - 72 • 7 3 - 81  NOTE:  Contour  84  Points  C o n t o u r M e t h o d : S c h a i d t (1925) C o u n t i n g A r e a : 0.010 C o n t o u r I n t e r v a l : 9% P o i n t s p e r 1* Max1BUB c o n t o u r : 18  P a t t e r n s Repeat Every  164  9  Intervals  Area  CREEK  B:  J O I N T PLOT North I  32  165  Points  Total  CREEK  C SO  BEDDING AND North I  EQUAL  AREA  S2  CLEAVAGE  _  PROJECTION  Symbol 38 32  SO B e d d i n g F o l i a t i o n C r e e k C 32 C l e a v a g e F o l i a t i o n , C r e e k C  Points Points  70 P o i n t s  166  • A Total  CREEK  C SO BEDDING  AND  S 2 C L E A V A G E : CONTOUR North  PLOT  I  +  70 P o i n t s (Cor f i r s t 9 Intervals) 16 S 3 1 - 36 C o n t o u r Method: Schmidt (1925) 7- 12 3 7 - 42 0 C o u n t i n g A r e a : 0.010 1 3 - 18 4 3 - 48 C o n t o u r I n t e r v a l : 6% P o i n t s p e r 1% 19 24 4 9 - 54 Maximum C o n t o u r : 24 25 30 NOTE: C o n t o u r 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  LEGEND  m 5  s  167  Area  Joint  Orientations, North  Creek  C  29  168  Points  Total  J O I N T P L O T FOR  CREEK  A, B ,  AND  C  North I  EQUAL AREA P R O J E C T I O N Joint Joint Joint Joint Joint  Symbol  R e a d i n g s , C r e e k A, A u g . 4,5 1 9 8 8 R e a d i n g s , C r e e k A, S e p t . 23 Measurements i n Creek B M e a s u r e m e n t s i n C r e e k B, S e p t . 2 3 , 1 9 8 8 O r i e n t a t i o n s , Creek C  21 33 31 1 29  Points Points Points Points Points  11S. P o i n t s  169  + + A A  • Total  COUNTOUR  P L O T " OF  P O L E S TO North  A L L JOINTS  I  115 P o i n t s (for first 9 intervals) 1- 3 Contour Method: Schmidt S3 1 6 - 18 (1925) 41 9 - 21 6 C o u n t i n g A r e a : 0.010 2 2 - 24 7- 9 Contour I n t e r v a l : 3% P o i n t s p e r 1% 1 0 - 12 2 5 - 27 Maximum C o n t o u r : 9 1 3 - 15 NOTE: C o n t o u r 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  LEGEND  m a EB 9 E9  •  170  SCARP T R A V E R S E  EQUAL SO SO S2 S2  SO BEDDING AND S2 North  CLEAVAGE  AREA P R O J E C T I O N  Symbo  BEDDING F O L I A T I O N , SCARP, AUG. 1 0 , 1 1 , 1 3 BEDDING F O L I A T I O N UP SCARP FROM S T A . 1 3 7 , AUG CRENULATION CLEAVAGE, SCARP, AUG. 1 0 , 1 1 , 1 3 CRENULATION CLEAVAGE UP SCARP FROM S T A . 137  11  54 4 41 3 102  171  Points Points Points Points Points  • • A A Total  SCARP TRAV.  SO BEDDING,  S2 C L E A V A G E : CONTOUR  PLOT  North  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 17 S 3 6 - 42 C o n t o u r Method: S c h m i d t (1925) B 8-14 0 4 3 - 49 C o u n t i n g A r e a : 0.010 ffl 1 5 - 21 IS 5 0 - 56 C o n t o u r I n t e r v a l : 1% P o i n t s p e r 1% A r e a BE 2 2 - 28 • 5 7 - 63 Maximum C o n t o u r : 21 2 9 - 35 NOTE: C o n t o u r 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  172  JOINTS  ON  SCARP  TRAVERSE, AUGUST 10, 1 1 , 1 3 , 1988 North I  I EQUAL JOINTS  ON  AREA  PROJECTION  SCARP  Symbol  T R A V E R S E , AUGUST 1 0 , 1 1 , 1 3 , 1988  173  71 P o i n t s  +  71 P o i n t s  Total  J O I N T S ON  SCARP  TRAVERSE, AUGUST 1 0 , North  B EB EB  13,  1988  71 P o i n t s ( f o rf i r s t 9 i n t e r v a l s ) Contour Method: Schmidt (1925) 2 6 - 30 15 C o u n t i n g A r e a : 0.010 3 1 - 35 6- 10 C o n t o u r I n t e r v a l : 5% P o i n t s p e r 1% 3 6 - 40 11- 15 Maximum C o n t o u r : 10 4 1 - 45 16- 20 2 1 - 25 NOTE: C o n t o u r 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  LEGEND  m  11,  174  APPENDIX 3 Data Input F i l e  f o r UDEC M o d e l  175  of Heather H i l l  Landslide.  * * DATA F I L E FOR HEATHER H I L L BASE **FDEF BLOCKS* **New D a t a Deck, w i t h c h a n g i n g s p 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 L E V E L GLACIAL EXCAVATION CRACK AND VALLEY BOTTOM CRACK 0,-790 450,-790 CRACK 350,-700 565,-700 CRACK 190,-790 750,-530 * * I N I T I A L 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 I N I T I A L 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 F I X 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 J S E T -65,0 700,0 0,0 25,0 0,-1300 JREGION 600,-1300 390,-840 750,-530 1016,-1110 J S E T -65,0 700,0 0,0 25,0 0,-1300 JREGION 1016,-1110 750,-530 1111,-363 1375 -944.4 J S E T -65,0 720,0 0,0 33,0 1015,-1110 JREGION 1375,-944.4 1111,-363 1483.3,-191.2 1747.2,-772.2 J S E T -65,0 700,0 0,0 41,0 1374,-944 JREGION 1747.2,-772.2 1483.3,-191.2 1870,-10 2137,-590 J S E T -65,0 700,0 0,0 49,0 1746,-773  ***************  **GENERATE FDEF ZONES** **CREATE A R T I F I C I A L CRACK TO F A C I L I T A T E 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  * * F I X A R T I F I C I A L CRACK CHANGE ANGLE 10 35 JMAT=10 *CHANGE REG 419,-1170 419,-1150 1710,-557 1710,-577 JMAT=10 ****************** **DELETE BOTTOM L E F T 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 I N I T I A L STRESSES, Ko=l INSITU 0 2200 -1300 0 STR 0,0,0 YGRAD .0265, 0, .0265 * C O N S O L I D A T E 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 J D I S P ROTA TIME RESET HIST **ASSIGN HISTORIES ON UPPER FINAL SLOPE** HIST XVEL 1500,-200 YVEL 1500,-200 XDIS 1500,-200 YDIS **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  1500,-200  **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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