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The reliability of the rail network of British Columbia given catastrophic events Glowitz, Joseph A. 1980

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THE R E L I A B I L I T Y OF THE BAIL NETSOBK OF BBITISH COLUMBIA GIVEN CATASTBOPHIC  EVEBTS  by JOSEPH  A. GLOWITZ  B. S c . . C i v i l Tufts  Engineering  U n i v e r s i t y 1978  Bedford  A THESIS SUBMITTED  , Massachusetts  IH PARTIAL FULFILLMENT OF  THE BEQU1BEMENTS FOB THE DEGBEE  OF  MASTEB OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES { Department Of C i v i l  8e  accept to  this  Engineering )  t h e s i s as conforming  the required  standard.  THE UNIVERSITY OF BRITISH COLUMBIA April  ©  19 80  J o s e p h Andrew G l o w i t z  , 1980  In  presenting  requirements Columbia for  I  thesis  I agree that  further  the L i b r a r y  permission  scholarly  D e p a r t m e n t o r by h i s copying not  or  be a l l o w e d  without  University  1H5  f u l l f ilment  make i t f r e e l y  f o r extensive be g r a n t e d  representatives. of t h i s  thesis  my w r i t t e n  It  is  permission..  Columbia  Vancouver, B r i t i s h  copying  of of  the  British  available  Columbia  of  this  by t h e Head o f my understood  for financial  Engineering  of B r i t i s h  2075 Wesbrook P l a c e V61  shall  p u r p o s e s may  publication  Department o f C i v i l  The  partial  and study.„  agree t h a t  for  in  o f an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y  reference  thesis  this  gain  that shall  ABSTRACT  The  transportation  susceptable s u c h as  to  network  service  A method was  network o f This in  the  the  links.  gained  analysis of  October  1979  network o f operating  i n order  reliability  improvement an  estimate  ( redundancy ).  performed  The  the  a reliability  Southern Bainland  p h y s i c a l makeup o f t h e  was  the  by  i n the  form  of c l o s u r e s  i s then  of  cost  network  a n a l y s i s of t h e  to  analysis of  to i d e n t i f y  the  changes  enhance these  it's  proposed  most c o s t - e f f e c t i v e  p e r f o r m e d t o show  these p h y s i c a l changes. A l s o  Second Narrows H a i l  rail  ,  used t o recommend  network i n o r d e r A  to  of B r i t i s h Columbia  analyswas i s again  included  Bridge c l o s u r e  ( From  t o 3 March  1980  ) and  the  c o n s e q u e n c e s on  province,  as  well  as  a  p r o c e d u r e s and  events  floods.  p r o b a b i l i t i e s of f a i l u r e  undertake  reliability  flexibility links  to  be  ,and  is  centres.  of a s s i g n i n g  used  would  Columbia  to catastrophic  : earthquakes, r o c k s l i d e s , snowslides  between p o p u l a t i o n  links  British  d i s r u p t i o n s due  Such s e r v i c e d i r u p t i o n s links  of  review  of  recommendations f o r f u r t h e r  the  the was 12 rail  emergency study.  iii. TABLE OF CONTENTS  r  r  ]SECTION |__  ——•  1 j.  .  CONTENTS  •  :—  T  1  j.  1  I PAGE,  |A.  |List  o f F i g u r e s and I l l u s t r a t i o n s  |iv. ]  |fi.  |List  of Tables  I v.  |C.  |Acknowledgement  J Chapter  )vi.  1. | I n t r o d u c t i o n 2. 1 P a s t e f f e c t s o f c a t a s t r o p h i c e v e n t s : | Alaska | California  JChapter 1  3  —  J  J8., | I 10. | I 11. I  I Review o f b a s i c p r o b a b i l i t y I theory .  J  I 1.  IChapter 12.t 12.2  j  |  | | 1 19. I +  —  ^  IChapter 14.1 14.2 14.3 |4.4 J4.5 J4.6 j4.7 14.8 J4.9  4  ] R e l i a b i l i t y T h e o r y S Network A n a l y s i s 1 Network C h a r a c t e r i s t i c s J Network T h e o r y 1 L i n k P r o b a b i l i t y Theory 1 Attenuation Prediction I L i n k P r o b a b i l i t y Assignment | T i e - Set Reduction 1 B e a l i a b i l i t y A n a l y s i s : E x i s t i n g Network | R e l i a b i l i t y A n a l y s i s : P r o p o s e d Network | Discussion  125. J 126, | 1 38. 1 |42. | |45. | 153. j ,57. 1 1 59. | J61...J 164. |  IChapter  5  JBeview o f Second  J70- |  IChapter  6  | P o l i c y / Procedure  IChapter  7  1 Summary  f  _  IChapter > |D. r — IE.  1  |F.  I  _  +  8  Narrows B r i d g e C l o s u r e review  and improvement  176. J 180. |  ._  _  __  +—-—i  jBecommendations and C o n c l u s i o n +  +  1 Bibliography + |Appendicies  +  —  iHistorical i  •  — —  +  Biography  ...  | 83. | 1 J84. | + ^ 188. |  -I  199. J  —  i  j  iv.  As  i  '  m *^  list  of F i a u r e s  &  Illustrations  Figure  1  I  L o c a t i o n a l Haps  | 9  Figure  2  I  Recurrence  j 24  Figure  3  i  The  rail  graph  network of  B.  Figure 4  J Schematic B a i l  Network  Figure  | The  the  5  network of  C.  Southern Mainland  J  28  J  30  } 33  Figure 6  |  Numbered S c h e m a t i c Network  | 35  Figure  7  I  A general  network  | 39  Figure  8  I  Any  reaching  Figure  9  | P r e s e n t network c o n n e c t i v i t y m a t r i x  | 41  Figure  10  | Proposed  J 41  Figure  11  | Subjective  Figure  12  J E a r t h q u a k e s i n B.  Figure  13  I  Figure  14  | Expected  Figure  15  I  Figure  16  | S e d u c e d •'( e x i s t i n g  Figure  17  | Additional ( possible ) t i e - sets  | 62  Figure  18  | Beduced  | 63  Figure  19  | Recommended n e t w o r k w.  Figure  20  J S p a c e - Time d i a g r a m  \ 72  Figure  21  J Average d e l a y  | 73  input  any  j 40  output  network c o n n e c t i v i t y m a t r i x probability  Begional fault  assignment  C.  l 44 j 48  system  | 49  peak a c c e l e r a t i o n s  | 52  F r a s e r Canyon  rail  ( proposed  times  j 58  schematic ) t i e - set  matrix  ) t i e - set matrix link  j 59  p r o b a b i l i t i e s ! 66  Si |  Table  |  Table 2  1  1 -List of Tables  I Beliability I List  service  levels  | 5 I  of Abbreviations  \  ] Table 3  I Summary  ] Table 4  I L i n k / Node r e p r e s e n t a t i o n o f t h e network  of B a i l  Network C h a r a c t e r i s t i c s  |  T a b l e 4 A I L i n k - Node r e p r e s e n t a t i o n ( p r o p o s e d  I  Table 5  I Table 6  I Cost  e s t i m a t i o n s f o r proposed  I Subjective probability  assignment  |  Table 7  Earthquake c h a r a c t e r i s t i c s  I  Table 8  Predicted  |  Table 9  |  Table  J Table  Link  1 1  Summary  I T a b l e 12  o f B.,C.,  accelerations  I Link r e s i s t a n c e s  10  ( failure  ) probabilities  cf Results  Diverted B a i l  Traffic  links  29  | 31 | 34  n e t w o r k | 35 | 37 | 43 J  47  j 51 | 55 j 56 ] 65 j 71  vi.  C. i  I  would  like  formulating Professor Abdulla early their  to  this Karl  Jamal  thank  thesis Bury  staff Railway  of  topic  Frank  and  funding  the  with  of the  project,  Columbia  Pacific  with  the  the s t a t i s t i c a l literature  the Transportation  British  t o me.  Navin f o r h i s i d e a s i n  h i s help  f o r h i s assistance i n the  and C a n a d i a n  information  Professor  f o r h i s help  investigation, partial  ACKNQWLEDSEMENT  Railway  the ,  Railway f o r t h e i r  theory,  search  Development  and  work.  Agency f o r  engineers  Canadian a i di n  and  and  National providing  1  CHAPTER ONE Z INTRODUCTION  British earthquake of  faults  energy.  consequences may  be  reaching capacity and  rock  Columbia which  Given  to  i n that to  situated  in  may a t any t i m e ,  this  o f such  taken  is  fact,  an  area  release  thought  must  of  strong be  amounts  given  o c c u r r e n c e s and what p r e c a u t i o n s , lessen  their  e f f e c t s . These  such  forces.  f o r m a t i o n s a r e a l s o prone  Natural  t o the  i f any,  effects are f a r  most man made s t r u c t u r e s have a l i m i t  resist  active  features,  to  their  such as  soil  t o damage i n t h e e v e n t o f  an  earthquake. This the  thesis deals  Province  of  w i t h t h e e f f e c t s on t h e r a i l  British  Columbia  network o f  as a r e s u l t o f c a t a s t r o p h i c  event. For criteria  an  event  to  be  considered  catastrophic  must be met. They would i n c l u d e  1.  That  the event  be sudden  ,  certain  :  , usually  without  warning. 2.  T h a t t h e e f f e c t s o f t h e e v e n t be s u b s t a n t i a l ( That or  is,effect  e f f e c t a small  a large portion segment w i t h  o f t h e system  large  disruption.) 3.  T h a t s e r i o u s e c o n o m i c e f f e c t s would  be  felt  by s u c h a d i s r u p t i o n , and t h a t t h e e f f e c t s be f e l t  f o r a s i g n i f i g a n t period  o f time.  2 Catastrophic Landslides,  Due  investigation  Columbia  Columbia over  16  and  include  i s u s e f u l due  the nature  i n an  of the  -  west  to  3 , the , and  geography  direction  within  - south  British  distance  Highway  Columbia  the  , B r i t i s h Columbia  Highway no.  highway and  rail  this situation  1.  Bhich  97  corridors  of  Highway  Highway  ) . .These r o u t e s  t o e a s t e r n C a n a d a . I f one  t o a c a t a s t r o p h i c event  of  , only f o u r t r a n s p o r t a t i o n  Trans-canada  only surface access  Given  the  ( They i n c l u d e B r i t i s h C o l u m b i a  of  due  Floods.  kilometres.  British  locations  Earthquakes,  t r a n s p o r t a t i o n network.  . These c o r r i d o r s encompass a n o r t h  1400  are cut  east  :  Tsunamis,and  t o the rugged mountainous t e r r a i n  corridors exist  no.  would  S o c k s l i d e s , Avalanches,  Such an British  events  no.  are  the  and  represent  the  of  these  there exist  routes  few a l t e r n a t e s .  , i t i s a d v a n t a g e o u s t o know :  routes are  most v u l n e r a b l e  to  disruptions? 2.  8hat i s the  probability  t h a t such  an e v e n t  will  occur? 3.  I f such  a disruption occurs,  alternative  at  Hhat would t h e e f f e c t s  5.  Hhat s t e p s can  fully  past  historical Both  are  4.  these To  routes  potential  understand  experiences.  the  experienced  available. of such  taken  trouble nature  Two  i n s p e c t i o n , those areas  be  areas  what  to  r o u t i n g be  ?  alleviate  spots?  of the are  p r o b l e m , we prime  must  look  canidates  for  places being C a l i f o r n i a devistating  earthguakes  and  Alaska.  in  recent  3 time. C a l i f o r n i a the  Lower  built  Mainland  probability  mathematical  a high density because  Finally,  Columbia  i n that  o f p o p u l a t i o n and i s a  i t i s very s i m i l a r  t o the  understand  expanded  to  model  any manrail  o f emergency p o l i c i e s and p r o c e d u r e s  will  and i m p r o v e  on t h e s e  procedures.,  t h e c o m p l e x i t y o f s u c h an i n v e s t i g a t i o n  complex  than  This i s because the  a l t e r n a t i v e routes o f the to  the  the  network i s s t u d i e d .  rationalize  to  and d i s t r i b u t i o n s w h i c h g o v e r n  t o update  to  studied  n e t w o r k o f the p r o v i n c e . , a review  undertaken  difficult  i s  T h i s theory i s then  transportation  Due  theory  eguaticns  made s y s t e m .  less  to British  areas o f the p r o v i n c e .  Basic  rail  has  up a r e a . A l a s k a i s i d e a l  northern  be  i s somewhat s i m i l a r  try  to  highway  highway  analyize  the behaviour  the  rail  network. system,  that  network  Given  i t  is  the  many  be  very  would  system.  o f m o t o r i s t s would  , only the  Also , t r y i n g t o  be  an  impossible  task. The  four  major r a i l w a y s o f w e s t e r n  Canada a r e i n c l u d e d i n  t h e s t u d y . The r a i l w a y s a r e : t h e C a n a d i a n Canadian ibn  .  Pacific Only  analysis In  at was  necessary  will  Columbia the  Bailway  ,and t h e  ,bn be i n c l u d e d  the course of developing t h i s t h e s i s a  i nthe  Erica  closed  fortunate  ( In so f a r a s t h i s t h e s i s i s concerned  t h e Second  severed  when  ,the B r i t i s h  s i n c e i t s main r o u t e s a r e i n U n i t e d S t a t e s .  occurred. " Japan  Bailway  N a t i o n a l Bailway ,the  n  s t r u c k the Canadian Narrows C r o s s i n g o v e r  from  12 O c t o b e r  the southern  link  National Bailway Burrard Inlet  1979 t o 3 March  of the B r i t i s h  event  ).,The rail  . , The  tanker  bridge bridge  1980. T h i s c l o s u r e  Columbia  Bailway  .  The  4 only  connection  was  at  to  Prince  the  r e s t of  George  .  A  the  British  study  of  Columbia r a i l  this  network  s i t u a t i o n has  been  included. The Bisk  a n a l y s i s undertaken i n the  A n a l y s i s and  been g a i n i n g Pipelines, and to  keep an  field in  has  heavily The  systems  i s a part of L i f e l i n e  promenance  in  l i n k s and  inhabited  area  been shown by populated  be  Lifelines  those s e r v i c e s The  disasterous  Lifeline  vulnerable  importance  e f f e c t s of  to  Engineering  i s to  d i s r u p t i o n s , by  means  of  a  more  Criteria  l e v e l s of s e r v i c e achieved  f o r acceptable  the  nature of the  Ho.  9 ) have o u t l i n e d a  lifeline  levels  to  railway  systems the  » B e f e r e n c e No.  wide  11  has  include: utility required of  the  earthquakes  three range  l e v e l s of  373  by  lifeline  building into  performance the  would  system.  Horan  (  upon  Reference  reliability  l e v e l s and  of  s y s t e m s . . F o r highway  lifeline  l e v e l s were  the  network  s e r v i c e would depend  s y s t e m . Duke and  following  Page  make  flexible  backup c a p a b i l i t y . A measure o f s y s t e m  the o p e r a t i n g  , which  areas.  objective of less  Lifeline  Highways, R a i l w a y s , other  c o r r i d o r s or  the  as  Engineering  years.  functioning.  s y s t e m s more r e d u n d a n c y by and/or  recent  H y d r o Power L i n e s ,  communication  s t u d y i s known  applied  suggested:  1  these and  5 1 : RELIABILITY  TABLE  SERVICE LEVELS  High I n t e n s i t y Ground M o t i o n ( MMI 1  Bridges  1 ,  ) IX-X  Level  A  where  J  ,--  Level  5.0 % ov  A:  B:  VI-VII  Fully  Functional  Fully  Functional  less  ^  of  intensity  area  w i t h o u t s e r v i c e f o r one  day,  fully  one Level  ) - - -  Level B  I  Intensity Motion  ( MMI  |  --1  I RoadbedsJ  i  Moderate Ground  |  _.  j  |  | |  restored  within  week.  20.0 % o r l e s s i n t e n s i t y a r e a w i t h o u t s e r v i c e f o r one week, fully  restored  within  one  month.  Note t h a t t h e s e Intensity  (  MMI  l e v e l s o f earth the  l e v e l s are given )  i n the  ,which i s f r e q u e n t l y  Modified  used  movement a r e d e s i r e d . T h i s s c a l e  when is  Mercalli subjective  related  to  R i c h t e r s c a l e by t h e f o l l o w i n g r e l a t i o n s h i p :  Richter where MMI fiefering include  to  a failure  with r e p a i r s .  =  ( 2/3 ) MMI  i s the M o d i f i e d Table  1,  the  + 1  EQ0ATION 1  M e r c a l l i Scale, various  t i m e i n which t h e r e  levels  of service a l l  i s a down t i m e  associated  6 In  the  probably  case  of  highways,  be a v a i l a b l e , o r ,  constructed.  Temporary  many a l t e r n a t e r o u t i n g s  temporary  bridges  road  could  surfaces  would  could  be  a l s o be used i n s u c h an  event. Railways a r e another matter. Proper grading are are  important  not feasable. Also,  vibrations practical  so a l i n k  were  It  i s  operation,  due  experienced,  repairs  the  to a railway  to  the  temporary  would  be  and  alignment  thus temporary extreme  bridge  unusable  dead  by-passes loads  structures  until  full,  and  a r e not permanent  completed., important  t o t r y to prevent  such d i s r u p t i o n s s i n c e  r e p a i r t i m e w o u l d be s u b s t a n t i a l . Levels  inflicted  o f s e r v i c e o f networks a r e a f f e c t e d on  them  by  damage s t a t e s a r e :  events.  by  the  damage  Four d e s c r i p t i v e c a t a g o r i e s o f  2  1- G l o b a l  damage  2. P a t h i n t e r r u p t i o n 3. .Network  impedance  <*. F l o w c a p a c i t y  Global (nodes  6  ( system links)  damage s u s t a i n e d  restrictions.,  j damage i s t h e sum o f a l l t h e  damages. by d i f f e r e n t  This  i s  component  u s e f u l when c o m p a r i n g t h e  s y s t e m s . Path i n t e r r u p t i o n i s  the  2 These i d e a s were p u t f o r t h i n a p r e s e n t a t i o n by H. C. S h a h , head o f t h e S t a n f o r d U n i v e r s i t y E a r t h q u a k e C e n t r e a t t h e ASCE c o n v e n t i o n a t P o r t l a n d , O r e g o n On 15 a p r i l 1980.,  7 description  of  of concern before links  after  time  an  dual  f o r dual tracked  tracked  Buby C r e e k .  of a l i n k  link  ( 100 km e a s t  a single tracked  that  increased  may  a l s o be  rail  i s on t h e CPH  only  deals  altered  may  (decreased)  t r u e f o r h i g h w a y s b u t may  mainline  B  C  the  only  between V n a c o u v e r and  of Vansouver i n the F r a s e r  operation  with  impedance c o s t s  systems. I n  Valley.  the c a p a c i t y i s already  i s , maximum p o t e n t i a l c a p a c i t y )  probability  impedence  f r o m one node t o a n o t h e r . I f ,  event. This i s e s p e c i a l l y  a l s o be v a l i d  of  Network  or cost of a t r i p  The c a p a c i t y  to  for  severed.  an e v e n t , a l i n k i s s e v e r e d ,  result.  This i s  and a f t e r an e v e n t . T h i s r e l a t e s t h e number o f  which h a v e been  distance,  due  t h e c o n n e c t i v i t y o f t h e nodes by l i n k s .  and t h e r e  defined  ) (  e x i s t s i n terms  a two s t a t e c o n d i t i o n o f e i t h e r f l o w  or  no  flow. , These of t h i s  potential  objective of Lifeline  only t o i d e n t i f y to  predict  performance, To  in  those  Earthquake  lifelines  Engineering  which a r e v u l n e r a b l e  t h e s c o p e o f t h e damage, t h e e f f e c t s  due  an to  understanding catastrophic  of  the  events,  types the  a n d t h e San F e r n a n d o V a l l e y , C a l i f o r n i a  the next  chapter.  i s not  t o damage,  and t o recommend c h a n g e s t o m i n i m i z e s u c h  obtain  experienced Alaska  be one o f t h e c o n c e r n s  thesis.  The  but  damage s t a t e s w i l l  on s y s t e m damage.  of  damage  earthquakes i n  ,will  be e x a m i n e d  8 z  CHAPTER TWO  PAST EXPERIENCES WITH TRANSPORTATION  The  investigation  British  Columbia  without a look Two  into  cannot  at past  places  the  be  potential  fully  disruptions  are  of  DISRUPTIONS  hazards  understood  of  service  particular  or  faced  anticipated  in other  interest:  in  places.  Alaska  and  California. On  27  richter  8.5  state  March  the  Gulf  "populated" part  are  also  9  magnitude  as  of  the  February of  1971  richter  . This  earthquake  southern  part  to  province.  The  types  and  level  of  of  the  that  this  northern  and  i s important i n similar  portion  of  physical  of governmental  p o t e n t i a l damage t o c f Vancouver  by  1  of  Los of  service was  Fernando  i s also  studied  utilities,  Figure  San  6.6  disruption of  including  followed  the  an  quite  w e l l as c l i m a t e  populated  The  portions  Alaska  Alaska i s of  most documented and  the  experienced  services  similar.  The  heavily  of  sections  structures  Alaska  m a g n i t u d e which a f f e c t e d  along  interior  1964  of  earthquake  value i n that  with  i t struck  A n g e l e s , C a l i f o r n i a , and  any  earthquake  to  the  substantial  be s u f f e r e d  by  to  the  can Lower  is  a the  date.  transportation , and  its  help  network, understand  Mainland  and  Island.  shows t h e  a description  l o c a t i o n s of of  each.,  both of these  earthquakes  9  FIGOB.E  1  :  L O C A T I O N AL  INDEX M A P O F A L A S K A  MAPS  10 THE 27 33ABCH  The  Alaska  (alaska  with  damage was c a u s e d  a magnitude o f r i c h t e r  and  an  by t h i s  estimated  ground  earthquake.  shaking,  landslides  also  must r e a c h  Hajor  airport  million  occurred.  For  facilities.  This  were r e q u i r e d f o r r e l i e f to  the  Alaska  loss  and f a u l t i n g of  strength  liquefaction.  dollars  movements were  liquefaction.  damage t o o c c u r  present  Several  ground  shaking  o f t h e s t r u c t u r e s i n v o l v e d , and amount o f t i m e .  causing The  was  This  was s e v e r e ,  fortunate  was  the  except f o r  since  massive  efforts.  fiailroad  was e s t i m a t e d  u s u a l l y occur in  caused  route  along  t o be $27.0  of the  soils  in silty  shaking  can  sandy  of  cause  soils.  the  The  saturated  pressure.,,  f r o m A n c h o r a g e t o Seward  damaged d u r i n g t h e e a r t h q u a k e . by  established faults.  foundation  an i n c r e a s e i n p o r e w a t e r  rail  extensively  some  This i s usually present  loss of strength i s a result  and  million  114.0  .  Cracks  was  ground  t o t h e t r a n s p o r t a t i o n system  Damage  soil  o f Anchorage.  i n Alaska.  airlifts  The  8.5 . The e p i c e n t r e  $311.0  cracking,faulting,and  the n a t u r a l frequency  Damage the  1736  c a u s e s o f p h y s i c a l damage were due  must be s u s t a i n e d f o r a r e s o n a b l e case  at  earthquake.  h o r i z o n t a l and v e r t i c a l  during t h i s to  1964 o c c u r r e d  120.0 k i l o m e t r e s e a s t s o u t h - e a s t  were k i l l e d  Both  EABTHpOAKE  e a r t h q u a k e o f 27 H a r c h  time)  was l o c a t e d people  1964 ALASKA  Host  ( The p o r t ) was of  l a n d s l i d e s , embankment f a i l u r e s ,  movement, and by i n u d a t i o n by u n u s u a l l y h i g h  the  damage  ground  cracks  tides.  11 At Seward and H h i t t i e r waves,  caused  much  waves a l s o c a u s e d  of  of the r a i l  were a l s o damaged.  were open wood t r e s t l e s ,  the l a r g e r  yards  and  the  t o be d e s t r o y e d .  supported  b r i d g e s were s u p p o r t e d  P e r m a n e n t h o r i z o n t a l and displacements  on  on wood p i l i n g s .  steel  pilings.  3. ;,  High a c c e l e r a t i o n s generated  were  million  .  amplification  o f 52.0 s t e e l  damaged  and  had  o f ground  had  two t y p e s  bridges  motions.  on t h e r o a d b e d  i n areas  and was u n c o n s o l i d a t e d  bridges  and t r a c k .  Nearly  u n d e r l a i n by s a t u r a t e d  . Only  damage on b e d r o c k o r t i l l .  along  Turnaquin  Embankment f a i l u r e s  soil Arm  were o f  : *  1.  Fill  failures  (embankment  Reference  No. ,27 Page  * Reference  No. 22 Page  3  within  3  settled the  o f the ground,  t o be r e p a i r e d a t a t o t a l c o s t o f $ 1.5  o f t h e damage o c c u r r e d  was  Bridge  :  b r i d g e s and 73.0 wood t r e s t l e  Damage was a l s o i n f l i c t e d all  Some  of t h e f o u n d a t i o n ,  Transient h o r i z o n t a l displacements  A total  the  vertical  2.  by  Tsunami  Most o f t h e b r i d g e s on  damage was g e n e r a l l y due t o t h e f o l l o w i n g f a c t o r s  1.  resulting  e x t e n s i v e damage. .,  Many b r i d g e s system  submarine s l i d e s  at a c t i v e  faults  m a t e r i a l added weight  D17  to foundation  so  that 2.  the  r e s i s t a n c e to f a i l u r e  Passive f a i l u r e s cracking The  due  embankments were, f o r t h e 1914  organic  m a t e r i a l . Host of  Their  and  slopes  altered.)  { Embankment f a i l e d  to foundation  before  was  only  by  failure.)  most  part  placed  by  hand  c o n s i s t e d o f s i d e burrow which c o n t a i n e d the  were d e t e r m i n e d  s u b g r a d e s were by  the  angle  5.0  metres  of repose  some wide.  of the  fill  material.  THE  9 FBBOABY  On  1971  9 February  1971  earthguake of r i c h t e r The downtown The vertical of  0.1  The over  area  i n the  slip and  200  at  6.6  e p i c e n t r e was  approximately  45  strong  areas. this  the  caused  plane  before, sere  vertical  t h e r e f o r e many not  Beference  No.  17  )  an  area. of  the  almost  possible  equal  Accelerations 1.0  g  forces  fold.  First ,  3  were p r e s e n t , t h u s  earthguakes to  date.  m o t i o n s which had structures  d e s i g n e d . /And  Valley i s a h e a v i l y populated  5  with  motion r e c o r d i n g d e v i c e s most documented  which they  therfore  earthquake i s t h r e e  earthquake i s the  for  k i l o m e t r e s northwest  degrees  g were e x p e r i e n c e d  of  PST  Angeles  h o r i z o n t a l f o r c e s were e x p e r i e n c e d .  importance  experienced  (  G a b r i e l Mountains .  was  i n non-populated  slip  0600  magnitude s t r u c k the L o s  l o c a t e d 45.0  San  plane  g t o 0.5  exhibited  FJIMfiBO EARTHQUAKE  SAN  a r e a , and  third,  , the  Second,  never  recieved San  t h i s earthquake  this  been  forces Fernando was  the  13 first  major The  test for  e f f e c t of  mixed. I f one quite  the  e a r t h g u a k e on  The  most  fatalities.  notable  Hospital.  Fatalities  limited  occupants of  2  to  damage, w i t h no  hospital  had  ,  when  an  earthquake  two  estimated struck.  major  91.0 Had  factors  Norman  lasted  % of the  the  freeways  dams  longer,  were or  close had  important t o note i s the mainy  the  northern  hospitals,two  freeway  correctional  centre  switching/converter r e s t of  was  part  of the  the  been  to  the  able San  Freeway,  fact  part  of  a  failure.,  water  the  with Pocoma  Had  the  l e v e l been t o  a  failed. this  earthquake  v a l l e y where  two  $50.0  filled  dams, t h e  that  interchanges, and  the  dams, million  a  four youth  electrical  s t a t i o n were damaged.  the  Los  to provide Fernando  Damage t o t h e State  structures  p e o p l e were a t home when  maximum, a l m o s t c e r t a i n l y t h e s e dams would h a v e  and  58  fatality  Van  The  the  kept  and  affected  of  onto  i t might h a v e been a n o t h e r s t o r y . Two  Also  out  collapsed  traffic,  earthguake  Veteran^s  transportation  overpass  fare  a v e h i c l e underneath. ,  low. „, an  the  failures.  the 46  was  fared  , however, d i d n o t was  to  structures  modern s t r u c t u r e s  failure  relating  B o t e , however/ t h a t figure  This  designs.,  engineering  e x c l u d e s freeway b r i d g e s ,  administration  were  their  pre-earthquake r e s i s t a n t designs  well.  the  and  w e l l , r e c i e v i n g minimal c o s m e t i c  Older, so  many s t r u c t u r e s  Angeles area, assistance  and  relief  was  unaffected  f o r the  northern  Valley.  freeway system  The  however,  was  located  F o o t h i l l s F r e e w a y , And  The  on  the  Antelope  Golden Valley  14 Freeway.  ( I n t e r s t a t e 5,  I n t e r s t a t e 210  and  California  Route  Ho.  bridges  as  14 r e s p e c t i v e l y . ) Damage was well.  Damage  sustained to  themselves but  the  to the  pavements and  bridges  was  not  the  only  t o the  structures  a l s o t o t h e a p p r o a c h e s , t h e embankments, and  the  piles. Three major l a n d s l i d e s a l s o o c c u r r e d still  under  traffic  construction  would n o t  The following 1.  although  :  Department o f  they  were  been i n s e r v i c e  Transportation  recommends  the  6  Large c u t s should high Low  2..  had  freeways  have b e e n d i s r u p t e d .  California changes  ,  where  failure  for  e l i m i n a t e d due  to  p o t e n t i a l , i n high r i s k  cut slopes  Also, high  be  areas.  are d e s i r a b l e .  fill  their  their  areas  failure  c o m p a c t i o n must be  must  be  re-evaluated  p o t e n t i a l . , Increased  carefully  considered  to  d e t e r m i n e i f i t i s worth t h e e x t r a c o s t . 3.  S u b s i d e n c e due  to d e n s i f i c a t i o n  c a n n o t be  eliminated entirely,  reduced  by  keeping  within but  heights  fills  i t can  as  low  be as  possible. , 4.,  Flexible for to  5.  6  R e f e r e n c e No.  drainage  couplings should  be  used  where a c t i v e f a u l t s a r e  known  exist.  A new  11  p i p e s and  system  o f emergency f u n d i n g  i s desired  since and Failures  of  damage i n the concentrated out  of  destroyed, repair. 50.0  three  emergency million million.  not  a  t o t a l of  these  available  d i v e r t e d from o t h e r the  67  bridges  damaged b r i d g e s :  costs,  $6.5  failures  of  were  that  this  does not  Interstate  5  and  $1.7  bridge  60  required  is  damaged 7  million  for  repair costs, a  total  include those was  completely  m i n o r damage.  were:  for  were  % were s e v e r e l y  % had  restoration million  repair,  25.0  damaged 25.0  for  Angeles.  These  : 5 bridges  f o r highway r e p a i r c o s t s , w h i c h  o f Los  sources.  most e x t e n s i v e p a r t  earthquake.  were damaged beyond  costs  Note  immediately  interchanges.  % were m o d e r a t e l y Total  city  must be  Fernando  2 others  Of  are  f r e e w a y b r i d g e s was  San on  funds  shut  $5.7  of  $13.9  costs for  north  and  the  south  bound. T y p e s o f damage were :  1.  Ground caused  shaking the  2.  The  columns  deck t o  be  thus  causing  the  to  shift  removed bridge  which  from  its  deck t o  drop  ground.  large  (possibly buckle  cause  bridge  restrainers to the  8  vertical exceeding  i n the  middle  by a c o m p r e s s i o n  7  Beference  No.  23 Page 207  8  Beference  No.  23  -  and 0.5  g )  as i f they  testing  212  horizontal caused  motions columns  were b e i n g  machine.  to  tested  3.  Improperdesign  of  restraining  bridges to slipped 4.  approach f i l l s  off their  liquified,  devices  column  caused  supports.  creating differences i n  profile. 5.  Columns  lost  their  anchorages  were  an  bond  in  integral  especially 6.  their  the  between t h e m s e l v e s ground.  part  of  their  structure to  a t abutments  rock  back  and  a l l o w i n g the bridge t o destroy Steel  reinforcing  were  too  the  footings  a l l o w e d the forth,  spaced  entire  itself.  allowing  enough  the  o u t and l e t t h e column  the anchorages,  n o t e d i n t h e San F e r n a n d o  footings,  mountings,  and  and  crushed collapse.  the b r i d g e themselves remained i n t a c t ,  other f a i l u r e s  were  eventually  r o d s were n o t s t r o n g  widely  concrete to f a l l  Basically,  which  ineffective.)  Lack o f r e s t r a i n t  7.  Columns  and  as  with  e a r t h g u a k e , i t was  the s u b s t r u c t u r e  which  failed. Another g t o 0.2 initiated been  g  deficiency was  to  as  Transportation  1.  9  inadequate.  allow  adopted  that  by  34  Fage  research  load  programme  California  0.1  factors of  design f o r briges.  the  , w h i c h recommend  require  the s t a t i c  A  f o r dynamic  policy  Columns  R e f e r e n c e Ho.  was  had  been  T h i s has  now  Department  the f o l l o w i n g changes  :  stronger containment i n the  9  form  of  of s p i r a l  wrappings.  Stronger  reinforcing  columns.  Also, bars  bars  are  reguired  that are c l o s e r  desired. Suggestions  a r e no.  5 bars  for  together at  15.25  are cm  (6.0 i n . ) c e n t r e s . A  better  for  restraining  large scale  inadequate.  movement. The  Hew  methods  L o n g i t u d i n a l hinge cm  (3/4  system at expansion  inch)  bolts  have  would  include:  restrainers  b.  c a b l e s through  f o r new  c o n s t r u c t i o n c. S e v e n  cables  encased  in  proven  B o l t s with  hinge  1.9  concrete  joints  cm  a. 1.9  restrainers (3/4  inch)  pipes f o r e x i s t i n g  s t r u c t u r e s . ... Approach f i l l s  must be  b e t t e r designed  to  prevent  liquifaction. Bestrictions especially  on  a t maximum movement  Larger shear Provide  where column b a r s c a n  that support Develop  spliced,  locations..  keys a t abutments s h o u l d  a t o p mat  be  of reinforcements  be  for  used. footings  columns.  a new  technique  of f o o t i n g s t h a t  support  columns. Horizontal  and  vertical  tie-bars  should  be  specified. Some  flexing  severe  of c o l u m n s s h o u l d be  during  earthquakes.  B r i d g e d e s i g n s h o u l d be for  allowed  past earthquake  site  activity.  specific  to  account  Virtually  no  Fernando V a l l e y o c c u r r e d , of  an  overpass  damage  potential by t h e s e  s h o u l d be i m p l e m e n t e d  serious the  the  the  collapse  two  earthquakes. ( especially  in British  railroad.  trestles.  The  throughout  t h e s y s t e m so t h e A l a s k a  examinimg  the types  where t h e damage w i l l  Clearly,  some  of  i n the C a l i f o r n i a  earthquake  the  case )  which  inflicted  Much o f t h e damage was t o damage  occured  experience  o f damage and o f l i t t l e occur.  i s vividly  Columbia .  i t was t h e 1964 A l a s k a  wooden  any  of s o i l s .  f o r damage t o t h e Lower M a i n l a n d  damage on t h e A l a s k a  smaller  in  i n the San F e r n a n d o V a l l e y p r e c l u d e d  p r e c a u t i o n s o u t l i n e d above  However,  railways  the only i n s t a n c e b e i n g  r o c k / l a n d s l i d e s or s e r i o u s slumping  demonstrated  the  o n t o t h e t r a c k s . One p o s s i b l e e x p l n a t i o n may be  that the l e v e l t e r r a i n  The  to  randomly  i s o n l y o f use i n  value  i n predicting  S  1 9  REVIEH OF Basic  probability  transportation understanding will  be  Columbia  be  applied  of  , there e x i s t s probability  two  or  : P  state  structures. This operational In  will  (rail)  the  i n order to gain  then rail  these  an  principles  network o f  between  a probability  (success)  and  + P  nodes  of f a i l u r e  British  (failure)  =  case  allow  not  (or s u r v i v a l ) . ,  1.,  to redundant  does  (population  the p r o b a b i l i t y o f  case, a p p l i c a b l e  practical  terms,  Some  introduced  to i n d i c a t e  Generally,  these  operation  ).  P(  element this  for  This  survival is  the  or  non-redundant  any  intermediate  failure  middle  items  which do  life  t i m e . These f a i l u r e s is,  number o f s u r v i v o r s  be or  in various stages, complete  (down)  time  a  would o c c u r  :  Random  not f u n c t i o n a r e modeled  function up t o t i m e  3.  5 Page  487  by  to t h e i r  :  l  may  be  ° Wearout  items,  average  a hazard  which measures t h e x or  failure  g r o u n d . ..,  are a s s o c i a t e d with substandard  those  No.  Success)  2.  is,  »o B e f e r e n c e  may  three types of f a i l u r e  failures  that  links  of  1. E a r l y Early  links  of f a i l u r e  P( f a i l u r e  )  to  governing  phase.  between c o m p l e t e  (x}  theory  reviewed  b a s i c p r i n c i p l e s and  a network  to unity  simple  of the  reliability  .  The sum  and  systems  specifically  Given centres)  BASIC FRQBABILITY THEORY  that  product  function,  (  h  instantaneous  20 h(x)  directly  using  life  c h o o s e a model, over a time  o f x. T h i s  length  test  t h e model b e i n g  failures  (link's)  life  modeled  by  a  types  occur  history.  their  They  by  are  an  of for  wearout  of  usually  a  failures  component's  failures,  attempts  can  be  are  made  failures  to  are  &n i n c r e a s i n g  t o a hazard function except t h a t , of f a i l u r e increases. preventative  as  Bote t h a t ,  maintenance  mode  has  a  distinct  should  life-length  l  * obviously  there are  down t o a s m a l l e r  unique  a measure o f s y s t e m  g o a l d e f i n e d whether  R e f e r e n c e So. 5 Page 488  system  models.  of r e l i a b i l i t y  matching r e q u i r e d  efficiency,  models  models c a n  number o f g e n e r a l  to the fundamental d e f i n i t i o n  model  representation  component. ; However, t h e s e many d i f f e r e n t  pre-determined  and  T h e r e i s no way t o p r e v e n t  hazard f u n c t i o n .  a measure o f a c h i e v e d p e r f o r m a n c e  1 1  of  with i t i n the form of a mathematical  be n a r r o w e d  effect  of  failures.  failure  This leads  in  i s t h e n used t o  component. , T h e s e  railways,  i t ' s operational l i f e , every  measured  due t o t h e g r a d u a l d e t e r i o r a t i o n o f  increased  i s similar  context  associated  memoryless  however  time proceeds, the :probability-  Each  be  distribution  independently  properties of the  hazard f u n c t i o n  eliminate  the  are  failures,  failures  physical  the  can  impact.  characterized  in  rate  d a t a , which  Ppisson d i s t r i b u t i o n .  of  Wearout the  - f(x)  range.  Random  minimize  1  /  f{x)  1 - f(x) = r e l i a b i l i t y  where  these  =  as  performance,  where a c h i e v i n g performance  had  some been  21 attained.  These  there  no  i s  goals  one  a r e d i f f e r e n t f o r d i f f e r e n t s y s t e m s and  measure  of  what  an  acceptable  level  of  reliability. Factors  The and  which  influence  1. L o c a t i o n a l  3. Human  2. E n v i r o n m e n t a l  4. M a t e r i a l  include:  most i m p o r t a n t f a c t o r s i n t h i s c a s e would  environmental,  reliability factors  should  Thus, be  both  h e a v i l y . On  maintainance  must  a c h i e v e d performance  be  of the  which other  eliminated  influence hand, as  be l o c a t i o n a l  the  human  factors  and by  defined  or  achievement  of  In  performance  exist  in  detailed order  to  would  or  indirectly.  be t h e measure o f p e r f o r m a n c e  system., I n d i r e c t  measurement  evalutation  which  would  f o r an  requires  a  be used f o r  i n t h e d e s i g n phase. the  case o f the r a i l be u s e d  particular  operational,  the  must  c a n be measured d i r e c t l y  method o f s y s t e m  methods would  In  performance  and  (  operational  theoretical  the  system  measurement  systems  performance  measure r e l i a b i l i t y . .  System  existing  function  performance.  An a c c u r a t e d e s c r i p t i o n o f s y s t e m components  Direct  material preventive  i n order t o determine i fachieved  approaches r e q u i r e d  accurately  of  and q u a l i t y c o n t r o l .  some measure o f p e r f o r m a n c e  knowledge  degree  this  network  , depending  link.  That  of B r i t i s h  on t h e is,fully  Columbia,  operational  both  level  operational,  of  semi-  o r proposed.) s t u d y , t h e method o f m o d e l i n g e a r t h q u a k e s  method o f p r e d i c t i n g c a t a s t r o p h i c  will  be  events. This i s acceptable  22 because  earthquakes  will  Also,this  gives  rockslide. catastrophic In  one  precede  with an average  rate  t years i s :  -vt  1  year,  landslide  model  or  for a l l  network  a Poisson a r r i v a l  o f v per  any  convenient  o c c u r r a n c e s on t h e r a i l  g e n e r a l , assuminq  events over  often  the  rate  o f earthquakes  probability  P  of  k  2  k e P  (vt)  =  Equation 2 k !  where ; k = 0,1,2, . . ,. n P  (network)  such  = 1 - P( z e r o f a i l u r e s  that  :  i n t i m e t)  f -v (p  ) (t) V  1 - e This would of is  method  c o u l d be u s e d  occur over a g i v e n time  (a R i c h t e r to  match  t o p r e d i c t how many  as well as predict  value) these earthguakes these  two  predictions  the  over time together  earthquakes magnitudes  t . The to  problem  obtain  the  m a g n i t u d e and t i m e o f o c c u r r a n c e . Milne relationship  has  discussed  between m a g n i t u d e  this  problem  (m) and f r e g u e n c y  N) known a s t h e r e c u r r e n c e e q u a t i o n . , * log  and  3  has  used  a  of occurrence (  t h i s i s expressed  as :  N = a - b M  where  : a = a c o n s t a n t r e f l e c t i n g t h e average s e i s m i c i t y o f t h e r e g i o n and b = the ratio of large to small earthquakes. N = t h e cummulative e v e n t s / year m = R i c h t e r magnitude o f e v e n t .  1  2  Reference  No.,32 Page 58  1  3  Reference  No..27 Page 1183  23 The and  N  squares  constants and  a and  applying  regression  earthquake  Canada  "maximum  is  divided  occurrences  likelihood"  three  4.0  log  up  N  t o 6.0  =  earthguakes with This  4.2  M i l n e used a  three  magnitudes,  - 0.74  one  log  relating  the  Bichter  magnitude  small  this  Queen  m a g n i t u d e o f M,  was  equation  - 0.72  linear  N is  M  { < richter  range  3.0  is difficult.  values, from  number  of  M.  method  Fitzell ,  ( Bef.  recalculated  t o a magnitude yielding  of the  :  M  Equation  r e l a t i o n s h i p can  )•  the  3  the  to Milne's  number o f c u m m u l a t i v e e v e n t s {  in  equation:  a l s o used by  squares  use  magnitudes  Equation  be  per  year  This relationship  ) events  over  This results  4  shown  except f o r s m a l l e r magnitudes of earthquakes.  in  for  ,and  composite  i n c l u d e d e a r t h q u a k e s up  N = 4.13  -  The  resulting  . H i s r e s u l t s were s i m i l a r  log  for  v a l u e , and  H  used a l e a s t  and  recurrence  This  into  equation  10 ) , however he  many  normal  sections  compiled  a magnitude g r e a t e r t h a n  recurrence  7.5  was  y i e l d e d the  Thus, given a r i c h t e r  following  into  method o f p r e d i c t i o n .  r e g i o n s combined  greater than  Bichter  analysis,  known d a t a , fl  Transform.  Data f o r past  the  using  a n a l y s i s . They a r e : C o n t i n e n t a l , O f f s h o r e  Charlotte  No.  by  method.  Western  all  b are determined  graphically  { N )  i s fairly Since  the  linear  there  a l a r g e area, i n the  vs  are  modeling  following  graph  24 1 4  cummulative events per year  where  = Milne S x =  Fitzell  J  > 7. 0 , 0.1  cuom. e v e n t s / y e a r  i  > 6.0  , 1.0  cuma. e v e n t s / y e a r  1*  > 5.0  , 10.  cumm. e v e n t s / y e a r  > 4.0  , 100.,  1,0 +  I  o.  i l  I i  .01*  I  This  richter  7 magnitude  method  is  uncertainties those  due  events  uncertainty various  with  magnitudes  low  events  which  are  of  earthquakes and  faults.  There  can  are  well  go u n d e t e c t e d .  rare,  their  thus  now  as Also  statistical  ( f r e q u e n c y ) of be e s t i m a t e d .  a c c e l e r a t i o n s are  The  still  given.  order to a s s i g n p r o b a b i l i t i e s  probabilities)  the  method f o r p r e d i c t i n g  explored  i n the next  No.  of f a i l u r e  to l i n k s  l o c a t i o n s o f t h e peak a c c e l e r a t i o n s  known. A  Reference  its  magitude e s t i m a t i o n as  magnitudes  these earthquakes  not p r e c i c e l y  *  without  i s i n t r o d u c e d . Even s o , o c c u r r e n c e s  l o c a t i o n s of  In  not  8  to inaccurrate  occurrences of very l a r g e  J  cummulative e v e n t s per year  peak a c c e l e r a t i o n s  A  1185  S Reference  No.  10  must  (s) w i l l  chapter.  29 Page  (link  Page  103  be be  25 CHAFTES 4 J. R E L I A B I L I T Y THEORY AND This  chapter  reliability outline  theory  applies  1.  and  network  of B r i t i s h  Columbia  . , An  follows:  Establishing taking  AjAilSIS  t h e f u n d a m e n t a l s o f p r o b a b i l i t y and  to the r a i l  of the process  NETWORK  the  schematic  rail  network  i n t o account e x i s t i n g r i g h t s of  important  population  centres  way,  of  the  province. 2.  Predict  the  choosing  level  of  appropriate  ground  criteria  movement by which  by this  movement c a n be measured and d e v e l o p a model of 3.  prediction.  Determine l i n k s of high a,  Proximity  b  Location  i n an  slide  potential  A  c.  Having  risk  t o an a c t i v e  a  area  bridge  (due to) :  earthguake f a u l t , of  of  high  land/rock  o v e r 30 m e t r e s i n  length d. Convergence node  o f many  thus  links  having  a  at  high  a  single  volume  of  traffic. 4.  Establish failure)  5. .  Transform  a  method  Perform networks.  probability  assignment f o r each these  managable s i z e 6.  of  super  (of  link.  networks  into  a  f o r analysis.  reliability  analysis  to  these  26 4.1  2  NETWORK CHABACTERISTICS  The  analysis  existing  operational  reliability, rail  is  then,  two  network  two is  reliabilities  i s appreciably higher,  and t h e r e l i a b i l i t y major  method  and  proposed  figure,  emphasis.  shown i n F i g u r e 3. solid  the  U.S.A. The c e n t r e centres  The  rail  links.  major  identification  important  Chetwynd.  these  c e n t r e s . These are a l s o important  their  survival  lines  Narrows ( Fraser  of  colour  the  Crossing  Vancouver  and  ( Burrard  B i v e r ) ,and t h e  Inlet  point  a c t i v i t y centres Prince  traffic  are : George  flows through  The t h r e e  They  and  i n and  however,  calculations in  shown.  -  for  "switching" centres  ) , t h e New  Mission  These  a major c o m m e r c i a l  that only the mainlines  are  are  of the p r o v i n c e  Junction,  n o t i n f l u e n c e the r e l i a b i l i t y  metro  coded  of  are l o c a t e d r e l a t i v e l y c l o s e together. in  be  List  junction  the r a i l  Note  cost  will  V a n c o u v e r a r e shown. T h e r e a r e many more l i n e s ,  t h i s should  bridges  i s important.,  system  and d a s h e d l i n e s  were e i t h e r  /Kamloops  majority  i f the  c o n s i d e r both  are  (nodes)  ,and  around  A  to the  provides  were a m a j o r  more l i n e s . The most  V a n c o u v e r , L y t t o n , Kamloops  1  and  number i s a l s o i n c l u d e d .  were c h o s e n b e c a u s e t h e y  or  links  Table  centres  be t e s t e d .  of B r i t i s h Columbia i s  carriers  l i n e s are present  abandoned  reliability  network  major  and p o p u l a t i o n c e n t r e o r t h e y three  the  The  for i t s  some  a r e compared  will  parts.  tested  improvements  although  The f o u r  o r abandoned  Abbreviations  the  will  be recommended. T h e s e i m p r o v e m e n t s  given  distinct  first  and/or proposed l i n k s  different  second f i g u r e will  rail  in  an i m p r o v e d n e t w o r k , u t i l i z i n g  rights-of-way The  performed  since major  a r e the Second  Westminster C r o s s i n g  Matsgui  (  Abbotsford  )  Crossing  ( Fraser  This  fiiver  concept  ).  of  combining  many  links  into  a  single  c c m p a r a b l e c o n f i g u r a t i o n i s known a s a " s u p e r l i n k " . I n t h i s  case  t h i s has been  This  analysis a  method  performed  without  mathametical  analysis.  i s a n o t h e r f a c e t o f network a n a l y s i s , t h a t t o model a c o m p l i c a t e d  network  by  a  determines  comparable  yet  simple eguivilent... Note the  that  Canadian  carriers  catasrophe, This study This  rail  A  are  traffic  ,however, w i l l  i s done f o r t h r e e  operating S  the Burlington  point  would  be  ICC w h i l e  part,  is  could only  In  Bailroad connections the  event  be r e - r o u t e d  use t h e r a i l  costly  due t o i n c r e a s e d  Canadian  0 S frieght  within  from  a  since  major  practical  administrative  been,  Canada.  through t h e U  r a t e s are s t i l l  f r e i g h t r a t e s have  a  to  t h r o u g h t h e U.S.A.  links  that  of  o f view, t h e r e - r o u t i n g o f t r a f f i c  deregulated  l i n k s could  shown.  r e a s o n s . One i s  mainly customs ) . A l s o , the  Northern  costs (  regulated  for  the  by  most  1967. I t i s n o t c e r t a i n whether t h e D S  handle the increased  traffic.  T h i r d l y , the  analysis  much s i m p l i e r w i t h o u t t h e i n t r o d u c t i o n o f t h e U S l i n k s .  28 F I G QBE  3 x  IM  MIL  NETWORK  { YUKON  OF B B I T I S H  COLUMBIA  )  *DEAS  (  NWT /  TN-0 )  FN E L *  DBIF*, \  FSJA |<FSJN  BCB "»>"»>>>  CHET/  X  PBEP * T EBB  "*"''owe-* / »  BN  CN  P^GEO  CP TEJN  f i  /  /  /  i  f  / ( PA¥N  ^*  ASHC f-  fKJCT * LAHL  ALBEBTA  B E V L  GOL1 >ICA  kFELD  5PBB LXTNl COBTA  HTCB  ^A7N  ASMS  I BOD VANC  *KELO  WES=<Sr^fHl§S SOT  -»HOPE  HABD  'PENT  PBIN* i*  BELL  MIDW  CASr YAHK (  USA ) '''•JU:..'.  CBOW  )  TABLE 2 1 M § I OF A B BB E VIATIQN S T  T  CODE I  NUMBEB  | LOCATION  ABOT A BUS ASCH BELL BBOD CAST CBET COST CBAN CBOS DAWC DBAS DBIF EVEB PNEL FSJA FSJN GOLD HOPE K A ML KJCT KELO KITI LYTN HIDW HISS J3TCB NANI NHES NVAN OSOY PAVN PENT PGEO PBIN PBBP BE7L SEAT SIC A SPBfi SPQK  1 2 3 4 5  | I | | I I J | | | i 1 ] | j | | j j I | I i ) I I | I | I j | | | I | I j ] j I J | I | | 1 I I  sum  TAKL TEJN VANC VICT WARD WHOP YAHK  | | | | j | 1 i | | J 1 | | | i I | | ) | j | J | | J | | | J | | | 1 | j | | | |  6  7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  26 27  i  | J | | | I |  28 29 30  Abbotsford* Armstrong Ashcroft Beilingham ( fa.) Broodie Castlegar Chetwyad Courtenay Cranbrook Croasnest Dawson C r e e k Deas L a k e Driftwood E v e r e t t ( Ha.) F o r t Nelson F o r t S t . James F o r t S t . John Golden Hope Kamloops Kamloops J u n c t i o n Kelowna Kitimat Lytton Midway Mission Monte C r e e k Nanimo New S e s t m i n s t e r North Vancouver Osoyoos Pavillion Pentiction P r i n c e George Princeton P r i n c e Bupert Bevelstoke S e a t t l e { Wa.) Sicamous Spence's B r i d g e Spokane ( Ha.) Summit Takla Landing Tete Juane Vancouver Victoria Bard Hope C H e s t ) Yank  FIGURE 4 z SCHEMATIC REPRESENTATION OF THE RAIL NETWORK O F B R I T I S J COLUMBIA  Figure  4 shows t h i s network i n a s c h e m a t i c  still  using the four  that  this  distances  i s  to  realize  a d i s t o r t e d view o f t h e a c t u a l s i t u a t i o n  i n that  and p r o x i m i t i e s o f l i n k s  reality. , For more r e a d i l y Table carrier.  l e t t e r code. I t  analysis,  do  i s  representation,  important  not  represent  however, p a r a l l e l a n d s e r i e s l i n k s a r e  apparent as a r e s i n g l e l i n k s and/or  3 gives a basic o u t l i n e o f the s i z e  Note t h a t  while  existing  nodes.  and scope o f each  t h e C a n a d i a n N a t i o n a l B a i l w a y and  31 Canadian The  P a c i f i c Railway cover  British  single  Columbia Railway c o v e r s  the  the largest  province.  distance f o r a  mainline.  The  volume o f f r e i g h t  o r t h e amount c a r r i e d importance are  major p o r t i o n s o f  of  more h e a v i l y  the  into  represents  t h e amount l o a d e d  in  B  C  B C . These f i g u r e s g i v e the r e l a t i v e  major c a r r i e r s '  mainlines,,  ( That i s , which  travelled).  TABLE 3 1 SOJJARY OF THE RAIL JETSORK CHARACTERISTICS OF BRITISH COLUMBIA s 1  |  BRITISH COLOMBIA  J | | |  volume o f f r e i g h t i n B. C. ( m e t r i c km o f m a i n l i n e t r a c k i n B. C. number o f m a i n l i n e s number o f major t e r m i n a l s  1  CANADIAN  j | I |  NATIONAL  CANADIAN  j J J |  BURLINGTON  | j | | |  NORTHERN BAILBOAD  (B.C..  volume o f f r e i g h t km o f m a i n l i n e t r a c k number o f m a i n l i n e s number o f c o n n e c t i o n s t o C a n a d i a n number o f major t e r m i n a l s  s  tonnes )  R e f e r e n c e Nos. 38 & 39 and d i s c u s s i o n s w i t h o f f i c i a l s  i  1  | 1 f J  3.02 m.| 2066., | 3 | 13 |  1  1  I I  i i  !  P A C I F I C RAILWAY  volume o f f r e i g h t i n B. „C., { m e t r i c km o f m a i n l i n e t r a c k i n B. C. number o f m a i n l i n e s number o f major t e r m i n a l s  I  tonnes )  BAILWAY  volume o f f r e i g h t i n B. ,C. ( m e t r i c km o f m a i n l i n e t r a c k B. C. number o f m a i n l i n e s number o f major t e r m i n a l s  |  *  RAILWAY  tonnes )  23.6 m. | 2838. | 5 i  i  1  I i  railways  i  | |  1 \ POBTION)  24.79 m.J 2227. I 3 | 14 1  1 1 1  o f t h e BCB, CN, S CP  1  !  n. a. | 120. | 1. J 3. , | 2. |  32 The  main  the  Southern  of  the  interest Mainland.  t r a f f i c ,  centres,  and  fiedundancy  has  ).  the  e f f e c t i v e  of  5 the  v l u n e r a b i l i t y  become  the  "weak *  major  i n  the  the  r a i l  on  this  such  nodes  Broodie  f e a s a b i l i t y  for  distances 30  4  lines  imaginary  r e l i a b i l i t y allows Each nodes.  for l i n k  (  l i n e  as  the  major  higher  f l e x i b i l i t y  number  Mainland  i s  degree  of  ( of  possible  the  most  cost  of  the  r a i l  note  is  the  improvements. representation  Important  to  portion  t h i s  of  course,  lytton  network.  allows is  A l l  Lytton  a  node  t h i s  problem  that  The  elimination  of  Ascacroft  permits l i n k s  the and  links  focuses  )  the  to  f o r  This  (  amount  the  a  of  large  enhance  Lytton.  is  a  network  to  not  is the  a  the t o t a l  links.)  drawn  network  number  It  inclusion  the  analysis the  .  two  nodes,  are  past  ( O f  or  outlines  between  or  link  These  Canyon  thesis.  such  e n t i r e l y .  Table  These  Fraser  of  -  Mainland.  r a i l  carries  greatest  schematic  network  Hope  their  the  to  such  the  services  Southern  undertake  link  links  the  be  i t  provide  the  through  Proposed  Canyon  an  on  1  focus  reliance  solely  the  flow  Because  potential  o f  w i l l  important  to  Southern of  study  i s  order  shows  must  )  best  to  t r a f f i c  link  This  network  location  Figure network  the  based  r a i l  this  provides  In  r e l i a b i l i t y , paths  of  the  w i l l in  the  l i n k s , the of  the  reduction represents  be  studied  of  the  to  i d e n t i f i e s  Kamloops links.  procedure a  l i n k  and  Fraser  determine  network.  Southern  these  P a v i l l i o n  by-passing  operational  from on  -  d i r e c t  the  status  of  Mainland, to  the  link.  south  P a v i l l i o n .  Numbering to  c a r r i e r ,  be  connection  them  of The also  implemented. between  two  33 FIGURE  1  5  THE  BAIL  METHOBK  ASHC  Table These  links  network.  A  H  They  maximum  )  or  status  column  operational  the are  are  {  0  ,  feasable  either  located  )  or  SOUTHERN  information  most  denotes  THE  MAINLAND  ±  8.  ;  1  C.  KJCT  provides  are  OF  on  for  to  the  be  included  r e l a t i v e l y an  proposed  short  abandoned  whether  the (  P  r a i l  link ).  four  proposed in  an  distances  links.  improved (  100  right-of-way. i s  abandoned  km The  (  A  ),  TABLE 4 I NODE/ LINK S EPS E S E NT ATIO N OF THE F A I L NETWORK link I l i n k | between I distance | status I c a r r i e r letr 1 no ] nodes 1 (km) a  1  b  1 2  c  1  d  1  19-21  1  300  1  o  I  |  19-29  I  10  1  o  I  3  |  18-29  I  20  1  o  i bn/cn  1  4  1  1-18  I  60  1  o  I cn  e  1  5  |  16-29  !  10  1  °  cp  f  1  6  |  1-16  I  20  1  o  cn/cp  g  1  1  1  1-10  J  80  1  o  cn  h  1  8  t  10-14  |  110  1  o  cn  i  1  9  1  14-16  |  130  1  o  cp  j  |10  |  3-14  |  85  \  o  cn  k  111  1  14-27  |  40  1  o  cp  1  1 12  |  11-27  j  125  1  °  cp  tn  1 13  1  3-12  |  80  1  O  n  1 14  |  11-12  |  5  1  o  o  |  15  |  11-17  |  30  1  o  cn/cp  P  1 16  |  2-17  1  80  1  o  cn/cp  g  I  17  |  2-26  I  45  1  o  cp  r  1 18  |  17-26  |  120  \  o  cp  s  I  19  I  2-13  ]  70  \  o  t  1 20  |  9-26  |  215  1  o  u  1 21  1  9-30  i  250  1  o  V  1 22  |  15-30  1  350  i  o  w  1 23  |  20-22  |  50  1  o  X  i  24  I  22-24  |  200  1  °  cp  y  1 25  |  5-24  |  60  1  . o  cp  z  1 26  |  5-27  |  95  i  o  cp  1  !  bcr cn/c p  cn cn  cn/cp cp  1  cp cp  !  cp  MBkl  J i l l  MEM  NODE REPRESENTATION FOR THE PROPOSED/ ABANDONED LINKS  aa  1 27  J  3-22  ]  UO  P  bb  1  28  |  5-10  \  100  a  cc  t 29  I  13-23  |  50  P  dd  1 30  I  15-22  |  150  a  I (ber) J (cp) I 1  (cp) I 1 • (cp) «  FI60BB 6 J. NODE / LINK SCHEMATIC OF THE BAI£ NETWORK OF THE SOOTHESN MAINLAND  36 Refering shown  as  to  Figures  dashed The  Aschroft  2.  The  Driftwood  3.  The  Hope  4.  The  Kelowna  5*  The  Penticton  construction  by  Dease  l i n k  although major  in  authorities and  1970's link  i s  to  one  These be  the  of  network  In  the  l e t t e r s scheme  a  -  r a i l  lines  are  was  lack  l i n k ,  link  under  B  scheduled  C  R  i s  policy. to  off -  desingated.  four  Southern  Mainland  considered is  be  which  has  years. link  due the  links  are  Their  t h e i r  a  southern  -  Broodie  abandoned -  to  considered  Hope  Kelowna  point.  while  constructed  been  The  were  The  this  great  be  w i l l  proposed  at  to  for  Driftwood  l i n e  t r a f f i c .  have  The  1977  many  Midway  •  in  Alaska  for  consideration  halted  This  I  enhancement  i s  temporarily  and  and  Railway  ofrevenue  number  l i n k ,  Columbia  connection on  l i n k ,  link.  P a v i l l i o n  the  Clinton)  link,  Hidway  B r i t i s h  (  which  in  the  Penticton  l i k e l y  to  potential  distances  are  short.  order  numbered  following  Lake  Penticton  Penticton  maximum  r e l a t i v e l y  with  r a i l  the  due  Cease  government  by  link  the  P a v i l l i o n -  -  of  f o r  S  a  5 ,  Eroodie  construction  s h i f t  -  -  the  t i e - i n 0  -  Ashcroft  Lake  5  l i n e s :  1.  The  4  to  links nodes are  are  perform  reguired.  numbered. translated  manipulates  the  the  When  network I n i t i a l l y  the  into network  reduction the  analysis  numbers. by  links is  This  procedure are  l e t t e r e d  performed, network  eliminating  the  the  reduction inherent  37 redundancies  thus  This  i s Figure  i s shown Cost  making t h e r e l i a b i l i t y 6 with  considerations  reconditioning construction These  of  reference  for aguisition  present  bridges  i s outlined i n Table figures  comparisicns  are  analysis simpiler.  to Table of  estimates  1  6  2.  the  rights-of-way,  6 roadbeds,  5 .  1  as well  a s new  7  and  should  be  used  for  only.  TABLE 5 i COST ESTIMATIONS  i  BIGHT OF HAY AQUASITION  $ MILLION  FOB PBOPOSED L l i K S  OPGBADING OF | FACILITIES  I  I  j TOTAL |  NEW  I CONSTRUCTION  COST |  | DRIFTWOOD| DEASE LAKE j  • 0.  1  o  I  829.5  829.5 |  | ASCHCBOFTi | PAVILLION  .492  |  0  |  140,0  140.5 1  | HOPE J BBOODIE  1. 23  I  175.0  1  i  1 KELGWNA | PENTICTON  o  0  1  o  |  o  1  262.5  1  176.3 J 175.0 i  175.0  i  I PENTICTON- i J MIDWAY  Omitting  the Driftwood  a f f e c t t h e Southern Mainland costs  should have  *  be t h e f i r s t more  Reference  1 6  7  o f view o n l y , link  potential  n e t w o r k . , The  No.,41 P a g e s  Penticton  - P a v i l l i o n costs  the Ashcroft  to construct.  in  262.5 }  - Dease L a k e l i n k s i n c e  t h e most w h i l e A s h e r o f t  a cost point  o  -  terms o f t h e i r  ability  12-22  See A p p e n d i x A F o r D e t a i l e d  Calculations.  -  Midway  t h e l e a s t . From  Pavillion  Note t h a t  i t does not  therefore  different links t o enhance the  38 (reliability only,  the  be  proven  link  by  of the  costs later  terns be,  the  o b j e c t i v e s of  i f  any,  due  t o the  Costs  should  this be  closing  associated  c o s t s due  to the  study  effective -  to  Midway,  i s to  constructed of a l i n k  with  with  least  Hope will  link  determine  now  which  to avoid  given  a  penalty  catastrophic  closure  are:  Increasedd  time. Delay time,  and  increased  resulting  inefficient  operation.  NETJOBK THBOBY In  any  extensive  p a t h s between one unique  while  group  of  network  times they  known as  links  (  In  not  the  outputs  network  ,  different number  of  as  two  inputs  and  12  those  ( or  different  32  there  two  these  by  paths  could  defined  outputs. : 11  possible t i e -  Page  40  as  7  number o f shows  There  t o 01  In  1  in  8  inputs general  then e x i s t  , 11  complex  a  a  nodes.  which  bi-directional. be any  are  node-pairs.  restrictions,  Figure  ).  paths  other  are  different  ) which c o n n e c t two  are  being  many  t o 02. J J i t h i n e a c h major s u b s e t  t i e - sets  B e f e r e n c e No.  and  exist  which  to flow  end-nodes.  of t r a v e l  shared  link  a l l links  case,  between t h e  major s u b s e t s 01  exist  general  using  are  or a s i n g l e  may  Sometimes  " t i e - sets"  This interconnection i s subject t h i s c a s e do  , there  node t o a n o t h e r .  other  These paths a r e  1 8  enhancement  analysis.  labour  to  most  - P a v i l l i o n , Penticton  travel  and  reliability  from  t r a v e l c o s t s , Increased  4. 2  of  Kelowna - P e n t i c t o n . T h i s s u b j e c t i v e r a n k i n g  later  (s),  event.  would  : Aschcroft ,and  One  network. In  ranking  effective Broodie  of)  t o 02  four ,  12  ther are  many  networks  the  sets combinations could  be  39 e n o r m o u s . Remember t h e s e c o m b i n a t i o n s a r e n o t j u s t output r a i s e d the  t o power o f t h e i n p u t s .  number o f t h e major  In  any g e n e r a l  combiantions. 1.  Any i n p u t  subsets).,  network, t h e r e  t o each t o each  4. E a c h i n p u t  one  ultimate  objective  t o any  which  traverses  Kamloops. T h i s with  on  chosen., T h i s  to Figure  outputs  to establish to traverse  , so t h e a b i l i t y  output  related  staying  tie-set  output  network , t h e a b i l i t y  possibility  possible  t o any o u t p u t  the case o f t r y i n g  side  exists five  output  5. Some i n p u t s t o seme  the  of  t o any o u t p u t  3. Any i n p u t  C rail  That i s the d e f i n i t i o n  They a r e :  2. E a c h i n p u t  In  t h e number o f  the i s  7. In t h e c a s e i t  is  other  the r e l i a b i l i t y the  side  gathered  case:  is  shown by F i g u r e of  Canyon  is  t o go f r o m any i n p u t on  the  together  the  t i e set  8 , which i s not  canyon,  makes i t a c a s e o f e a c h i n p u t  the general  Fraser  o f the B  at  a l l  traffic  Vancouver  t o each i n p u t ,  or but  40 FIGURE 8 i ANY a 1  INPUT TO  ANY  OUTPUT  b c  J  ,  )  d e f  INPUT  §  •  1  g  OUTPUT  I  b  where the dashed lines individual links identified  The the  total  sua  of  probability the  of the  probabilities  probability  of a series  individual  probabilities.  traversing is  from  the  each  parallel  i s simply  Therefore  input to the  the  output,  simply  link.  product  , the t o t a l  of  The  of  the  probability  i n the case  in  of F i g u r e  8  5  P  total  failure  =  (a) (b) * ( c ) * (d) (e) <f)*(g) ( M l  -  (abc)-(abdef|-(abgh)-(cgh)  -  ( d e f g h ) - ( c d e f ) ••• ( a b c d e f g h )  BELIABILITY  This  w i l l i n c r e a s e or  or  d e l e t i o n s of  Connectivity  where :  and  failure decrease  depending  whether t h o s e  matrix  method f o r the  Matrix  of links  as shown by  catalouging in a  No.  32  Page  43  a  network  Parnoussis.  which i n d i c a t e s where a c o n n e c t i o n  Reference  5  links  on  the  are  in  series.  convenient  destination  links  Eaguation  P  reliability  parallel  matrix  -  total  and  A  1  = total  addition  1 9  network i n F i g u r e 8 i s of  of l i n k s  represent a series by l e t t e r s a - h.  1  9  exists  form is this  of o r i g i n known  as  i s simply  between any  / a a two  41 nodes. I f such is  " 1 " while  a connection e x i s t s  "0" indicates  that  a " 1 " then  no d i r e c t  FIGURE 9 i CONNECTIVITY HJTRIX FOB THE PRESENT RAIL NETWORK  t h e matrix  connection  element  exists.  FIGURE JO \i CONNECTIVITY HATRIX FOR PROPOSED NETWORK  OOOOOOOQOilboOOO 101000000000000 000000000000000110000000000000 00000000 0001010000000000000000  000000000100000101000000000000 000000000000100110000000000000 000000000001010000000100000000  0Q000O000000O0000000000000000 0  oooooooooooooooooooooooooooooo  OJjg20OOOOOOOOOOOOOOQOOOO1O1OOOO 000000000000000000000000000000 000000000000000000000000000000 oooooooooooooooooooooooooooooo 0O000O000OOG00OO00000000010001 000000000000010000000000000000 00000000 0000000010000000001000 00100000 001000000000000000000 0 010000000 00000000000000000000 0 001000000100000100000000001000 000000000000000000000000000001 100000000000010000000000000010 0100000000000000100000OQOOQO00 100000000000000000000000000010 000000000000000000001000000010 000000000000000000000 100000010 000000000000000000010000000010  000000000100000000000001010000  oooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooo  000000000000000000000000010001 000010000000010000000000000000 000000000001000010000000001000 001000000010000000000000000000 010000000000000000000010000000 001000000100000100000000001000 000000000000000000000100000001 100000000000010000000000000010 010000000010000000000000000000 100 000000000000000000000000010 0000000000OOOOO000O000OO000O10 00000000000000 0000000000000010 000000000000000000101010000010 001000000000000100000000000000 000000000000100000000000000000 0000 10000000000000000000000000  oooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooo  00001000 0000000000000000000000 00000000000000000000001000000 0 010000001000000100000000000000 000010000010010000000000000000  oooooooooooooooooooooooooooooo 010000001000000010 000000000000 000O100OOO1OO10000000000000000  oooooooooooooooooooooooooooooo  oooooooooooooooooooooooooooooo  000000000000000101100000000000 000000001000001000000000000000  Figures network  and  sets i n these  Also,  shown.  9 a n d 10 show t h e m a t r a c i e s the  proposed  existing  rail  A l l the t i e -  matracies are b i - d i r e c t i o n a l . 1 through  t o t h e rows and c o l u m n s o f t h e s e Thus,  which s i g n i f i e s t h a t yields  f o r tthe  network r e s p e c t i v e l y .  t h e number o f t h e n o d e s f r o m  incrementally not  000000000000000101100000000000 000000001000010000000000000000  the  connection  from  connection  correspond  matracies but are  1 t o 10 y i e l d s  a connection exists..While  a a " 0 " t h u s no d i r e c t  30  a " 1 "  the 5 to 3  exists.  pair  42 4. 3 i  LINK To  determine  available 1.  PR0B&BILIT3 THEORY the  link  probabilities,  three  methods  are  :  Subjective  p r o b a b i l i t i e s based  on  topography  and  past  experience.,, 2.  Random  probabilities.  3.  Probabilities  assigned  predicting  m a g n i t u d e o f some c a t a s t r o p h i c  Certainly, differs  Method reliability  is  the  between  sophistication  obtain  the  a  1 would and  apparent  failure  than  province, railway  0.0  a  would  of the that  0  is  equation  event.  increasing  in  3.  i n v e s t i g a t i o n a simple e x e r c i s e  to  links  the  and  be  useful  are  to  system.  It  more v u l n e r a b l e  geographic  the  of  , however,  c o n d i t i o n of the  certain  makeup,  an  investigation  used,  Method  current  due  of  reliability  nature  of  physical condition  1.0  survival to  0.0  c e r t a i n success.  ( or  with  f a i l u r e ) ; may  1.0  being  of  T h i s type of  the  disadvantage  H e f e r i n g t o F i g u r e No. 2 t h e and s e r i e s l i n k s a r e c l e a r l y  of  this  parallel evident.  be  to the the  assigned  certain failure  probability  t a k e i n t o a c c o u n t c e r t a i n p h y s i c a l and  Obviously,  2  basis  zo  scale of  being  1 to  make t h i s  P r o b a b i l i t i e s of using  the  method  Method  others  network  line,  of  the  network a n a l y s i s . I t may  basic idea  also  complexity which  from  on  with  assignment  man-made f e a t u r e s .  approach  is  that  the  assignment This  i s s u b j e c t i v e and may v a r y i s  an  example  p r o b a b i l i t y assifnment "return  of  may  how  greatly. the  perform.  Note  p e r i o d " a s s o c i a t e d provided with  c h o i c e f o r t h e r e t u r n p e r i o d must be choices.  One  occurrence  i s to  while  probabilities  choose  the  would  other  probabilty  following  there  i s no  probabilities. A  and  there  return period of structure  are  earthquakes  lifr.  as p r o b a b i l i t y  two  These  o f f a i l u r e per  per year.  table  assignment  of subjective  that  these  made  i s the  be e x p r e s s e d  year o r cummulative events The  the  process  shows  an  example  of  subjective  :  TABLE 6 1 SUBJECTIVE PROBABILITY ASSIGNMENT  HAZ ARD  1 PROB. OF FAILURE  1 CANYON AREA WITH UNSTABLE 1 SLOPES. , 1 PROXIMITY TC AN FAULT.  ACTIVE  0.08  1 i  0.-Q-6  i  i M. LENGTH i i LEVEL GRADE ON F I L L i *~ l LEVEL GRADE ON STABLE S 0 I L |  BRIDGE OVER 30.  0.04 0.02 0.01  P r o b a b i l i t i e s a r e a s s i g n e d w i t h t h e view t h a t e a c h situations  can  acceleration  due t o e a r t h q u a k e s .  Assigning Southern  only  these  Mainland,  withstand  probabilities is  in  Figure  certain  to 11.  the A  o f these  levels  of  peak  network  of  the  high p r o b a b i l i t y of  44 failure  h a s been a s s i g n e d  between  Abbotsford  -  to  Hatsgui  V a n c o u v e r And new W e s t m i n s t e r For  precise  probability used  the  analysis,  assignment  Fraser (  Misson  the  ) , Vancouver -  not  method  of  recommended  using  North  subjective  but should  t o g a i n a g e n e r a l i d e a o f what t h e r e l i a b i l i t y  FIGORE  bridges  - Surrey. this  is  Canyon,  o n l y be  might b e .  11 ; SUBJECTIVE PROBABILITY ASSIGNMENT  22 ASCH  KJCT  .01  .01 MTCB  KAHL  SICA  GOLD  \ . 01 . 01 ARMS  .03  PENT NHES  HOPE .0 1 The  ABOT  second  generator certain  the  range o f v a l u e s c o r r e s p o n d i n g  i s that sucessive results  memoryless  results  processes.  , In  WARD  random  number  with each s p e c i f i c s i t e o r  ) . T h i s method a l l o w s a c e r t a i n  previous  M.ID8  probabilities of failure, within a  be i n c l u d e d i n t h e p r o b a b i l i t y  however,  OSOY*  method would e n t a i l t h e u s e o f a  which would s u p p l y  situation to  PR IN  since the  amount  of  a s s i n g m e n t . The would n o t t a k e random case  randomness  disadvantage, into  account  numbers g e n e r a t o r s a r e of  earthquakes  and  45 land/rockslides Thus , a f t e r period"  each occurrance  associated  modeled by The  a certain  this  third  intensity  ,  where  i n terms o f  release" exists.  be a form  occurrance.  of  "  return  Since t h i s  i s not  probabilities  c a t a s t r o p h i c events  Bichter  can  or  experienced,  MMI  or  which  be  any  achieving a  measure o f  magnitudes,  fault  based  Agha u s e d  earthquake  peak  e x i s t s f o r any degree o f  a  method t h a t p r e d i c t s  accelerations.  s t r u c t u r e which  failure  minimum  earthquake  2  This  or  qualifer  1  > s actual  The  Given activity  and  ,  uses  refined  either  A maximum peak  acceleration  be  before  tolerated  an  an by  ) failure  equation  active  fault be  will  occur.  developed  Donovan, M i l n e  a t t e n u a t i o n s can  or  ,and a  by  Taleb  zone  p r e d i c t e d f o r any  of  Esteva - Agha.  distance  t h i s i n v o l v e s t h e s t a t i s t i c a l p r o c e s s known a s c e n s o r i n g where unwanted d a t a c a n be e x c l u d e d f o r m c o n s i d e r a t i o n .  2  Beference reference  7 6 Beference 27  No.  41  Pages  7-10  5 2  2  earthquake  2 1  No. No.  some  critical  < some d e g r e e o f  method  Rosenblueth  attenuations  A s  -  then  can  the  o c c u r s . Thus i f :  A  2  the  velocities  movement.  are i n s i g n i f i g a n t .  on  ATTENUATION PBBDICTION Taleb -  of  next  intensity  eliminates intensities  1  would  method i s t o e s t i m a t e  accelerations  "strain  method, i t i s u n s a t i s f a c t o r y .  of a s p e c i f i c  4.4  there  with the  occurrence  force  amount o f  from  46 the f a u l t ,  or centre  a s where  :  a  of a c t i v i t y ,  (m,d ) | EQS s =  | =  by t h e f o l l o w i n g e q u a t i o n : (b m) -b ) 2 3 b e (d * c) E q u a t i o n 6 1 s 2  peak a c c e l e r a t i o n i n cm/sec  2  3  given  s EQS = some e a r t h q u a k e e v e n t s r  at a  = =  p o i n t s i t e w i t h some d e t e r m i n i s t i c r e s i s t a n c e and  =  richter  maqnitude  =  max o  ,d  s m d s d  (d s  )  ,  such  t h a t z.  with  = d i s t a n c e between t h e s i t e and e p i c e n t r e  (km)  s d o  = d i s t a n c e between e p i c e n t r e where a c c e l e r a t i o n s attenuates f r o m u p p e r bound w h i c h i s t h a t o f e p i c e n t r e , where t h i s v a l u e depends on t h e s o i l & rock c o n s i t i o n s a t t h e e p i c e n t r e ,  b ,b ,b ,£ c = a r e c o n s t a n t s w h i c h a r e d e t e r m i n e d u s i n g known 1 2 3 d a t a 6 depend on l o c a l s e i s m i c c o n s i t i o n s ,  There are a v a r i e t y based  on  California, Boston.  work  line.  to  British  b  by  Southern  San F r a n c i s c o ,  Using  fit  done  o f e s t i m a t i o n s o f the c o n s t a n t s  some form  the  various  Western  Canada,  Puget  in  Sound  informations  2  3  *  , y i e l d s the f o l l o w i n g values f o r the b»s:  E s t e v a , L u i s / B o s e n b l u e t h , E. S p e c t r a o f E a r t h g u a k e s a t Moderate S Large Soc. Hex. De I n g . S i s m i c a , 2,1964 See A p p e n d i x  ,and  applicable  24  2  c  of regression a n a l y s i s t o obtain a best  These e s t i m a t i o n s a s w e l l as Columbia  authors  S  B f o r detailed  calculations.  Distances  47 fa = 1 The  1402 2  b  resulting  = 0.69  =  1402  (ni)  e  To show t h e v a l i d i t y six  Columbia  most  strong are 2  5  o v e r t h e p a s t 35  of s u c h a method T a b l e  5  earthquakes  7  occurring  EARTHQUAKE  MAGNITUDE  1946  7.3  49.9  124.9  1949  7.1  47.2  122. 6  1949  8.0  53.6  133.3  1957  6.0  49.8  126.5  1965  6.5  47.4  122.3  1972  5.7  49.5  127.2  region  of  earthquakes i n recent  B C i s divided  kM.  British  LONG H  1  Canada  has  experienced  t i m e s a s shown i n F i g u r e  i n t o f o u r earthquake  the g e o g r a p h i c a l c l u s t e r i n g  R e f e r e n c e No.,27 Page  in  CHARACTEfilSTICS  DATE  western  summarizies  years.  t i m e . ..  2  Equation 7  t h e e a r t h q u a k e s with a magnitude o f R i c h t e r  represet  25  -1.65  signifigant  TABLE 7 1  The  c =  ( d + 25 ) s  s  the  1.65  equation i s : 0.69  A  b = 3  1176  4.0  and  numerous 12.  greater.  z o n e s , a t h r o u g h D. of  the  These  earthquakes  These over  48 Zone  A  earthquakes magnitude, southern Fuca  represents in  can  Juan  this be de  the  area,  f e l t Fuca  i n  i f the  fault  Puget of  a  Loner  while  Sound  area  strong Mainland  Zone  C  is  (  earthquakes. richter  area. the  Zone  6.0 B  northern  i s Juan  fault.  EARTHQUAKES  This  figure  taken  from  IN  BRITISH  W.,G.  Milne  COLUMBIA  (reference  No.  21  )  The ) the de  49 It  is  from  Columbia  part,  two  earthquakes  i n t e n s i t i e s i n t e r i o r  these  of  vary the  from  zones  where  originate. about  province  4.0  where  the  Note to  the  7.5  majority  in  Figure  . Z o n e  earthquakes  D are  insignifigant.  U S ORB  This  figure  V3 -£ B M l S I A i lAHkl  from F i t z e l l  (reference no.  SYSTEM  10)  of  B r i t i s h 12  represents for  the  the the most  50 The is  regional fault  shown i s F i g u r e  three l i n e three  sources  faults  J u a n de  origingated  from  the  of  these  that  that  7  accelerations These e s t i m a t e s used  them value  are  of  t o the  distances,  now  t o the  be  stronger  This  sources  acceleration.  f o r instance the  along  extends i n fault  c e n t r e of  S.  &  No.,10 Page  114  is  a a  have  activity  point  allows f o r the line to  This  is  (s) between  the the  s o u r c e s . . Note uncertainty in  source. forecat  the  expected  system o f i n F i g u r e  values obtained  separately  13.  Fitzell  then  combined  H i s method g i v e s a more  "average"  Distances  and  by  are  straight  d i s t a n c e t o V a n c o u v e r i s 50  o f 75  the  G u l f I s l a n d s , ft c o m p o s i t e  earthquake  the  by  2. „, T h e s e  earthquakes  distance d  used  V  activity  i s designated the  with  c or a t o t a l  Reference  the  regional fault  compared  and  source  Sound.  d i s t a n c e t o the  the c o n s t a n t  2  1 line  Puget  (c) o f 25  a composite value. peak  PS  v i c i n i t y of the  a l l three l i n e  into  the  determines  may  due  majority of  a r e a . T h i s s i t u a t e s the  value  focal  1 ,,  of  Sound  i n t h e r e g i o n a r e shown 1 , V  along  province  Equation  ; PS  i s drawn and  which  measuring the  who  this  the constant  being  many  three l i n e s  centres i n the  faults  Note t h a t t h e  r e g i o n i n the  source  Vancouver I s l a n d / Puget  The  6  f o r the  direction in  of  2  those  account  signifigant  line  13.  Fuca p l a t e .  north-south  system of  km.  line km  plus  51 TABLE 8 1  PREDICTED ACCELERATIONS  predicted centre  ( km  (using attenuation 4 5 6 6.5  )  35.  70.  138J  Vancouver  50.  18.  36.  71.|  6.  12.|  16.|  23.  49,  4.  8.J  12-t  18.  10,  Lytton  200. ,  3.  Kamloops  250.  2.  The  note  Fitzell  for  the  fault  higher  1.0  the  accelerations  and the  the  ( up  a l s o f o r the  V a n c o u v e r and by  taking  tc richter  page.  2  2  7  These two  7  e n t i r e Southern  P u g e t Sound l i n e  source e f f e c t i v e l y 0.5  9  i  8-147  No.  10  121  Equation  the  obtained  7.5  given  ).  This  l e v e l s of  on  analysis  the  Page  has  magnitude.  work i s shown i n F i g u r e Lower M a i n l a n d  i n t e r e s t i s the Southern  the e x p e c t e d  S  true  closer to  Fitzell  7  which  maps show the  source  Page  by  into account a l l earthquakes  M a i n l a n d . Of  increases  centres  Victoria..  g.  Reference  141.  as c a l c u l a t e d  A g r a p h i c a l summary o f F i t z e l l * s next  100.J  a g r e e m e n t . -This i s e s p e c i a l l y  peak a c c e l e r a t i o n s f o r s p e c i f i c  the  196.  1  attenuations  m a g n i t u d e s and  such as  have o c c u r r e d  276.  a c c e l e r a t i o n s a r e i n cm/second 2 g = 980.0 cm / s e c )  r e s u l t i n ^general  system  {  I  196.i  that these  r e s u l t s of  and  *  Fitzell  25.  ( where  on  egn.) 7  Victoria  *  his  peak . a c c e l e r a t i o n s  distance  137  area  effect  Mainland.,  a c c e l e r a t i o n s by  14  of  This about  FIGUBE Ui  J. EXPECTED  SCAUt  PEAK ACC EL EBftTI 0 HS  r a p n u D U 10 ra.  zoos,  COITOUI  i n i a i i T I O U L B0U1SART  _  1 0  iCCHJDUTIOK(Ig) f o r T>1007T(.,b>23ra.  This figure from F i t z e l l (reference no. 10)  53  HsJ2 1  LINK  PROBABILITY  Taleb  -  predictive  Agha  peak  p r o b a b i l i t i e s assigning link  i s  case  a  may  the  minimum  the  area  S  41  eguation  {  no.  i s  (  7  )  as  an  r i c h t e r  )  s p e c i f i c  in  any  probability  that  the  the  link  is  done  by  each  link.  Each  source,  Figure  magnitudes For  so  to  earthguake  shown  manipulated  This  accelerations  experience. a  has  d i r e c t l y *  from  source  )  13).  in  Then  this  maximum  are  determined  for  given  magnitude  of  of  f a i l u r e  that  is  to  calculated. For  a  system  acceleration  eguations, less to  This where  than an P  of  or  idea a  equal  r  < i  A  1  to  EQS  links, greater  (i) the  w i l l  {  r  peak  EQS  }  i  P  {  m >  b  in  w i l l or  the  i f  i t s  occur  equal following  a  (s)  i f  the  a  resistance  acceleration  link set r  of (i)  experienced  or: substituting  • b  < -  than  f a i l  equation  6  yields:  -b 3  2  P  f a i l u r e  contained  event  I  -  is is  link  earthquake {  series  experienced  resistance.  due  distance  past  there  40  allowable  line  to  No.  obtained  earthguake  due  earthguake  i s  be  s p e c i f i c  from  Reference  acceleration  maximum  and  be  {  A S S I G N MB NT  e  I  EQS  }  re-arranging  :  1  (  1/b  )  In  ( B  /  b  2  )  I  EQS  }  Equation  8  1 -b  where  :  B  =  r  ( i  Expressing has  a  magnitude  in H  a of  d  )  3  s  different greater  way, than  i f or  an  earthguake  equal  to  a  event  EQS  c r i t i c a l  54 magnitude will link  M  (cr)  produce can  ( where ti ( c r ) i s a c r i t i c a l  peak a c c e l e r a t i o n s g r e a t e r  withstand  simplified  by  ,  then  failure  using Eguations P  ( m  >  than  8 6  H  will  magnitude  those  which  which  o c c u r . T h i s can  the be  9:  )  Equation  9  cr where:  -b 1  r  (d • c) s  i a  — — b  = cr  In  3  • b  2  Equation  10  1  S u b s t i t u t i n g t h e known c o n s t a n t s i n t o E q u a t i o n 10 r e s u l t s i n t h e f o l l o w i n g : -1.65 1  r  (d + c) s  i =  ln 0.69  ct  To link,  find the  4)  H  the p r o b a b i l i t y of  ( c r ) must be  f  of s u r v i v a l  occurrence  of occurrence  poisson a r r i v a l  rate  of  ( or f a i l u r e  H will  richter  be  used  )  this c r i t i c a l  p r e d i c t e d . , The  which r e l a t e s e a r t h q u a k e  freguency  XI  Equation 1402.  frequency  earthquake (no.  —•  of  magnitude  recurrence  equation  magnitudes a with for  this  the  purpose.  the A  yields:  - < v )< t ) P  =  1 - e  E q u a t i o n J.2  where :  failure v = H  ( H  )  with  :  cr N = t h e mean a n n u a l of t h e c r i t i c a l t Values  of  = the link  number o f resistance  network. T h e s e r e s i s t a n c e s a r e t h e  r a t e of occurrence magnitude H and cr years must r  now  be a s s i g n e d  ( i ) which i s t o be  to  the  used  in  55 Equation the  10  and  then  probabilities  of  These a s s i g n e d  i s substituted  r e s i s t a n c e s are found  Structure  steel  loose  To  1.  the  Assign  |  |  0.25  230.0  |  I  0.20  196.0  |  Nest  of s u r v i v a l  requires  resistances  i n Table  9.  determine  T h i s has  t o each  link  using  b e e n done and  the c r i t i c a l  1.0. H o s t o f t h e  estimated  for  magnitude H  data  this,  has  all  the  are  in  (cr)  by  i s the d i s t a n c e d  (s)  link  Determine  the  r a t e of occurrence  (cr) u s i n g Eguation  Substitute  those  link  these  link  values  probability  given the  the  be  line  resistance.  magnitude M  the  been  needs to  from  the  obtain  already  that  s o u r c e and  A summary o f  four  10.  predetermined  the  a  which i s :  link  Equation  4.  138.0  probability  process  Table  3.  0.15  fill  guides  2.  J  I  fill  J j  98.0  bridge  IB  9:  Resistances 2 g - force cm/sec. 1.0  determine  step c a l c u l a t i o n  \ j  30  i n Table  RESISTANCES  I  <  stable  9 to obtain  failure.  TABLE 9 .: LINK  bridge  into Equation  into  o f the  4. Equation  of f a i l u r e  seismicity  critical  12  to  (survival)  of  of the r e g i o n . ,  p r o b a b i l i t i e s a r e shown i n t h e  last  56 column o f T a b l e instance  and  10.  link  Links  11 ' w i l l  11 and  12  designate  have been combined  in  this  both.  TABLE JO i . LINK P BOB A B I L I T I E S | LINK ] 0 i NO. | (KB)  *1 I RESISTANCE| 0 J (CH/S.SQ) | CR 1  1  1 150  |  230.  I  9.3 1. 0005 )  1  50  |  138. ,  1  7.0 1 0.5  |  .500  1  | 2  *I PROBABILITY OF | ]SURVIVAL J FAILURE | .995  1  .005  |  1  .5  |  1  3  |  50  |  138. ,  1  7.5 1 .04  1  .74 0  i  .26  |  I  4  1  75  |  196.  1  7.5 1 .04  I  .740  1  .26  |  1  5  | 100  |  196.  I  8.2 ] .01  |  .920  i  .08  )  1  6  ] 125  |  138.;  1  8.2 1 .01  |  .920  1  .080  |  i  7  | 125  |  196. ,  |  8.6 1. 0065 1  -950  1  -050  J  1  3  1  175  |  98.  I  8.5 1. 009  1  .930  1  .070  |  1  9  1 175 |  98. ,  J  8.5 1. 009  |  .920  1  .008  |  I  10  I 225 |  |  11/12} 250  j  13  |  230.  \  10.3 1- 0001 1  -998  I  .002  |  230. ,•  |  10.3 1- 0001 I  .998  I  .002  |  I 275 |  230.  |  10.0  |. 0001 |  .998  |  .002  |  14  | 300  |  230.  1  10.9 1. 0001 J  .999  1  .Q01  |  1 15  | 200  |  230.  I  10.0 1. 0001 I  .999  I  .001  |  * Where The  |  : H = c r i t i c a l m a g n i t u d e and N = curnm. E v e n t s / y e a r  link  r e s i s t a n c e s were c h o s e n on  stability,  types  geographic  location.  It  of  i s important  have been d e t e r m i n e d and  N  this  yields  therefore,  have  a low  bridge  to note  structures  present,  t h a t the c r i t i c a l  are g u i t e high occurrence  a low  the b a s i s of the  probability  and  the  magnitudes  which  , being are over  o f event  value  soil  N.  richter Host  o f f a i l u r e . L i n k s 2,  8.0  links, 3 and  4  57 however, their  have a r e l a t i v e l y  close proximity  4. 6 1 T I E The in  - SET  15  possible  are  are  and  now  two  inputs  29 a n d  chosen a s  19  the  two  outputs  {  are  designated  ports  and  Canyon Norht  most e x p o r t  Prince Rupert  the  inputs  to t h e i r  due  11  as  12  and  to  i s becoming  are  to  North while  Vancouver the  outputs  l o c a t i o n i n the  p o i n t . Both the but  CN  and  and  leaves  increasingly  from  North they them.  important).  ). are were  province  i n close proximity  Vancouver  the  Kamloops  Kamloops J u n c t i o n  strategic  shown  all  5  Kamloops  V a n c o u v e r were c h o s e n as freight  Canyon a s  sets  5  Vancouver  switching  west  Fraser  (  r e s p e c t i v e l y . Kamloops and  and  failure  source. .  These t i e -  then t r a v e l separately  Fraser  Vancouver  paths through  between  i n p u t s due  and  of  earthquake l i n e  presented.  a t a m a j o r j u n c t i o n and here  probability  REDUCTION PROCEDURE  paths  Junction) Theses  to the  t i e - s e t s or  Figure  high  CP  join  through  Vancouver.  are {  the  major  Although  58  FIGORE J 5 ± FRASER CANYON BAIL  These -  29 , 12 - 19 , and 12 - 29.  matracies Agha. as  f o u r t i e - s e t ma t r a d e s  a r e reduced  ( Reference  the  Appendix  tie -  Input  12  Input  11  a r e denoted  ( Matracies  as 1 1 -  by  12 - 2 2 ) . These m a t r a c i e s  r e d u c t i o n procedure  of this  procedure  Taleb as w e l l  a r e shown i n d e t a i l i n  D.  The r e s u l t s  19 , 11  1 - 4 ) . The t i e - s e t  by u s i n g an a l g o r i t h m d e v e l o p e d  No. ,41 P a g e s set  SCHEMATIC  i s shown i n F i g u r e 16.  59 FIGD8E J6  l REJDOCJD ±  EXISTING 1 T I E - SET  Matrix  13 13 13 13 14 14 14 14  One  10 10 10 10 11 11 11 11  8 8 9 9 8 8 9 9  ID  7 7 6 5 7 7 6 5  can see t h a t the  6 4 3  5 3  6 4 4  5 3 3  | 1 | I  Letter ( a ( b ( c  1 I  I  |  reduction  MftTBIX  <  a  ( ( ( (  g h  e  f  procedure  eliminated  four input / output t i e - set matracies to a s i n g l e enables  the  matrix and memory  reliability  for larger  space,  possible  tie  Vancouver  / North  4.7  tie  -  that set  performed. 11  Table  sets  from  on one  much  computer  a n a l y s i s was  performed  16)  represents  Kamloops  /  single  time  and  manually  a l l the  .  reduced  kamloops J u n c t i o n  to  Vancouver. ,  ANALYSIS - EXISTING NETWORK  matrix  and  this  ( In F i g u r e  the l i n k  The  saves  performed  This  link  probailities  reduced,  the  probabilities  substituted  for  have been a s s i g n e d reliability of  failure  the s p e c i f i c  and  the  a n a l y s i s may are links  taken  be  from  as shown i n  16.  Figure The that  -  J. R E L I A B I L I T Y  Now  systems  although  This simple matrix  a n a l y s i s t o be  matrix.  the  the  d e t e r m i n a t i o n o f the r e l i a b i l i t y original  network  S e r i e s Systems i n P a r a l l e l  )  has  is  quite  easy,  been made t h e s i m p l i f i e d  network.  now SSP  (  60 The  reliability  is : I  B E L I A B I L I T Y OF  SSP  i = ^»  Equation J3  1  ) a  \a  L  1  ).-.. ( i ) ]  * J  2  J  series components This states that are  the  product  reliability For  the r e l i a b i l i t y  of  their  o f the  individual  parallel components series  reliabilities  o f t h e p a r a l l e l components i s t h e i r  components while  the  sum. ,,  the g i v e n n e t w o r k t h e b a s e e q u a t i o n i s : P  = failure  P  1 - P  where  :  survival =  1 - A * ( B - C ) - D  E00ATION  J4  failure where :  A = the sumation o f the product o f the individual t i e - set probabilities, (those b e i n g A B C D E F G H I J ) B = the sumation of the p r o d u c t o f the individual links., ( t h o s e b e i n g 13 11 10 9 8 7 6 5 4 3 ) C = a c o r r e c t i o n f a c t o r to e l i m i n a t e those i n d i v i d u a l l i n k s which were c o u n t e d more than once. D = the p r o d u c t of the p r o d u c t of the t i e set p r o b a b i l i t i e s . ( a through j )  Each t i e - s e t i s a s s i g n e d a l e t t e r of i d e n t i f i c a t i o n through  h ) a s shown t o t h e r i g h t  of the  matrix i n Figure  ( 16.,  a  61 The in  detailed  Appendix E.  which r e s u l t s P  The  c a l c u l a t i o n of  the  r e s u l t s are  follows  as  reliabilities  5. 199  C =  7.271  B =  11.613  D =  .024  *  following  1 - 5. 119  +  equation  be  found  :  A =  i n the  can  :  (11.613 - 7.271) -.024  EQUATION  J5  failure P  =  0.119  failure BELIABI1ITI  = sub  This of  the  links, and  reliability  Fraser  where  The possible  how  or  l i n k s not  real  rockslide,  question  posed  t o r a i s e the  greater  chance of  much w i l l  increase be  the  if  the one  to  the  the  l i n k to  entire  of  especially  one  reliability  of  is  these  - redundant i n the  system  closure caused  by  additional  of  network o f  an of  the  the  the  a  .881  , is  that  i t  event?  Southern  it has  Also,  Mainland  l i n k i s added? Would i t  additional the  to  earthquake.  a catastrophic  (redundant)  i f two  e x i s t s due  t h i s network s o  s u r v i v a l given  reliability  network. I t  i s , with a r e l i a b i l i t y  reliability  the  network i s t h e  most non  answer t h e s e s q u e s t i o n s ,  additional  the  possibility  s u f f i c i e n t l y increased  begin  .881  network  e s t i m a t e of  h o w e v e r , which a r e  landslide  a  Canyon  -  l i n k s were added?  analysis Fraser  now  Canyon.  adds  To one  62  i**J 1 R E L I A B I L I T Y ANALYSIS z PROPOSED NETWORK Having  performed the r e l i a b i l i t y  rail  network  i n the F r a s e r  will  now  failure for in  be added t o t h e listed  i n Table  Canyon,  the Ashcroft - P a v i l l i o n  network.  The  11 a r e s t i l l  t h e p r o p o s e d network i n c r e a s e s Figure sets  a n a l y s i s f o r the e x i s t i n g  link  valid.  those  link  probabilities  The t i e - s e t  of  matrix  of t h e e x i s t i n g network  16 a s w e l l a s 8 a d d i t i o n a l t i e - s e t s . .These e x t r a t i e effectively  increase  t h e number o f r o u t e s  These a d d i t i o n a l t i e - s e t s a r e t a b u l a t e d  in Figure  available . 17.  F i g O B E J 7 2 ADDITIONAL J POSSIBLE 1 T I E - SETS input / 1 output 1  I  11-19  1  11 10 15 1 2  s  14 13 15 1  i  J  12-19  I  11 10 15 1  s  14 13 15 1 2  |  J  11-29  |  14 13 15 1 2  &  14 11 10 13 1 2 |  I  11 13 15 1  &  14 11 10 15 1  i  The major  12 -  29  Additional  input  - output matracies,  of  11  -  12 w i t h  that they  are subsets  possible  tie -  half.  The f o u r cf  the  reduced  being  other  t i e- set summarized  with  Matrix  |  the  therefore  four  1 through 4  a t the comparable  a s shown i n F i g u r e  the e x i s t i n g network,  obtainedis  included  and 11 - 29 w i t h  t i e - s e t s are then  analysis final  sets  o f each  Sets  those being  , looking  11-19  -  Tie  a d d i t i o n a l t i e- sets are f i r s t  as shown i n A p p e n d i x D. Then sets  !  J |  tie  12 - 29 n o t i c e the  additional  17 a r e now r e d u c e d i n  reduced  as  before  in  the  as d e t a i l e d i n Appendix D. ,  matrix i n Figure  for 18:  the  proposed  network  MATRIX 13 13 13 13 14 14 14 14 14 14 It new  is  10 10 10 10 11 11 11 11 13 11  8 7 8 7 9 6 9 5 8 7 8 7 9.6 9 5 15 1 10 15  now  the  extra  two  two  has  only  6 4 4 1  beginning, only final  t i e - sets  networks two  into  the  storage  for  Appendix  E and  calculating  the  the  additional  need be  and  ) ) ) ) ) ) ) ) ) ) reliability  18  ( I  reliability  i s s e e n . The &  j  ).  calculations as  algorithm. as  this  reliability due  shows d i f f e r e n c e  proposed) sets  the  of  to  the  performed.  Figure  time  r e s u l t s are  a b c d e f g h i j  re-calculating  existing  computer the  the  tie -  calculation a  ( ( ( ( ( ( ( ( { (  with  (existing  additional  incorporated shortening  16  LETTER  5 J 3 | | | 5 | 3 1 3 ] ] ] |  Rather than  Comparing F i g u r e the  6 4 3  a m a t t e r of  configuration.  from  ID  well The  follows:  A =  7.174  B =  17.03  C =  10.794  D =  .025  as  new  These  quite  between matrix can  easily,  simplifing  be thus data  method i s d e t a i l e d  in  64 Which  r e s u l t e d i n the  P  =  7.174  following  +  equation:  {17.03 -  10.794) -.Q25  EQUATION  15  failure resulting P  in: =  .037  =  .963  failure RELIABILITY sun  Again,  this  - network  reliability  n e t w o r k shown i n F i g u r e  4.9  2  of the  o f one  n e t w o r k has of  issue  improved 10 %»  reduction  (construction To this  in  the  the  of the  Canyon  occasional small  entails.  and  a  failure  as another  in reliability  to decide  link  must g a i n  At i t s p r e s e n t  )  i f  and  .082  addition  i s worth  link. the  no  A  cost  benefit  extra  costs  the  costs  outweighs  resonable way  opearation. of  looking  a a perspective level  resonably  r o c k s l i d e or snowslide.  for  of  Pavillion.  service  network o p e r a t e s  allows  , a gain  Ashcroft - P a v i l l i o n  of  reliability  link) .  d e c i s i o n one  the  the  made t h r o u g h t h e  increase  level of  t o .963  was  performed  to a closing  reliability  .881  between A s h c r o f t  (cost) of  make t h i s  events,  from  This gain  b e n e f i t a n a l y s i s must be  due  a n a l y s i s shows t h a t  i s whether t h i s  construction  incurred  no  about  single link  At  (DC  Fraser  15.,  second r e l i a b i l i t y  or a g a i n  -  i s f o r the  DISCUSSION The  the  estimate  The  Using  at the  of  of  service,  what given  well except f o r estimate the  of  .881  probability  reliability,  the  the  of  figure  65 o f ,119 g i v e s service  an i n d i c a t i o n  disrapt.io.ns g i v e n  subsequent much l e s s failure  reduction  that  the  an e v e n t . With  of  failure  o f a chance o f f a i l u r e ,  a s a measure g i v e s a  potential  by  additonal  link  decreasing shuld  network  from  probability  %  experience  t h e a d d i t i o n a l l i n k and  (also using  70  will  t o ,037 t h e r e i s  the probability of  reduction  in  the  failure  ,119 t o 0 . 3 7 ) , In t h i s l i g h t , t h e  be c o n s i d e r e d .  TABLE 11 £ S M H & E Y OF RESULTS  J PROBABILITY OF | RELIABILITY OF | | NETWORK FAILURE | THE NETWORK J | ,  EXISTING  |  |  PROPOSED |  .119 .037  |  .881  J ,  J  .963  |  H a v i n g shown t h a t i n c r e a s i n g t h e r e l i a b i l i t y leads  to  desirable the  the  question,  has  increments  likely.  doubtful, required  of  higher  change  very  have  2)  to  n e t w o r k a t .963 , o n l y  (increasing r e l i a b i l i t y ) greater  a railway  than  I n some h i g h  high  consideration  the  of  level  are  .963  a r e now  any  technology  more areas,  desirable, , I t i s  , i f any g r e a t e r  reliability i s  t h a n t h e .963 •  have t o i n c l u d e increase  a  i n operating  Another  would  of  t h a n t h e .963 i t s e l f ?  reliabilities  enough? I s i t  ( making a t o t a l  of the improved  Indeed, i s a r e l i a b i l i t y  beneficial  beneficial  to increase i t s r e l i a b i l i t y ?  With t h e r e l i a b i l i t y smaller  i t been i n c r e a s e d  t o add a n a d d i t i o n a l l i n k  network i n o r d e r  i s  a size  to  be  i s that  signifigantly cf  the  enlarged  any f u r t h e r a n a l y s i s would  larger  network.  t i e - setp o s s i b i l i t y to  include  a l l  That  would  matrix  which  the  possible  66 inputs/outputs. algorithm possible One analysis Figure in  would  With  increase  have t o be used due  must  guest!on  to i n t e r i o r 13 shows how  Figure  originating  includes  t o the  and  the  validity  a computer  enormous  northern  off  the  province. line  experienced.  of  using  portions  based  number  of  of  seismic the  risk  province.  the occurrence of earthquakes are g e n e r a l l y or  off  shows  the  effects  the  coast  in  that  recommended  probabilities  source  size  14  a c c e l e r a t i o n s a r e low The  in  t i e - sets.,  t h e S t r a i g h t o f Juan de F u c a  coast.  the  this  the of the  { .05 g ) o r n o n - e x i s t a n t network  individual  link  British the  earthquakes  predicted i n these  peak areas.  i s shown i n F i g u r e  19 w h i c h  also  probabilities  failure.  The  of  decrease d r a m a t i c a l l y i n the i n t e r i o r T h i s i s due  Columbia  to the d i s t a n c e  from  which r e s u l t e d i n a l o w e r m a g n i t u d e s  the  sections of earthquake  of earthquakes  67 This  dicussion  to  increase  l i n k s based when  solely using  on  of  l i n k  from  each If  i s  has  certain  try  f i t t i n g for  to  link  many  P a v i l l i o n  use and  link  (at  North  network trains.,  a  a  in  type  this  although  of  and  changed  can  only  the  link  but  the  of  what  i t  results  may  This  involved. withstand  be  in  a a  advisable  type  C a l i f o r n i a  reasons  distance  structure  resistance.  for  the  resistance,  in  estimation  Determination  f a i l u r e ,  effect  however,  the  area,  be  structure  of  l i n k » s  been  in  plan of  are  increases the  the  using  i t  p o l i t i c a l l y ,  addition  There  link  on  instances  develop  the  has  bridges,  ,economically,  that  the  the  cannot  analysis  d i f f e r e n t .  account  of  extra  For  s u f f i c e ,  notice  54)  manipulated.  that  by  network.  is  into  adding  of  r e t r o -  since  1973  than  those  differents  here.  In  to  takes  probability  increase  procedure  presented  be  a  of  would  seismicity  based  and  of  page  parameters  may  method  situation  (on  10  determined  high  highway  view,  and  acceleration  the  the  two  r e s i s t  been  r e l a t i v e l y to  made  the  that  f a i l u r e  #  f i r s t  could  studies  Equation of  on  r e l i a b i l i t y  c r i t e r i a  source  The  man  link i t  to  l i n e  resistance. t h i r d  the  probability  the  focused  network  seismic  Refering  has  the  new  than  time)  of  be  from  an  and  more  advantageous  engineering  roadbed  point  upgrading  of  rather  route. of  from  capacity  Vancouver. terms  bridge  advantages  other  this  a  of  or  may  a  of  constructing r e l i a b i l i t y  the  the  point  CN  and  CP  under-utilized  BCR  line  This  allows  for  a v a i l a b i l i t y  and  l i n k  marketing  ,  also  by  Ashcroft of  view.  allowing between a  more  them  The to  Pavillion f l e x i b l e  scheduling  of  68 Qsing  some  determination each  link  be  made,  of  soct  in  d o l l a r  It  must  bre  returns,  each  addition  -  benefit  terms,  remembered l i n k  the  that, adds  analysis  due  less  some  advantage  of  to  of  the  and  law  less  to  r e l i a b i l i t y .  link  I  recommend  to  increase  operating Columbia be  must  added.  diminishing the  method  .  The -  r e l i a b i l i t y ,  If  resistance  addition  e f f e c t i v e further  r e t r o f i t t i n g  other  the  construction  c h a r a c t e r i s t i c s  cost  result.  the  to  events  the  further the  r e l i a b i l i t y  i s  seismic as  due  be  snow  r a i l  l i n k s  (  Ashcroft  Or  shelters  at  and  -  general  of  B r i t i s h  network this  desirable,  time  a or  to  method rock  a  P a v i l l i o n  the  u n d e r - u t i l i z a t i o n  undertaken  events.  the  f l e x i b i l i t y ,  to  should  such  of  of  of  would which  would  programme  increase of  not  a  l i n k ' s  r e t r o - f i t t i n g  sheds  ,  etc.  of  )  for  69 5  ceapfER  :  REVIEW OF THE SECOND N&RROWS BRIDGE CLQSDBE  On 12 O c t o b e r  1979 t h e t a n k e r J a p a n  Canadian  N a t i o n a l Railway  the  c e n t r e span  main  closed  until  towers.  3 March  with the  Canadian  Railway •  The  loss  disruptions,  of  which  The 738.5 metre,  1. B a r g i n g c a r g o ,  Inlet.,  passing  Canadian the 7.0  Columbia  Vancouver  alternative  coal,  Prince  million  The well  outlined  i n lost  i n Appendix  and  major  and  south  Railway •  through  Prince Rupert  thus by-  entirely.  Railway  profits.  the  service  sulphur,  methods were expensive., „The c o s t  N a t i o n a l Railway  Railway  George, t h e n  were $ 11.2 m i l l i o n  b r i d g e , $ 7.0 m i l l i o n i n e x t r a t r a n s p o r t a t i o n  contained  as  through  Re-routing t r a f f i c  Railway  was  by :  potash a c r o s s B u r r a r d  the B r i t i s h  one o f  bridge  Columbia  caused  grain,  via  These  link  mainly  2. R e - r o u t i n g t r a f f i c  3.  National  vital  were a l l e v i a t e d  7 span  the B r i t i s h  Canadian  this  with the  Narrows B r i d g e , s t r i k i n g  1980 s e v e r i n g  •s s o u t h e r n l i n k Pacific  Second  Erica collided  A complete  list  costs  to  the  to r e p a i r ,and  $  of major c l a i m s i s  C.  e x t r a volume g e n e r a t e d on t h e B r i t i s h as t h e f r e i g h t  which  below i n T a b l e 12.  was b a r g e d  Columbia  Railway  across Burrard I n l e t i s  70 TABLE i l  1  I  DIVESTED RAIL  carloads  TRAFFIC  |  empties  j metric  1  208.  |  |  15 788.  ]  tons |  rail  southbound  i |  rail  northbound  ]  barge northbound  |  7  116.  I  n. a .  1  n. a . , J  targe  |  3  767.  I  n. a. ,  |  n. a.  southbound  These northbound  figures  2 southbound  1  t r a i n s per  |  096.  day  |  |  and  2  day. in  Table  12  point  traffic in British  volume o f c a r g o  southbound  135 939. 484  out a most i n t e r e s t i n g  Columbia  , that  u n i - d i r e c t i o n a l . W h i l e t h e number o f t r a i n  equal, the  total  926.  t r a i n s per  o f the r a i l  highly  663.  d i v e r s i o n s added  These aspect  11  direction.  is  This  volume. T h i s s h o u l d  overwhelmingly  traffic  be  of  no  is, i t  movements a r e  greater  represents surprise  is  in  70.0  the  % o f the  since  the  B  C  economy i s a r e s o u r c e - b a s e d e x p o r t economy. Of  immediate  British could the  Columbia handle  capacity  number  of  southbound Prince  maximum  o f the l i n k .  train  movements  with the t o t a l and 8 -  During  increased  capacity  Vancouver  i n t h e f u t u r e , the B  sidings  of  the cr  C  link.  even  750.0 George  link  and  o f the  Vancouver)  main c o n s i d e r a t i o n the  crisis  the  northbound  of the B  C  R  presently  link  traffic  To i n c r e a s e double  and  will  tracking  Thus,  reach  the t o t a l  7  between  constructed,  f o r each d i r e c t i o n .  was  total  6  R  some  km  to  ,as  10 t r a i n s p e r day  capacity  additional  whether  R a i l w a y between P r i n c e  limit  approximately  was  t h e a d d i t i o n a l t r a f f i c . The  George  some p o i n t  concern  is at the  capacity may  be  71 necessary. Using assumed  the  freight  following  is at  km  trains  )  t r a i n  -  time  speed  of  observed.  starting 100  space  km  0  w i l l  be  given  can  c l e a r l y  seen  be  more  thus  200  and  FIGURE  km/h  a  km  upgrade  50  Given  and  t r a v e l l i n g  diagram  {  20  :  and  meeting  one  i s  Figure SPACE  1 hour  kilometre  p r i o r i t y  which in  200  relationship,  -  the  depending  with  an the  upgrades  centre on  t r a v e l l i n g  20  headways  l i n k  at  with  which  or  at  one  is  downgrade.  This  below..  TIME  DIAGRAM  NORTH  60  120  180  240  Headway  A 100 shows  t r a i n  but that  provided  t r a v e l l i n g  must  yield  with  the  every  20  300  (minutes)  northbound p r i o r i t y  speed  and  has  from  km  headways  kilometres  in  p r i o r i t y 100  to  given,  order  to  from km  km  200.  sidings allow  the  0  to  km  Figure  20  must  be  trains  to  72 p a s s . These s i d i n g s i n t r o d u c e must p u l l  o f f the mainline  Figure  a delay time  of 8 t r a i n s  a  16 h o u r day i s u s e d , t h e c a p a c i t y  If  the s i d i n g  , with  the  16  hour  that  one  train  track.  20 shows t h e c a p a c i t y  distance  in  would  be  p e r 8 hour d a y . I f 16 t r a i n s  was i n c r e a s e t o one s i d i n g day, t h e n t h e r e s u l t i n g  p e r day.  every  40  headway would  km be 2  hours. , FIGDSJ  2J 1 M M M J S  DELftY TIME  2  Example of relationship between volume and delay for a railroad line with various track configurations, (a) Mix of trains and their characteristics, (b) Volume-delay curves.  [From Prokopy  and Rubin (1975), pp. 16 and  27.] T mt Penaltiaa (Minutttl  Avaraga Running Length, ft . Clan  1 2 3 4  { This figure  2  8  FVoant of  SpMd. mi/h Starling  1.500 3.000 5.000 3.000  50 40 25 25  1 2 4 2  Stopping  Crottovtn  2 6 a 5  1 3 5 3  all Traint  13.9% 27 8% 52.9% 5.5%  i s f r o m Edward M o r l o c k , r e f e r e n c e  R e f e r e n c e No. 21 Page 209. ,  No. 21)  »  73 The by  point i s clear, i f capacity  decreasing  must be  at  closer together,  be  and  therefore  increased  showed t h e delay  day  time. This  additional this  time  dramatically  track.,  s i n c e the due  to  will  be  closer  and  (note delay  the  double  times f o r  manouvering  to  the  traffic.  0.5  h o u r s t o 0.9 George B C  increase  future,if  the  delay.  The  completion  of the  the  by-pass  distance  t h r o u g h P r i n c e G e o r g e by eliminate  the  signifigant  by-passes, w i l l  only  Pavillion  2.3  f o r one link  result,  50  km  2/3. of  and  North  train.  train  750  North  with  km  would r e s u l t to  4.2  Thus, a t  i s again  the  the  of  i t  time  for  extra  on  Vancouver.  It  link  not  the  will Bridge  totally  eliminate  facilities,  c a r r i e d out  costs  Narrows  will  or  some  increased  While t h i s w i l l  in a  hours  required  Second  delay,  Also, upgrading have t o be  time per  aschcroft - Pavillion  around  about  hours  from 4 t r a i n s with  the  this  21.  operation  delay  For  railways.  configurations  track  B mainline,  introduction  portion.  track  the  hours.  this  Delays f o r a l l w i l l with  then  from  2 hours longer  near  associated  between  for a single  from  approximately the  day  kilometres,  delay  times f o r  f i g u r e , i f demand i n c r e a s e s  40  Vancouver - P r i n c e total  of delay  r e l a t i o n s h i p i s shown i s F i g u r e  every  increases  cut  have t o be  r e l a t i o n s h i p between v a r i o u s  t o 8 t r a i n s per  sidings  in  sidings will  an  before  p o i n t , double t r a c k i n g  addressed t h i s problem  Befering per  either  reguired. Horlok  He  in effect,  would o c c u r  t r a i n s would time  some c r i t i c a l  since,  tracking  increased,  headways o r i n c r e a s i n g s p e e d s , t h e n more s i d i n g s  built,  necessary  i s t o be  due 300  will  a  to  these  km  link  also  help  74 alleviate Tete  congestion  on t h e CNB  mainline  between  Kamloops  and  Bridge i l l u s t r a t e d  most  Jaune. The  clearly  closing  o f t h e Second  the v u l n e r a b i l i t y  and t h e c o n s e g u e n c e s shipment  costs,  difficlties,  and  This experience formulate  o f any one  t o system  increased lost  Barrows link  to service  disruption  performance i n terms of i n c r e a s e d  travel  times,  general  scheduling  profits. was  f u t u r e p l a n s by  costly making  but  was  valuable  use o f t h e knowledge  in  helping  gained. ,  75 CHAPTER 6 1 POLICY/ PBOCBDOBE R E V I E f AND  Given important set  any  failure  a  link  or  node, one o f t h e most  a s p e c t s o f t h e r e c o v e r y o p e r a t i o n i s t o have  of procedures  of a s p e c i f i c longer,  of  IMPROVEMENT  t o follow  plan w i l l  when t h e s i t u a t i o n  tend  to  make  such  and t h e i r e f f e c t s g r e a t e r , t h a n  a  clear  o c c u r s . The l a c k occurrances  would o t h e r w i s e  last be t h e  case. The planning  California and  and A l a s k a e x p e r i e n c e s  coordination  agencies  i s essential  possible  plan.  The  following  in  between  the  public  effort  problems  to  represent  freguent a f t e r  t h e A l a s k a and C a l i f o r n i a  1.  Many t i m e s , d i s a s t e r overlapped developed  2.  Belief one  or  3.  There  4.  9  References  to  The  of  small  were many t i m e s  29,  best  which were most  due  :  to  to  2  9  either  separately  communicate on  o f proper a l t e r n a t e to relief  No. 1 9 , 2 7 ,  the  jurisdiction  reliance  power a v a i l a b l e failure  relief  with  conventional  systems.  was a l a c k  structures  2  gaps  proper  plans.  due  communications  implement  earthquakes  a g e n c i e s were u n a b l e  another  that  and p r i v a t e  those  relief  had  relief  showed  & 36  {  backup  )  agencies. components  on  major  the  of  total  cause  76 failure 5.  o f the s t r u c t u r e . ,  Hany  times,  available  due  funds,  ongoing  to  the  lack  monies had t o be  projects  to  of  immediate  diverted  provide  for  from relief  operations. 6.  Hany t i m e s emergency s y s t e m s h a s t o (started  These to  be l e s s  cost in  of operations,  the a b i l i t y  eventually To  operated  up) m a n u a l l y .  s i x problems allowed efficient  be  t h e emergency r e l i e f  i n terms o f r e s p o n s e and d e c r e a s e d  of officials  time,  the confidence  operations  increased  the  t h e p u b l i c had  t o handle the s i t u a t i o n . T h i s  could  lead to a possible increase i n f a t a l i t i e s .  alleviate  these  problems,  the  f o l l o w i n g changes a r e  recommended :  1.  A comprehensive, must  2.  be  developed  input  relief  be  realized.  A r a d i o system  using  all  on  agencies to  Auxiluary other A  plan  developed  a l t e r n a t i v e power common  ensure  i s  also  will  connecting  frequency constant  between a g e n c i e s  power  vital  a  plan  from a l l concerned  t h a t t h e maximum c o o r d i n a t i o n o f e f f o r t s  communication  4.  with  disaster  so  operated  3.  overall  must  be  reliable  during  a disaster.  necessary  to continue  operations. ,  for retro-fitting so  that  structures  f a i l u r e s o f minor  must  be  components  77 does  not  cause  components  would  restrainers, for  total  system  failure.  i n c l u d e such i t e m s  as  :  anchorage b o l t s f o r towers,  emergency  eguipment,  and  These bridge  brackets  approach  fill  subsidence. 5.  k  legislative  must be can  be  procedure  for  e s t a b l i s h e d beforehand implemented  without  emergency  funding  so  funding  that  undo d e l a y  or  specific  legislative authorization. 6.  Hore  automation  must be  of  developed  backup and and  constructed  minimum number o f p e r s o n n e l emergency  operations,  In  British  disaster  relief  Columbia i s The  the  are  such  floodgates, s i g n a l l i n g ,  emergency  that  required to  as  power  the  systems, etc.  responsible  Provincial  a  start  r a d i o communication,  p r o v i n c i a l agency  Department of  so  systems  for  Secretary  in  under  the  with  the  Victoria., The  responsibility  jurisdiction overall  of  local  of  disaster  municipalities  coordination  the  relief  and  responsibility  is  districts of  the  provincial  government. Funding used  i s approximately  mainly  information  for  Planning  coordinate  federal  jurisdiction  s u c h as  1.6  maintaining  programmes.  Emergency  $  The  Canada, relief the  million an  where  year  organization  federal whose  per  ministry main  federal  Armed F o r c e s ,  RCMP, and  and  is  is  public  counterpart  function  the  which  is  to  help  government  has  the Coast  Guard  78 as  well  as a s s i s t i n g  The relief  development plan  georaphical  is  and r e a d i n e s s  essential  given  of a comprehensive d i s a s t e r British  l o c a t i o n i n a zone o f h i g h  must be r e v i e w e d and employed.  i n the a f t e r m a t h o f such d i s a s t e r s .  updated  so  that  Columbia's  natural risks. new  techniques  unique This may  plan be  79  This  thesis  Engineering B r i t i s h  and  C a l i f o r n i a  application  previous  consequences  The  network  could  were  r a i l  be  explored  prediction  of  events  that  sophisticated  I n i t i a l l y , f a i l u r e  made  the A  a  based  accelerations system,  accelerations  and  was  easier,  province  the  of  various  of  was the  of  of  the  mapped inherent  probability of  these  methods  of  unacceptable  and  subjective  this  predicting  earthquake  peak  the  de  were  was  p r o b a b i l i t i e s While  fault  magnitudes  the  r e l i e f .  that  were  Alaska  desirable.  Given  predominant  some  conventional  lacked  method  as  understanding  magnitude was  in about  province  so  an  with  well  methods  that  i t  as  disaster  experience  implemented.  i s of  the  Earthquake  obtained  the  assigning  previous  much  of  gain  method of  was  Various  t h e i r  sophisticated  which  of  experiences  outlined  determined  method on  process more  L i f e l i n e  network  with  network  to  was  more  of  earthquake,  assessed.  It  of  an  associated  processes.  a  r a i l  information  characteristics  weaknesses theory  the  SUMARI  earthquake  of  problems  basic  i t s  on  valuable  administrative  with  been  an  Z  .  reviewing  physical  7  concentrating  Columbia  By  has  CHAPTEB  attemted.  precision.  Juan  system  in  assigned  Fuca  fault  western  Canada  throughout  the  province. These  estimated  predictions Jurkovics favourably  made  ,and with  accelerations by  F i t z e l l . the  various Generally  other  were  then  researchers the  researchers.  results  compared  to  including obtained  other Milne,  compared  80  Acclerations expected g  of  around  on V a n c o u v e r I s l a n d  { 98 -  174 cm/s.,Sg.  t h a n 0.05  g  ( 49  0.2 with  g  { 196 cm/s.  Sg.) c o u l d  a c c e l e r a t i o n s o f 0.1  g -  be  0.15  ) i n V a n c o u v e r and a c c e l e r a t i o n s o f l e s s  cm/s., Sg., )  in  interior  sections  of  the  ( or l i n k  resistances ) for  province. Maximum a l l o w a b l e various  structures  accelerations  were  assigned  and p r o b a b i l i t i e s o f  failure  calculated. , Beliability of  the  Southern  opportunity  reliability  manipulation analysis  this  point  criteria,  the  most  cost  best  Clinton The  estimate  of  the  link  is  the  probabilities  Fraser  Biver  effective  mathematical  of failure.  Canyon  The  was t h e most  province.  , a f t e r some c o s t  four  simply  additional  a n a l y s i s was a g a i n  a n a l y s i s and some  links  were  practical  introduced,  The  p e r f o r m e d and t h e two s i t u a i t o n s  a c o s t p o i n t o f view and t h e r e l i a b i l i t y link  )  t c construct  was t h e A s c h c r o f t  -  point  increase  in  the  reliability  went f r o m .881  increase  c o u l d be i m p o r t a n t i f an e a r t h g u a k e o c c u r s  included  (  link.  network t o .963 f o r t h e  i t  o f view  Pavillion  existing  if  network  compared. From  the  that  portions  reliability were  where  of the assigned  showed  vulnerable  siting  Mainland  p e r f o r m e d on t h e r a i l  e x i s t s f o r n e t w o r k enhancement. ,  This  At  a n a l y s i s was t h e n  precipitates that  proposed  network.  land/rock/snowslides.,  the Ashcroft  - Pavillion  w e l l a s a method o f r e t r o - f i t t i n g  link  be  f o r the  This  9  %  , especially  Recommendations constructed  be i n v e s t i g a t e d . ,  as  81  The the  review  need  r e l i e f  t o t a l l y  study  to  comes  objective  emergency  before, has  capable  vulnerable  The  the  greater  agencies  This  danger  f o r  of  service from is  coordination during,  showed of  that  and  disrutions. systems  minimize  the  procedures  between  after  many  resisting  natural to  operating  a  public  physical  not  f a c t ,  of  private  systems  are  not  events  and  are  probably  withstanding  e f f e c t s  and  disaster.  catastrophic In  emphasized  such  the these  greatest forces.  disruptions.  82 CHAPTER  8  BECOHMENDATIOHS AND  i CONCLOSIONS  Besearch of t h i s nature i s r a r e l y complete i n t h a t answers a l l of the gained i n  1.  the  questions  study  the  The  posed.  following  feasability  Pavillion order  the  flexibility  the  network  method  of  which  key  may  u p d a t e d , and  4.  A  be  so  in  costs  this link  Southern  those  a  of  will  Mainland  bridges  need be  procedured  utilities  alternate  system  of of  of  in  the  structural  established  and  be  revised  plan and  and  between  the  governmental  be  power  developed  source so  that  between a l l c o n c e r n e d i s p o s s i b l e . ,  account the  that  studied  established.  A s e r i e s of s t u d i e s into  be  -  inspected.,  other  communications  5.  have  non-conventional  contact  Aschcroft  thus r e l i a b i l i t y  that a coordination  and  a g e n c i e s be  the  of  (strengthening)  bridges  the  •  Emergency o p e r a t i n g  railways  and  identifying  retrofitting those  should  construction  of  information  actual presents  enhance  A  the  recommendations:  ) link  The  rail  on  constructing  construction.  system  3.  of  the  determine the  B r i t i s h Columbia 2.,  are  ( Clinton  to  Based  i s never  their  of flow  three  upgrading  other and  capacity proposed  demands t a k e rail  i n c l u s i o n i n the  links rail  83  system  be  considered.  Some f u r t h e r t o p i c s f o r p o s s i b l e s t u d y  1.  The d e v e l o p m e n t entire  rail  include:  o f a computer  system  b a s e d model f o r t h e  t o show a r e a s o f h i g h  failure  potential., 2.  The d e v e l o p m e n t Earthguake Columbia  3.  of s p e c i f i c  Engineering  criteria  for Lifeline  as i t a p p l i e s  to  British  .,  A reliability  and c o s t  a n a l y s i s on t h e e f f e c t s o f  construction  and e a r t h g u a k e r e s i s t a n t s t r u c t u r e s  s u c h as l a n d s l i d e s h e l t e r s , e t c . 4.  The  development  programme the  The rather  field new  especially  true  Lifeline more  disruptions  physicla  geography  lifeline  cooridors,  thesis  British  will  Columbia  .,  Earthguake  research  in British  service  this  vulnerable  most a c t i v e e a r t h g u a k e  of  and  for  of a c o s t - e f f e c t i v e  are  which  needs  Columbia quite places  a  structures located  Engineering  is  still  t o be p e r f o r m e d . T h i s i s the  Given  heavy  potential  British  reliance  for  Columbia's on  a  e s p e c i a l l y i n t h e i n t e r i o r . , I t i s hoped generate  in  zones.  where  high.  retrofitting  more i n t e r e s t i n t h i s t o p i c  few that  within  84 BIBLIOGRAPHY B a i n , Lee S t a t i s t i c a l T h e o r y Of B e l i a b i l i t y M a r c e l D e c k e r I n c Hew York 1978  And  B a r l o w , R i c h a r d E. S t a t i s t i c a l A n a l y s i s Of B e l i a b i l i t y Models Holt,  R i n e h a r d t , & Winston  New  Life  And  Testing  Life  York C i t y ,  N Y  Testing 1975  B e n j a m i n , J a c k / C o r n e l l , C. A l l i n P r o b a b i l i t y , S t a t i s t i c s , - And D e c i s i o n F o r -EngineersMc Graw H i l l S Co. T o r o n t o (1970) B r i t z , K. I . / E d e l s t e i n , P. / Oppenheim, I . J . Measurement Of Earthguake Performance Of T r a n s p o r t a t i o n Systems A S C E P r o c . Tech. Council On Lifeline Earthquake E n g i n e e r i n g ( Aug 30,1977) Bury, K a r l S t a t i s t i c a l Models I n A p p l i e d S c i e n c e J o h n W i l e y £ Sons T o r o n t o (1975) C o u r i n n o , John ( 0. S, Army Aberdeen P r o v i n g Grounds) B e l i a b i l i t y S M a i n t a i n a b i l i t y R e s e a r c h Needs I n D e s i g n C o n t r o l 6 R i s k Management Failure  Prevention  And  Beliability  1975  P g s . 26 9-283  Donovan, N e v i l l e C., A S t a t i s t i c a l E v a l u a t i o n Of S t r o n g M o t i o n D a t a 5th International Earthquake Engineering Conference Rome ( 1975) Duke, C. H. / E u g u c h i , B. T. / C a m p b e l l , K. W. The Use Of Beliability In Lifeline Earthguake Engineering A S C E Conf. Prob. Mechanics £ S t r u c t u r a l R e l i a b i l i t y Jan 1979 T u c s o n Duke, C M . / Moran, D. F. Guidelines For Evolution Of Lifeline Earthquake E n g i n e e r i n g P r o c e e d i n g s 0. S. N a t i o n a l C o n f . e a r t h q u a k e E n g i n e e r i n g Ann A r b o r 7 5 1  F i t z e l l , T r e v o r P. S e i s m i c B i s k I n The Lower M a i n l a n d R e g i o n Canada M. Sc. T h e s i s U n i v e r s i t y Of London C i v i l Dept. 1978  Of  Western  Engineering  85 G a t e s , J.,H. C a l i f o r n i a S Seismis Design C r i t e r i a For Bridges ASCI? Journal Structural Division V o l . , 102 12 { Dec 1976) George, «. / L y l e , B. E . The Alaska Earthquake Beconstructipn By E n g i n e e r s . Methods And A c c o m p l i s m e n t s 541 U. S. G e o l o g i c a l S u r v e y P r o f . Paper No. Pgs.81-89 G r e e n , A. B e l i a f c i l i t y Technology Wiley Interscience Toronto  Ho.  Corps (  Of 1966)  1972  Grantz/ P l a f k e r / Kachadoorian A l a s k a S Good F r i d a y E a r t h q u a k e U.  S. G e o l o g i c a l S u r v e y C i r c u l a r No.  491  {  1964)  Hansen, W. , B.,/ E c k e l , E- B. Alaska Earthquake Summary And D e s c r i p t i o n Of E a r t h q u a k e , I t s S e t t i n g And E f f e c t s 0.  S. G e l o g i c a l  Survey P r o f .  The  P a p e r No.,541 Pgs.,1-37  Hawkins, N. H. / C r o s s o n , 8.,S. C a u s e s . C h a r a c t e r i s t i c s , And E f f e c t s Of Puget Sound Earthquakes 0. . S. N a t i o n a l C o n f . On E a r t h g u a k e E n g i n e e r i n g 1975, P r o c e e d i n g s Pgs. 104-112 H o u s n e r , G. / » . , / J e n n i n g s , P. C. The San F e r n a n d o E a r t h q u a k e , C a l i f o r n i a I n t e r . J o u r n a l Of E a r t h q u a k e E n g i n e e r i n g ( J u l y Sept 1972) Pgs.5-31 J u r k o v i c s , Aridrejs Method For Simulating S Representing Strong Motion Ground Data 0*. B. C.  Department  o f G e o p h y s i c s H.  Kachadoorian, 8. E f f e c t s Of The E a r t h q u a k e Of March A l a s k a Highway System 0. S. G e o l o g i c a l S u r v e y P r o f . P a p e r  Sc. T h e s i s  27  M  1964  No.,545- C  Kozak, J . J . Maintaining Transportation L i f e l i n e s A S C E Proceedings Tech. , C o u n c i l E a r t h q u a k e E n g i n e e r i n g ( Aug 30 1977) M o r l o c k , Edward L. I n t r o d u c t i o n To T r a n s p o r t a t i o n Mc Graw H i l l C c . New York C i t y  Engineering 1978  On  1978  On  The  (1968)  Lifeline  S Planning  86 He C u l l o c h , D. S. / B o n i l l a , E f f e c t s Of The E a r t h q u a k e Of Alaska B a i l r p a d  13. G. March  0.  No.545 D  S,  G e o l o g i c a l P r o f . Paper  28  x  1964  On  The  (1970)  Meehan, J . , F. The San F e r n a n d o E a r t h q u a k e z_ Damage To T r a n s p o r t a t i o n Systems 0. .,' S. Geological Survey P r o f . P a p e r No. ,733 (1971) P g s . 241-244 M e n d e n h a l l , W . , / S c h e a f l e r , 8. M a t h e m a t i c a l S t a t i s t i c s With A p p l i c a t i o n s Duxbury P r e s s N. S c i t u a t e , Mass. (1973) M i l n e , W. G. E a r t h q u a k e E p i c e n t r e s And S t r a i n R e l e a s e I n C a n a d a Canada J o u r n a l Of E a r t h S c i e n c e s V o l . 4 No.5 ( Oct 1965) Pgs. 797-814 M i l n e , W. G., D i s t r i b u t i o n Of Earthguake B i s k I n Canada Seismological S o c i e t y Of A m e r i c a B u l l e t i n 2 ( A p r i l 1969 ) P g s . 729-754 M i l n e , R. G. S e i s m o l o g y C f W e s t e r n Canada C a n a d i a n J o u r n a l Of E a r t h S c i e n c e s J u l y 1978) Pgs. ,1170-1193  Vol.,15  V o l . 59  No.  7  M i s r a , K. B. An Algorithm For The Beliability Evaluation Redundant Net. I E E E T r a n s a c t i o n s B-19 No. 4 November 1973  No.  (  Of  Murphey, L e o n a r d ( C o o r d i n a t o r ) San F e r n a n d o E a r t h g u a k e Of 9 F e b r u a r y 1971 0. S. Department Of Commerce N 0 A A (1973) O a k e s h o t t , Gordon San F e r n a n d o E a r t h q u a k e Of 9 F e b r u a r y 1971 California D i v i s i o n Of M i n e s And G e o l o g y B u l l e t i n 196  No.  Oppenheim, I r v i n g J . V u l n e r a b i l i t y Of T r a n s p o r t a t i o n s And Water Systems To S e i s m i c Hazards A S C E P r o c e e d i n g s Tech., C o u n c i l On Lifeline Earthquake Engineering P a r n o u s s i s , George S e i s m i c B e l i a b i l i t y Of L i f e l i n e Networks M I T C i v i l E n g i n e e r i n g Dept. S e i s m i c D e s i g n A n a l y s i s B e p o r t No. 15  Decision  87 Feckover / Kerr T r e a t m e n t Of Bock S l o £ e s On T r a n s p o r t a t i o n Eput.es 2 9 t h C a n a d i a n G e o t e c h n i c a l C o n f . V a n c o u v e r , B. C. Pond, S. ..P. Performance Of Bridges During The Earthguake Journal Prestressed Concrete Institute 1972) Pgs. 65-75 B i c e , E. F. Alaska Earthguake A S C E C i v i l Engineering Pgs. ,52-56  V o l . 34  No.  San (  5  1974  Fernando July-  { may  Aug  1964)  Shah, H. C. / B e n j a m i n J . B. l i f e l i n e S e i s m i c C r i t e r i a And B i s k ; S t a t e Of The Art Report A S C E Proceeding Tech. C o u n c i l L i f e l i n e Earthguake Engineering S i n g h , Chanan / B i l l i n t o n , Boy System R e l i a b i l i t y - M o d e l l i n g And H u t c h i s o n L t s . London 1977  Evaluation  S t a t i s t i c s Canada R a i l w a y T r a n s p o r t --Part 3 j_ B a i l F r e i g h t B e p o r t No. 52-201 O t t a w a , O n t a r i o 1978 S t a t i s t i c s Canada Railway Transport^ Part 4 Operating Statistics B e p o r t No.,52-210 O t t a w a , O n t a r i o 1978 T a l e b - Agha, G h i a t h S e i s m i c B i s k A n a l y s i s Of M.  I . T.  Seismic  Design  6  Traffic  Networks D e c i s i o n A n a l y s i s Beport  No.22  T a l e b - Agha , G h i a t h S e i s m i c R i s k A n a l y s i s Of L i f e l i n e N e t w o r k s M. I . T. S e i s m i c D e s i g n D e c i s i o n A n a l y s i s R e p o r t No.24 Whitman/ C o r n e l l / T a l e b - a g h a A n a l y s i s Of E a r t h g u a k e R i s k F o r L i f e l i n e S y s t e m s Proceedings 0. S. N a t i o n a l C o n f e r e n c e Of E a r t h g u a k e Engineeringann Arbor 1975 Whitman/ B i g g s / B r e n n a n / C o r n e l l / d e S e i s m i c Design D e c i s i o n A n a l y s i s A S C E J o r n a l S t r u c t u r a l Div.  N e u v i l l e / Vanmarke  Vol.„101 S t 5 Hay  1975  Whitman, H. V. R i s k Based S e i s m i c D e s i g n C r i t e r i a F o r L i f e l i n e s A S C E National Meeting Los Angeles, California P r e p r i n t No. 2148 1974  88 APPENDICIES  APPENDIX A 2 TOTAL COST CALCULATIONS  Morlok rail  ( R e f e r e n c e No. .21 Page 401  transport  2.5 - $4.6  a r e from  million  us$ 4.0  - $ 7.0  per kilometre.  c$3.3  railway 3.5  m i l l i o n / km.  i n the i n t e r i o r  million Half  for  - $ 6.0  will  that  be used f o r new  f i g u r e o r c$1.75  land,  an e x i s t i n g r o a d b e d Land  acre  interior rail  link  acguasition  costs.  right-of-way  Thus l a n d  already  acguasition  links  i s that  figure of  a  a f i g u r e o f c$  be used  as t h e c o s t  o r remnants t h e r e o f . has t h e s i t e  This  surveyed,  bridges.  Again these c o s t s  are based  31 metre  per running  km  distances  and t h e r e s u l t s a r e summarized  000 on  ( 100 f o o t )  c o s t s a r e $ 12 300 / l i n e a r km to the l i n k  is  cleared  a r e b a s e d on a f i g u r e o f $ 10  are 3 hectares  These f i g u r e s a r e a p p l i e d proposed  will  Using the standard  there  o r us$  o r exchange o f  costs, this  of the province  of s o r t s , and some  costs  per mile  construction  million  o r $ 4 100 p e r h e c t a r e . land  labour  costs for  construction.  upgrading e x i s t i n g f a c i l i t i e s  b e c a u s e an abandoned  per  Since  sections  million  that  Adding the r a t e  15 % and an a d d i t i o n a l 15 % f o r h i g h e r is  ) suggest  of  track.  of t r a c k . , of the  i n Table  5.  four  89 APPENDIX  The  B X  following  constants  i s  a  b  2 b  =  l i s t i n g  b  1  A  CALCULATION  b  REFERENCE  |  of  the  and c  ,  THE  CONSTANT'S  various  to  be  B  values  used  I  c  1 1.32  I  25  I  !  0 . 6 7 | 1.60  ]  25  !  !  3  ( a  e  1  LOCATION  SAN FERNANDO  • c s  )  B  |  B  |  2  1  1 1  |  1080 | 0.5  J  1300  B  3  i  ]  U. S . A .  ESTEVA  |  WESTERN U.S.A.  ,  MILNE  |  BRITISH COLUHBI  1 | 0 . 6 9 | 1.64  |  WESTERN J  1 1230 | 0.8  o  J FOR USE | IN E Q U .  | AJ  1  o  !  i  o  | J  1 25  |  1.0  1  |  1.7  1.15 |  1.0  | 2000 | 0 . 8  BOSTON  1 1.183)  b  1,1m  m  -b  3  2 A  A  b  =  (1.lie  e  b Equation  A  B s  r  )  1  s  =  E  b  1  e  m 2  ( a s  -b  3 •  c  )  ]  !  2.0  CALIF.  COMMENTS  i  |  SOUTHERN  Equation  :  -b  m  2  DONOVAN  |  equation  the  |  TALEB-AGHA  the  in  DONOVAN  PARNOUSSISI  for  3  1  s  OF  ! FOR USE IN EQU.  | B|  90  Since  Hilne  and T a l e b  attenuation eguation four  they  will  =  1402., b  1  By  approximation Of  = 0.69  b  2  using  these  course,  =  are :  1.65  these constants  25  resonably  faults  the majority of the earth  which may be e x p e r i e n c e d .  movements a r e i n c o n j u n c t i o n  sources. ,  a  a r e b a s e d on t h o s e  w e s t e r n C a n a d a . T h i s does n o t p r e c l u d e  these  =  good  peak a c c e l e r a t i o n s c a n be o b t a i n e d .  have, i n t h e past, generated  movement  c  3  values f o r the constants,  o f expected  of the basic  not be u s e d . Thus u s i n g t h e o t h e r  and o b t a i n i n g a n a v e r a g e t h e v a l u e s  b  in  - Agha use a l t e r a t i o n s  a new s o u r c e  This i s especially with  movements  which  movements of true  from  earth when known  91 APPENDIX  Canadian Canyon  Creek  Imperial  O i l  Ltd,  Canadian  Wheat  C.  Foods  a r t i c l e 1980.  Columbia  O f f i c e r  for  written (  page  A17  by )  Bailway  Board  was  $  25.2  $  2.9  Million  $  1.7  M i l l i o n  1  1.2  M i l l i o n  $  1. 1  Million  M i l l i o n  $ 150  000.  $ 116  751. 926.  $ 43 2 0 0 . ,  Corp. , Hydro  CLAIMS  $ 61  Ltd.  Copper  information  Products Pool  Northern  Harbours  B r i t i s h  OF  Board  National  Bethlehem  Belations  Forest Wheat  P.  LIST  Bailway  Saskatchewan  S.  £  National  Burlington  This  C.  Auth.  obtained  the  British  Larry  S t i l l  $ 2  form  Hugh  Columbia in  the  200.  Armstrong  Bailway  Vancouver  and Sun  on  ,  Public for 3  an  A p r i l  92 APPENDIX JO.. ,x  This Agha  DETAILED T I E - SET BE DOC TIP N  t i e - set reduction 41 P a g e s  ( B e f e r e n c e No.  redundancies.  The b a s i c  13 13 13 13 14 14 14 14  10 10 10 10 11 11 11 11  12 -  SSP  8 8 9 9 8 8 9 9  7 7 6 5 7 7 6 5  JJ 6 5 1 4 3 i 4 3 1 1 6 5 4 3 1 4 3 I 1  2.  t  Check of other the  8 8 9 9 13 13 13 13  7 7 6 5 10 10 10 10  6 5 4 3 4 3 8 8 9 9  | j  |  7 6 5 I 7 4 3 I 6 4 3 ! j 5  delete  those  Canyon i s :  | 13 10 8 7 6 1 13 10 8 7 4 ] 13 10 9 6 4 | 13 10 9 5 2 1 14 11 8 7 6 | 14 11 8 7 4 | 14 11 9 6 4 | 14 11 9 5 2  1 | I 4. , 1 I 1 I 1  12 "  29  13 13 13 13 8 8 9 9  10 10 10 10 7 7 6 5  14 14 14 14 11 11 1 1 11  p a i r s must be l i n k e d  redundancies.  In  matracies  f r o m Kamloops a r e p a i r e d  matracies  from  Kamloops J u n c t i o n  existing  Z. 29  t o see i f t h e o b j e c t i v e r e g u i r e s  input/output  -  T I E - SETS  J9  —  by T a l e b  22 ) and e l i m i n a t e s  J 2 2_- _ 11 11 1 1 11 14 14 14 14  was d e v e l o p e d  t i e - s e t f o r the Fraser  COMPONENT JJ  procedure  this  together  are paired  8 8 9 9 6 4 4 2  7 7 6 5 5 3 3  that  5 2 3 2 3 2 5 2 3 2 3 2  6 5 2 4 3 2 4 3 2 2 2 2 2  the t i e -  in parallel. case and  If  t h e two the  together.,  two  sets so, inout input  Thus  , we  y i e l d s the 11  | f | | | i | |  o b t a i n two  -  19 8 11  13 10 13 10 13 10 13 10 14 11 14 11 14 11 14 11  Next, f i n d any  of the  8 8 9 9 8 8 9 9  7 7 6 5 7 7 6 5  - 29  in  vived, the To Matrix  6 5 4 3 4 3  the  input / output  t i e - set w i l l  A,  a t a time.  A to i t . ( i n other rows o f  eliminated  by  deleting  29  6 5 4 3 4 3 8 8 9 9  7 6 5 7 3 6 4 3 5  B  t h a t the  survival  pairs  o f the  must  be  parallel  linked  links  sur-  The  B  will  first  B and  words, a d d i n g A).  step  Then  "double"  be  "crossed"  will  be  shown a s  a s s i g n i n g each the f i r s t row  row  Thus  an  row  of  redundanceies  entries..  with  the  of  Matrix are first  is :  \ Matrix After  each  eliminated  the  new  Matrix  Matrix  12 -  met..  This e n t a i l s taking Matrix  B to a i l the  The  This  the o b j e c t i v e , t h a t i s ,  output  t h a t i f any  t h i s the  iteration  7 7 6 5 10 10 10 10  p a i r s such  satisfy  input /  o b j e c t i v e would be  row  6  Matrix  A  p a r a l l e l so  one  - 19  118 11 8 11 9 11 9 14 13 14 13 14 13 14 .13  accomplish  example. Matrix  12  6 5 4 3 * 3  the t i e - s e t s of these together  t i e - set matracies.  following :  Matrix  of  i n t e r m e d i a t e SSP  matrix  B |  row  has  remainder i s made up  XX been  | 13 crossed  i s saved of t h e  1 0 8 7 6 5 ) and  the  t o form the  remainders  of  redundancies  final each  matrix.  (  crossing  94 operation).  This  been c h e c k e d  f o r redundancies  the  sets  tie  -  i s after  in  each  this  o f these saved  between t h e m s e l v e s . c a s e a r e unique  simply the exact remainders  remaineders  the  Since final  o f t h e i n t e r m e d i a t e SSP  have  a l l  of  matrix i s  tie -  sets.  Thus : reduced  matrix f o r e x i s t i n g  | 13 | 13 J 13 I 13 | 14 | 14 | 14 I 14  PBOPOS BD  7 7 6 5 7 7 6 5  6 5 J 4 3 | 3 | I 6 5 J 4 3 | 4 3 | |  NETWOEK  So, reduced  10 8 10 8 10 9 10 9 11 8 11 8 11 9 119  network  from  a  start  them t o one  of  single  four  matracies t h i s  m a t r i x i n which  procedure  the a n a l y s i s  can  has be  performed.  that  The  analysis  8  additional  configuration reliability  Note t h o s e on  is  t h e same f o r t h e p r o p o s e d  tie  resulting  analysis.  -  sets  are  included  i n an a d d i t i o n a l two  Those a d d i t i o n a l  network in  the  basic  t i e - sets  i n the  t i e - s e t s are :  |  11  10  15  1 2  J  <-->  | 11  10  15  1  I  |  14  13  15  1 2  |  <—>  | 14  13  15  1  J  |  14  13 15  1 2  J  <—>  | 14  11  15  1  J  |  14  11  1 2  J  <—>  | 14  11  10-15  10  that the t i e - sets the l e f t  and  can  on t h e r i g h t  t h u s be  except  1 2 \  are simply s u b s e t s of  eliminated.  This  leave  four  95 tie  -  then  the  reduced  sets  t o be  assigned  t o each  r e d u c t i o n i s again performed  matrix  This  final  10 10 10 10 11 11 11 11 13 11  8 7 7 8 9 6 9 5 7 8 7 8 9 6 9 5 15 10 15  reduced  t o 4 ) above  results in  t i e - s e t matrix f o r the proposed 13 13 13 13 14 14 14 14 14 14  (1  network  the  following  :  6 5 4 3 3 6 5 4 3 4 3 1 matrix i s the  same as F i g u r e  and  18.  96 APPENDIX  The  DETAILED B E L I A B I L I T Y CALCULATIONS  calculation  Parallel  o f the r e l i a b i l i t y  uses t h e f o l l o w i n g  B = 1 - { 1 - A where t h e s e v a l u e s calculation The  = =  =  A  described  follows.  calculation  of  (.930) (.930) (.920) (.920) (.930) (.930) (.920) (.920) (.999) (.998)  the c a l c u l a t i o n  commence.  this  were  eguation:  ( B - C ) - D }  o f them  (. 998) (.998) {. 998) (.998) {. 998) (.998) (.998) (.998) (. 999) (.998) (.999) (.998) (.999) (.998) (. 999) (.998) (.999) (.998) (.999) (.998)  Now  the  +  System i n  the  on  page  lettered  .  The  t i e - sets  detailed  i s outlined  • •  below a b c d e f g h i j  basic  of the Series  A  existing  is  (.950) (.920) (.950) (.740) (.920) (.740) (.920) (.950)=(. 920) ( . 9 5 0 H .740) (.920) (. 74 0) (.920)  (.920) (.740)  (.920)  (. 740) (.740)  (.999) (.995) of the  A,  B,  C  =  . 745 .472 . 581 .581 = — .746 — .482 .467 .853 = = .991 . 984  ,  S  t h e sum o f a l l o f t h e l e t t e r e d  network  D  values  can  t i e - s e t s . For  t h i s i s a t o h and f o r t h e p r o p o s e d n e t w o r k  i s a t o i . Thus :  (existing)  =  (. 745) • (. 472) + (. 581) • (. 853) • + (.746)*(.482) M - 4 6 7 ) +(.853) = 5. 199  for  t h e p r o p o s e d network t h i s A (proposed To  :  ) = 5.199 • (.941) (.984) = 7. 174  determine D simply  groups t o g e t h e r .  i s just  multiply  F o r the e x i s t i n g  the  network :  lettered  tie  set  97 D (existing)  =  (.745) (.472) (.581) (.853)  (,746) (.482) (.467) (.853) = .024  The  are in  D value f o r the proposed  D  (proposed)  To  calculate  multiplied the t a b l e  exist  in  and  .024  by a n o t h e r  )  group.  l i n k s o f one - t i e s e t  T h i s h a s been done and i s shown  b e l o w . However, t h e r e a r e  some  redundacies  and must be s u b t r a c t e d f r o m  the c o r r e c t i o n  factor  accounted  for  C. T h i s c o r r e c t i o n  t h e number o f t i m e s they  they  factor  by  have been  may h a v e been c o u n t e d  which  the t o t a l o f B  the i n d i v i d u a l l i n k p r o b a b i l i t i e s multiplied  counted., (although here over.  (-941) (.984) = .025  B, a l l t h e i n d i v i d u a l  this table  by e m p l o y i n g simply  =  network i s s i m p l y :  is  tmeselves "double"  m many  times  98  a  1  .352J  J a| 1 hi a b 1  d|  a  a  -  I  J  d  e  1  f  1  g  h  1  I  .2271  . 220 1  -495|  .433J  .2801 w271l  .495|  -5751  .5721  -410J  .7271  .845J  .839|  -  i  b 3 1 c  |  a i  1 ,6361  -  e |  1 .3601  -  .3481  . 400| .4671 .464|  .348) .636) .739) .7341  b g i c  g |  a  g | e g I  1 h| a h  1 b h 1 c  h 1  a  h i g h l f  1 11 a i  i b i 1 c i | a i i e i I f i 1 g i 1 h i |  jl  a  j  1 b  For group  For  is  1  c  j  1  the e x i s t i n g  * j  factor the  1  e  j  f g 1  1 f  .4771  .4741  1 .3531 .463J  .460J  1 ^225|  -  -  .410J  |  h | g h |  j  1 g  j i  h  j  .8451 -  1 i  .8391  1 .975J 3 1  -  1  network t h e v a l u e f o r B uses t h e l e t t e r e d  of t i e - s e t s from  correction  using  j  .738 | .7331  .3521  f i e f 1  1  1  .400j  a  1 91 a g i  j  ,348| ,635|  f I  f la f  1  .3591  1 b f 1 c  1  i  .556J  b € 1 c e l d  1 ej a e  1  .4331 .635| .2701  b c  1 cj a c 1  c  b  a t o h and i t s v a l u e i s 11.613  C o f 7.271  with  a  .  proposed network t h e v a l u e f o r B i s o b t a i n e d from  the l e t t e r e d  group  of t i e- sets  17.03 w i t h a c o r r e c t i o n  factor  from a t o j  C o f 10.794  .  and i t s v a l u e  

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