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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 RELIABILITY OF THE BAIL NETSOBK OF BBITISH COLUMBIA GIVEN CATASTBOPHIC EVEBTS by JOSEPH A. GLOWITZ B. Sc. . C i v i l E n g i n e e r i n g T u f t s U n i v e r s i t y 1978 Bedford , Massachusetts A THESIS SUBMITTED IH PARTIAL FULFILLMENT OF THE BEQU1BEMENTS FOB THE DEGBEE OF MASTEB OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES { Department Of C i v i l E n g i n e e r i n g ) 8e accept t h i s t h e s i s as conforming to the r e q u i r e d standard. THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 19 80 © Joseph Andrew Gl o w i t z , 1980 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l l f i l m e n t of the requirements of an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study.„ I f u r t h e r agree t h a t permission f o r ext e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.. Department of C i v i l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, B r i t i s h Columbia V61 1H5 ABSTRACT The t r a n s p o r t a t i o n network of B r i t i s h Columbia i s s u s c e p t a b l e t o s e r v i c e d i s r u p t i o n s due to c a t a s t r o p h i c events such as : earthquakes, r o c k s l i d e s , snowslides ,and f l o o d s . Such s e r v i c e d i r u p t i o n s would be i n the form of c l o s u r e s of l i n k s between p o p u l a t i o n c e n t r e s . A method of a s s i g n i n g p r o b a b i l i t i e s of f a i l u r e t o network l i n k s was used to undertake a r e l i a b i l i t y a n a l y s i s of the r a i l network of the Southern Bainland of B r i t i s h Columbia , T h i s r e l i a b i l i t y e stimate i s then used t o recommend changes i n the p h y s i c a l makeup of the network i n order to enhance i t ' s f l e x i b i l i t y ( redundancy ). A c o s t a n a l y s i s o f these proposed l i n k s was performed i n order to i d e n t i f y the most c o s t - e f f e c t i v e l i n k s . The r e l i a b i l i t y analyswas i s again performed t o show the improvement gained by these p h y s i c a l changes. A l s o i n c l u d e d was an a n a l y s i s o f the Second Narrows H a i l Bridge c l o s u r e ( From 12 October 1979 to 3 March 1980 ) and the consequences on the r a i l network of the province, as well as a review of emergency o p e r a t i n g procedures and recommendations f o r f u r t h e r study. i i i . TABLE OF CONTENTS r r — — • • :— T 1 ]SECTION 1 CONTENTS I PAGE, |__ j. . j. 1 |A. | L i s t of F i g u r e s and I l l u s t r a t i o n s | i v . ] | f i . | L i s t o f Tables I v. | |C. |Acknowledgement ) v i . J J Chapter 1. | I n t r o d u c t i o n I 1. J IChapter 2. 1 Past e f f e c t s of c a t a s t r o p h i c events: J8., | 12.t | Alaska I 10. | 12.2 | C a l i f o r n i a I 11. I JChapter 3 I Review of b a s i c p r o b a b i l i t y | | 1 I theory 1 19. I j . — — + ^ IChapter 4 ] R e l i a b i l i t y Theory S Network A n a l y s i s 125. J 14.1 1 Network C h a r a c t e r i s t i c s 126, | 14.2 J Network Theory 1 38. 1 14.3 1 L i n k P r o b a b i l i t y Theory |42. | |4.4 1 Attenuation P r e d i c t i o n |45. | J4.5 I Link P r o b a b i l i t y Assignment 153. j J4.6 | T i e - Set Reduction ,57. 1 j4.7 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 1 59. | 14.8 | R e l i a b i l i t y A n a l y s i s : Proposed Network J61...J J4.9 | D i s c u s s i o n 164. | IChapter 5 JBeview of Second Narrows Bridge C l o s u r e J70- | IChapter 6 | P o l i c y / Procedure review and improvement 176. J IChapter 7 1 Summary 180. | f _ + _ ._ _ __ +—-—i IChapter 8 jBecommendations and C o n c l u s i o n | 83. | > + + 1 |D. 1 B i b l i o g r a p h y J84. | r — + — — + ^ IE. |Appendicies 188. | 1 + — • + -I |F. i H i s t o r i c a l Biography 199. J I i . . . — i j i v . As m ' * ^ l i s t of F i a u r e s & I l l u s t r a t i o n s F i g u r e 1 I L o c a t i o n a l Haps | 9 F i g u r e 2 I Recurrence graph j 24 F i g u r e 3 i The r a i l network of B. C. J 28 i F i g u r e 4 J Schematic B a i l Network J 30 F i g u r e 5 | The network of the Southern Mainland } 33 F i g u r e 6 | Numbered Schematic Network | 35 F i g u r e 7 I A general network | 39 F i g u r e 8 I Any input r e a c h i n g any output j 40 F i g u r e 9 | Present network c o n n e c t i v i t y matrix | 41 F i g u r e 10 | Proposed network c o n n e c t i v i t y matrix J 41 F i g u r e 11 | S u b j e c t i v e p r o b a b i l i t y assignment l 44 F i g u r e 12 J Earthquakes i n B. C. j 48 F i g u r e 13 I B e g i o n a l f a u l t system | 49 F i g u r e 14 | Expected peak a c c e l e r a t i o n s | 52 Figure 15 I F r a s e r Canyon r a i l schematic j 58 F i g u r e 16 | Seduced •'( e x i s t i n g ) t i e - s e t matrix j 59 F i g u r e 17 | A d d i t i o n a l ( p o s s i b l e ) t i e - s e t s | 62 F i g u r e 18 | Beduced ( proposed ) t i e - set matrix | 63 Figure 19 | Recommended network w. l i n k p r o b a b i l i t i e s ! 66 F i g u r e 20 J Space - Time diagram \ 72 F i g u r e 21 J Average delay times | 73 S i 1 - L i s t of Tables | Table 1 I B e l i a b i l i t y s e r v i c e l e v e l s | 5 I | Table 2 I L i s t of A b b r e v i a t i o n s \ 29 ] Table 3 I Summary of B a i l Network C h a r a c t e r i s t i c s | 31 ] Table 4 I L i n k / Node r e p r e s e n t a t i o n of the network | 34 | Table 4 A I L i n k - Node r e p r e s e n t a t i o n (proposed network| 35 I Table 5 I Cost e s t i m a t i o n s f o r proposed l i n k s | 37 I Table 6 I S u b j e c t i v e p r o b a b i l i t y assignment | 43 | Table 7 Earthquake c h a r a c t e r i s t i c s o f B.,C., J 47 I Table 8 P r e d i c t e d a c c e l e r a t i o n s j 51 | Table 9 I Link r e s i s t a n c e s | 55 | Table 10 Link ( f a i l u r e ) p r o b a b i l i t i e s j 56 J Table 1 1 Summary cf R e s u l t s ] 65 I Table 12 D i v e r t e d B a i l T r a f f i c j 71 v i . C. i ACKNQWLEDSEMENT I would l i k e t o thank P r o f e s s o r Frank Navin f o r h i s i d e a s i n f o r m u l a t i n g t h i s t h e s i s t o p i c and h i s help with the work. P r o f e s s o r K a r l Bury f o r h i s help with the s t a t i s t i c a l theory, Abdulla Jamal f o r h i s a s s i s t a n c e i n the l i t e r a t u r e search and e a r l y i n v e s t i g a t i o n , the T r a n s p o r t a t i o n Development Agency f o r t h e i r p a r t i a l funding of the p r o j e c t , and the engineers and s t a f f o f the B r i t i s h Columbia Railway , Canadian N a t i o n a l Railway and Canadian P a c i f i c Railway f o r t h e i r a i d i n p r o v i d i n g i n f o r m a t i o n to me. 1 CHAPTER ONE Z INTRODUCTION B r i t i s h Columbia i s s i t u a t e d i n an area of a c t i v e earthquake f a u l t s which may a t any time, r e l e a s e s t r o n g amounts of energy. Given t h i s f a c t , thought must be given t o the consequences of such occurrences and what p r e c a u t i o n s , i f any, may be taken t o l e s s e n t h e i r e f f e c t s . These e f f e c t s are f a r reaching i n that most man made s t r u c t u r e s have a l i m i t t o t h e i r c a p a c i t y to r e s i s t such f o r c e s . N a t u r a l f e a t u r e s , such as s o i l and rock formations are a l s o prone t o damage i n the event of an earthquake. T h i s t h e s i s d e a l s with the e f f e c t s on the r a i l network of the P r o v i n c e of B r i t i s h Columbia as a r e s u l t of c a t a s t r o p h i c event. For an event t o be c o n s i d e r e d c a t a s t r o p h i c , c e r t a i n c r i t e r i a must be met. They would i n c l u d e : 1. That the event be sudden , u s u a l l y without warning. 2. That the e f f e c t s of the event be s u b s t a n t i a l ( That i s , e f f e c t a l a r g e p o r t i o n of the system or e f f e c t a s m a l l segment with l a r g e d i s r u p t i o n . ) 3. That s e r i o u s economic e f f e c t s would be f e l t by such a d i s r u p t i o n , and t h a t the 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 p e r i o d of time. 2 C a t a s t r o p h i c events would i n c l u d e : Earthquakes, L a n d s l i d e s , S o c k s l i d e s , Avalanches, Tsunamis,and Floods. Such an i n v e s t i g a t i o n i s u s e f u l due to the geography of B r i t i s h Columbia and the nature of the t r a n s p o r t a t i o n network. Due to the rugged mountainous t e r r a i n , only f o u r t r a n s p o r t a t i o n c o r r i d o r s e x i s t i n an e a s t - west d i r e c t i o n w i t h i n B r i t i s h Columbia . These c o r r i d o r s encompass a north - south d i s t a n c e of over 1400 k i l o m e t r e s . ( They i n c l u d e B r i t i s h Columbia Highway no. 3 , the Trans-canada Highway , B r i t i s h Columbia Highway no. 16 , and B r i t i s h Columbia Highway no. 97 ) . .These routes are the l o c a t i o n s of the highway and r a i l c o r r i d o r s and r e p r e s e n t the only s u r f a c e access to e a s t e r n Canada. I f one o f these r o u t e s are cut due t o a c a t a s t r o p h i c event t h e r e e x i s t few a l t e r n a t e s . Given t h i s s i t u a t i o n , i t i s advantageous to know : 1. Bhich r o u t e s are most v u l n e r a b l e t o d i s r u p t i o n s ? 2. 8hat i s the p r o b a b i l i t y t h a t such an event w i l l occur? 3. I f such a d i s r u p t i o n o c c u r s , what a l t e r n a t i v e r o u t e s are a v a i l a b l e . 4. Hhat would the e f f e c t s of such r o u t i n g be ? 5. Hhat st e p s can be taken to a l l e v i a t e these p o t e n t i a l t r o u b l e spots? To f u l l y understand the nature of the problem, we must look at past e x p e r i e n c e s . Two areas are prime c a n i d a t e s f o r h i s t o r i c a l i n s p e c t i o n , those p l a c e s being C a l i f o r n i a and Alaska. Both areas experienced d e v i s t a t i n g earthguakes i n r e c e n t 3 time. C a l i f o r n i a i s somewhat s i m i l a r to B r i t i s h Columbia i n t h a t the Lower Mainland has a high d e n s i t y of p o p u l a t i o n and i s a b u i l t up area. Alaska i s i d e a l because i t i s very s i m i l a r t o the northern areas o f the p r o v i n c e . B a s i c p r o b a b i l i t y theory i s s t u d i e d t o understand the mathematical e g u a t i c n s and d i s t r i b u t i o n s which govern any man-made system. T h i s theory i s then expanded to model the r a i l t r a n s p o r t a t i o n network of the p r o v i n c e . , F i n a l l y , a review of emergency p o l i c i e s and procedures w i l l be undertaken t o update and improve on these procedures., Due to the complexity of such an i n v e s t i g a t i o n , on l y the r a i l network i s s t u d i e d . This i s because the r a i l network i s l e s s complex than the highway network. Given the many a l t e r n a t i v e r o u t e s of the highway system, i t would be very d i f f i c u l t to t r y to a n a l y i z e t h a t system. Also , t r y i n g t o r a t i o n a l i z e the behaviour of m o t o r i s t s would be an i m p o s s i b l e task. The f o u r major r a i l w a y s of western Canada are i n c l u d e d i n the study. The r a i l w a y s are : the Canadian N a t i o n a l Bailway ,the Canadian P a c i f i c Bailway ,the B r i t i s h Columbia Bailway ,and the ibn . Only when necessary w i l l the ,bn be i n c l u d e d i n the a n a l y s i s s i n c e i t s main routes are i n United S t a t e s . In the course o f developing t h i s t h e s i s a f o r t u n a t e event o c c u r r e d . ( In so f a r as t h i s t h e s i s i s concerned ).,The tanker " Japan E r i c a n s t r u c k the Canadian N a t i o n a l Bailway r a i l b r i d g e at the Second Narrows C r o s s i n g over Burrard I n l e t . , The brid g e was c l o s e d from 12 October 1979 to 3 March 1980. T h i s c l o s u r e severed the southern l i n k of the B r i t i s h Columbia Bailway . The 4 only connection t o the r e s t of the B r i t i s h Columbia r a i l network was a t P r i n c e George . A study o f t h i s s i t u a t i o n has been i n c l u d e d . The a n a l y s i s undertaken i n the study i s known as L i f e l i n e B i s k A n a l y s i s and i s a p a r t of L i f e l i n e E n g i n e e r i n g , which has been g a i n i n g promenance i n r e c e n t years. L i f e l i n e s i n c l u d e : P i p e l i n e s , Hydro Power L i n e s , Highways, Railways, other u t i l i t y and communication l i n k s and c o r r i d o r s or those s e r v i c e s r e q u i r e d t o keep an i n h a b i t e d area f u n c t i o n i n g . The importance of the f i e l d has been shown by the d i s a s t e r o u s e f f e c t s of earthquakes i n h e a v i l y populated areas. The o b j e c t i v e of L i f e l i n e E n g i n e e r i n g i s to make l i f e l i n e systems l e s s v u l n e r a b l e to d i s r u p t i o n s , by b u i l d i n g i n t o the systems more redundancy by means of a more f l e x i b l e network and/or backup c a p a b i l i t y . A measure of system performance would be the o p e r a t i n g l e v e l s o f s e r v i c e achieved by the system. C r i t e r i a f o r a c c e p t a b l e l e v e l s of s e r v i c e would depend upon the nature of the l i f e l i n e system. Duke and Horan ( Reference Ho. 9 ) have o u t l i n e d three r e l i a b i l i t y l e v e l s and a p p l i e d these l e v e l s t o a wide range of l i f e l i n e systems..For highway and r a i l w a y systems the f o l l o w i n g l e v e l s were suggested: 1 » Beference No. 11 Page 373 5 TABLE 1 : RELIABILITY SERVICE LEVELS High I n t e n s i t y | Moderate I n t e n s i t y Ground Motion | Ground Motion ( MMI ) IX-X | ( MMI ) VI-VII j _ . | - - -| Bridges 1 L e v e l A J F u l l y F u n c t i o n a l 1 , - -1 , - - ^ I RoadbedsJ L e v e l B i I F u l l y F u n c t i o n a l where L e v e l A: 5.0 % ov l e s s of i n t e n s i t y area without s e r v i c e f o r one day, f u l l y r e s t o r e d w i t h i n one week. L e v e l B: 20.0 % or l e s s i n t e n s i t y area without s e r v i c e f o r one week, f u l l y r e s t o r e d w i t h i n one month. Note that these l e v e l s are given i n the M o d i f i e d M e r c a l l i I n t e n s i t y ( MMI ) ,which i s f r e q u e n t l y used when s u b j e c t i v e l e v e l s o f e a r t h movement are d e s i r e d . T h i s s c a l e i s r e l a t e d to the R i c h t e r s c a l e by the f o l l o w i n g r e l a t i o n s h i p : R i c h t e r = ( 2/3 ) MMI + 1 EQ0ATION 1 where MMI i s the M o d i f i e d M e r c a l l i S c a l e , fiefering t o Table 1, the v a r i o u s l e v e l s of s e r v i c e a l l i n c l u d e a f a i l u r e time i n which there i s a down time a s s o c i a t e d with r e p a i r s . 6 In the case of highways, many a l t e r n a t e r o u t i n g s would probably be a v a i l a b l e , o r , temporary road s u r f a c e s c o u l d be c o n s t r u c t e d . Temporary b r i d g e s c o u l d a l s o be used i n such an event. Railways are another matter. Proper grading and alignment are important t o a r a i l w a y o p e r a t i o n , thus temporary by-passes are not f e a s a b l e . A l s o , due t o the extreme dead l o a d s and v i b r a t i o n s experienced, temporary b r i d g e s t r u c t u r e s are not p r a c t i c a l so a l i n k would be unusable u n t i l f u l l , permanent r e p a i r s were completed., I t i s 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 the r e p a i r time would be s u b s t a n t i a l . L e v e l s of s e r v i c e of networks are a f f e c t e d by the damage i n f l i c t e d on them by events. Four d e s c r i p t i v e c a t a g o r i e s of damage s t a t e s are : 2 1- G l o b a l damage 2. Path i n t e r r u p t i o n 3. .Network impedance <*. Flow c a p a c i t y r e s t r i c t i o n s . , G l o b a l ( system j damage i s the sum of a l l the component (nodes 6 l i n k s ) damages. T h i s i s u s e f u l when comparing the damage s u s t a i n e d by d i f f e r e n t systems. Path i n t e r r u p t i o n i s the 2 These i d e a s were put f o r t h i n a p r e s e n t a t i o n by H. C. Shah, head o f the S t a n f o r d U n i v e r s i t y Earthquake Centre a t the ASCE conv e n t i o n a t P o r t l a n d , Oregon On 15 a p r i l 1980., 7 d e s c r i p t i o n of the c o n n e c t i v i t y of the nodes by l i n k s . T h i s i s of concern before and a f t e r an event. T h i s r e l a t e s the number of l i n k s which have been severed. Network impedence d e a l s with d i s t a n c e , time or c o s t of a t r i p from one node to another. I f , a f t e r an event, a l i n k i s severed, i n c r e a s e d impedance c o s t s may r e s u l t . The c a p a c i t y of a l i n k may a l s o be a l t e r e d (decreased) due to an event. T h i s i s e s p e c i a l l y t r u e f o r highways but may a l s o be v a l i d f o r d u a l t r a c k e d r a i l systems. I n B C the only dual tracked l i n k i s on the CPH mainline between Vnacouver and Buby Creek. ( 100 km east of Vansouver i n the F r a s e r V a l l e y . ) f o r a s i n g l e t r a c k e d o p e r a t i o n the c a p a c i t y i s a l r e a d y d e f i n e d ( that i s , maximum p o t e n t i a l c a p a c i t y ) and there e x i s t s i n terms of p r o b a b i l i t y only a two s t a t e c o n d i t i o n of e i t h e r flow or no flow. , These p o t e n t i a l damage s t a t e s w i l l be one of the concerns of t h i s t h e s i s . The o b j e c t i v e o f L i f e l i n e Earthquake E n g i n e e r i n g i s not only t o i d e n t i f y those l i f e l i n e s which are v u l n e r a b l e t o damage, but t o p r e d i c t the scope o f the damage, the e f f e c t s on system performance, and to recommend changes t o minimize such damage. To o b t a i n an understanding of the types of damage experienced due to c a t a s t r o p h i c events, the earthquakes i n Alaska and the San Fernando V a l l e y , C a l i f o r n i a , w i l l be examined i n the next chapter. 8 CHAPTER TWO z PAST EXPERIENCES WITH TRANSPORTATION DISRUPTIONS The i n v e s t i g a t i o n i n t o the p o t e n t i a l hazards faced i n B r i t i s h Columbia cannot be f u l l y understood or a n t i c i p a t e d without a look at past d i s r u p t i o n s of s e r v i c e i n other p l a c e s . Two p l a c e s are of p a r t i c u l a r i n t e r e s t : Alaska and C a l i f o r n i a . On 27 March 1964 Alaska experienced an earthquake of r i c h t e r 8.5 magnitude which a f f e c t e d the southern part of the s t a t e a l o n g the G u l f of Alaska . T h i s i s important i n that t h i s "populated" p a r t of Alaska i s q u i t e s i m i l a r t o northern and i n t e r i o r s e c t i o n s of the p r o v i n c e . The types of p h y s i c a l s t r u c t u r e s as w e l l as c l i m a t e and l e v e l of governmental s e r v i c e s are a l s o s i m i l a r . The 9 February 1971 San Fernando earthquake with i t s magnitude of r i c h t e r 6.6 i s a l s o of value i n that i t s t r u c k a h e a v i l y populated p o r t i o n of Los Angeles, C a l i f o r n i a , and i s the most documented and s t u d i e d of any earthquake to date. The d i s r u p t i o n o f s e r v i c e to the t r a n s p o r t a t i o n network, i n c l u d i n g u t i l i t i e s , was s u b s t a n t i a l , and can help understand the p o t e n t i a l damage to be s u f f e r e d by the Lower Mainland and p o r t i o n s c f Vancouver I s l a n d . F i g u r e 1 shows the l o c a t i o n s of both o f these earthquakes f o l l o w e d by a d e s c r i p t i o n of each., 9 FIGOB.E 1 : L O C A T I O N AL MAPS INDEX MAP OF ALASKA 10 THE 27 33ABCH 1964 ALASKA EABTHpOAKE The Alaska earthquake of 27 Harch 1964 occurred a t 1736 (alaska time) with a magnitude of r i c h t e r 8.5 . The e p i c e n t r e was l o c a t e d 120.0 k i l o m e t r e s east south-east o f Anchorage. 114.0 people were k i l l e d and an estimated $311.0 m i l l i o n d o l l a r s damage was caused by t h i s earthquake. Both h o r i z o n t a l and v e r t i c a l ground movements were present d u r i n g t h i s earthquake. Hajor causes of p h y s i c a l damage were due to ground shaking, c r a c k i n g , f a u l t i n g , a n d l i q u e f a c t i o n . S e v e r a l l a n d s l i d e s a l s o o c c u r r e d . For damage to occur ground shaking must reach the n a t u r a l frequency o f the s t r u c t u r e s i n v o l v e d , and must be s u s t a i n e d f o r a resonable amount of time. T h i s was the case i n A l a s k a . Damage to the t r a n s p o r t a t i o n system was severe, except f o r the a i r p o r t f a c i l i t i e s . T h i s was f o r t u n a t e s i n c e massive a i r l i f t s were r e q u i r e d f o r r e l i e f e f f o r t s . Damage to the Alaska fiailroad was estimated to be $27.0 m i l l i o n . Cracks and f a u l t i n g u s u a l l y occur along e s t a b l i s h e d f a u l t s . The l o s s of s t r e n g t h i n some foundation s o i l s can cause l i q u e f a c t i o n . T h i s i s u s u a l l y present i n s i l t y sandy s o i l s . The l o s s of s t r e n g t h i s a r e s u l t of the shaking of the s a t u r a t e d s o i l c a u s i n g an i n c r e a s e i n pore water pressure.,, The r a i l r oute from Anchorage t o Seward ( The p o r t ) was e x t e n s i v e l y damaged during the earthquake. Host of the damage was caused by l a n d s l i d e s , embankment f a i l u r e s , ground c r a c k s and movement, and by i n u d a t i o n by unusually high t i d e s . 11 At Seward and H h i t t i e r submarine s l i d e s and the r e s u l t i n g waves, caused much of the r a i l yards t o be destroyed. Tsunami waves a l s o caused e x t e n s i v e damage. ., Many b r i d g e s were a l s o damaged. Most of the b r i d g e s on the system were open wood t r e s t l e s , supported on wood p i l i n g s . Some of the l a r g e r b r i d g e s were supported on s t e e l p i l i n g s . Bridge damage was g e n e r a l l y due t o the f o l l o w i n g f a c t o r s : 1. Permanent h o r i z o n t a l and v e r t i c a l displacements of the f o u n d a t i o n , 2. T r a n s i e n t h o r i z o n t a l displacements of the ground, 3. ;, High a c c e l e r a t i o n s generated w i t h i n b r i d g e s by a m p l i f i c a t i o n of ground motions. A t o t a l of 52.0 s t e e l b r i d g e s and 73.0 wood t r e s t l e b r i d g e s were damaged and had t o be r e p a i r e d a t a t o t a l c o s t of $ 1.5 m i l l i o n . 3 Damage was a l s o i n f l i c t e d on the roadbed and t r a c k . Nearly a l l of the damage occurred i n areas u n d e r l a i n by s a t u r a t e d s o i l had s e t t l e d and was unconsolidated . Only along Turnaquin Arm was the damage on bedrock or t i l l . Embankment f a i l u r e s were of two types : * 1. F i l l f a i l u r e s at a c t i v e f a u l t s (embankment m a t e r i a l added weight to found a t i o n so 3 Reference No. ,27 Page * Reference No. 22 Page D17 t h a t the r e s i s t a n c e to f a i l u r e was a l t e r e d . ) 2. P a s s i v e f a i l u r e s { Embankment f a i l e d only by c r a c k i n g due t o f o u n d a t i o n f a i l u r e . ) The embankments were, f o r the most p a r t placed by hand before 1914 and c o n s i s t e d of s i d e burrow which contained some or g a n i c m a t e r i a l . Host of the subgrades were 5.0 metres wide. T h e i r s l o p e s were determined by the angle of repose of the f i l l m a t e r i a l . THE 9 FBBOABY 1971 SAN FJIMfiBO EARTHQUAKE On 9 February 1971 at approximately 0600 ( PST ) an earthguake of r i c h t e r 6.6 magnitude s t r u c k the Los Angeles area. The e p i c e n t r e was l o c a t e d 45.0 k i l o m e t r e s northwest of the downtown area i n the San G a b r i e l Mountains . The s l i p plane was 45 degrees t h e r f o r e almost equal v e r t i c a l and h o r i z o n t a l f o r c e s were experienced. A c c e l e r a t i o n s of 0.1 g to 0.5 g were experienced with p o s s i b l e 1.0 g f o r c e s e x h i b i t e d i n non-populated a r e a s . 3 The importance of t h i s earthquake i s t h r e e f o l d . F i r s t , over 200 s t r o n g motion r e c o r d i n g d e v i c e s were present, thus t h i s earthquake i s the most documented earthguakes to date. Second, the s l i p plane caused v e r t i c a l motions which had never been experienced b e f o r e , t h e r e f o r e many s t r u c t u r e s r e c i e v e d f o r c e s f o r which they sere not designed. /And t h i r d , , the San Fernando V a l l e y i s a h e a v i l y populated a r e a , and t h i s earthquake was the 5 Beference No. 17 13 f i r s t major t e s t f o r many s t r u c t u r e s and t h e i r d e s igns., The e f f e c t o f the earthguake on e n g i n e e r i n g s t r u c t u r e s was mixed. I f one excludes freeway b r i d g e s , modern s t r u c t u r e s f a r e d q u i t e w e l l , r e c i e v i n g minimal cosmetic damage, with no f a i l u r e s . O l d e r , pre-earthquake r e s i s t a n t designs , however, d i d not f a r e so w e l l . The most notable f a i l u r e was the Veteran^s a d m i n i s t r a t i o n H o s p i t a l . T h i s h o s p i t a l had 46 out of the 58 f a t a l i t i e s . F a t a l i t i e s r e l a t i n g t o t r a n s p o r t a t i o n s t r u c t u r e s were l i m i t e d to 2 , when an overpass c o l l a p s e d onto the occupants of a v e h i c l e underneath. , Bote, however/ t h a t two major f a c t o r s kept the f a t a l i t y f i g u r e low. „, an estimated 91.0 % o f the people were a t home when the earthquake s t r u c k . Had the freeways been f i l l e d with t r a f f i c , i t might have been another s t o r y . Two dams, the Pocoma and the Van Norman dams were c l o s e to f a i l u r e . , Had the earthguake l a s t e d longer, or had the water l e v e l been to a maximum, almost c e r t a i n l y these dams would have f a i l e d . A l s o important t o note i s the f a c t t h at t h i s earthquake a f f e c t e d mainy the n o r t h e r n p a r t o f the v a l l e y where f o u r h o s p i t a l s , t w o freeway i n t e r c h a n g e s , two dams, a youth c o r r e c t i o n a l c e n t r e and a $50.0 m i l l i o n e l e c t r i c a l s w i t c h i n g / c o n v e r t e r s t a t i o n were damaged. The r e s t of the Los Angeles a r e a , however, was u n a f f e c t e d and was a b l e to provide a s s i s t a n c e and r e l i e f f o r the n o r t h e r n p a r t of the San Fernando V a l l e y . Damage t o the freeway system was l o c a t e d on the Golden S t a t e Freeway, The F o o t h i l l s Freeway, And The Antelope V a l l e y 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 C a l i f o r n i a Route Ho. 14 r e s p e c t i v e l y . ) Damage was s u s t a i n e d to the pavements and the b r i d g e s as w e l l . Damage to the b r i d g e s was not only t o the s t r u c t u r e s themselves but a l s o t o the approaches , the embankments, and the p i l e s . Three major l a n d s l i d e s a l s o occurred where freeways were s t i l l under c o n s t r u c t i o n , although had they been i n s e r v i c e t r a f f i c would not have been d i s r u p t e d . The C a l i f o r n i a Department of T r a n s p o r t a t i o n recommends the f o l l o w i n g changes : 6 1. Large c u t s should be e l i m i n a t e d due to t h e i r high f a i l u r e p o t e n t i a l , i n high r i s k a r e a s . Low cut s l o p e s are d e s i r a b l e . 2.. A l s o , high f i l l areas must be r e - e v a l u a t e d f o r t h e i r f a i l u r e p o t e n t i a l . , I n c r e a s e d compaction must be c a r e f u l l y c o n s i d e r e d to determine i f i t i s worth the e x t r a c o s t . 3. Subsidence due to d e n s i f i c a t i o n w i t h i n f i l l s cannot be e l i m i n a t e d e n t i r e l y , but i t can be reduced by keeping h e i g h t s as low as p o s s i b l e . , 4., F l e x i b l e p i p e s and c o u p l i n g s should be used f o r drainage where a c t i v e f a u l t s are known to e x i s t . 5. A new system of emergency fun d i n g i s d e s i r e d 6 Reference No. 11 s i n c e funds are not a v a i l a b l e immediately and must be d i v e r t e d from other s o u r c e s . F a i l u r e s of freeway b r i d g e s was the most e x t e n s i v e p a r t of damage i n the San Fernando earthquake. These f a i l u r e s were concentrated on three i n t e r c h a n g e s . out of a t o t a l o f 67 b r i d g e s : 5 bridges were completely d e s t r o y e d , 2 others were damaged beyond r e p a i r , and 60 r e q u i r e d r e p a i r . Of these damaged b r i d g e s : 25.0 % were s e v e r e l y damaged 50.0 % were moderately damaged 25.0 % had minor damage. 7 T o t a l c o s t s f o r r e s t o r a t i o n were: $1.7 m i l l i o n f o r emergency c o s t s , $6.5 m i l l i o n f o r bridge r e p a i r c o s t s , $5.7 m i l l i o n f o r highway r e p a i r c o s t s , which i s a t o t a l of $13.9 m i l l i o n . Note t h a t t h i s does not i n c l u d e those c o s t s f o r the c i t y of Los Angeles. I n t e r s t a t e 5 was shut n o r t h and south bound. Types of damage were : 8 1. Ground shaking cause columns to s h i f t which caused the bridge deck to be removed from i t s r e s t r a i n e r s thus causing the bridge deck t o drop to the ground. 2. The l a r g e v e r t i c a l and h o r i z o n t a l motions ( p o s s i b l y exceeding 0.5 g ) caused columns to buckle i n the middle as i f they were being t e s t e d by a compression t e s t i n g machine. 7 Beference No. 23 Page 207 - 212 8 Beference No. 23 3. Improperdesign of r e s t r a i n i n g d e v i c e s caused b r i d g e s t o s l i p p e d o f f t h e i r column supports. 4. approach f i l l s l i q u i f i e d , c r e a t i n g d i f f e r e n c e s i n p r o f i l e . 5. Columns l o s t t h e i r bond between themselves and t h e i r anchorages i n the ground. Columns which were an i n t e g r a l part of t h e i r f o o t i n g s were e s p e c i a l l y i n e f f e c t i v e . ) 6. Lack o f r e s t r a i n t at abutments allowed the e n t i r e s t r u c t u r e t o rock back and f o r t h , e v e n t u a l l y a l l o w i n g the bridge t o des t r o y i t s e l f . 7. S t e e l r e i n f o r c i n g rods were not s t r o n g enough and were too widely spaced a l l o w i n g the crushed c o n c r e t e to f a l l out and l e t the column c o l l a p s e . B a s i c a l l y , the bridge themselves remained i n t a c t , as with the other f a i l u r e s noted i n the San Fernando earthguake, i t was the anchorages, f o o t i n g s , mountings, and the s u b s t r u c t u r e which f a i l e d . Another d e f i c i e n c y was t h a t the s t a t i c l o a d f a c t o r s of 0.1 g to 0.2 g was inadequate. A r e s e a r c h programme had been i n i t i a t e d to allow f o r dynamic design f o r b r i g e s . T h i s has now been adopted as p o l i c y by the C a l i f o r n i a Department of T r a n s p o r t a t i o n , which recommend the f o l l o w i n g changes : 9 1. Columns r e q u i r e s t r o n g e r containment i n the form 9 Reference Ho. 34 Fage of s p i r a l wrappings. Stronger r e i n f o r c i n g bars are r e g u i r e d f o r columns. A l s o , bars t h a t are c l o s e r t o g e t h e r are d e s i r e d . Suggestions are no. 5 bars at 15.25 cm (6.0 i n . ) c e n t r e s . A b e t t e r r e s t r a i n i n g system at expansion j o i n t s f o r l a r g e s c a l e movement. The b o l t s have proven inadequate. Hew methods would i n c l u d e : a. L o n g i t u d i n a l hinge r e s t r a i n e r s b. B o l t s with 1.9 cm (3/4 inch) c a b l e s through hinge r e s t r a i n e r s f o r new c o n s t r u c t i o n c. Seven 1.9 cm (3/4 inch) c a b l e s encased i n c o n c r e t e 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 l i q u i f a c t i o n . B e s t r i c t i o n s on where column bars can be s p l i c e d , e s p e c i a l l y at maximum movement l o c a t i o n s . . Larger shear keys at abutments should be used. Provide a top mat of r e i n f o r c e m e n t s f o r f o o t i n g s t h a t support columns. Develop a new technique of f o o t i n g s that support columns. H o r i z o n t a l and v e r t i c a l t i e - b a r s should be s p e c i f i e d . Some f l e x i n g of columns should be allowed d u r i n g severe earthquakes. Bridge design should be s i t e s p e c i f i c to account f o r past earthquake a c t i v i t y . V i r t u a l l y no damage to the r a i l w a y s i n the S Fernando V a l l e y o c c u r r e d , the only i n s t a n c e being the c o l l a p s e of an overpass onto the 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 th a t the l e v e l t e r r a i n i n the San Fernando V a l l e y precluded any r o c k / l a n d s l i d e s or s e r i o u s slumping of s o i l s . The p o t e n t i a l f o r damage t o the Lower Mainland i s v i v i d l y demonstrated by these two earthquakes. C l e a r l y , some of the p r e c a u t i o n s o u t l i n e d above ( e s p e c i a l l y i n the C a l i f o r n i a case ) should be implemented i n B r i t i s h Columbia . However, i t was the 1964 Alask a earthquake which i n f l i c t e d s e r i o u s damage on the Alaska r a i l r o a d . Much o f t h e damage was to the s m a l l e r wooden t r e s t l e s . The damage occured randomly throughout the system so the Alaska experience i s only of use i n examinimg the types of damage and of l i t t l e v a lue i n p r e d i c t i n g where the damage w i l l occur. 1 9 REVIEH OF BASIC FRQBABILITY THEORY B a s i c p r o b a b i l i t y and r e l i a b i l i t y theory governing t r a n s p o r t a t i o n systems w i l l be reviewed i n order to g a i n an understanding of the b a s i c p r i n c i p l e s and then these p r i n c i p l e s w i l l be s p e c i f i c a l l y a p p l i e d t o the r a i l network of B r i t i s h Columbia . Given a network of ( r a i l ) l i n k s between nodes ( p o p u l a t i o n centres) , there e x i s t s a p r o b a b i l i t y of f a i l u r e (or s u r v i v a l ) . , The p r o b a b i l i t y of f a i l u r e and the p r o b a b i l i t y of s u r v i v a l sum to u n i t y or : P (success) + P ( f a i l u r e ) = 1., T h i s i s the simple two s t a t e case, a p p l i c a b l e to redundant or non-redundant s t r u c t u r e s . T h i s case does not allow f o r any i n t e r m e d i a t e o p e r a t i o n a l phase. In p r a c t i c a l terms, these l i n k s may be i n v a r i o u s s t a g e s , between complete o p e r a t i o n P( Success) or complete f a i l u r e P( f a i l u r e ) . Some element of f a i l u r e (down) time may be i n t r o d u c e d to i n d i c a t e t h i s middle ground. ., G e n e r a l l y , three types o f f a i l u r e would occur : l ° 1. E a r l y 2. Random 3. Wearout E a r l y f a i l u r e s are a s s o c i a t e d with substandard items, t h a t i s , those items which do not f u n c t i o n to t h e i r average product l i f e time. These f a i l u r e s are modeled by a hazard f u n c t i o n , ( h (x} ) t h a t i s , a f u n c t i o n which measures the i n s t a n t a n e o u s number o f s u r v i v o r s up to time x or : »o Beference No. 5 Page 487 20 h(x) = f{x) / 1 - f(x) where 1 - f ( x ) = r e l i a b i l i t y of x. T h i s r a t e can be measured d i r e c t l y using l i f e l e n g t h t e s t data, which i s then used to choose a model, the model being the d i s t r i b u t i o n of f a i l u r e s over a time range. Random f a i l u r e s occur independently of a component's ( l i n k ' s ) l i f e h i s t o r y . They are memoryless f a i l u r e s , and are modeled by a Ppis s o n d i s t r i b u t i o n . There i s no way t o prevent these types of f a i l u r e s , however attempts can be made to minimize t h e i r impact. Wearout f a i l u r e s are due t o the g r a d u a l d e t e r i o r a t i o n of the p h y s i c a l p r o p e r t i e s of the component. , These f a i l u r e s are c h a r a c t e r i z e d by an i n c r e a s e d hazard f u n c t i o n . &n i n c r e a s i n g hazard f u n c t i o n i s s i m i l a r t o a hazard f u n c t i o n except t h a t , as time proceeds, the :probability- o f f a i l u r e i n c r e a s e s . Bote t h a t , i n the context of r a i l w a y s , p r e v e n t a t i v e maintenance should e l i m i n a t e wearout f a i l u r e s . Each f a i l u r e mode has a d i s t i n c t l i f e - l e n g t h model a s s o c i a t e d with i t i n the form of a mathematical r e p r e s e n t a t i o n of i t ' s o p e r a t i o n a l l i f e , l * o b v i o u s l y there are unique models f o r every component. ; However, these many d i f f e r e n t models can u s u a l l y be narrowed down t o a s m a l l e r number o f ge n e r a l models. T h i s l e a d s to the fundamental d e f i n i t i o n of r e l i a b i l i t y as a measure of achieved performance matching r e q u i r e d performance, i n e f f e c t a measure of system e f f i c i e n c y , where a c h i e v i n g some pre-determined goal d e f i n e d whether system performance had been 1 1 Reference So. 5 Page 488 21 a t t a i n e d . These goals are d i f f e r e n t f o r d i f f e r e n t systems and there i s no one measure of what an a c c e p t a b l e l e v e l of r e l i a b i l i t y . F a c t o r s which i n f l u e n c e achieved performance i n c l u d e : 1. L o c a t i o n a l 3. Human 2. Environmental 4. M a t e r i a l The most important f a c t o r s i n t h i s case would be l o c a t i o n a l and environmental, both of which i n f l u e n c e the degree of r e l i a b i l i t y h e a v i l y . On the other hand, human and m a t e r i a l f a c t o r s should be e l i m i n a t e d as f a c t o r s by p r e v e n t i v e maintainance and q u a l i t y c o n t r o l . Thus, some measure of performance or achievement f u n c t i o n must be d e f i n e d i n order t o determine i f achieved performance approaches r e q u i r e d performance. An a c c u r a t e d e s c r i p t i o n of system components and d e t a i l e d knowledge o f system performance must e x i s t i n order to a c c u r a t e l y measure r e l i a b i l i t y . (. System performance can be measured d i r e c t l y or i n d i r e c t l y . D i r e c t measurement would be the measure of performance f o r an e x i s t i n g o p e r a t i o n a l system., I n d i r e c t measurement r e q u i r e s a t h e o r e t i c a l method of system e v a l u t a t i o n which would be used f o r systems i n the design phase. In the case of the r a i l network of B r i t i s h Columbia, both methods would be used , depending on the o p e r a t i o n a l l e v e l o f the p a r t i c u l a r l i n k . That i s , f u l l y o p e r a t i o n a l , semi-o p e r a t i o n a l , or proposed.) In t h i s study, the method of modeling earthquakes w i l l be the method of p r e d i c t i n g c a t a s t r o p h i c events. T h i s i s a c c e p t a b l e 22 because earthquakes w i l l o f t e n precede any l a n d s l i d e or r o c k s l i d e . A l s o , t h i s g i v e s one convenient model f o r a l l c a t a s t r o p h i c occurrances on the r a i l network In g e n e r a l , assuminq a Poisson a r r i v a l r a t e of earthquakes with an average r a t e of v per year, the p r o b a b i l i t y P of k events over t years i s : 1 2 - v t k e (vt) P = Equation 2 k ! where ; k = 0,1,2, . . ,. n such that : P (network) = 1 - P( zero f a i l u r e s i n time t) f -v (p ) (t) V 1 - e T h i s method could be used t o p r e d i c t how many earthquakes would occur over a given time as w e l l as p r e d i c t the magnitudes of (a R i c h t e r value) these earthguakes over time t . The problem i s t o match these two p r e d i c t i o n s together t o o b t a i n the magnitude and time of occurrance. Milne has d i s c u s s e d t h i s problem and has used a r e l a t i o n s h i p between magnitude (m) and freguency of occurrence ( N) known as the recurrence e q u a t i o n . , * 3 t h i s i s expressed as : lo g N = a - b M where : a = a con s t a n t r e f l e c t i n g the average s e i s m i c i t y of the r e g i o n and b = the r a t i o of l a r g e to smal l earthquakes. N = the cummulative events / year m = R i c h t e r magnitude of event. 1 2 Reference No.,32 Page 58 1 3 Reference No..27 Page 1183 23 The c o n s t a n t s a and b are determined by using known d a t a , fl and N and a p p l y i n g r e g r e s s i o n a n a l y s i s , Milne used a normal squares method. Western Canada i s d i v i d e d i n t o three s e c t i o n s f o r earthquake 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 ,and Queen C h a r l o t t e Transform. Data f o r past occurrences was compiled f o r use i n the "maximum l i k e l i h o o d " method of p r e d i c t i o n . The composite v a l u e s , a l l t h r e e r e g i o n s combined i n t o one value, and magnitudes from g r e a t e r than 4.0 up to 6.0 y i e l d e d the r e s u l t i n g equation: l o g N = 4.2 - 0.74 H Equation 3 Thus, given a r i c h t e r magnitude of M, N i s the number of earthguakes with a magnitude g r e a t e r than M. T h i s r e c u r r e n c e equation was a l s o used by F i t z e l l ( Bef. No. 10 ) , however he used a l e a s t squares method , r e c a l c u l a t e d the magnitudes, and i n c l u d e d earthquakes up to a magnitude of B i c h t e r 7.5 . His r e s u l t s were s i m i l a r t o M i l n e ' s y i e l d i n g the f o l l o w i n g r e c u r r e n c e equation : l o g N = 4.13 - 0.72 M Equation 4 T h i s l o g - l i n e a r r e l a t i o n s h i p can be shown g r a p h i c a l l y r e l a t i n g the number of cummulative events per year { N ) vs the B i c h t e r magnitude { M )• T h i s r e l a t i o n s h i p i s f a i r l y l i n e a r except f o r s m a l l e r magnitudes of earthquakes. Since t h e r e are many s m a l l { < r i c h t e r 3.0 ) events over a l a r g e area, modeling i n t h i s range i s d i f f i c u l t . T h i s r e s u l t s i n the f o l l o w i n g graph 24 1 4 cummulative events per year J 1,0 + I i i o. 1* l I i . 0 1 * I 7 where = Milne S x = F i t z e l l > 7. 0 , 0.1 cuom. events/year > 6.0 , 1.0 cuma. events/year > 5.0 , 10. cumm. events/year > 4.0 , 100., cummulative events per year 8 r i c h t e r magnitude T h i s method i s not without i t s f a u l t s . There are u n c e r t a i n t i e s due to i n a c c u r r a t e magitude e s t i m a t i o n as w e l l as those events with low magnitudes which go undetected. A l s o occurrences of very l a r g e events are r a r e , thus s t a t i s t i c a l u n c e r t a i n t y i s i n t r o d u c e d . Even so, occurrences ( f r e q u e n c y ) of v a r i o u s magnitudes of earthquakes can now be estimated. The l o c a t i o n s of these earthquakes and t h e i r a c c e l e r a t i o n s are s t i l l not p r e c i c e l y given. In order to a s s i g n p r o b a b i l i t i e s of f a i l u r e t o l i n k s ( l i n k p r o b a b i l i t i e s ) the l o c a t i o n s of the peak a c c e l e r a t i o n s must be known. A method f o r p r e d i c t i n g peak a c c e l e r a t i o n s A (s) w i l l be explored i n the next chapter. J * Reference No. 29 Page 1185 S Reference No. 10 Page 103 25 CHAFTES 4 J. RELIABILITY THEORY AND NETWORK A j A i l S I S T h i s chapter a p p l i e s the fundamentals of p r o b a b i l i t y and r e l i a b i l i t y theory to the r a i l network of B r i t i s h Columbia . , An o u t l i n e of the process f o l l o w s : 1. E s t a b l i s h i n g the schematic r a i l network t a k i n g i n t o account e x i s t i n g r i g h t s of way, and important p o p u l a t i o n c e n t r e s of the pr o v i n c e . 2. P r e d i c t the l e v e l of ground movement by choosing a p p r o p r i a t e c r i t e r i a by which t h i s movement can be measured and develop a model of p r e d i c t i o n . 3. Determine l i n k s of high r i s k (due to) : a, P r o x i m i t y t o an a c t i v e earthguake f a u l t , b A L o c a t i o n i n an area o f high land/rock s l i d e p o t e n t i a l c. Having a b r i d g e of over 30 metres i n l e n g t h d. Convergence of many l i n k s at a s i n g l e node thus having a high volume of t r a f f i c . 4. E s t a b l i s h a method of p r o b a b i l i t y (of f a i l u r e ) assignment f o r each l i n k . 5. . Transform these super networks i n t o a managable s i z e f o r a n a l y s i s . 6. Perform r e l i a b i l i t y a n a l y s i s t o these networks. 26 4.1 2 NETWORK CHABACTERISTICS The a n a l y s i s i s performed i n two d i s t i n c t p a r t s . The e x i s t i n g o p e r a t i o n a l r a i l network i s f i r s t t e s t e d f o r i t s r e l i a b i l i t y , then, an improved network, u t i l i z i n g some abandoned r a i l r i g h t s - o f - w a y and/or proposed l i n k s w i l l be t e s t e d . The two d i f f e r e n t r e l i a b i l i t i e s are compared and i f the second f i g u r e i s a p p r e c i a b l y h i g h e r , improvements to the system w i l l be recommended. These improvements w i l l c o n s i d e r both c o s t and the r e l i a b i l i t y f i g u r e , although the r e l i a b i l i t y w i l l be given major emphasis. The r a i l network of B r i t i s h Columbia i s shown i n Fi g u r e 3. The f o u r major c a r r i e r s are c o l o u r coded method and s o l i d l i n e s are present l i n k s and dashed l i n e s are proposed or abandoned l i n k s . Table 1 p r o v i d e s the L i s t of A b b r e v i a t i o n s the major c e n t r e s (nodes) of the p r o v i n c e and U.S.A. The c e n t r e i d e n t i f i c a t i o n number i s a l s o i n c l u d e d . These c e n t r e s were chosen because they were e i t h e r a major commercial and p o p u l a t i o n c e n t r e or they were a major j u n c t i o n p o i n t f o r three o r more l i n e s . The most important a c t i v i t y c e n t r e s are : Vancouver, L y t t o n , Kamloops /Kamloops J u n c t i o n , P r i n c e George ,and Chetwynd. A majo r i t y of the r a i l t r a f f i c flows through these c e n t r e s . These are a l s o important " s w i t c h i n g " c e n t r e s and t h e i r s u r v i v a l i s important., Note t h a t only t h e ma i n l i n e s i n and around Vancouver a r e shown. There are many more l i n e s , however, t h i s should not i n f l u e n c e the r e l i a b i l i t y c a l c u l a t i o n s i n s i n c e the l i n e s are l o c a t e d r e l a t i v e l y c l o s e together. The t h r e e major b r i d g e s i n metro Vancouver are shown. They are the Second Narrows C r o s s i n g ( B u r r a r d I n l e t ) , the New Westminster C r o s s i n g ( Fraser B i v e r ) ,and the M i s s i o n - Matsgui ( Abbotsford ) C r o s s i n g ( F r a s e r fiiver ). T h i s concept of combining many l i n k s i n t o a s i n g l e ccmparable c o n f i g u r a t i o n i s known as a " s u p e r l i n k " . In t h i s case t h i s has been performed without mathametical a n a l y s i s . T h i s a n a l y s i s i s another f a c e t of network a n a l y s i s , that determines a method to model a complicated network by a comparable yet simple e g u i v i l e n t . . . Note t h a t the B u r l i n g t o n Northern B a i l r o a d connections to the Canadian c a r r i e r s are shown. In the event of a major catasrophe, r a i l t r a f f i c c o u l d be re- r o u t e d through the U.S.A. T h i s study ,however, w i l l only use the r a i l l i n k s w i t h i n Canada. T h i s i s done f o r three reasons. One i s that from a p r a c t i c a l o p e r a t i n g p o i n t of view, the r e - r o u t i n g of t r a f f i c through the U S A would be c o s t l y due to i n c r e a s e d a d m i n i s t r a t i v e c o s t s ( mainly customs ) . A l s o , 0 S f r i e g h t r a t e s are s t i l l r e g u l a t e d by the ICC while Canadian f r e i g h t r a t e s have been, f o r the most p a r t , d e r e g u l a t e d s i n c e 1967. I t i s not c e r t a i n whether the D S l i n k s c o u l d handle the i n c r e a s e d t r a f f i c . T h i r d l y , the a n a l y s i s i s much s i m p l i e r without the i n t r o d u c t i o n of the U S l i n k s . 28 F I G QBE 3 x IM MIL NETWORK OF B B I T I S H C O L U M B I A * D E A S { YUKON ) ( NWT / TN-0 ) FN E L * D B I F * , \ F S J A P B E P * T E B B X |<FSJN C H E T / "*"''owe-* /» P^GEO T E J N f i / / i / f / BCB "»>"»>>> BN CN C P ASHC f K J C T P A ¥ N ^ * f - * 5PBB C O B T A ^ A 7 N VANC L X T N l LAHL HTCB I BOD WES=<Sr^fHl§S - » H O P E SOT i* B E L L B E V L >ICA ASMS * K E L O ' P E N T GOL1 PB IN * MIDW ( USA ) CASr ( A L B E B T A ) kFELD HABD YAHK CBOW ' ' ' • J U : . . ' . TABLE 2 1 M § I OF A B BB E VIATIQN S T T CODE I NUMBEB | LOCATION ABOT | 1 | Abbotsford* A BUS | 2 I Armstrong ASCH | 3 | A s h c r o f t BELL | 4 | Beilingham ( fa.) BBOD j 5 I Broodie CAST | I C a s t l e g a r CBET 1 6 J Chetwyad COST i | Courtenay CBAN | | Cranbrook CBOS | | Croasnest DAWC J i Dawson Creek DBAS 1 1 Deas Lake DBIF | 7 ] Driftwood EVEB | | E v e r e t t ( Ha.) PNEL | 8 j F o r t Nelson FSJA i | F o r t S t . James FSJN I | F o r t S t . John GOLD | 9 j Golden HOPE | 10 j Hope K A ML ) 11 I Kamloops KJCT | 12 | Kamloops J u n c t i o n KELO j 13 I Kelowna KITI | i K i t i m a t LYTN J 14 ) L y t t o n HIDW | 15 I Midway HISS | 16 I M i s s i o n J3TCB J 17 | Monte Creek NANI | I Nanimo NHES | 18 | New Sestminster NVAN | 19 I North Vancouver OSOY J 20 j Osoyoos PAVN | 21 | P a v i l l i o n PENT | 22 | P e n t i c t i o n PGEO | 23 | P r i n c e George PBIN 1 24 I P r i n c e t o n PBBP | 25 | P r i n c e Bupert BE7L j I B e v e l s t o k e SEAT | j S e a t t l e { Wa.) SIC A | 26 ] Sicamous SPBfi | 27 j Spence's Bridge SPQK | I Spokane ( Ha.) sum i J Summit TAKL | | T a k l a Landing TEJN J 28 I Tete Juane VANC | 29 | Vancouver VICT | | V i c t o r i a WARD | 30 1 Bard WHOP I I Hope C Hest ) YAHK | I Yank FIGURE 4 z SCHEMATIC REPRESENTATION OF THE RAIL NETWORK O F BRITISJ COLUMBIA F i g u r e 4 shows t h i s network i n a schematic r e p r e s e n t a t i o n , s t i l l u sing the f o u r l e t t e r code. I t i s important to r e a l i z e t h a t t h i s i s a d i s t o r t e d view of the a c t u a l s i t u a t i o n i n t h a t d i s t a n c e s and p r o x i m i t i e s of l i n k s do not re p r e s e n t e x i s t i n g r e a l i t y . , For a n a l y s i s , however, p a r a l l e l and s e r i e s l i n k s are more r e a d i l y apparent as are s i n g l e l i n k s and/or nodes. Table 3 giv e s a b a s i c o u t l i n e o f the s i z e and scope of each c a r r i e r . Note that while the Canadian N a t i o n a l Bailway and 31 Canadian P a c i f i c Railway cover major p o r t i o n s of the p r o v i n c e . The B r i t i s h Columbia Railway covers the l a r g e s t d i s t a n c e f o r a s i n g l e m a i n l i n e . The volume of f r e i g h t r e p r e s e n t s the amount loaded i n B C or the amount c a r r i e d i n t o B C . These f i g u r e s g i v e the r e l a t i v e importance o f the major c a r r i e r s ' mainlines,, ( That i s , which are more h e a v i l y t r a v e l l e d ) . TABLE 3 1 SOJJARY OF THE RAIL JETSORK CHARACTERISTICS OF BRITISH COLUMBIA 1 s | BRITISH COLOMBIA RAILWAY i 1 J volume of f r e i g h t i n B. C. ( m e t r i c tonnes ) | km of mainline t r a c k i n B. C. | number of mai n l i n e s | number of major t e r m i n a l s | 3.02 m.| 1 2066., | f 3 | J 13 | 1 CANADIAN NATIONAL BAILWAY 1 1 j volume of f r e i g h t i n B. ,C. ( m e t r i c tonnes ) | km o f mainline t r a c k B. C. I number of mainlines | number of major t e r m i n a l s I 24.79 m.J I 2227. I i 3 | i 14 1 | CANADIAN PACIFIC RAILWAY ! i j volume of f r e i g h t i n B. „C., { m e t r i c tonnes ) J km of mainline t r a c k i n B. C. J number of ma i n l i n e s | number of major t e r m i n a l s | 23.6 m. | | 2838. | 1 5 i \ 1 1 I BURLINGTON NORTHERN BAILBOAD ( B . C . . POBTION) i ! | volume of f r e i g h t j km of mainline t r a c k | number of ma i n l i n e s | number of connections to Canadian r a i l w a y s | number of major t e r m i n a l s I n. a. | i 120. | 1 1. J 1 3. , | 1 2. | * s Reference Nos. 38 & 39 and d i s c u s s i o n s with o f f i c i a l s of the BCB, CN, S CP 32 T h e m a i n i n t e r e s t o f t h i s s t u d y w i l l b e t h e r a i l n e t w o r k o f t h e S o u t h e r n M a i n l a n d . T h i s i s B e c a u s e i t c a r r i e s a l a r g e a m o u n t o f t h e t r a f f i c , p r o v i d e s i m p o r t a n t s e r v i c e s t o t h e m a j o r c e n t r e s , a n d h a s t h e b e s t p o t e n t i a l t o e n h a n c e t h e f l e x i b i l i t y ( fiedundancy ) . I n o r d e r t o p r o v i d e f o r a h i g h e r d e g r e e o f r e l i a b i l i t y , b a s e d s o l e l y o n t h e g r e a t e s t n u m b e r o f p o s s i b l e p a t h s t h e r a i l n e t w o r k o f t h e S o u t h e r n M a i n l a n d i s t h e m o s t c o s t e f f e c t i v e l o c a t i o n t o u n d e r t a k e s u c h i m p r o v e m e n t s . F i g u r e 5 s h o w s t h e s c h e m a t i c r e p r e s e n t a t i o n o f t h e r a i l n e t w o r k o f t h e S o u t h e r n M a i n l a n d . I m p o r t a n t t o n o t e i s t h e v l u n e r a b i l i t y o f t h e F r a s e r C a n y o n p o r t i o n o f t h i s n e t w o r k . A l l t r a f f i c m u s t f l o w t h r o u g h o r p a s t L y t t o n . T h i s a l l o w s L y t t o n t o b e c o m e t h e " w e a k 1 * l i n k ( O f c o u r s e , l y t t o n i s a n o d e n o t a l i n k ) i n t h e r a i l n e t w o r k . I t i s t h i s p r o b l e m t h a t i s t h e m a j o r f o c u s o f t h i s t h e s i s . ( T h e e l i m i n a t i o n o f t h e t o t a l r e l i a n c e o n s u c h n o d e s o r l i n k s . ) P r o p o s e d l i n k s s u c h a s t h e A s c a c r o f t - P a v i l l i o n l i n k a n d t h e H o p e - B r o o d i e l i n k p e r m i t s t h e b y - p a s s i n g o f t h e F r a s e r C a n y o n e n t i r e l y . T h e s e t w o l i n k s w i l l b e s t u d i e d t o d e t e r m i n e t h e i r f e a s a b i l i t y f o r i n c l u s i o n i n t h e n e t w o r k . T a b l e 4 o u t l i n e s t h e l i n k s , i d e n t i f i e s t h e c a r r i e r , d i s t a n c e s b e t w e e n n o d e s , a n d t h e o p e r a t i o n a l s t a t u s o f t h e l i n k . T h e s e 30 l i n e s a r e t h e l i n k s o f t h e S o u t h e r n M a i n l a n d , s o u t h o f a n i m a g i n a r y l i n e d r a w n f r o m K a m l o o p s t o P a v i l l i o n . T h e r e l i a b i l i t y a n a l y s i s f o c u s e s o n t h e s e l i n k s . N u m b e r i n g t h e m a l s o a l l o w s f o r t h e n e t w o r k r e d u c t i o n p r o c e d u r e t o b e i m p l e m e n t e d . E a c h l i n k ( n u m b e r ) r e p r e s e n t s a d i r e c t c o n n e c t i o n b e t w e e n t w o n o d e s . 33 F I G U R E 5 1 T H E B A I L METHOBK O F T H E S O U T H E R N M A I N L A N D ± 8. ; C . 1 A S H C K J C T T a b l e H A p r o v i d e s i n f o r m a t i o n f o r t h e f o u r p r o p o s e d l i n k s . T h e s e l i n k s a r e t h e m o s t f e a s a b l e t o b e i n c l u d e d i n a n i m p r o v e d n e t w o r k . T h e y a r e e i t h e r r e l a t i v e l y s h o r t d i s t a n c e s ( 100 km m a x i m u m ) o r a r e l o c a t e d o n a n a b a n d o n e d r a i l r i g h t - o f - w a y . T h e s t a t u s c o l u m n d e n o t e s w h e t h e r t h e l i n k i s a b a n d o n e d ( A ) , o p e r a t i o n a l { 0 ) , o r p r o p o s e d ( P ) . TABLE 4 I NODE/ LINK S EPS E S E NT ATIO N OF THE FAIL NETWORK l i n k I l i n k | between I d i s t a n c e | s t a t u s I c a r r i e r l e t r 1 no ] nodes 1 (km) a 1 1 1 19-21 1 300 1 o I bcr b 1 2 | 19-29 I 10 1 o I cn/c p c 1 3 | 18-29 I 20 1 o i bn/cn d 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 | 1 0 | 3-14 | 85 \ o cn k 1 1 1 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 ! cn n 1 14 | 11-12 | 5 1 o cn 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 cn/cp t 1 20 | 9-26 | 215 1 o cp u 1 21 1 9-30 i 250 1 o 1 cp V 1 22 | 15-30 1 350 i o cp w 1 23 | 20-22 | 50 1 o ! cp 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 MBkl J i l l MEM NODE REPRESENTATION FOR THE PROPOSED/ ABANDONED LINKS aa 1 27 J 3-22 ] UO P I (ber) bb 1 28 | 5-10 \ 100 a J I (cp) cc t 29 I 13-23 | 50 P 1 I (cp) dd 1 30 I 15-22 | 150 a 1 • « (cp) FI60BB 6 J. NODE / LINK SCHEMATIC OF THE BAI£ NETWORK OF THE SOOTHESN MAINLAND 36 R e f e r i n g t o F i g u r e s 4 5 5 , t h e f o l l o w i n g r a i l l i n e s a r e s h o w n a s d a s h e d l i n e s : 1. T h e A s c h r o f t - P a v i l l i o n ( C l i n t o n ) l i n k , 2 . T h e D r i f t w o o d - C e a s e L a k e l i n k , 3 . T h e H o p e - E r o o d i e l i n k , 4 . T h e K e l o w n a - P e n t i c t o n l i n k , a n d 5 * T h e P e n t i c t o n - H i d w a y l i n k . T h e A s h c r o f t - P a v i l l i o n l i n k i s u n d e r c o n s i d e r a t i o n f o r c o n s t r u c t i o n b y t h e B r i t i s h C o l u m b i a R a i l w a y • T h e D r i f t w o o d D e a s e L a k e l i n k o f t h e B C R i s s c h e d u l e d t o b e c o n s t r u c t e d a l t h o u g h c o n s t r u c t i o n w a s t e m p o r a r i l y h a l t e d i n 1 9 7 7 d u e t o a m a j o r s h i f t i n g o v e r n m e n t p o l i c y . T h i s l i n e w i l l b e t h e s o u t h e r n t i e - i n f o r a r a i l c o n n e c t i o n t o A l a s k a w h i c h h a s b e e n c o n s i d e r e d b y 0 S a u t h o r i t i e s o n a n d o f f f o r many y e a r s . T h e H o p e - B r o o d i e l i n k a n d t h e P e n t i c t o n - M i d w a y l i n k w e r e a b a n d o n e d i n t h e 1 9 7 0 ' s d u e t o a l a c k o f r e v e n u e t r a f f i c . T h e K e l o w n a - P e n t i c t o n l i n k i s o n e w h i c h I h a v e d e s i n g a t e d . T h e s e f o u r S o u t h e r n M a i n l a n d p r o p o s e d l i n k s a r e l i k e l y t o b e t h e m a x i m u m n u m b e r c o n s i d e r e d a t t h i s p o i n t . T h e i r p o t e n t i a l o f n e t w o r k e n h a n c e m e n t i s g r e a t w h i l e t h e i r d i s t a n c e s a r e r e l a t i v e l y s h o r t . I n o r d e r t o p e r f o r m t h e n e t w o r k r e d u c t i o n p r o c e d u r e n u m b e r e d l i n k s a r e r e g u i r e d . I n i t i a l l y t h e l i n k s a r e l e t t e r e d w i t h t h e n o d e s n u m b e r e d . When t h e a n a l y s i s i s p e r f o r m e d , t h e l e t t e r s a r e t r a n s l a t e d i n t o n u m b e r s . T h i s n e t w o r k r e d u c t i o n s c h e m e m a n i p u l a t e s t h e n e t w o r k by e l i m i n a t i n g t h e i n h e r e n t 37 redundancies thus making the r e l i a b i l i t y a n a l y s i s s i m p i l e r . 1 6 T h i s i s shown i s F i g u r e 6 with r e f e r e n c e to Table 2. Cost c o n s i d e r a t i o n s f o r a g u i s i t i o n of the r i g h t s - o f - w a y , r e c o n d i t i o n i n g of present b r i d g e s 6 roadbeds, as well as new c o n s t r u c t i o n i s o u t l i n e d i n Table 5 . 1 7 These f i g u r e s are est i m a t e s and should be used f o r com p a r i s i c n s only. TABLE 5 i COST ESTIMATIONS FOB PBOPOSED L l i K S $ MILLION BIGHT OF HAY AQUASITION i OPGBADING I OF | FACILITIES I NEW j I CONSTRUCTION TOTAL | COST | | DRIFTWOOD-| DEASE LAKE j • 0. 1 o I 829.5 829.5 | | ASCHCBOFT-| PAVILLION i .492 | 0 | 140,0 140.5 1 | HOPE -J BBOODIE i 1. 23 I 175.0 1 o 176.3 J 1 KELGWNA -| PENTICTON 0 1 o | 175.0 175.0 i I PENTICTON-J MIDWAY i i o 1 262.5 1 o 262.5 } Omitting the Driftwood - Dease Lake l i n k s i n c e i t does not a f f e c t the Southern Mainland network. , The P e n t i c t o n - Midway c o s t s the most while A s h e r o f t - P a v i l l i o n c o s t s the l e a s t . From a c o s t p o i n t o f view on l y , the A s h c r o f t - P a v i l l i o n t h e r e f o r e should be the f i r s t l i n k t o c o n s t r u c t . Note t h a t d i f f e r e n t l i n k s have more p o t e n t i a l i n terms of t h e i r a b i l i t y t o enhance the 1 6 Reference No.,41 Pages 1 2 - 2 2 * 7 See Appendix A For D e t a i l e d C a l c u l a t i o n s . 38 ( r e l i a b i l i t y of) network. In t e r n s of r e l i a b i l i t y enhancement only, the r a n k i n g would be, from most e f f e c t i v e t o l e a s t e f f e c t i v e : A s c h c r o f t - P a v i l l i o n , P e n t i c t o n - Midway, Hope Broodie ,and 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 w i l l be proven l a t e r by the a n a l y s i s . One of the o b j e c t i v e s of t h i s study i s t o determine which l i n k ( s ) , i f any, should be c o n s t r u c t e d now to avoid p e n a l t y c o s t s l a t e r due t o the c l o s i n g of a l i n k given a c a t a s t r o p h i c event. Co s t s a s s o c i a t e d with with l i n k c l o s u r e are: Increasedd t r a v e l c o s t s , Increased t r a v e l time. Delay time, and i n c r e a s e d labour c o s t s due to the r e s u l t i n g i n e f f i c i e n t o p e r a t i o n . 4. 2 NETJOBK THBOBY In any e x t e n s i v e network , there may e x i s t many d i f f e r e n t paths between one node to another. Sometimes these paths are unique while other times they are shared by o t h e r n o d e - p a i r s . These paths a r e known as " t i e - s e t s " which are d e f i n e d as a group o f l i n k s ( or a s i n g l e l i n k ) which connect two nodes. T h i s i n t e r c o n n e c t i o n i s s u b j e c t to flow r e s t r i c t i o n s , which i n t h i s case do not e x i s t as a l l l i n k s are b i - d i r e c t i o n a l . 1 8 In the g e n e r a l case, there c o u l d be any number of i n p u t s and outputs between the end-nodes. F i g u r e 7 shows a g e n e r a l network using two i n p u t s and two outputs. There then e x i s t f o u r major subsets of t r a v e l those being : 11 to 01 , 11 to 02 , 12 to 01 , and 12 t o 02. J J i t h i n each major subset t h e r are many d i f f e r e n t t i e - s e t s ( or paths ). In complex networks the number o f d i f f e r e n t p o s s i b l e t i e - s e t s combinations c o u l d be 1 8 Beference No. 32 Page 40 39 enormous. Remember these combinations are not j u s t the number of output r a i s e d to power of the i n p u t s . That i s the d e f i n i t i o n of the number of the major s u b s e t s ) . , In any g e n e r a l network, there e x i s t s f i v e p o s s i b l e t i e - s e t combiantions. They are : 1. Any i n p u t t o any output 2. Each i n p u t to each output 3. Any i n p u t to each output 4. Each i n p u t to any output 5. Some i n p u t s t o seme outputs In the case of t r y i n g t o e s t a b l i s h the r e l i a b i l i t y o f the B C r a i l network , the a b i l i t y to t r a v e r s e the F r a s e r Canyon i s the u l t i m a t e o b j e c t i v e , so the a b i l i t y to go from any i n p u t on one s i d e t o any output on the other s i d e i s the t i e set p o s s i b i l i t y chosen., T h i s i s shown by Fig u r e 8 , which i s not r e l a t e d t o Fig u r e 7. In the case of the canyon, a l l t r a f f i c which t r a v e r s e s i t i s gathered together at Vancouver or Kamloops. T h i s makes i t a case of each i n p u t t o each i n p u t , but s t a y i n g with the g e n e r a l case: 40 FIGURE 8 i ANY INPUT TO ANY OUTPUT a b 1 c J , ) d e f § INPUT • OUTPUT 1 g b I where the dashed l i n e s r e p r e s e n t a s e r i e s of i n d i v i d u a l l i n k s i d e n t i f i e d by l e t t e r s a - h. The t o t a l p r o b a b i l i t y of the network i n F i g u r e 8 i s simply the sua of the p r o b a b i l i t i e s of each p a r a l l e l l i n k . The p r o b a b i l i t y of a s e r i e s of l i n k s i s simply the product of the i n d i v i d u a l p r o b a b i l i t i e s . T h e r e f o r e , the t o t a l p r o b a b i l i t y i n t r a v e r s i n g from the i n p u t to the output, i n the case of F i g u r e 8 i s 5 P = (a) (b) * ( c ) * (d) (e) <f)*(g) ( M l t o t a l f a i l u r e - (abc)-(abdef|-(abgh)-(cgh) Eaguation 5 - (defgh)-(cdef) ••• (abcdefgh) where : BELIABILITY = 1 - P t o t a l t o t a l f a i l u r e T h i s r e l i a b i l i t y w i l l i n c r e a s e or decrease depending on the a d d i t i o n and d e l e t i o n s of l i n k s and whether those l i n k s are i n p a r a l l e l or s e r i e s . A convenient method o f c a t a l o u g i n g a form of o r i g i n / d e s t i n a t i o n matrix f o r the l i n k s i n a network i s known as a C o n n e c t i v i t y Matrix as shown by P a r n o u s s i s . 1 9 t h i s i s simply a matrix which i n d i c a t e s where a connection e x i s t s between any two 1 9 Reference No. 32 Page 43 41 nodes. I f such a connection e x i s t s a " 1 " then the matrix element i s " 1 " w h i l e " 0 " i n d i c a t e s t h a t no d i r e c t c o n n e c t i o n e x i s t s . FIGURE 9 i CONNECTIVITY HJTRIX FOB THE PRESENT RAIL NETWORK OOOOOOOQOilboOOO 101000000000000 000000000000000110000000000000 00000000 0001010000000000000000 0Q000O000000O0000000000000000 0 OJjg20OOOOOOOOOOOOOOQOOOO1O1OOOO 000000000000000000000000000000 000000000000000000000000000000 oooooooooooooooooooooooooooooo 0O000O000OOG00OO00000000010001 000000000000010000000000000000 00000000 0000000010000000001000 00100000 001000000000000000000 0 010000000 00000000000000000000 0 001000000100000100000000001000 000000000000000000000000000001 100000000000010000000000000010 0100000000000000100000OQOOQO00 100000000000000000000000000010 000000000000000000001000000010 000000000000000000000 100000010 000000000000000000010000000010 oooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooo 00001000 0000000000000000000000 00000000000000000000001000000 0 010000001000000100000000000000 000010000010010000000000000000 oooooooooooooooooooooooooooooo 000000000000000101100000000000 000000001000001000000000000000 FIGURE JO \i CONNECTIVITY HATRIX FOR PROPOSED NETWORK 000000000100000101000000000000 000000000000100110000000000000 000000000001010000000100000000 oooooooooooooooooooooooooooooo 000000000100000000000001010000 oooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooo 000000000000000000000000010001 000010000000010000000000000000 000000000001000010000000001000 001000000010000000000000000000 010000000000000000000010000000 001000000100000100000000001000 000000000000000000000100000001 100000000000010000000000000010 010000000010000000000000000000 100 000000000000000000000000010 0000000000OOOOO000O000OO000O10 00000000000000 0000000000000010 000000000000000000101010000010 001000000000000100000000000000 000000000000100000000000000000 0000 10000000000000000000000000 oooooooooooooooooooooooooooooo 010000001000000010 000000000000 000O100OOO1OO10000000000000000 oooooooooooooooooooooooooooooo 000000000000000101100000000000 000000001000010000000000000000 F i g u r e s 9 and 10 show the matracies f o r t t h e e x i s t i n g r a i l network and the proposed network r e s p e c t i v e l y . A l l the t i e -s e t s i n these matracies are b i - d i r e c t i o n a l . A l s o , the number of the nodes from 1 through 30 correspond i n c r e m e n t a l l y to the rows and columns of these matracies but are not shown. Thus, the con n e c t i o n from 1 to 10 y i e l d s a " 1 " which s i g n i f i e s t h a t a co n n e c t i o n e x i s t s . . W h i l e the 5 to 3 p a i r y i e l d s a a " 0 " thus no d i r e c t c onnection e x i s t s . 42 4. 3 i LINK PR0B&BILIT3 THEORY To determine the l i n k p r o b a b i l i t i e s , three methods are a v a i l a b l e : 1. S u b j e c t i v e p r o b a b i l i t i e s based on topography and past experience.,, 2. Random p r o b a b i l i t i e s . 3. P r o b a b i l i t i e s assigned on the b a s i s of an equation p r e d i c t i n g the magnitude of some c a t a s t r o p h i c event. C e r t a i n l y , the complexity of the r e l i a b i l i t y i n v e s t i g a t i o n d i f f e r s between which method i s used, i n c r e a s i n g i n s o p h i s t i c a t i o n from Method 1 t o Method 3. Method 1 would make t h i s i n v e s t i g a t i o n a simple e x e r c i s e of r e l i a b i l i t y and network a n a l y s i s . I t may be u s e f u l , however, to o b t a i n a b a s i c i d e a of the c u r r e n t c o n d i t i o n o f the system. I t i s a l s o apparent t h a t c e r t a i n l i n k s are more v u l n e r a b l e to f a i l u r e than o t h e r s due t o the geographic nature of the p r o v i n c e , network makeup, and the p h y s i c a l c o n d i t i o n of the r a i l w a y l i n e , zo P r o b a b i l i t i e s o f s u r v i v a l ( or f a i l u r e ) ; may be assigned using a s c a l e o f 1.0 to 0.0 with 1.0 being c e r t a i n f a i l u r e with 0.0 being c e r t a i n success. T h i s type of p r o b a b i l i t y assignment would take i n t o account c e r t a i n p h y s i c a l and man-made f e a t u r e s . O b v i o u s l y , the disadvantage of t h i s approach i s t h a t the 2 0 H e f e r i n g t o F i g u r e No. 2 the p a r a l l e l and s e r i e s l i n k s are c l e a r l y e v i d e n t . assignment i s s u b j e c t i v e and may vary g r e a t l y . T h i s i s an example of how the process of s u b j e c t i v e p r o b a b i l i t y assifnment may perform. Note t h a t t h e r e i s no " r e t u r n p e r i o d " a s s o c i a t e d provided with these p r o b a b i l i t i e s . A c h o i c e f o r the r e t u r n p e r i o d must be made and there are two c h o i c e s . One i s t o choose the r e t u r n p e r i o d of earthquakes occurrence while the other i s the s t r u c t u r e l i f r . These p r o b a b i l i t i e s would be expressed as p r o b a b i l i t y of f a i l u r e per year o r cummulative events per year. The f o l l o w i n g t a b l e shows an example of s u b j e c t i v e p r o b a b i l t y assignment : TABLE 6 1 SUBJECTIVE PROBABILITY ASSIGNMENT HAZ ARD 1 PROB. OF FAILURE CANYON AREA SLOPES. , WITH UNSTABLE 1 1 1 0.08 PROXIMITY TC FAULT. AN ACTIVE 1 i i 0.-Q-6 BRIDGE OVER 30. M. LENGTH i i 0.04 LEVEL GRADE *~ ON FILL i i 0.02 LEVEL GRADE l ON STABLE S0IL| 0.01 P r o b a b i l i t i e s a re assign e d with the view t h a t each o f these s i t u a t i o n s can onl y withstand c e r t a i n l e v e l s of peak a c c e l e r a t i o n due to earthquakes. A s s i g n i n g these p r o b a b i l i t i e s to the network of the Southern Mainland, i s i n F i g u r e 11. A high p r o b a b i l i t y of 44 f a i l u r e has been assigned to the F r a s e r Canyon, the b r i d g e s between Abbotsford - Hatsgui ( Misson ), Vancouver - North Vancouver And new Westminster - Surrey. For p r e c i s e a n a l y s i s , t h i s method of us i n g s u b j e c t i v e p r o b a b i l i t y assignment i s not recommended but should only be used to gain a g e n e r a l i d e a of what the r e l i a b i l i t y might be. 22 FIGORE 11 ; SUBJECTIVE PROBABILITY ASSIGNMENT ASCH KJCT .01 .01 MTCB SICA GOLD KAHL \ . 01 . 01 ARMS NHES HOPE .0 1 ABOT PR IN .03 PENT OSOY* M.ID8 WARD The second method would e n t a i l the use of a random number generator which would supply p r o b a b i l i t i e s o f f a i l u r e , w i t h i n a c e r t a i n range of values c o r r e s p o n d i n g with each s p e c i f i c s i t e or s i t u a t i o n ). T h i s method a l l o w s a c e r t a i n amount of randomness to be i n c l u d e d i n the p r o b a b i l i t y assingment. The disadvantage, however, i s t h a t s u c e s s i v e r e s u l t s would not take i n t o account the p r e v i o u s r e s u l t s , s i n c e random numbers gen e r a t o r s are memoryless processes. In the case of earthquakes and 45 l a n d / r o c k s l i d e s a c e r t a i n amount of " s t r a i n r e l e a s e " e x i s t s . Thus , a f t e r each occurrance there would be a form o f " r e t u r n p e r i o d " a s s o c i a t e d with the next occurrance. S i n c e t h i s i s not modeled by t h i s method, i t i s u n s a t i s f a c t o r y . The t h i r d method i s to estimate p r o b a b i l i t i e s based on the occurrence of a s p e c i f i c c a t a s t r o p h i c events a c h i e v i n g a minimum i n t e n s i t y , where i n t e n s i t y can be any measure of earthquake f o r c e i n terms o f B i c h t e r or MMI magnitudes, v e l o c i t i e s or a c c e l e r a t i o n s experienced, or f a u l t movement. T h i s q u a l i f e r e l i m i n a t e s i n t e n s i t i e s which are i n s i g n i f i g a n t . 2 1 4.4 1 ATTENUATION PBBDICTION Ta l e b - Agha used a method t h a t p r e d i c t s the a t t e n u a t i o n s of earthquake peak a c c e l e r a t i o n s . A maximum peak a c c e l e r a t i o n e x i s t s f o r any s t r u c t u r e which can be t o l e r a t e d before some degree o f f a i l u r e o ccurs. Thus i f : A > A s - s a c t u a l c r i t i c a l then < some degree of ) f a i l u r e w i l l occur. The method uses an equation developed by E s t e v a 5 Rosenblueth and r e f i n e d by Donovan, Milne ,and T a l e b - Agha. 2 2 Given e i t h e r an a c t i v e f a u l t or a zone of earthquake a c t i v i t y , a t t e n u a t i o n s can be p r e d i c t e d f o r any d i s t a n c e from 2 1 t h i s i n v o l v e s the s t a t i s t i c a l p r ocess known as c e n s o r i n g where unwanted data can be excluded form c o n s i d e r a t i o n . 2 2 Beference No. 7 6 Beference No. 41 Pages 7-10 r e f e r e n c e No. 27 46 the f a u l t , or centre of a c t i v i t y , by the f o l l o w i n g e q u a t i o n : 2 3 (b m) -b ) 2 3 a (m,d ) | EQS | = b e (d * c) Equation 6 s s 1 s 2 where : a = peak a c c e l e r a t i o n i n cm/sec given s EQS = some earthquake event a t a s = p o i n t s i t e with some r = d e t e r m i n i s t i c r e s i s t a n c e and s m = r i c h t e r maqnitude , such t h a t z. d = max (d ,d ) with s o s d = d i s t a n c e between the s i t e and e p i c e n t r e (km) s d = 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 o a t t e n u a t e s from upper bound which i s t h a t of e p i c e n t r e , where t h i s value depends on the s o i l & rock c o n s i t i o n s a t the e p i c e n t r e , b ,b ,b ,£ c = are c o n s t a n t s which are determined using known 1 2 3 data 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 of e s t i m a t i o n s of the c o n s t a n t s b S c based on work done by the v a r i o u s authors i n Southern C a l i f o r n i a , San F r a n c i s c o , Western Canada, Puget Sound ,and Boston. Using some form of r e g r e s s i o n a n a l y s i s t o obtain a best f i t l i n e . These e s t i m a t i o n s as w e l l as i n f o r m a t i o n s a p p l i c a b l e to B r i t i s h Columbia , y i e l d s the f o l l o w i n g values f o r the b»s: 2 4 2 3 E s t e v a , L u i s / Bosenblueth, E. Sp e c t r a o f Earthguakes at Moderate S Large D i s t a n c e s Soc. Hex. De Ing. S i s m i c a , 2,1964 2 * See Appendix B f o r d e t a i l e d c a l c u l a t i o n s . 47 fa = 1402 b = 0.69 b = 1.65 c = 25 1 2 3 The r e s u l t i n g e q uation i s : 0.69 (ni) -1.65 A = 1402 e ( d + 25 ) Equation 7 s s To show the v a l i d i t y of such a method Table 7 summarizies the s i x most s i g n i f i g a n t earthquakes o c c u r r i n g i n B r i t i s h Columbia over the past 35 years. TABLE 7 1 EARTHQUAKE CHARACTEfilSTICS DATE MAGNITUDE kM. 1 LONG H 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 The western r e g i o n of Canada has experienced numerous s t r o n g earthquakes i n recent times as shown i n F i g u r e 12. These are the earthquakes with a magnitude o f R i c h t e r 4.0 and g r e a t e r . 2 5 B C i s d i v i d e d i n t o f o u r earthquake zones, a through D. These r e p r e s e t the g e o g r a p h i c a l c l u s t e r i n g of the earthquakes over time. .  2 5 Reference No.,27 Page 1176 48 Z o n e A r e p r e s e n t s t h e P u g e t S o u n d a r e a e a r t h q u a k e s . T h e e a r t h q u a k e s i n t h i s a r e a , i f o f a s t r o n g ( r i c h t e r 6.0 ) m a g n i t u d e , c a n b e f e l t i n t h e L o n e r M a i n l a n d a r e a . Z o n e B i s t h e s o u t h e r n J u a n d e F u c a f a u l t w h i l e Z o n e C i s t h e n o r t h e r n J u a n d e F u c a f a u l t . E A R T H Q U A K E S I N B R I T I S H C O L U M B I A T h i s f i g u r e t a k e n f r o m W . , G . M i l n e ( r e f e r e n c e N o . 21 ) 49 I t i s f r o m t h e s e t w o z o n e s w h e r e t h e m a j o r i t y o f B r i t i s h C o l u m b i a e a r t h q u a k e s o r i g i n a t e . N o t e i n F i g u r e 12 t h e i n t e n s i t i e s v a r y f r o m a b o u t 4 . 0 t o 7 . 5 . Z o n e D r e p r e s e n t s t h e i n t e r i o r o f t h e p r o v i n c e w h e r e t h e e a r t h q u a k e s a r e f o r t h e m o s t p a r t , i n s i g n i f i g a n t . U S ORB V3 -£ B M l S I A i lAHkl SYSTEM T h i s f i g u r e f r o m F i t z e l l ( r e f e r e n c e no . 10) 50 The r e g i o n a l f a u l t system of Vancouver I s l a n d / Puget Sound i s shown i s F i g u r e 13. 2 6 The f a u l t s i n the r e g i o n are shown by three l i n e sources those being ; PS 1 , V 1 ,, and V 2. „, These three f a u l t s account f o r the m a j o r i t y of the a c t i v i t y a long the Juan de Fuca p l a t e . Note that the PS 1 l i n e s ource extends i n a north-south d i r e c t i o n along Puget Sound. T h i s f a u l t i s a s i g n i f i g a n t i n t h a t many of the s t r o n g e r earthquakes have o r i g i n g a t e d from t h i s a r e a . T h i s s i t u a t e s the c e n t r e of a c t i v i t y of the r e g i o n i n the v i c i n i t y of the Gulf I s l a n d s , ft composite of these t h r e e l i n e s i s drawn and i s designated S. T h i s i s the l i n e source which determines the d i s t a n c e d (s) between the c e n t r e s i n the province t o the earthquake point sources. . Note th a t the constant value (c) of 25 a l l o w s f o r the u n c e r t a i n t y i n measuring the f o c a l d i s t a n c e t o the l i n e source. Equation 7 may now be used to f o r e c a t the expected a c c e l e r a t i o n s due t o the r e g i o n a l f a u l t system of i n F i g u r e 13. These e s t i m a t e s are compared with the values o b t a i n e d by F i t z e l l who used a l l three l i n e sources s e p a r a t e l y and then combined them i n t o a composite value. His method g i v e s a more "average" value of peak a c c e l e r a t i o n . D i s t a n c e s are s t r a i g h t l i n e d i s t a n c e s , f o r i n s t a n c e the d i s t a n c e to Vancouver i s 50 km p l u s the c o n s t a n t c or a t o t a l of 75 km. 2& Reference No.,10 Page 114 51 TABLE 8 1 PREDICTED ACCELERATIONS ce n t r e d i s t a n c e ( km ) p r e d i c t e d peak . a c c e l e r a t i o n s * (using a t t e n u a t i o n egn.) 4 5 6 6.5 7 F i t z e l l V i c t o r i a 25. 35. 70. 138J 196.i 276. I 196. Vancouver 50. 18. 36. 71.| 100.J 141. 1 i 12.| 16.| 23. 9 8-147 L y t t o n 200. , 3. 6. 49, Kamloops 250. 2. { 4. 8.J 12-t 18. 10, * note that these a c c e l e r a t i o n s are i n cm/second 2 ( where 1.0 g = 980.0 cm / sec ) The r e s u l t s of the a t t e n u a t i o n s as c a l c u l a t e d by Equation 7 and F i t z e l l r e s u l t i n ^general agreement. -This i s e s p e c i a l l y t r u e f o r the h i g h e r magnitudes and a l s o f o r the c e n t r e s c l o s e r t o the f a u l t system such as Vancouver and V i c t o r i a . . F i t z e l l obtained h i s a c c e l e r a t i o n s by t a k i n g i n t o account a l l earthquakes which have occurred ( up t c r i c h t e r 7.5 ). T h i s a n a l y s i s has given 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 l e v e l s of magnitude. A g r a p h i c a l summary of F i t z e l l * s work i s shown i n F i g u r e 14 on the next page. 2 7 These two maps show the Lower Mainland area and the e n t i r e Southern Mainland. Of i n t e r e s t i s the e f f e c t of the Puget Sound l i n e source on the Southern Mainland., T h i s source e f f e c t i v e l y i n c r e a s e s the expected a c c e l e r a t i o n s by about 0.5 g. 2 7 Reference No. 10 Page 121 S Page 137 FIGUBE Ui J. EXPECTED PEAK ACC EL EB ft TI 0 HS SCAUt 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) for T>1007T(.,b>23ra. This figure from F i t z e l l (reference no. 10) 53 HsJ2 1 L I N K P R O B A B I L I T Y A S S I G N MB NT T a l e b - A g h a { R e f e r e n c e N o . 40 S 41 ) h a s m a n i p u l a t e d t h e p r e d i c t i v e p e a k a c c e l e r a t i o n e g u a t i o n { n o . 7 ) s o t h a t t h e l i n k p r o b a b i l i t i e s may b e o b t a i n e d d i r e c t l y * T h i s i s d o n e b y a s s i g n i n g m a x i m u m a l l o w a b l e a c c e l e r a t i o n s t o e a c h l i n k . E a c h l i n k i s a s p e c i f i c d i s t a n c e f r o m a n e a r t h g u a k e s o u r c e , i n t h i s c a s e f r o m t h e l i n e s o u r c e a s s h o w n i n F i g u r e 1 3 ) . T h e n m a x i m u m a n d m i n i m u m e a r t h g u a k e ( r i c h t e r ) m a g n i t u d e s a r e d e t e r m i n e d f o r t h e a r e a d u e t o p a s t e x p e r i e n c e . F o r a n y g i v e n m a g n i t u d e o f e a r t h g u a k e t h e r e i s a s p e c i f i c p r o b a b i l i t y o f f a i l u r e t h a t i s t o b e c a l c u l a t e d . F o r a s y s t e m o f s e r i e s l i n k s , f a i l u r e w i l l o c c u r i f t h e a c c e l e r a t i o n e x p e r i e n c e d i s g r e a t e r t h a n o r e q u a l a l i n k r e s i s t a n c e . T h i s i d e a i s c o n t a i n e d i n t h e f o l l o w i n g s e t o f e g u a t i o n s , w h e r e a l i n k 1 ( i ) w i l l f a i l i f i t s r e s i s t a n c e r ( i ) i s l e s s t h a n o r e q u a l t o t h e p e a k a c c e l e r a t i o n a ( s ) e x p e r i e n c e d d u e t o a n e a r t h q u a k e e v e n t E Q S o r : P { r < A I EQS } s u b s t i t u t i n g e q u a t i o n 6 y i e l d s : i -• b 2 P { r < b e i - 1 - b 3 I EQS } r e - a r r a n g i n g : P { m > ( 1 /b ) I n ( B / b ) 2 1 I E Q S } E q u a t i o n 8 - b w h e r e : B = r ( d ) i s 3 E x p r e s s i n g i n a d i f f e r e n t w a y , i f a n e a r t h g u a k e e v e n t EQS h a s a m a g n i t u d e H o f g r e a t e r t h a n o r e q u a l t o a c r i t i c a l 54 magnitude M (cr) ( where ti (cr) i s a c r i t i c a l magnitude which w i l l produce peak a c c e l e r a t i o n s g r e a t e r than those which the l i n k can withstand , then f a i l u r e w i l l occur. T h i s can be s i m p l i f i e d by using Eguations 8 6 9: P ( m > H ) Equation 9 c r where: -b 1 r (d • c) 3 i s a = — — In • Equation 10 c r b b 2 1 S u b s t i t u t i n g the known c o n s t a n t s i n t o Equation 10 r e s u l t s i n the f o l l o w i n g : -1.65 1 r (d + c) i s = l n —• Equation XI ct 0.69 1402. f To f i n d the p r o b a b i l i t y of s u r v i v a l ( or f a i l u r e ) of the l i n k , the frequency of occurrence o f t h i s c r i t i c a l magnitude earthquake H (cr) must be p r e d i c t e d . , The r e c u r r e n c e equation (no. 4) which r e l a t e s earthquake r i c h t e r magnitudes a with the freguency of occurrence H w i l l be used f o r t h i s purpose. A poisson a r r i v a l r a t e y i e l d s : - < v ) < t ) P = 1 - e Equation J.2 where : f a i l u r e v = H ( H ) with : cr N = the mean annual r a t e of occurrence of the c r i t i c a l magnitude H and c r t = the number of years Values of l i n k r e s i s t a n c e must now be assigned t o the network. These r e s i s t a n c e s are the r (i) which i s to be used i n 55 Equation 10 and then i s s u b s t i t u t e d i n t o E q u a t i o n 9 to o b t a i n the p r o b a b i l i t i e s of f a i l u r e . These assigned r e s i s t a n c e s are found i n Table 9: TABLE 9 . : LINK RESISTANCES S t r u c t u r e \ R e s i s t a n c e s 2 J j g - f o r c e cm/sec. j bridge < 30 IB I 1.0 98.0 J s t e e l bridge I 0.15 138.0 | s t a b l e f i l l | 0.25 230.0 | lo o s e f i l l I 0.20 196.0 | To determine the p r o b a b i l i t y of s u r v i v a l r e q u i r e s a f o u r step c a l c u l a t i o n process which i s : 1. Assign l i n k r e s i s t a n c e s to each l i n k u s i n g the guides i n Table 9. T h i s has been done and are i n Table 10. 2. Nest determine the c r i t i c a l magnitude H (cr) by Equation 1.0. Host of the data has already been predetermined f o r t h i s , a l l t h a t needs to be estimated i s the d i s t a n c e d (s) from the l i n e source and the l i n k r e s i s t a n c e . 3. Determine the r a t e of occurrence of the c r i t i c a l magnitude M (cr) u s i n g Eguation 4. 4. S u b s t i t u t e those values i n t o Equation 12 to o b t a i n the p r o b a b i l i t y o f f a i l u r e ( s u r v i v a l ) of the l i n k given the s e i s m i c i t y of the r e g i o n . , A summary o f these l i n k p r o b a b i l i t i e s are shown i n the l a s t 56 column o f Table 10. L i n k s 11 and 12 have been combined i n t h i s i n s t a n c e and l i n k 11 ' w i l l designate both. TABLE JO i . LINK P BOB ABILITIES | LINK ] i NO. | 0 I (KB) J RESISTANCE| 0 * (CH/S.SQ) | CR 1 1 N * I PROBABILITY OF | ]SURVIVAL J FAILURE | 1 1 1 150 | 230. I 9.3 1. 0005 ) .995 1 .005 | | 2 1 50 | 138. , 1 7.0 1 0.5 | .500 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 | 230. \ 10.3 1- 0001 1 -998 I .002 | | 11/12} 250 | 230. ,• | 10.3 1- 0001 I .998 I .002 | j 13 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 : H = c r i t i c a l magnitude and N = curnm. Events/year The l i n k r e s i s t a n c e s were chosen on the b a s i s of the s o i l s t a b i l i t y , t y p e s of bridge s t r u c t u r e s p r e s e n t , and the geographic l o c a t i o n . I t i s important to note t h a t the c r i t i c a l magnitudes which have been determined are g u i t e high , being are over r i c h t e r 8.0 and t h i s y i e l d s a low occurrence o f event value N. Host l i n k s , t h e r e f o r e , have a low p r o b a b i l i t y of f a i l u r e . L i n k s 2, 3 and 4 57 however, have a r e l a t i v e l y high p r o b a b i l i t y of f a i l u r e due to t h e i r c l o s e p r o x i m i t y to the earthquake l i n e s o urce. . 4. 6 1 TIE - SET REDUCTION PROCEDURE The t i e - s e t s or paths through the F r a s e r Canyon as shown i n F i g u r e 15 are now presented. These t i e - s e t s are a l l the p o s s i b l e paths between two i n p u t s ( Kamloops 5 Kamloops Junction) and two outputs { Vancouver 5 North Vancouver ). Theses i n p u t s are designated as 11 and 12 while the outputs are are 29 and 19 r e s p e c t i v e l y . Kamloops and Kamloops J u n c t i o n were chosen a s i n p u t s due to t h e i r s t r a t e g i c l o c a t i o n i n the p r o v i n c e at a major j u n c t i o n and s w i t c h i n g p o i n t . Both the CN and CP j o i n here and then t r a v e l s e p a r a t e l y but i n c l o s e p r o x i m i t y through the F r a s e r Canyon west to Vancouver and North Vancouver. Vancouver and Norht Vancouver were chosen as they are the major po r t s and most export f r e i g h t l e a v e s from them. { Although P r i n c e Rupert i s becoming i n c r e a s i n g l y i m p o r t a n t ) . 58 FIGORE J5 ± FRASER CANYON BAIL SCHEMATIC Input 12 Input 11 These f o u r t i e - s e t ma t r a d e s are denoted as 1 1 - 19 , 11 - 29 , 12 - 19 , and 12 - 29. ( Ma t r a c i e s 1 - 4 ) . The t i e - set matracies are reduced by u s i n g an a l g o r i t h m developed by Taleb Agha. ( Reference No. ,41 Pages 12 - 22). These matracies as w e l l as the t i e - s e t r e d u c t i o n procedure are shown i n d e t a i l i n Appendix D. The r e s u l t s of t h i s procedure i s shown i n F i g u r e 16. 59 FIGD8E J6 l REJDOCJD ± EXISTING 1 TIE - SET MftTBIX Matrix ID L e t t e r 13 10 8 7 6 5 | ( a 13 10 8 7 4 3 1 ( b 13 10 9 6 3 | ( c 13 10 9 5 I < a 14 11 8 7 6 5 1 ( e 14 1 1 8 7 4 3 I ( f 14 11 9 6 4 3 I ( g 14 11 9 5 | ( h One can see t h a t the r e d u c t i o n procedure e l i m i n a t e d the f o u r i n p u t / output t i e - set matracies to a s i n g l e matrix. T h i s enables the r e l i a b i l i t y a n a l y s i s t o be performed on one s i n g l e matrix and f o r l a r g e r systems saves much computer time and memory space, although t h i s a n a l y s i s was performed manually . T h i s simple matrix ( In F i g u r e 16) represents a l l the reduced p o s s i b l e t i e - s e t s from Kamloops / kamloops J u n c t i o n to Vancouver / North Vancouver. , 4.7 J. RELIABILITY ANALYSIS - EXISTING NETWORK Now t h a t the l i n k p r o b a i l i t i e s have been assigned and the t i e - s e t matrix reduced, the r e l i a b i l i t y a n a l y s i s may be performed. The l i n k p r o b a b i l i t i e s o f f a i l u r e are taken from Table 11 and s u b s t i t u t e d f o r the s p e c i f i c l i n k s as shown i n F i g u r e 16. The d e t e r m i n a t i o n of the r e l i a b i l i t y i s q u i t e easy, now that the o r i g i n a l network has been made the s i m p l i f i e d SSP ( S e r i e s Systems i n P a r a l l e l ) network. \ a ) a ).-.. ( i ) ] L 1 2 * J 60 The r e l i a b i l i t y i s : I i BELIABILITY OF SSP = ^» Equation J 3 1 J p a r a l l e l s e r i e s components components T h i s s t a t e s t h a t the r e l i a b i l i t y of the s e r i e s components ar e the product of t h e i r i n d i v i d u a l r e l i a b i l i t i e s while the r e l i a b i l i t y o f the p a r a l l e l components i s t h e i r sum. ,, For the given network the base equation i s : P = 1 - P where : f a i l u r e s u r v i v a l P = 1 - A * ( B - C ) - D E00ATION J4 f a i l u r e where : A = the sumation of the product of the i n d i v i d u a l t i e - s e t p r o b a b i l i t i e s , (those being A B C D E F G H I J ) B = the sumation of the product o f the i n d i v i d u a l l i n k s . , (those being 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 t o 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 counted more than once. D = the product of the product of the t i e -s e t 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 ( a through h ) as shown to the r i g h t of the matrix i n F i g u r e 16., 61 The d e t a i l e d c a l c u l a t i o n of the r e l i a b i l i t i e s can be found i n Appendix E. The r e s u l t s are as f o l l o w s : A = 5. 199 C = 7.271 B = 11.613 D = .024 which r e s u l t s i n the f o l l o w i n g e quation : P * 1 - 5. 119 + (11.613 - 7.271) -.024 EQUATION J5 f a i l u r e P = 0.119 f a i l u r e BELIABI1ITI = .881 sub - network T h i s r e l i a b i l i t y e stimate of the network i s the r e l i a b i l i t y of the F r a s e r Canyon l i n k s not the e n t i r e network. I t i s these l i n k s , however, which are the most non - redundant i n the system and where the r e a l p o s s i b i l i t y of c l o s u r e e x i s t s due t o a l a n d s l i d e or r o c k s l i d e , e s p e c i a l l y one caused by an earthquake. The q u e s t i o n posed i s , with a r e l i a b i l i t y of .881 , i s i t p o s s i b l e t o r a i s e the r e l i a b i l i t y of t h i s network so t h a t i t has a g r e a t e r chance of s u r v i v a l given a c a t a s t r o p h i c event? A l s o , how much w i l l the r e l i a b i l i t y of the the Southern Mainland i n c r e a s e i f one a d d i t i o n a l (redundant) l i n k i s added? Would i t be s u f f i c i e n t l y i n c r e a s e d i f two a d d i t i o n a l l i n k s were added? To begin to answer theses q u e s t i o n s , the a n a l y s i s now adds one a d d i t i o n a l l i n k to the network of the Fraser Canyon. 62 i**J 1 RELIABILITY ANALYSIS z PROPOSED NETWORK Having performed the r e l i a b i l i t y a n a l y s i s f o r the e x i s t i n g r a i l network i n the F r a s e r Canyon, the A s h c r o f t - P a v i l l i o n l i n k w i l l now be added t o the network. The l i n k p r o b a b i l i t i e s of f a i l u r e l i s t e d i n Table 11 are s t i l l v a l i d . The t i e - s e t matrix f o r the proposed network i n c r e a s e s those of the e x i s t i n g network i n F i g u r e 16 as well as 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 s e t s e f f e c t i v e l y i n c r e a s e the number of routes a v a i l a b l e . These a d d i t i o n a l t i e - s e t s are t a b u l a t e d i n F i g u r e 17. FigOBE J 7 2 ADDITIONAL J POSSIBLE 1 TIE - SETS J i n p u t / | output 1 1 A d d i t i o n a l T i e - Sets ! I 1 1 - 1 9 1 11 10 15 1 2 s 14 13 15 1 i J 1 2 - 1 9 I 11 10 15 1 s 14 13 15 1 2 | J 1 1 - 2 9 | 14 13 15 1 2 & 14 11 10 13 1 2 | i 12 - 29 I 11 13 15 1 & 14 11 10 15 1 | The a d d i t i o n a l t i e - s e t s are f i r s t i n c l u d e d with the f o u r major i n p u t - output matracies, those being Matrix 1 through 4 as shown i n Appendix D. Then , l o o k i n g a t the comparable t i e s e t s of 11 - 12 with 1 1 - 1 9 and 11 - 29 with 12 - 29 n o t i c e t h a t they are subsets of each other t h e r e f o r e the a d d i t i o n a l p o s s i b l e t i e - s e t s as shown i n F i g u r e 17 are now reduced i n h a l f . The f o u r t i e - s e t s are then reduced as before i n the a n a l y s i s c f the e x i s t i n g network, as d e t a i l e d i n Appendix D. , the f i n a l reduced t i e - s e t matrix f o r the proposed network being o b t a i n e d i s summarized i n F i g u r e 18: MATRIX ID LETTER 13 10 8 7 6 5 J ( a ) 13 10 8 7 4 3 | ( b ) 13 10 9 6 3 | ( c ) 13 10 9 5 | ( d ) 14 11 8 7 6 5 | ( e ) 14 11 8 7 4 3 1 ( f ) 14 11 9 . 6 4 3 ] ( g ) 14 11 9 5 ] ( h ) 14 13 15 1 ] { i ) 14 11 10 15 1 | ( j ) I t i s now a matter of c a l c u l a t i n g the r e l i a b i l i t y of t h i s new c o n f i g u r a t i o n . Rather than r e - c a l c u l a t i n g the r e l i a b i l i t y from the beginning, only the a d d i t i o n a l r e l i a b i l i t y due to the e x t r a two f i n a l t i e - s e t s need be performed. Comparing F i g u r e 16 with F i g u r e 18 shows d i f f e r e n c e between the two networks ( e x i s t i n g and proposed) i s seen. The new matrix has only two a d d i t i o n a l t i e - s e t s ( I & j ). These can be i n c o r p o r a t e d i n t o the e x i s t i n g c a l c u l a t i o n s q u i t e e a s i l y , thus s h o r t e n i n g the c a l c u l a t i o n time as w e l l as s i m p l i f i n g data storage f o r a computer a l g o r i t h m . The method i s d e t a i l e d i n Appendix E and the r e s u l t s are as f o l l o w s : A = 7.174 B = 17.03 C = 10.794 D = .025 Which r e s u l t e d i n the f o l l o w i n g e q u a t i o n : 64 P = 7.174 + {17.03 - 10.794) -.Q25 EQUATION 15 f a i l u r e r e s u l t i n g i n : P = .037 f a i l u r e RELIABILITY = .963 sun - network Again, t h i s r e l i a b i l i t y e s t i mate i s f o r the F r a s e r Canyon network shown i n Figure 15., 4.9 2 DISCUSSION The second r e l i a b i l i t y a n a l y s i s shows t h a t the r e l i a b i l i t y of the network has improved from .881 to .963 , a gain of .082 or a g a i n of about 10 %» T h i s g a i n was made through the a d d i t i o n of one s i n g l e l i n k between A s h c r o f t and P a v i l l i o n . At i s s u e i s whether t h i s i n c r e a s e i n r e l i a b i l i t y i s worth the c o n s t r u c t i o n (cost) of the A s h c r o f t - P a v i l l i o n l i n k . A c o s t - b e n e f i t a n a l y s i s must be performed to decide i f the b e n e f i t ( D C r e d u c t i o n i n the l e v e l of s e r v i c e and no e x t r a c o s t s i n c u r r e d due t o a c l o s i n g of a l i n k ) outweighs the c o s t s ( c o n s t r u c t i o n of the l i n k ) . To make t h i s d e c i s i o n one must g a i n a a p e r s p e c t i v e of what t h i s r e l i a b i l i t y e n t a i l s . At i t s present l e v e l of s e r v i c e , given no events, the network operates resonably w e l l except f o r the o c c a s i o n a l s m a l l r o c k s l i d e or snowslide. The estimate of .881 allows f o r resonable o p e a r a t i o n . Using the p r o b a b i l i t y of f a i l u r e as another way of l o o k i n g at the r e l i a b i l i t y , the f i g u r e 65 of ,119 give s an i n d i c a t i o n t h a t the network w i l l experience s e r v i c e disrapt.io.ns given an event. With the a d d i t i o n a l l i n k and subsequent r e d u c t i o n of f a i l u r e p r o b a b i l i t y t o ,037 the r e i s much l e s s of a chance of f a i l u r e , ( a l s o using the p r o b a b i l i t y of f a i l u r e as a measure giv e s a 70 % r e d u c t i o n i n the f a i l u r e p o t e n t i a l by decr e a s i n g from ,119 to 0.37), In t h i s l i g h t , the a d d i t o n a l l i n k shuld be c o n s i d e r e d . TABLE 11 £ SMH&EY OF RESULTS J PROBABILITY OF | RELIABILITY OF | | NETWORK FAILURE | THE NETWORK J | EXISTING | .119 | .881 J , , | PROPOSED | .037 J .963 | Having shown t h a t i n c r e a s i n g the r e l i a b i l i t y i s b e n e f i c i a l l e a d s t o the q u e s t i o n , has i t been i n c r e a s e d enough? I s i t d e s i r a b l e to add an a d d i t i o n a l l i n k ( making a t o t a l of 2) t o the network i n order to i n c r e a s e i t s r e l i a b i l i t y ? With the r e l i a b i l i t y of the improved network at .963 , only s m a l l e r increments of change ( i n c r e a s i n g r e l i a b i l i t y ) are now l i k e l y . Indeed, i s a r e l i a b i l i t y g r e a t e r than .963 any more b e n e f i c i a l than the .963 i t s e l f ? In some high technology areas, r e l i a b i l i t i e s of a very high l e v e l are d e s i r a b l e , , I t i s d o u b t f u l , i n o p e r a t i n g a r a i l w a y , i f any g r e a t e r r e l i a b i l i t y i s r e q u i r e d h i g h e r than the .963 • Another c o n s i d e r a t i o n i s t h a t any f u r t h e r a n a l y s i s would have to i n c l u d e a s i g n i f i g a n t l y l a r g e r network. That would i n c r e a s e the s i z e c f the t i e - s e t p o s s i b i l i t y matrix which would have to be enlarged to i n c l u d e a l l the p o s s i b l e 66 i n p u t s / o u t p u t s . With t h i s i n c r e a s e i n s i z e a computer based a l g o r i t h m would have to be used due t o the enormous number of p o s s i b l e t i e - s e t s . , One must guest!on the v a l i d i t y of u s i n g s e i s m i c r i s k a n a l y s i s to i n t e r i o r and northern p o r t i o n s of the p r o v i n c e . F i g u r e 13 shows how the occurrence of earthquakes are g e n e r a l l y i n the S t r a i g h t of Juan de Fuca or o f f the B r i t i s h Columbia c o a s t . F i g u r e 14 shows the e f f e c t s of the earthquakes o r i g i n a t i n g o f f the c o a s t i n t h a t the p r e d i c t e d peak a c c e l e r a t i o n s are low { .05 g ) or n o n - e x i s t a n t i n these ar e a s . The recommended network i s shown i n F i g u r e 19 which a l s o i n c l u d e s 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 of f a i l u r e . The p r o b a b i l i t i e s decrease d r a m a t i c a l l y i n the i n t e r i o r s e c t i o n s of the p r o v i n c e . T h i s i s due to the d i s t a n c e from the earthquake source l i n e which r e s u l t e d i n a lower magnitudes of earthquakes experienced. 6 7 T h i s d i c u s s i o n h a s f o c u s e d o n t h e m e t h o d o f a d d i n g e x t r a l i n k s t o i n c r e a s e t h e r e l i a b i l i t y o f a n e t w o r k . F o r a n a l y s i s b a s e d s o l e l y o n n e t w o r k s t u d i e s t h a t w o u l d s u f f i c e , h o w e v e r , w h e n u s i n g s e i s m i c c r i t e r i a t h e s i t u a t i o n i s d i f f e r e n t . R e f e r i n g t o E q u a t i o n 10 ( o n p a g e 54) n o t i c e t h e e s t i m a t i o n o f l i n k p r o b a b i l i t y o f f a i l u r e t a k e s i n t o a c c o u n t t h e d i s t a n c e f r o m t h e l i n e s o u r c e # t h e s e i s m i c i t y o f t h e a r e a , a n d t h e l i n k r e s i s t a n c e . T h e f i r s t t w o p a r a m e t e r s c a n n o t b e c h a n g e d b u t t h e t h i r d i s man made a n d may b e m a n i p u l a t e d . D e t e r m i n a t i o n o f w h a t e a c h l i n k c o u l d r e s i s t b a s e d o n t h e t y p e o f s t r u c t u r e i n v o l v e d . I f i t h a s b e e n d e t e r m i n e d t h a t a s t r u c t u r e c a n o n l y w i t h s t a n d a c e r t a i n a c c e l e r a t i o n a n d b y u s i n g t h i s r e s i s t a n c e , r e s u l t s i n a r e l a t i v e l y h i g h l i n k p r o b a b i l i t y o f f a i l u r e , i t may b e a d v i s a b l e t o t r y t o i n c r e a s e t h e l i n k » s r e s i s t a n c e . T h i s t y p e o f r e t r o -f i t t i n g p r o c e d u r e h a s b e e n i n e f f e c t i n C a l i f o r n i a s i n c e 1973 f o r h i g h w a y b r i d g e s , a l t h o u g h f o r r e a s o n s d i f f e r e n t s t h a n t h o s e p r e s e n t e d h e r e . I n many i n s t a n c e s i t may b e m o r e a d v a n t a g e o u s , e c o n o m i c a l l y , p o l i t i c a l l y , o r f r o m a n e n g i n e e r i n g p o i n t o f v i e w , t o d e v e l o p a p l a n o f b r i d g e a n d r o a d b e d u p g r a d i n g r a t h e r t h a t t h e a d d i t i o n o f a n e w r o u t e . T h e r e a r e a d v a n t a g e s o f c o n s t r u c t i n g t h e A s h c r o f t -P a v i l l i o n l i n k o t h e r t h a n f r o m a r e l i a b i l i t y p o i n t o f v i e w . T h e l i n k i n c r e a s e s t h e c a p a c i t y o f t h e C N a n d C P b y a l l o w i n g t h e m t o u s e t h e ( a t t h i s t i m e ) u n d e r - u t i l i z e d BCR l i n e b e t w e e n P a v i l l i o n a n d N o r t h V a n c o u v e r . T h i s l i n k a l s o a l l o w s f o r a m o r e f l e x i b l e n e t w o r k i n t e r m s o f m a r k e t i n g , a v a i l a b i l i t y a n d s c h e d u l i n g o f t r a i n s . , 68 Q s i n g s o m e m e t h o d o f s o c t - b e n e f i t a n a l y s i s s o m e d e t e r m i n a t i o n m u s t b e m a d e , i n d o l l a r t e r m s , t h e a d v a n t a g e o f e a c h l i n k a d d e d . I t m u s t b r e r e m e m b e r e d t h a t , d u e t o t h e l a w o f d i m i n i s h i n g r e t u r n s , e a c h a d d i t i o n l i n k a d d s l e s s a n d l e s s t o t h e r e l i a b i l i t y . I r e c o m m e n d t h e c o n s t r u c t i o n o f t h e A s h c r o f t - P a v i l l i o n l i n k t o i n c r e a s e t h e r e l i a b i l i t y , f l e x i b i l i t y , a n d t h e g e n e r a l o p e r a t i n g c h a r a c t e r i s t i c s o f t h e r a i l n e t w o r k o f B r i t i s h C o l u m b i a . T h e a d d i t i o n o f f u r t h e r l i n k s a t t h i s t i m e w o u l d n o t b e c o s t - e f f e c t i v e d u e t o t h e u n d e r - u t i l i z a t i o n w h i c h w o u l d r e s u l t . I f f u r t h e r r e l i a b i l i t y i s d e s i r a b l e , a p r o g r a m m e o f r e t r o f i t t i n g s h o u l d b e u n d e r t a k e n t o i n c r e a s e a l i n k ' s r e s i s t a n c e t o s e i s m i c e v e n t s . ( O r a m e t h o d o f r e t r o - f i t t i n g f o r o t h e r e v e n t s s u c h a s s n o w s h e l t e r s o r r o c k s h e d s , e t c . ) 69 ceapfER 5 : REVIEW OF THE SECOND N&RROWS BRIDGE CLQSDBE On 12 October 1979 the tanker Japan E r i c a c o l l i d e d with the Canadian N a t i o n a l Railway Second Narrows Bridge , s t r i k i n g one of the main centr e span towers. The 738.5 metre, 7 span b r i d g e was c l o s e d u n t i l 3 March 1980 s e v e r i n g the B r i t i s h Columbia Railway •s southern l i n k with the Canadian N a t i o n a l Railway and the Canadian P a c i f i c Railway • The l o s s of t h i s v i t a l l i n k caused major s e r v i c e d i s r u p t i o n s , which were a l l e v i a t e d by : 1. Barging cargo, mainly g r a i n , c o a l , s u l p h u r , and potash a c r o s s B u r r a r d I n l e t . , 2. R e - r o u t i n g t r a f f i c through Prince George, then south v i a the B r i t i s h Columbia Railway • 3. Re-routing t r a f f i c through Prince Rupert thus by-passing Vancouver e n t i r e l y . These a l t e r n a t i v e methods were expensive., „The c o s t to the Canadian N a t i o n a l Railway Railway were $ 11.2 m i l l i o n to r e p a i r the 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 c o s t s ,and $ 7.0 m i l l i o n i n l o s t p r o f i t s . A complete l i s t of major c l a i m s i s contained i n Appendix C. The e x t r a volume generated on the B r i t i s h Columbia Railway as well as the f r e i g h t which was barged a c r o s s Burrard I n l e t i s o u t l i n e d below i n Table 12. 70 TABLE i l I DIVESTED RAIL TRAFFIC 1 i southbound | c a r l o a d s | empties j metric tons | r a i l 11 663. 1 208. | 1 135 939. | r a i l northbound ] 926. | 15 788. ] 484 096. | barge northbound | 7 116. I n. a. 1 n. a. , J targe southbound | 3 767. I n. a. , | n. a. | These d i v e r s i o n s added 2 southbound t r a i n s per day and 2 northbound t r a i n s per day. These f i g u r e s i n Table 12 p o i n t out a most i n t e r e s t i n g aspect o f the r a i l t r a f f i c i n B r i t i s h Columbia , that i s , i t i s h i g h l y u n i - d i r e c t i o n a l . While the number of t r a i n movements are e q u a l , t h e volume of cargo i s overwhelmingly g r e a t e r i n the southbound d i r e c t i o n . T h i s t r a f f i c r e p r e s e n t s 70.0 % of the t o t a l volume. T h i s should be of no s u r p r i s e s i n c e the B C economy i s a resource-based export economy. Of immediate concern was whether 750.0 km l i n k of the B r i t i s h Columbia Railway between P r i n c e George and Vancouver) c o u l d handle the a d d i t i o n a l t r a f f i c . The main c o n s i d e r a t i o n was the c a p a c i t y l i m i t o f the l i n k . During the c r i s i s the t o t a l number of t r a i n movements i n c r e a s e d to 6 northbound and 7 southbound with the t o t a l c a p a c i t y of the B C R l i n k between P r i n c e George and Vancouver ,as p r e s e n t l y c o n s t r u c t e d , i s approximately 8 - 10 t r a i n s per day f o r each d i r e c t i o n . Thus, at some p o i n t i n the f u t u r e , the B C R t r a f f i c w i l l reach the maximum c a p a c i t y of the l i n k . To i n c r e a s e the t o t a l c a p a c i t y a d d i t i o n a l s i d i n g s cr even some double t r a c k i n g may be 71 n e c e s s a r y . U s i n g t h e s p a c e - t i m e d i a g r a m r e l a t i o n s h i p , w i t h a n a s s u m e d f r e i g h t t r a i n s p e e d o f 50 k m / h a n d 1 h o u r h e a d w a y s t h e f o l l o w i n g i s o b s e r v e d . G i v e n a 2 0 0 k i l o m e t r e l i n k w i t h u p g r a d e s s t a r t i n g a t km 0 a n d km 2 0 0 { t h u s m e e t i n g a t t h e c e n t r e o r a t km 1 0 0 ) t r a i n s w i l l b e g i v e n p r i o r i t y d e p e n d i n g o n w h i c h o n e i s t r a v e l l i n g u p g r a d e a n d w h i c h o n e i s t r a v e l l i n g d o w n g r a d e . T h i s c a n b e m o r e c l e a r l y s e e n i n F i g u r e 20 b e l o w . . F I G U R E 20 : S P A C E - T I M E D I A G R A M NORTH 6 0 120 180 2 4 0 3 0 0 H e a d w a y ( m i n u t e s ) A t r a i n t r a v e l l i n g n o r t h b o u n d h a s p r i o r i t y f r o m km 0 t o km 100 b u t m u s t y i e l d p r i o r i t y f r o m km 100 t o km 2 0 0 . F i g u r e 20 s h o w s t h a t w i t h t h e s p e e d a n d h e a d w a y s g i v e n , s i d i n g s m u s t b e p r o v i d e d e v e r y 20 k i l o m e t r e s i n o r d e r t o a l l o w t h e t r a i n s t o 72 pass. These s i d i n g s i n t r o d u c e a delay time i n t h a t one t r a i n must p u l l o f f the mainline t r a c k . F i g u r e 20 shows the c a p a c i t y of 8 t r a i n s per 8 hour day. I f a 16 hour day i s used, the c a p a c i t y would be 16 t r a i n s per day. I f the s i d i n g d i s t a n c e was i n c r e a s e t o one s i d i n g every 4 0 km , with the 16 hour day, then the r e s u l t i n g headway would be 2 hours. , FIGDSJ 2J 1 MMMJS DEL ft Y 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.] Length, ft Avaraga Running SpMd. mi/h T mt Penaltiaa (Minutttl FVoant of all Traint . Clan Starling Stopping Crottovtn 1 1.500 50 1 2 1 13.9% 2 3.000 40 2 6 3 27 8% 3 5.000 25 4 a 5 52.9% 4 3.000 25 2 5 3 5.5% { T h i s f i g u r e i s from Edward Morlock, r e f e r e n c e No. 21) 2 8 Reference No. 21 Page 209. , 73 The p o i n t i s c l e a r , i f c a p a c i t y i s to be i n c r e a s e d , e i t h e r by d e c r e a s i n g headways or i n c r e a s i n g speeds, then more s i d i n g s must be b u i l t , at some c r i t i c a l p o i n t , double t r a c k i n g w i l l be necessary s i n c e , i n e f f e c t , s i d i n g s w i l l have to be c l o s e r and c l o s e r t o g e t h e r , t h e r e f o r e an a d d i t i o n a l track., (note double t r a c k i n g would occur before t h i s time s i n c e the delay times f o r t r a i n s would be i n c r e a s e d d r a m a t i c a l l y due to the manouvering time r e g u i r e d . Horlok addressed t h i s problem of delay times f o r r a i l w a y s . He showed the r e l a t i o n s h i p between v a r i o u s t r a c k c o n f i g u r a t i o n s and delay time. T h i s r e l a t i o n s h i p i s shown i s F i g u r e 21. B e f e r i n g to the f i g u r e , i f demand i n c r e a s e s from 4 t r a i n s per day t o 8 t r a i n s per day f o r a s i n g l e t r a c k o p e r a t i o n with s i d i n g s every 40 k i l o m e t r e s , then the delay time per t r a i n i n c r e a s e s from 0.5 hours to 0.9 hours. For the 750 km North Vancouver - P r i n c e George B C B m a i n l i n e , t h i s would r e s u l t i n a t o t a l delay i n c r e a s e from 2.3 hours to 4.2 hours or approximately 2 hours longer f o r one t r a i n . Thus, at some time i n the near f u t u r e , i f t h i s l i n k i s a g a i n r e q u i r e d f o r e x t r a t r a f f i c . Delays f o r a l l w i l l r e s u l t , with the i n c r e a s e d c o s t s a s s o c i a t e d with the delay. The completion of the 50 km a s c h c r o f t - P a v i l l i o n l i n k w i l l c u t the by-pass d i s t a n c e around the Second Narrows Bridge through P r i n c e George by about 2/3. While t h i s w i l l not t o t a l l y e l i m i n a t e the i n t r o d u c t i o n of d e l a y , i t w i l l e l i m i n a t e a s i g n i f i g a n t p o r t i o n . A l s o , upgrading of f a c i l i t i e s , due t o these by-passes, w i l l only have to be c a r r i e d out on the 300 km l i n k between P a v i l l i o n and North Vancouver. I t w i l l a l s o help 74 a l l e v i a t e c o n g e s t i o n on the CNB m a i n l i n e between Kamloops and Tete Jaune. The c l o s i n g of the Second Barrows Bridge i l l u s t r a t e d most c l e a r l y the v u l n e r a b i l i t y of any one l i n k t o s e r v i c e d i s r u p t i o n and the conseguences to system performance i n terms of i n c r e a s e d shipment c o s t s , i n c r e a s e d t r a v e l times, g e n e r a l s c h e d u l i n g d i f f i c l t i e s , and l o s t p r o f i t s . T h i s experience was c o s t l y but was v a l u a b l e i n h e l p i n g formulate f u t u r e p l a n s by making use of the knowledge gained. , 75 CHAPTER 6 1 POLICY/ PBOCBDOBE REVIEf AND IMPROVEMENT Given any f a i l u r e of a l i n k or node, one of the most important a s p e c t s of the recovery o p e r a t i o n i s t o have a c l e a r s e t of procedures t o f o l l o w when the s i t u a t i o n o c c u r s . The l a c k of a s p e c i f i c plan w i l l tend t o make such occurrances l a s t l o n g e r , and t h e i r e f f e c t s g r e a t e r , than would otherwise be the case. The C a l i f o r n i a and Alaska e x p e r i e n c e s showed t h a t proper planning and c o o r d i n a t i o n between p u b l i c and p r i v a t e r e l i e f agencies i s e s s e n t i a l i n the e f f o r t t o implement the best p o s s i b l e p l a n . The f o l l o w i n g problems r e p r e s e n t those which were most fre g u e n t a f t e r the Alaska and C a l i f o r n i a earthquakes : 2 9 1. Many times, d i s a s t e r r e l i e f j u r i s d i c t i o n e i t h e r overlapped o r had gaps due to s e p a r a t e l y developed r e l i e f p l a ns. 2 . B e l i e f agencies were unable t o communicate with one another due t o r e l i a n c e on c o n v e n t i o n a l communications systems. 3. There was a l a c k of proper a l t e r n a t e { backup ) power a v a i l a b l e t o r e l i e f a g e n c i e s . 4. The f a i l u r e of s m a l l components on major s t r u c t u r e s were many times the cause of t o t a l 2 9 References No. 1 9 , 2 7 , 2 9 , & 36 76 f a i l u r e of the s t r u c t u r e . , 5. Hany times, due to the l a c k of immediate a v a i l a b l e funds, monies had to be d i v e r t e d from ongoing p r o j e c t s t o provide f o r r e l i e f o p e r a t i o n s . 6. Hany times emergency systems has t o be operated ( s t a r t e d up) manually. These s i x problems allowed the emergency r e l i e f o p e r a t i o n s to be l e s s e f f i c i e n t i n terms of response time, i n c r e a s e d the c o s t of o p e r a t i o n s , and decreased the conf i d e n c e the p u b l i c had i n the a b i l i t y o f o f f i c i a l s t o handle the s i t u a t i o n . T h i s c o u l d e v e n t u a l l y l e a d to a p o s s i b l e i n c r e a s e i n f a t a l i t i e s . To a l l e v i a t e these problems, the f o l l o w i n g changes are recommended : 1. A comprehensive, o v e r a l l d i s a s t e r r e l i e f p l a n must be developed with i n p u t from a l l concerned so t h a t the maximum c o o r d i n a t i o n o f e f f o r t s w i l l be r e a l i z e d . 2. A r a d i o system using a l t e r n a t i v e power con n e c t i n g a l l agencies on a common frequency must be operated to ensure co n s t a n t r e l i a b l e communication between agencies d u r i n g a d i s a s t e r . 3. A u x i l u a r y power i s a l s o necessary to con t i n u e other v i t a l o p e r a t i o n s . , 4. A pl a n f o r r e t r o - f i t t i n g s t r u c t u r e s must be developed so that f a i l u r e s o f minor components 77 does not cause t o t a l system f a i l u r e . These components would i n c l u d e such items as : b r i d g e r e s t r a i n e r s , anchorage b o l t s f o r towers, brackets f o r emergency eguipment, and approach f i l l s ubsidence. 5. k l e g i s l a t i v e procedure f o r emergency funding must be e s t a b l i s h e d beforehand so t h a t funding can be implemented without undo d e l a y or s p e c i f i c l e g i s l a t i v e a u t h o r i z a t i o n . 6. Hore automation of backup and emergency systems must be developed and c o n s t r u c t e d so t h a t a minimum number of personnel are r e q u i r e d t o s t a r t emergency o p e r a t i o n s , such as power systems, f l o o d g a t e s , s i g n a l l i n g , r a d i o communication, e t c . In B r i t i s h Columbia the p r o v i n c i a l agency r e s p o n s i b l e f o r d i s a s t e r r e l i e f i s The Department of the P r o v i n c i a l S e c r e t a r y i n V i c t o r i a . , The r e s p o n s i b i l i t y of d i s a s t e r r e l i e f i s under the j u r i s d i c t i o n of l o c a l m u n i c i p a l i t i e s and d i s t r i c t s with the o v e r a l l c o o r d i n a t i o n the r e s p o n s i b i l i t y of the p r o v i n c i a l government. Funding i s approximately $ 1.6 m i l l i o n per year which i s used mainly f o r maintaining an o r g a n i z a t i o n and p u b l i c i n f o r m a t i o n programmes. The f e d e r a l m i n i s t r y c o u n t e r p a r t i s Emergency Planning Canada, whose main f u n c t i o n i s to h e l p c o o r d i n a t e f e d e r a l r e l i e f where the f e d e r a l government has j u r i s d i c t i o n such as the Armed Forces, RCMP, and the Coast Guard 78 as well as a s s i s t i n g i n the aftermath of such d i s a s t e r s . The development and r e a d i n e s s of a comprehensive d i s a s t e r r e l i e f plan i s e s s e n t i a l given B r i t i s h Columbia's unique g e o r a p h i c a l l o c a t i o n i n a zone of high n a t u r a l r i s k s . T h i s plan must be reviewed and updated so that new techniques may be employed. 79 C H A P T E B 7 Z S U M A R I T h i s t h e s i s h a s b e e n a n a p p l i c a t i o n o f L i f e l i n e E a r t h q u a k e E n g i n e e r i n g c o n c e n t r a t i n g o n t h e r a i l n e t w o r k o f t h e p r o v i n c e o f B r i t i s h C o l u m b i a . By r e v i e w i n g p r e v i o u s e a r t h q u a k e e x p e r i e n c e s w i t h i n A l a s k a a n d C a l i f o r n i a v a l u a b l e i n f o r m a t i o n w a s o b t a i n e d a b o u t t h e p h y s i c a l c o n s e q u e n c e s o f a n e a r t h q u a k e , a s w e l l a s s o m e o f t h e a d m i n i s t r a t i v e p r o b l e m s a s s o c i a t e d w i t h d i s a s t e r r e l i e f . T h e b a s i c n e t w o r k r a i l n e t w o r k o f t h e p r o v i n c e was m a p p e d w i t h i t s c h a r a c t e r i s t i c s o u t l i n e d s o t h a t t h e i n h e r e n t w e a k n e s s e s c o u l d b e a s s e s s e d . V a r i o u s m e t h o d s o f p r o b a b i l i t y t h e o r y w e r e e x p l o r e d t o g a i n a n u n d e r s t a n d i n g o f t h e s e p r o c e s s e s . I t w a s d e t e r m i n e d t h a t c o n v e n t i o n a l m e t h o d s o f p r e d i c t i o n o f e v e n t s a n d t h e i r m a g n i t u d e w e r e u n a c c e p t a b l e a n d t h a t a m o r e s o p h i s t i c a t e d m e t h o d was d e s i r a b l e . I n i t i a l l y , a m e t h o d o f a s s i g n i n g s u b j e c t i v e p r o b a b i l i t i e s o f f a i l u r e b a s e d o n p r e v i o u s e x p e r i e n c e w a s a t t e m t e d . W h i l e t h i s made t h e p r o c e s s m u c h e a s i e r , i t l a c k e d p r e c i s i o n . A m o r e s o p h i s t i c a t e d m e t h o d o f p r e d i c t i n g e a r t h q u a k e p e a k a c c e l e r a t i o n s w a s i m p l e m e n t e d . G i v e n t h e J u a n d e F u c a f a u l t s y s t e m , w h i c h i s t h e p r e d o m i n a n t f a u l t s y s t e m i n w e s t e r n C a n a d a a c c e l e r a t i o n s o f v a r i o u s m a g n i t u d e s w e r e a s s i g n e d t h r o u g h o u t t h e p r o v i n c e . T h e s e e s t i m a t e d a c c e l e r a t i o n s w e r e t h e n c o m p a r e d t o o t h e r p r e d i c t i o n s made b y v a r i o u s r e s e a r c h e r s i n c l u d i n g M i l n e , J u r k o v i c s , a n d F i t z e l l . G e n e r a l l y t h e r e s u l t s o b t a i n e d c o m p a r e d f a v o u r a b l y w i t h t h e o t h e r r e s e a r c h e r s . 80 A c c l e r a t i o n s o f around 0.2 g { 196 cm/s. Sg.) c o u l d be expected on Vancouver I s l a n d with a c c e l e r a t i o n s of 0.1 g - 0.15 g { 98 - 174 cm/s.,Sg. ) i n Vancouver and a c c e l e r a t i o n s of l e s s than 0.05 g ( 49 cm/s., Sg., ) i n i n t e r i o r s e c t i o n s of the p r o v i n c e . Maximum a l l o w a b l e a c c e l e r a t i o n s ( or l i n k r e s i s t a n c e s ) f o r v a r i o u s s t r u c t u r e s were assigned and p r o b a b i l i t i e s of f a i l u r e c a l c u l a t e d . , B e l i a b i l i t y a n a l y s i s was then performed on the r a i l network o f the Southern Mainland where the most c o s t e f f e c t i v e o p p o r t u n i t y e x i s t s f o r network enhancement. , T h i s r e l i a b i l i t y estimate i s simply the mathematical manipulation of the assigned l i n k p r o b a b i l i t i e s o f f a i l u r e . The a n a l y s i s showed t h a t the F r a s e r B i v e r Canyon was the most v u l n e r a b l e p o r t i o n s of p r o v i n c e . At t h i s p o i n t , a f t e r some c o s t a n a l y s i s and some p r a c t i c a l s i t i n g c r i t e r i a , f o u r a d d i t i o n a l l i n k s were i n t r o d u c e d , The r e l i a b i l i t y a n a l y s i s was again performed and the two s i t u a i t o n s were compared. From a c o s t p o i n t o f view and the r e l i a b i l i t y p o i n t of view the best l i n k t c c o n s t r u c t was the A s c h c r o f t - P a v i l l i o n ( C l i n t o n ) l i n k . The i n c r e a s e i n the r e l i a b i l i t y went from .881 f o r the e x i s t i n g network t o .963 f o r the proposed network. T h i s 9 % i n c r e a s e c o u l d be important i f an earthguake occurs , e s p e c i a l l y i f i t p r e c i p i t a t e s l a n d / r o c k / s n o w s l i d e s . , Recommendations in c l u d e d that the A s h c r o f t - P a v i l l i o n l i n k be c o n s t r u c t e d as well as a method of r e t r o - f i t t i n g be i n v e s t i g a t e d . , 81 T h e r e v i e w o f t h e e m e r g e n c y o p e r a t i n g p r o c e d u r e s e m p h a s i z e d t h e n e e d f o r g r e a t e r c o o r d i n a t i o n b e t w e e n p u b l i c a n d p r i v a t e r e l i e f a g e n c i e s b e f o r e , d u r i n g , a n d a f t e r a d i s a s t e r . T h i s s t u d y h a s s h o w e d t h a t many p h y s i c a l s y s t e m s a r e n o t t o t a l l y c a p a b l e o f r e s i s t i n g c a t a s t r o p h i c e v e n t s a n d a r e v u l n e r a b l e t o s e r v i c e d i s r u t i o n s . I n f a c t , p r o b a b l y t h e g r e a t e s t d a n g e r c o m e s f r o m n a t u r a l s y s t e m s n o t w i t h s t a n d i n g t h e s e f o r c e s . T h e o b j e c t i v e i s t o m i n i m i z e t h e e f f e c t s o f s u c h d i s r u p t i o n s . 82 CHAPTER 8 i BECOHMENDATIOHS AND CONCLOSIONS Besearch of t h i s nature i s r a r e l y complete i n t h a t i s never answers a l l of the questions posed. Based on the i n f o r m a t i o n gained i n the study the f o l l o w i n g are the recommendations: 1. The f e a s a b i l i t y of c o n s t r u c t i n g the A s c h c r o f t -P a v i l l i o n ( C l i n t o n ) l i n k should be s t u d i e d i n order to determine the a c t u a l p r e s e n t s c o s t s of c o n s t r u c t i o n . The c o n s t r u c t i o n of t h i s l i n k w i l l enhance the f l e x i b i l i t y and thus r e l i a b i l i t y of the r a i l network of the Southern Mainland of B r i t i s h Columbia • 2., A method of i d e n t i f y i n g those bridges i n the system which may have a need o f s t r u c t u r a l r e t r o f i t t i n g (strengthening) be e s t a b l i s h e d and those key b r i d g e s be i n s p e c t e d . , 3. Emergency o p e r a t i n g procedured be r e v i s e d and updated, and t h a t a c o o r d i n a t i o n p l a n between the r a i l w a y s and other u t i l i t i e s and governmental agencies be e s t a b l i s h e d . 4. A non-conventional a l t e r n a t e power source communications system be developed so t h a t c o n t a c t between a l l concerned i s p o s s i b l e . , 5. A s e r i e s of s t u d i e s of flow c a p a c i t y demands take i n t o account the t h r e e other proposed r a i l l i n k s so that t h e i r upgrading and i n c l u s i o n i n the r a i l 83 system be c o n s i d e r e d . 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 study i n c l u d e : 1. The development of a computer based model f o r the e n t i r e r a i l system to show areas of high f a i l u r e p o t e n t i a l . , 2. The development of s p e c i f i c c r i t e r i a f o r L i f e l i n e Earthguake E n g i n e e r i n g as i t a p p l i e s t o B r i t i s h Columbia ., 3. A r e l i a b i l i t y and c o s t a n a l y s i s on the e f f e c t s of c o n s t r u c t i o n and earthguake r e s i s t a n t s t r u c t u r e s such as l a n d s l i d e s h e l t e r s , e t c . 4. The development of a c o s t - e f f e c t i v e r e t r o f i t t i n g programme f o r v u l n e r a b l e s t r u c t u r e s l o c a t e d i n the most a c t i v e earthguake zones. The f i e l d of L i f e l i n e Earthguake Engineering i s s t i l l r a t h e r new and more r e s e a r c h needs to be performed. T h i s i s e s p e c i a l l y t r u e i n B r i t i s h Columbia where the p o t e n t i a l f o r s e r v i c e d i s r u p t i o n s are q u i t e h i g h . Given B r i t i s h Columbia's p h y s i c l a geography which p l a c e s a heavy r e l i a n c e on a few l i f e l i n e c o o r i d o r s , e s p e c i a l l y i n the i n t e r i o r . , I t i s hoped t h a t t h i s t h e s i s w i l l generate more i n t e r e s t i n t h i s t o p i c w i t h i n B r i t i s h Columbia ., 84 BIBLIOGRAPHY Ba i n , Lee S t a t i s t i c a l Theory Of B e l i a b i l i t y And L i f e T e s t i n g Marcel Decker Inc Hew York 1978 Barlow, Richard 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 And L i f e T e s t i n g  Models H o l t , Rinehardt, & Winston New York C i t y , N Y 1975 Benjamin, Jack / 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 For -Engineers-Mc Graw H i l l S Co. Toronto (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 Proc. Tech. C o u n c i l On L i f e l i n e 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 In A p p l i e d Science John Wiley £ Sons Toronto (1975) Courinno, John ( 0. S, Army Aberdeen Proving 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 Research Needs In Design  C o n t r o l 6 Risk Management F a i l u r e P revention And B e l i a b i l i t y 1975 Pgs. 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 Strong Motion Data 5th I n t e r n a t i o n a l Earthquake E n g i n e e r i n g Conference Rome ( 1975) Duke, C. H. / Euguchi, B. T. / Campbell, K. W. The Use Of B e l i a b i l i t y In L i f e l i n e Earthguake E n g i n e e r i n g 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 Tucson Duke, C M . / Moran, D. F. G u i d e l i n e s For E v o l u t i o n Of L i f e l i n e Earthquake E n g i n e e r i n g Proceedings 0. S. N a t i o n a l Conf.earthquake E n g i n e e r i n g Ann Arbor 175 F i t z e l l , T r evor P. Seismic B i s k In The Lower Mainland Region Of Western  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 E n g i n e e r i n g Dept. 1978 85 Gates, J.,H. C a l i f o r n i a S S e i s m i s Design C r i t e r i a For B r i d g e s A S C I ? J o u r n a l S t r u c t u r a l D i v i s i o n V o l . , 102 Ho. 12 { Dec 1976) The Corps Of 541 ( 1966) Green, A. B e l i a f c i l i t y Technology Wiley I n t e r s c i e n c e Toronto 1972 Grantz/ P l a f k e r / Kachadoorian Alaska S Good F r i d a y Earthquake U. S. G e o l o g i c a l Survey 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 The  Earthquake, 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 . Paper No.,541 Pgs.,1-37 Hawkins, N. H. / Crosson, 8.,S. Causes. 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 Conf. On Earthguake E n g i n e e r i n g 1975, Proceedings Pgs. 104-112 Housner, G. /».,/ J e n n i n g s , P. C. The San Fernando Earthquake, C a l i f o r n i a I n t e r . J o u r n a l Of Earthquake 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 S i m u l a t i n g S Representing Strong Motion  Ground Data 0*. B. C. Department of Geophysics H. Sc. T h e s i s 1978 Kachadoorian, 8 . E f f e c t s Of The Earthquake Of March 27M 1964 On The Alaska Highway System 0. S. G e o l o g i c a l Survey Prof. Paper No.,545- C (1968) George, «. / L y l e , B. E. Alaska Earthquake B e c o n s t r u c t i p n By  E n g i n e e r s . Methods And Accomplisments U. S. G e o l o g i c a l Survey P r o f . Paper No. Pgs.81-89 Kozak, J . J . M a i n t a i n i n g T r a n s p o r t a t i o n L i f e l i n e s A S C E Proceedings Tech. , C o u n c i l On L i f e l i n e Earthquake E n g i n e e r i n g ( Aug 30 1977) Morlock, 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 E n g i n e e r i n g S P l a n n i n g Mc Graw H i l l Cc. New York C i t y 1978 86 He C u l l o c h , D. S. / B o n i l l a , 13. G. E f f e c t s Of The Earthquake Of March 28 x 1964 On The Alaska B a i l r p a d 0. S, G e o l o g i c a l Prof. Paper No.545 D (1970) Meehan, J . , F. The San Fernando Earthquake z_ Damage To T r a n s p o r t a t i o n  Systems 0. .,' S. G e o l o g i c a l Survey P r o f . Paper No. ,733 (1971) Pgs. 241-244 Mendenhall, W . , / S c h e a f l e r , 8. Mathematical S t a t i s t i c s With A p p l i c a t i o n s Duxbury Press N. S c i t u a t e , Mass. (1973) Milne, W. G. Earthquake E p i c e n t r e s And S t r a i n Release In Canada 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 Milne, W. G., D i s t r i b u t i o n Of Earthguake B i s k In Canada S e i s m o l o g i c a l S o c i e t y Of America B u l l e t i n V o l . 59 No. 2 ( A p r i l 1969 ) Pgs. 729-754 Milne, R. G. Seismology Cf Western Canada Canadian J o u r n a l Of E a r t h Sciences Vol.,15 No. 7 ( J u l y 1978) Pgs. ,1170-1193 Misra, K. B. An Algorithm For The B e l i a b i l i t y E v a l u a t i o n Of Redundant Net. I E E E T r a n s a c t i o n s B-19 No. 4 November 1973 Murphey, Leonard ( C o o r d i n a t o r ) San Fernando Earthguake Of 9 February 1971 0. S. Department Of Commerce N 0 A A (1973) Oakeshott, Gordon San Fernando Earthquake Of 9 February 1971 C a l i f o r n i a D i v i s i o n Of Mines And Geology B u l l e t i n No. 196 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 Seis m i c Hazards A S C E Proceedings Tech., C o u n c i l On L i f e l i n e Earthquake Engineering P a r n o u s s i s , George Seismic 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. Seismic Design D e c i s i o n A n a l y s i s Beport No. 15 87 Feckover / Kerr Treatment Of Bock Slo£es On T r a n s p o r t a t i o n Eput.es 29th Canadian G e o t e c h n i c a l Conf. Vancouver, B. C. 1974 Pond, S. ..P. Performance Of Bridges During The San Fernando Earthguake J o u r n a l P r e s t r e s s e d Concrete I n s t i t u t e ( J u l y - Aug 1972) Pgs. 65-75 B i c e , E. F. Alaska Earthguake A S C E C i v i l E n g i n e e r i n g V o l . 34 No. 5 { may 1964) Pgs. ,52-56 Shah, H. C. / Benjamin J . B. l i f e l i n e S eismic C r i t e r i a And B i s k ; St ate 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 E n g i n e e r i n g Singh, 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 E v a l u a t i o n Hutchison L t s . London 1977 S t a t i s t i c s Canada Railway T r a n s p o r t --Part 3 j_ B a i l F r e i g h t Beport No. 52-201 Ottawa, O n t a r i o 1978 S t a t i s t i c s Canada Railway Transport^ Part 4 Operating 6 T r a f f i c  S t a t i s t i c s Beport No.,52-210 Ottawa, O n t a r i o 1978 T a l e b - Agha, Ghiath Seismic B i s k A n a l y s i s Of Networks M. I . T. Seismic Design D e c i s i o n A n a l y s i s Beport No.22 Taleb - Agha , Ghiath Seismic Risk A n a l y s i s Of L i f e l i n e Networks M. I . T. Seismic Design D e c i s i o n A n a l y s i s Report No.24 Whitman/ C o r n e l l / Taleb-agha A n a l y s i s Of Earthguake Risk For L i f e l i n e Systems Proceedings 0. S. N a t i o n a l Conference Of Earthguake Engineeringann Arbor 1975 Whitman/ Bi g g s / Brennan/ C o r n e l l / d e N e u v i l l e / Vanmarke Seismic 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. Vol.„101 S t 5 Hay 1975 Whitman, H. V. Risk Based Seismic Design C r i t e r i a For L i f e l i n e s A S C E N a t i o n a l Meeting Los Angeles, C a l i f o r n i a P r e p r i n t No. 2148 1974 88 APPENDICIES APPENDIX A 2 TOTAL COST CALCULATIONS Morlok ( Reference No. .21 Page 401 ) suggest t h a t c o s t s f o r r a i l t r a n s p o r t are from us$ 4.0 - $ 7.0 m i l l i o n per mile or us$ 2.5 - $4.6 m i l l i o n per k i l o m e t r e . Adding the r a t e or exchange of 15 % and an a d d i t i o n a l 15 % f o r hig h e r labour c o s t s , t h i s f i g u r e i s c$3.3 - $ 6.0 m i l l i o n / km. Since c o n s t r u c t i o n i s that of a r a i l w a y i n the i n t e r i o r s e c t i o n s of the province a f i g u r e of c$ 3.5 m i l l i o n w i l l be used f o r new c o n s t r u c t i o n . H a l f t h a t f i g u r e or c$1.75 m i l l i o n w i l l be used as the c o s t f o r upgrading e x i s t i n g f a c i l i t i e s or remnants t h e r e o f . T h i s i s because an abandoned l i n k a l r e a d y has the s i t e surveyed, c l e a r e d l a n d , an e x i s t i n g roadbed of s o r t s , and some b r i d g e s . Land a c g u a s i t i o n c o s t s are based on a f i g u r e of $ 10 000 per acre or $ 4 100 per h e c t a r e . Again these c o s t s are based on i n t e r i o r l a n d c o s t s . Using the standard 31 metre ( 100 f o o t ) r a i l r i ght-of-way there are 3 h e c t a r e s per running km of t r a c k . Thus land a c g u a s i t i o n c o s t s a r e $ 12 300 / l i n e a r km of t r a c k . , These f i g u r e s are a p p l i e d to the l i n k d i s t a n c e s of the f o u r proposed l i n k s and the r e s u l t s are summarized i n Table 5. 89 A P P E N D I X B X C A L C U L A T I O N OF T H E C O N S T A N T ' S B T h e f o l l o w i n g i s a l i s t i n g o f t h e v a r i o u s v a l u e s f o r t h e c o n s t a n t s b 1 2 b , a n d 3 c t o b e u s e d i n t h e e q u a t i o n : A = b s b m 2 e 1 ( a • c ) s - b 3 R E F E R E N C E | L O C A T I O N 1 B | 1 1 1 B | 2 i B 3 I c | COMMENTS ] DONOVAN | SAN FERNANDO | 1080 | 0.5 1 1.32 I 25 I ! DONOVAN ] WESTERN U. S . A . J 1300 J 0.67 | 1.60 ] 25 ! ! E S T E V A | WESTERN U . S . A . , 1 1230 | 0.8 | 2.0 1 25 i ! M I L N E | B R I T I S H C O L U H B I 1 | 0.69 | 1.64 | 1.0 1 o J F O R U S E | | I N E Q U . AJ P A R N O U S S I S I S O U T H E R N C A L I F . | 2000 | 0.8 | 1.7 1 o ! ! T A L E B - A G H A | B O S T O N 1 1.183) 1.15 | 1.0 i o | FOR U S E | J I N E Q U . B| E q u a t i o n A A = s b m 2 b e 1 ( 1 . l i e 1,1m - b r ) 3 E q u a t i o n B A s = E b e 1 b m 2 ( a s • c ) - b 3 90 Since H i l n e and Taleb - Agha use a l t e r a t i o n s of the b a s i c a t t e n u a t i o n eguation they w i l l not be used. Thus using the other f o u r and o b t a i n i n g an average the values are : b = 1402., b = 0.69 b = 1.65 c = 25 1 2 3 By using these values f o r the c o n s t a n t s , a resonably good approximation of expected peak a c c e l e r a t i o n s can be ob t a i n e d . Of course, these c o n s t a n t s are based on those f a u l t s which have, i n the past, generated the m a j o r i t y of the ea r t h movements i n western Canada. T h i s does not preclude a new source of e a r t h movement which may be e x p e r i e n c e d . T h i s i s e s p e c i a l l y t r u e when these movements are i n c o n j u n c t i o n with movements from known sources. , 91 A P P E N D I X C . £ L I S T OF C L A I M S C a n a d i a n N a t i o n a l B a i l w a y $ 2 5 . 2 M i l l i o n C a n y o n C r e e k F o r e s t P r o d u c t s $ 2 . 9 M i l l i o n S a s k a t c h e w a n W h e a t P o o l $ 1.7 M i l l i o n I m p e r i a l O i l L t d , 1 1.2 M i l l i o n C a n a d i a n W h e a t B o a r d $ 1. 1 M i l l i o n B u r l i n g t o n N o r t h e r n B a i l w a y $ 1 5 0 0 0 0 . N a t i o n a l H a r b o u r s B o a r d $ 116 7 5 1 . C . S . P . F o o d s L t d . $ 61 9 2 6 . B e t h l e h e m C o p p e r C o r p . , $ 43 20 0 . , B r i t i s h C o l u m b i a H y d r o A u t h . $ 2 2 0 0 . T h i s i n f o r m a t i o n w a s o b t a i n e d f o r m H u g h A r m s t r o n g , P u b l i c B e l a t i o n s O f f i c e r f o r t h e B r i t i s h C o l u m b i a B a i l w a y a n d f o r a n a r t i c l e w r i t t e n b y L a r r y S t i l l i n t h e V a n c o u v e r S u n o n 3 A p r i l 1 9 8 0 . ( p a g e A 1 7 ) 92 APPENDIX JO.. ,x DETAILED TIE - SET BE DOC TIP N T h i s t i e - s e t r e d u c t i o n procedure was developed by Taleb -Agha ( Beference No. 41 Pages 12 - 22 ) and e l i m i n a t e s e x i s t i n g redundancies. The b a s i c t i e - s e t f o r the Fr a s e r Canyon i s : COMPONENT SSP TIE - SETS J J — J 9 J J Z. 29 13 10 8 7 6 5 1 | 13 10 8 7 6 5 2 13 10 8 7 4 3 i 1 13 10 8 7 4 3 2 13 10 9 6 4 3 1 ] 13 10 9 6 4 3 2 13 10 9 5 1 2. | 13 10 9 5 2 14 11 8 7 6 5 t 1 14 11 8 7 6 5 2 14 11 8 7 4 3 1 | 14 11 8 7 4 3 2 14 11 9 6 4 3 I | 14 11 9 6 4 3 2 14 11 9 5 1 | 14 11 9 5 2 J2 2_- _ 12 " 29 11 8 7 6 5 | 1 14 13 10 8 7 6 5 2 11 8 7 4 3 | 14 13 10 8 7 4 3 2 1 1 9 6 4 3 j I 14 13 10 9 6 4 3 2 11 9 5 | 4. , 1 14 13 10 9 5 2 14 13 10 8 7 6 5 I I 11 8 7 6 5 2 14 13 10 8 7 4 3 I 1 11 8 7 4 3 2 14 13 10 9 6 4 3 ! I 1 1 9 6 4 3 2 14 13 10 9 5 j 1 11 9 5 2 Check t o see i f the o b j e c t i v e r e g u i r e s t h a t the t i e - s e t s of other i n p u t / o u t p u t p a i r s must be l i n k e d i n p a r a l l e l . I f so, the d e l e t e those redundancies. In t h i s case the two i n o u t matracies from Kamloops are p a i r e d t o g e t h e r and the two i n p u t matracies from Kamloops J u n c t i o n are p a i r e d t o g e t h e r . , Thus , we o b t a i n two i n t e r m e d i a t e SSP t i e - s e t matracies. T h i s y i e l d s the f o l l o w i n g : 11 - 19 8 11 - 29 12 - 19 6 12 - 29 | 13 10 8 7 6 5 f 13 10 8 7 4 3 | 13 10 9 6 * 3 | 13 10 9 5 | 14 11 8 7 6 5 i 14 11 8 7 4 3 | 14 11 9 6 4 3 | 14 11 9 5 M a t r i x A 1 1 8 7 6 5 11 8 7 4 3 11 9 6 4 3 11 9 5 14 13 10 8 7 6 5 14 13 10 8 7 3 14 13 10 9 6 4 3 14 .13 10 9 5 Matrix B Next, f i n d the i n p u t / output p a i r s such t h a t the s u r v i v a l of any of the t i e - s e t w i l l s a t i s f y the o b j e c t i v e , t h a t i s , the t i e - s e t s of these input / output p a i r s must be l i n k e d together i n p a r a l l e l so t h a t i f any of the p a r a l l e l l i n k s s u r -v i v e d , the o b j e c t i v e would be met.. To accomplish t h i s the Matrix B w i l l be " c r o s s e d " with Matrix A, one row a t a time. The f i r s t step w i l l be shown as an example. T h i s e n t a i l s t a k i n g M a t r i x B and a s s i g n i n g each row of Matrix A to i t . ( i n other words, adding the f i r s t row of Matrix B to a i l the rows of Matrix A). Then row redundanceies are e l i m i n a t e d by d e l e t i n g "double" e n t r i e s . . Thus the f i r s t i t e r a t i o n i s : \ Matrix B | X X | 13 1 0 8 7 6 5 ) A f t e r each row has been c r o s s e d and the redundancies e l i m i n a t e d the remainder i s saved to form the f i n a l matrix. ( The new matrix i s made up of the remainders of each c r o s s i n g 94 o p e r a t i o n ) . T h i s i s a f t e r each of these saved remaineders have been checked f o r redundancies between themselves. Since a l l of the t i e - s e t s i n t h i s case are unique the f i n a l matrix i s simply the exact remainders of the i n t e r m e d i a t e SSP t i e - s e t s . Thus : reduced matrix f o r e x i s t i n g network | 13 10 8 7 6 5 J | 13 10 8 7 4 3 | J 13 10 9 6 3 | I 13 10 9 5 I | 14 11 8 7 6 5 J | 14 11 8 7 4 3 | | 14 11 9 6 4 3 | I 14 1 1 9 5 | PBOPOS BD NETWOEK So, from a s t a r t of f o u r matracies t h i s procedure has reduced them to one s i n g l e matrix i n which the a n a l y s i s can be performed. The a n a l y s i s i s the same f o r the proposed network except t h a t 8 a d d i t i o n a l t i e - s e t s are i n c l u d e d i n the b a s i c c o n f i g u r a t i o n r e s u l t i n g i n an a d d i t i o n a l two t i e - s e t s i n the r e l i a b i l i t y a n a l y s i s . Those a d d i t i o n a l 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 10 1 2 J <—> | 14 11 10-15 1 2 \ Note that the t i e - s e t s on the r i g h t are simply subsets of those on the l e f t and can thus be e l i m i n a t e d . T h i s leave f o u r 95 t i e - s e t s to be assigned to each matrix ( 1 to 4 ) above and then the r e d u c t i o n i s again performed r e s u l t s i n the f o l l o w i n g reduced t i e - s e t matrix f o r the proposed network : 13 10 8 7 6 5 13 10 8 7 4 3 13 10 9 6 3 13 10 9 5 14 11 8 7 6 5 14 11 8 7 4 3 14 11 9 6 4 3 14 11 9 5 14 13 15 14 11 10 15 1 T h i s f i n a l reduced matrix i s the same as F i g u r e 18. 96 APPENDIX DETAILED BELIABILITY CALCULATIONS The c a l c u l a t i o n o f the r e l i a b i l i t y of the S e r i e s System i n P a r a l l e l uses the f o l l o w i n g b a s i c e g u a t i o n : B = 1 - { 1 - A + ( B - C ) - D } where these values were d e s c r i b e d on page . The d e t a i l e d c a l c u l a t i o n o f them f o l l o w s . The c a l c u l a t i o n of the l e t t e r e d t i e - s e t s i s o u t l i n e d below • • a (. 998) (.998) (.930) (.950) (. 920) (.920) = . 745 b = {. 998) (.998) (.930) (.950) (. 740) (.740) .472 c {. 998) (.998) (.920) (.920) (. 740) . 581 d (.998) (.998) (.920) (.920) = .581 e (. 999) (.998) (.930) (.950)=(. 920) (.920) — .746 f = (.999) (.998) (.930) (.950H. 740) (. 740) — .482 g (.999) (.998) (.920) (.920) (. 74 0) (.740) .467 h = (. 999) (.998) (.920) (.920) = .853 i (.999) (.998) (.999) = .991 j (.999) (.998) (.998) (.999) (. 995) . 984 Now the c a l c u l a t i o n of the A, B, C , S D values can commence. A i s the sum of a l l of the l e t t e r e d t i e - s e t s . For the e x i s t i n g network t h i s i s a to h and f o r the proposed network t h i s i s a to i . Thus : A ( e x i s t i n g ) = (. 745) • (. 472) + (. 581) • (. 853) • + (.746)*(.482) M-467) +(.853) = 5. 199 f o r the proposed network t h i s i s j u s t : A (proposed ) = 5.199 • (.941) (.984) = 7. 174 To determine D simply m u l t i p l y the l e t t e r e d t i e groups t o g e t h e r . For the e x i s t i n g network : set D ( e x i s t i n g ) = (.745) (.472) (.581) (.853) (,746) (.482) (.467) (.853) = .024 97 The D value f o r the proposed network i s simply : D (proposed) = .024 (-941) (.984) = .025 To c a l c u l a t e B, a l l the i n d i v i d u a l l i n k s of one - t i e s e t are m u l t i p l i e d by another group. T h i s has been done and i s shown i n the t a b l e below. However, there are some redundacies which e x i s t i n t h i s t a b l e and must be s u b t r a c t e d from the t o t a l o f B by employing the c o r r e c t i o n f a c t o r C. T h i s c o r r e c t i o n f a c t o r i s simply 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 m u l t i p l i e d by tmeselves and accounted f o r the number of times they have been "double" counted., (although here they may have been counted m many times over. ) 98 1 a b c J d 1 e 1 f 1 g 1 h I i 1 j 1 J a| .352J .4331 .635| .556J .3591 ,348| ,635| .738 | .7331 1 hi a b 1 - .2701 .400j .3521 .2271 . 220 1 . 400| .4671 .464| 1 cj a c b c i - | -495| .433J .2801 w271l .495| -5751 .5721 1 d| a a I b 3 1 c a i - 1 ,6361 -410J .3481 .7271 .845J .839| 1 ej a e b € 1 c e l d e | - 1 .3601 .348) .636) .739) .7341 1 f l a f 1 b f 1 c f I a f i e f 1 - 1 ^225| .410J .4771 .4741 1 91 a g i b g i c g | a g | e g I f g 1 - 1 .3531 .463J .460J 1 h| a h 1 b h 1 c h 1 a h i g h l f h | g h | | .8451 .8391 1 11 a i i b i 1 c i | a i i e i I f i 1 g i 1 h i | - 1 .975J 1 j l a j 1 b j 1 c j 1 * j 1 e j 1 f j 1 g j i h j 1 i 3 1 - 1 For the e x i s t i n g network the value f o r B uses the l e t t e r e d group of t i e - s e t s from a to h and i t s value i s 11.613 with a c o r r e c t i o n f a c t o r C of 7.271 . For the proposed network the value f o r B i s obtained from using the l e t t e r e d group of t i e - s e t s from a to j and i t s value i s 17.03 with a c o r r e c t i o n f a c t o r C of 10.794 . 

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