Water Resources Research Report

Transcription

1 THE UNIVERSITY OF WESTERN ONTARIO DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING Water Resources Research Report Mult-hazard reslence model of an nterdepent nfrastructure system By: Jngjng Kong and Slobodan P. Smonovc Report No: 102 Date: November 2017 ISSN: (prnt) ; (onlne) ISBN: (prnt) ; (onlne)

2 Mult hazard reslence model of nterdepent nfrastructure system By Jngjng Kong Slobodan P. Smonovc Department of Cvl and Envronmental Engneerng Western Unversty, Canada November 2017

3 Abstract: Mult hazard reslence s of sgnfcant practcal value, as most of the world regons are subject to multple natural and technologcal hazards. An analyss and assessment approach for mult hazard spatotemporal reslence of nterdepent nfrastructure system s developed by ntegratng network theory, geographc nformaton system and numercal analyss. Frst, we defne mult hazard reslence and present a quanttatve probablstc metrc based on the expanson of sngle hazard determnstc reslence model. Second, we defne mult hazard relaton analyss model wth focus on hazards mpacts on nfrastructure. The relaton cube s constructed wth two temporal and one spatal dmensons. Developed methodology s used for drect damage probablty analyss of an nfrastructure under twelve spatotemporal combnatons of two dfferent hazards. A general method for evaluaton of drect mpacts on an nfrastructure under multple hazards s proposed. Thrd, we present an analyss of ndrect mult hazard mpacts on nterdepent nfrastructure. The methodology s mplemented on the case study of Greater Toronto Area energy system (ncludng electrc, gas, and ol transmsson networks). The results confrm that the effects of sequental hazards on reslence of nfrastructure (network) are qute dfferent than the smple sum of multple sngle hazard effects. The reslence deps on the magntude of the hazards, ther spatotemporal relatonshp and dynamc combned mpacts, and nfrastructure nterdepences. The paper presents a comparson between physcal and functonal reslence of electrc transmsson network, and fnds functonal reslence s always hgher than physcal reslence. The multple hazard reslence evaluaton approach s applcable to any type of nfrastructure and hazard and t can contrbute to the mprovement of the nfrastructure plannng, desgn and mantenance decson makng. Key words: multple hazards reslence, nterdepent nfrastructure system, restoraton strategy, Greater Toronto Area

4 ACKNOWLEDGMENTS We are grateful to the Natural Scences and Engneerng Research Councl (NSERC) of Canada, and the Insttute of Catastrophc Loss Reducton (ICLR) supported by Chaucer PLC for fundng of ths research. Any opnons, fndngs, and conclusons or recommatons expressed n ths report are those of the authors and do not necessarly reflect the vews of the sponsors.

5 TABLE OF CONTENTS ACKNOWLEDGMENTS... 3 TABLE OF CONTENTS... 4 LIST OF TABLES... 6 LIST OF FIGURES INTRODUCTION MULTI HAZARD RESILIENCE MODEL Interdepent Infrastructure System Model Determnstc Sngle Hazard Reslence Metrc Probablstc Mult Hazard Reslence Metrc MULTI HAZARD RELATIONSHIPS AND DIRECT IMPACTS ON INFRASTRUCTURE Relatonshps Between Multple Hazards Temporal relatonshps of multple hazards Spatal relatonshps of multple hazards Relatonshp cube of multple hazards Impacts of Multple Hazards on Infrastructure Systems Drect mpacts of two hazards Drect mpacts of multple hazards Falures propagaton mechansm and ndrect mpacts of multple hazards on nfrastructures 21 4 MULTI HAZARDS RESILIENCE ASSESSMENT APPROACH MULTILAYER INTERDEPENDENT INFRASTRUCTURE NETWORK GTA Energy Infrastructure Spatal Network Infrastructure Interdepence Models Physcal and Functonal Reslence Metrc SEQUENTIAL HAZARS SCENARIO AND ITS IMPACTS Sequental Hurrcane and Flood Scenaro Sngle Hazard Impacts on Infrastructure Sequental Hazard Impacts on Infrastructure SEQUENTIAL HAZARD RESILIENCE SIMULATION Jont Restoraton Model of Interdepent Infrastructure System Sequental Hazard Reslence Smulaton Process GTA ENERGY INFRASTRUCTURE SYSTEM PHYSICAL RESILIENCE Infrastructure Physcal Performance Spatal Analyss... 37

6 8.2 Dynamc Infrastructure System Physcal Reslence GTA ENERGY INFRASTRUCTURE SYSTEM FUNCTIONAL RESILIENCE Infrastructure Functonal Performance Spatal Analyss Dynamc Infrastructure System Functonal Reslence DISCUSSION Sngle Hazard Margnal Impacts Cascadng Falure and Recovery Effects Restoraton Resource Lmts CONCLUSIONS REFREENCES APPENDIX A: Data Resources APPENDIX B: Model Code for MATLAB (1) Calculaton of the performance of electrc power system under hazard (2) Calculaton of the performance of gas supply system under hazard (3) Calculaton of the performance of ol supply system under hazard (4) Generaton of the flood scenaro (5) Generaton of the hurrcane scenaro (6) Calculaton of the performance of three systems under combned hurrcane and flood scenaro (7) Calculaton of the performance of three systems under flood scenaro (8) Calculaton of the performance of three systems under hurrcane and flood scenaro APPENDIX C: Lst of Prevous Reports n the Seres... 89

7 LIST OF TABLES Table 1 GTA three-layer energy nfrastructure spatal network nformaton... 26

8 LIST OF FIGURES Fgure 1 Mult-layer nfrastructure network... 4 Fgure 2 Typcal nterdepent nfrastructure system performance under a sngle hazard/dsturbance... 5 Fgure 3 Typcal nfrastructure system performance under two sequental hazards... 7 Fgure 4 Typcal nfrastructure system performance under two sequental hazards... 8 Fgure 5 Typcal nfrastructure system performance under two concurrent hazards... 9 Fgure 6 Temporal relatonshps between two hazards Fgure 7 Spatal relatonshps between two hazards Fgure 8 Relaton cube of multple hazards Fgure 9 Framework for the assessment of multple hazards reslence of nterdepent nfrastructure system Fgure 10 GTA three-layer energy nfrastructure spatal network Fgure 11 Populaton supported by electrc transmsson substatons n GTA Fgure 12 Sequental hurrcane and flood mpacts on GTA Fgure 13 Smulaton procedure of GTA nfrastructure system reslence under sequental hurrcane and flood Fgure 14 Spatal physcal performance of GTA three-layer energy nfrastructure network under dfferent hazard scenaros Fgure 15 GTA three-layer nfrastructure network dynamc physcal reslence Fgure 16 Spatal functonal mpacts of GTA three-layer energy nfrastructure network under dfferent hazards scenaros Fgure 17 GTA electrc transmsson network dynamc functonal and physcal reslence Fgure 18 Reslence profles for dfferent magntude of hazards Fgure 19 Reslence profles for dfferent tme nterval of hazards Fgure 20 Reslence profles for dfferent spatal overlap area of hazards Fgure 21 Reslence profles for dfferent resource constrants... 53

9 1 INTRODUCTION Infrastructure systems, ncludng electrc power, telecommuncatons, natural gas and ol, transportaton, water supply, and others, are large scale, man-made systems that functon nterdepently to produce and dstrbute essental goods and servces for socety and economy (1). Infrastructure system reslence has ganed attenton of practtoners and researchers durng the past decades due to ts role n better understandng of rsks assocated wth the nevtable dsruptons of system components (2-4). Mult hazard reslence s of sgnfcant practcal value, as most world regons are subject to multple natural and technologcal hazards (5). Some examples nclude Prnce Wllam Sound regon of USA Alaska n 1964 attacked by earthquake and followng landsldes and tsunam (6) ; Mount Pnatubo 1991 volcanc erupton whch trggered earthquake n Phlppnes; New Orleans destructon by Hurrcane Katrna and follow up flood n 2005; and 2011 Tohoku dsaster n Japan caused by sequental mpacts of earthquake, flood and tsunam. Mult hazard reslence s crtcal for enhancng nfrastructure system reslence. Reslence mples the ablty of a system to return to normal condton after an nternal or external dsturbance. Its orgns are n ecology and work of C. S. Hollng (7). Due to the wde nterest and applcaton n varous dscplnes there s nether unversal defnton nor wdely accepted general quanttatve approach for ts assessment. Excellent revews are avalable n a number of publshed papers (4,8-10). Infrastructure system reslence s always seen as the ablty of the nterconnected nfrastructure system: () to resst (prevent, absorb and wthstand) any possble hazard (11) ; () reduce the magntude of mpact and/or duraton of dsruptve event (12) ; and () recover and reconsttute crtcal servces to the publc wth mnmum damage (13). Accordngly, reslence s not only the capacty of an nfrastructure system, but also relates to the type, magntude and other characterstcs of the hazardous event (14-15). Though most of the research focuses on reslence defnton and outcome-orented metrcs (9,16-18), some nclude the analyss of specfc event reslence of nfrastructure systems. Ouyang and Dueñas-Osoro (13,19) quantfy annual expected hurrcane reslence of contemporary electrc power systems. Oddsdóttr et al. (20) evaluate the transportaton and power supply system reslence subject to Hurrcane Sandy. Shnozuka et al. (2) evaluate sesmc reslence of electrc power and water supply systems. Smonovc (21) and Kong et al. (22) focused on flood reslence of nterdepent nfrastructure system. 1

10 Generally, mult hazard reslence or rsk analyss methods used up to now, smply sum up specfc mpacts of sngle hazards usng hstorcal data (23-26). There are three major platforms for the computaton of mult-hazard rsks on a natonal level: Hazus, RskScape, and CAPRA (27,28). Ther methodologes consder hazards as ndepent events (29,30). Potental nteractons between hazards and mxed mpacts are rarely consdered. Only a few approaches and studes on ths topc are avalable (31). Recently, two dstnct approaches focusng on cause-and-effect of mult hazards have been proposed to tackle the problem of hazard nteractons (32). One s spatally orented and ams at ncludng all relevant hazards (33), and the other s prmarly thematcally defned (31). But hazard relatons and nteractons may have unexpected effects and pose threats that are not captured by means of separate sngle-hazard analyses. Advanced understandng of hazard processes, elements at rsk and ther vulnerabltes, wthout analysng the nteractons between these components and ther spatal and temporal dynamcs, mght not provde adequate support for developng preparedness, mtgaton and response strateges to ncrease reslence or reduce rsk (34,35). The prmary objectves of ths report are to propose a methodology for () development of complex mult hazard relatons; () consderaton of complex nfrastructure nterdepences; and () ntegraton of spatotemporal mpacts on nfrastructure. It s our expectaton that the proposed methodology wll be able to capture and quantfy mult-layer nfrastructure network reslence subject to dsturbng events caused by multple hazards. Formulated as a large-scale, nonlnear, and combnatoral system evoluton problem, the reslence assessment s performed usng smulaton. The remander of the report s organzed as follows. Secton 2 presents the mult hazard reslence defnton and probablstc model based on sngle hazard reslence metrc. In Secton 3, mult hazard mpacts analyss framework s ntroduced. Drect mpacts of multple hazards on nfrastructure are modeled usng fraglty curves. Indrect mult hazard mpacts on nterdepent nfrastructure s also analyzed. Secton 4 ntegrates the mult hazard reslence model. In Secton 5, the Greater Toronto Area (GTA) energy nfrastructure system (ncludng electrc, gas and ol transmsson networks) s used as a case study to present an applcaton of the sequental hazard reslence assessment method. GTA energy nfrastructure system s modeled as a mult-layer network, and ntra- and nter-network nterdepence models are developed. Secton 6 ntroduces sequental hurrcane and flood dsaster scenaro, analyzes ther drect mpacts on nfrastructure and ndrect falure probabltes as a consequence of varous nterdepences. Secton 7 2

11 descrbes sequental hazard reslence smulaton procedure. Sectons 8 and 9 are presentng temporal and spatal nfrastructure system performance and reslence, usng both, physcal and functonal perspectves. The report s n Secton 10 wth the dscusson of sngle hazard margnal mpacts, cascadng recovery effects, and cumulatve reslence results. Conclusons are lsted n Secton MULTI HAZARD RESILIENCE MODEL Ths secton ntroduces the mult hazard reslence defnton and probablstc model based on sngle hazard reslence metrc. 2.1 Interdepent Infrastructure System Model Indvdual nfrastructure systems, such as power grds, water supply networks and telecommuncaton networks, functon together as a system of systems, n whch two or more nfrastructure types nteract wth one another (36). A system-of-systems can be descrbed by a topology that accounts for the representaton of ts components and the way they nteract. Infrastructure systems (defned here as the systems of publc works of a country, state, or regon), wth dverse clearly defned components, can be modeled as a network of networks (37) or a multlayer networks (38). Here nfrastructure system s modeled as a multlayer spatal network IS G (Fgure 1), n whch sngle layer denotes one knd of nfrastructure system (22). Each layer (such as power grd, water supply network, transportaton network, nformaton nfrastructure network) s modelled n the same fundamental way (39). Nodes are used to represent functon source and transmsson facltes, such as power plants and substatons of electrc network G and pumpng statons of water supply network G W E, water treatment plants G, gas compressor statons and storage facltes of gas network G, and so on. Arcs/edges represent functon transmsson facltes, such as power lnes of electrc transmsson network E G, ppelnes of gas transmsson network G G, ol transmsson network O G, and so on. Nodes and edges n the same layer belong to the same type of nfrastructure (shown usng the same color sold lnes wthn a sngle layer network n Fgure 1). Edges between dfferent layers denote nterdepences between dfferent types of nfrastructure (shown as dotted lnes between dfferent layers n Fgure 1). The color of an edge dentfes the drecton of depency. 3

12 Fgure 1 Mult-layer nfrastructure network Infrastructure components located n the same area may be subject to a specfc dsturbance/dsaster, and the locaton of nfrastructures and dstance between them have mportant effects on topologcal propertes, and consequently, on nfrastructure functonng processes (37). The spatal attrbutes of nodes and edges are ncluded n a realstc nfrastructure network model wth geographcal coordnates defned n a two-dmensonal Eucldean coordnate system. Each node has three coordnates (, xy, ), where denotes the type of nfrastructure, and ( xydenote, ) the geographcal locaton of the node. Edges are denoted by the two adjacent nodes and can be dvded n to two types: () ntra-nfrastructure connecton, same value of ; and () nter-nfrastructure connecton, dfferent value. The length of an arc can be represented as the weght of ts mportance. 2.2 Determnstc Sngle Hazard Reslence Metrc The nfrastructure system reslence s defned as the ablty to prepare for, and adapt to changng condtons, and wthstand and recover rapdly from dsruptons, ncludng the ablty to wthstand and recover from delberate attacks, accdents, or naturally occurrng threats or ncdents (40,41). Orgnal Space-Tme Dynamc Reslence Measure developed by Smonovc (21,22,42) s adapted n ths research to complex network nfrastructure systems. It quantfes reslence as the dfference between the area under expected system performance (dotted lne n Fgure 2) 4

13 and actual system performance (sold or dashed lne n Fgure 2). The mathematcal representaton of quanttatve reslence s r t t t A 0 A O A O A O t t t SP ( t) dt ( SP ( t) SL ( t)) dt SL ( t) dt ( t) 1 SP ( t) dt SP ( t) dt SP ( t) dt A O A O A O (1) A where r () t s reslence of nfrastructure system to hazard/dsturbance A at t, SP () t s actual performance of multlayer nfrastructure network, SP () 0 t s the expected performance of multlayer nfrastructure network, SL () t s A A system performance loss of multlayer nfrastructure network, O t s the hazard/dsturbance occurrence tme. Multlayer nfrastructure network performance always uses an unform measure to capture the nterdepent system servce level, such as the proporton of survvng nodes (13,30), operaton rates of edges (43), or sze of the largest connected component (44). The number of customers served by the nfrastructure system can also be used as the performance measure (45,46). System Performance Expected System Performance SP 0 (t) A System Performance SP(t) WITH Restoraton Measures Robustness Resourcefulness (t ) System Performance SP(t) WITHOUT Restoraton Measures 0 Dsaster Preventon Damage and Propagaton t Rapdty Evoluton and Recovery t Fgure 2 Typcal nterdepent nfrastructure system performance under a sngle hazard/dsturbance In Fgure 2, wdth of a red arrow dsplays the duraton of the dsturbance. Typcal dynamc nfrastructure performance can be dvded nto three phases: dsaster preventon, damage and propagaton, evoluton and recovery (30,47,48). Based 5

14 on the reslence model derved by MCEER (Multdscplnary Center for Earthquake Engneerng Research) (16), the system reslence s a functon of system performance and system adaptve capacty. System adaptve capacty can be descrbed usng four features of the dagram shown n Fgure 2: Robustness, Redundancy, Resourcefulness and Rapdty. Robustness refers to the ablty of a systems to wthstand a gven level of stress wthout sufferng degradaton or loss of functon mnmum level of performance after the system dsturbance. It s computed as the rato of mnmum number of operatonal elements after multple dsturbances to the total number. Redundancy descrbes the alternate functons and desgns for the system mechancs to operate (49). Redundancy s always seen as a functon of robustness (50,51). Resourcefulness s the capacty to develop and mplement mtgaton and response strateges for recovery from a specfc dsturbance. It s a functon of restoraton strateges, and can be calculated as the dfference between system performance wth and wthout restoraton strategy. Rapdty s measured by the duraton of all nfrastructures recovery to normal operatonal levels. It s worth mentonng that performance metrcs used should be based on the research focus and avalable data. 2.3 Probablstc Mult Hazard Reslence Metrc Multple hazard/dsturbance refers to a stuaton when hazards of dfferent knds or magntudes occur at the same tme, or more often, follow one another wth damagng force. Examples nclude floods n the mdst of drought, or hurrcane followed by landsldes and floods (52) and smlar. Wth ther dverse ntensty, return perods, mpacts, and uncertan relatons, multple hazards may have complex mpacts and create unexpected threats very dfferent from those caused by a sngle hazard/dsturbance (5,24,31). Mult hazard reslence s the dynamc nonlnear superposton of sngle hazard s spatotemporal mpacts on a complex nfrastructure system. There are dfferent relatons between multple hazards: cause-and effect; temporal relaton (such as co-occurrence, sequence); and spatal relaton (such as scatter, block and overlap). They make ther mpacts much more complcated. In the event of two or more hazards occurrng at the same locaton the nfrastructure may be placed under greater stress than f the hazards occurred at dfferent locatons. Sequence s a typcal temporal relaton of multple hazards. Generally, nfrastructure system reslence s analyzed ndvdually wth the assumpton of later events occurrng before full system recovery from the prevous one, whch s llustrated n Fgure 3. Infrastructure system performance 6

15 and reslence can be calculated as sngle hazard reslence at dfferent tme perods, and evaluated ndvdually. The nfrastructure system performance can be expressed as O SP () t t t t SP() t O SP () t t t t RE RE Aj Aj Aj (2) where SP() t s actual performance of multlayer nfrastructure network. SP () t and SP () t are actual performances A A j of multlayer nfrastructure network under hazard A and A j ; O O t A and t Aj are the occurrence tmes of hazard/dsturbance A and A j ; and RE RE ta and Aj t are the recovery tmes of hazard/dsturbance A and A j. System Performance A Expected System Performance SP0(t) A j Robustness(Aj) System Performance SP(t) WITH Restoraton Measures Robustness() Resourcefulness (t) System Performance SP(t) WITHOUT Restoraton Measures 0 t Rapdty t Fgure 3 Typcal nfrastructure system performance under two sequental hazards Actually, ths llustraton captures the stuatons when there are not enough tme and resources for full nfrastructure system recovery from the frst dsturbance before the second event occurs. The mpact of one hazard on the physcal nfrastructure could ncrease the vulnerablty to the secondary or future hazard events, therefore potentally amplfyng the mpacts of secondary or future hazards. For example, an earthquake may weaken buldngs makng them more susceptble to collapse n the event of the follow up earthquake, f the repars are not completed. In ths stuaton, nfrastructures damaged by the ntal hazard could not be repared as planned, or they can be destroyed agan by later hazards. In ths case the operaton or recovery of nfrastructures would be mpacted by later hazards. 7

16 The nfrastructure reslence s not an ntegral of reslence of ndvdual hazards at dfferent tme perods as llustrated n Fgure 3. Contrary t s a result of nteracton between mpacts of multple hazards on nfrastructure system as shown n Fgure 4. Process of nfrastructure adaptaton can be dvded nto two phases. System performance evoluton curve n each phase has the shape very dfferent from the shape of the performance curve under a sngle hazard. Also, nfrastructure system performance under the two sequental hazards would be expressed as O O SPA () t A t Aj SP() t O SPA () j A t t A j (3) where SPA A() t s the actual system performance of multlayer nfrastructure network under hazard/dsturbance A j j followed by hazard/dsturbance A. SP () t usually does not equal to SP () t as t s a functon of hazard and Aj A j nfrastructure system. In ths stuaton, the state of nfrastructure system when A j occurs s dfferent from the state of the system before the hazard happens. The adaptve capacty of nfrastructure system after occurrence of hazard changes due to the mpacts of hazard A and correspondng consumpton of repar resources. A j System Performance Expected System Performance SP 0(t) A A j System Performance SP(t) WITH Restoraton Measures Robustness(A ) Robustness(A j A ) Resourcefulness (t) System Performance SP(t) WITHOUT Restoraton Measures 0 Rapdty t t Fgure 4 Typcal nfrastructure system performance under two sequental hazards 8

17 Another typcal relatonshp of two hazards s concurrent occurrence of hazards. Infrastructure systems are exposed to two hazards smultaneously. State of the sngle nfrastructure system under the nteracton of the two hazards s usually much more complex due to varous nfrastructure nterdepences. The two concurrent hazards can be consdered as one sever hazard as the result of two jont forces to be addressed by nfrastructures adaptve capacty. The multlayer nfrastructure network performance under two concurrent hazards s llustrated n Fgure 5, whch s smlar to the system performance under the sngle hazard. However, robustness, resourcefulness and rapdty of multlayer nfrastructure network under two concurrent hazards are lower than those exposed to a sngle hazard wth the same avalable repar resources. System Performance A j Expected System Performance SP 0(t) A System Performance SP(t) WITH Restoraton Measures Robustness(A A j) Resourcefulness (t) System Performance SP(t) WITHOUT Restoraton Measures 0 t Rapdty t Fgure 5 Typcal nfrastructure system performance under two concurrent hazards Expandng on the determnstc reslence model n Equaton (1) and system performance under multple hazards relaton, such as Fgures 3-5 and Equatons (2) and (3), mult hazard reslence could be expressed as r t SP() t dt * * t m A t SP( t) dt SL( t) dt 1,, O O A A O m t 1 t 1 t A 1 A ( t) 1 t t t m SP ( t) dt SP ( t) dt SP ( t) dt O 0 O 0 O t 0 A t 1 A t 1 A1 (4) 9

18 where A1,, A r m () t s mult hazards A,, ( 2) 1 A m reslence of multlayer nfrastructure network. Subscrpts of m hazard A,, 1 A m are n order of precedence. The t s the occurrence of hazard O A, t mn{ t, t }. * RE 1 As vulnerablty functons (fraglty curves) of nfrastructures obtaned generalzed agreement on mult-rsk analyss (32,33), state of nfrastructures s random, and the actual system performance ( SP() t ) and system loss ( SL() t ) of multlayer nfrastructure network are also of stochastc character. The mult hazards reslence can be seen as an expected value, and Equaton (4) can be modfed as r A1,, Am P * * * u () t m t m A t m A t u 1 E SP( t) dt E SL( t) dt dt O O O 1 t 1 t 1 t A A N ( t) 1 1 t t N E SP0( t) dt E SP0( t) dt E O O t () A t P 1 A u t 1 t u 1 dt O t A 1 N N (5) where E( SP( t)) s the expected value of actual performance of mult-layer nfrastructure network; E( SP0 ( t)) s the expected value of expected performance of multlayer nfrastructure network; E SL() t s the expected value of expected loss of multlayer nfrastructure network; N s the sze of multlayer nfrastructure network; damage probablty of uth nfrastructure; and Pu s the E Pu s the expected damage probablty of uth nfrastructure, whch always equals to 0. Accordngly, features (robustness, resourcefulness, rapdty) of mult hazards reslence are also the correspondng expected values. Actually, nfrastructure systems always have backup facltes, slack resources, redundancy or structure modularty (51), so the functonal loss would not be the same as the physcal damages (53). The normal way to analyze functonal reslence of mult hazards s to measure mportance of nfrastructure ( I u ) wth correspondng metrcs. Examples may nclude operaton facltes for system techncal performance, populaton served, economc benefts of ndustry supported, or areas of socety unnfluenced (53,54), etc. Then the mult hazard functonal reslence can be expressed as 10

19 Pu() t Iu E SP t dt E SL t dt N dt m * * * t m A t m A t u 1 ( ) ( ) ,, t O t O t O A A A A m F ( t) 1 1 t t N r O 0 O t 0 A t 1 A1 t u 1 t E SP ( t) dt E SP ( t) dt E Pu () t Iu dt O A 1 N N (6) The former reslence can be seen as the physcal reslence of nfrastructure system. The features (robustness, resourcefulness, rapdty) of mult hazard functonal reslence would also change correspondngly. 3 MULTI HAZARD RELATIONSHIPS AND DIRECT IMPACTS ON INFRASTRUCTURE Ths secton provdes framework for the analyses of mult hazard mpacts. 3.1 Relatonshps Between Multple Hazards A multtude of approaches s n use to descrbe relatonshps between multple hazards (33). Two basc deas for the assessment of mpacts of multple hazards are: () to nvestgate the possble ndvdual chans of hazardous events and to assess probablty of mpacts n order to develop rsk maps or assess the rsk of concdences of multple hazards; and () to develop a matrx of possble hazard cascades and nfluences by proposng the respectve processes (56). Temporal and spatal relatonshps between multple hazards are analyzed usng the mpacts of multple hazards on nfrastructure system, especally damage probablty P u (n Equaton (2)) of each nfrastructure. Therefore, dverse forms of mpacts have to be consdered: sngle hazard mpact, mpact of jont hazards, and condtonal hazard mpact Temporal relatonshps of multple hazards The temporal relatonshps of multple hazards are classfed accordng to occurrence tme of multple hazards. Two man types of relatonshps are: () concdence of multple hazards n the event of more than one hazard occurrng n the same general area and wthn a short tme (5) ; and () sequence of multple hazards when one hazard trggers other hazards wth dfferent occurrence probabltes (52). Consderng three sectons of the dynamc system performance curve under a sngle hazard, both tme and duraton are relevant for multple hazard reslence. Also, hazards can cause 11

20 fatgue damage n the case of a long duraton. In ths work, the tme of hazard occurrence and are consdered as two dmensons of temporal relatonshps. It s worth notng that mutex hazards would never co-occur, so ths knd of relatonshp s not beng consdered n ths research. Gven dsturbance event E ncludng multple hazards A1, A2,,, A n, where A s th hazard, and assumng that all hazards occur n the same area, there are three basc temporal relatonshps between multple hazards: mpacts of a sngle hazard; jont mpacts; and condtonal mpacts. Sngle hazard mpacts occur when only one hazard hts the area and no other hazards occur before or at the same tme. Jont mpacts occur when the area s mpacted by two or more hazards at the same tme. Condtonal mpacts descrbe the stuaton when the area s mpacted by subsequent hazards before the of ntal hazardous event. Dverse temporal relatonshps between multple hazards result n possbly large combnatons of mpacts. Let us consder two hazards A and A j ( j ). There are four possble types of temporal relatonshps that could result n dfferent mpacts on the nfrastructure. Here t O and t denote the begnnng and tmes of hazard A, E and D s the duraton of hazard A. Type 1: Jont mpacts occur when hazards s shown n Fgure 6 (a), and can be expressed as A and A j begn and at the same tme. Temporal relatonshp of the two t O t and O Aj t E t (7) E Aj Type 2: Jont and condtonal mpacts occur when A and Aj begn at the same tme and at dfferent tmes. Temporal relatonshp of the two hazards s shown n Fgure 6 (b), and can be expressed as t O t and O Aj t E t (8) E Aj Durng mn{ D, D } j, the nfrastructure s mpacted by the two hazards jontly. Durng max{ D, D } mn{ D, D }, the nfrastructure would be mpacted by the hazard wth longer duraton but wth j j the condtonal mpacts. 12

21 Type 3: Sngle and condtonal mpacts occur when not later then the begnnng tme of expressed as A and A j begn at dfferent tme and the tme of the A s A j.temporal relatonshp of the two hazards s shown n Fgure 6 (c), and can be t O t and O Aj t E t (9) O Aj Assumng A begns earler than the nfrastructure s mpacted by A j, durng D, the nfrastructure s mpacted only by A j condtonal on mpacts of Type 4: Sngle, jont and condtonal mpacts occur when s later then the begnnng tme of and can be expressed as A. A and A. After the Aj begnnng, A j begn at dfferent tmes and the tme of A j.temporal relatonshps of the two hazards are shown n Fgures 6 (d) and (e), A t O t and O Aj t E t (10) O Aj Assumng A begns earler than A j, durng A TO j TO the nfrastructure s only mpacted by A. Durng E E O mn{ t, t } t, t s mpacted by the and Aj E E E E A jontly. Durng max{ t t, t t }, the nfrastructure s only j Aj Aj mpacted by the hazard that s later and s exposed to condtonal mpacts by the both hazards. A A A A A A j A j A j A j A j (a) (b) (c) (d) (e) Lght grey and dark gray rectangles denote two dfferent hazards. Rectangle length denotes the duraton. Fgure 6 Temporal relatonshps between two hazards In the case of n hazards, there wll be theoretcally 2 nn ( 1) types of temporal relatonshps among them. Accordng to ther cause-and-effect relatonshps, temporal relatons among them mght not occur n realty or may have a very small probablty of co-occurrence. Most often the temporal relatonshps between multple hazards mght be the latter two condtons (dfferent begnnng and tmes of multple hazards). Multple hazards result n dverse combnatons of condtonal and jont mpacts on the area. Consderaton of hazards duratons usng the event chan 13

22 and event tree methods could clearly show multple hazards temporal relatonshps (and mpacts) durng the whole tme an area s affected by hazards Spatal relatonshps of multple hazards Spatal relatonshps between multple hazards descrbe ther mpacts wthn an area and ther geographc nteractons wth more detaled evoluton progress. Hazards usually affect lmted areas wth specfc exposure. The damages from multple hazards could be dfferent, even f they have the same magntude, due to ther spatal evoluton wthn the affected area. Multple hazards may have dfferent spatal relatonshps wth dverse magntudes wthn a gven area. The possble relatonshps may nclude: () overlap of areas mpacted by multple hazards as shown n Fgure 7 (a); () partal overlap of areas mpacted by multple hazards as llustrated n Fgures 7 (b) and (c). Usually, the secondary hazards mpact the smaller areas than the prmary hazards - for example, the earthquake followed by fre, or hurrcane followed by flood, and smlar; and () no overlap between areas mpacted by multple hazards as shown n Fgure 7 (d). It s worth notng that the above three types of spatal relatonshps could occur n combnaton wth any of the temporal relatonshps ntroduced earler. (a) (b) (c) (d) Lght grey and dark grey crcles denote two dfferent hazards. Dark blue color s the overlap area mpacted by two hazards. Fgure 7 Spatal relatonshps between two hazards The three types of spatal relatonshps between multple hazards wll result n a sngle and jont mpacts on the affected area. Let us consder an event E ncludng multple hazards A, A,, A, A where 1 2 n S A denotes the spatal area 14

23 mpacted by the hazard as follows. A. Then, at a gven tme, the three spatal relatons between multple hazards can be expressed Type 1: Jont mpacts occur when all the hazards mpact areas of overlap as shown n Fgure 7 (a). Spatal relatonshp between the multple hazards can be expressed as ( A, A E, j) (11) S S S S A1 A2 An j Type 2: Sngle and jont mpacts occur when the mpacted areas by multple hazards partly overlap as n Fgures 7 (b) and (c). Spatal relatonshp between the multple hazards can be expressed as S SA ( A,, ) j Aj E j and SA S A ( A,, ) j Aj E j (12) Type 3: Sngle mpact of multple hazards occur when the mpacted areas by multple hazards do not overlap as n Fgure 7(d). Spatal relatonshp between the multple hazards can be expressed as S S ( A, A E, j) (13) Aj j Relatonshp cube of multple hazards The multple hazards mpact analyss framework could be constructed as a cube (see Fgure 8) by combnng temporal and spatal relatonshps dscussed prevously. As nfrastructure systems (lke water storage facltes, pumpng statons, electrc substatons, and so on) are sparsely located n space, ther components could be mpacted at dfferent tme by dfferent hazards. The model presented n ths study focuses on the mpacts of multple hazards on nfrastructure system. Multple hazards relatonshps wthn each sub-cube of the relatonshp cube (Fgure 8) may result n dfferent mpacts on the nfrastructure system. 15

24 Begnnng tme of multple hzards Same Dfferent Full overlap Partal overlap No overlap Spatal relatonshps of multple hazards Fgure 8 Relaton cube of multple hazards Note, that both spatal and temporal scales can be very broad. Hazards can nfluence spatal areas, from fractons of a klometer squared, such as a landslde, to hundreds of mllons of klometers squared, such as tsunam. The duratons of hazards can also range from seconds, such as an earthquake, to mllenna, such as long-term clmate change (52). Temporal and spatal scales used for multple hazards rsk analyses should not focus on the characterstcs of an ndvdual hazards, but consder ther mpact and nteracton ranges. Snce the nfrastructure systems are always sparsely located and operated wthn a governng structure, the spatal scale could be the same as the geographc boundares of a communty, a cty, a provnce, or a country. Hourly temporal scale of multple hazards mpacts s approprate n most cases, snce the repar tme of most nfrastructure systems s measure n hours (19,57). 3.2 Impacts of Multple Hazards on Infrastructure Systems In current practce, there s almost a general agreement for usng vulnerablty functons (fraglty curves) to facltate rsk analyses of multple hazards (32,33). Fraglty stands for the probablty of a system or a system component reachng or exceedng an establshed performance level under the mpact of a perturbaton of known ntensty (58), The falure probablty of each element of nfrastructure system deps on the type and ntensty of hazards they are exposed to, whle takng nto account the local terran and nfrastructure structural characterstcs. Mostly, fraglty curves of dverse nfrastructures can be obtaned from the doman research. For example, the electrc transmsson staton fraglty curves under hurrcane can be developed from the research n electrcal engneerng (13,19), the hydropower 16

25 fraglty curve under flood can be developed from the research n hydro techncal engneerng (59), and so on. More recently, some statstc methods have been ntroduced to obtan the fraglty curve/rule of sngle buldng/faclty wthout expermental data (60) Drect mpacts of two hazards Let us consder two hazards and A j ( j ). Pu( A ), Pu( A j) are correspondng damage probabltes of the uth nfrastructure subject to sngle hazard and Aj exceedng specfc threshold (lke flood nundaton depth, gust wnd speed of hurrcane, or peak ground acceleraton of an earthquake). Usually, P ( A ) and P ( A ) are knd of physcal nfrastructure characterstcs correspondng to specfc desgn crtera. They can be obtaned from the statstcal data, and are known as the fraglty curves. u u j Based on the relatonshp cube, there are twelve types of relatonshps between two hazards. Ther drect (physcal) mpacts on nfrastructures are as follows: () Impacts of hazards by Equaton (11) and A j wth temporal relatonshp shown by Equaton (7) and spatal relatonshp shown The two hazards and Aj begn and at the same tme. Infrastructures located n the area are affected smultaneously. The state of the nfrastructure would be determned by two hazards jont damage probablty Pu ( A j ) durng D (or D ), whch s known as the fraglty surface (61-63), nstead of sum of separate fraglty curves. j () Impacts of hazards by Equaton (12) The two hazards and A j wth temporal relatonshp shown by Equaton (7) and spatal relatonshp shown and A j begn and n two areas wth ntersecton. Infrastructures located n the ntersected area are affected by the two hazards smultaneously, and ther damage probablty s determned by two hazards jont damage probablty Pu ( A j ) durng D (or D j ). Infrastructure located n other areas s only affected by a sngle 17

26 hazard, (or D ). j or () Impacts of hazards by Equaton (13) The two hazards or A, and ther damage probabltes could be obtaned correspondngly as Pu( A ) or P ( A ) durng D j and and A j wth temporal relatonshp shown by Equaton (7) and spatal relatonshp shown Aj begn and n dfferent areas. Infrastructures are only mpacted by a sngle hazard, A j. The damage probablty of nfrastructure located n specfc area s determned by correspondng hazard, and equals to Pu( ) or P ( A ) durng D (or D ). (v) Impacts of hazards by Equaton (11) The two hazards j u and j j and A j wth temporal relatonshp shown by Equaton (8) and spatal relatonshp shown Aj begn n the same area at the same tme, but at dfferent tme. Assumng j u j D shorter than D, nfrastructures would be mpacted by both hazards durng D, and mpacted by hazard A durng D. So, the damage probablty of nfrastructures durng D s two hazards jont damage probablty P ( A A ), and equals to Pu ( Aj Aj ) durng Dj D. (v) Impacts of hazards Equaton (12) The two hazards Assumng D j u j and A j wth temporal relatonshp shown by Equaton (8) and spatal relatonshp shown by and Aj begn at the same tme, at dfferent tme, and affect two areas wth ntersecton. D shorter than D j, there are two stuatons as the ntersected area affected s dfferent durng j D or D. If the ntersected areas are affected durng D, the state of nfrastructures located n these areas would be determned by two hazards jont damage probablty Pu ( A j ), or else would be determned by condtonal damage probablty P ( A A ). The damage probabltes of nfrastructures located n other mpacted areas are determned by u j correspondng sngle hazards, equal to Pu( ) or P ( A ) durng the D or D. u j j 18

27 (v) Impacts of hazards by Equaton (13) The two hazards and A j wth temporal relatonshp shown by Equaton (8) and spatal relatonshp shown and A j begn at the same tme, at dfferent tme, and affect two dfferent areas. Infrastructures could only be affected by sngle hazard A or A j.damage probablty of nfrastructures located n specfc area s determned by correspondng hazard, and equals to Pu( ) durng D or Pu( Aj) durng D j. (v) Impacts of hazards by Equaton (11) The two hazards and and A j wth temporal relatonshp shown by Equaton (9) and spatal relatonshp shown Aj begn at dfferent tme and affect the same area. D, nfrastructure can only be attacked by sngle hazard D j, nfrastructures are only affected by a sngle hazard A j begns later than the of A. Durng A, and the damage probablty s equal to P ( A ). Durng A. Then the damage probablty s equal to P ( A A ), j u u j where s a restoraton parameter. It denotes the state of an nfrastructure at the begnnng tme of functon of the restoraton strategy. (v) Impacts of hazards by Equaton (12) The two hazards and A j, and s a and A j wth temporal relatonshp shown by Equaton (9) and spatal relatonshp shown Aj begn at dfferent tme, don t have temporal overlap but overlap n space. Durng D, nfrastructure can only be affected by a sngle hazard A, and ts damage probablty s equal to Pu( A ). Durng D j, nfrastructures located n the ntersecton area would have damage probabltes of P ( A A ), or else as P ( A ). (x) Impacts of hazards by Equaton (13) The two hazards u j and A j wth temporal relatonshp shown by Equaton (9) and spatal relatonshp shown and Aj begn at dfferent tme and n dfferent areas, and don t have temporal overlap. Then the nfrastructures could only be affected by sngle hazard A or A j. The damage probablty of nfrastructures located n specfc area s determned by correspondng hazard, equals to Pu( ) durng D and Pu( Aj) durng D j. u j 19

28 (x) Impacts of hazards by Equaton (11) and A j wth temporal relatonshp shown by Equaton (10) and spatal relatonshp shown The two hazards and A begn at dfferent tme and n the same area, and have temporal overlap. Assumng t j O t, O Aj the damage probablty of nfrastructures s equal to P ( A ) durng u t O Aj t O. Durng the temporal overlappng perod, t s equal to P ( A A A ). Durng the remanng tme, t s equal to P ( A A A ) or P ( A A A ). u j (x) Impacts of hazards by Equaton (12) u j u j j and A j wth temporal relatonshp shown by Equaton (10) and spatal relatonshp shown The two hazards and A begn at dfferent tme, and have both temporal and spatal overlap. Assumng t j O t, O Aj the damage probablty of nfrastructures s equal to P ( A ) durng t u O Aj t O. Durng the temporal overlappng perod, there are two stuatons. Damage probablty of nfrastructures located n the spatal overlappng area equals to P ( A A A ), or else P ( A) or P ( A ). Durng the remanng tme, the damage probablty of nfrastructures u j u u j located n the spatal overlappng area s equal to P ( A A A ), or else P ( A) or P ( A ). (x) Impacts of hazards by Equaton (13) The two hazards u j j and A j wth temporal relatonshp shown by Equaton (10) and spatal relatonshp shown and Aj begn at dfferent tme and n dfferent areas, and have temporal overlap. Infrastructures u u j could only be affected by sngle hazard or A j. The damage probablty of nfrastructure s determned by correspondng hazard and equals P ( A ) or P ( A ). u u j The drect mpact on nfrastructures of two hazards wth twelve temporal-spatal relatonshps analyzed above s the framework further developed n ths study. The mplementaton takes nto consderaton: () that the damage probablty of nfrastructures characterzed by dfferent materal and structural characterstcs and acceptable loss threshold levels, affected by hazards of dfferent magntudes s dfferent; () the changng magntude and force of hazards result n dfferent damage probablty of nfrastructures that may be calculated wth the same set of relatonshps; and () dfferent restoraton strateges. Multple hazard drect mpact analyss framework ncludes two stuatons arsng from combnaton of Equatons (10) and (11), and combnaton of Equatons (10) and (12). In these 20

29 scenaros, there are ntervals between two hazards when the mplementaton of restoraton strateges can be ntated. Besdes, the mplementaton of response strateges can be ntated n the stuatons when the dsaster lasts for more than several days and does not destroy the whole area Drect mpacts of multple hazards Based on the analyss of two hazards above, t can be generalzed that the nfrastructure damage probablty subject to events E wth more than two hazards A, A,, A, A can be expressed wth combnaton of condtonal and 1 2 jont damage probabltes caused by ndvdual hazards, as follows: n P ( E) u P ( A A ) durng T s u overlap _ m P ( A ) else u (14) where m denotes the number of spatally overlappng hazards durng specfc perod; T s the duraton of overlappng multple hazards before begnnng tme of hazard before A ; A ; and s the restoraton parameter whch s a functon of restoraton strategy. overlap _ S denotes hazards affectng the nfrastructure Falures propagaton mechansm and ndrect mpacts of multple hazards on nfrastructures Indvdual nfrastructure systems consst of numerous and dstrbuted components. Several components damage or localzed mpact of natural or manmade dsasters would cause the whole system to fal (64). In addton, the small falures of a few components could propagate to other nfrastructure, and result nto a huge dsaster to the socety and economy. Therefore, cascadng falures need to be addressed n the analyses of nfrastructure system reslence and rsk. Two types of nterdepences need to be consdered: ntra-network and nter-network falure propagaton mechansms. As dfferent knd of nfrastructure systems have dfferent operatng rules, they may have dfferent falure propagaton mechansms. Some examples nclude Motter-La (ML) model (65,66) and ORNL-Pserc-Alaska (OPA) model (67,68) of 21

30 power grd falure propagaton (69), router-based model of telecommuncaton system (70), ppelne flow model of gas system (71), and so on. Infrastructures are nterdepent n multple ways. The nterdepences can be characterzed as ether physcal, cyber, geographc and logcal (72), or physcal, geospatal, polcy and nformatonal (40). Based on these qualtatve studes, network based approaches always use nter-lnks along wth detaled descrptons of ther topologes and flow patterns to descrbe nter-network nterdepences. Therefore, the network nterdepences can be classfed nto topology- based methods and flow-based methods (73). In many cases approprate ntra-network and nter-network nterdepences can be modeled by the exstng models or wth some approprate modfcatons to construct mult layer nfrastructure network falure propagaton mechansms. The ntra-network and nter-network falure nterdepence modes wthout ndrect (or functonal) lnk falures are determned by the falure of connectng nodes. Then ndrect or actual damage probablty of each node can be calculated as P ( t) P ( t ) (15) ndrect t u u _ pn u_ p p_ n ndrect where P () t s nterdepent node damage probablty at t ; u_ p s the number of paths connectng the uth u node to source nodes; p_ n s the number of nodes on each path; and P _ () t s the node s damage probablty. u pn 4 MULTI HAZARDS RESILIENCE ASSESSMENT APPROACH A multple hazards reslence assessment methodology of nterdepent nfrastructure system s developed by ntegratng all the models presented above. The general approach contans three steps. The frst step nvolves the nterdepent nfrastructure system modellng, whch ncludes () sngle type of nternally nterdepent nfrastructure; and () multple types of externally nterdepent nfrastructures (51). The second step nvolves development of multple hazards relatonshp model and assessment of ndrect mpacts on nfrastructures. The thrd 22

31 step ncludes assessment of ndrect falures as a consequence of nfrastructure nterdepences, and spatal-temporal system reslence. The research framework and process are llustrated n Fgure 9. E lectrcty transm sson netw ork O l transm sson netw ork S ngle layer netw ork operaton m echansm M ult-layer nfrastructure netw ork M ult-layer netw ork nterdepency m echansm M ultple hazards tem poral relatonshp M ult hazards SpatalR elaton M ultple hazards relaton cube Infrastructure com ponents fraglty curve M ultple hazards drect m pacts on nfrastructure com ponents R estoraton strategy m odel M ult-layer nfrastructure netw ork reslence and spatal dstrbutaton D ynam c nfrastructure com ponents dam age probabltes N etw ork m odellng G IS processng Inductve generalzaton M onte C arlo analyss G IS processng Fgure 9 Framework for the assessment of multple hazards reslence of nterdepent nfrastructure system Network theory offers an mportant set of methods that can be used to model complex nfrastructure system behavor under varous dsturbances. The spatal/geographc characterstcs of the regon under consderaton play an essental role n the descrpton of nfrastructure system and characterzaton of hazards. Therefore, spatal network modellng s startng to get more serous attenton. Many applcatons are beng developed n dsaster analyss and preventon usng Geographcal Informaton Systems (GIS) (45) as approprate tools for processng spatal data. Network theory and GIS technology are combned n ths study to model the response of large-scale nterdepent nfrastructure system under multple dsturbances/hazards. Formulaton of relatonshps between multple hazards s the crtcal problem of rsk and reslence analyss. Wth focus on ther dverse combned mpacts on the nfrastructure system, temporal and spatal decompostons of relatonshps are done accordng to the relatonshp cube. Inductve generalzaton s used to construct the multple hazards relatonshp analyss framework, whch s not lmted to a specfc hazards chan. Statstcal fraglty of components and nfrastructure network topology are combned to capture composte mpacts of multple hazards. Infrastructure system reslence s not drectly related to geographc dstrbuton, topology and spatal nterdepence of nfrastructure components. However, the characterstcs of reslence are drectly related to the type, scale and 23

32 relatonshp of the dsturbances. Some ntal work on ntegratng temporal and spatal characterstcs of complex system behavour under dsturbance n order to assess spatally dynamc reslence s avalable n the area of flood rsk management (48) and multpurpose reservor operatons (74,75). As the mpacts of hazards always contan uncertanty and occur randomly, the nfrastructure system reslence metrc s defned n a probablstc form and conssts of a multple hazards performance network analyss combned wth Monte Carlo smulaton. The results of the probablstc nfrastructure system reslence analyses are the mult-layer network temporal reslence curves and spatal dstrbuton of damage probabltes. 5 MULTILAYER INTERDEPENDENT INFRASTRUCTURE NETWORK Ths secton presents nterdepent nfrastructure system model of the Greater Toronto Area (GTA) energy nfrastructure system. All the data used n ths study are n publc doman provded by the owners of the nfrastructure. To valdate the data, maps and reports avalable by the nfrastructure owners ncludng IESO (The Indepent Electrcty System Operator), Hydro One and CEPA (Canadan Energy Ppelne Assocaton) are used together wth the CanVec data. CanVec s a dgtal cartographc reference product of Natural Resources Canada (NRCan) combnng the Natonal Topographc Data Base (NTDB), the Mappng the North process conducted by the Canada Center for Mappng and Earth Observaton (CCMEO), the Atlas of Canada data, the GeoBase ntatve, and avalable satellte magery. 5.1 GTA Energy Infrastructure Spatal Network The Greater Toronto Area (GTA) s the most populated metropoltan area n Canada, whch s defned as the central Cty of Toronto and ts four surroundng regonal muncpaltes: Durham, Halton, Peel, and York. In ths paper, electrc, gas and ol transmsson networks of the GTA are taken for the mplementaton of the proposed approach. GTA electrc transmsson network s bult from the CanVec data (76), IESO and Hydro One reports (77,78). GTA gas and ol transmsson networks are bult from the CanVec data (76) and CEPA maps (79,80). GTA three-layer energy nfrastructure spatal network s llustrated n Fgure

33 Fgure 10 GTA three-layer energy nfrastructure spatal network GTA electrc transmsson network refers to the Bulk Power System (BPS) of GTA, ncludng the generaton and transmsson statons and power lnes. There are three types of power plants n GTA: nuclear, gas-fred and solar power statons; three types of transmsson lnes wth dfferent voltage- 500kv, 230kv and 115kv. GTAA Cogeneraton Plant s not consdered here as ts capacty s only 90 MW and ts prmary role s to provde the power to the Toronto Pearson Internatonal rport. There are no gas or ol producton facltes n GTA. Therefore, the gas and ol transmsson networks contan only transmsson facltes: compressor statons, meter statons, pump statons and ppelnes. Due to lmted data avalablty, no nformaton on the capacty of gas and ol facltes are provded here. GTA energy nfrastructure system nformaton s provded n Table 1. 25

34 Table 1 GTA three-layer energy nfrastructure spatal network nformaton Infrastructure Number Electrc Transmsson Network Power Generaton Nuclear 2 Gas -fred 6 500kv 4 Transmsson Statons 230kv kv kv 13 Power lne 230kv kv 30 Gas Transmsson Network Compressor Statons 2 Meter Statons 15 Ppelnes 22 Ol Transmsson Network Pumpng Statons 4 Meter Statons 1 Ppelnes Infrastructure Interdepence Models Indvdual nfrastructure systems consst of numerous and dstrbuted components. Damage to several components or localzed mpact of natural or manmade dsasters would cause the whole system to fal. In addton, the small falures of a few components could propagate to other nfrastructure, and result nto a large dsaster to the socety and economy. Therefore, cascadng falures need to be addressed n the analyses of nfrastructure system reslence and rsk. Based on the three-layer GTA energy nfrastructure network, two types of nterdepences need to be consdered: ntranetwork (wthn a layer) and nter-network (between the layers) falure propagaton mechansms. Intra-network nterdepence s always modeled as operaton mechansm for one type of nfrastructure. Some examples nclude Motter-La (ML) model (80,81) of power grd falure propagaton, ppelne flow model of gas system (82), and so on. Inter-network nterdepence focuses on the physcal and functonal nteracton between dfferent types of nfrastructure, whch ncludes topology-based or flow-based methods. 26

35 There are three types of nfrastructure n the GTA energy nfrastructure system: electrc, gas and ol transmsson networks. For electrc transmsson network, ML model s a promnent approach used to analyze cascadng falures. In ths model, nodes are dfferentated as generators N G (electrcty generatng plants) and loads N L(substatons). All nodes are nterconnected by a set of edges representng power lnes. The load of each substaton node s defned as the number of most effcent paths from generatons to substatons that pass through that substaton node (83). Each substaton node u s characterzed by ntal load L u (0), real load Lu () t, and maxmum load Cu Lu(0) tp, where constant tp s a tolerance parameter. Each path connectng node u and v s characterzed by the path effcency euv () t, representng relatve lnk capacty. It s assumed that electrcty s flowng between any par of generator nodes and substaton nodes through the most effcent path. An ntal breakdown of edges surroundng a node causes power to be redstrbuted n the network, reflected by changes n the most effcent paths and, consequently, changes n the load at each node. Some nodes are then forced to operate above capacty (beng overloaded), represented by decreases n effcency of the edges of that node euv (0) else Lu(0) Lv(0) e ( t 1) e (0)mn(, ) f L (0) L ( t) C Lu( t) Lv( t) 0 f Lu( t) Cu uv uv u u u (16) The substaton fals when ts path effcency equals to 0. The faled substatons would change the path effcency of other substaton nodes, and ndeed change the electrc transmsson path n the network. Convergence n ths teratve process occurs when the nodes states become stable. If we assume that the maxmum load of every substaton node n the network s the same, then the performance Pt () of electrc power network can be computed as the fracton of avalable substaton nodes. Here tp s set to 2 (84). As the szes of gas and ol transmsson networks are small, ther ntra-network nterdepence s also modeled usng modfed ML model wthout flow dstrbuton or tolerance. The value of tp n each nterdepence model s also set to 2. The topology-based model s used for nter-network nterdepence among the three types of nfrastructure systems here. Ths report assumes that gas-fred power plants requre gas to keep normal operaton, and all types of gas and 27

36 ol nodes requre electrcty to keep ther normal operaton. As the networks consdered are all lmted to the major transmsson systems, nter-network lnks are not shown n Fgure 10 but are defned as follows: () gas-fred electrc plants are supported by the nearest gas meter statons through gas transmsson ppelnes; () gas and ol nodes are powered by the nearest electrc transmsson substatons through power lnes; and () bufferng s ntroduced as a popular emergency preparedness strategy that makes the nfrastructure nterdepence less tght. Each gas-fred electrc plant has buffers n form of gas stock. The compressor statons, pumpng statons and meter statons of gas and ol transmsson networks have buffers n form of standby power generators. Buffers of the above nfrastructure are measured n unts of tme and all assumed to be equal to one-tme step (2 hours). Nodes would be non-operatonal n the case of malfuncton of supportng nodes or destroyed connectng edges. 5.3 Physcal and Functonal Reslence Metrc Dfferent aspects of nfrastructure performance could be measured by usng dfferent unts. To analyze detals of the nfrastructure dynamc evoluton process, n ths study the nterdepent nfrastructure system physcal and functonal reslence are evaluated respectvely, whch means dfferent I u n Equaton (6). For physcal reslence, I u of each node n the mult-layer nfrastructure network s calculated usng ts capacty. Then physcal system performance s measured by the expected value of the proporton of weghted operatonal nodes. For example, the electrc transmsson substatons weght s calculated proportonal to ther voltage. The functonal reslence, I u of each node n the mult-layer nfrastructure network s calculated usng the number of customers beng served. The functonal system performance s measured by the expected value of the mpacted populaton. As electrc nfrastructure s seen as the most mportant n the energy nfrastructure system, populaton unaffected by electrc loss s used as a measure of functonal system performance here. Consderng that the electrc substatons wth larger than 500 kv capacty always functon as the hub substatons, populaton of GTA s allocated to a partcular electrc substaton wth 115 kv and 230 kv usng the Thessen Polygons (Fgure 11). The Thessen Polygons defne areas of nfluence around each of a set of ponts whose boundares defne the area that s closest to gven pont relatve to ts neghbors. So, each sngle polygon can be consdered as area served by one transmsson 28

37 staton. GTA populaton and the dssemnaton area boundares data are obtaned from the Canadan Census Analyser 2011 (85). Fgure 11 Populaton supported by electrc transmsson substatons n GTA 6 SEQUENTIAL HAZARS SCENARIO AND ITS IMPACTS Ths secton descrbes a sequental hurrcane-flood scenaro used for GTA case study reslence analyses. 6.1 Sequental Hurrcane and Flood Scenaro Sequental hurrcane and flood scenaro s modelled based on the record of Hurrcane Hazel, whch was followed by a flood and struck Toronto on October 15, The path of Hurrcane Hazel (Hurrcane Hazel Storm Story Map) s downloaded from NOAA GeoPlatform. The nformaton of the hurrcane, storm surge and flood mpacts are from government webstes: Hurrcane Hazel: 60th Annversary and Envronment and Clmate Change Canada. The records of Canadan Dsaster Database (86) show that Hurrcane Hazel, followed by flood, klled 81 people and left 1,896 famles homeless. The record ranfall that the storm brought was unable to nfltrate the ground because the above-average ranfall n the precedng month had already saturated the sol. Most of the ran smply ran off the surface 29

38 nto rvers and creeks, rapdly fllng them to capacty and beyond. One estmate of runoff was that 90 percent of the precptaton ran off the land drectly nto rvers rasng the water level by 6 to 8 meters (87). Ths dsaster caused by combned mpact of hurrcane and flood s taken as the prototype dsaster scenaro for the mplementaton of the methodology developed n ths study. Based on the hstorcal records, the hurrcane lasted for 24 hours wth ranfall, then the flood occurred. It means the flood occurred durng the damage and propagaton phase, or evoluton and recovery phase of the hurrcane, depent on the restoraton startng tme. Snce the whole GTA area was affected by the hurrcane, and only nfrastructure located wthn the rver basns was mpacted by the floodng, there was a spatal overlap between the two hazards. Based on the Saffr-Smpson Hurrcane Wnd Scale (88), only hurrcanes above category 3 (wnd speed hgher than 110 mph) cause floodng. The followng assumptons are ncluded n the GTA case study: () Hurrcane Hazel was assumed to be a category 3 hurrcane wth gust wnd speed of 120 mph and weakenng to 40 mph after 24 hours; () the hurrcane path s the same as the path of Hurrcane Hazel as retreved form the ArcGIS web resources (89) ; () the area 50 klometers from the hurrcane path (90) was mpacted by the hurrcane wth the same wnd speed (91) ; and (v) mpacted area of GTA s dvded nto four zones (wth dfferent hurrcane occurrence tme) perpcular to hurrcane path, and attacked successvely from south to north. Fgure 12 shows the spatal dstrbuton of combned hurrcane and flood mpacts. Accordng to the flood classfcaton of the Natonal Weather Servce Alaska-Pacfc Rver Forecast Center, the flood followng Hurrcane Hazel s categorzed as a major floodng event. As GTA s dssected by rvers and streams, nfrastructure affected by the flood s also along rvers and streams. Based on the flood plan map of Toronto and Regon (92) and Flood Vulnerable Area Clusters of GTA (93), most mpacted areas nclude Holland Marsh, Humber Rver basn, Woodbrdge, Thstletown, Raymore Drve, Mount Denns, Long Branch and Don Rver basn, and the flood depth n these areas exceeds 10 feet (94). Combnng the records of Hurrcane Hazel mpacts, hurrcane occurrence tme and the dstance from the hurrcane path, the flooded areas are dentfed and shown n Fgure 12. There are only a lmted number of nfrastructure elements mpacted drectly (two power generatng statons, sx transmsson substatons, one submarne powerlne, and one submarne gas transmsson ppelne). 30

39 Fgure 12 Sequental hurrcane and flood mpacts on GTA 6.2 Sngle Hazard Impacts on Infrastructure Infrastructure component drect falure probabltes under sngle hazard can be computed by ther fraglty models under dfferent hazards. All the nfrastructure components vulnerablty data under hurrcane and flood are all from publshed papers, reports and HAZUS-MH platform. In the case of a hurrcane and power grd, power plants are mostly nsenstve to structural hurrcane damage and therefore ther fragltes are not consdered. The fragltes of transmsson substatons and transmsson lnes are estmated based on the work of Ouyang and Dueñas-Osoro (18). The damage probablty of substatons s represented va log-normal fraglty curves. These curves generate the probablty of damage for a gven wnd gust speed (Ws) whle takng nto account the local terran and structural characterstcs of the substaton under consderaton. The general form of the fraglty curve s gven as follows (95,96). ln w 2 x 1 _,, u ul P exp trans sub u l D dul Ws xu dw ulw (17) 31

40 These curves generate four probabltes of the uth transmsson staton wth dfferent damage level ( d ul ): low, moderate, severe, and complete. Moderate level s used n ths work. trans _ sub, u, l s the uth electrc transmsson P substaton moderate damage probablty of exceedance gven wnd speed x u at the substaton ste, calculated usng the fraglty curve correspondng to the terran near the substaton. The parameters ul and represent the logarthmc mean and standard devaton of the pertnent fraglty curve. Fraglty curves for each type of modeled terran and buldng type are taken from HAZUS-MH techncal report (96). Transmsson lnes consst of transmsson support structures, conductors and varous peces of hardware. Due to desgn requrements (97), the fraglty of a transmsson lne under wnd load (wthout consderng debrs mpacts) s manly determned by the falures of towers. The number of towers along a lne s computed as the lne length dvded by the average span between two adjacent towers, whch s set as 0.30 km based on the regonal utlty data. Based on the nvestgatons by Quanta Technology (96), the falure probablty of the uth transmsson support structure can be approxmated by an exponental functon under a gven wnd speed x u (97), x u Ptrans _ tower, u Ws xu mn 2 10 e,1 (18) For the gas system subject to a hurrcane, underground ppelnes are mostly nvulnerable to wnd hazards, and only the gas node falures are consdered. The damage probabltes of compressor statons, pumpng statons and meter statons are also calculated usng Equaton (18). Underground cables and ppelnes mght be destroyed by the storm surge. The uth underground cable or ppelne damage probablty can be approxmated as functons of hurrcane and flood severty (97), Punder _ lne, u a b( H S) I H S (19) 32

41 P where under _ lne, u s the uth underground facltes damage probablty for gven hurrcane and storm surge categores. H s the hurrcane category (1-5), S s the storm surge zone category (1-5), and a and b are tunng parameters, I H S s an ndcator functon showng whether the area s affected by an ncomng hurrcane, and equals to 1 f H S 0, else equals to 0. For the flood mpacts on the power grd, transmsson support structures are consdered as safe, and only electrc node falures are ncluded n the model. For gas and ol networks, all knds of components could be affected by floodng. HAZUS (95) provdes the nfrastructure falure probablty under flood wthn specfc areas. In accordance wth the hurrcane data, the relatonshp between nfrastructure damage probablty and flood depth are based on the data from US. Two damage levels are consdered: low and hgh. The hgh damage probabltes wth 10 feet flood depth are: 0.30 for power plants, 0.15 for transmsson substatons, 0.40 for compressor, pumpng and meter statons of both, gas and ol transmsson networks. 6.3 Sequental Hazard Impacts on Infrastructure Damage probablty functons dscussed n the prevous secton are for separate hazards, hurrcane or flood. Based on the temporal and spatal relatonshps of the two hazards, ther mpacts on nfrastructure are not ndepent. Damage probabltes of nfrastructure should be calculated accordng to ther locaton and hazard occurrence tme. Durng t=1 to t=12, hurrcane affected the whole GTA, all nfrastructure would be damaged wth specfc probablty P t ( H) that can be calculated by Equaton (17) and (18) except the underground ppelnes. u From t=13 floodng begns to affect areas along rvers and streams of GTA. Only nfrastructure located n these areas would be drectly mpacted by the flood. The damage probablty of nfrastructure only drectly affected by the flood t (submarne ppelnes) P ( F ) can be calculated usng Equaton (19). Other flooded nfrastructure damage probablty can be calculated by u 33

42 P t ( F H) P t ( F) (1 P t ( F)) P t ( H ) (20) u u u u where s a restoraton parameter, whch could be 0 or 1. As gust wnd speed occurs at t=1, there may be some tme to restore hurrcane damaged nfrastructure. Wth lmted resources, parts of the hurrcane damaged nfrastructure t mght be recovered. For ths nfrastructure, 0, and ts damage probablty under the flood would be P ( F ). For other nfrastructure affected by hurrcane and flood wthout restoraton, 1. In addton, the nfrastructure not located n the blue areas n Fgure 12, would not be damaged by floodng due ts locaton. u Based on the ntra-network and nter-network falure nterdepence models dscussed n Secton 5.2, nfrastructure may also be non-operatonal due to nterdepences. As the functon of arcs are determned by ther connectng nodes, there s no undrected arcs falure, only nodes would be non-operatonal when they lose the connecton wth the source nodes. Actual damage probablty of each node can be calculated as Equaton (15). 7 SEQUENTIAL HAZARD RESILIENCE SIMULATION 7.1 Jont Restoraton Model of Interdepent Infrastructure System Return to ntal level of performance after the dsturbance s the crtcal characterstc of system reslence, whch s llustrated as the rasng lmb of the system performance curve shown n Fgure 2-5. There s emergng lterature studyng the restoraton processes of nfrastructure systems. Most of the publshed research deals wth the optmzaton of post-dsaster ndvdual nfrastructure system restoraton applyng a varety of modellng approaches and focusng on dfferent aspects of the restoraton strategy. Examples nclude: mnmzaton of the power systems restoraton tme under hurrcane event (98,99) ; maxmzaton of power system reslence wth dfferent operatons models; maxmzaton of performance and mnmzaton of a telecommuncaton system cost; maxmzaton of resource effcency n spatally dstrbuted networks; and others. The jont restoraton strategy work mostly consders a sngle layer nfrastructure network reslence. Restoraton strateges are always focused on the repar order of damaged system components or the addton of new components. The man questons are where and how to allocate lmted repar resources. 34

43 In ths study, the reslence of mult-layer nfrastructure network s ntroduced as an objectve that can be mplemented n the assessment of varous recovery strateges. So analytcally, the objectve of restoraton s set to maxmze the reslence of a mult-layer nfrastructure network durng a selected duraton, whch can be expressed as A1 max,, A ( * n ) r t (21a) s.t. u u RN ( t) C ( t) u RN TN ( t) C ( t) u TN (21b) where A1,, A r ( * n t ) s the multple hazard,, ( 2) 1 n O * A A n expected reslence value durng [ ta, t ] ; t * s the specfc tme 1 set for reslence assessment; t s the begnnng tme of the frst hazard A 1 ; O A1 RNu denotes physcal resources needed to repar the damage of uth ndvdual nfrastructure component at * t ( t t ) ; CRN () t denotes physcal resources * avalable at t ( t t ); TN () t s the tme needed to repar the damaged uth ndvdual nfrastructure component at * t ( t t ); and CTN () u t s the total tme avalable at t step, whch can be measured as t * t. The formulated restoraton model (Equatons 21a and 21b) s not easy to solve wth standard optmzaton technques, as the dynamc spatal mpacts of hazards on nfrastructures and falures propagaton wthn and across networks are nonlnear and of hgh level of complexty. The evolutonary programmng methods as for example, genetc algorthm proposed by Ouyang (18) can be used here, whch has been successfully used n the lterature to optmze falure components restoraton sequences of nfrastructure systems. 7.2 Sequental Hazard Reslence Smulaton Process System reslence analyss shows expected nfrastructure system response to component fragltes and nteracton of hazards and ther ntenstes. Monte Carlo method s used for smulaton of damage propagaton due to ts ablty to nclude complex phenomena lke cascadng falures n the model (100). As multple hazards mght occur at dfferent tmes, smulaton process could be dvded nto several phases to ntegrate components damage probabltes 35

44 calculaton and ther cascadng falure effects. Every phase starts wth a hazard occurrence, and ncludes drect hazards mpact evoluton, ntra-network falure propagaton analyss, and nter-network falure propagaton analyss, as shown n Fgure 13. In ths case, the smulaton progress s dvded nto two phases. The frst phase s focused on the nfrastructure network performance subject to hurrcane. The second phase combnes the flood mpacts on the nfrastructure system. Phase I : Impacts of Hurrcane Hurrcane occurs at t=1 Check nfrastructure physcal damage probabltes subject to HURRICANE Update ELECTIRC nfrastructures functonal falures as the results of ntra-network nterdepence wth CLM model Update GAS nfrastructure functonal falures as the results of ntra-network nterdepence Phase II : Impacts of Hurrcane and Flood Check nfrastructure physcal damage probabltes subject to FLOOD and Hurrcane Update ELECTIRC nfrastructures functonal falures as the results of ntra-network nterdepence wth CLM model Update GAS nfrastructure functonal falures as the results of ntra-network nterdepence Update OIL nfrastructures functonal falures as the results of ntra-network nterdepence Update OIL nfrastructures functonal falures as the results of ntra-network nterdepence Use the GAS nfrastructures functonal falures as the results of Inter-network depence wth ELECTRIC nfrastructures consderng buffers Use the OIL nfrastructures functonal falures as the results of Inter-network depence wth ELECTRIC nfrastructures consderng buffers Use the ELECTIC nfrastructures functonal falures as the results of Inter-network depence wth GAS nfrastructures consderng buffers No Is t the tme for recovery Calculate nfrastructure network performance t=t+1 No Does Flood occur Yes Yes Restoraton strategy mplementaton wth Dfferental Evoluton Algorthm Use the GAS nfrastructures functonal falures as the results of Inter-network depence wth ELECTRIC nfrastructures consderng buffers Use the OIL nfrastructures functonal falures as the results of Inter-network depence wth ELECTRIC nfrastructures consderng buffers Use the ELECTIC nfrastructures functonal falures as the results of Inter-network depence wth GAS nfrastructures consderng buffers Is t the tme for recovery No Calculate nfrastructure network performance Does all nodes recovered Ends Yes Yes No Restoraton strategy mplementaton wth Dfferental Evoluton Algorthm t=t+1 Fgure 13 Smulaton procedure of GTA nfrastructure system reslence under sequental hurrcane and flood In ths smulaton, delvery tme of electrc, gas and ol s set to be equal to one-tme step (two hours). Buffers usually have lmted capacty n terms of the tme, and are usually ncorporated as a tme delay between the node falure and ts depency loss. In ths study, we set every node to have a backup of two hours. 36

45 To develop the restoraton strategy at components level,.e. determne the restoraton sequence of damaged components at each tme step, the followng assumptons are added to the restoraton model lst: () restoraton begns at the tme step when component falures occur, or later; () damaged component can recover to normal functon n one-tme step wth restoraton; and () at most two damaged components can be restored n one-tme step wth the exstng resource constrants. Wth gustng wnd speeds occurrng at t=1, there s 11 tme steps before the floodng begns. After the wnd speed weakens below a specfc threshold, the restoraton can begn. In our case ths moment s at t=8. So, two restoraton strateges wth dfferent startng tmes would be used n the smulaton. One s a twophase strategy, restoraton from t=8 to t= 12 and then startng at t=18 after the floodng s. The other s a one-phase strategy, startng at t=18 after both hazards. The fnal smulaton results are averaged over 100 runs. 8 GTA ENERGY INFRASTRUCTURE SYSTEM PHYSICAL RESILIENCE 8.1 Infrastructure Physcal Performance Spatal Analyss GTA three-layer energy nfrastructure network reslence s a measure of dynamc performance of all the components together. Wth the nterdepence among nfrastructure components, mult hazards would have sgnfcant dverse mpacts on the mult-layer network. Electrc transmsson network, gas transmsson network, and ol transmsson network performance at sx tme ponts subject to dfferent hazards are shown n Fgure 9. The sx tme ponts are selected as the hazard occurrence tme, one-tme step after hazard occurrence tme, the tme when systems reslence returns to a new stable state after the frst hazard, the second hazard occurrence tme, the tme when systems reslence returns to a new stable state after the second hazard, and the tme when all nodes recover to normal state. As shown n Fgure 14, dfferent hazards mpact on the mult-layer nfrastructure network have notable dynamc spatal features. Combnng wth dsaster scenaro n Fgure 12, t s easy to fnd the drectly damaged nfrastructures by the hazards at dfferent tme, and easy to dentfy the ndrectly faled nfrastructures. For example, comparng the fgures at t=1 and fgures at t=2 n Fgure 9, the number of nfrastructures wth damage probablty larger than 0 are not only located n the area where hurrcane occurs at t=2. These nfrastructures are faled due to ther nterdepence on the damaged nfrastructures. In Fgure 14 (a), only a few nfrastructures mpacted by the flood drectly are of darker color, and the falures don t spread through the whole mult-layer nfrastructure network. In Fgure 14 (b) (c) and (d), from t=1 to t=8, damage probabltes of nfrastructure components are the same, and the falures propagate wth the hurrcane path. From t=9, the nfrastructure performances n the last three rows of Fgure 14 begn to be dfferent. In 37

46 the case of sngle hurrcane, nfrastructure component damage probabltes turn to be smaller and smaller wth restoraton begnnng at t=8. But for the mult-layer nfrastructure network subject to sequental hurrcane and flood, ther performances are worse at t=19 than at t=13 after the flood mpact, whether there s n-between restoraton or not. 38

47 (a) Components performance under the flood wth one-phase restoraton strategy startng at t=7 t=1 t=2 t=6 t=8 t=9 t=25 (b) Components performance under the hurrcane and flood wth one-phase restoraton strategy startng at t=8 t=1 t=2 t=8 t=13 t=19 t=25 (c) Components performance under the sequental hurrcane and flood wth one-phase restoraton strategy startng at t=19 t=1 t=2 t=8 t=13 t=19 t=25 (d) Components performance under the sequental hurrcane and flood wth two-phase restoraton strategy startng at t=8 and t=19 respectvely t=1 t=2 t=8 t=13 t=19 t=25 Fgure 14 Spatal physcal performance of GTA three-layer energy nfrastructure network under dfferent hazard scenaros 39