modeling the propagation of the effects of a disturbance

Urbanism Modeling the propagation of the effects of a disturbance ina critical infrastructure system [..] • A. Benmokhtar et al.

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MODELING THE PROPAGATION OF THE EFFECTS OF ADISTURBANCE IN A CRITICAL INFRASTRUCTURE SYSTEM

TO INCREASE ITS RESILIENCE

Amin BENMOKHTARPhD Candidate, Built Environment Research Laboratory Faculty of Civil

Engineering, University of Science and Technology. Houari Boumediene,Algiers, Algeria, E-mail: [email protected]

Djillali BENOUARProfessor of Earthquake Engineering and Disaster Risk Management at the Faculty

of Civil Engineering at the University of Science and Technology. HouariBoumediene, Algiers, Algeria, E-mail: [email protected]

Adel RAHMOUNEAssociate Professor HDR in Computer Science, Department of Computer Science,

University M'Hamed Bougara of Boumerdès, Algeria, E-mail: [email protected]

Abstract. In the urban environment, disaster risk management focusesmore on prevention, mitigation and intervention than on resilience.Securing our critical infrastructure systems (CISs) strengthens the resilienceof our urban sites. The objective of this research work is to propose amethodological approach and modeling of disturbance effects for theirmonitoring, which contributes to the understanding of CISs and theirfunctioning before, during or after a disaster (flood, earthquake, etc.).Failure scenarios will be developed and used by urban designers in aproactive manner. The modeling contributes to the establishment of atheoretical framework for the creation of a collaborative space between theactors of the urban site. An overall weighted average mission degradationindex of a CIS is proposed. The degradation of a water supply system’smission following a flood was taken as an example and discussed tovalidate the model. The purpose of this study is also to contribute to thestrengthening of the resilience of an urban site, by securing its CISs, andsensitize governments to consider their vulnerabilities in their disaster riskmanagement and territorial and urban development strategies and toestablish a process of resilience building.

Key words: critical infrastructure, failure, propagation modeling, riskmanagement, urban resilience.

1. IntroductionOur urban environments are increasinglydependent on distribution andtransmission networks to ensure the

availability and provision of essentialresources (ER): transportation, energyresources, communications, connectionand delivery of drinking water,

• Urbanism. Arhitectură. Construcţii • Vol. 11 • Nr. 2 • 2020

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evacuation and wastewater treatment,considered critical infrastructures (CIs).Therefore, urban sites are complex andinterdependent systems that areextremely vulnerable to natural hazardsand terrorism (Godschalk, 2003).

Indeed, the structural and architecturalaspect, the concentration and density ofthe population, the spaces and places ofassembly and the systems ofinfrastructure interconnected expose theurban sites to the disturbances of thefloods, earthquakes, hurricanes and eventerrorist attacks (Godschalk, 2003).

CIs present in these urban environmentsconsidered to be systems and assets,physical or virtual, the importance ofwhich is such that the total or partialdestruction of the latter would have aserious impact on security, economicsecurity, public health, etc. (Robert et al.,2003). Countries around the world havebeen confronted with several eventsgenerated by various causes affecting theCIs (Too, 2011).

The earthquake in Boumerdès (Algeria)in May 2003 and the floods in Bab ElOued (Algiers, Algeria) in November2001 have clearly shown the vulnerabilityof our critical infrastructure systems(CISs). The latter were out of use, forseveral days, greatly complicating therecovery actions and prolonging theduration of the return to normal.

Two factors contributed to theworsening situation in the two urbansites, each with a population of morethan three million. The first is the highdensity caused by the anarchicextension of the city. The second is theencroachment on service spacesreserved for CISs, which makes theirmaintenance and operations complex.

Governments are aware that CIs play acrucial role in urban function, especiallyin life (work, economic support, securityand societal well-being, etc.) (Tian et al.,2010).

The proper functioning of energy,transportation, water supply,telecommunications, financial and otherservices is vital to all communities andcountries (Robert, 2004). In addition,these CIs face exogenous risks such asmore frequent and more severe extremehydro-meteorological events due toclimate change or endogenous risks thatare caused by the complexity andinterdependence between CIs.

In an urban territory, the CIs are notisolated from each other but are ratherinterdependent. The relationshipsbetween them need to be identified inorder to conduct realistic analyses(Ouyang, 2014). Multiple CIs can berelated, resulting in multi-impact failuresthrough domino effects (Allen, 1997;Moses, 1998; Lemperiere, 1999). Theirfacilities and locations must be welldesigned during the planning of theurban territory, to not only ensure vitalservices and improve the livingenvironment of the populations, but alsofor their protection in case of disaster.

The full characterization of thevulnerability of the CIs, contributes tothe assessment of the vulnerability ofour urban environments to variousnatural or anthropogenic andtechnological disturbances. Thisrequires modeling the dynamics of theflow of physical quantities in thenetwork or in a CIS (Zio and Sansavini,2011). As a result, CISs should bemodelled as part of an overall securityanalysis process and identify areas ofweakness or vulnerability (Pye and


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Warren, 2006). This implies not onlytaking into account the interactionbetween the structural and architecturalcharacteristics and the dynamic aspects,but also the whole transformationwithin the components of the CIs. Thelatter depend on other secondaryresources (Rs) to be able to transport theelement conveyed through the CIS.Consequently, the principal mission ofthe latter is guaranteed by the fulfilmentof the tasks of the various CIscomposing it. A mission is a functionfor which the network or a CIS has beendesigned and constructed, andcorresponding to a population need.

The interest of research on CISs no longerconsiders them as simple isolatedsystems but as multiple, interconnectedand dependent systems, while assessingthe influence of interacting infrastructureon the operating conditions of each CI(Zimmerman, 2001). Interdependence,domino effects and especiallyvulnerability related to CISs are the threeaspects that form this problem.

In the urban environment, risk mitigationand recovery have traditionally focusedon prevention, protection and resistancerather than resilience. (Allan and Bryant,2011).

This article aims to model thepropagation of effects following one ormore disturbances in a CIS throughoutthese CIs. Inter-CI interdependence willbe taken into account when decomposingCIs into components and more preciselyat the level of their resources (R). Thisresearch work is mainly oriented on theconsequences of disturbances in the CIscaused by technical malfunction, error ofhuman intervention or even naturalhazard.

Although Algeria has legal mechanismsgoverning the management of majorrisks, in particular Framework Law(04/20), on the prevention of major risksand disaster risk management in thecontext of sustainable development,transcribed in Official Journal of theRepublic of Algeria, studies to safeguardthe CIs are rare, which only amplifies thedifficulty of disaster management.

The objective of this research work is theunderstanding and monitoring, thepropagation of the effects of one or moredisturbances, as well as the behaviour ofCISs, in the face of different risks(industrial and transformation) andhazards (natural and anthropogenic).This is for the perfect integration ofrecovery planning and urban planning inthe design process. Indeed, there is astrong link between an urban sitestructure and its ability to recover froman earthquake (Allan and Bryant, 2011).This will, contribute to the enrichment ofseismic risk maps, for example (Benouar,1996).

The other objective is to contribute to theestablishment of a methodologicalframework to facilitate the creation ofcollaborative space between urbandesigners and recovery planningengineers for information exchangepurposes already in the design phase ofstudies. To finally design resilient urbansites and strengthen those that are less.

A contribution through a methodologicalapproach is described. Modeling of thepropagation of these effects and asimulation of disturbance within andacross the CISs was carried out, thusproviding a contribution to thedevelopment of a methodologicalframework for a resilient urban site


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combining design, functionality, andemergency and recovery planning.

An example, of the propagation of theeffects of two disturbances following aflood, of a water network in an urbanarea, composed of four CIs is discussedand treated.

2. Literature review

2.1. Resilience and urban resilienceUnderstanding the concept of urbanresilience can only be achieved if weaddress the notion of resilience and itsorigin.

The term resilience is often used inpsychology and engineering, used in theliterature dealing with globalenvironmental change; resilience isgenerally attributed to environmentalistC.S. Holling (Brown, 2014). According toMeerow and Newell (2019), Hollingdefines resilience as the ability of anecosystem to maintain basic functionalcharacteristics during a disturbance.

Holling characterizes ecosystems ashaving multiple steady states and in aconstant flow state, with a distinctionbetween “engineering” static resilience,linked to a system’s ability to bounceback to its previous state, and“ecological” dynamic resilience (Meerowand Newell, 2019). Resilience focuses onmaintaining key functions when they aredisrupted (Meerow et al., 2016).

This definition is more than interestinginsofar as these key functions can beperformed by the CISs to provide what isvital to the populations in water,electricity, gas, etc. to guarantee thecontinuity of the activities in an urbansite. This can only be achieved throughresilient urban development.

There are more than 20 definitions ofurban resilience in the scientific literature,creating ambiguity (Meerow et al., 2016).

Godschalk’s definition seems moreappropriate for understanding theconcepts of urban resilience. The latterconsiders that a resilient urban site is anetwork, sustainable, of physical systemsand human communities. Physicalsystems are the elements built (roads,buildings, infrastructure, energyfacilities) but also natural (fauna andflora) forming the environment of thecity. During a disaster, these physicalsystems must survive and operate underextreme constraints. If many of them fail,which cannot be repaired, the lossesincrease and the recovery slows down.Human communities are the social andinstitutional components of the urbansite. An urban site without physicalsystems, such as resilient CISs, will beextremely vulnerable to disasters(Godschalk, 2003).

The concept of resilience offers a broadervision of the urban system and thedisruptions it faces. Thus, urbanresilience is in this perspective seen as theability of the perennial parties (actors ofthe urban site and manager of thephysical systems) reconciled their effortsin the sense of sustainability but also for arapid return to normal followingdisturbances, from the design of urbansystems to their use.

2.2. Critical infrastructure system (CIS)CISs are considered life support networks(water, electricity, rail, telephone, etc.)distributed in the urban environment. Inan urban site, a network carries anelement that can be either a service or asubstance. As a result, networks are thusassimilated to a set of infrastructuresdistributed over an urban environment,


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with direct or indirect links, which ensurethe good functioning of a society throughthe provision of essential services (ES) topopulation in terms of health, and theeconomy (Robert et al., 2007).

The networks are in harmony (spatial andfunctional links) according to a well-established layout, their rapiddevelopment and evolution, thetechnology used, and the geographicdistribution of the populations theyserve, are likely to create increasinglylarge disturbances.

Traffic congestion, power outages andmajor communications system outagesbreakdown are causing disturbances toessential public services with significantsocial consequences. In short, accidentsare becoming increasinglyunpredictable (Perrow, 1984). There isno need to demonstrate the inducedseverity of any malfunction because ofthe disturbances.

2.2.1. Infrastructure characterization(functional)

The infrastructure characterization isdone by several properties according to(Mc Daniels et al., 2007):● The Operational state expressed as a

percentage (0-100%) also indicatingthe quality of service provided to thenetwork and therefore to the CIS,

● The Integrity defined by at least oneservice threshold provided and mayalso be applied to the network and itsexchanged services,

● The Mitigation measures to ensureminimal maintenance of service,

● The "Inputs" is a small variableindependent of the output. Entries areoften referred to resources received(raw materials) or as services received(water, electrical energy, etc.),

● The "Outputs" is a variable thatdepends on the internal input andprocesses of the infrastructure and onthe demand made to meet the urbansite need,

● Internal Processes refer to thetransformation activities andoperations within the infrastructureitself.

Within the infrastructure, one or moreprocesses can take place to transforminputs into outputs (Haimes et al., 2005).This characterisation will be used toformalize the generation of the missionof a CI. These processes transform inputresources into a well-defined coremission. In urban planning, thedifferent states of a CI missions must betaken into account in order to developthe palliative means necessary for thecontinuity of an urban is activities in theevent of disturbances.

2.2.2. Infrastructure characterization(dysfunctional)

The criticality is related to theconsequences of disrupting theoperation of an infrastructure (Herderand Thissen, 2003). This explains thegreat differences in the assessment ofcriticality or even the degree ofessentiality of these CIs. For this reason,modeling all aspects related to the CIsremains a difficult job to do. Thecriticality of infrastructure is due to(Amin, 2000):● The multi-scale, multi-component,

heterogeneous and distribution inurban space and especially in areas ofinfluence,

● The vulnerability to disturbancespropagating instantly,

● The multiple interaction pointsincreasing with the number ofparticipants.


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This characterization is of paramountimportance since it allows an initialunderstanding of the functioning andimportance of the CIs. Nevertheless, anyinfrastructure can be considered criticalunder certain circumstances andconditions. Ignorance of the highinterdependence of infrastructure stemsfrom the fact that the majority of thetypes of disturbances that cause severecascading effects are part of "lowprobability high impact" events (Dunn,2005).

Interdependence is considered a two-wayrelationship between two CIs in whichthe state of one is influenced or correlateswith the state of the other (Rinaldi et al.,2001). Four categories are identified asillustrated in Table 1.

Interdependencies are an integral partof the design and operation of aninfrastructure, but can generate avulnerability far greater than anysingle system: inter-interdependencyCIs also causes the propagation ofdisturbances (Schneider, 1999). Inaddition, these interdependenciescontinue to rise, increasing the risk ofcascading failures.

Domino Effects, because of the linkbetween the CIs, result in multi-impactfailures through domino effects (Allen,1997; Moses, 1998; Lemperiere, 1999).The latter cause an increase in thevulnerability of our urban sites andsocieties. CIs have physical

interdependencies. Domino effects area series of cascading events where theconsequences of a previous accidentare increased to cause a major accident(Reniers and Cozzani, 2013). Two typesof domino effects are recognized:internal and external. Internals dominoeffects begin in the CI itself, whileexternals begin near these CIs (Reniersand Cozzani, 2013). The termpropagation is then used. This meansthat the impact affects more than onesystem (system n-1 affects the systemn).

The vulnerability of the urban site isaccentuated by its own infrastructuresand their interdependencies. Inaddition, accelerating urbanizationmakes our urban sites increasinglyvulnerable to cascading failures causedby natural, environmental and technicalevents (Lewis and Mioch, 2005). Inaddition, technological advancesincrease vulnerability and even createnew ones (Nozick et al., 2005). Forexample, the terrorist attacks on theWorld Trade Center in 2001, the poweroutage in the summer of 2003 in NorthAmerica that paralyzedtelecommunications, transportation,and even the financial sector and banksare examples of this.

This situation has led to widespreaddisturbances in the functioning of societyover a long period. Protecting our urbanenvironments from this vulnerability isbecoming a great necessity.

Table 1. Types of interdependencies (Rinaldi et al., 2001)Interdependences

Physical Cybernetic Geographic LogicMaterial link used to receiveresources or to issue a product,which CIS is supposed toprovide

Informatics as aninstrument forexchange.

Two or more CISs share a limitedspace. Belonging to this space oftengenerates effects between systems.

Financial orregulatorylinks.


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2.3. Modeling of critical infrastructureAt the beginning of the 21st century,Rinaldi, Peerenboom, and Kelly (Rinaldiet al., 2001) initiated research on theinterdependencies of the CIs, proposingdimensions that frame the main aspectsof interdependencies. Their research hasraised new questions. Some of thesequestions have been answered, but othersremain unanswered. The confidentialityof the data surrounding the CIs has madethe latter non-public and rare. This makesqualitative studies more availablecompared to quantitative studies. Inaddition, other researchers haveproposed approaches to quantifycascading impacts in the CIs(Zimmerman and Restrepo, 2006).

Min Ouyang in his review (Ouyang,2014), of the different approaches usedin modeling and simulation of CISs-inter-dependencies, and had identifiedfive approaches: Empirical, agent-based,and based on system dynamics, basedon economic theory and based onnetworks.

2.3.1. Empirical approachesThey analyse the interdependencies ofthe CIs according to the historical data ofaccidents or disasters and the experienceof experts, to identify frequent andsignificant failure models and to quantifyinterdependency relationships throughvarious indicators.

These approaches help identifypotentially important patterns ofinterdependence and established spacesfor collaboration between urbandesigners and emergency plan managers.

However, some weaknesses are noted:● Failures and deficiencies reporting is

often overlooked,

● Lack of a unified methodologicalframework for the definition of aCIS and the collection of failuredata,

● Slow analysis of failure data.

2.3.2. Agent-Based approachesThese consider the components of a CISas agents and model the behaviours ofdecision makers and key managers ofinterdependent CIS. They also support alltypes of interdependencies between CISsthrough discrete event simulations in theform of scenarios. However, there aresome weaknesses:● The quality of the simulation

depends strongly on the startinghypotheses,

● The calibration of simulationparameters is a challenge due tolack of relevant data and difficultiesin modeling human behaviour.

2.3.3. System dynamics approachesThese use a top-down approach tomanage and analyze complex adaptivesystems involving interdependencies(Sterman, 2000; Kollikkathara et al., 2010).They model the interdependent CISs by acausal loop diagram considering thecausal influence between diversevariables and by a stock-and-flowdiagram; they describe the flow ofinformation and products through thesystem (Brown et al., 2004; Brown, 2007;Stapelberg, 2008).

Indeed, these approaches model thedynamics and evolutionary behaviourof interdependent CISs by consideringthe causes and significant effects indisruptive scenarios by taking intoaccount other effects (managementand technical factors) to reflect thelong-term evolution of the system andprovide investment recommendations.


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Weaknesses in this type of approach are:● Causal loop diagram: based on expert

knowledge (semi-quantitative method),● Parameters and functions in models

that require calibration and data thatis difficult to access for safetyreasons,

● Use of differential equations todescribe behaviours at the CIS level.This approach cannot analyse thedynamics at the component level(adjustment or change ofinfrastructure topologies),

● Difficulty in obtaining relevant data,therefore, validation efforts consistmore of conceptual validation for theimportant descriptive variables ofeach CIS in order to determinewhether the model provides areasonable response to thedisturbances. This makes thevalidation of the model relativelylimited.

These weaknesses require the integrationof other modeling approaches into auniform analytical framework to supportoverall decision-making.

2.3.4. Approaches based on economic theoryMost researchers use economic theorybased on Leontief’s input-output (I-O)model (Leontief, 1966). This modeldescribes the degree of interconnectionbetween the various economic sectors.

In this equation, xi is the total output ofthe sector i. The coefficient aij describesthe ratio of the contribution of sector ito sector j relative to the total needs ofsector j. cj describes the demand forsector i that was not expressed bysector-to-sector interconnections.Haimes et al. with a research group have

used an inoperability input-outputmodel for these infrastructures based onLeontief’s theory (Haimes et al., 2005).

The model assumes that the differenttypes of interdependencies can bemodelled by financial interactions.Moreover, the degree of interdependenceis specified by the percentage ofconsumption of each sector in relation tothe output of the other sectors. The otheraspect of this model is the great difficultyof writing a complete model.

It is quite possible that, as the number ofsectors concerned increases, more detailwill be added. The complexity of models,such as that presented by Haimes et al.(2005) will increase significantly andtherefore complicate the modeling andsimulation process.

2.3.5. Network-based approachesThese approaches describe CISs asnetworks, where nodes represent variouscomponents, and their links mimicphysical and relational connectionsbetween them. Depending on the particleflow modeling on the CISs, the methodsare described below.

Methods based on topology: Thesemethods model interdependent CISs onlyaccording to their topologies, withdiscrete states for each component (nodeor link) and usually with two states:failing and normal.

Nodes may fail directly from hazards,or indirectly due to source nodedisconnections in the same CIS(Patterson and Apostolakis, 2007) ordue to simultaneous failures of theirnodes dependent on another CIS, alsodue to other factors, such as failures ofbackup systems (Adachi andEllingwood, 2008).


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The modeling of the topologies of theCISs can be analyzed by analyticalmethods and by simulations methods:● Analytical methods: These methods

build a model that does not take intoaccount the heterogeneity of nodes(source nodes, transmission nodesand well nodes). Each CIS can becharacterized by its degreedistribution of nodes represented by agenerator function.

● Simulation methods: These methodsmainly consider the topologicalcharacteristics of the interdependentCISs while identifying the criticalcomponents of the CIS, and providesuggestions for improvements intopological robustness. Despite thetopology of the system, thatdetermines its functionality, recentstudies have shown that thetopological model alone cannotprovide enough information on theactual flow performance of CISs(Ouyang, 2014).

As a result, these methods cannot be usedalone as tools for managing CISs. Theyrequire the integration of other modelingapproaches into the urban planningframework and specific to each CI, that isto say its mission, its spatial position andthe inter-CIs and this for theimplementation of a global decisionsupport in the collaborative frameworkinvolving all the actors of the urban site.

Complexity of interdependence modelingforces researchers to consider only oneinfrastructure (Eusgeld et al., 2009).

Recently, the CIs approach as a “systemof systems” (Eusgeld et al., 2011) and the“network of networks” approach (Gao etal., 2014) have advanced understandingof dependencies and interdependenciesamong the CIs.

3. Proposed modelRisk management is more focused onconsequences rather than causes offailure (Hémond and Robert, 2014). Thisapproach is tedious and very slow toachieve. In addition, it does not considerany domino effects, as well asvulnerabilities.

The risk analysis (RA) of CISs, such asstrategic networks (water, gas, electricity,etc.) useful for human well-being, isperformed by methods that consider therisk (R) as the product of the “probabilityof occurrence (P)” of an event, by theseverity of the “consequences (G)” whichit generates (Kaplan, 1997). This approachis penalizing because only the mostcatastrophic scenarios will be considered.The main risk analysed would be theavailability of the resource transported bythe CIS. Resilient networks should bedesigned to build territorial and urbanresilience.

Fig. 1. CI Components.

3.1. ConceptsCIs are composed of a multitude ofcomponents, Activities (As), Operations(Os) supported by the infrastructure(building, hydraulic development, etc.) toguarantee Missions (Ms) useful for thepopulation. Fig. 1 and Table 2 illustratethese components and their relationships.


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Table 2. Decomposition of a CI (inspired from Robert et al., 2003)CI (sub-system)

Resources(Rs)

Infrastructures(Is)

Operations(Os)

Activities(As)

Missions(Ms)

Elements material,operational,human andnatural enablingthe realization ofAs.

Hardware elementsdesigned (building,hydraulic development,etc.) to operate As of CI.These elements arenecessary for therealization of Os.

Technical process director indirect actions onthe whole or parts of theCI to achieve the Ms.Automated (computer-electronic) or manual.

Actionsrequired andto beperformed toenable Ms tobeaccomplished.

The functionfor which a CIwas designedandimplementedto satisfy aneed.

Table 3. Decomposition of a hydraulic pumping stationCI : Hydraulic pumping station

Resources(Rs)

Infrastructures(Is)

Operations(Os)

Activities(As)

Missions(Ms)

Water atatmosphericpressure

Building housing theStation and pumps

Pressure andFlow control

ExploitationTransformationMaintenanceRepair

Water underpressure for publicuse

Fig. 2. Decomposition of a hydraulic pumping station (A0-SADT).

Fig. 3. Inter-CI flow.

All the CIs constitute a CIS (Fig. 3), theproper functioning of which depends onthe ability of the CIs to carry out each oftheir missions. This vision has theadvantage of the contribution to: the RA,through a perfect knowledge of theircomponents and the assessment of theresilience of these systems, this couldprotect the users against the risk ofrupture of the main mission of a CIS.

It is therefore essential to identify theCIs, their main components and theirMs. The accomplishment of the definedMs is achieved through thetransformation of all resources throughthe As and Os.

Take the example of a CI a hydraulicpumping station belonging to a CIS,which is the water network.


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After a functional decomposition accordingto the Structured Analysis and DesignTechnics (SADT) method, level A0 asshown in Fig. 2. The various componentsof the station are defined in Table 3.

The model developed is based on theprinciple of flows. In the same way, eachCIS has its own mission called globalmission (Mg) to satisfy a vital need, inurban planning, while itself needing theproducts, the other CIs and possibly theother CIS (other resources), to fullyaccomplish its mission. In addition, each CIhas its own M which will be consideredand disseminated as an R at subsequent CIsFig. 3 illustrates the inter-CI flow.

In the following, we formalize themission of a sub-system noted mkSi andthe input resource noted rKei

3.2. MethodologyThe safety of CISs requires an analysis ofthe risks associated with disturbancesaffecting its CIs. This means answeringthe following questions:● How does a disrupted component

affect the CI own mission?● How does an affected CI affect other

CIs?● How does an affected CI subsequently

(after that) affect the CIS (globalsystem)?

To make the urban environment resilient,these three questions need to be answered.The collaborative space is able to contributeto answering them. Thus, the answer tothese three questions is through modeling,the propagation of the effects of adisturbance, throughout a CIS according tothe state of the missions of its CIs. As aresult, urban designers and emergencymanagers to mitigate the effects of adisruption and to move quickly to recoverycan make good decisions.

In the way the difficulties, which must beovercome in order to secure the CISs byprotecting the components ofinterdependent CIs, are identified. It istherefore essential to plan recoverymeasures to protect against the risk ofcascading disturbances. This is done bymonitoring, as closely as possible, thepropagation of effects in case ofdisturbance(s) on all CIs belonging to agiven urban development.

The methodology developed requires thestudy of the interrelationships of theinterdependent CIs. A methodology is thenproposed, using the following approach:

A demarcation of the urban area isnecessary to identify the CISs and theirassociated CIs, with a perfect knowledge oftheir respective missions. The identificationof these latter makes it possible torecognize all the stakeholders of a givenCIS and to mention each time whether thissame CIS is also a supplier of another CIS.For example, CIS1 (Water-Supplier)supplies water in the urban area, but itselfis a client of CIS2 (Electricity-Customer).This approach makes it possible toconstitute a collaborative space relatedwith a given CIS.

Under these conditions, the problem ofconfidentiality will not arise, sincemanagers are from the sameorganization. It is important to select asingle CIS because it is difficult to treat allCISs in the urban area studied. CIS byCIS (water, gas, electricity, etc...) is thenconsidered. However, an indication willbe given when the resource conveyed bythe CIS, the subject of the study, is usedby another CIS. For example, reportingwhen a CIS-supplier becomes a client ofanother CIS. Decompose the selected CISinto CIs (sub-systems) and then intocomponents. Thus, the CIS will be


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considered as a global system (GS) and itsCIs as sub-systems with preciseindication of the missions of each.

3.2.1. Select a CIS missionFor each CIS a global mission isidentified. Formalizing the generation ofthe latter allows us to analyze the risk ofits unavailability, degradation or evenloss (cessation). Thus, we can determinethe effect of degradation on urbanfunction. The Mg can be discredited inseveral missions specific to each CIs. Inother words, the Mg can only be achievedby carrying out the tasks of each CI. It isunnecessary to examine all of thesemissions at once.

Therefore, missions will be consideredone after the other to assess the effects ofa disruption at the end of the CIS. Thiswill allow the monitoring of effectsresulting from a given disturbancethroughout the CIS.

The Mission of each CI and itsrelationship with the Inter-CIs Resources:

For each sub-system i output k missionmkSi is induced.

K Є {K1, K2, K3}, K1= Main mission, K2=Secondary mission and K3=Tertiarymission. Only the main mission K1 will beconsidered in this article. To concretizethe inter-CIs flow, the output M of a CI

turns into an R for the subsequent CI. Fig.4 illustrates the inter-CIs flow and thetransfer of M to R. The input resources

of each sub-system i are:

For the 1st sub-system i=1For the rest of the sub-systems, the valueof the input resource of a CIi is calculatedbased on the value of the output missionof a CIi-1

Where: - mkSj : is exit mission - rkEn : is input resource

The inter-CI flow is not done all the timein the same way but according to acertain dependence, for expressionof input resources rkEi is given:

εkji : is percentage of inter-CIs flow in theinterval [0, 1], indicated in Table 4.

Table 4. Nature of inter-CIs flowNature of the flow εkji

None 0Minor 0.25

Moderate 0.5Important 0.75

Full 1

Fig. 4. Transforming Mission into Resource.


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In this section, we have seen that themission of a CI depends on thetransformation of the input resource andaccording to the nature of the inter-CIsflow.

3.2.2. Formalize the contribution of As andOs in the achievement of the M of a CI

Considering not only the interactionbetween: the structural, operational anddynamic aspects, but also the whole ofthe transformations within thecomponents of a CI; in terms of Os andAs, which also depend on other Rs(human resources and more) used toconvey the element transported throughthe CIS. This element is mostly volumesthat vary widely in space and time andconsidered, in our case, as the mainresource.

The mki mission of a CI depends on its I,it is As, its Os and its Rs of entry.

So the mki of a CIi is the transformation ofthe R (received from the i-1 sub-system)with a series of transformations obtainedthrough the contribution of As and Os. Aweighting of these would be establishedto monitor and assess the flow afterprocessing. The new form of the missionof a CI can be written as follows:

( )÷÷

ø

ö

çç

è

æ+= å

=

)()()(1

2,1,i

ji

jkSjkjikikikikiki ss

ssmOcoefAcoefm e

The mki mission of a CI is writtenaccording to the contribution of As andOs for the transformation of resourcesinto missions according to the nature ofthe inter-CIs flow.

The mission k of a sub-system i is:

Where:● mkji : is the outgoing k mission of a

subsystem j going to sub-system i

● Coefki,1(Aki) : is contribution As in therealization of the mk

● Coefki,2(Oki) : is contribution Os in therealization of the mk

The mki mission of a CI is a refinedfunction of As and Os. On the other hand,it increases when the values of As and Osincrease.

The CIS in its normal operation issupposed to guarantee an Mg. The latterresults from the set of mki missions suchas: V0k is the nominal value of the kmission. When i =n.

V01: CI1 mission rating m1,1 and V0n: CIn

mission rating m1,n

Mg is the overall mission of CISrepresented by a one-dimensional vectorof n lines.

01

02

03

0

( )

n

VV

Mg SICVV

æ öç ÷ç ÷=ç ÷ç ÷è ø

In conclusion, the achievement of themission of a CI depends on the strongcontribution of As and Os after receivingthe resource.

3.2.3. Generate disturbancesThe disturbances may originate in the Iinfrastructure itself; this will have animpact on the As and Os. Therefore, onlythe affecting disturbances will beconsidered.

The proposed model assesses the degreeof alteration or degradation of Mg at theend of the CIS taking into account allresource requirements. That is, even ifsome Os and As of a CI belonging to aCIS are disrupted, the system may stillbe able to accomplish its mission byproviding services and responding to


170

demand. Thus, a disturbance in one ofthe components, its effects are felt on theglobal system. In addition, the effects arerelated to the importance of thecomponent and the nature of its linkswith other components. The proposedmodel will contribute to thedevelopment of CISs business continuityplans (BCP).

Ri is replaced by its value in rkEi equation.Disturbances λki and σki are localized,respectively, at the As and Os levels.With 0 ≤ λki , σki ≤ 1 and able to take thevalues presented in Table 5.

Table 5. Magnitude of disturbanceNature of thedisturbance

Values

None 0Minor 0.25

Moderate 0.5Severe 0.75

Very severe (Rupture) 1

After disturbance, the expression ofdegraded mission m’ki is written as follows:

For i = n m’ki becomes Vk.

Where:● λki is magnitude of disruption

affecting activities.● σki is magnitude of disruption

affecting operations.

The value α being the disturbancecoefficient:α=((1-λki)Coefki,1(Aki)+(1-σki) Coefki,2(Oki))The degraded mission m’ki of a CI is afunction refined to the coefficient of

disturbance α. It decreases when αdecreases.

In this section, we note that theaccomplishment of the mission of a CI isstrongly linked to the coefficient ofdisturbance. The latter depends on themagnitude of the disturbances affectingthe As and Os.

3.2.4. Assess and monitor the propagation ofthe disturbance effect

Which will determine its impact on theMg of CIS. For each CI dm1,n degradationindicator is calculated by:

The mission degradation indicator isstrongly linked to the value of thedisturbed mission. As a result, toincrease the resilience of a CIS, it isnecessary to reduce the degradationindicator of all CIs of a system to zero.With:● V0n is the value of the mission not

degraded m1n of CIn.● V1n is the value of the disrupted

mission m’1n of CIn

Similarly, these mission degradationindicators will be weighted according tothe importance and essentiality of therespective CIs, in the achievement of theCIS Mg in the chosen urban area.

βk weighting coefficient according to theimportance of the contribution of the kmission in Mg. The allocation of theimportance coefficient is left to the CImanager. Table 6 gives the differentvalues βk.

Table 6. Importance of the mission of a CI/MgImportance of the M Minor Sizeable Significant Essential

kb 1 2 3 4


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Table 7. CIS mission degradation indexMission weighted average degradation index % Moderate sizeable Significant Severe

M 0-30 30-50 50-80 80-100

M Is defined as the weighted averagedegradation indicator of CIS Mg, alsoknown as the magnitude of the effect ofCIS disturbance in the study area.

This average is obtained by summing theweighted degradation indicators of allCIs divided by the sum of all weightingvalues.

M

Thus, this average strongly depends onthe size of a CI’s mission and theindicator of degradation relative to eitherCI. It is important to note that a smallmission degradation in an essential CIwill have a large impact on the Mg of thesystem.

3.2.5. Establish potential disturbance impactclasses

A typology of mission degradation indexfollowing disturbance on CIS is chosenand ranges from moderate to severe,Table 7 illustrates the different cases.

According to the equation giving theexpression of dMi

dMi = 1-

Consider that:

Qi =

CIS can accomplish its mission despitemoderate disturbances. According toTable 7 the overall mission degradationindex, weighted average, is moderate if0 ≤ dMi ≤ 0.3.

The equation giving the value dMi

becomes:

dMi = 1 -å

å

=

=

×

n

kk

n

kkiQ

1

1

b

b

Always with Qi ≤ 1

This equation reads: the degradationindex of a Mi is a refined function of thedegraded mission value of a CI expressedin the numerator. It cancels when there isno mission degradation and is equal to 1when the degradation is total.

The last equation must be reduced

1-

å

å

=

=

×

n

kk

n

kkiQ

1

1

b

b

≤ 1- Min Qi

When i increase mathematically

0 - 1 - Max Qi ≤ 1 -

å

å

=

=

×

n

kk

n

kkiQ

1

1

b

b

The weighted average degradation indexof the overall mission of the CIS must be:

1 - Max Qi ≤ 1-

å

å

=

=

×

n

kk

n

kkiQ

1

1

b

b

≤ 1- Min Qi

The weighted average degradation indexis a finite amount, framed by: 1 - Max Qi

and 1- Min Qi

This equation provides a snapshot ofthe weighted average degradation indexof the overall CIS mission. Thus, at least


172

one of the CIs is not disturbed and onlyone of the CIs the Min Qi ≥ 0.7 and thisto remain in the zone of moderatedegradation of the mission.

Thus, in practice, designers can predicthouseholds without electricity, if apower grid is treated, as well as thepopulation without water if it is a watersupply system. Therefore, arrangementsmust be made for each other during thedesign phase to the extent possible, if notduring the emergency planning phase.

4. Model application exampleThis example focuses on emergencyplanning to implement the best actionsfor a return to normal following twodisturbances caused by a flood. TheCIS chosen is the water supply networkto illustrate the propagation of theeffects of two disturbances along thenetwork.

The CIS selected is the water system toillustrate the propagation of the effect

of one or more disturbances on thesystem. Water supply systems affectthe activity and development of urbanareas. Thus, these networks constitute aCIS of an urban site or urbanenvironment.

The main mission of the latter is notonly the supply of drinking water tothe population, but also the other CISssuch as the gas network or theelectricity network serving a commonarea of influence. That is why it isessential to ensure that it functionsproperly. A water supply systemconsists mainly of the followinginfrastructure (Fig. 5) CI1: Dam, CI2:Water treatment plant, CI3: Pumphouse and CI4: Storage.

A water supply system has as its mainmission the supply of drinking water.Quantity, quality, pressure andstorage are part of this mission. Thesemissions are supported by CIsconstituent CIS.

Fig. 5. Critical infrastructure system (water system).


173

Table 8. Parameters by CI.Designations CI1 CI2 CI3 CI4

βk Coef of importance 3 3 4 3Flux Inter-CIs kjie 1,11e =1 1,12e =1 2,13e =1 3,14e =1

Resources r1E1= a 1000 r1E2= m1S1(ss1/ss2) r1E3= m1S2(ss2/ss3) r1E4= m1S3(ss3/ss4)Coef11,1(A11)

Coef11,2(O11)

Coef12,1(A12)

Coef12,2(O12)

Coef13,1(A13)

Coef13,2(O13)

Coef14,1(A14)

Coef14,2(O14)

Contribution:Activities and

Operations (%)0.65 0.30 0.55 0.40 0.50 0.45 0.65 0.30

These missions are expressed as follows:● m1: Have a quantity Q (m3) through

CI1: Dam;● m2: Deliver quality Qa (coliform

levels) through CI2: Water treatmentplant;

● m3: Provide pressure, P (mPa)through CI3: Pump house;

● m4: Keep a quantity C (m3) throughCI4: Storage.

The overall mission of the water systemwould be degraded if one of the missionsof its CIs is degraded or impaired becauseof one or more disturbances. In our casetwo disturbances, having as origin aflood, affects the two treatment andpumping stations, are considered.

Mission of each CI and relationship withinter-CIs Resources.

For each sub-system i given, the koutput mission mkSi induced. Just K1 =main mission that is considered, foreach CI are m1, m2, m3, and m4. Toconcretize the inter-CIs flow, the outputM of a CI turns into an R for thesubsequent CI.

The input resources for each sub-system iare:● r1E1= a, pour i=1● r2E2= m1S1(ss1/ss2)● r1E3= m1S1(ss1/ss3) + m1S2(ss2/ss3)● r1E4=m1S1(ss1/ss4)+m1S2(ss2/ss4)+

m1S3(ss3/ss4)

The M of an CI depends on his I, his As,his Os and his Rs of entries● V01 is the nominal value of Mission 1:

m1,1 of CI1;● V02 is the nominal value of Mission 2:



m1,4 of CI4.

Mg is the global mission represented by aone-dimensional 4-lines vector.

÷÷÷÷÷

ø

ö

ççççç

è

æ

=

4,1

3,1

2,1

1,1

)(

mmmm

SICMg

5. Results and discussionsThe CIS selected is the water system toLet us consider r1E1= 1000 m3 to have inCI1, the links and the inter-CIs flows areconfigured as indicated in Table 8. Thecontribution of the activities andoperations relating to theaccomplishment of each mission of the CIis fixed. A weighting is also assignedaccording to the importance of the CI inthe CIS.

The mission value of each CI is thendetermined (Table 9).

Table 9. Mission values (functional state)Designations CI1 CI2 CI3 CI4

Nominal valuesof missions V0

950 902.5 857.38 814,51


174

Table 10. Mission values after flood (dysfunctional state)

Fig. 6. Missions values by CI before and after flood/degradation index.

A flood simulation is then considered toaffect CI2 and CI3 as follows:● CI2: Activities and operations are

affected by 50% and 25% respectively,● CI3: Activities and operations are

affected both by 25%.

The mission values of each CI after floodare then calculated (Table 10).

The flood had impacts on the watersupply system for this purpose for eachCI a mission degradation indicator is thenestimated and represented in Table 11.

Table 11. CI and CIS Mission Degradation IndexInfrastructures CI1 CI2 CI3 CI4

D mission degradationindex

0 0.43 0.59 0.59

Global MissionWeighted Average

Degradation Index ofCIS

0.42

Flooding caused two disruptions at CI2

and CI3 levels a severe degradation, themain mission of the storage tank of theorder of 0.59 is observed. The waterresource deficit is 479.1 m3. The weightedaverage degradation of the overallmission of the CIS is of the order of 0.42considered significant. This degradationwill have impacts in terms of theavailability of the resource forpopulations and other users. In our case,measures must be taken to improve theCIS degradation index.

These measures will affect CI4 by fullyreplacing the treated water deficit (479.1m3) which would reduce this average to0.28. The intervention on CI4 is justifiedby the fact that it is at the level of thisinfrastructure that the disturbance indexis the most important of the order of0.59.

Infrastructure CI1 CI2 CI3 CI4

Disturbance / ü ü /Activities Operations Activities Operations

Impact of the floodkil = 0.5 kis =0.25 kil = 0.25 kis =0.25

Coefficient ofperturbation

r1E1= a1000 r1E2= m1S1(ss1/ss2) r1E3= m1S2(ss2/ss3)

r1E4=m1S3(ss3/ss4)

Mission values afterflood 950 523.45 353.07 335.41


175

In addition, the infrastructure inquestion is the starting point for thedistribution of the resource transportedby the CIS, so technically thecontribution of resources as a palliativemeans remains technically feasible.Definitely, the supply of resources willimprove the average degradation indexof the overall mission of the CIS fromlarge to moderate. To remain in themoderate range a minimum intake of405.79 m3, water treatment, mustguaranteed.

These measures will only be temporaryso that the flood will not paralyze theactivities of the urban site, which willmake it resilient. Thus, the emergencyplanning engineers must take therecommended measures. As for thefeasibility of these measures, they arethe responsibility of the urban planner,hence the need for collaborationbetween the two specialties. Because thefeasibility of these measures is backedby the predisposition of the layout andthe spaces.

6. ConclusionThe notion of resilience offers a valuablehelp in understanding the place, thetime and how to intervene. Recovery isbased primarily on the spatial aspect.Indeed, the precept of resilience alreadypromotes when designing spaces forefficient recovery.

The resilience of an urban site dependson the sustainability and performanceof critical infrastructure systems (CISs).In addition, to strengthen the resilienceof a site inevitably requires theassessment of the mission status of theCIS and the monitoring of the effects offailures in case of disturbances affectingthe CIs. Thus, the effects of thesedisruptions affect not only the overall

mission (Mg) of the CIS, but also themissions of its own CIs.

This is a new conceptualisation ofexisting relationships between thedifferent infrastructures of a networkallowing modeling of the propagationof effect of one or more disturbances.This makes it possible to simulate acertain number of disturbances andidentify the most critical subsystems topromote safety actions either during thedesign phase or during recoveryplanning. As a result, establishing thecollaborative space between urbandesigner and emergency planningengineer would be very useful.

Modeling the functioning of the CIs andtheir interdependencies is far from aneasy task. The developed model willallow an analysis showing the causalinterdependence between the varioussubsystems that affect the core missionof a network instantaneously, which isnot possible under other existingmethods, and which constitutes theoriginality of this work. The effect ofdisturbances affecting a CI felt in termsof degradation of the overall mission ofthe CIS. This deterioration mainlyinduced by the importance of theaffected CI and the magnitude of thedisturbances affecting it, which willfacilitate the identification of the CIs toincrease their resilience.

The proposed model is therefore adecision support tool dedicated not onlyto monitoring effects followingdisturbances to anticipate dominoeffects, in a given system, but also acontribution to risk management(prevention, protection, recoveryplanning, etc.) by implementing riskcontrol measures to make urban spacemore resilient. In addition, it provides a


176

methodological framework to establisha collaborative space between the actorsof the urban site.

The results obtained from the model areof a semi-quantitative type and takeinto account only the main resource,which is the element transported; thedevelopment model can be supportedby IT applications and used as adashboard by urban site actors and CISmanagers.

This work can be expanded to includeother resources such as support andhuman resources.

AcknowledgmentThe authors would like to thank thelaboratory managers: Laboratory of BuiltEnvironment at University of Science andTechnology Houari Boumediene, Algiers,Algeria and The Environmental Sciencesand Techniques Laboratory at NationalPolytechnic School, Algiers, Algeria forsupporting this research.

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Received: 29 April 2020 • Revised: 3 June 2020 • Accepted: 10 June 2020

Article distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND)

modeling the propagation of the effects of a disturbance

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