Identifying critical elements of road infrastructure using cascading impact assessment

*Co esponding au ho . E-mail: da id. ehak@ sb.cz Copy igh © 2020 The Au ho (s). Published by VGTU P ess This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un e- s ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed. TRANSPORT ISSN 1648-4142 / eISSN 1648-3480 2020 Volume 35 Issue 3: 300–314 h ps://doi.o g/10.3846/ anspo .2020.12414 IDENTIFYING CRITICAL ELEMENTS OF ROAD INFRASTRUCTURE USING CASCADING IMPACT ASSESSMENT Da id REHAK1*, Da id PATRMAN2, Ve onika BRABCOVÁ3, Zdeněk DVOŘÁK4 1, 2, 3Facul y o Sa e y Enginee ing, Technical Uni e si y o Os a a, Czech Republic 4Facul y o Secu i y Enginee ing, Uni e si y o Žilina, Slo ak Republic Recei ed 3 Oc obe 2019; e ised 16 No embe 2019; accep ed 9 Janua y 2020; i s published online 4 May 2020 Abs ac . Road anspo is a key means o anspo ing people and ca go on land. I s pa icula ad an ages a e speed and ope abili y, which a e balanced, howe e , by dependence on oad in as uc u e. Road in as uc u e eliabili y is anim- po an ac o in i s unc ioning. I some elemen s o oad in as uc u e a e dis up ed o ail, he unc ion o dependen in as uc u es, such as he in eg a ed escue sys em o indus y, a e also impai ed and may ail. These impo an elemen s o oad in as uc u e should be iden i ied as c i ical and be gi en g ea e a en ion when iden i ying weaknesses and im- plemen ing subsequen secu i y measu es. This a icle in oduces he Iden i ying C i ical Elemen s o Road In as uc u e (ICERI) me hod, which was designed o make use o Cascading Impac Assessmen s (CIA). The use o CIA allows c i ical elemen s o be iden i ied h ough impac escala ion analysis. These impac s can he e o e be moni o ed no only in oad anspo in as uc u e bu also ac oss he en i e c i ical in as uc u e sys em. Keywo ds: c i ical in as uc u e, oad in as uc u e, c i ical elemen s, cascade e ec s, iden i ica ion, ICERI me hod. In oduc ion The impo ance o anspo in he mode n wo ld is e- lec ed by i s inclusion in 2008 in o he Eu opean c i ical in as uc u e sec o s (EC 2008), unde which he Eu o- pean Council speci ied ou sub-sec o s: oad anspo , ail anspo , ai anspo and wa e way anspo (in- cludes inland wa e ways anspo and ocean and sho - sea shipping and po s). Road anspo cu en ly has an i eplaceable ole in he Eu opean anspo a ion ne wo k. This ac is suppo ed by a signi ican ly g ea e a e o mo- o iza ion and in he g ow h o mo o way ne wo k densi y in 2006–2016, which ook place in i ually all Eu opean coun ies (UNECE 2018). Ano he s a is ic showing he inc easingly impo an ole o oad anspo is he ongo- ing g ow h o cabo age oad anspo ac oss Eu ope in 2013–2017 (Eu os a 2018). The ounda ion o a unc ioning anspo sys em is high-quali y and highly eliable in as uc u e. This anspo in as uc u e comp ises elemen s (EC 2006) so signi ican ha hei ailu e would cause a ic collapse (Jenelius 2007). These elemen s a e e e ed o as c i ical, and hei impo ance in he anspo in as uc u e sys- em can be de i ed om hei le el o impac on depend- en elemen s (Rinaldi e al. 2001). Indeed, in he con ex o his a icle, c i icali y is unde s ood as he ela i e im- po ance and signi icance o a gi en elemen ha also ex- p esses he ulne abili y o ha elemen and he po en ial ad e se e ec s o i s ailu e wi h ega d o he links in ha sys em. Assessmen o he c i icali y o elemen s in e ms o sa e y (e.g., Amb os e al. 2019) is no he subjec o his a icle. C i ical elemen s equi e g ea e a en ion, which means hey mus be iden i ied ea ly and ha e hei e- silience le els analysed (e.g., Rehak e al. 2019a; Nan, Sansa ini 2017; Be occhi e al. 2016). In he con ex o assessing cu en isks (e.g., Giannopoulos e al. 2012), adequa e secu i y measu es can subsequen ly be adop ed o enhance hei p o ec ion (e.g., Š olle e al. 2018; Klein, Hu e 2017; Labaka e al. 2015; H omada, Lukas 2012). Cu en s udies and publica ions dealing wi h iden i- ying c i ical elemen s in oad anspo can be ca ego- ized in o wo g oups. The i s g oup ep esen s uni e sal me hods applicable o all a eas o anspo , namely oad, ail, ai , ship (e.g., D ořák e al. 2017). The second g oup comp ises speci ic me hods ha ocus exclusi ely on oad T anspo , 2020, 35(3): 300–314 301 anspo . This g oup mos o en iden i ies c i ical links o nodes in he oad ne wo k. To iden i y hese c i ical elemen s, a ull ne wo k scan me hod is mos o en ecom- mended (e.g., Jenelius e al. 2006; Taylo e al. 2006). This me hod is based on a sys ema ic analysis o he impac on accessibili y o ne wo k sec ions in he e en o hei clo- su e. Howe e , in cases o e y la ge oad ne wo ks, his in ol es a complica ed and leng hy ma hema ical calcula- ion (e.g., la ge ci ies o agglome a ions). Fo his eason, a ull ne wo k scan app oach may in some cases appea imp ac ical (Chen e al. 2012). Because o hese compu a ional demands, an al e na- i e me hod was de eloped. This me hod uses a pa ial ne wo k scan algo i hm based on analysing he leng h and numbe o eplacemen ou es o gi en sec ions (Yang e al. 2016). Ano he iew o e s a me hod based on he link edundancy o a sub-ne wo k, namely he a ailabili y o eplacemen ou es (Yu e al. 2014). This me hod uses wo indexes o assess c i icali y: he link edundancy index and link c i icali y index. The au ho s men ion ha his me hod is much mo e e ec i e in iden i ying he same c i ical elemen s han he ull ne wo k scan me hod men- ioned abo e. Ano he me hod is o iden i y c i ical elemen s based on he mac oscopic undamen al diag am heo y (Dong e al. 2017). The au ho s desc ibe his app oach as he e- la ionship be ween a ic olume and he densi y o a oad ne wo k and he ela ionship be ween a ea-weigh ed ol- ume and he o al a ic amoun in a ne wo k. Ye ano he me hod is based on he Ne wo k Robus ness Index (Sco e al. 2006), which makes i possible o de e mine he al- ue o indi idual segmen s o links in he en i e mo o way sys em while iden i ying c i ical links equi ing imp o e- men . Ano he possible me hod is assessing he c i ical- i y o elemen s h ough hei ulne abili y (Oli ei a e al. 2014; Taylo , D’Es e 2007) o signi icance (Rupi e al. 2015). This e iew e ealed ha no speci ic me hod o iden- i ying he c i ical elemen s o all linea , poin and a eal opological s uc u es is cu en ly a ailable (Sli ko a e al. 2018). One o he main, ob ious easons is he inabili y o e alua e he co ela ion be ween elemen s wi h di e - en opologies. I is also e iden ha none o he speci ic me hods allows a sys emic assessmen o he in ensi y o sp eading impac . When he c i icali y o elemen s and hei signi icance and links o dependen elemen s a e e alua ed in he scope o e alua ing he e i o ial uni , an analysis o sp eading impac could help d aw a en ion o hei signi icance and links o hese dependen elemen s. A po en ial solu ion can be ound in implemen ing he esul s o cascade impac assessmen (Rehak e al. 2018). Based on he abo e, he a icle in oduces he Iden i ying C i ical Elemen s o Road In as uc u e (ICERI) me hod, which is sui able o ICERI using Cascading Impac As- sessmen (CIA). The use o CIA allows c i ical elemen s o be iden i ied using an impac sp ead analysis. These im- pac s can be moni o ed no only in he sub-sec o o oad anspo bu also ac oss he en i e c i ical in as uc u e sys em. 1. In as uc u e elemen s o oad anspo Road in as uc u e consis s mainly o oads o di e en class (mo o ways, exp essways, oads, local oads). Ac- co ding o he Commission Regula ion (EC 2006), o he elemen s o oad in as uc u e a e land, oad bodies ( u - ows, embankmen s, d ainage equipmen ), ci il enginee - ing (b idges, unde passes, o e passes, unnels, a alanche and alling ock p o ec i e s uc u es, snow ba ie s), le el c ossings, a ic signs and signalling, elecommunica ions equipmen and ligh ing equipmen (Lei ne e al. 2019). Depending on hei impo ance, some elemen s a e indica ed as c i ical in as uc u e elemen s and can be classi ied a Eu opean o na ional le els. How Eu opean c i ical in as uc u e elemen s a e designa ed is de ined by he Council Di ec i e (EC 2008). Elemen s ha can be ca ego ized as such all in o wo sub-sec o s: ene gy and anspo . Designa ing na ional elemen s o c i ical in a- s uc u e, howe e , is dependen on he indi idual coun- y. The es ablished c i e ia ha elemen s mus mee o be designa ed as elemen s o na ional c i ical in as uc u e o en a y widely be ween coun ies, esul ing in ambigu- ous classi ica ion (Sli ko á e  al. 2015). Some membe s a es also o en illogically assign he abo e-men ioned c i e ia. The le el o signi icance o an elemen in a c i i- cal in as uc u e sys em may also no be app op ia ely conside ed when i is de ined. In p ac ice, si ua ions hen a ise unde speci ic c i e ia whe e no elemen o only ew elemen s can be iden i ied as elemen s o c i ical in a- s uc u e. 1.1. Links be ween elemen s o oad in as uc u e When assessing he impo ance o indi idual elemen s, hei signi icance and co ela ion in he c i ical in a- s uc u e sys em mus be conside ed. The co ela ion o elemen s, meanwhile, is de e mined by he links be ween hem. The wo k o au ho s Rinaldi e al. (2001) is pi o al in e alua ing he links be ween elemen s. This esea ch demons a ed he in e dependence o c i ical in as uc- u e elemen s and de ined ou ypes o link: – physical ( he ype o in e dependency when each o wo in as uc u es a e dependen on he ma e ial ou pu (s) o he o he ); – cybe ( he ype o in e dependency when an in a- s uc u e is dependen on he in o ma ion ansmi - ed h ough he in o ma ion in as uc u e); – geog aphic ( he ype o in e dependency when local en i onmen al e en s can c ea e s a e changes in all in as uc u es); – logical ( he ype o in e dependency when he s a e o each o wo in as uc u es depends on he s a e o he o he h ough a mechanism ha is no a physical, cybe o geog aphic connec ion). These ypes o links can be u he classi ied acco ding o hei s a e, which can ha e h ee o ms: dependence, in e dependence and in luence (Rehak, No o ny 2016). Dependence is de ined as a link o connec ion be ween wo in as uc u es h ough which he s a e o one in a- 302 D. Rehak e al. Iden i ying c i ical elemen s o oad in as uc u e using cascading impac assessmen s uc u e is a ec ed by o co ela es wi h he s a e o he o he . In e dependence e e s o a wo-way ela ionship be ween wo in as uc u es ha a ec s o co ela es wi h he s a e o each in as uc u e. Gene ally speaking, wo in as uc u es a e in e dependen i each is dependen on heo he . By con as , in luence is cha ac e is ic ha has no need o iden i y a ela ionship o i . An example may be a si ua ion in which he assessed elemen B is no dependen on he unc ion o elemen A, bu may be posi- i ely o nega i ely in luenced by elemen A. Ano he possible me hod o classi ying links is ep e- sen ed by hei di ision acco ding o he le el o he link, speci ically (Rehak e al. 2016): – sys emic le el– his is he ype o link ep esen ed by he dependence o in luence o sec o s ac oss he en i e c i ical in as uc u e sys em (e.g., he depend- ency o he in eg a ed escue sys em on oad in a- s uc u e); – sec o al le el– his is he ype o link ep esen ed by he dependence o in luence o sub-sec o s wi hin a gi en c i ical in as uc u e sec o (e.g., he impac o dis up ed oad in as uc u e on ail anspo ); – sub-sec o al le el– his is he ype o link ep esen ed by he dependence o in luence o indi idual ele- men s wi hin a gi en sub-sec o (e.g., he dependence o a mo o way on a mo o way b idge o he e ec o mo o way ailu e on su ounding oads). 1.2. Classi ica ion o in as uc u e elemen s acco ding o hei opological s uc u e An impo an ac o in iden i ying c i ical elemen s o oad anspo is hei opological s uc u e. F om he pe - spec i e o opology, hese elemen s can be classi ied simi- la ly o ailway in as uc u e in o h ee basic g oups: (1) linea , (2) poin , (3) a eal elemen s (Sli ko a e al. 2018). The i s g oup ep esen s linea o line elemen s, which in he case o oad in as uc u e a e he linea elemen s o mo o ways and oads o di e en ca ego ies. Thei impo ance depends on he pe o mance hey p o- ide, such as he capaci y and in ensi y o a ic in a gi en a ea (Pa man e al. 2019) and he le els o he links o dependen o in luenced elemen s. The second g oup is poin elemen s, which in he case o oad in as uc u e a e ep esen ed by, o example, b idges, unnels o junc ions. The pe o mance o hese el- emen s is usually de ined by a ic pe meabili y (Pa man e al. 2019), whe eas dependen o in luenced elemen s a e oad sec ions (i.e., linea elemen s) connec ed o hese poin elemen s. The hi d g oup comp ises a eal elemen s. In he case o oad in as uc u e, hese a e, o example, bus s a- ions. The pe o mance o hese elemen s is de ined by he numbe o ehicles passing pe uni o ime. Iden i ying dependen o in luenced elemen s in his g oup in oad in as uc u e is al eady no longe possible. The impac s a e al eady a ec ing commu e s. 2. Sp ead and assessmen o cascading impac s in a c i ical in as uc u e sys em The co e o impac s ha sp ead h ough a c i ical in a- s uc u e sys em is he ailu es occu ing om he ad e se e ec s o sa e y isks (i.e., he causes o dis up ion o o ailu e o c i ical in as uc u e elemen s). These isks can be o an ex e nal o in e nal na u e. The impac s can hen di ec ly a ec socie y (di ec impac s), sp ead ac oss c i i- cal in as uc u e and c ea e addi ional dis up ions ha ha e addi ional impac s (cascading impac s). As a esul , he cascading impac s can a ec a single elemen simul a- neously (syne gis ic e ec s) (Rehak e al. 2018). A g aphic ep esen a ion o how hese impac s sp ead in a c i ical in as uc u e sys em is shown in Figu e 1. Cascading e ec s a e he e ec s caused by dis up ion o o he ailu e o c i ical in as uc u e elemen s. These hen u he sp ead ac oss he c i ical in as uc u e and cause dependen elemen s o ail, which esul s in o he impac s escala ing (Rehak e al. 2018). An example migh be he e ec o a sa e y isk R2 (e.g., e o is a ack) in sec o S2 (e.g., he elec ic powe indus y). As a esul o his ad e se e ec , he unc ionali y o S2 sec o is dis- up ed, which hen cascades in o he dependen S3 sec o (e.g., anspo sec o ). Dis up ing bo h sec o s esul s in a cascading impac on socie y as a whole. This speci ic si u- a ion ep esen s he sp ead o cascading e ec s o com- mon-cause ailu es, i.e. when wo o mo e in as uc u e ne wo ks a e dis up ed simul aneously (Ko zanikolaou e al. 2013). Figu e 1. Rep esen a ion o how e ec s sp ead in a c i ical in as uc u e sys em (Rehak e al. 2018) S1S2 S a e secu i y Economy Basic human needs Syne gy In e nal and ex e nal secu i y isks S1S1 S2 RRR C i ical in as uc u e sys em Socie y S Rsecu i y isks c i ical in as uc u e sec o s cause o dis up ion o o ailu e o he c i ical in as uc u e di ec impac cascading impac syne gis ic impac T anspo , 2020, 35(3): 300–314 303 CIA is an impo an ool in examining c i ical in a- s uc u e. Wi hou p edic i e modelling ools, he po en- ial impac s o dis up ion o o ailu e o c i ical in a- s uc u e elemen s canno be iden i ied p omp ly. The s a ing poin o cascade impac assessmen is a de ailed analysis o he sys em in which links be ween elemen s a e assumed (Zimme man, Res epo 2009). Analysing hese links and de e mining hei in ensi y is hen necessa y. Me hods ha assess cascading impac s in a c i ical in as uc u e sys em p ima ily ocus on he elec ici y sec o , which was designa ed in he P esiden ial Policy Di ec i e PPD-21 as a uniquely c i ical sec o (The Whi e House 2013). Howe e , om he pe spec i e o e alua ion, hese me hods a e applicable e en o o he echnically o i- en ed c i ical in as uc u e sec o s. The i s majo s udy o he assessmen o cascade e - ec s in he con ex o powe ailu e was conduc ed by Bie and Wang (2002). Acco ding o he au ho s, cascad- ing ailu es in he powe gene a ion indus y a e usually caused by common mode ailu es such as connec ion ail- u e, cabine ailu e, e c. In hei wo k, hey published a i e-pa algo i hm comp ising ailu e analysis, ne wo k opology, ne wo k connec i i y assessmen , sys em s a us e alua ion and index s a is ics. Ano he a ea o impo ance is examining he p obabil- i y o a cascading ailu e de eloping om an un o eseeable e en wi h ega d o ne wo k load (Liao e al. 2004). This app oach is based on he phase ansi ions o he p ob- abili y o cascading ailu es, e i ied expe imen ally us- ing lowe and highe esolu ion ne wo ks. Bo h ypes o ne wo k demons a e phase ansi ions. The esul s o he expe imen con i med a a ian whe e he cascade ailu e isk assessmen is based on a sea ch nea he cu en op- e a ing poin o he phase ansi ion o he p obabili y o cascading impac s. The me hod o s udy cascading e ec s (Hassel e al. 2014) deals wi h he na u e and p ocesses o cascading impac s. The au ho s poin ou ha unde s anding he p ocesses o cascading impac s can help add ess and mi iga e hei e ec s. A he same ime, hey p esen a me hodology designed o cha ac e ize and analyse hese impac s. In he desc ip ion, hey d aw on inpu da a om he analyses o eme gencies ha ha e al eady happened in he pas . They also examine he condi ions ha con ib- u e o he de e io a ion o he ex en o cascading impac s and o he condi ions ha educe he e ec s o cascading impac s. The p esen ed me hod is based on a concep ual model o cascading impac s, which comp ises h ee basic s eps. The i s is iden i ying a dis up ed (dependen ) sys- em, speci ically whe he his sys em is di ec ly a ec ed by he ini ia ion e en o is indi ec ly in luenced h ough a link o he in luencing sys em. The second s ep is desc ib- ing he impac s on all o he dis up ed sys ems in o de o unde s and how and o wha ex en a dependen sys em is in luenced by an in luencing sys em. The las s ep ex- amines he impac sys em a ge ing all dependen sys ems a ec ed by he ini ia ion e en . In he ollowing yea s, a comp ehensi e me hodol- ogy based on eliabili y me hods was in oduced o au- oma ically gene a e scena ios du ing c i ical in as uc- u e ailu es wi h subsequen cascading impac s (Gonz a e al. 2016). In hei s udy, he au ho s p esen ed exis - ing me hods o assessing in e dependencies in he c i i- cal in as uc u e sys em wi h a ocus on assessing hei eliabili y. In he case s udy, hey assessed he cascading impac s be ween elec ici y and ail anspo . This as- sessmen was based on he use o he aul ee analysis (IEC 61025:2006) and ailu e mode and e ec s analysis (IEC 60812:2006) me hods. An app op ia e me hod o assessing cascading impac s is an app oach based on e alua ing echnical sys ems (Renge e al. 2017). Sys em e alua ion heo y applies bo h sys emic hinking and sys em heo y. Using h ee s eps, an e alua o can (1) de ine he sys em, (2) e alua e sys em e - iciency, (3) e alua e sys em e ec i eness. The au ho s also s a e ha he e ec i eness o a sys em depends on p omp , su icien ly equen , speci ic, ele an and eliable sha - ing o in o ma ion a and be ween sub-sys ems h ough eedback mechanisms, i.e., eedback in he con ex o he sub-sys em o be ween indi idual sub-sys ems. Ano he possible iew o he issue in ques ion is o - e ed in he esea ch by Chen and Milano ić (2017). The au ho s p esen ed selec ed me hods o modelling and simula ions designed o analyse in as uc u e in e - dependencies on models based on a ac o o so-called agen . These a e mos o en used because o he de ailed depic ion o sys em beha iou . In his model, he unde - lying elemen o agen is designed o p o ide a pa icula se ice and ollows a se ies o “wha i ” ules and p ede- ined a ibu es, making i possible o lea n and espond acco dingly. Zucca o e al. (2018) desc ibed he possibili y o ex- ao dina y e en s occu ing o assessed elemen s in which mul iple e en s may ac simul aneously on one elemen . This phenomenon can signi ican ly a ec he sp ead o impac s by cascading e ec s. I also has o be ca e ully assessed in e ms o eme gency planning and managemen . The a icle discusses, om a heo e ical poin o iew, he needs o modelling and he main issues o conside a ion when simula ion ools a e de eloped ha aim o inco po a e he analyses o cascading impac s and e ec i ely suppo s akeholde s in hei p epa a ions o sol e and mi iga e hei consequences h ough plan- ning a local, na ional and in e na ional le els. The aim o his model is o desc ibe scena ios o sp eading cascading impac s a di e en le els acco ding o he a ailabili y o da a o di e en ca ego ies o elemen s and models o di e en sou ces o isk. The inal cu en ool is he CIA me hod, which was de eloped o quan i y he sp ead o cascading impac s in c i ical in as uc u e sys em (Rehak e al. 2018). The basis o he e alua ion p ocess is o mula ing a s a ic s ochas ic model o c i ical in as uc u e elemen s and he depend- 304 D. Rehak e al. Iden i ying c i ical elemen s o oad in as uc u e using cascading impac assessmen encies be ween hem. This model is based on p edic ing he pe cen age o p obabili y and he impac in ensi y. This me hod assesses all elemen s ound in a selec ed a ea and e alua es hei esilience (NIAC 2009) and links (Rinaldi e al. 2001). A s uc u al map o he isk o he sp ead o cascading impac s can hen be c ea ed. E alu- a ion o he isk o sp eading cascading impac s is based on h ee limi ing ac o s: (1) he in ensi y o he ini ia ion h ea (i.e., he d op in he le el o se ice deli e y om he p e ious sec o ), (2) he le el o esilience o he de- penden b anches, (3) he in ensi y o he link be ween he e alua ed b anches. 3. Me hod o ICERI P uden iden i ica ion o c i ical elemen s allows hei esilience o be acco dingly e alua ed (e.g., Rehak e al. 2019a; Nan, Sansa ini 2017; Be occhi e al. 2016). Weak- nesses can be iden i ied and e oac i ely s eng hened (e.g., Public Sa e y Canada 2018; Labaka e  al. 2015). Howe e , no sui able me hod o comp ehensi ely iden- i ying elemen s o all linea , poin and a eal opological s uc u es is cu en ly a ailable (Sli ko a e al. 2018). Fo his eason, he au ho s o he a icle p opose he ICERI me hod, which was c ea ed speci ically o iden i y c i ical elemen s o oad in as uc u e. This me hod analyses he sp ead o impac s o po en- ially dis up ed oad in as uc u e elemen s in o depend- en and in luenced elemen s in he c i ical in as uc u e sys em – bo h inside and ou side he oad anspo sub-sec o (e.g., impac s on elec ici y supply, heal hca e acili ies, in eg a ed escue sys ems, se ices and indus- y). This analysis is based on p og essi ely e alua ing he pe meabili y o impac s be ween hose elemen s whose dependence o in luence has been iden i ied (Rehak, No- o ny 2016). The isk o sp ead o cascading impac s is hen e alua ed o hese elemen s h ough he in ensi y o hei links and he le el o esilience in indi idual ele- men s. This e alua ion is pe o med om a mac oscopic poin o iew, i.e., whole componen s o he sys em a e examined, ega dless o hei de ailed s uc u e. 3.1. F amewo k o he ICERI me hod ICERI using CIA is a ela i ely demanding p ocess ha equi es a clea ly de ined amewo k. This amewo k consis s o ou basic a eas: (1) elemen s o oad in a- s uc u e, (2) h ea s o oad in as uc u e elemen s, (3) dependen and in luenced c i ical in as uc u e elemen s, (4) me hodology (Figu e 2). The basic a eas o iden i ying c i ical elemen s a e in he oad in as uc u e elemen s hemsel es. These can be classi ied in o h ee basic g oups acco ding o hei opo- logical s uc u e (Sli ko a e al. 2018): (1) linea elemen s (e.g., mo o ways and oads), (2) poin elemen s (e.g., b idges and unnels), (3) a ea elemen s (e.g., bus s a ions). The c i icali y o hese elemen s can be assessed no only in he oad anspo sub-sec o bu also in o he ele an c i ical in as uc u e sub-sec o s (e.g., ail anspo , he in eg a ed escue sys em, elec ici y supply). An assessmen o cascading impac s can only be con- duc ed in ela ion o speci ic h ea s ha may cause dis- up ion o o he ailu e o oad in as uc u e elemen s (Pa man e  al. 2019). To his end, eigh basic h ea g oups we e de ined (Table 1) based on he pe il e en ypology (IRDR 2014), which is used in la ge-scale e en da abases. F om hese e en s, only hose h ea s in which he ocus was p ima ily on in as uc u e we e selec ed. As wi h classi ying h ea s ha a ec oad in as uc- u e elemen s, c i ical in as uc u e elemen s dependen on o a ec ed by oad in as uc u e elemen s also ha e o be classi ied. The i s g oup comp ises dependen ele- men s ha canno unc ion wi hou oad in as uc u e elemen s. These elemen s occu no only in he anspo sec o (e.g., mo o way dependency on a mo o way b idge o unnel) bu also in o he c i ical in as uc u e sec o s (e.g., he in eg a ed escue sys em’s dependence on oad in as uc u e). The second g oup comp ises elemen s whose unc ion may be a ec ed by he dis up ion o o ailu e o oad anspo elemen s. Again, hese elemen s no only occu in he anspo sec o (e.g., he e ec o mo o way ailu e on he su ounding oads) bu also in o he sec o s o c i ical in as uc u e (e.g., he impac o oad ailu es on heal hca e se ices o elec ici y supply). Figu e 2. F amewo k o ICERI me hod Me hods o iden i ying dependen elemen s Me hods o assessing he esilience o c i ical in as uc u e elemen s Me hods o assessing he in ensi y o links Elemen s o he oad anspo sub-sec o Elemen s o he anspo sec o Elemen s o he c i ical in as uc u e sys em Na u ogenic h ea s An h opogenic h ea s Technogenic h ea s Linea elemen s Poin elemen A eal elemen s Elemen s o oad in as uc u e Me hodology Dependen and in luenced elemen s o c i ical in as uc u e Th ea s ac ing on elemen s o oad in as uc u e Iden i ying C i ical Elemen s o Road In as uc u e (ICERI) T anspo , 2020, 35(3): 300–314 305 The mos impo an pa o he amewo k o he ICERI me hod is he me hodology o ming he s a - ing poin o p oposing he p ocedu e o applying o his me hod. The me hodology includes h ee impo an me hod g oups, which a e: – me hods sui able o iden i ying dependen and in luenced elemen s, such as e en ee analysis (IEC 62502:2010) o aul ee analysis (IEC 61025:2006), – C i ical In as uc u e Elemen s Resilience Assessmen (CIERA) me hods, such as he complex app oach o assessing c i ical in as uc u e elemen s (Rehak e al. 2019a) o he guidelines o c i ical in as uc u e esil- ience e alua ion (Be occhi e al. 2016), – me hods o iden i ying and assessing he in ensi y o links (e.g., Seppänen e al. 2018; Gonz a e al. 2016; Min e al. 2007). 3.2. P ocedu e o he ICERI me hod The abo e amewo k allows a p ocedu e o ICERI o be de ined. The s uc u e o his p ocedu e is based no only on gene al me hods (e.g., IEC 31010:2019) bu also on speci ic me hods ha assess c i ical elemen s in simila ields (e.g., Sli ko a e al. 2018; Lei ne e al. 2017; Pan e al. 2016). A p ocedu e o applying he ICERI me hod was de eloped om hese backg ound ma e ials and com- p ises eigh consecu i e s eps (Figu e 3). The s a ing poin in ICERI is delimi ing he e i o y unde e alua ion (S ep 1). Selec ing he e i o y is no limi ed by any hing, howe e , selec ing smalle e i o ial uni s is ecommended because o ime cons ain s. I a la ge e i o ial uni is e alua ed, di iding i in o se e al smalle pa s is ecommended. In his case, he occu ence o links be ween he elemen s o he indi idual pa s mus also be checked unde he e alua ion p ocedu e. This is ollowed by selec ing he oad in as uc u e ini ia o s (S ep 2) loca ed in he gi en e i o y. These a e assessed agains he speci ic, p edic ed h ea (see he ICERI amewo k). Ini ia ing elemen s a e oad in a- s uc u e elemen s ha a e subsequen ly assessed o he isk o sp eading cascading e ec s when he elemen is dis up ed o ails. The elemen s wi h he highes le el o isk a e hen designa ed as c i ical elemen s. These ele- men s can be selec ed ei he acco ding o documen a ion om he ele an au ho i ies (e.g., Minis y o T anspo o he Czech Republic) o h ough app op ia e me h- ods (e.g., Lei ne e al. 2018; D ořák e al. 2017), such as he S eng hs, Weaknesses, Oppo uni ies and Th ea s (SWOT) analysis me hod (Weih ich 1982). This me hod is ecommended and may be used o iden i y weaknesses in elemen s and any ex e nal h ea s. Mainly, he highes p i- o i y elemen s o he “a oid” s a egy should be e alua ed. The nex s ep in applying he ICERI me hod is se- lec ing elemen s ha depend on ini ia ing elemen s and any elemen s ha may be a ec ed by hei dis up ion o ailu e (S ep 3). Selec ing elemen s is conduc ed in wo s ages. In he i s s age, he sec o s o in e es and sub- sec o s o c i ical in as uc u e (e.g., elec ici y, medical acili ies o in eg a ed escue sys em) a e selec ed a he disc e ion o he e alua o . In he second s age, dependen o in luenced c i ical in as uc u e elemen s in hese sec- o s and sub-sec o s a e selec ed. Selec ing hese elemen s is based on iden i ying links be ween hese elemen s and he ini ia ing elemen s, wi h an emphasis on dependence and in luence (Rehak, No o ny 2016). Me hods sui able o iden i ying and e alua ing link in ensi ies may be used o his pu pose (e.g., Seppänen e al. 2018; Gonz a e al. 2016; Min e al. 2007). A e selec ing he ini ia ing, dependen and in luenced elemen s, a s uc u al map o cascading impac s can be c ea ed (S ep 4). Fo his pu pose, he e en ee analysis (IEC 62502:2010) me hod is sui able. This me hod is used o analyse e en s ha may lead o a po en ial acciden . In he e alua ion, he e alua o hypo hesizes “wha i ”, and in his manne sea ches o e en s ha could po en ially a ise a e an ini ia ion e en . F om his e alua ion s age, a s uc u al map o he dis ibu ion o cascading e ec s be ween elemen s can be compiled and hen quan i ied (Figu e 4). Table 1. Classi ica ion o h ea s o assessing cascading e ec s in c i ical in as uc u e sys em Na u ogenic h ea s Technogenic h ea s An h opogenic h ea s In e nal h ea s – p ocedu al- echnological pe sonnel Ex e nal h ea s me eo ological cascading cybe ne ic geological physical Figu e 3. P ocedu e o applying he ICERI me hod Delimi ing he assessed e i o y Selec ing ini ia ing elemen s o oad in as uc u e Selec ing dependen and in luenced elemen s o c i ical in as uc u e C ea ing a s uc u al map o cascading impac s De e mining he link in ensi y be ween he e alua ed elemen s De e mining he le el o esilience o e alua ed elemen s De e mining he isk le el o cascading impac s Iden i ying C i ical Elemen s o Road In as uc u e (ICERI) 1 2 3 4 5 6 7 8 S eps 306 D. Rehak e al. Iden i ying c i ical elemen s o oad in as uc u e using cascading impac assessmen Fo hose elemen s be ween which a link has been iden i ied, he in ensi y o his link is subsequen ly de e - mined (S ep 5). The in ensi y o he link is no only de e - mined be ween he ini ia ing elemen and i s dependen elemen s in he oad anspo sec o bu also be ween dependen elemen s. The link in ensi y is measu ed ac- co ding o he ollowing c i e ia: (1) ype o link, (2) s a e o link, (3) le el o link, (4) subs i u ion o link, (5) em- po al cha ac e o he link, (6) s uc u e o he link. The poin sco e alues o each c i e ia (i.e., 1– c i e ion wi h a low-le el link, 2– c i e ion wi h a mid-le el link, 3– c i e ion wi h a high-le el link) we e es ablished using he pai compa ison me hod (Da id 1988) and a e p esen ed in Table 2. The c i e ia de e mining link in ensi y di e in hei signi icance du ing e alua ion. Fo his eason, no mal- ized weigh s we e de ined o hese c i e ia (Table 3). The no malized weigh s we e de ined using he pai compa i- son me hod (Da id 1988). The inal calcula ion o link in ensi y be ween elemen s is calcula ed om a weigh ed a e age acco ding o Equa- ion (1): max 1 100 n iii i IL C w C = = ⋅⋅ ∑ , (1) whe e: IL– in ensi y o he link be ween he e alua ed ele- men s [%]; Ci– poin alue o he i- h c i e ia; n– numbe o c i e ia; wi– no malized weigh o he i- h c i e ia [%]; max i C – maximum poin alue o he i- h c i e ia. The nex s ep in he p ocedu e o ICERI is de e min- ing he le el o esilience o he elemen s unde assess- men (S ep 6). The CIERA me hod (Rehak e al. 2019a) is ecommended o his, as i pe mi s he echnical and o ganiza ional esilience o elemen s o be comp ehen- si ely assessed and hei weaknesses iden i ied in o de o s eng hen hei esilience. The a iables o esilience e alua ion can be ca ego ized in o h ee g oups acco d- ing o he esilience de e mining componen s: obus ness, eco e abili y and adap abili y (NIAC 2009). An o e iew o hese a iables is p esen ed in Table4. The poin alues o indi idual c i e ia and he p ocess o assigning hem a e desc ibed in de ail in he CIERA me hod (Rehak e al. 2019a). The inal calcula ion o e- silience le el o he elemen s is calcula ed acco ding o Equa ion(2): 1 11 11 n nm j kk j jk RE K V w nn = = = =⋅=⋅ ⋅ ∑ ∑∑ , (2) whe e: RE– c i ical in as uc u e elemen esilience [%]; Kj– j- h c i ical in as uc u e elemen esilience com- ponen [%]; n– o al numbe o esilience de e mining componen s; Vk– he k- h c i ical in as uc u e elemen esilience a iable [%]; wk– k- h no malized weigh o he k- h a iable esilience o he c i ical in as uc u e ele- men 0; 1   ; m– o al numbe o a iables in he j- h componen . F om he link in ensi y assessmen and elemen esil- ience le els, he isk le el o he sp ead o cascading im- pac s can hen be de e mined (S ep 7). This isk is always assessed sepa a ely in each pai o elemen s. The assess- men ’s s a ing poin is he gene al ela ionship whe e he Figu e 4. Gene al depic ion o a s uc u al map o he sp ead o cascading impac s Dependen elemen o he in eg a ed escue sys em In luenced elemen o he elec ici y supply Ini ia o elemen 1 o he oad in as uc u e Dependen elemen 1 o he oad in as uc u e In luenced elemen o he oad in as uc u e P esump i e h ea Dependen elemen 2 o he oad in as uc u e In luenced elemen o he chemical indus y Ini ia o elemen 2 o he oad in as uc u e Table 2. Poin alues o he c i e ia de e mining link in ensi y C i e ia de e mining link in ensi y CiPoin alue Type o link (Rinaldi e al. 2001) physical link 3 geospa ial link 2 cybe ne ic link 2 logical link 1 S a e o link (Rehak and No o ny 2016) mu ual dependence 3 dependence 2 in luence 1 Le el o link (Rehak e al. 2016) sys em link 3 sec o link 2 sub-sec o link 1 Subs i u ion o link no subs i u e link exis s 3 only one subs i u e link exis s 2 wo o mo e subs i u e links exis 1 Tempo al cha ac e is ic link unin e up ed 3 pe iodic 2 s and-by 1 S uc u e o link di ec 3 indi ec ac oss one node 2 indi ec ac oss wo o mo e nodes 1 T anspo , 2020, 35(3): 300–314 307 isk is exp essed by a combina ion o he p obabili y o occu ence o an undesi able e en and i s impac le el (IEC 31010:2019). The p obabili y o occu ence o cas- cading impac s, in his case, is de e mined by he link in- ensi y IL. The cascading impac le el is de e mined by he esilience o he e alua ed elemen s RE. Highe esilience means ad e se impac s a e minimized because he ulne - abili y o hese elemen s, which acili a es he sp ead o cascading impac s, is also minimized. F om he abo e, Equa ion (3) was de i ed o calcula e he isk o a cascading impac sp eading du ing dis up ion o o ailu e o oad in as uc u e elemen s: 3 IE DE R V V IL= ⋅ ⋅= ( ) ( ) 311 IE DE RE RE IL− ⋅− ⋅ , (3) whe e: R– le el o isk o a sp eading cascading impac [%]; VIE– ulne abili y o he in luencing elemen [%]; VDE– ulne abili y o he dependen elemen [%]; REIE– le el o esilience o he in luencing elemen [%]; REDE– le el o esilience o he dependen elemen [%]; IL– link in en- si y be ween he in luencing and dependen elemen [%]. The inal s ep in he applying he ICERI me hod is iden i ying he c i ical elemen s o oad in as uc u e (S ep 8). This is done using he esul s om he isk le el assessmen o cascading e ec s sp eading be ween ele- men s. These alues a e included in he s uc u al map and hen compa ed wi h e e ence alues in o de o ca - ego ize he le el o sp ead o cascading impac s (Table 5). The ca ego iza ion o cascading e ec le els and e e - ence alues is philosophically based on he ailu e mode, e ec s and c i icali y analysis (IEC 60812:2006). This me hod uses mul iple a iables o de e mine isk le el and is based on a ia ions in ex eme alues when e alu- a ing s a es. Indi idual le els o c i icali y ha ac o in ex eme alue a ia ion in he ou -s age e alua ion scale we e de e mined in a manne simila o he me hod o assessing he c i icali y o ailway in as uc u e elemen s (Sli ko á 2018): – 1,1,1,4=> ⌀ 1.75=> 43.7%; – 1,1,4,4=> ⌀ 2.50=> 62.5%; – 1,4,4,4=> ⌀ 3.25=> 81.3%; – 4,4,4,4=> ⌀ 4.00=> 100%. The inal iden i ica ion o c i ical elemen s o oad in- as uc u e is achie ed using he e e ence alues o ca e- go izing hele el o sp ead o cascading impac s (Table 5). Elemen s demons a ing a c i ical isk le el (i.e., Ca ego- y I) be ween each o he a e subsequen ly designa ed as c i ical. Weaknesses should be iden i ied in hese elemen s and adequa e sa e y measu es hen in oduced in o de o educe link in ensi y and inc ease esilience (e.g., Š olle e al. 2018; Klein, Hu e 2017; Labaka e al. 2015; H o- mada, Lukas 2012). A en ion should also be gi en o ele- men s demons a ing a high le el o isk (i.e., Ca ego y II) be ween each o he . In all o he elemen s, signi ican p o- li e a ion o cascading impac s is no o eseen. Table 4. Va iables de e mining he esilience o c i ical in as uc u e elemen s (Rehak e al. 2019a) Resilience componen s o c i ical in as uc u e elemen s Ki Va iables o assessing esilience Vj Robus ness c isis p epa edness edundancy de ec ion abili y esponsi eness physical esilience Reco e abili y ma e ial esou ces inancial esou ces human esou ces eco e y p ocess Adap abili y isk managemen inno a ion p ocesses educa ional and de elopmen p ocesses Table 3. No malized weigh s o c i e ia de e mining link in ensi y C i e ia Type o link S a e o link Le el o link Subs i u ion o link Tempo al cha ac e o link S uc u e o link S Weigh coe icien s 29% 24% 19% 14% 10% 4% 100% Table 5. Re e ence alues o ca ego izing he le el o sp ead o cascading impac s In e al Risk le el o sp eading Desc ip ion ( 81;100 Ca ego y I C i ical isk le el o he sp ead o cascading impac s. The esul o such cascading impac s may be he ailu e o a dependen elemen ( 62; 81 Ca ego y II High- isk le el o he sp ead o cascading impac s. The esul o such cascading impac s may be signi ican dis up ion o he unc ioning o a dependen elemen ( 43; 62 Ca ego y III Accep able isk le el o he sp ead o cascading impac s. The esul o such cascading impac s may be pa ial dis up ion o o limi ed unc ioning o a dependen elemen 0; 43 Ca ego y IV Low isk le el o he sp ead o cascading impac s. This ype o cascading impac will no esul in dis up ion o o limi ed unc ioning o a dependen elemen 308 D. Rehak e al. Iden i ying c i ical elemen s o oad in as uc u e using cascading impac assessmen 4. Case s udies in applying he ICERI me hod The p ac ical applica ion o he ICERI me hod is p esen - ed as a case s udy o demons a e he sequen ial e alua- ion o selec ed elemen s in eigh consecu i e s eps (see below). The esul s ob ained we e subsequen ly discussed wi h s akeholde s (i.e., Minis y o T anspo o he Czech Republic, Czech Road and Mo o way Di ec o a e, Czech Railway and T a ic Rou e Adminis a ion, Regional Au- ho i y o he Mo a ian–Silesian Region, Eme gency Med- ical Se ice o he Mo a ian–Silesian Region). The au hen- ici y and p edic i e alue o he esul s we e con i med. S ep 1: Delimi ing he assessed e i o y. The s a ing poin in ICERI is delimi ing he e i o y unde assess- men . In o de o es he ICERI me hod, he sou h-wes - e n pa o he ci y o Os a a was selec ed. Asigni ican numbe o impo an elemen s o anspo in as uc u e a e ound in his ci y. Os a a is loca ed in he no heas - e n pa o he Czech Republic and is an impo an oad and ail anspo hub o Slo akia and Poland. S ep 2: Selec ing ini ia ing elemen s o oad in a- s uc u e. The nex s ep in ol ed selec ing he oad in- as uc u e ini ia o s loca ed in he gi en e i o y. These we e assessed agains he speci ic, p edic ed h ea (see ICERI amewo k). Because o he case s udy’s scale, only one oad in as uc u e elemen was selec ed, namely he in e change o he D1 Mo o way and Exp essway 11 (Fig- u e5). This ini ia o elemen was selec ed using he as- sessmen o c i ical in as uc u e elemen s in anspo me hod (D ořák e al. 2017). The po en ial isk o his elemen collapsing due o he use o inapp op ia e back- g ound ma e ials (RSD 2012) was conside ed. Fo his ea- son, he ini ia o was e alua ed in e ms o he isk c ea ed by poo echnical condi ion. S ep 3: Selec ing dependen and in luenced elemen s o c i ical in as uc u e. The nex s ep in applying he ICERI me hod was selec ing elemen s ha may be ad- e sely a ec ed by dis up ion o o ailu e o he ini ia o elemen . Selec ing hese elemen s was conduc ed in wo s ages. In he i s s age, he ele an c i ical in as uc u e sub-sec o s we e selec ed, speci ically oad anspo , ail anspo and he in eg a ed escue sys em. In he second s age, he dependen and in luenced elemen s o c i ical in as uc u e in hese sub-sec o s we e selec ed. These elemen s we e iden i ied om he links be ween hese el- emen s and he ini ia ing elemen , wi h an emphasis on dependence and in luence (Rehak, No o ny 2016). F om his, a o al o ou elemen s we e selec ed, which a e shown in Figu e 5. Two dependen elemen s and wo in luenced elemen s we e iden i ied om he abo e map backg ound. Exp ess- way 11 and he in eg a ed escue sys em (speci ically he eme gency medical se ices) a e elemen s dependen on he lyo e in e sec ion. The exp essway acili a es ans- po a ion o pa ien s om he Os a a–Jih and Zábřeh dis- ic s o he hospi al in Po uba (see op le ). I he unc- ioning o he lyo e in e sec ion ails (in he con ex o he selec ed h ea , his would be he s uc u e collapsing), a ic on he D1 Mo o way and he high-speed ailway co ido would be a ec ed. S ep 4: C ea ing a s uc u al map o cascading im- pac s. Based on he selec ed ini ia o and dependen and in luenced elemen s, a s uc u al map o he cascading im- pac s was c ea ed (Figu e6). Fo his pu pose, he e en ee analysis me hod (IEC 62502:2010) was used in o de o analyse e en s ha may lead o a po en ial acciden . S ep 5: De e mining he link in ensi y be ween he e alua ed elemen s. The in ensi y o he links be ween elemen s sha ing a link was hen measu ed. In ensi y was e alua ed acco ding o he de e mining c i e ia (Table 2) and hen calcula ed acco ding o Equa ion (1). The esul - ing alues o link in ensi y be ween indi idual co ela ed elemen s a e p esen ed in Table 6. Figu e 5. The selec ed elemen s plo ed on a map backg ound ini ia o elemen dependen elemen o oad in as uc u e in luenced elemen o oad in as uc u e in luenced elemen o ailway in as uc u e dependen elemen o in eg a ed escue sys em