PSI - Issue 30

Dmitry O. Reznikov et al. / Procedia Structural Integrity 30 (2020) 128–135 Dmitry O. Reznikov/ Structural Integrity Procedia 00 (2020) 000–000

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cascading failures, which occur after local failure of their individual components, as shown by Baker (2008), Starossek and Haberland (2010), Makhutov and Reznikov (2015), Doronin (2019). These systems as a rule are subjected to multiple regimes of loading and multiple failure scenarios. Owing to the high level of uncertainty concerning the governing parameters of CTSs, environmental conditions, and external impacts, the estimation of system performance should be made in a probabilistic formulation. Their evolution should be described by multivariate scenario trees that include scenarios of accidents and catastrophes. In the view that the processes of damage accumulation and failure develop at various scale levels these scenario trees should be multi-level, as pointed by Makhutov and Reznikov (2016), Makhutov (2014), Reznikov (2018).

Nomenclature C

Consequences expected value designed end state survival end state damaged end state

E (•) ES 0 ES δ ES i ES i , F

( s )

( s ) denotes failed end state of the system { ES ( e ) } vector of the end states of the system’s environment { ES ( s ) } vector of the end states of the system IS initial state { L } vector of loading regimes LD local damage at the component level MD material damage at the component level L load F failure R risk R dir direct risk R ind indirect risk S 0 success scenario s i ( m ) scenario of damage accumulation at the material level s i ( c ) component damage scenario S F (s) survival structural scenario S i ( δ ) the survival structural scenario T threat U loss { U dir } vector of direct losses in the system { U ( e ) } vector of indirect losses that in the environment V Vulnerability

[ V Mat ] matrix of the material vulnerability [ V Comp ] matrix of the component vulnerability [ V Str ] matrix of the structural vulnerability [ V Sys ] matrix of the system vulnerability δ survival region

It should be also noted that CTSs are usually closely interrelated with other engineering facilities that are hereafter referred to as CTS environment. Damage or failure of the CTS may trigger secondary and cascading failures in its environment. Thus, a general probabilistic approach is needed that would allow: (i) describing the process of accident initiation and propagation at four scale levels: the level of structural material, the level of system components, the systemic level and the upper level of the system environment, and (ii) developing risk assessment framework. The approach should provide the opportunity to assess not only the so-called direct risks that