**2. Methodology**

a vulnerability analysis to an electric power system. Moreover, Johansson et al. [32] proposed a model that could be useful in the framework of vulnerability analyses of interdependent infrastructures that are described by both a network model (based on the graph theory) and a functional model. Stergiopoulos et al. [33] explored the interdependencies among CIs that cause cascading effects in the case of failure. For this purpose, the authors started from the dependency risk methodology proposed by Kotzanikolaou et al. [34, 35] and introduced graph centrality metrics in order to identify the nodes that mainly affect the risk paths and that can thus be controlled in order to improve risk mitigation. Furthermore, Stergiopoulos et al. [36] extended the studies performed by Kotzanikolaou et al. [34, 35, 37] by considering the time evolution of each dependency (using fuzzy models) and the concurrent commoncause cascading failures, developing a supporting tool for decision making (named CIDA, i.e. Critical Infrastructure Dependency Analysis). This tool can be useful in assessing the CI's resilience under different scenarios and the effectiveness of possible mitigation actions. Fu et al. [38] also focused on the opportunity of treating infrastructure networks as interdependent system-of-systems, while Utne et al. [39] proposed a methodological approach to model the interdependencies among CIs built starting from the use of relatively simple cascade diagrams. Furthermore, the JRC developed the Geospatial Risk and Resilience Assessment Platform (GRRASP), a graphical tool for analysing network systems that can be adopted to identify the critical elements of the network and to evaluate the cascading effects of CI disruptions, taking into account cross-sectoral and cross-border interdependencies [40]. Finally, with reference to the impact analysis of different threats on CIs, specific models have been developed in order to assess the physical security and the resilience of CIs themselves against single kinds of hazards. In particular, Khalil et al. [41] focused on the modelling of physical security of CIs under attack scenarios by using a Monte Carlo-based probabilistic dynamic approach. Urlainis et al. [42] implemented instead a supporting tool for decision making suitable to evaluate the risk related to oil & gas critical infrastructures after the occurrence of a seismic event. This tool adopts fault-trees, decision trees and fragility curves and allows the identification of the most critical sections of the analysed system based on the damage state of its components. Shakou et al. [43] proposed a framework for increasing the resilience of CIs with respect to climate change phenomena, based on different timescales and promoting flexibility, modularisation and diversification. In comparison with the mentioned studies available in the scientific literature, the new methodological approach proposed in this paper mainly focuses on single large infrastructures (like energy corridors for oil and gas supply) and aims at taking into account their geographical dimension, allowing analyses characterised by a high spatial granularity. Furthermore, the proposed procedure is able to consider the most relevant interdependencies among the parameters that could impact on the criticality of an infrastructure with a simple mathematical formulation. Therefore, this work aims at being a supporting tool not only for infrastructures

*Issues on Risk Analysis for Critical Infrastructure Protection*

management companies and for the civil protection but also for public

The paper considers the energy CIs: according to the 2008 EU Directive, this category includes facilities and infrastructures for power generation and transmission, for oil and gas production, treatment, storage and transmission and LNG terminals [7]. In particular, it focuses on the energy corridors (oil and gas pipelines,

Its goal is to define a methodology for the evaluation of a criticality index, related to the failure of an energy infrastructure due to extreme natural hazards like earthquakes, floods, storms, landslides and wildfires. This criticality index is useful to assess the criticality level of each section of the infrastructure itself (taking into

administrations.

power lines).

**40**

The proposed approach starts from the concept of energy corridor. A corridor can be defined as an extensive infrastructure (like natural gas and oil pipelines and large power lines), characterised by a start point and an end point, that links production/refining facilities with distribution hubs. Energy corridors are usually strategic elements for the economy of the countries that are connected to them, and their influence spreads over a large area not limited to the geographical neighbourhood of the infrastructure. In a future world that is expected to be increasingly interconnected with large scale energy markets, the role of energy corridors could become crucial: the diversification of the sources and the possibility to ensure the functionality of the infrastructures could significantly impact on the security of energy supply and on the economic systems of several countries, especially those characterised by a high level of energy import dependency.

For these reasons, the quantitative evaluation of the resilience of the energy corridors against possible adverse events through the numerical estimation of their criticality level and the simultaneous identification of suitable criteria for risk acceptability are essential in order to identify the sections that require attention and investments for preventing potentially severe failures which could impact on the GDP (Gross Domestic Product) with losses at different scales.

According to the methodology described in the following sections, a set of parameters influencing the criticality status of the corridor and their interdependencies have been firstly defined (Section 2.1). A relationship linking these parameters has then been built to define a new Criticality Index (Section 2.2). A criterion for the risk acceptability (Section 2.3) and the application of the whole procedure to a simplified case study have been eventually discussed (Section 3).

#### **2.1 Identification of the parameters and their interdependencies**

The proposed methodology focuses on the quantitative assessment of the criticality of a single section of an energy corridor under an all-hazard perspective, i.e. with respect to all the possible extreme natural events.

For this purpose, the first step has been represented by the definition of a set of parameters that could affect the criticality level of an energy infrastructure, by their clustering into different groups and by the analysis of their interdependencies. Moreover, in order to take into account the spatial dimension of the energy corridors, the possible dependency of each parameter on the geographical position *zc* (ranging between 0 and the corridor length *lc* and measured in km) along the corridor itself has been explored. In fact, an infrastructure like a pipeline can typically run over long lengths and the natural environment surrounding it could significantly change along the route: consequently, certain natural hazards could be considered only for a limited set of branches and not for the overall length of the corridor. Eventually, the effects of a variation in the value of each parameter on the damage have been estimated. In particular, in this study 15 parameters and 4 groups ("Event related", "Corridor related", "Backup sources related" and "Users related") have been considered: the parameters taken into account are listed in **Table 1** and the dependency matrix is shown in **Table 2**. The interdependencies are identified assuming as increasing the value of each independent parameter and reporting the effect on the dependent parameter (decreasing or increasing when the independent parameter increases). The table reports also the effect of each parameter on damage.

Referring to Group 1, the seasonality *s* – that represents the variability of the considered natural event across the year – is the parameter that mainly affects the other ones. The probability *p* that the natural event could have an impact not only on the analysed corridor but also on other infrastructures supplying the same commodity (backup sources) is strictly related to the magnitude of the event itself and on the geographical context: it depends on the distance between the corridor (or corridor branch) and the considered backup source and on the potential damage area for the considered event, quantified through the damage distance *λ*. All the facilities located at a distance lower than or equal to *λ* are certainly involved by the event to such a degree that their functionality is lost.

In general, an increase in all the parameters related to the corridor (Group 2) causes an increase in the potential damage. It has to be highlighted that *RT* – which includes not only the time needed to repair the infrastructure but also the time for reaching the damaged section of the corridor and the time to get the requested spare parts – depends not only on the season but also on the temporal and spatial scale of


the event: the greater the geographical extension of the natural event and its dura-

As it can be reasonably expected, an increase in the parameters related to the availability of backup sources causes a decrease in the damage. It can be underlined that the average distance between the backup sources provides information about the probability that a backup source could be involved in the considered extreme event: in fact, the higher the value of this parameter, the lower the probability. The availability of these sources depends not only on the seasonality, but also indirectly on the distance between the corridor and the source: in particular, it increases if the

Considering Group 4, the parameters are related with the reference market: in case of a possible corridor failure, the market operator could decide a supply interruption for some selected users, in order to reduce the load of the considered infrastructure; the interruptible capacity could depend on the season. The energy intensity *e* (i.e. the amount of energy needed to produce a unit of GDP), instead, gives a measure of the importance of the commodity delivered by the considered corridor, allowing to quantify the economic damage deriving from the supply lost as

It can be highlighted that the event related parameters can be evaluated on the

basis of geological surveys and studies on natural hazards with respect to the specific site analysed. Among them, the probability of involving more facilities needs *ad hoc* formulations and cannot be generically expressed by means of a single mathematical relationship (as further discussed in Section 2.2). The majority of the corridor related and the backup sources related parameters are instead technical

tion, the longer the time needed to reach the damaged section.

*e* Energy intensity X

**Parameter Description Dependency on the**

*λ* Damage distance X

*lc* Corridor length X X

*db* Distance source-corridor X X

*τ* Event time scale X *s s*

*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors*

*cp,c* Corridor peak capacity X *s s RT* Repair time X X *τ*, *s s*

*cp,b* Source peak capacity X *s s rm,b* Minimum reserve of the source X *s s α<sup>b</sup>* Availability of the source X X *s*, *db λ*, *s αtec* Technical availability X *s s i* Interruptible capacity X *s s α<sup>i</sup>* Availability of *i* X *s s*

*p* Probability to involve more

*DOI: http://dx.doi.org/10.5772/intechopen.94755*

*s* Season

*Interdependencies and effects on damage.*

**Table 2.**

**43**

facilities

**position** *zc*

**Effects on damage**

X X *λ db*

**↑↓ ↑**

**with**

**Interdependencies**

> **↓ with**

source is far from the epicentre of the event.

a consequence of an extreme event.

**Table 1.** *Considered parameters by group.*


*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors DOI: http://dx.doi.org/10.5772/intechopen.94755*

#### **Table 2.**

("Event related", "Corridor related", "Backup sources related" and "Users related") have been considered: the parameters taken into account are listed in **Table 1** and the dependency matrix is shown in **Table 2**. The interdependencies are identified assuming as increasing the value of each independent parameter and reporting the effect on the dependent parameter (decreasing or increasing when the independent parameter increases). The table reports also the effect of each

Referring to Group 1, the seasonality *s* – that represents the variability of the considered natural event across the year – is the parameter that mainly affects the other ones. The probability *p* that the natural event could have an impact not only on the analysed corridor but also on other infrastructures supplying the same commodity (backup sources) is strictly related to the magnitude of the event itself and on the geographical context: it depends on the distance between the corridor (or corridor branch) and the considered backup source and on the potential damage area for the considered event, quantified through the damage distance *λ*. All the facilities located at a distance lower than or equal to *λ* are certainly involved by the

In general, an increase in all the parameters related to the corridor (Group 2) causes an increase in the potential damage. It has to be highlighted that *RT* – which includes not only the time needed to repair the infrastructure but also the time for reaching the damaged section of the corridor and the time to get the requested spare parts – depends not only on the season but also on the temporal and spatial scale of

**Group Parameter Description Unit**

the event)

*p* Probability to involve more than a single facility *λ* Damage distance (measure of the potential damage area of

*τ* Time scale of the event (measure of its duration) s *s* Seasonal factor (influence of the season on the event) —

*lc* Length of the corridor km *cp,c* Peak capacity of the corridor GJ/s *RT* Repair time s

*db* Distance between a single source and the corridor km *cp,b* Peak capacity of the source GJ/s *rm,b* Minimum available reserves for the single source GJ *α<sup>b</sup>* Availability of the source *αtec* Technical availability of the source —

*i* Interruptible capacity GJ/s *α<sup>i</sup>* Availability of interruptible capacity *e* Energy intensity for the considered commodity €/GJ

km

event to such a degree that their functionality is lost.

*Issues on Risk Analysis for Critical Infrastructure Protection*

parameter on damage.

1. Event related

2. Corridor related

3. Backup sources related

4. Users related

*Considered parameters by group.*

**Table 1.**

**42**

*Interdependencies and effects on damage.*

the event: the greater the geographical extension of the natural event and its duration, the longer the time needed to reach the damaged section.

As it can be reasonably expected, an increase in the parameters related to the availability of backup sources causes a decrease in the damage. It can be underlined that the average distance between the backup sources provides information about the probability that a backup source could be involved in the considered extreme event: in fact, the higher the value of this parameter, the lower the probability. The availability of these sources depends not only on the seasonality, but also indirectly on the distance between the corridor and the source: in particular, it increases if the source is far from the epicentre of the event.

Considering Group 4, the parameters are related with the reference market: in case of a possible corridor failure, the market operator could decide a supply interruption for some selected users, in order to reduce the load of the considered infrastructure; the interruptible capacity could depend on the season. The energy intensity *e* (i.e. the amount of energy needed to produce a unit of GDP), instead, gives a measure of the importance of the commodity delivered by the considered corridor, allowing to quantify the economic damage deriving from the supply lost as a consequence of an extreme event.

It can be highlighted that the event related parameters can be evaluated on the basis of geological surveys and studies on natural hazards with respect to the specific site analysed. Among them, the probability of involving more facilities needs *ad hoc* formulations and cannot be generically expressed by means of a single mathematical relationship (as further discussed in Section 2.2). The majority of the corridor related and the backup sources related parameters are instead technical

data that are usually available for the specific infrastructures considered. Only the repair time should be estimated by means of suitable databases or specific investigations (Maintainability Analyses). Eventually, referring to the users related parameters, the interruptible capacity is an information that should be known as depending on already signed contracts and agreements, while the energy intensity for the commodity carried by the corridor can be obtained from statistical sources. by several relationships or by more complex considerations that do not allow a simple mathematical formulation according to the different classes of natural events. For example, in the case of a river flood, *p* is a function not only of the distance between the corridor and the facility but also of the distance between the river and the facility. Furthermore, *p* is equal to 0 if the considered facility is outside the boundaries of the natural hazard, regardless of the distance between the source and the corridor. A possible relationship that can be adopted for some classes of events, like earthquakes, is the one expressed in Eq. (4) where the possible involved facilities are supposed to be the backup sources *b*. If the distance between the backup source and the corridor *db* is lower than the damage distance *λ*, the facility is assumed to be certainly involved by the event. If the distance *db* is higher than *λ* (i.e. the facility is located outside the potential damage area) the probability that the facility is involved by the event decreases in a proportional way with the

*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors*

*λ db*ð Þ *zc*

8 ><

>:

*db*ð Þ *zc* ≥*λ*

*Tb*ð Þ*s RT s*, *zc* ð Þ , *τ* � � <sup>&</sup>gt;<sup>0</sup> (4)

(5)

1 *db*ð Þ *zc* <*λ*

*αb*ð Þ� *s*, *p cp*,*<sup>b</sup>*ðÞ� *s*

For this reason, the proposed relationship for defining the criticality index *CI* as

<sup>1</sup> <sup>þ</sup> *D s*, *<sup>p</sup>*, *zc* <sup>½</sup> ð Þ , *<sup>τ</sup>* � � <sup>1</sup> <sup>þ</sup> *<sup>e</sup>*�*D s*,*p*,*zc* ð Þ ,*<sup>τ</sup>* � � � <sup>1</sup> *D s*, *<sup>p</sup>*, *zc* ð Þ , *<sup>τ</sup>* <sup>≥</sup><sup>0</sup>

In this case, *CI* does not correspond to an economic value of the damage caused by the considered event (like *D*), but it allows to associate a numerical value also to the corridor sections that are not strictly critical (i.e. those for which *D* is negative) thus measuring their "proximity" to a real potential damage and ranking them according to a criticality perspective, as the safety margins progressively reduce

As it can be noticed, the *CI* relationship is built in order to have lim *<sup>D</sup>*!<sup>∞</sup>*CI* ¼ *D* and *CI* = 1 for *D* = 0 (i.e., when the infrastructure status changes from "non-critical"

A graphical representation of *CI* as a function of *D* can be observed in **Figure 1**.

In the scientific literature, few studies are available to identify risk acceptability

criteria for the socio-economic risk, and the differences among the economic

<sup>1</sup> � *D s*, *<sup>p</sup>*, *zc* ð Þ , *<sup>τ</sup> D s*, *<sup>p</sup>*, *zc* ð Þ , *<sup>τ</sup>* <sup>&</sup>lt;<sup>0</sup>

as, from the risk analysis point of view, the damage *D* has to be positively defined. A negative value of *D* means that the corresponding corridor section is not critical: negative values of this term could be obtained, for instance, in the case that no other facilities are involved by the natural event and the loss of corridor capacity

*p z*ð Þ¼ *<sup>c</sup>*

Moreover, it has to be highlighted that Eq. (1) is defined if

*b*

a function of the socio-economic damage is the one reported in Eq. (5):

1

*cp*,*<sup>c</sup>*ð Þ�*<sup>s</sup> <sup>α</sup>i*ðÞ� *<sup>s</sup> i s*ð Þ�<sup>X</sup>

is completely supplied by backup sources.

*DOI: http://dx.doi.org/10.5772/intechopen.94755*

when a negative value of *D* approximates to 0.

**2.3 Criteria for risk acceptability**

*CI* ¼

to "critical").

**45**

8 ><

>:

increase of *db*.

Furthermore, for the proposed method, the corridor can be assumed as onedimensional, i.e. only characterised by the running coordinate *zc*. This is because only the position along the corridor, the distance between the backup sources with respect to the corridor and the distance between the epicentre of the considered natural hazard and the corridor itself are relevant for the analysis.

#### **2.2 Definition of the criticality index**

Starting from the parameters and interdependencies identified in Section 2.1, in order to define a criticality index able to quantify the criticality of a single branch/ corridor, a relationship expressing the socio-economic damage *D* due to a certain extreme natural hazard has been defined (Eq. (1)). It expresses the damage *D* in the section of the branch/corridor identified by the coordinate *zc* (running over the corridor length, from 0 to *lc*).

$$D(s, p, z\_c, \tau) = \left\{ RT(s, \mathbf{z}\_c, \tau) \cdot \left[ c\_{p, \epsilon}(s) - a\_i(s) \cdot i(s) - \sum\_b a\_b(s, p) \cdot c\_{p, b}(s) \cdot \left( \frac{T\_b}{RT(s, \mathbf{z}\_c, \tau)} \right) \right] \cdot \frac{1}{e} \right\} \tag{1}$$

where:

$$\begin{cases} T\_b = T\_b(\varsigma, \mathbf{z}\_c, \tau) = RT(\varsigma, \mathbf{z}\_c, \tau) & RT(\varsigma, \mathbf{z}\_c, \tau) \le \frac{r\_{m,b}}{c\_{p,b}} \\ \\ T\_b = T\_b(\varsigma) = \frac{r\_{m,b}(\varsigma)}{c\_{p,b}(\varsigma)} & RT(\varsigma, \mathbf{z}\_c, \tau) > \frac{r\_{m,b}}{c\_{p,b}} \end{cases} \tag{2}$$
 
$$a\_b(\varsigma, p) = a\_{\text{loc}}(\varsigma) \cdot [1 - p(\mathbf{z}\_c)] \tag{3}$$

Eq. (1) defines the economic value of the share of the commodity carried by corridor *c* over the emergency time period (identified by *RT*) that cannot be directly delivered notwithstanding the contribution of interruptible users and the availability of backup sources. In fact, focusing on the square bracket in the equation:


Referring to the probability that the event could involve other facilities (in particular, the backup sources) than the considered corridor, this can be expressed *Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors DOI: http://dx.doi.org/10.5772/intechopen.94755*

by several relationships or by more complex considerations that do not allow a simple mathematical formulation according to the different classes of natural events. For example, in the case of a river flood, *p* is a function not only of the distance between the corridor and the facility but also of the distance between the river and the facility. Furthermore, *p* is equal to 0 if the considered facility is outside the boundaries of the natural hazard, regardless of the distance between the source and the corridor. A possible relationship that can be adopted for some classes of events, like earthquakes, is the one expressed in Eq. (4) where the possible involved facilities are supposed to be the backup sources *b*. If the distance between the backup source and the corridor *db* is lower than the damage distance *λ*, the facility is assumed to be certainly involved by the event. If the distance *db* is higher than *λ* (i.e. the facility is located outside the potential damage area) the probability that the facility is involved by the event decreases in a proportional way with the increase of *db*.

$$p(\mathbf{z}\_c) = \begin{cases} \frac{\lambda}{d\_b(\mathbf{z}\_c)} & d\_b(\mathbf{z}\_c) \ge \lambda \\\\ 1 & d\_b(\mathbf{z}\_c) < \lambda \end{cases} \tag{4}$$

Moreover, it has to be highlighted that Eq. (1) is defined if

$$a\_{p, \epsilon}(s) - a\_i(s) \cdot i(s) - \sum\_b a\_b(s, p) \cdot c\_{p, b}(s) \cdot \left(\frac{T\_b(s)}{RT(s, z\_\epsilon, \tau)}\right) > 0$$

as, from the risk analysis point of view, the damage *D* has to be positively defined. A negative value of *D* means that the corresponding corridor section is not critical: negative values of this term could be obtained, for instance, in the case that no other facilities are involved by the natural event and the loss of corridor capacity is completely supplied by backup sources.

For this reason, the proposed relationship for defining the criticality index *CI* as a function of the socio-economic damage is the one reported in Eq. (5):

$$CI = \begin{cases} \left[1 + D(\mathfrak{s}, p, \mathfrak{z}\_{\mathfrak{c}}, \mathfrak{r})\right] \cdot \left[1 + e^{-D(\mathfrak{s}, p, \mathfrak{z}\_{\mathfrak{c}}, \mathfrak{r})}\right] - 1 & D(\mathfrak{s}, p, \mathfrak{z}\_{\mathfrak{c}}, \mathfrak{r}) \ge 0 \\\\ \frac{1}{1 - D(\mathfrak{s}, p, \mathfrak{z}\_{\mathfrak{c}}, \mathfrak{r})} & D(\mathfrak{s}, p, \mathfrak{z}\_{\mathfrak{c}}, \mathfrak{r}) < 0 \end{cases} \tag{5}$$

In this case, *CI* does not correspond to an economic value of the damage caused by the considered event (like *D*), but it allows to associate a numerical value also to the corridor sections that are not strictly critical (i.e. those for which *D* is negative) thus measuring their "proximity" to a real potential damage and ranking them according to a criticality perspective, as the safety margins progressively reduce when a negative value of *D* approximates to 0.

As it can be noticed, the *CI* relationship is built in order to have lim *<sup>D</sup>*!<sup>∞</sup>*CI* ¼ *D* and *CI* = 1 for *D* = 0 (i.e., when the infrastructure status changes from "non-critical" to "critical").

A graphical representation of *CI* as a function of *D* can be observed in **Figure 1**.

#### **2.3 Criteria for risk acceptability**

In the scientific literature, few studies are available to identify risk acceptability criteria for the socio-economic risk, and the differences among the economic

data that are usually available for the specific infrastructures considered. Only the repair time should be estimated by means of suitable databases or specific investigations (Maintainability Analyses). Eventually, referring to the users related parameters, the interruptible capacity is an information that should be known as depending on already signed contracts and agreements, while the energy intensity for the commodity carried by the corridor can be obtained from statistical sources. Furthermore, for the proposed method, the corridor can be assumed as onedimensional, i.e. only characterised by the running coordinate *zc*. This is because only the position along the corridor, the distance between the backup sources with respect to the corridor and the distance between the epicentre of the considered

Starting from the parameters and interdependencies identified in Section 2.1, in order to define a criticality index able to quantify the criticality of a single branch/ corridor, a relationship expressing the socio-economic damage *D* due to a certain extreme natural hazard has been defined (Eq. (1)). It expresses the damage *D* in the section of the branch/corridor identified by the coordinate *zc* (running over the

*Tb* ¼ *Tb s*, *zc* ð Þ¼ , *τ RT s*, *zc* ð Þ , *τ RT s*, *zc* ð Þ , *τ* ≤

*rm*,*<sup>b</sup>*ð Þ*s cp*,*<sup>b</sup>*ð Þ*s*

Eq. (1) defines the economic value of the share of the commodity carried by corridor *c* over the emergency time period (identified by *RT*) that cannot be directly delivered notwithstanding the contribution of interruptible users and the availability of backup sources. In fact, focusing on the square bracket in the equation:

• the term *cp,c* identifies the maximum amount of commodity that can be delivered per second in season *s* and that is lost due to the failure; as a consequence, the product between *cp,c* and *RT* defines the amount of energy unavailable during the

• the product between *αi*, *i* and *RT* defines the part of this supply that can be avoided during the emergency due to the fact that some users are interruptible

• the product between *αb*, *cp,b* and *Tb* corresponds to the amount of energy commodity that can be certainly supplied by the backup sources during the

Referring to the probability that the event could involve other facilities (in particular, the backup sources) than the considered corridor, this can be expressed

repair time after the adverse event that caused the corridor failure

*b*

( )

" # � �

*RT s*, *zc* ð Þ , *τ* >

*αb*ð Þ¼ *s*, *p αtec*ð Þ� *s* 1 � *p z*ð Þ*<sup>c</sup>* ½ � (3)

*<sup>α</sup>b*ð Þ� *<sup>s</sup>*, *<sup>p</sup> cp*,*<sup>b</sup>*ðÞ� *<sup>s</sup> Tb*

*rm*,*<sup>b</sup> cp*,*<sup>b</sup>*

*rm*,*<sup>b</sup> cp*,*<sup>b</sup>*

*RT s*, *zc* ð Þ , *τ*

� 1 *e*

(1)

(2)

natural hazard and the corridor itself are relevant for the analysis.

**2.2 Definition of the criticality index**

*D s*ð Þ¼ , *<sup>p</sup>*, *zc*, *<sup>τ</sup> RT s*ð Þ� , *zc*, *<sup>τ</sup> cp*,*<sup>c</sup>*ðÞ�*<sup>s</sup> <sup>α</sup>i*ð Þ� *<sup>s</sup> i s*ðÞ�<sup>X</sup>

*Issues on Risk Analysis for Critical Infrastructure Protection*

*Tb* ¼ *Tb*ðÞ¼ *s*

corridor length, from 0 to *lc*).

8 >><

>>:

where:

repair time.

**44**

where:

where:

where:

by insurance companies.

**47**

istic for each class of events (**Figure 3**).

productive sectors [46, 47].

*DOI: http://dx.doi.org/10.5772/intechopen.94755*

factor *fc*, is defined as:

*VAen*: value added of the energy sector; it has to be noticed that the GDP at market prices is the sum of the gross value added at market prices for all the

*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors*

• The contribution of the analysed corridor to the regional energy supply is given by the economic value of the commodity carried by the corridor *c* per year; the

> *fc* <sup>¼</sup> *EVc VAen*

• The annual value of economic losses and expenditures related to the failure of the corridor *c* due to the natural event *ne* is assumed as the maximum

*<sup>f</sup> ne* <sup>¼</sup> *Lne*

It has to be highlighted that specific estimations of the total economic losses and expenditures *Lne* are not commonly available as public data and should be provided

Once the current risk is defined, the maximum tolerable frequency (number of

From the obtained maximum acceptable frequency, the corresponding event intensity can be evaluated using the frequency-intensity curve, which is character-

Several studies are available in literature regarding the relationship between the frequency and the intensity (or magnitude) of natural events. For example purpose, the ones performed by Hungr et al. [48], Jakob et al. [49, 50], Riley et al. [51] (related to the debris flow landslides), Hooke [52], Zhang et al. [53] (focusing on floods), and Papadakis [54] (considering earthquakes in Greece) can be mentioned. In general terms, the intensity is associated to specific characteristics of the considered event (like the peak ground acceleration for the earthquakes, the maximum water level for floods, the maximum wind speed for storms and the heat flux

events per year) for a given damage in the corridor section identified by the coordinate *zc* is assessed by adopting a graphical approach which starts from the previously defined Criticality Index (i.e. the economic value of the damage caused

by the service disruption due to the analysed event) (**Figure 2**).

*Lne*: total economic losses and expenditures due to the natural event *ne*. As no statistical data is available to evaluate the expenditures and economic losses for a specific natural event *ne* causing the failure of corridor *c*, the average value *fne*, defined at regional/country scale, is used as equivalent of the "local" ratio between the annual economic losses and expenditures associated to the failure of corridor *c* and the economic value *EVc* of the commodity carried by *c* per year. The previously described steps can be summarised into a single relationship (Eq. (9)), which allows to quantify the current economic risk in terms of monetary

*GDP* (8)

*Ra* ¼ *f ne* � *f en* � *fc* � *GDP* (9)

*EVc*: economic value of energy commodity delivered by corridor *c*

acceptable risk, and the factor *fne* is defined as:

losses as a consequence of the adverse natural event *ne*:

(7)

**Figure 1.** *Graphical representation of* CI *as a function of* D.

systems do not allow to define easy procedures suitable to be applied to different contexts (like developed, developing and less developed countries).

For this reason, in the present paper a specific criterion has been proposed, based on the overall economic estimation of damages due to natural events, which takes into account both direct (i.e. to houses, infrastructures, industrial facilities, etc.) and indirect (i.e. productive losses, lack of basic services to population) damages.

According to the Munich Re insurance company statistical data, related to the global natural loss events worldwide (including geographical, meteorological, hydrological and climatological events) over the period 1980–2015 [44], the 2015 overall losses accounted for about 0.14% of the global GDP (GDP data from World Bank statistics [45]). However, during previous years significantly higher percentage values have been reached, in particular in 2011 (mostly due to the Tōhoku earthquake and tsunami in Japan), when the losses peaked at about 380 billion US dollars, and in 2005, mainly related to the hurricane Katrina in the U.S.. These two events, in particular, highlight that extreme events involving developed countries generally lead to more relevant economic effects even at a global scale.

The proposed expression for the acceptable annual economic damage related to a certain corridor is evaluated as a fraction of the annual GDP, by taking into account the contribution of the energy sector to the GDP composition, the contribution of the analysed corridor to the overall energy supply of the country/area, the weight of the economic losses due to an extreme natural event.

In particular:

• The contribution of the energy sector to the GDP is expressed by the *fen* factor, defined as:

$$f\_{en} = \frac{VA\_{en}}{GDP} \tag{6}$$

*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors DOI: http://dx.doi.org/10.5772/intechopen.94755*

#### where:

*VAen*: value added of the energy sector; it has to be noticed that the GDP at market prices is the sum of the gross value added at market prices for all the productive sectors [46, 47].

• The contribution of the analysed corridor to the regional energy supply is given by the economic value of the commodity carried by the corridor *c* per year; the factor *fc*, is defined as:

$$f\_c = \frac{EV\_c}{VA\_{en}}\tag{7}$$

where:

*EVc*: economic value of energy commodity delivered by corridor *c*

• The annual value of economic losses and expenditures related to the failure of the corridor *c* due to the natural event *ne* is assumed as the maximum acceptable risk, and the factor *fne* is defined as:

$$f\_{\text{ue}} = \frac{L\_{\text{ne}}}{GDP} \tag{8}$$

where:

systems do not allow to define easy procedures suitable to be applied to different

For this reason, in the present paper a specific criterion has been proposed, based on the overall economic estimation of damages due to natural events, which takes into account both direct (i.e. to houses, infrastructures, industrial facilities, etc.) and indirect (i.e. productive losses, lack of basic services to population)

According to the Munich Re insurance company statistical data, related to the global natural loss events worldwide (including geographical, meteorological, hydrological and climatological events) over the period 1980–2015 [44], the 2015 overall losses accounted for about 0.14% of the global GDP (GDP data from World Bank statistics [45]). However, during previous years significantly higher percentage values have been reached, in particular in 2011 (mostly due to the Tōhoku earthquake and tsunami in Japan), when the losses peaked at about 380 billion US dollars, and in 2005, mainly related to the hurricane Katrina in the U.S.. These two events, in particular, highlight that extreme events involving developed countries generally lead to more relevant economic effects even at a

The proposed expression for the acceptable annual economic damage related to a certain corridor is evaluated as a fraction of the annual GDP, by taking into account the contribution of the energy sector to the GDP composition, the contribution of the analysed corridor to the overall energy supply of the country/area, the weight of

• The contribution of the energy sector to the GDP is expressed by the *fen* factor,

*<sup>f</sup> en* <sup>¼</sup> *VAen*

*GDP* (6)

contexts (like developed, developing and less developed countries).

the economic losses due to an extreme natural event.

damages.

**Figure 1.**

*Graphical representation of* CI *as a function of* D.

*Issues on Risk Analysis for Critical Infrastructure Protection*

global scale.

In particular:

defined as:

**46**

*Lne*: total economic losses and expenditures due to the natural event *ne*.

As no statistical data is available to evaluate the expenditures and economic losses for a specific natural event *ne* causing the failure of corridor *c*, the average value *fne*, defined at regional/country scale, is used as equivalent of the "local" ratio between the annual economic losses and expenditures associated to the failure of corridor *c* and the economic value *EVc* of the commodity carried by *c* per year.

The previously described steps can be summarised into a single relationship (Eq. (9)), which allows to quantify the current economic risk in terms of monetary losses as a consequence of the adverse natural event *ne*:

$$R\_{\rm at} = f\_{\rm ne} \cdot f\_{\rm en} \cdot f\_{\rm c} \cdot \text{GDP} \tag{9}$$

It has to be highlighted that specific estimations of the total economic losses and expenditures *Lne* are not commonly available as public data and should be provided by insurance companies.

Once the current risk is defined, the maximum tolerable frequency (number of events per year) for a given damage in the corridor section identified by the coordinate *zc* is assessed by adopting a graphical approach which starts from the previously defined Criticality Index (i.e. the economic value of the damage caused by the service disruption due to the analysed event) (**Figure 2**).

From the obtained maximum acceptable frequency, the corresponding event intensity can be evaluated using the frequency-intensity curve, which is characteristic for each class of events (**Figure 3**).

Several studies are available in literature regarding the relationship between the frequency and the intensity (or magnitude) of natural events. For example purpose, the ones performed by Hungr et al. [48], Jakob et al. [49, 50], Riley et al. [51] (related to the debris flow landslides), Hooke [52], Zhang et al. [53] (focusing on floods), and Papadakis [54] (considering earthquakes in Greece) can be mentioned.

In general terms, the intensity is associated to specific characteristics of the considered event (like the peak ground acceleration for the earthquakes, the maximum water level for floods, the maximum wind speed for storms and the heat flux

where:

follows:

account;

reported in **Table 3**.

**Figure 4.**

**49**

been considered;

from the corridor itself;

• there is no interruptible capacity;

reduction of one order of magnitude.

*Spatial layout of the corridor and of the backup sources.*

*R'a*: reassessed limit for risk acceptability (see **Figure 2**)

related to the class of natural events *ne*; *α* ∈ *[0,1]*

*DOI: http://dx.doi.org/10.5772/intechopen.94755*

**3. Case study and results discussion**

*αne*: reassessment factor for the definition of the limit for risk acceptability

*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors*

In this case, the same *CI* value corresponds to a lower maximum acceptable frequency, which – in turn – corresponds to a higher intensity that could exceed the design conditions of the infrastructure. In such a situation, new structural analyses have to be performed in order to verify its resilience and the possible need for mitigation actions, such as structural reinforcement, redundancy or relocation.

The methodological approach described in Section 2 has been tested by applying it to a simplified case study. The main assumptions adopted can be summarised as

• an ideal corridor and related surrounding environment have been taken into

• only two classes of extreme natural events (river floods and earthquakes) have

• three backup sources are available, able to cover the load for the entire period of unavailability of the corridor; these alternative sources are independent

• a reassessment of the limit for risk acceptability has been assumed, with a risk

The spatial layout of the corridor and of the backup sources is shown in **Figure 4**, while their characterisation and the values of the main parameters are

It has to be underlined that, in this simplified case study, the values of the parameters have been chosen in order to be realistic but they are not corresponding to a real case. In particular, all the parameters have been assumed to be seasonally

**Figure 2.** *Identification of the maximum tolerable frequency according to the* CI *value.*

**Figure 3.**

*Evaluation of the event intensity related to the maximum tolerable frequency according to frequency-intensity curve.*

for fires) and the link between intensity and frequency is evaluated on the basis of historical data analyses.

The obtained intensity has to be compared with the design limit value for the analysed infrastructure.

It has to be further underlined that *Ra* represents the current overall risk related to the event *ne*. If a lower limit for risk acceptability for that event is desired, a reassessment (i.e. a reduction) has to be performed, according to Eq. (10).

$$R\_a' = a\_{\text{ref}} \cdot R\_a \tag{10}$$

*Resilience of Critical Infrastructures: A Risk Assessment Methodology for Energy Corridors DOI: http://dx.doi.org/10.5772/intechopen.94755*

where:

*R'a*: reassessed limit for risk acceptability (see **Figure 2**)

*αne*: reassessment factor for the definition of the limit for risk acceptability related to the class of natural events *ne*; *α* ∈ *[0,1]*

In this case, the same *CI* value corresponds to a lower maximum acceptable frequency, which – in turn – corresponds to a higher intensity that could exceed the design conditions of the infrastructure. In such a situation, new structural analyses have to be performed in order to verify its resilience and the possible need for mitigation actions, such as structural reinforcement, redundancy or relocation.
