**3. Case study and results discussion**

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 follows:


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 reported in **Table 3**.

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

for fires) and the link between intensity and frequency is evaluated on the basis of

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

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

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*0

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

*Issues on Risk Analysis for Critical Infrastructure Protection*

It has to be further underlined that *Ra* represents the current overall risk related

*<sup>a</sup>* ¼ *αne* � *Ra* (10)

historical data analyses.

**Figure 2.**

**Figure 3.**

*curve.*

**48**

analysed infrastructure.


#### **Table 3.**

*Values of the main considered parameters.*

independent. Furthermore, the values have been set in order to describe a realistic configuration from a physical point of view, while from the economic perspective a unitary value for current risk limit (1 €/y) has been selected mainly due to the unavailability of specific public data on the total economic losses and expenditures. In the reassessment of the limit for risk acceptability, the hypothesis of reducing it by an order of magnitude has been made. In general, if the proposed procedure is applied to a real system, the evaluation of the parameters should be performed according to the considerations expressed in Section 2.1.

The obtained *CI* (z*c*) is shown in **Figure 5** for both earthquake (E) and flooding (F) events. In particular, it can be observed that the corridor sections characterised by the highest *CI* values are those close to the backup sources in the seismic area (in the case of earthquake event) and to the river (in the case of flooding event). The sections where *CI* < 1 are those corresponding to a damage *D* < 0, i.e. the capacity of the backup sources is more than the one requested to ensure the coverage of the load in the case of unavailability of the corridor.

**Figure 7(a)** shows the frequency-*CI* curves corresponding to the original limit for risk acceptability and to the reassessed one. **Figures 7(b)** and **(c)** represent the frequency-magnitude curves, which have been built by using two different

*Evolution of the availability of the backup sources with respect to the position along the corridor* zc*.*

• a logarithmic relationship based on the one proposed by Wald et al. [56] in the

The vertical lines correspond to the design base earthquake magnitude (DBE)

Starting from these curves and from the previously defined *CI* evolution, the maximum acceptable frequencies and the related intensities for both earthquake

approaches for the two considered classes of natural events:

case of flooding.

**Figure 5.**

**Figure 6.**

**51**

and flood (DBF) for the corridor.

• the Gutenberg-Richter law [55] in the case of earthquakes;

CI *evolution with respect to the position along the corridor* zc*;* CI *< 1 corresponds to D < 0.*

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

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

However, it has to be remarked that all the sections characterised by *CI* value slightly lower than 1 have to be considered as they are close to a critical condition.

Referring to the evolution of the availability parameter *α<sup>b</sup>* (*s*,*p*) for the three backup sources, it can be noticed (**Figure 6**) that the lower the distance between the corridor and the source, the lower the availability: this is because if the natural event involves an area in which the corridor and the backup are close to each other, the probability for the backup source to be damaged is higher, and so its availability is lower.

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

**Figure 5.** CI *evolution with respect to the position along the corridor* zc*;* CI *< 1 corresponds to D < 0.*

**Figure 6.** *Evolution of the availability of the backup sources with respect to the position along the corridor* zc*.*

**Figure 7(a)** shows the frequency-*CI* curves corresponding to the original limit for risk acceptability and to the reassessed one. **Figures 7(b)** and **(c)** represent the frequency-magnitude curves, which have been built by using two different approaches for the two considered classes of natural events:


The vertical lines correspond to the design base earthquake magnitude (DBE) and flood (DBF) for the corridor.

Starting from these curves and from the previously defined *CI* evolution, the maximum acceptable frequencies and the related intensities for both earthquake

independent. Furthermore, the values have been set in order to describe a realistic configuration from a physical point of view, while from the economic perspective a unitary value for current risk limit (1 €/y) has been selected mainly due to the unavailability of specific public data on the total economic losses and expenditures. In the reassessment of the limit for risk acceptability, the hypothesis of reducing it by an order of magnitude has been made. In general, if the proposed procedure is applied to a real system, the evaluation of the parameters should be performed

*DBF* Maximum discharge of the design base flood 2000 m<sup>3</sup>

*Ra* Current risk value 1 €/y

*<sup>a</sup>* Reassessed limit for risk acceptability 0.1 €/y

/s

*DBE* Magnitude of the design base earthquake 4.8

**Parameter Description Value Unit** *p1,f* Probability to involve backup source 1 – flooding 0.5 *p2,f* Probability to involve backup source 2 – flooding 0.5 *p3,f* Probability to involve backup source 3 – flooding 0 *λ<sup>e</sup>* Earthquake damage distance 5 km *λ<sup>f</sup>* Flooding damage distance 5 km *s* Seasonal factor (influence of the season on the event) 0 *cp,c* Peak capacity of the corridor 100 J/h *RT* Repair time 1 h *cm,b1* Minimum operative margin in capacity – backup source 1 50 J/h *cm,b2* Minimum operative margin in capacity – backup source 2 35 J/h *cm,b3* Minimum operative margin in capacity – backup source 3 45 J/h *αt,b1* Technical availability of the backup source 1 0.95 *αt,b2* Technical availability of the backup source 2 0.95 *αt,b3* Technical availability of the backup source 3 0.95 *i* Interruptible capacity 0 J/h *e* Energy intensity for the considered commodity 1 €/J

*Issues on Risk Analysis for Critical Infrastructure Protection*

The obtained *CI* (z*c*) is shown in **Figure 5** for both earthquake (E) and flooding (F) events. In particular, it can be observed that the corridor sections characterised by the highest *CI* values are those close to the backup sources in the seismic area (in the case of earthquake event) and to the river (in the case of flooding event). The sections where *CI* < 1 are those corresponding to a damage *D* < 0, i.e. the capacity of the backup sources is more than the one requested to ensure the coverage of the

However, it has to be remarked that all the sections characterised by *CI* value slightly lower than 1 have to be considered as they are close to a critical condition. Referring to the evolution of the availability parameter *α<sup>b</sup>* (*s*,*p*) for the three backup sources, it can be noticed (**Figure 6**) that the lower the distance between the corridor and the source, the lower the availability: this is because if the natural event involves an area in which the corridor and the backup are close to each other, the probability for the backup source to be damaged is higher, and so its availability is

according to the considerations expressed in Section 2.1.

load in the case of unavailability of the corridor.

lower.

**50**

*R'*

**Table 3.**

*Values of the main considered parameters.*

**Figure 7.** *Frequency-*CI *(a) and frequency-magnitude curves (b, c) for the analysed case study.*

and flood events and for both the original (E/F old) and reassessed (E/F new) limit for risk acceptability have been estimated, as reported in **Figure 8**.

As it can be observed in **Figure 8a**, the maximum acceptable frequency for earthquakes reaches its minimum value (corresponding to the maximum intensity, visible in **Figure 8b**) in the section where the corridor and the backup source 3 are closest each other and are both affected by the natural event (*p* = 1 in Eq. (4)). Furthermore, it can be observed that in the case of reassessed risk limit the intensity is beyond the design condition (DBE, **Figure 8b**), thus leading to the need for performing tests in order to assess the robustness of the involved corridor section and to define suitable mitigation actions. The same considerations are valid for the flood (**Figure 8c** and **d**): the main difference is that – in this case – in the most critical corridor section the intensity overcomes the design value also for the original risk limit (DBF, **Figure 8d**), requiring further resilience tests also without hypothesising a reassessment of the limit for risk acceptability.

As mentioned before, the values of the considered parameters have been assumed without a specific reference to a real case, as the goal of the analysed case study is to show the functioning and the applicability of the proposed methodology through a theoretical example. For this reason, an analysis of the uncertainties has not been performed. Future works aiming at deeply exploring the criticality of existing infrastructures will include this aspect, especially regarding the event related parameters, with a particular attention devoted to the probability that different facilities are involved. As previously discussed, in fact, this probability needs detailed and complex considerations to be properly quantified with respect to the specific natural hazard and site studied.

On the other hand, it also allows to identify some aspects that could be more deeply investigated in future studies in order to enhance the applicability to real cases and the effectiveness of the obtained results. In particular, among them, the unambiguous definition of the system boundaries can be mentioned. In fact, the identification of boundaries can be not easy in the case of meshed networks like natural gas distribution systems or power lines, for which it is difficult to define a single entry point and a single end point. Another relevant aspect is represented by

*Maximum tolerable frequencies and intensities of earthquakes (a-b) and floods (c-d) for the analysed*

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

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

**Figure 8.**

*cased study.*

**53**

This simplified case study, however, shows the potentiality of this approach in evaluating the possible critical sections of the infrastructures, prioritising the investments and the interventions in reinforcing them and in making them resilient to adverse extreme natural events.

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

**Figure 8.** *Maximum tolerable frequencies and intensities of earthquakes (a-b) and floods (c-d) for the analysed cased study.*

On the other hand, it also allows to identify some aspects that could be more deeply investigated in future studies in order to enhance the applicability to real cases and the effectiveness of the obtained results. In particular, among them, the unambiguous definition of the system boundaries can be mentioned. In fact, the identification of boundaries can be not easy in the case of meshed networks like natural gas distribution systems or power lines, for which it is difficult to define a single entry point and a single end point. Another relevant aspect is represented by

and flood events and for both the original (E/F old) and reassessed (E/F new) limit

As it can be observed in **Figure 8a**, the maximum acceptable frequency for earthquakes reaches its minimum value (corresponding to the maximum intensity, visible in **Figure 8b**) in the section where the corridor and the backup source 3 are closest each other and are both affected by the natural event (*p* = 1 in Eq. (4)). Furthermore, it can be observed that in the case of reassessed risk limit the intensity is beyond the design condition (DBE, **Figure 8b**), thus leading to the need for performing tests in order to assess the robustness of the involved corridor section and to define suitable mitigation actions. The same considerations are valid for the flood (**Figure 8c** and **d**): the main difference is that – in this case – in the most critical corridor section the intensity overcomes the design value also for the original risk limit (DBF, **Figure 8d**), requiring further resilience tests also without

As mentioned before, the values of the considered parameters have been assumed without a specific reference to a real case, as the goal of the analysed case study is to show the functioning and the applicability of the proposed methodology through a theoretical example. For this reason, an analysis of the uncertainties has not been performed. Future works aiming at deeply exploring the criticality of existing infrastructures will include this aspect, especially regarding the event related parameters, with a particular attention devoted to the probability that different facilities are involved. As previously discussed, in fact, this probability needs detailed and complex considerations to be properly quantified with respect to the

This simplified case study, however, shows the potentiality of this approach in

evaluating the possible critical sections of the infrastructures, prioritising the investments and the interventions in reinforcing them and in making them resilient

for risk acceptability have been estimated, as reported in **Figure 8**.

*Frequency-*CI *(a) and frequency-magnitude curves (b, c) for the analysed case study.*

*Issues on Risk Analysis for Critical Infrastructure Protection*

hypothesising a reassessment of the limit for risk acceptability.

specific natural hazard and site studied.

to adverse extreme natural events.

**52**

**Figure 7.**

the availability of complete and uniform databases for both the technical characteristics of the analysed infrastructures/backup sources and the classes of natural events affecting the environment surrounding the infrastructure.

Further studies could also be devoted to the analysis of multi-risk scenarios, i.e.

to the concurrent occurrence of two or more extreme natural events, defining suitable strategies to allocate the acceptable risk (for instance by taking into account the safety margins of the infrastructure, if they are present), in order to test the infrastructure resilience in the worst (and low-frequency) conceivable conditions.

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

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

**Author details**

**55**

Andrea Carpignano<sup>1</sup>

1 Politecnico di Torino, Torino, Italy

provided the original work is properly cited.

, Daniele Grosso<sup>2</sup>

\*Address all correspondence to: raffaella.gerboni@polito.it

, Raffaella Gerboni<sup>1</sup>

2 LINKS Foundation, EST@Energy Center – Politecnico di Torino, Torino, Italy

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\* and Andrea Bologna<sup>1</sup>
