A Seismic Network Reliability Evaluation on a GIS Environment – a Case Study on Catania Province

A seismic network reliability evaluation on a GIS environment – a case study on Catania province

S. Cafiso, A. Condorelli, G. Cutrona & G. Mussumeci Department of Civil and Environmental Engineering, University of Catania, Viale Andrea Doria, 6, 95125 Catania, Italy

Abstract

Human society is nowadays strongly dependent on an articulated and complex network of road infrastructures. Essential services for current users as well as for every kind of human activity have been entrusted to this network that takes the name of “lifeline”. Network Reliability Analysis mainly measures network performance related to its capability to oppose or react against the failure of single elements. When a catastrophic event strikes a wide area, it is necessary that the infrastructure system is designed with a high redundancy, to have effective alternatives in choosing a route to maintain network function. However, if in mathematical analysis of a simple structure, a redundancy rate could clearly be defined, it would not be sufficient to quantify the redundancy effect in a more complex and real-life structure such as a road network. In this paper, we propose a GIS (Geographic Information System) based methodology to study the road Network effectiveness after a seismic event. The method is based on the concepts of Encountered Reliability and Terminal Reliability and it has been applied to the Catania Province area. The results show which towns and links are in the most critical condition and must be considered for road planning and management prioritization. Keywords: road network, lifelines reliability, seismic risk, GIS, bridge vulnerability.

1 Reliability and risk of lifelines network

The analysis of the effects induced by calamities on the transport system clearly shows how the destruction or severe damage of even one element has serious consequences for all the territory, such as the impossibility to access the urban network, interruptions or overloading of part of the transport system or on other means of transport, delay in emergency services arriving at the scene of the calamity, etc. The examination of the transport system and its functionality is thus very important for the wider evaluation of territorial risk. The transport network is affected by two different phenomena that can modify its reliability: 1) Variation in what is offered for transportation; 2) Variation in the demand on the transport services. In the case of damage produced by seismic events it is obvious that the effects of the interruption of the local network and the consequence reduction in what remains available profoundly affect the overall performance of the system (increase in travel time, distance and costs). Furthermore, the effects of this damage induce the users to change their behavior which then changes the demand on the system. The effects of the damage to the system can be reduced by the capacity of the users to adapt to the new circumstances. This means that the user should have a high degree of information so as to be able to awarely decide beforehand from among the available options. On the other hand, if there is a low degree of available information the only option is that of changing route when an interruption is encountered, when the user is already involved in the congestion of the system [1]. The reduction of the risk on the transport network has generally been made by the structural improvement of some of its components, but other aspects should also be taken into consideration such as: - The improvement of the global configuration of the network; - The construction of alternative infrastructures that can guarantee the redundancy of the system; - The monitoring of critical components; - The carrying out of regular preventative maintenance; - The identification of the priority for repair of the damaged components. Operations of this type can be carried out using the methodologies of analysis for reliability engineering, applied to the road network and to the relative traffic flow both in normal conditions and in the case of an emergency [2]. Reliability can be defined as the “the probability of a device performing its purpose adequately for the period of time intended under the operating conditions encountered” (Wakabayashi and Idia, 1992 [3]), accepting that this is with the various meanings of the term “correctly” assumed by the different users. A road network, in particular, will be reliable if “…. provides a safe and not fluctuating service for the traffic and offers the users alternative routes, even when some parts of the system are not available due to road accidents,

Risk Analysis IV, C. A. Brebbia (Editor) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-736-1 Risk Analysis IV 133 maintenance or natural disasters”. In some cases, however, it could be of primary importance that the journey finishes in a determined period of time, while in other cases it is more important to evaluate if there are interruptions along the route. With this aim in mind there are two concepts of reliability. Terminal reliability is “the probability that nodes are connected, i.e. it is possible to reach the destination” and this is surely the parameter that is easier to evaluate. With this approach reliability assumes the value of one or zero, in relationship to the probability that it is possible or not to reach the destination by any route, but it is not possible to describe the situations in which the system works in intermediate conditions within the range 0-1. The encountered reliability can be defined as “the probability of not encountering a link degradation on the path with least (expected) cost”. Another concept that is complimentary that will be used in the proposed methodological approach is the reliability of the time and cost of the journey, commonly defined as “the probability that a trip can be successfully finished within a specified time interval”. In parallel to the concepts of reliability it is indispensable to address the problems linked to the network risk. It should be remembered that the risk, following an approach that has been well consolidated in literature, can be seen as the product of three independent factors: - hazard, linked to the probability that in a certain place there will be an event of a certain intensity with a given return time; - exposure, given by the number of people (and goods) that can be damaged by the event; - vulnerability, that defines the propensity of the infrastructural element that can undergo damage during the event [4,5].

2 Study area and the road lifeline network

The province of Catania has an area of about 3,552 Km2 with a population of 1,054,778 inhabitants, in which there are 58 towns. Among these the most important is the province capital (Catania), with 313,110 inhabitants. There are also five urban centres with a population of more than 30,000 inhabitants (Acireale, Paternò, Misterbianco, Caltagirone, and Adrano). A value was assigned to each city for its “direct exposure ” equal to the number of inhabitants in the towns multiplied by the “index for seismic risk” defined in Italy proportionally to the values of the expected losses and with a value varying between about 0 and 0.8 [6]. The GIS, developed using Arcview®, contains all the data necessary for the analysis of risk and emergency management, organized in shape-files and Relational data bases [7]. In particular, the shape-file relative to the roads present in the province of Catania (classified as urban, communal, provincial, state and motorways) and the segmentation of the network and stretches allow the application of the functionality of the Network Analyst®. This was carried out integrating the road network Tele Atlas® with the information obtained from maps and recent orthophotographs, providing all the

Risk Analysis IV, C. A. Brebbia (Editor) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-736-1 134 Risk Analysis IV information requested by the detailed analysis: toponymy, length of the branch, width of the carriage ways, number of carriage ways, direction, speed limits, functional classification of the road stretch, eventual presence of restrictions for some types of traffic, eventual need to pay a transit toll, belonging to the lifeline network or not and the time necessary to complete the route at the design speed. All the bridges and viaducts present on the network were positioned within the GIS with the help of provincial maps with a scale of 1:10,000. Based on this information all the routes that could be used by emergency services were identified. For the definition of these routes, which provide communication for all the 58 towns of the Province, three hypotheses of traffic accessibility were considered, having identified in the areas of Messina, Palermo and Ragusa/Gela the possible origins (O) for emergency services [8]. The scheme produced allowed the determination of the network of lifelines of the province of Catania, on which to analyze risk and reliability (Figure 1).

Messina

m Palermo 247ֹ252 m 214ֹ291˙1 m 664ֹ883˙2 m 239ֹ663˙1 m 334ֹ544 m 64ֹ339 m 71ֹ967

Ragusa - Gela

Figure 1: The road network diagram created by Arcview®.

3 Indirect exposure on the stretches of the road network

The indirect exposure on the single stretches of the road network can be defined in relationship to the number of people who would experience a delay in the arrival of emergency services due to an interruption of that given stretch of the road network. The shortest route between each origin and each of the 58 towns of the province was calculated by ArcView®, both in terms of distance and time needed to cover the route. To each of the stretches of each route an “indirect exposure” was assigned equal to the value of direct exposure of the town of destination. Based on the values obtained, the five classes of Indirect Exposure (IE) were identified and are shown in table 1.

On the obtained routes (348 in total, that is 116 for each origin-destination, 58 with calculated by total route time and 58 calculated be route length), the number of bridges and underpasses was determined, independently of the vulnerability of the single construction, which, however, can be considered the “weakest” element of the road system in a seismic event.

Table 1: Indirect exposure classes.

Class Indirect exposure values 1 0 ≤ IE < 10,000 2 10,000 ≤ IE < 20,000 3 20,000 ≤ IE < 50,000 4 50,000 ≤ IE < 75,000 5 IE ≥ 75,000

Finally, after having identified the number of bridges present on the various stretches, a risk value was assigned equal to the indirect exposure of the stretch, in the presence of at least one bridge, while zero was assigned if there were no bridges in that stretch. Therefore there is a first risk hierarchy based on the major or minor exposure of the stretch combined with the presence of vulnerable structures. In relation to the minimization of the times to cover a given route, the most critical ones, for each of the three origins, are concentrated on the roads of greatest importance that allow the highest road speeds (Figure 2).

Figure 2: Risk classes (minimization of route times).

If we consider the routes that minimize the distances we obtain a road network graph that is more complex and with more stretches that spread out from the previous axes using roads of less importance (Figure 3).

Figure 3: Risk classes (minimization of route times).

4 Lifeline encountered reliability

For the attribution of an Encountered Reliability the new routes that from each origin lead to a single destination with the minimum number of bridges (lpmin) were identified, both in terms of length (L) and in terms of time (T), as long as the variations in length (∆L) and time (∆T) obtained with the new routes were not greater than 1.5 of the length of the original route (Lmin) and 1.5 of the original route time (Tmin). The route having the least number of bridges for each origin was identified automatically thanks to the GIS functionality, associating to each stretch a cost function equal to the length of the stretch multiplied by an amplification factor α>1, in the case in which the stretch coincides with a bridge/viaduct, or, alternatively, α=1. The concept applied was that of assigning greater weight to the bridge/viaduct stretch with respect to all the others, proportionally to the length of the same, so as to induce the system to find the routes characterized by the least total length of viaducts. After some attempts, the optimum value of 100 was determined for the factor α. The index of Encountered Reliability, for the entire road network was obtained by the formula: 58 2 ∑ Ol )( min,D D=1 (OE ) R = (1) 58 2 ∑ p Ol )( min,D D=1 where: D = 1, 2, …, 58 (destination town for emergency services);

l(O)min, D = minimum distance (in terms of time or length) from the origin (O) to the destination D (original route); l(O)Pmin, D = minimum distance along which there are the minimum number of bridges (in terms of time or length) from the origin (O) to the destination D (new route). The results are shown in Table 2.

Table 2: Values of encountered reliability (ER) evaluated on the routes of least length (L) and least time (T).

Origin ER(Length) ER(Time) Messina 0.67 0.43 Palermo 0.79 0.63 Ragusa/Gela 0.65 0.54

Using this approach the most reliable routes are characterized by higher values of ER, in as much as the emergency services meet a minor number of bridges (that could be unusable in cases of earthquakes); thus, from table 2, it can be seen how the most reliable itineraries are those with an origin in Palermo, while those less reliable have an origin in Messina. It is also possible to determine for each destination town the reliability of the single routes for the various origins: l 2 OE )( = min,D (2) ,DR 2 l min,DP with D, lmin, D and lPmin, D previously defined. Once the values of E(O)R,D have been defined for each origin for the emergency services (Palermo, Messina, Ragusa/Gela), it is possible to establish a general value for the Encountered Reliability for each town ERTOT(D), as an average weighted on the itineraries with respect to the three origins:

∑ o OEp )( RD O ERTOT D)( = (3) ∑ po O where: O = 1, 2, 3 and represents the three origins; pi = 1 for the routes with an origin in Palermo and Messina, 0.6 for the routes with an origin in Ragusa/Gela; From the relationship between the direct exposure values for each town (D) and the relative total value of E(D)RTOT it is possible to obtain the risk factor R: Direct exposure R = (4) E RTOT The risk factors for 10 towns of the 58 considered, with respect to the shortest routes in terms of time and length, are shown in figure 4.

140.000 R(E) - time R(E) - distance 120.000

100.000

80.000

60.000

40.000

20.000

0 Catania Misterbianco Acireale Gravina Paternò Mascalucia Giarre San Giovanni Adrano Motta S. la Punta Anastasia

Figure 4: Risk factors connected to the encountered reliability.

Observing fig.4, it can be seen that, as was foreseeable, the town with the highest risk is Catania, this is due to the high value of indirect exposure of this city. Regarding the weight played by exposure in this analysis, it can be seen, for example as Motta S. Anastasia, even if it has a level of reliability much lower than Adrano (ERTOT(T) about half), in the routes that minimize time it is characterized by a risk factor only slightly less in as much as its indirect exposure is much less.

5 Lifelines terminal reliability

For the definition of Terminal Reliability we used the determination of the routes that lead, from each of the three origins to the 58 towns, bypassing the bridges nearer to the destination and calculating how many interruptions are necessary before obstructing the entry to the destination. The procedure stops either when there are no more bridges to by pass along an alternative route and as long as ∆L or ∆T are not greater than a fixed threshold value, or it is no longer possible to reach the destination. The higher the number of interruptions necessary to make a node inaccessible or to obtain maximum ∆L or ∆T, the more reliable is the route that goes from the origin to the destination. The maximum increase of time was fixed at 50 % of the average time to travel the route from an origin to all the destinations (results: 15 min from Messina, 20 min from Palermo and 30 min from Ragusa). For each origin (O) it is possible to establish an index of Terminal Reliability T(O)RD for each destination town (D from 1 to 58) as the sum of the number of bridges closed to traffic on the respective routes.

In the same way for the calculation of Encountered Reliability, it is possible to determine a value of Total Terminal Reliability (TRTOT) as the weighted average of the sum of the weighted values of Terminal Reliability.

∑ OTp )( RDo O TRTOT D)( = (5) ∑ po O where: O = 1, 2, 3 and represents the three origins; pO = 1 for the routes with origin in Palermo and Messina, 0.6 for the routes with origin in Ragusa/Gela; Also in this case the greater the value of Terminal Reliability, the more reliable is the route. It is possible to estimate also the value for risk with respect to Terminal Reliability dividing the value of direct exposure of the town by the value of Terminal Reliability of the same town. Direct exposure (6) R = TRTOT

1.800 R(T) - time R(T) - distance 1.600

1.400

1.200

1.000

800

600

400

200

0 Catania Militello Scordia Giarre Raddusa Vizzini Paternò Acireale Caltagirone Misterbianco

Figure 5: Risk factors connected to encountered reliability.

Also in this case (Figure 5), the town with the highest risk index is Catania, even if it has a discrete coefficient of Terminal Reliability (29.15) due to the high number of accesses to the urban area. Among the towns with high risk indexes there are also Militello in Val di Catania and Raddusa that, even if they have a very low indirect exposure value they are among those with the lowest coefficient of Terminal Reliability. It is possible to see how the towns of Raddusa and Militello in Val di Catania are in the condition in which the eventual interruption of only two bridges completely isolates the towns from the provincial road network.

6 Conclusions

In this paper we present a methodology for the evaluation of reliability of road networks in relation to seismic events, experimentally applied to the province of Catania, Italy. The analyses were carried out considering bridges as the “weak” element of the road infrastructure in cases of seismic events. In this phase of the research this assumption was done independently of the structural characteristics of the bridge. We used the concepts of Encountered Reliability and Terminal Reliability, identifying the routes that lead to each of the 58 towns of the province, from three possible origins for emergency services (Palermo, Messina and Ragusa/Gela), crossing the minimum number of bridges, both in terms of length and time to cover the given distance. These values are referred to the various towns and compared the direct exposure allowing the definition of a risk index relative to emergency service accessibility in case of earthquakes. Moreover, based on the values of indirect exposure of the town and on the value of reliability calculated on the various stretches of the road network, it was possible to define a risk hierarchy on the stretches and routes. This information is useful to find the parts of the road network where more resources should be employed both to program retrofitting work on structures and for a more in depth analysis evaluating in detail the vulnerability of bridges.

References

[1] Selçuk A.S., Yücemen M.S., Reliability of lifeline networks under seismic hazard. Reliability Engineering and System Safety, pp. 213-227, 1999 [2] DU Z.P., Nicholson A.J., Degradable Transportation System: Sensitivity and Reliability Analysis, Transportation Research B, 31(3), 225-237, 1997. [3] Wakabayashi H., Idia Y., Upper and Lower bounds of terminal reliability of road networks: an efficient method with Boolean Algebra. Journal of Natural Disaster Science 14, pp. 29-44, 1992. [4] Nicholson A., Schmöcker J.D., Bell M.G.H., Assessing Transport Reliability: Malevolence and User Knowledge. “The Network Reliability of Transport”, Proceedings of the 1st International Symposium on Transportation Network Reliability (INSTR), pp. 1-22, 2003. [5] Husdal J., Analyzing Risk Vulnerability of Transportation Lifelines. Online www.husdal.com (visited, May 2003). [6] Ord.P.C.M. n. 2788 del 12/06/1998, Individuazione delle zone ad elevato rischio sismico del territorio nazionale, 1998 [7] Cutrona G., Le Infrastrutture Viarie nella Pianificazione e Gestione dell’Emergenza a seguito di Catastrofi Natura”. PhD thesis, Department of Civil and Environmental Engineering, Catania, 2003. [8] Cafiso S., Colombrita R., D’Andrea A., Mussumeci G., Colombrita F., Condorelli A., Un modello di GIS per la valutazione del rischio sulle infrastrutture stradali nelle emergenze della protezione civile, Proc. of the XI Convegno Nazionale Società Italiana di Infrastrutture Viarie (SIIV), Verona, 2001.