Downtime estimation and analysis of lifelines after an earthquake
Introduction
Estimating the infrastructure downtime following an earthquake is a subject on which scientists and policy makers have recently focused their attention. The downtime can be defined as the time required to achieve a recovery state after a disastrous event; therefore, it is strictly linked to the indirect losses of the damaged infrastructure [1]. Downtime is usually caused by the construction repair of the damaged structure and the arrangements needed to mobilize resources. Comerio defined downtime as the sum of rational and irrational components [2]. The rational components include construction costs and repair time, while the irrational components consider the time needed to mobilize resources and make decisions.
The downtime is an essential parameter to estimate resilience [3]. Several attempts have been made recently to quantify the disaster resilience considering the downtime. Some of these studies tackled the engineering resilience on the country level [4], [5] and some on the local level [6], [7], [8]. In engineering, resilience is defined as “the ability of social units (e.g. organizations, communities, etc.) to mitigate hazards, contain the effects of disasters when they occur, and carry out recovery activities in ways to minimize social disruption” [9], [10], [11], [12]. Under this context, downtime is the time span between the moment the disaster occurs (t0), when the functionality Q(0) drops to Q(1), and the time when the functionality of the utility is completely restored (t1) [9], [13], [14] (Fig. 1). Some of the factors that can possibly affect the downtime include: the structural inspection, the assessment of damage, the finance planning, the bidding process, the repair effort, and the engineering consultation [15], [16].
One of the first attempts to evaluate the disruption time following a disaster event was done by Basöz and Mander [17]. In their work, they developed downtime fragility curves for the transportation lifeline. The fragility curves were later integrated in the highway transportation lifeline module of HAZUS. Another downtime estimation methodology was developed based on a modified repair-time model [18]. This methodology estimates the downtime of only the rational structural components of a system, due to the uncertainty involved in the process. In addition, the Federal Emergency Management Agency (FEMA) has introduced the Performance Assessment Calculation Tool (PACT). PACT is an electronic calculation tool, and repository of fragility and consequence data, that calculates and accumulates losses. It includes a series of utilities used to specify building properties and update or modify fragility and consequence information in the referenced databases. PACT is considered the companion to FEMA P-58, a significant 10-year project funded by FEMA to develop a framework for performance-based seismic design and risk assessment of buildings [19]. Almufti and Willford have proposed the Resilience-based Earthquake Design Initiative (REDi™) based on the results coming from PACT [20]. The goal was to provide owners and other stakeholders with a framework for implementing resilience-based earthquake design and achieving higher performances. Moreover, a performance-based earthquake engineering method to estimate the downtime of infrastructures using fault trees was introduced in [21]. This method is applicable only when the downtime is mostly controlled by the non-structural damage. It assumes that the restoration starts immediately after the event and the damaged components are repaired in parallel.
Another concern regarding the downtime evaluation is the infrastructure interdependencies. This is a subject on which most of current research effort is placed, mainly because of its complexity and uncertainty. Critical infrastructure systems are highly interconnected and mutually interdependent where damage to one infrastructure can promote cascading failures on other systems [22]. For instance, telecommunication and water systems require continuous supply of energy to maintain their normal functions, while the power infrastructure needs the water and various telecommunication services to generate and deliver electricity. Although the presence of interdependencies can significantly improve the operational efficiency of infrastructure, recent worldwide events have shown that interdependencies can increase systems’ vulnerability. The level of interdependencies between systems can determine how long a dependent system can stay inoperable. The Lifelines Council of San Francisco completed a study on the interdependencies of the city’s infrastructure systems [23]. They evaluated the infrastructures’ performance following a hypothetical major earthquake with a magnitude of 7.9. The study suggests that some of the lifelines were closely coupled and interdependent with the performance and restoration of the other lifelines. The interdependency was responsible for a significant recovery delay when the infrastructures have only experienced a moderate damage.
Generally, several factors are involved in the downtime estimation, such as the characteristics of the exposed structure, the earthquake intensity, and the amount of human force that is assigned to recover the damaged structure. With these factors, the process of estimating the downtime becomes harder. Therefore, it is crucial to have a simple model for estimating the downtime of infrastructures [16]. The aim of this study is to develop a probabilistic model to evaluate the downtime of lifelines following a seismic event. Four different types of lifelines are analyzed in this work, namely power, water, gas, and telecommunication. First, a large database has been collected from a wide range of literature. The database contains real restoration data for many seismic events that occurred in the last century [24]. Probabilistic restoration functions have been constructed using the gamma distribution, which has been selected because of its good fit to the empirical data. For each of the four lifelines, a group of fragility curves has been developed based on several factors, such as the earthquake magnitude, development level of the affected country, and countries with enough data. The restoration curves have been presented in terms of probability of recovery and time; the longer is the time after the disaster, the higher is the probability of the infrastructure to recover its functionality.
Section snippets
Downtime data analysis and interpretation
Fig. 2 shows the location of all 32 earthquakes considered in this study. Approximately, 90% of the earthquakes analyzed in this research took place along the Ring of Fire of the Pacific Ocean, a string of volcanoes and seismic activity sites. The other 10% of the earthquakes took place along the Alpide belt, a line that passes through the Mediterranean region, Turkey, Iran, and northern India. The database was gathered from renowned authors and official institutions, and belongs to earthquakes
Methodology
The main challenge faced in this work is to illustrate the gathered data in the form of restoration curves. Typically, real data is complex to handle because they are exposed to a series of errors that vary in nature and magnitude. In this paper, the collected restoration raw data are fitted with a statistical distribution. Choosing the right distribution can be a difficult task due to the relevant number of distributions available in literature. To characterize new raw data with a
Results: the restoration curves
Restoration curves were developed for the power, water, gas, and telecommunications systems using the collected downtime data. The variables considered to plot the curves are: (i) the number of days required to restore full service to customers (horizontal axis) and (ii) the probability that the utility is completely restored to the customers (vertical axis). To provide a better understanding of the restoration process, the collected data has been divided based on different categories, as
Discussion
The results presented above show some interdependencies and coupling behaviors among the lifelines. The power system was always the first infrastructure to recover its normal functions following the disaster, usually because all lifelines depend on the power system, and so right after the event it should restore as soon as possible. For the telecommunication system, the restoration process starts fast, but then the probability of restoration in the following days becomes less than that of the
Conclusions
Downtime is one of the most difficult parameters to estimate in the resilience analysis. Estimating the resilience of infrastructures due to earthquakes has been studied in the past; however, none of the studies highlighted a clear procedure to estimate the disruption time of damaged systems. This paper provides an empirical model to estimate the downtime of damaged infrastructures following an earthquake. The model uses a large database for earthquake events that occurred over the last few
Acknowledgements
The research leading to these results has received funding from the European Research Council under the Grant Agreement n° 637842 of the project IDEAL RESCUE Integrated Design and Control of Sustainable Communities during Emergencies.
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