1. Introduction
Damage to infrastructure during disasters is a major challenge for countries around the world, and various kinds of measures such as seismic retrofitting of infrastructure facilities are taken in place to mitigate it. Simulation-based evaluations are commonly used to determine the most appropriate measure to choose from, and various modeling frameworks have been developed. In many modeling frameworks, the focus is on reproducing infrastructures precisely, but as urban systems are complex and composed of a variety of interacting elements, it is necessary to include not only physical lifeline infrastructures but also important human activities to the society. Against this background, Kanno et al. developed a human-centered modeling framework of urban systems that captures various types of interdependencies underlying urban sociotechnical and socioeconomic systems, by integrating three subsystems: civil life, manufacturing/service industry, and lifeline infrastructure to the model. Following that, Wakayama et al. applied this model to optimize the post-disaster recovery of water supply system and showed the practical feasibility of this model. However, since the simulations only assume specific fixed disaster scenarios, cases with low probability of occurrence but extensive damage could not be considered. Therefore, we developed a modeling framework that can consider both interdependency and uncertainty, by modifying the model of the previous study to enable random scenario generation and applying the Monte Carlo method. In order to evaluate the validity of the proposed framework, we compared two results: with/without simple post-disaster countermeasures.
2. Method
2.1 Overview of the model
The simulation model consists of three main subsystems: civil life, manufacturing/service industry, and lifeline infrastructure, and nine different types of interdependencies existing within and between these subsystems are considered. For example, citizens need to use lifelines to live, while lifelines need workers to commute to the lifeline facilities to work properly. Lifelines are expressed as multi-layered networks of links and nodes, with each link having parameters that represent the connection and length. Enterprises and citizen agents are placed on the road network. When a disaster occurs, it is assumed that some lifeline links will be out of service, and repair squads will be dispatched to repair those links. The resilience index of the system is evaluated by calculating the resilience triangle throughout the simulation, where performance of the whole urban system is calculated as a linear sum of each of the subsystems, and the objective is to minimize the resilience index. A brute-force Monte Carlo method is applied to this simulation, and the lifeline links that get destroyed after the disaster are sampled from a uniform distribution for each run.
2.2 Application to the water supply network
In this study, we focused on the resilience of water supply system. An additional parameter for whether the link is a main pipe with larger diameter or not was given to the water pipes, and we assumed that only water pipes get damaged when a disaster occurs. Then, we compared the results with and without restoration planning. In case of having a restoration plan, main pipes were prioritized, and when the pipes are the same type, priority was given to the pipe closer to upstream. In case of no restoration plan, the order of restoration was selected randomly.
2.3 Simulation Settings
The road network model consists of 2310 nodes and 1951 links, and 6990 citizen agents (each representing 4 people) and 628 enterprises are placed on the network. As for the water distribution network, 4910 pipes are placed, and 13 water repair squads work to repair the pipes after a disaster occurs. 100,000 simulations will be conducted, with each simulation lasting 20 days, with a disaster occurring on the fifth day, when 100 water pipes are randomly destroyed.
3. Results
In case of no restoration plan, the average resilience index was 16.1 and the maximum resilience index was 758.2. In the case of having a restoration plan, the average resilience index was 14.4 and the maximum resilience index was 82.5. Over 99% of the simulations in both cases resulted in a resilience index below 50, so the worst cases where the resilience index exceeds 50 could be overlooked without the Monte Carlo method. In addition, while a numerical comparison alone only shows a slight improvement in the average resilience index, a graphical comparison shows a significant reduction in the possibility of an extremely high resilience index.
4. Conclusion
We developed a modeling framework based on previous research to enable resilience assessment of urban infrastructure systems considering multiple interdependency and uncertainty. Simulation results showed that the effectiveness of measures can be evaluated from more perspectives than comparing numbers obtained from a simulation with a fixed scenario. The next step will be randomizing the scale of the disaster and adding attributes that affect the failure probability to the pipes. As the number of random factors increases, the variance of the simulation results will increase, and more simulation runs will be needed, so we will apply variance reduction methods to reduce computational effort. After that, we will implement more reality-based pre-disaster and post-disaster measures and comparing the results of their effectiveness, so that the model could be put to practical use.
References
T. Kanno, T. Suzuki, S. Koike, and K. Furuta, “Human centered modeling framework of multiple interdependency in urban systems for simulation of post disaster recovery processes,” Cognition, Technology & Work, 21(6), pp. 301-316, 2019.
Wakayama, K., T. Kanno, Y. Kawase, H. Takahashi, and K. Furuta, “Comparison of the post-disaster recovery of water supply system by GA optimization and heuristics”, Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference (2020) |