System Dynamics Modeling and Simulation of Disaster Recovery Process of Interdependent Infrastructure Systems. Shojiro Kataoka 1

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1 System Dynamics Modeling and Simulation of Disaster Recovery Process of Interdependent Infrastructure Systems by Shojiro Kataoka 1 ABSTRACT A simulation model is developed for disaster recovery process of infrastructure systems. The model is based on the system dynamics and the interdependency among infrastructures is taken into account. Disaster recovery process of the infrastructure system in the Tokyo metropolitan area, where the infrastructures are highly interdependent, is simulated using the model and the effects of the interdependency are investigated. KEYWORDS: Infrastructure System, Influence Diagram, System Dynamics, Interdependency 1. INTRODUCTION Infrastructures such as roads, railroads, electric, gas, and water supplies, sewerage, and telecommunications are vital for our daily lives and industrial activities. Natural and human disasters, however, have damaged the infrastructures and the damage has caused social and economic losses from time to time. The longer the disaster recovery takes, the larger the losses become; thus, prompt recovery is important to mitigate the losses. Since the infrastructures are interdependent and compose a highly complex system, especially in urban areas, damage to one of the infrastructures may affect the others (damage spreading). For example, if the electric supply is damaged, the road traffic capability is deteriorated until the electric recovers traffic lights. If the gas supply and the road network are damaged, the recovery of the gas supply is delayed because road traffic is necessary for the recovery works. Tsuruta et al. (2008) surveyed interdependency of the infrastructure system during past disasters and developed a damage propagation model based on matrix equation [1]. Though the case study simulation using the model successfully demonstrated the earthquake damage spreading among infrastructures, dynamic behavior such as recovery process of the infrastructure system was not investigated. In this study, the disaster recovery process of the infrastructure systems is modeled based on the system dynamics and the time history of the recovery process from a hypothetical earthquake (M7.3) in the Tokyo metropolitan area is simulated taking account of the interdependency. 2. SYSTEM DYNAMICS MODELING First, the s and components of infrastructures and their relationships are organized as influence diagrams. A base model that shows relationships among facilities, resources, and infrastructures necessary for disaster recovery is developed for each of infrastructures. Then the base models are assembled into a system dynamics model of disaster recovery process of the infrastructure system. The details of the modeling are described in Kataoka et al. (2009). The influence diagrams illustrate the s and components of infrastructures and their relationships; the diagram of the gas supply system is shown in Fig. 1 as an example. The gas supply system consists of many facilities but only the low pressure pipes are assumed to be damaged during earthquakes. Not only the facilities managed by gas suppliers but also the electric are necessary to maintain the gas supply. 1 Senior Researcher, Earthquake Disaster Prevention Division, National Institute for Land and Infrastructure Management, Tsukuba , Japan

2 Then, based on the influence diagrams, the base models are developed taking account of facilities, resources, and infrastructures that are necessary for disaster recovery. For example, the base model of the gas supply system is developed as shown in Fig. 2. The road traffic and telecommunication s are considered necessary for the disaster recovery of the gas supply. Since the electric is required to maintain the gas supply, either backup electric or physical recovery of substations is necessary for the recovery of the system. The system dynamics model is constructed by assembling the base models of all infrastructures. Given the initial damage to the infrastructures, the disaster recovery process of the whole infrastructure system can be simulated using the model. 3. SIMULATION CASE STUDY Disaster recovery process of the infrastructure system in the Tokyo metropolitan area, where the infrastructures are highly interdependent, is simulated using the system dynamics model. 3.1 Initial Damage and Interruption Central Disaster Management Council (CDMC) announced the estimated damage due to Tokyo metropolitan earthquakes in 2005 [3]. The most disastrous one is the hypothetical northern Tokyo Bay earthquake (M7.3), which causes strong ground motion with JMA seismic intensity of 6 upper in the eastern half area of the 23 special wards of Tokyo as shown in Fig. 3. Following CDMC, Tokyo Metropolitan Government (TMG) also conducted estimation of damage caused by the earthquake [4]. In this study, the damage to the infrastructures estimated by TMG is used as the initial damage in the simulation. Table 1 shows the damage in Chiyoda and Sumida wards and the 23 wards in total. Railroads are ordered a halt for inspection just after earthquakes even though no damage is reported. Road traffic is also controlled and only emergency vehicles can be admitted to path through disaster areas. Thus, the initial interrupted ratios are assumed as follows: - 100% for the railroad network (all lines are once halted for inspection of the damage), - 0% everywhere for emergency vehicles, - 100% in the road traffic prohibited area and 5 in the other area with seismic intensity of 6 upper for non-emergency vehicles. Once a Tokyo metropolitan earthquake occurs, Metropolitan Police Department regulates the traffic so that non-emergency vehicles are prohibited to pass through the road traffic prohibited area, which covers 75% of the area of the 23 special wards. In this study, the traffic regulation is assumed to last for 10 days. 3.2 Recovery Rate without Interdependency CDMC surveyed the recovery rates of the infrastructures based on interviews and obtained the following results [3]: - 95% of electric recovers in 6 days, - 95% of telecommunications recovers in 14 days, - 80% of gas supply recovers in 55 days, - 95% of water supply recovers in 30 days, - 95% of sewerage pipes recover in 30 days. The recovery rates for railroads and roads are assumed as follows: - 100% of railroads are available in 1 day in the area with seismic intensity of 5 upper (no damage and only inspection), - 90% of railroads are available in 1 day, then 95% recover in 5 days in the area with seismic intensity of 6 lower, - 80% of railroads are available in 1 day, then 95 % recover in 15 days in the area with seismic intensity of 6 upper, - 95% of roads recover in 18 days in the area with seismic intensity of 6 upper. These rates are assumed to be those when the recovery process is not influenced by the interdependency among infrastructures and used as initial recovery rates. For example, the recovery rate of low pressure pipe in Fig. 2 is set to be the recovery rate of the gas supply mentioned above.

3 3.3 Simulation Results Fig. 4 shows the time histories of recovered ratios of the infrastructures in Chiyoda and Sumida wards. In this simulation, 10% of the vehicles used for the disaster recovery work are assumed to be the emergency vehicles. Thus, 90% of them are affected by the traffic regulation or interruption. The recovery of the infrastructures is delayed significantly compared with the recovery rates mentioned in 3.2. The delays are longer in Sumida wards because it suffers greater damage than Chiyoda wards (Table 1). Fig. 5 is the same as Fig. 4 but 9 of the vehicles used for the disaster recovery work are assumed to be the emergency vehicles. In Fig. 5, the delays still exist but much shorter than those in Fig. 4. To achieve this improvement, road facilities must not collapse during earthquakes so that the road networks maintain the traffic at least for emergency vehicles. 4. CONCLUSIONS A simulation model is developed to investigate the effects of the interdependency among infrastructures on the recovery process of the infrastructure system. The simulation case study shows the importance of smooth traffic of emergency vehicles for prompt disaster recovery of the highly interdependent infrastructure systems. Further research and investigation are needed to improve accuracy and actuality of the simulation model and data in order to discuss the simulation results quantitatively. 5. REFERENCES 1. Tsuruta, M., Goto, Y., Shoji, Y. and Kataoka, S.: Damage propagation caused by interdependency among critical infrastructures, 14th World Conference on Earthquake Engineering, Kataoka, S., Tsuruta, M. and Shoji, Y.: Model development of interdependency among critical infrastructures and simulation of earthquake damage spreading, Technical Note of National Institute for Land and Infrastructure Management, No. 510, Central Disaster Management Council: Documents of the 15th Tokyo metropolitan earthquake disaster management council, Tokyo Metropolitan Government: Estimated damage in Tokyo due to the Tokyo metropolitan earthquakes, 2006.

4 Gas ガス供給機能 supply (for home ( 家庭等 use ) etc.) Resource 機能維持のためのリソース for maintaining Resource 物理的復旧が必要なリソース possibly damaged Function 機能 Low pres- 低圧ガス sure gas Infrastructure インフラ Gas ガス供給機能 supply (for industrial ( use 工場等 etc.) ) 電力 電力 Area 地区ガバナ governor Medium pressure 中圧ガス gas Governor ガバナステーション station High pres- 高圧ガス sure gas Low pres- 低圧導管 sure pipe Medium pressure 中圧導管 pipe Governor control ガバナ制御情報 information Central control 中央制御機能 製造工場 Plant High 高圧導管 pressure ( 幹線 pipe ) 電力 LNG タンク Tank 電力タンカー Tanker Fig. 1 Influence diagram of the gas supply system. 中央制御室 Facilities of central control 設備 room Function of インフラ機能 infrastructure 変数 Variable 入力変数 Input parameter f6a=min(f41, f44) f6a=gas ガス供給機能 supply (for ( home 家庭等 use ) etc.) f6b=gas ガス供給機能 supply (for industrial ( 工場等 ) use etc.) f61=f62 f63 f61=f52 f53 f61=physical f61= 低圧導管 recovery of low pressure 物理的復旧 pipe f64=recovery 中圧以上 of high and middle pressure の復旧 pipes f64=min(f65, f67) f62=g6b f7a=road f7a= traffic 道路輸送機能 ( (emergency 緊急車両 vehicle) ) f62=impact 低圧導管 on recovery of low 復旧への影響度 pressure pipe g6b=recovery 復旧要員 workforce, machinery and material 機材調達 g6b=min(f7a, g6a) g6a=recovery g6a= instruction 復旧指示 g6a=f(f1a, f1b, f1c) f63=recovery 低圧導管 rate of low pressure 復旧設定値 pipe f1a=telecommunication f1a= 固定電話 情報通信機能 (fixed phone) f1b=telecommunication f1b= 携帯電話情報通信機能 (mobile phone) f1c=telecommunication f1c= 災害時用 for emergency 通信機能 use f65=recovery 拠点設備 of governor station and の復旧 plant f65= min(max(f34, f69), f66) f66=physical f66= recovery 拠点設備 of governor の物理的復旧 station and plant f34=physical 変電所の recovery of 物理的復旧 substation f67=information ガバナ制御 for governor 情報 control f68=recovery 中央 of central 制御室の復旧 control room f67=f68 f69= f69=backup バックアップ electric 電源 f68= min(max(f34, f69), f610) f610= f610=physical 中央制御室 recovery of central の物理的復旧 control room Fig. 2 Base model showing relationships among facilities, resources, and infrastructures necessary for disaster recovery of the gas supply system.

5 > Fig. 3 Map of Kanto region showing JMA seismic intensity due to the northern Tokyo Bay earthquake (M7.3) and its source fault (Central Disaster Management Council, 2005)[3]. Table 1 Estimated damage to infrastructures caused by the northern Tokyo Bay earthquake (M7.3) in Chiyoda and Sumida wards and the 23 wards in total (Tokyo Metropolitan Government, 2006)[4]. Wards supply ( failure ratio) Telecommunications (interrupted ratio) Gas supply (cut off ratio) Water supply (cut off ratio) Sewerage (ratio of damaged pipe) Chiyoda 6.l% 0.9% 59.4% 37.4% 23.3% Sumida 48.6% 17.6% 100.0% 79.5% 31.8% 23 wards total 22.9% 13.2% 22.9% 46.3% 25.4%

6 (a) Telecommunication (fixed phone) (b) Telecommunication (mobile phone) (c) supply (d) Gas supply e) Water supply (f) Sewerage (g) Railroad (h) Road Fig. 4 Time histories of recovered ratios of the infrastructures in Chiyoda and s. 10% of the vehicles used for disaster recovery work are assumed to be the emergency vehicles.

7 (a) Telecommunication (fixed phone) (b) Telecommunication (mobile phone) (c) supply (d) Gas supply (e) Water supply (f) Sewerage (g) Railroad (h) Road Fig. 5 Time histories of the recovered ratios of the infrastructures in Chiyoda and s. 90% of the vehicles used for disaster recovery work are assumed to be the emergency vehicles.