# Seismic Reliability Assessment of Water Supply Systems Considering Critical Paths
## 1 Introduction  
Water supply systems (WSSs) consist not only of above-ground infrastructure, such as water reservoirs (tanks), pumps, valves, etc., but also of a vast array of pipelines, most of which are buried underground. The basic function of a water supply system is to satisfy the demand for water quantity, quality and pressure by continuously supplying water from the water source to each customer's faucet. Unfortunately, water supply systems are quite susceptible to seismic disasters as the relevant infrastructure is large in scale and widely distributed. Major earthquakes of magnitudes greater than 7.0, such as the Northridge quake in the United States in 1994 and the quake in Kobe, Japan in 1995, often cause severe damage to water supply systems [1,2]. The water supply systems in areas affected by an earthquake fail due to primary damage,such as water leakage and pipeline rupture, resulting in a decrease in water supply and a reduction in firefighting capability. In addition, such disruptions hinder the residential, commercial, and industrial sectors, and have a profound impact on the economic and social structures of local communities [3; 4; 5; 6]. In order to accurately understand the pattern of damage to a water pipe system caused by earthquakes, the hydraulic characteristics of the water supply system must be considered. A basic seismic reliability assessment study reflecting the hydraulic characteristics of the water pipe system was conducted by [7; 8]. In early studies, complex water supply systems were either simplified, or the evaluation was performed only on the main lines. In addition, a water supply system was depicted as a network of points and lines, and not as a detailed hydraulic system. Furthermore, supply and demand were assessed by simple arithmetic addition of the supply and demand of the areas cut off by the earthquake. Since the late 2000s, research has been conducted to evaluate seismic reliability using EPANET2 [9], a general-purpose mathematical analysis software program for water pipe network systems. Studies that model the seismic reliability of water supply systems can be classified into three categories: (1) model development through hydraulic analysis, (2) establishment of post-earthquake recovery strategies, and (3) robust design in preparation for earthquakes and the development of improvement techniques. Regarding the first category, the GIRAFFE model [10] (Graphical Iterative Response Analysis for Flow Following Earthquakes) is a seismic reliability assessment model for water pipe networks which was developed based on the research in [11; 12; 13; 14; 15; 16]. It is significant in that it visually implements the results of reliability evaluation and provides various analytical functions by linking mathematical analysis techniques and GIS functions. Later, [PERSON] et al. [17] published a Quasi-PDA (Pressure Driven Analysis)-based reliability evaluation model, REVAS.NET (Reliability Evaluation model of Seismic hazard for water supply NETwork), which partially supplemented the GIRAFFE model's demand-driven analysis technique. Recently, [PERSON] et al. [18] developed the Water Network Tool for Resilience (WNTR), an open-source Python package that helps water utilities investigate water availability and recovery times given earthquake scale, location and repair strategy. WNTR was used to propose the latest hydraulic analysis technique, the PDA (Pressure Driven Analysis) method, but it has not yet been verified in the field. With regard to the second category, studies related to the establishment of a recovery strategy after an earthquake were conducted by [19; 20; 21; 22; 23]. System damage was investigated by first modeling the series of steps which various types of recovery personnel make as part of the repair process, and the hydraulic performance of the system was evaluated using the GIRAFFE model. The developed model was verified by simulating the Northridge earthquake, a large earthquake that occurred in LA in 1994.