# Seismic Reliability Assessment of Water Supply Systems Considering Critical Paths
## 1 Introduction
This study showed that the sequence and pattern of the earthquake damage recovery process can be modeled with a good degree of accuracy, but it made no attempt to suggest or evaluate various recovery plans. [PERSON]. [20; 21; 22] proposed a method of evaluating the supply of a water pipe network system by increasing not only quantitative supply, but also water quality performance. Water delivery, quality, quantity, fire protection, and functionality were each subdivided into four categories, and the recovery pattern of each category was quantified and presented. The resulting patterns were analyzed and compared based on water pipe network system data from the Northridge earthquake. After, [PERSON] et al. [23] established various recovery strategies that can be used after an earthquake (recovery priority, allocation of recovery personnel, etc.) and presented a numerical index that can be used to aid decision makers in determining how to recover the system quickly. The index enables estimation of time required for recovery, calculation of resources required for recovery, understanding of temporal and spatial recovery progress, statistical results of recovery personnel, etc., and was applied to an actual water supply network. The third category, construction methods/materials that mitigate earthquake damage, is very significant as it is arguably the most active earthquake damage prevention countermeasure, but research into this category is lacking. [PERSON] et al. [24; 25] suggested the concept of a \"critical link\" by connecting the reliability of the water supply system to the main supply points and conducting performance evaluations on pipes that service individual customers. [PERSON] et al. [26; 27] used metaheuristic techniques to determine which individual pipelines most need improvement and optimization when money is limited. However, due to the nature of the water supply system, it may not be possible to determine whether individual pipes are seismically resistant or to consider the connectivity between reinforced pipes. For the evaluation of individual pipes, [PERSON] et al. [17] considered the destruction of multiple pipelines due to earthquakes as one of the assessment categories in a proposed method of prioritizing improvements in water supply pipelines. Later, [PERSON] et al. [28] evaluated the seismic reliability of a water supply system according to the cost of pipe construction, and identified that a uniform increase in pipe construction costs did not lead to a remarkable increase in seismic reliability. Based on this finding, [PERSON] et al. [29; 30] proposed and assessed a single-objective optimization method of maximizing the seismic reliability of a water supply system under limited construction cost conditions, as well as a multi-objective optimization method that simultaneously satisfies construction cost and reliability. However, such an optimization study cannot be used to assess strategies for supplementing the seismic reliability of an existing system by upgrading the entire water supply pipeline to optimal design specifications. This study assesses a seismic design strategy that aims to protect against earthquake-related damage. The study quantifies the improvement in seismic reliability that occurred when seismic protection was performed on each water supply route in industrial water supply systems with various sources and water supply routes. A single water supply path consists of a combination of pipes of various sizes and lengths, and the amount of water to be supplied also differs between paths. By quantifying the effects of intervention on the water supply system and the characteristics of each route with regard to seismic reliability, a basic methodology is presented to determine the critical path for seismic protection when limited construction costs are to be invested.