# Efficient Seismic Fragility Analysis for Large-Scale Piping System Utilizing Bayesian Approach
## 1 Introduction  
Recently, two earthquakes having a moment magnitude greater than 5.0 occurred in Gyeongju (2016) and Pohang (2017) on the Korean peninsula, where such strong earthquakes had been observed only rarely in the past. These earthquakes resulted in considerable damage that directly affected structural safety, causing damage such as cracks and the collapse of columns and walls that were the main structural components of buildings. In particular, the intensity of the ground motions observed in the city center (for example, USN2 of Ulsan) near the epicenter of the 2016 Gyeongju earthquake exceeded the design seismic intensity of the nuclear power plant (i.e., 0.2 g or 0.3 g-anchored USNRC R.G. 1.60 [1] design ground response spectrum) (see Figure 1). Additionally, the earthquake extensively damaged non-structural components such as ceilings and plumbing in the downtown area, threatening the safety of human life, as well as causing significant economic losses. Due to this, the perception that earthquakes might threaten the structural safety of key social infrastructure and human life has been increased in Korean society. The post-investigation for the 1994 Northridge earthquake in the United States revealed that economic losses from damage to non-structural components accounted for more than 50% of the total economic loss induced by the earthquake [2]. Specifically, during the Northridge earthquake, failures of three plumbing lines, more than 1500 water pipelines, and 709 gas plumbing systems were reportedas plumbing damage accidents, and the Olive View Medical Center in Sylmar, California, was closed. Similarly, during the 1995 Kobe earthquake in Japan, it was found that the failure of non-structural components, especially fire sprinkler piping systems, accounted for 40.8% of all failures [3]. In particular, among the non-structural components of a building, the piping system is installed and supported at several different points of the building. Due to this characteristic of the piping system, earthquake motion inputs to the support points of a piping system are different from each other, and this may cause a large displacement in the piping system. In addition, the fundamental frequency of the piping system has a value between about 1 and 10 Hz, unlike that of other non-structural components, which overlaps with the primary natural frequency of a low-rise building (\(F_{N}\) = 10/N Hz, \(N\): total number of floors of a building) [4] and the concentrated frequency range of the design earthquake input motion energy (1-10 Hz). This causes a resonance effect in the piping system and ultimately increases the possibility of an even larger displacement of the piping system. Based on this background, several researchers have conducted studies to determine the seismic safety of piping systems. Specifically, a study was conducted to investigate the limit states of T-joints [5; 6], elbows [7; 8], etc., which were structurally fragile components of the piping system, through a dynamic cyclic test for the piping. In addition, studies have been carried out to experimentally and analytically investigate the earthquake responses of actual piping subjected to ground shaking [9; 10; 11]. Based on these findings, several groups performed studies on the seismic fragility of piping systems that considered the uncertainties of earthquake loading and the piping model to assess the probabilistic seismic safety of piping [12; 13; 14; 15]. Recently, in relation to seismically vulnerable piping systems, a study was conducted aimed at directly improving the seismic performance of piping systems by applying seismic isolators, damper devices, etc. [16; 17]. On the other hand, piping systems are not usually installed alone as secondary structural systems; rather, they are supported/fixed at multiple locations on buildings, bridges, etc., which are the primary structural systems.