## 4 Probabilistic Seismic Hazard Analysis and Evaluation of Example Scenario Earthquake
### Development of a Uniform Hazard Spectrum as the Risk Assessment Spectrum
In SECY-93-087 [26], a seismic margins analysis based on probabilistic risk assessment considered the sequence-level high confidence of the low probability of failures and fragilities for all sequences that result in core damage or containment failures of up to approximately twice the magnitude of the SSE. As stated above, many criteria require the evaluation of structures with seismic intensities that exceed the design level. Accordingly, the aim of this study is to present a spectrum for risk assessment of intensities greater than the design level and a procedure for generating a ground motion time history compatible with this spectrum. In this study, a simplified PSHA model with a homogeneous area seismic source and one GMPE was assumed. PSHA was performed using the OpenQuake engine (version 3.21.0) [27], open-source software supported by the Global Earthquake Model. The input parameters used are listed in Table 1 below. The area of the source model was determined to be 100 \(\times\) 100 km\({}^{2}\), which was sufficiently large to avoid affecting PSHA results. Gutenberg-Richter \(a\) and \(b\) values for the Korean peninsula vary depending on research results, with a value generally ranging at 4.32-6.25 [28]. Considering a simplified single-area source model, parameter \(a\) was set to 2.843. To test the validity of the selected parameter values of \(a\), an analysis was conducted based on the ratio of the area of the simplified single-area source model to that of the Korean Peninsula. The area of the Korean Peninsula is 300,000 km\({}^{2}\), which is 30 times larger than the simplified single-area source model used in this study. That is, the parameter value of a decreases by log30 from 4.32 and 6.25, as described in Equation (2), in relation to the frequency of occurrence and magnitude of earthquakes:  
\[\log N(N\geq M)=a-bM \tag{2}\]  
where \(N\) is the cumulative number of earthquakes with magnitudes greater than or equal to magnitude (\(M\)). The range of the value converted to 30 times the area reduction was 2.843-4.773; thus, a value of 2.843 for the seismic source area in this study is reasonable. The value of parameter \(b\) was set to 0.95, which has been suggested to be optimal for Korea, which has low to moderate seismic activity [29]. A GMPE model developed for an area with a seismic environment similar to that of Korea was reviewed, and the selected GMPE model was developed by [PERSON] and [PERSON] (2006) [30]. A truncation level of two standard deviations (2\(\sigma\)) was applied. The GMPE model supported a stable, shallow continental tectonic region. The selected GMPE was validated by comparing the response spectra of the two horizontal components of the MKL station from the 912 Gyeongju Earthquake, which was the largest instrumental earthquake in Korea. This comparison was conducted using median GMPE values corresponding to the magnitude and distance of the MKL station from the 912 Gyeongju Earthquake (Figure 2). The PSHA calculation results from these parameters are shown as seismic hazard curves in Figure 3a. Figure 3: (**a**) Seismic hazard curves for each spectral period; (**b**) Uniform hazard spectrum corresponding to the seismic intensities required for seismic risk assessment. Figure 2: Comparison of the response spectra of the two horizontal components of the MKL station from the 912 Gyeongju Earthquake with the median values of GMPE. The median spectrum of GMPE is related to the magnitude of 5.5 and distance of 13.0 km, which are characteristics of the 912 Gyeongju earthquake. For critical structures such as nuclear power plants, a risk assessment against a design basis earthquake must be considered to quantitatively evaluate the safety as well as conservative seismic design. For this purpose, the seismic intensity must be determined for seismic risk assessment. For example, a stress test conducted on the Wolseong Unit 1 in Korea evaluated whether the seismic safety of a nuclear power plant was maintained beyond the design basis earthquake, which exceeded the design criteria [31].