## 5 Conclusions  
1. This research proposed a method to construct hazard-consistent fragility curves for soil liquefaction using Monte Carlo simulation. The seismic parameters for evaluating liquefaction damage are the pair of earthquake magnitude and associated peak ground acceleration (\(M\), \(\mathrm{PGA_{R}}\)), which is superior to traditional methods where \(M\) and \(\mathrm{PGA_{R}}\) are usually determined separately. In addition, the soft site effects and uncertainties about the SPT-N values and groundwater table were also included in the analyses. The results of the liquefaction potential and damages thus obtained are more reasonable.
2. Based on the analysis results of the case study for the sand-boil site located in Yuanlin City in Changhua County, the probabilities corresponding to the damage status of at least \"Medium damage\" or \"Moderate liquefaction\" obtained from the fragility curves of \(I_{L}\) (liquefaction potential index), \(S_{t}\) (settlement after liquefaction), and \(P_{W}\) (liquefaction probability index) are 0.80, 0.74, and 0.76, respectively, which adequately reflect the characteristics of the soil at the liquefaction site and verify the practicality of the fragility curves developed. It is also shown that the parameters of \(I_{L}\), \(S_{t}\), and \(P_{W}\) are all appropriate parameters for assessing the damage of liquefaction.
3. By the hazard-consistent fragility curves of soil liquefaction developed here, a tool of scenario simulation for liquefaction damage is provided. It will be beneficial to the Taiwan Earthquake Loss Estimation System (TELES), which was developed to assess and manage earthquake risks and damages in Taiwan. Furthermore, it can serve as a guide for the decision making of countermeasure design against liquefaction.  
\begin{table}
\begin{tabular}{c c c} \hline \(I_{L}\) & **Median, \(m\) (g)** & **Log-Standard Deviation, \(\zeta\)** \\ \hline \(>\)5 & 0.183 & 0.172 \\ \hline \(>\)10 & 0.206 & 0.187 \\ \hline \(>\)15 & 0.234 & 0.202 \\ \hline \(>\)20 & 0.266 & 0.210 \\ \hline \(>\)25 & 0.303 & 0.214 \\ \hline \(>\)30 & 0.345 & 0.223 \\ \hline \(>\)35 & 0.395 & 0.240 \\ \hline \(S_{t}\) & Median, \(m\) (g) & Log-standard deviation, \(\zeta\) \\ \hline \(>\)5 & 0.165 & 0.160 \\ \hline \(>\)10 & 0.193 & 0.163 \\ \hline \(>\)15 & 0.203 & 0.166 \\ \hline \(>\)20 & 0.214 & 0.179 \\ \hline \(>\)25 & 0.237 & 0.203 \\ \hline \(>\)30 & 0.281 & 0.188 \\ \hline \(>\)35 & 0.332 & 0.169 \\ \hline \(P_{W}\) & Median, \(m\) (g) & Log-standard deviation, \(\zeta\) \\ \hline \(>\)0.1 & 0.134 & 0.164 \\ \hline \(>\)0.2 & 0.163 & 0.162 \\ \hline \(>\)0.3 & 0.188 & 0.160 \\ \hline \(>\)0.4 & 0.216 & 0.158 \\ \hline \(>\)0.5 & 0.250 & 0.155 \\ \hline \(>\)0.6 & 0.297 & 0.147 \\ \hline \(>\)0.7 & 0.370 & 0.134 \\ \hline \(>\)0.8 & 0.524 & 0.141 \\ \hline \end{tabular}
\end{table}
Table 5: Parameters of the fragility curves of the BH-29 site.  
**Author Contributions:** Conceptualization, G.S.W.; Methodology, F.-K.H.; Formal analysis, F.-K.H.; Investigation, F.-K.H.; Writing--original draft, F.-K.H.; Writing--review & editing, G.S.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.