## 3 A Demonstration of the Proposed Framework: A Case Study
### Evaluation of Functional Recovery  
Figures 10-12 illustrate the functional recovery curves at both the median and 90 th percentile levels, depicting the evolution of building functionality from the moment of seismic impact (time = 0) until full recovery is achieved. At the 50%-in-50-years hazard level, the median outcomes indicate that all three PC frame buildings retain approximately 80% of their initial functionality and recover fully within 40 to 55 days. As shown in Figures 10a-12a, the differences in functionality loss among the three systems are relatively minor at this seismic intensity, suggesting low levels of damage. However, the median recovery time for the cast-in situ PC frame is 14 days longer than that of the other two building types, due to its lower level of prefabrication and reliance on cast-in situ repair processes. Figure 10: Functional recovery curves of cast-in situ PC. (**a**) represents the 50%-in-50-yrs. hazard level. (**b**) represents the 10%-in-50-yrs. hazard level. (**c**) represents the 5%-in-50-yrs. hazard level. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{6}{c}{**Hazard Level**} \\ \hline \multicolumn{6}{c}{**50\% in 50 yrs.**} & \multicolumn{3}{c}{**10\% in 50 yrs.**} & \multicolumn{3}{c}{**5\% in 50 yrs.**} \\ \hline \multirow{2}{*}{**EDP**} & **Cast-In Situ PC/** & **PCaCPC** & **Cast-In Situ PC/** & **PCaC** & **Cast-In Situ PC/** & **PCaCPC** \\  & **PCa 50\% PC** & **with MT** & **PCa 50\% PC** & **with MT** & **PCa 50\% PC** & **with MT** \\ \hline \(\text{du}_{1}\) [\%] & 0.46 & 0.37 & 1.03 & 0.64 & 1.56 & 1.27 \\ \(\text{du}_{2}\) [\%] & 0.59 & 0.31 & 1.13 & 0.51 & 1.81 & 1.01 \\ \(\text{du}_{3}\) [\%] & 0.53 & 0.32 & 1.01 & 0.52 & 1.86 & 1.12 \\ \(\text{du}_{4}\) [\%] & 0.41 & 0.15 & 0.97 & 0.26 & 1.66 & 0.74 \\ \(\text{a}_{1}\) [\%] & 0.68 & 0.44 & 0.79 & 0.73 & 1.19 & 0.98 \\ \(\text{a}_{2}\) [\%] & 0.59 & 0.43 & 0.56 & 0.37 & 1.33 & 0.91 \\ \(\text{a}_{3}\) [\%] & 0.49 & 0.28 & 0.52 & 0.34 & 1.19 & 0.84 \\ \(\text{a}_{4}\) [\%] & 0.29 & 0.21 & 0.36 & 0.24 & 0.99 & 0.53 \\ \hline \end{tabular}
\end{table} 
Table 5: Engineering demand parameters. At the 10% in 50 years hazard level, both the median and 90 th percentile outcomes show that the three PC systems retain a majority of their functional capacity. However, the 90 th percentile recovery time for the cast-in situ PC frame is nearly three times longer than that of the PCaPC frame, as illustrated in Figure 10b, indicating an increased probability of prolonged downtime due to uncertainty in repair scheduling and greater reliance on site-cast construction. At the 5% in 50 years hazard level, the PCaPC frame with MT connection exhibits better resilience performance, achieving both median and 90 th percentile recovery times that are approximately 50% shorter than those of the other two frames. It is important to note that although the cast-in situ PC and PCa 50% PC frames share identical structural layouts and member dimensions, their recovery times and functional restoration paths differ significantly across all hazard levels. These differences primarily stem from variations in the repair sequencing strategies adopted for each structural system (see Section 2.2). Again, for partially prefabricated buildings, prioritizing the use of prefabricated elements in critical or damage-prone components, such as stairs, can notably shorten the recovery duration. As shown in Figures 13-15, the observed functionality loss is predominantly attributed to damage in nonstructural components, particularly stairs and elevators. The absence of structural repair time in Figure 15 reflects that the damage probability of structural components is below 50% at this hazard level, and thus, the structural systems remained largely intact. These results demonstrate that the framework, which is used to model functionality recovery, offers a comprehensive representation of the recovery process by considering all component systems.