## 2 Methodology
### Flood Intensity Level and Fragility Curve
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DS Level** & **Description** & **Damage Scale** & **Functionality** & **Loss Ratio** \\ \hline DS0 & In significant damage condition & Insignificant & Operational & 0.00–0.03 \\ \hline DS1 & Water touches floor joists up to & & & \\  & minor water entering the building; & & & \\  & floodwater touches the foundation & & & \\  & with a height of about 2.5 cm from & & & \\  & ground level. & & & \\ \hline DS2 & Drywall damage up to a 30 cm & Moderate & Restricted & 0.15–0.50 \\  & water level from the ground level. & & & \\ \hline DS3 & Damage to the nonstructural & & & \\  & components such as electrical & & & \\  & appliances and cabinets; equipment, & & & \\  & devices, and furniture on the upper & & & \\  & floors are also damaged (e.g., attic, & & \\  & second floor, etc.) & & & \\ \hline DS4 & Fully structural damage & Complete & Restricted entry & 0.50–0.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The description and functionality of each DS. The exceedance probability (fitted) of each DS conditioned on the flooding hazard intensity measure (IM) is uncertain and assumed to be fitted by a lognormal cumulative distribution function (CDF) in Equation (2):  
\[F_{r}(IM=x)=\phi\left[\frac{Ln_{(x)}-\lambda_{DS_{i}}}{\xi_{DS_{i}}}\right] \tag{2}\]  
where \(F_{r}\) is the lognormal fitted fragility function when \(IM\) is \(x\), and \(\lambda_{DS_{i}}\) and \(\xi_{DS_{i}}\) are the logarithmic median and standard deviation of each damage state, respectively. For individual buildings, the fragility function indicates the fitted probability that the individual building fails to provide safe occupancy; and for building sectors consisting of various buildings, the fragility function describes the ratio of buildings failing to provide safe occupancy for people living in the community. The fragility information on individual buildings, like the logarithmic median and standard deviation, can be obtained from [PERSON]'s work [6]. This foundational study provides a robust portfolio of minimal building flood fragility and loss functions, directly supporting our community-level resilience analysis. The fragility curves utilized in this study were derived from a curated dataset based on specific inclusion and exclusion criteria to ensure applicability to flood resilience assessment. The inclusion criteria for the flood damage data included the following: (1) empirical or simulated flood depth-damage relationships from peer-reviewed sources, primarily [6], covering a range of building archetypes relevant to the virtual community; (2) data reflecting damage states (DS0 to DS4) aligned with population dislocation as the resilience metric; and (3) availability of probabilistic parameters suitable for lognormal cumulative distribution functions. The exclusion criteria comprised the following: (1) datasets lacking flood depth as a primary intensity measure, as this study focuses on depth-dependent damage; (2) data from non-representative building types not applicable to the wood-frame dominated virtual community; and (3) studies with insufficient sample sizes or unvalidated simulation outputs, which could compromise the reliability of fragility estimates. This rigorous selection ensured that the fragility curves accurately represented the vulnerability of the selected archetypes under varying flood intensities.