# A Story-Based Random Structure Modeling Method for Regional Buildings Earthquake Loss Estimation
## 4 Case Study
### Earthquake Loss of Single Buildings  
The SBRS model is mainly used for the loss estimation of buildings under different ground shaking effects from a regional buildings perspective rather than selecting ground motion records that match the target design spectrum based on the principle of the most unfavorable set of defenses from the seismic design perspective, thus using a site condition-based wave selection. According to [PERSON] et al. [39], 20 ground motion records \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{5}{c}{**Statistics**} \\ \cline{2-6}  & **Max** & **Min** & **Mean** & **Standard** & **Dispersion** \\  & **Max** & **Min** & **Mean** & **Deviation** & **Coefficient** \\ \hline \(GA\) (\(10^{10}\) N / \(m\)) & 1.8290 & 0.4833 & 1.0163 & 0.3745 & 0.3685 \\ \(EI\) (\(10^{9}\) N -m\({}^{2}\)) & 6.5899 & 2.9024 & 4.5731 & 0.8160 & 0.1784 \\ \(\lambda\) & 1.9502 & 1.0938 & 1.4673 & 0.2093 & 0.1427 \\ \(m\) (\(10^{5}\) kg) & 9.8294 & 6.2419 & 7.5343 & 0.7310 & 0.0970 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter statistics of RC wall-frame SBRS model. inputted in an IDA analysis are sufficient to respond to the uncertainty of ground shaking, and 22 ground motion records from the FEMA-P695 report [40] with a shear wave velocity similar to the site condition are selected. The modulation step is taken to be 0.1 g. Due to the large number of buildings in the area and the significant difference in the fundamental period, the preferred method for determining ground shaking intensity is Peak Ground Acceleration (PGA). Subsequently, the selected ground motion records are inputted into the model for Incremental Dynamic Analysis (IDA) analysis. Assuming that \(m\) ground motion records are inputted at each intensity for each SBRS model, the seismic demand parameter EDP of each story can be formed into an \(m\times 1\) vector \(V_{records}\) and the EDP of each story of the \(n\) models is an \(m\times n\) matrix, with each element value denoted as \(V_{element}\). The median value of the fetched vector \(V_{records}\) is taken as a representative of that model's value, denoted as \(M_{records}\). Therefore, for all models, \(M_{records}\) can be composed of a \(1\times n\) vector, and the median value of this vector is used as the representative value of the peak inter-story displacement of each story of the building, denoted as \(M_{building}\). When the amplitude-modulation step is 0.1 g, the change in the seismic response is more stable between the steps, and due to the excellent seismic performance of the wall-frame structure, the seismic response still does not reach the limit value of collapse when PGA = 1.0 g. Considering that there are few seismic events with PGA reaching 1.0 g, to improve the computational efficiency, we did not continue to increase the intensity of the inputted ground shaking until most of the models collapsed and stopped the process of the IDA computation at PGA = 1.0 g.  
The damage state of structures is usually defined by discrete damage states, such as HAZUS, Vision 2000 [41], EMS-98 [42], and the China specification GB/T 24335-2009, the Classification of Earthquake Damage to Buildings and Special Structures [43], which classifies the damage state of buildings as Intact, Slight, Moderate, Severe, and Complete. China's seismic code defines the elastic limit and plastic limit of a structure using 1/550 and 1/50 of the inter-story drift ratios, respectively [32]. On the other hand, 1%, 2%, and 4% are used to define the limit states of immediate occupancy, life safety, and collapse prevention [44], so the inter-story drift ratio intervals for each damage state used in this paper are shown in Table 4.  
For each damage state of the structures, the type, number, and damage degree of components are determined based on their respective damage state definitions.