## 3 Collapse Performance of Seismically Isolated Buildings
### Collapse Capacity Evaluation of the Prototype Isolated Buildings
#### 3.2.1 Results of Incremental Dynamic Analysis
For the prototype isolated buildings designed for low-to-moderate seismicity regions especially for strong windy regions, 3L\({}_{\text{E}}\)40C, 5L\({}_{\text{E}}\)40C, and 10L\({}_{\text{E}}\)40C buildings in the figures, the superstructures are in the collapse damage state, resulting from large side-sway displacements. On the other hand, the isolation systems do not reach the collapse damage state. Hence, the distributions of the collapse points are concentrated near the collapse damage criterion in terms of the maximum story drift ratio of the superstructure, as presented in Figure 9. At the collapse state, the isolation systems in the 3L\({}_{\text{E}}\)40C building suffer the extensive damage defined as 200% of shear strains [31]. The isolation systems in the 5L\({}_{\text{E}}\)40C and 10L\({}_{\text{E}}\)40C buildings are approximately in the moderate and slight damage states, respectively when the corresponding superstructures reach the collapse damage state. This results from the loss of the beneficial decoupling effects that should expect to be developed in the L\({}_{\text{E}}\)40C buildings. This phenomenon is magnified as their heights are increased. Of the L\({}_{\text{E}}\)30B buildings subjected to smaller design wind loads, the 3L\({}_{\text{E}}\)30B building develops the promising decoupling effects, whose damage is concentrated on the isolators. Both the 5L\({}_{\text{E}}\)30B and 10L\({}_{\text{E}}\)30B buildings suffer significant structural damage on the superstructure rather than the isolators. The several IDA curves show the structural resurrection in which response is again stiffer at larger ground motion intensities after a flattened response at a particular ground motion intensity. The structural resurrection is also found in the IDA curves presented in terms of the story drift ratio of the superstructure. Such structural resurrection contributing the larger variation on IDA curves is notable to isolated buildings, which commonly capture the critical failures due to the side-sway of the superstructures. With the resurrection, the dispersion of collapse points is mainly dependent on seismic design conditions of isolated buildings. The larger dispersions are observed for isolated buildings designed for low seismicity regions compared to those for high seismicity regions. Similar findings are also observed for taller isolated buildings under larger design wind loads. The fragility curve of each  
Figure 8: IDA curves for isolated buildings located at high seismicity regions. prototype isolated building was determined from a cumulative distribution function (CDF) of collapse points on its IDA curve with an assumption that they follow the well-known log-normal distribution characterized by two parameters, a median and a standard deviation. Record-to-record uncertainties can be directly quantified by the logarithmic standard deviation of a distribution. Based on these probabilistic parameters, the fragility curves of the isolated buildings considered in this study are found in Figure 10.  
Figure 10: Fragility curves of prototype isolated buildings: (a) 3-story; (b) 5-story; (c) 10-story. Figure 9: Incremental dynamic analyses (IDA) curves for isolated buildings located at low-to-moderate seismicity regions. 2.2 Assessment of Probabilistic Propagation of Modeling Uncertainty Sources Related to Isolated Buildings  
There are various sources resulting variations on the seismic response of a structural system [34]. Uncertainties are typically classified into record-to-record uncertainties, modeling uncertainties, design requirement uncertainties, and test data uncertainties. Of them, record-to-record variability can be, as mentioned above, quantitatively evaluated from IDA results that can be obtained by repeated seismic analyses of structures using various ground motion records. Design requirement-related uncertainty and the test data uncertainty can be quantified in terms of their quality rating in accordance with requirements in FEMA P695 [17].