## 3 Collapse Performance of Seismically Isolated Buildings
### Collapse Capacity Evaluation of the Prototype Isolated Buildings  
#### 3.2.1 Results of Incremental Dynamic Analysis  
Since isolated buildings should assure stable behaviors subjected to more severe earthquakes than conventional structures and their seismic performance is mainly dependent upon the cyclic behavior of the isolation systems, more rigorous evaluations for isolators are required. In this study, the structural capacities of the prototype isolated buildings were evaluated using the incremental dynamic analysis (IDA). The maximum story drifts of the superstructures and the maximum deformation of the isolation systems were observed with incremental earthquake intensities. The rigorous IDA methodology is based on the relation between the seismic response of a structure considered and the intensity levels of potential ground motion records. For the IDA procedure, this study implemented a hunt-and-fill algorithm that increases earthquake intensities until a structure reaches collapse. At a step finding the collapse of a structure, the process carries out backward filling between earthquake intensities in the previous steps [33]. The collapse points are defined as the spectral acceleration \(S_{\alpha}(T_{M})\) at the effective period, \(T_{M}\), of an isolated building at the collapse. Figures 8 and 9 present the IDA curves of the prototype isolated buildings built at high and low-to-moderate seismicity regions, respectively. The slight, moderate, extensive, and collapse damage states presented in the figures are referred from HAZUS-MH [30]. In addition, the figures contain an earthquake record that the median collapse IDA curve is generated, and a collapse margin ratio (CMR) is defined as a ratio of a median collapse spectral acceleration to the MCE spectral acceleration, \(S_{MT}\). Collapse points defined as a pair of the seismic demand and capacity are presented as scattered dots on the IDA curves. CMR values, median ordinates of scattered dots in the figures, of the prototype isolated buildings are significantly larger than 1.0 and are dependent on the critical failure modes of the isolated buildings. The CMR values of the isolated buildings located at low-to-moderate seismicity regions are larger than those at high seismicity regions. For the 3-story isolated buildings designed for high seismicity regions, 3S\({}_{\text{E}}\)40C and 3S\({}_{\text{E}}\)30B buildings in the figures, collapse points are collectively scattered around the collapse damage criteria for the maximum displacement of isolation systems, while collapse points gather far from the collapse damage criteria of the superstructures. This is demonstrated from the observation that at the collapse state, the superstructures experience slight or moderate damage states corresponding to 0.63% and 1.0% for story drift ratio rather than the collapse [30]. It is confirmed from this that the critical failure mechanism of the 3S\({}_{\text{E}}\)40C and 3S\({}_{\text{E}}\)30B buildings is the concentrated deformations at the isolators followed by the failure of isolation systems. These concentrated deformations at the isolation systems induce the pronouncing decoupling effect that let the superstructure almost behave as a rigid body (very small story drifts relative to isolator's displacements) and lower seismic energy transmitted. Similar observations are found on the 5- and 10-story isolated buildings, denoted as 5S\({}_{\text{E}}\)40C, 5S\({}_{\text{E}}\)30B, and 10S\({}_{\text{E}}\)30B buildings in the figures, which are designed for high seismicity regions except for the 10S\({}_{\text{E}}\)40C building where the governing collapse mode is determined by lateral displacements of the superstructure. The larger structural period of the tall 10S\({}_{\text{E}}\)40C building causes the decoupling effects to vanish.