## 4 Analysis of Structure Progressive Collapse Performance under Ordinary Ground Motion  
### Failure Condition of Isolation Bearing  
The new version of DoD2010 [16] strictly limits the large deformation beyond the ultimate deformation capacity of the remaining structural system after the components are removed. In this paper, when analyzing the base-isolated frames supported by stepped foundation in mountainous, the collapse failure criterion is adopted: that is, the failure criterion of the remaining structural system after the removal of the vertical members is that the maximum vertical displacement of the failure point is 20% of the connected shortest span. Take the two-story three-span seismic isolation structure C2K3 to remove the lower ground seismic isolation angle support, A, the lower ground internal seismic isolation support, B, and the upper ground seismic isolation angle support, F, as an example. Analyze the dynamic response of the structure under the condition of vertical unbalanced load and bidirectional dynamic coupling, and the load factors are all taken as 0.5. First, adjust the PGA of the ground motion to 0.7 g, and then remove the support at 1.5 s while inputting the horizontal seismic wave to the X-direction node of the seismic isolation support of the remaining structure. The duration of the seismic wave was 25 s.  
It can be seen from Figure 12 that the maximum displacement and stability value of the failure point of the seismic isolation structure only considering the effect of the vertical unbalanced load (only the support is removed) are much smaller than the case under the bidirectional dynamic excitation. Generally speaking, the remaining structure after only dismantling the support is stabilized in 4-5 s, but under the two-way dynamic coupling, the vertical displacement of the failure point of the remaining structure still increases to varying degrees due to the horizontal earthquake. It can be seen from Table 2 that, after the seismic isolation support A was removed, the displacement amplitude and the displacement stability value of the failure point under the bidirectional dynamic excitation were, respectively, higher than 2.8% and 2.2% when only considering the vertical unbalanced load; after the seismic isolation support was removed, the displacement amplitude and stability value of B under bidirectional coupling excitation were 4.3% and 4.4% larger than that without considering the horizontal seismic effect. The same situation increased by 4.7% and 4.9% at point F. The displacement of the failure condition of the inner support B and the upper grounding angle support F was significantly smaller than the failure condition of the corner support A. It can be seen from Table 2 that, for the flat ground isolation structure, after the corner support was removed, the displacement amplitude and the stability value of the failure point under the two-directional coupled dynamic excitation were, respectively, higher than 8.6% and 6.8%, which only consider the vertical unbalance. In the flat ground isolation structure, after the B support is removed, the displacement amplitude and the stability value of the two-directional coupled dynamic excitation are only considered to be 8.4% and 11.7%, respectively, when the vertical unbalance was considered. After the C bearing was removed, the ratio was 9.4% and 11%. In summary, the progressive collapse resistance of the seismic isolation structure under the two-directional coupled dynamic excitation is weaker than that when only the vertical unbalanced load is considered. Comparing Tables 1 and 2, it can be seen that, under the excitation of two-directional coupled dynamic excitation, the progressive collapse performance of the seismic isolation support of the base-isolated frames supported by stepped foundation in mountainous areas is weaker than that of the flat isolation structure.