## 6 Conclusions  
Through changing the number of dropped floors and spans, two groups of three structures were established, namely: C1K2 YBR, C2K2 YBR, and C3K2 YBR, and C2K1 YBR, C2K2 YBR, and C2K3 YBRR. Using incremental dynamic analysis (IDA), comprehensive discussions were conducted on the vulnerability of mountainous dropped-floor frame-energy dissipation brace structure systems from aspects including IDA fragility curves, seismic demand models, vulnerability functions, probability of failure, vulnerability indices, collapse margin ratios, and safety margin ratios. The following conclusions were drawn regarding the influence of the numbers of dropped floors and spans:  
1. The change in the number of dropped floors had a greater impact on the vulnerability of the mountainous dropped-floor frame-energy dissipation brace structure system compared to the change in the number of spans. 2. The variation in the numbers of dropped floors and spans did not effectively control the discreteness of \(\ln(\theta_{max})\), as observed from the comparison between the data distribution of the seismic probability model and the demand function. Under the same input seismic intensity, the slopes of the five demand functions remained around 1.1, indicating that the energy dissipation braces could uniformly distribute the structural deformation. The failure mode of the mountainous dropped-floor frame-energy dissipation brace structure system at the ground-connected side transitioned from a floor-by-floor failure mode to a global failure mode. 3. In frequent earthquakes, the exceedance probabilities of surpassing the immediate occupancy (IO) limit state for the mountainous dropped-floor frame-energy dissipation brace structures were all less than 0.5%, indicating that the structures can be safely occupied without the need for post-earthquake repairs. Similarly, for the life safety (LS) and collapse prevention (CP) limit states, the exceedance probabilities were both 0, signifying that the structures will not surpass the life safety and collapse prevention limit states, thus meeting the performance requirement of \"minor earthquakes do not cause damage\". In design basis earthquakes, the exceedance probabilities of surpassing the LS limit state for all structures were less than 5%, suggesting that the structures were only beginning to incur damage with a low level of destruction. Under the maximum considered earthquakes, the probabilities of surpassing the CP limit state for all structures were less than 5%, significantly lower than the acceptable collapse probability of 10%, as proposed in the ATC-63 report. This indicates that structures with varying numbers of dropped floors and spans can all meet the performance requirement of \"major earthquakes do not result in collapse\". 4. The trend of the damage state probability curve differed from that of the structural vulnerability curve. It did not simply increase monotonically with the increase in seismic intensity but exhibited a descending segment, indicating that as seismic intensity increased, the structural damage state continuously changed. Under design basis earthquakes, mountainous dropped-floor frame-energy dissipation brace structures were predominantly in the DS1 damage state, with little risk of collapse. Under maximum considered earthquakes, these structures were unlikely to exceed the DS3 damage state, meeting the performance criterion of \"resistance to major earthquakes\". Even under extremely rare earthquakes, these structures were mostly in the DS2 or DS3 damage states, with an extremely low probability of collapse. 5. According to the design specifications in China, for mountainous dropped-floor frame-energy dissipation brace structures with varying numbers of dropped floors and spans, under frequent earthquakes, the upper limit of the vulnerability index remained around 30%, with a lower limit of less than 1% and an average of about 15%. The damage ranges were all below 30%. The seismic damage of these structures was generally limited to minor damage levels.