## 7 Conclusions  
This paper mainly conducted the post-earthquake retrofitting analysis of the mainshock-damaged RC (MD-RC) frame while using soft steel damper as the passive energy dissipation device under near-fault aftershocks excitation. Firstly, a numerical evaluation framework for post-earthquake retrofitting of the MD-RC frame was proposed. Subsequently, three retrofitting schemes based on soft steel dampers and steel brace were designed for the MD-RC frame structure. Finally, through the nonlinear dynamic time history analysis of the MD-RC frame structure with and without retrofitting schemes, the retrofit effect of the three retrofitting schemes on the MD-RC frame was evaluated, and some conclusions were obtained, as follows:  
1. The CSSDB retrofitting systems have effectively improved the natural frequency (stiffness) of the MD-RC frame. The first-order natural frequency has a largest increase, with a maximum increase of nearly four times and the second and third-order natural frequencies have a maximum increase of three times. In addition, with the increase of the number of retrofitted stories of the MD-RC frame, the structural stiffness increases more obviously. The natural frequency of moderate damaged structures has increased significantly than that of minor damage. Especially for the first-order mode, the frequency increase in moderately damaged structures is more significant. Figure 13: IDR distribution of MS2 MD-RC frame with DS1 (**a**) and DS2 (**b**) damage state before and after retrofitting. 2. The reduction of the maximum story displacement and residual displacement of the retrofitted MD-RC frame under pulse-like aftershocks is more obvious than that under non-pulse-like aftershocks, which indicates that aftershock type has an important influence on the retrofit effect of CSSDB systems for the MD-RC frame. In addition, the retrofit effect of CSSDB systems on the MD-RC frame with minor damage is slightly better than that of the structure with severe damage, indicating that the damage state of the MD-RC frame should also be considered when carrying out the seismic retrofitting design of earthquake-damaged structures. 3. In the case of LS-1 scheme, the maximum IDR reduction rate is up to 97.7% (first story) when compared with un-retrofitted MD-RC frame. LS-1 scheme has better performance in reducing the IDR of the first story of MD-RC frame structure as compared with the other retrofitting schemes. However, the IDR reduction rate of the second and third story of MD-RC frame is lower than other schemes. Especially for the non-pulse-like aftershocks scenarios, in some MD-RC frames that were retrofitted using LS-1 scheme, and the IDRs of second and third story even exceed those of un-retrofitted MD-RC frame. The maximum IDR is 276.6% (third story) as large as the un-retrofitted case. For the LS-2 scheme, it is evident that the IDRs are lower than un-retrofitted MD-RC frame, except for the top story. Especially for LS-3, the IDR of each story of the MD-RC frame are significantly reduced no matter which damage state. Therefore, it can be seen that LS-3 plays a more positive effect on the seismic performance of the MD-RC frame. 4. The shock absorption rate (SAR) under only retrofitting bottom story (i.e., LS-1) of the MD-RC frame is lower than that of retrofitting more stories, and the difference is approximately 1.2-2.0 times lower than other retrofitting schemes for pulse-like aftershocks. However, under non-pulse-like aftershocks, the SAR of only retrofitting the structural bottom story is negative with a maximum amplitude of \(-\)74.1%. It indicates that only retrofitting the bottom story of the structure is not usually sufficient, especially for the non-pulse-like aftershocks., In addition, there is no noticeable difference in the SAR of MD-RC frames between retrofitting two stories (LS-2) and three stories (LS-3). In contrast, LS-2 might have a better economy and installation portability in engineering applications in this research.