## 6 Analysis of Retrofit Effect of SSDB Systems
### Story Displacement Response  
In this section, story displacement response analysis of MD-RC frames with and without retrofitting schemes is carried out for the purpose of evaluating the retrofit effect of CSSDB systems under three layout schemes. As was mentioned previously, two damage states (i.e., DS1 and DS2) of the MD-RC frame after MS1 and MS2 excitations are considered. Meanwhile, four aftershocks, including near-fault pulse-like earthquakes (AS1 and AS2) and non-pulse-like earthquakes (AS3 and AS4), are selected as secondary excitation. As an example, Figures 10 and 11 show the story displacement responses of retrofitted and un-retrofitted MD-RC frames subjected to AS1 and AS3 aftershock. In Figures 10 and 11, the first column shows the displacement time histories of the intact frame under the mainshock excitations, the second and third columns show the relative displacement during aftershocks with respect to the residual displacement after mainshock excitations. From the overall view of Figures 10 and 11, the peak story displacement of MD-RC frame after retrofitting significantly drops when compared with un-retrofitted MD-RC frame, which indicates that CSSDB systems can effectively control the peak displacement response of MD-RC frame. In addition, the peak story displacement of retrofitted MD-RC frame under AS1 aftershock decrease more significantly than that of AS3 aftershock. This result indicates CSSDB systems are more effective in controlling the dynamic response under pulse-like aftershock. Similar to the above conclusion, the residual displacement of MD-RC frames under pulse-like aftershocks also decreases significantly. As the number of retrofitted floors increases (i.e., from LS-1 to LS-3), the decrease of residual displacement becomes more obvious. However, for non-pulse-like aftershocks, the residual displacement of MD-RC frame slightly and irregularly changes. Especially for moderate damaged (DS2) structures (see Figures 10 and 11), the retrofitting devices caused a greater permanent displacement for MD-RC frames. The reason may be that the retrofit of MD-RC frame will cause the redistribution of internal force in the structure, which results in the change of structural natural period and mode shape. When non-pulse-like aftershocks (containing rich high-frequency components) act, the presence of high-frequency components will excite high-order mode shapes of the MD-RC frame, resulting in a complex displacement response and permanent displacement. Especially when the mainshock damage state of MD-RC frame is more serious, this phenomenon is more obvious. Therefore, in the retrofit design of seismic-damaged structures, it is necessary to ensure that the retrofitted structure has a reasonable internal force distribution form. In addition, the above results also indicate that both of retrofitting schemes and aftershock types have a significant influence on displacement response of MD-RC frame. Furthermore, when comparing the mainshock damage state of MD-RC frame, the retrofit effect of CSSDB systems on the MD-RC frame with minor damage (DS1) is slightly better than that of moderate damage (DS2) no matter that aftershock types. A similar conclusion could be observed from the results of other aftershocks listed in Table 4.  
Moreover, in order to quantitative assess the retrofit effect of CSSDB systems under three layout schemes on MD-RC frame, the peak displacement degradation percentage (PDDP) is defined by,  
\[PDDP=\frac{d_{ur}^{i}-d_{r}^{i}}{d_{ur}^{i}}\times 100\% \tag{3}\]  
where, \(d_{ur}^{i}\) and \(d_{r}^{i}\) are the maximum displacement at \(i\)th story of un-retrofitted and retrofitted MD-RC frame, respectively. Table 7 presents PDDP values (%) of MD-RC frame under different retrofit schemes for each story. Intuitively, the mean values of PDDPs under pulse-like aftershocks (i.e., AS1 and AS2) are generally greater than that of non-pulse-like aftershocks (i.e., AS3 and AS4) no matter which retrofitting schemes.