## 3 Results and Discussion
### Target Responses of FBR and BIR  
Figures 7 and 8 show the results of the target responses: maximum base shear load (\(Q_{o}^{max}\)) normalized by the seismic weight (\(P_{s}\)), maximum drift and maximum displacement of the top storage level, for all FBR and BIR analyzed. Figures 7a,d,g and 8a,d,g of both figures show the scatter plot. Figures 7c,f,i and 8c,f,i show the output response of the unconditional and conditional cumulative distribution curves (CDF) when setting a parameter \(x_{i}\). Figures 7b,e,h and 8b,e,h show the Kolmogorov-Smirnov (KS) statistic. The value of KS corresponds to the maximum difference in the vertical axis between the conditional and unconditional CDFs for the output variables, where random values of the input parameter are set. In these figures, circles of various gray colors are observed in the KS statistic, whereas in the CDFs these are represented by lines with the same color. The variation of the gray colors corresponds to the number of conditioning points of a certain input parameter. In other words, they represent all the set values of the parameters. In this way, by setting the input parameter to a certain value, it is possible to explain what happens when the variability of said parameter is eliminated. As mentioned in Section 2.4, the influence of the parameters on the target response in the conditional and unconditional CDF graphics (Figure 6), is represented by how far the conditional CDFs (gray lines) are from the unconditional CDFs (red lines). For the parameters that were not influencing the response, it was observed that their conditional CDFs tended to overlap with the unconditional CDFs. The above suggests that the particular response of the model was insensitive to these parameters. This can be corroborated with the KS statistic in Figures 7 and 8. In Figure 7b,c, it can be observed that in BIR, the parameter that had the greatest influence on the maximum normalized base shear load (\(\hat{Q}_{o}^{max}\)) was the height of the BIKD (\(H_{iso}\)). Whereas in rows of Figures 7e,f,h,i and 8e,f,h,i, it can be observed that the parameters with the greatest influence on the maximum drift and displacement were \(N_{sl}\) and \(H\). The influence of \(H_{iso}\) in the response \(\hat{Q}_{o}^{max}\) corroborates with the scatter plot of Figure 7a. The relationship between this parameter and \(\hat{Q}_{o}^{max}\) is explained by the fact that \(H_{iso}\) is related to a variation in the lateral stiffness of the BIKD, particularly for large displacements. The lower the parameter, the greater the \(u/H_{iso}\) ratio, and the greater the elongation of the elastic element \(\Delta l\) inside the BIKD--Equation (2)--forthe same lateral displacement \(u\). Due to the above, the tangent stiffness of the BIKD--term \(T(u)/H_{iso}\) in Equation (1)--grew at a higher rate as the lateral displacement \(u\) increases. This is so because when the BIKD had a low height, the tension of the elastic element \(T(u)\)--Equation (3)--grew at a higher rate as \(u\) increased, than in the case when the height was large. Therefore, with a higher the value of \(H_{iso}\), the lateral stiffness of the BIKD was practically constant, whereas for low values of this parameter an increase in the tangent lateral stiffness of the BIKD was observed as the lateral displacement increased. From the results shown in Figure 7a, it can be observed that in a range of \(H_{iso}\) approximately between 0.3 m and 0.5 m there was a significant variation in the response \(\hat{Q}_{o}^{max}\). However, for values greater than 0.5 m the response tended to be constant. The value of \(\hat{Q}_{o}^{max}\) was lower for values of \(H_{iso}\) > 0.5 m because the BIKD does not stiffen due to the large lateral displacements, which resulted in a lower demand for base shear load compared with the case with 0.3 m \(<H_{iso}\) < 0.5 m.  
Figure 7: Scatterplot, Kolmogorov-Smirnov Statistics (KS) and conditional and unconditional CDFs of the target responses.