## 4 Application of Record Selection Model
Furthermore, it was found that the _MSE_ values of selected GMs were dramatically low, and they were calculated as 0.23% and 0.05% for the horizontal and vertical GM sets, respectively. Figure 9: GM selection for uni-directional selection according to the TBEC for Soil ZD: **(a)** initial steps of the model for the horizontal direction; **(b)** initial steps of the model for the vertical direction; **(c)** final GM records for the horizontal direction; **(d)** final GM records for the vertical direction. Horizontal and vertical GM selection according to the TBEC and EC8 for different soil classes are plotted in Figure 10. As seen in the figures, the mean spectrum of the horizontal and vertical selected GMs aligns with the corresponding target spectrum. These figures also show that the vertical components correspond to the horizontal direction components (e.g., 3007y and 3007z for TBEC-ZC) and the same scaling value is used with the horizontal component. The _MSE_ values of the horizontal GM sets were calculated as 0.14%, 0.61%, and 0.45% for TBEC-ZC, EC8-B, and EC8-C, while the _MSE_ values of the vertical GM sets were calculated as 0.04%, 0.07%, and 0.07% for TBEC-ZC, EC8-B, and EC8-C. Besides the two-dimensional NDAs, determination of full structural behavior necessitates using three-dimensional NDAs. For this purpose, three components of GM records (X, Y, and Z) can be used for performing the NDAs. In this case, bi-directional GM selection, which accounts for both the horizontal orientation of GMs and their vertical component, should be selected accordingly. For this aim, the proposed model is run, and the results are plotted in Figure 11 for three components of the GM simultaneously according to ZC and ZD soil classes in the TBEC. It should be noted that the horizontal response spectrum of selected GMs was computed by the SRSS of the two horizontal components of the same GM,  
Figure 10: GM selection for uni-directional selection with the vertical component for different seismic codes and local soil classes **(left:** scaled GM of the X or Y direction; **right:** scaled GM of the Z direction). as suggested in the TBEC. For example, 627 represents the SRSS spectrum of 627x and 627y. Figure 11 shows that the refined solution model achieves excellent compatibility between the mean of selected GMs for both horizontal and vertical directions according to the TBEC compatible selection for both soil classes. The results demonstrated that the scaling values of GMs in a set for the ZD soil class were 2.110, 2.040, 1.160, 0.614, 2.885, 2.425, 2.054, 3.075, 3.159, 3.473, and 0.652 for 627, 955, 3575, 561, 649, 1180, 4153, 3276, 5975, 613, and 5782, respectively. The same scaling values were also applied for the vertical direction of GMs. Finally, it was observed that the _MSE_ values of selected records for ZC were considerably lower, such as 0.13% and 0.04% for horizontal and vertical GMs, respectively. Similarly, the _MSE_ values for ZD were calculated as 0.26% and 0.04% for the horizontal and vertical GMs set. Three components of records according to EC8-based GM selection using different local soil classes are plotted in Figure 12. It should be noted that the compatibility between the mean spectrum of scaled horizontal and vertical GM spectra and their target spectrum is quite high. The _MSE_ values of horizontal GM sets were calculated as 1.57% and 0.99% for EC8-B and EC8-C, respectively. For vertical GM sets, the _MSE_ values were found as 0.07% and 0.05% for B and C soil classes, as recommended in EC8, respectively. To make quantitative comparisons, three more GM sets (four sets in total) for different seismic codes were added and the _MSE_ values are aggregated in Table 2. It is worth noting that Table 2 results are obtained for \(T=1.0\) s. It can be seen in the table that the maximum _MSE_ value is 1.566% for the horizontal direction obtained for 3D analysis considering the ZC soil class for EC8. Nevertheless, the obtained _MSE_ value is quite low compared to the _MSE_ values in the literature [58].