## 3 Natural and Artificial Ground Motion Records
### Natural Records  
In this study the method recommended by ASCE/SEI Standard 7-16 [25] was chosen for the selection of the ground motion records. For the natural records, 22 pairs of records with the best spectrum match were selected from a large pool of records including 326 record pairs selected from the PEER-NGA ground motion database for the purpose of this study. The minimum limits on magnitude (M), peak ground acceleration (PGA) and peak ground velocity (PGV) were 6.0, 0.1 g and 10 m/s, respectively, for the records in the pool. These limits were chosen based on the recommendations available in different guidelines and research (e.g., [26; 27]) to select the records with sufficient strength and intensity that do not need large-scale factors to match the target spectrum and can cause structural damage. A computer code was developed for this purpose so that the records with the best matches to the target design spectrum were selected from the pool of records for each structure. For measuring the match with the target spectrum the sum of the squared errors between the logarithms of the ground motion's spectrum and the target spectrum was used [28]. For 3D analyses the records were selected so that the SRSS spectrum of the records matches 1.3 times the design spectrum [27]. For the 2D analyses the mean spectrum of the 44 horizontal components were matched to the design spectrum.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **T\({}_{\text{T}1}\) (s)** & **T\({}_{\text{T}2}\) (s)** & **T\({}_{\text{L}}\) (s)** & **T\({}_{\text{G}}\) (s)** \\ \hline Regular bridge & 0.75 (87\%) & 0.28 (8\%) & 0.90 & 0.82 \\ Irregular bridge & 0.93 (90\%) & 0.29 (5\%) & 1.28 & 1.09 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Modal properties including periods and (effective modal mass ratios).  
Figure 3: Comparison of the experimental data for the short column of the bridge B213C tested by [PERSON] et al. [21] and results from numerical analysis: (**a**) column displacement for the maximum earthquake; and (**b**) response of the column in reversed cyclic loading test.  
A period range of 0.2T to 3T was used for spectrum matching, where T is the fundamental period of the structure. The smaller fundamental period in the transverse and longitudinal directions was used to determine the lower bound of 0.2T and the larger period was used to determine the upper bound of 3T. It is noted that a shorter period range (i.e., 0.2T to 2T) is typically recommended in current seismic design provisions. However, some studies suggest that the period range up to 3T can influence the non-linear seismic response of ductile structures [27].  
The selected records had a magnitude, M, range of 6.5 to 7.6, PGA range of 0.11 to 0.54 g, PGV range of 11 to 54 m/s, range of 200 to 725 m/s and a hypo-central distance range of 11 to 54 km. The response spectra of the 44 horizontal components of the selected records are shown in Figure 4a. The target spectrum in Figure 4 is the uniform hazard spectrum for Vancouver, site class C, having a probability of exceedance of 2% in 50 years [29].  
The variation of the predicted mean response of the central column, C2, with the number of records is shown in Figure 5a,b for the regular and irregular bridges, respectively. The results suggest that the use of a minimum number of 7 records, as recommended in some seismic codes, leads to satisfactory predictions of the mean radial displacements. In this study for the case of the natural records the results obtained using 22 record pairs (i.e., 44 horizontal components) are presented. For the case of the artificial records since these records are closely matched and are compatible with the target spectrum, 14 horizontal components were used.  
Figure 4: Response spectra for all records and mean response spectrum for the case of: (a) natural records; (b) Atkinson records; and (c) SIMQKE records.  
Figure 5: Influence of the number of records on the predictions of the mean displacement of column C2 for: (a) regular bridge and (b) irregular bridge.