## 3 Ground Motion Time Histories  
For nonlinear response history analyses and the optimization algorithm in this study, instead of selecting input ground motion time histories from past earthquakes in areas other than the bridge site and modifying them significantly to match the current conditions, real records of strong motions are utilized that resemble the following conditions:  
1. Distance to the causative fault approximately the same as the distance of the bridge to the closest active seismic fault. 2. Size of the earthquake equal to the probable maximum magnitude at the closest fault. 3. Soil conditions and deeper geological surroundings of the recording station similar to those beneath the bridge. The bridge is located in Orange County of Southern California, and the two closest fault zones are the Whittier-Ellsinore, which is 11.6 km to the northeast, and the Newport-Inglewood, which is 20 km to the southwest of the bridge. Both faults are right-lateral strike-slip faults [42; 43]. The Whittier-Ellsinore fault has a slip rate of 2.5 to 3.0 mm/year and is estimated to be capable of a 6.0-7.2 magnitude (\(M_{\mathrm{w}}\)) earthquake, while the Newport-Inglewood fault has a slip rate of approximately 0.6 mm/year and could generate a 6.0-7.4 magnitude (\(M_{\mathrm{w}}\)) earthquake [44]. Therefore, in this study, it is decided to analyze the benchmark bridge when exposed to an \(M_{\mathrm{w}}\) = 7.2 earthquake with the causative strike-slip fault at around 11 km from the site. According to [PERSON] and [PERSON] [45], a geotechnical exploration at the location of the piers and near the end abutments was conducted before construction, down to a depth of about 35 m. The moderately stiff soil was identified, and the shear wave velocity of 200 m/s was estimated [45]. Hence, real strong motion records at the stations with similar local soil conditions were looked for. A further requirement is for the deeper geological conditions of the recording sites to resemble the geological surroundings of the benchmark bridge. The reason is that the geological characteristics up to depths of hundreds of meters or even a few kilometers may strongly affect the severity of surface seismic waves with both the shorter and longer oscillation periods [46]. Several recent seismic micro zonation and strong motion studies have shown that this influence is also regionally dependent [47; 48]. Therefore, to properly capture deeper geological conditions, it is decided to use the strong motion time histories recorded in Southern California as close to the benchmark bridge as possible. Usually, it is very difficult to find strong motion records that will match all defined criteria above, but in this study, fortunately, such records are found. Table 1 illustrates the two records (each with three orthogonal components, i.e., two horizontal and one vertical) available at PEER Ground Motion Database [49], which closely match the defined earthquake and site conditions. Table 1 includes PEER Record Sequence Numbers (RSN), station name, pulse period, significant duration, Peak Ground Acceleration (PGA), earthquake name, magnitude, fault mechanism, distance to the rupture, and shear wave velocity for the first 30 m of the stratigraphic profile. For both records, the causative earthquake was the 2010 \"El Mayor-Cucapah Mexico\" earthquake with \(M_{\mathrm{w}}\) = 7.2 and strike-slip fault mechanism. Moreover, both were recorded around 10 km from the fault, in Southern California, with the shear wave velocity parameter, Vs30, relatively close to 200 m/s. Another substantial point is that both records represent near-source ground motions that exhibit distinguishable strong acceleration and velocity pulses. In addition to the two real records, 10 synthetic accelerograms are generated to account for stochastic features of strong ground motion. Figure 3a,b show the recorded acceleration time histories described in Table 1, and the corresponding synthesized accelerograms, for both horizontal ground motion components.