## 3 Application Example
### Analysis Results  
In this section, the mean traffic quantity of various epicenters and earthquake magnitudes were estimated using the surrogate model which was described in Section 3.3. Twenty locations of the input earthquake ground motion were considered (Figure 5), and the earthquake magnitude range at the epicenter was considered to be M 4.5 to 7.5. The accuracy of the surrogate model was verified through the correlation coefficient of the generated surrogate model, and a surrogate model was applied to evaluate network performance according to the various earthquake magnitudes. In addition, to identify convergence of network performance, the relative error of the coefficient of variation (COV) of network performance according to the number of samples was confirmed. As an example, Figure 9 shows the convergence of the mean TSTT according to the number of samples at Epicenter 8 with an earthquake of magnitude 7.5. It is also noted in Figure 9 that 10,000 samples were required for only one set of epicenter and earthquake magnitude, and it took approximately 2 s to calculate a TSTT for each sample using EMME/4 and a general-purpose personal computer. For seismic risk assessment, similar analysis should be conducted repeatedly for many different sets of epicenters and earthquake magnitudes. In this example, the range of earthquake magnitudes (i.e., M 4.5 to 7.5) is divided by 0.1 intervals and 20 epicenters are considered, which means that the same MCS analysis with 10,000 samples should be conducted 620 times. For the proposed method, however, only one set of 100,000 samples was required to construct the surrogate model. Once the surrogate model is constructed, it took less than a minute to calculate TSTTs for each epicenter and earthquake magnitude with 10,000 samples. Figure 10 shows the mean TSTT values for earthquakes of 4.5 to 7.5 magnitude at 20 epicenters and uncertain locations. The mean TSTT of the bridge transportation network tended to increase as the magnitude of the earthquake increased, and the mean TSTT tended to decrease as the epicentral distance from the principal network component increased. This is because the reduction in capacity of each bridge component depends on the intensity and distance of the earthquake. Figure 10a,b show that the mean TSTT decreased because the epicenter was farther from the target network compared with the mean TSTT of uncertain locations (except for EQ8). In addition, earthquake magnitudes below 6.5 did not significantly affect the average TSTT because the location of the epicenter was far. However, as the earthquake magnitude gradually increased, the mean TSTT tended to increase rapidly. On the other hand, in Figure 10c,d, the mean TSTT at locations 11-20 was significantly increased compared  
Figure 9: Convergence of mean total system travel time (TSTT) according to the number of samples. to the mean TSTT of the uncertain location because the considered epicenter was located around the target network. Moreover, since the location of the epicenter was adjacent to the principal bridge structure, the mean TSTT tended to increase rapidly even at relatively small earthquakes of M 6.0. Figure 11 shows the distribution of the mean TSTT for uncertain earthquake magnitudes over 20 epicenters, and the red curve shows the mean TSTT for uncertain locations. As seen in Figure 10, it was found that the closer the epicenter location to the target network, the greater the impact of the mean TSTT. On the other hand, it was confirmed that the epicenter located relatively far away had a small effect on the mean TSTT. In particular, it was confirmed that the locations of epicenters 8 and 14 had a significant effect on the entire traffic flow of the target network. Figure 10: Evaluation of mean TSTT with different epicenters and earthquake magnitude. (**a**) Locations 1 to 5, (**b**) locations 6 to 10, (**c**) locations 11 to 15, and (**d**) locations 16 to 20.