# Stochastic Analysis of a Large-Span Continuous
## 3 Stochastic Seismic Response of the Large-Span CGHSR Bridge
### Structural Stochastic Seismic Response
Furthermore, the time-dependent dynamic displacement RMS of the gir  
Figure 7:1 Time-dependent absolute displacement RMS at the mid-span: (**a**) Vertical (\(z\) direction); (**b**) Transversal (\(y\) direction). Figure 7:2 Time-dependent absolute displacement RMS of the girder in \(y\) direction (Transversal): (**a**) MCS; (**b**) PEM (Unit: m). As shown in Figures 12 and 13, the time-dependent dynamic displacement RMS obtained by the MCS method fits well with that obtained by the PEM, indicating that the quasi-static displacement obtained by the PEM and MCS methods also agree well with each other. Thus, the reliability of the proposed POD-based method in Table 1 is validated. The vertical dynamic displacement is evidently relatively larger than that in the transversal direction. In addition, the time-dependent dynamic displacement RMS at the mid-span is shown in Figure 7:3  
In Figure 14, the maximum values of the dynamic displacement RMS in both directions are close to each other (0.036 m in \(z\) direction and 0.033 m in \(y\) direction). It can also be concluded that the structural dynamic and quasi-static displacement contributes almost the same to the nodal absolute displacement of the CGHSR bridge. Moreover, as there is no obvious increase in the dynamic displacement RMS from \(t=16\) s to 20 s, the second peak value for the absolute displacement is mainly caused by the quasi-static displacement. Hence, it is significant to determine the quasi-static displacement reasonably when considering the fully non-stationary seismic excitation. Meanwhile, the structural stochastic response is also estimated under the equivalent modulated non-stationary seismic excitation, as shown in Figure 7:4  
Figure 7:5 Time-dependent dynamic displacement RMS of the girder in \(z\) direction (Vertical): (**a**) MCS; (**b**) PEM (Unit: m). Figure 7:6 Time-dependent dynamic displacement RMS of the girder in \(y\) direction (Transversal): (**a**) MCS; (**b**) PEM (Unit: m). The time-dependent absolute displacement RMS is estimated using the PEM in Figure 7:7 From Figure 15, it can be seen that the estimated absolute displacement RMS also has time-varying characteristics, which are similar to those in Figures 9 and 10. To further compare the difference of the structural seismic response under fully and modulated non-stationary seismic excitations, the time-dependent absolute displacement RMS at the mid-span is compared in Figure 7:8  
Figure 7:9 Comparison of the absolute displacement RMS at the mid-span: (**a**) Vertical (\(z\) direction); (**b**) Transversal (\(y\) direction). Figure 8.0 Time-dependent absolute displacement RMS at the mid-span: (**a**) Vertical (\(z\) direction); (**b**) Transversal (\(y\) direction). Figure 8.1 Time-dependent absolute displacement RMS (Modulated non-stationary): (**a**) Vertical (\(z\) direction); (**b**) Transversal (\(y\) direction) (Unit: m). As shown in Figure 16, the maximum displacement RMS at the mid-span is 0.085 m in the \(z\) direction and decreases to 0.060 m in the \(y\) direction under the equivalent modulated non-stationary seismic excitation, which is lower than the corresponding values under the fully non-stationary seismic excitation. Furthermore, the second peak values of the absolute displacement RMS under modulated non-stationary seismic excitation are much lower than those under fully non-stationary seismic excitation in both directions, indicating that ignoring the frequency non-stationarity of the ground motion can underestimate the structural response caused by the surface waves for such a large-span CGHSR bridge. Thus, it is significant to consider the fully non-stationary characteristics (both intensity and frequency) of the earthquake ground motion to design the large-span CGHSR bridge. As for design process, the stochastic analysis are much simpler to be conducted for modulated cases, thus the amplification coefficients can be personally defined to modify the results in modulated cases in order to consider the seismic fully non-stationary characteristics.