## 4 Uncertainty Sensitivity Analysis
### Analysis Result
It is important to note that due to the soil layer at the target span's location, the shallowest sandy layer is situated at a depth of 23.5 m (beneath Pier #1), and for other piers, the sandy layer is even deeper. Therefore, the structural response discussed in this study is not significantly sensitive to variations in the sandy soil resistance \(P_{ult,clay}\). Under L2 seismic loading, the results of the parameter sensitivity analysis are illustrated in Figure 7. Due to space constraints, only the longitudinal bridge analysis is presented. The findings from the parameter sensitivity analysis for L2 show overall consistency with those from L1. Factors contributing to variance by more than 10% remain as follows: the specific weight coefficient \(\lambda_{w}\), the bearing friction coefficient \(\mu_{baring}\), the clay ultimate resistance \(P_{ult,clay}\), the damping ratio \(\zeta\), the elastic modulus \(E\), and the clay ultimate deformation \(y_{50,clay}\). Notably, unlike in the L1 scenario, the limit force of the isolation bearing \(F_{limit}\) has a diminished impact on the structural seismic response, resulting in a significant decrease in its variance contribution compared to L1. This can be attributed to the fact that at this level of seismic intensity, the fuse within the isolation bearings melts earlier, subsequently ceasing to influence the behavior of the structure during the remaining seismic events, thereby limiting its effect on the maximum seismic response of the bridge. Figure 7: _Cont._  
To investigate whether the influencing factors on structural seismic response change under more intense seismic loading and more pronounced end collision effects, Table 3 lists the variance contributions of each factor under the L3 seismic loading scenario using the first-order second-moment method. The analysis reveals that the factors contributing more than 10% variance under L3 remain consistent with those identified in L2. At the intensity associated with L3 loading, among the factors related to the collision effects (end gap \(\Delta\), collision stiffness \(K_{e\!f\!f1}\) between the left joint and the target joint, and collision stiffness \(K_{e\!f\!f2}\) between the target joint and the right joint), the end gap \(\Delta\) exhibits the most significant effect. However, its maximum variance contribution is only 0.82%, indicating a relatively limited impact on the structural seismic response, and it does not alter the selection results for the significant factors. Table 4 presents the variance contributions of various factors under higher-intensity L4 seismic loading, as determined by the first-order second-moment method. The results indicate a slight deviation from the previously discussed conditions, with the influence of the elastic modulus \(E\) showing a decrease, thereby excluding it from the tier of factors with more than 10% contribution. The selection results for the other parameters remain largely consistent with those observed in earlier scenarios. Under L4 seismic loading, the variance contribution of the steel damping yield force \(F_{dampe}\) has increased, nearing a maximum  
Figure 7: Sensitivity analysis results along the bridge direction under L2 action. contribution of approximately 4%. Although the influence of the beam end gap \(\Delta\) has risen, it remains insignificant when compared to other influencing factors. To enhance the generalizability of the results, scenarios excluding end collision effects were added for L3 and L4 seismic intensities. The outcomes indicate that the selection results remain largely unchanged when considering or disregarding end collision effects. The parameter sensitivity analysis results for L1, L2, L3, and L4 seismic intensities are summarized in Table 5. The limit force of the bearing \(F_{limit}\) is identified as a significant influential factor unique to the L1 seismic intensity. The impact of the elastic modulus \(E\) is observed to decrease under L4 loading, thereby excluding it from the cohort with a variance contribution greater than 10%.