## 4 Uncertainty Sensitivity Analysis
### Analysis Result  
For bridges designed with seismic isolation systems, the earthquake demand parameters of particular concern are the bending moments at the bottom of the piers and the relative displacements between the pier and the beams. This analysis focuses on the bending moment at the base of Continuous Pier #2 and Braking Pier #3, as well as the relative displacements between the beams of Continuous Pier #2, Braking Pier #3, and Transition Pier #1. The results of the parameter sensitivity analysis under the L1 seismic load are depicted in Figures 5 and 6, with the left side illustrating the tornado diagram and the right side showing the corresponding variance contribution diagram from the first and second moment methods. Where the ranking results of the two methods differ, red arrows have been used to indicate such discrepancies in the variance contribution diagram. The parameters with a variance contribution exceeding 10% include the specific weight coefficient \(\lambda_{w}\), the bearing friction coefficient \(\mu_{baring}\), the clay ultimate resistance \(P_{alt,clay}\), the damping ratio \(\zeta\), the elastic modulus \(E\), the clay ultimate deformation \(y_{50,clay}\), and the yield force of the seismic isolation bearing \(F_{limit}\). The counting rule applied in this study is as follows: for the engineering demand parameters of interest, regardless of whether they are assessed along the longitudinal or transverse direction of the bridge, any factor whose variance contribution exceeds the specified threshold (5% or 10%) at least once is considered a significant factor influencing the seismic response of the structure. Subsequentanalyses will adhere to this rule. If the factors are recounted using the criterion of a variance contribution exceeding 10%, the same factors will still be identified as having a considerable influence on the seismic response of the bridge structure. Among these, two factors arise from the seismic isolation device system, while five stem from the non-isolated system. Figure 5: Sensitivity analysis results along the bridge direction under L1 action. The ultimate resistance of clay exhibits a significant degree of variability relative to other factors and demonstrates a considerable impact on the calculation results of various engineering demand parameters. Since the Transition Pier lacks steel damping devices along the longitudinal direction of the bridge, the involvement of factors related to the seismic isolation device system is minimal; consequently, the clay ultimate deformation \(y_{50,clay}\) from the non-isolated system also emerges as a prominent factor. Notably, \(F_{limit}\) is a significant influencing factor unique to the L1 seismic loading scenario. In the longitudinal direction, \(F_{limit}\) has a pronounced effect on the seismic response of its corresponding pier(#3 Braking  
Figure 6: Sensitivity analysis results of transverse bridge direction under L1 action. Pier). In the transverse direction, the limited constraints exerted by the yield force appear in five locations. With variations in the set capacity threshold, whether and when the fuse mechanism engages, as well as the sequence of engagements, can significantly alter the seismic response of each bridge pier. This phenomenon explains the high variability in the bridge structure's seismic response as the threshold changes, leading to differences in the parameter sensitivity analysis results obtained from the first and second moment methods and the tornado diagram method. The first and second moment methods retain only linear terms during the derivation, making them most applicable under conditions where the changes in seismic response random variables are linear or exhibit weak nonlinearity. Nonetheless, the differences in the calculation results from the two methods mainly affect the ranking of less influential random variables without impacting the selection of the significant random variables.