## 4 Analysis of Structural Uncertainty
### Analysis of Structural Uncertainty  
In this paper, the PGA of the selected ground motions are adjusted to 0.7 g for the desired requirements of elastic-plastic dynamic analysis and a nonlinear dynamic time-history analysis of extradosed cable-stayed bridges subjected to the longitudinal and transverse ground motions is carried out. The maximum responses in these models are defined as the reference value, and the results of each SFDP are shown in Table 6. According to the distribution of random parameters as shown in Table 4, the variation of each SFDP can be obtained by substituting the random parameters into OpenSEES model for calculation. According to the nonlinear results calculated by the selected ground motions, regression analysis of each seismic demand parameter is carried out to obtain the demand value so that the influence of the uncertainty of earthquake excitations can be considered. Subsequently, the sensitivity of each SFDP can also be obtained, which is divided by the reference value as in Table 6. Sensitivity results of the SFDP under the longitudinal ground motion are shown in Figure 13a-f. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Seismic Response in Longitudinal Direction**} & \multicolumn{3}{c}{**Seismic Response in Transverse Direction**} \\  & **10\# Pier** & **11\# Pier** & **12\# Pier** & **13\# Pier** & **10\# Pier** & **11\# Pier** & **12\# Pier** & **13\# Pier** \\ \hline Displacement of pier & & & & & & & & \\ Top (units: m) & 0.38 & 0.33 & 0.363 & 0.338 & 0.059 & 0.123 & 0.149 & 0.043 \\ Main girder angle & & & & & & & & \\ (units: \(\times 10^{-3}\) rad) & 2.40 & 3.10 & 2.90 & 1.70 & 1.90 & 3.40 & 3.10 & 2.20 \\ Curvature of pier & & & & & & & & \\ bottom(/ \(\times 10^{-3}\)) & 3.80 & 4.70 & 3.30 & 7.60 & 0.12 & 1.10 & 1.30 & 0.11 \\ Bearing displacement & & & & & & & & \\ (units: m) & 0.015 & 0.048 & 0.043 & 0.025 & 0.016 & 0.123 & 0.13 & 0.016 \\ \hline  & & & & & & & & \\ \hline Curvature of pylon & & & & & & & & \\ Bottom (/\(\times 10^{-5}\)) & 4.10 & & \(-\)2.40 & & 110 & & 140 \\ Cable force & & & & & & & & \\ (units: KN) & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Result of SFDP under the benchmark model. According to the nonlinear results calculated by the selected ground motions, the regression analysis of each seismic demand parameter is carried out to obtain its calculated value, and then the influence of ground motion uncertainty is considered. According to Figure 13a-f, for pier-top displacement under longitudinal ground motions, the maximum influence of bearing friction coefficient is 42%, while the influence of concrete bulk density and damping ratio are nearly the same, at 34.4% and 34.1%, respectively. Meanwhile, the influence of the peak compressive strength of confined concrete, ultimate strain of confined concrete, component size and peak strain of confined concrete are also very close, at 33.2%, 32.2%, 32.3% and 31.3%, respectively. Compared with other random variables, these seven parameters, which are more sensitive, have a great impact on the dynamic response of the pier-top displacement of the extradosed cable-stayed bridge. For main girder angle, the influence of peak strain of confined concrete can reach up to 22.8%, and the maximum impact of concrete bulk density is 19.8%. The influence of damping ratio and component are very close as well, at 17.8% and 17.6%, respectively. Meanwhile, the influence of peak compressive strength of confined concrete is 12.2%, and the friction coefficient of the bearing is 9.6%. The influence of these six parameters is greater than that of the other parameters. For the influence of the pier-bottom curvature, the friction coefficient of bearing can reach 66.4%. The second largest influence on the curvature is concrete bulk density, which can reach 62.7%. The influence of damping ratio is 56.2%, while the peak compressive strength of confined concrete and component size are nearly the same, with influences of 53.3% and 53.2%, respectively.