## 1 Introduction
### Seismic Ground Motions  
The bridge is located in a class II site according to the Code for Seismic Design of Railway Engineering in China. Therefore, the selection of target response spectra can be obtained according to the code that can be written as  
\[S=\left\{\begin{array}{cc}S_{\max}(5.5T+0.45)&T<0.1s\\ S_{\max}&0.1s\leq T\leq T_{g}\\ S_{\max}(T_{g}/T)&T>T_{g}\end{array}\right. \tag{18}\]  
Figure 10: Detail of pile–soil (units: cm).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Calculation** & \multicolumn{6}{c}{**Longitudinal Direction Soil Spring Stiffness**} & \multicolumn{6}{c}{**Transverse Direction Soil Spring Stiffness**} \\ \cline{2-11}
**Parameters** & a & b1 & m & z & k & a & b1 & m & z & k \\ \hline Soil Division & (m) & (m) & (kN/m\({}^{4}\)) & (m) & (kN/m) & (m) & (kN/m\({}^{4}\)) & (m) & (kN/m) \\
1.0 & 2.0 & 1.6 & 21,425.1 & 1.0 & 69,631.6 & 2.0 & 1.4 & 21,425.1 & 1.0 & 60,847.3 \\
2.0 & 2.0 & 1.6 & 21,425.1 & 3.0 & 208,894.8 & 2.0 & 1.4 & 21,425.1 & 3.0 & 182,541.9 \\
3.0 & 2.0 & 1.6 & 21,425.1 & 5.0 & 348,158.0 & 2.0 & 1.4 & 21,425.1 & 5.0 & 304,236.5 \\
4.0 & 2.0 & 1.6 & 21,425.1 & 7.0 & 487,421.1 & 2.0 & 1.4 & 21,425.1 & 7.0 & 25,931.1 \\
5.0 & 2.0 & 1.6 & 21,425.1 & 9.0 & 626,684.3 & 2.0 & 1.4 & 21,425.1 & 9.0 & 547,625.7 \\
6.0 & 2.0 & 1.6 & 21,425.1 & 11.0 & 765,947.5 & 2.0 & 1.4 & 21,425.1 & 11.0 & 669,320.3 \\
7.0 & 2.0 & 1.6 & 21,425.1 & 13.0 & 905,210.7 & 2.0 & 1.4 & 21,425.1 & 13.0 & 791,014.9 \\
8.0 & 2.0 & 1.6 & 21,425.1 & 15.0 & 1,044,473.9 & 2.0 & 1.4 & 21,425.1 & 15.0 & 912,709.5 \\
9.0 & 2.0 & 1.6 & 21,425.1 & 17.0 & 1,183,373.7 & 2.0 & 1.4 & 21,425.1 & 17.0 & 1,034,404.1 \\
10.0 & 2.0 & 1.6 & 21,425.1 & 19.0 & 1,323,000.3 & 2.0 & 1.4 & 21,425.1 & 19.0 & 1,156,098.7 \\
11.0 & 2.0 & 1.6 & 21,425.1 & 21.0 & 1,462,263.4 & 2.0 & 1.4 & 21,425.1 & 21.0 & 1,277,793.3 \\
12.0 & 2.0 & 1.6 & 21,425.1 & 23.0 & 1,601,526.6 & 2.0 & 1.4 & 21,425.1 & 23.0 & 1,399,487.9 \\
13.0 & 2.0 & 1.6 & 21,425.1 & 25.0 & 1,740,789.8 & 2.0 & 1.4 & 21,425.1 & 25.0 & 1,521,182.5 \\
14.0 & 2.0 & 1.6 & 21,425.1 & 27.0 & 1,880,053.0 & 2.0 & 1.4 & 21,425.1 & 27.0 & 1,642,877.1 \\
15.0 & 2.0 & 1.6 & 21,425.1 & 28.0 & 1,9496,84.6 & 2.0 & 1.4 & 21,425.1 & 28.0 & 1,703,724.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Soil spring stiffness of 13# pier.  
Figure 9: Soil spring model.  
where \(T_{g}\) is the site period that the characteristic period is 0.45, \(T\) represents the natural vibration period and \(S_{\rm max}\) denotes the maximum value of horizontal design acceleration response spectra.  
When the target response spectrum is determined, the ground motions can be selected by the principle of minimum mean square deviation. The mean square deviation can be derived as  
\[\delta_{MSE}=\frac{\sum\limits_{i}w(T_{i})\left[\ln S_{at}(T_{i})-\ln(fS_{ar}( T_{i}))\right]^{2}}{\sum\limits_{i}w(T_{i})} \tag{19}\]  
where \(f\) is the linear scale factor for recording seismic response spectrum, \(w(T_{i})\) represents the weight coefficient, \(S_{at}(T_{i})\) is the target response spectrum and \(S_{ar}(T_{i})\) denotes the selected response spectrum.  
This paper studies the influence of structural uncertainty on the SFDP of an extradosed cable-stayed bridge under longitudinal and transverse direction earthquakes. Owing to the aforementioned information of the location and site condition of the examined bridge, the natural ground motions are selected from PEER of the United States. The selected spectrums are shown in Figure 11.