## 4 Analysis of Structural Uncertainty  
### Random Parameter Selection and Distribution of the Bridge  
In view of the parameter changes in the whole construction process of high-speed railway extradosed cable-stayed bridge, as well as the analysis of the static and dynamic characteristics of the bridge, the structural uncertainty research in this paper involves random parameters, such as material characteristic parameters, model constitutive parameters, dynamic characteristic parameters, structural size, etc. The parameters change according to the probability and statistics distribution, and the mean value is the design value as shown in Table 2. For example, for concrete bulk density, it satisfies the normal distribution, the standard deviation is 1.75 kN/m\({}^{3}\), and the mean value is 26.5 kN/m\({}^{3}\). For the damping ratio, it also satisfies the normal distribution, the coefficient of the variation is 0.2, and the standard deviation is 0.01. According to the literature [41; 42], the parameters and their probability distribution are shown in Table 4.  
Figure 11: Target response spectrum and response spectrum.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**No.** & **Uncertainty Parameter** & **Radom Variables** & **Variables Distribution Type** & **Standard Deviation** & **Coefficient of Variation** & **Unit** \\ \hline
1 & Peak compressive strength of & \(f_{Low}\) & Normal distribution & 4.07e/2.5889/2.5889 & 0.14 & MPa \\  & confined concrete & \(f_{Low}\) & Normal distribution & 0.8217/0.5218/0.5218 & 0.14 & MPa \\
2 & Ultimate compressive strength & \(f_{Low}\) & Normal distribution & 0.0008/0.0008/0.0008 & 0.15 & \\
3 & Peak strain of confined concrete & \(e_{Low}\) & Normal distribution & 0.002/0.002/0.0019 & 0.15 & \\
4 & Ultimate strain of & \(e_{Low}\) & Normal distribution & 0.0008/0.0008/0.0008 & 0.15 & \\  & confined concrete & \(e_{Low}\) & Normal distribution & 0.002/0.002/0.0019 & 0.15 & \\
5 & Peak compressive strength of & \(f_{Low}\) & Normal distribution & 3.351/2.1283/2.1283 & 0.14 & MPa \\  & unconfined concrete & \(f_{Low}\) & Normal distribution & 0.71/0.4509/0.4509 & 0.14 & MPa \\
6 & Ultimate compressive strength & \(f_{Low}\) & Normal distribution & 0.0003/0.0003/0.0003 & 0.15 & \\  & of unconfined concrete & \(e_{Low}\) & Normal distribution & 0.0006/0.0006/0.0006 & 0.15 & \\
8 & Ultimate strain of & \(e_{Low}\) & Normal distribution & 2880/2640/2640 & 0.08 & MPa \\
9 & Elastic modulus of concrete & \(E_{g}\) & Normal distribution & 16/16/16 & 0.045 & MPa \\
10 & Yielding strength of steel & \(E_{g}\) & Normal distribution & 6600/660/6600 & 0.10 & MPa \\
11 & Elastic modulus of steel & \(E_{g}\) & Normal distribution & 0.0017/0.0019/0.0029 & 0.2 & m \\
12 & Component size & \(D\) & Log-normal distribution & 0.02 & 0.08 & MPa \\
13 & Thickness of cover layer & C & Normal distribution & 1950 & 0.1 & MPa \\
14 & Elastic modulus of main spider & \(E_{g}\) & Normal distribution & 74.4 & 0.04 & MPa \\
15 & Elastic modulus of cubic & \(f_{Low}\) & Normal distribution & 0.002 & 0.5 & \\
16 & Yielding strength of cable & \(f_{Low}\) & Normal distribution & 0.005 & 0.2 & \\
17 & Friction coefficient of bearing & \(m\) & Normal distribution & 0.005 & 0.2 & \\
18 & Daming ratio & \(x\) & Normal distribution & 0.175 & 0.1 & \(\rm{N}/{m}^{3}\) \\
19 & Concrete bulk density & \(g\) & Normal distribution & 1.075 & 0.1 & \(\rm{N}/{m}^{3}\) \\ \hline \end{tabular}
\end{table}
Table 4: Probability distribution of uncertainty parameters.  
When analyzing the nonlinear dynamic time history and fragility analysis of reinforced concrete bridges, the parameters' correlation of fiber section cannot be ignored and their influence should be considered in the analysis of structural uncertainty. The parameter correlation coefficient matrix of concrete is shown in Table 5.