# Random Field-Based Time-Dependent Reliability Analyses of a PSC Box-Grider Bridge
## 5 Time-Dependent Reliability Analysis of the PSC Box-Girder Bridge
### Results and Discussion. Based on the proposed method considering random fields in this paper, the reliability evaluation of the Jinghang Canal Bridge was carried out under serviceability and ultimate limit states. The evolution of the reliability index was obtained, as shown in Figures 14 and 15. As indicated in Figure 14, the concrete creep and shrinkage have a significant effect on the reliability index of the deflection at midspan of the box girder. When the structural parameters are considered as random variables, the reliability index is 6.5 at the time of completion of the bridge, as shown in Figure 14a, implying that the bridge has a high reliability and can satisfy the requirements of serviceability. However, with the development of shrinkage and creep and the increase in the long-term prestress loss, the deflection at the midspan of the box girder continues to increase, resulting in the reduction in the reliability index. In the early stage of bridge operation, the reliability index of the deflection decreases rapidly, which is consistent with the time-dependent development of creep and shrinkage. The reliability index decreases to the target reliability index of 1.5 after approximately 30 years of service. When the influence of a random field is considered, the reliability index falls below the target value of 1.5 after approximately 40 years of service. It can be concluded that the results of the reliability analysis are conservative when the structural parameters are treated as random variables. However, it does not mean that the failure probability of the structure will decrease when the randomness of the spatial distribution of the parameters is considered. In fact, the random field can describe the reliable state of the structure more truthfully. As shown in Figure 14a, the number of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Random Field** & **Mean** & **COV** & **Distribution** & \
\begin{tabular}{c} **Correlation** \\ **Model** \\ \end{tabular} &
\begin{tabular}{c} **Correlation** \\ **Length** \\ \end{tabular} \\ \hline Elastic modulus (GPa) & 36.8 & 0.09 & Normal & Exp & 40 m \\ Secondary dead load (kN/m) & 60.3 & 0.11 & Normal & Exp & 40 m \\ Live load (kN/m) & 21.0 & 0.19 & Normal & Exp & 40 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Random field parameters of the Jinghang Canal Bridge. discrete elements in the random field has little influence on the reliability index of deflection, which is similar to the correlation functions of the random field, as shown in Figure 14b. This fact reveals that the reliability index is insensitive to the type of correlation function. The correlation length of the random field has a great influence on the reliability index of the deflection, which decreases with increasing of the correlation length, as shown in Figure 14c. Moreover, it is necessary to take corresponding maintenance and rehabilitation measures before the reliability index falls below the target value, such as tensioning back-up tendons, to ensure serviceability throughout the lifespan of the bridge. Figure 14: Influence of parameters of the random field on the deflection reliability: (**a**) Discrete element; (**b**) correlation model; (**c**) correlation length. As shown in Figure 15, the concrete creep and shrinkage also have a significant effect on the reliability index of stress at the bottom flange of the main pier section. When the parameters affecting the structural reliability are considered as random variables, the reliability index is 8.7 at the time of completion, which demonstrates that the reliability of the bearing capacity is very high and can ensure the safety of the structure, as shown in Figure 15a. Due to the stress redistribution in the section caused by creep and shrinkage and the long-term loss of prestress force, the compressive stress at the bottom flange of the main pier section increases continuously, and the reliability index of the stress decreases continuously.