## 4 Results and Analysis
### Analysis of Bridge Load Effect Considering Reinforcement Corrosion  
Considering that most small- and medium-span bridges lack historical data and reference information, which limits the bridge reliability analysis, it can be regarded as a problem without prior distribution for analysis and solution. The nonprior information Bayesian analysis method in Reference [43] is adopted for calculation in this paper, and the inspection data of concrete strength and concrete cover thickness are assumed to follow a normal distribution \(N\big{(}\mu,\sigma^{2}\big{)}\). The Bayesian estimation of parameter \(\mu\) is \(\overline{x}\), and the posterior distribution of \(\sigma^{2}\) is:  
\[\hat{\sigma}^{2}=\frac{2\lambda+\frac{n}{i=1}\big{(}x_{i}-\overline{x}\big{)} ^{2}}{2\alpha+n-3}, \tag{23}\]  
where \(\alpha\) and \(\lambda\) are the shape parameter and scale parameter of the inverse gamma distribution; \(\alpha=102\) and \(\lambda=154\) for analyzing the concrete cover thickness, while \(\alpha=102\) and \(\lambda=536\) for analyzing the concrete strength; and \(n\) is the number of samples. The inspection data in Table 1 were processed and analyzed by the above Bayesian update method without prior information, and the posterior probability distribution parameters of concrete strength and cover thickness were obtained, as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{5}{c}{**Concrete Cover Thickness/mm**} & \multicolumn{5}{c}{**Concrete Strength/MPa**} \\ \cline{2-10}  & **Beam 1** & **Beam 2** & **Beam 3** & **Beam 4** & **Beam 5** & **Beam 1** & **Beam 2** & **Beam 3** & **Beam 4** & **Beam 5** \\ \hline
1 & 28.1 & 32.5 & 29.9 & 29.6 & 32.5 & 24.6 & 35.8 & 34.1 & 35.3 & 33.3 \\
2 & 27.9 & 30.4 & 30.7 & 30.2 & 33.1 & 28.8 & 30.6 & 36.6 & 27.9 & 26.1 \\
3 & 29.3 & 30.3 & 29.6 & 33.5 & 29.5 & 33.6 & 30.0 & 28.1 & 30.2 & 32.6 \\
4 & 25.6 & 32.7 & 29.8 & 30.6 & 33.2 & 27.7 & 36.3 & 34.5 & 29.3 & 29.5 \\
5 & 27.5 & 29.8 & 30.0 & 31.3 & 30.5 & 26.9 & 29.9 & 28.8 & 36.5 & 31.4 \\
6 & 28.5 & 32.8 & 29.4 & 31.5 & 31.4 & 32.1 & 36.7 & 34.5 & 37.3 & 28.3 \\
7 & 27.0 & 30.9 & 28.4 & 30.7 & 30.9 & 28.4 & 30.8 & 33.2 & 31.4 & 28.7 \\
8 & 27.5 & 30.1 & 31.9 & 33.7 & 31.5 & 34.6 & 35.6 & 27.9 & 34.1 & 33.2 \\
9 & 28.9 & 30.1 & 31.8 & 32.9 & 29.9 & 32.3 & 28.1 & 35.5 & 33.7 & 35.8 \\
10 & 27.3 & 29.2 & 29.8 & 31.9 & 30.5 & 27.6 & 30.8 & 33.8 & 35.0 & 28.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detection data of concrete strength and concrete cover thickness of simply supported T-beam bridge. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multirow{2}{*}{**Dispersion Pattern**} & \multirow{2}{*}{**Mean Value**} & \multicolumn{1}{c}{**Coefficient**} & \multirow{2}{*}{**Explanation**} & \multirow{2}{*}{**Reference**} \\ \cline{6-6}  & & & & & **of Variation** & & \\ \hline \multirow{2}{*}{\(C_{s}\)} & \multirow{2}{*}{\%} & \multirow{2}{*}{Lognormal distribution} & \multirow{2}{*}{0.12} & \multirow{2}{*}{0.10} & Chloride & \multirow{2}{*}{[42]} \\  & & & & & & concrete surface & \\ \multirow{2}{*}{\(D_{c}\)} & m\({}^{2}\)/year & & & & Diffusion coefficient & \\  & & & & & of chloride & \\ \multirow{2}{*}{\(C_{cr}\)} & \multirow{2}{*}{\%} & \multirow{2}{*}{Lognormal distribution} & \multirow{2}{*}{0.045} & \multirow{2}{*}{0.10} & Critical chloride & \multirow{2}{*}{[42]} \\  & & & & & & central & \\ \multirow{2}{*}{\(f_{u0}\)} & MPa & & & & & & \\  & & & & & & & \\ \multirow{2}{*}{\(D_{0}\)} & mm & & & & & & \\  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Probability distribution and statistical parameters of influencing factors of simply supported T-beam bridge. In combination with the Monte Carlo and Latin hypercube sampling methods, Equation (5) was used to calculate the reinforcement corrosion rate modified based on the measured data.