## 4 Construction of the Safety Passage Redundancy Evaluation Model for the Taxiway Bridge  
Based on the analysis shown in Section III, the changing trend of the maximum deflection value in the middle of the two spans of the taxiway bridge can be used to analyze the fatigue characteristics of the taxiway bridge. Exceeding the allowable maximum deflection value in the middle of the bridge indicates that the bridge reaches the fatigue end standard. The maximum deflection value in the middle of the taxiway bridge is selected as the key index of the safe passage redundancy of the taxiway bridge and B747-400 is selected as the standard aircraft type. The number of aircraft and the aircraft load in relation to the taxiway bridge deck both play a key role in the fatigue accumulation of the taxiway bridge. This chapter intends to establish the change relationship model between the operation times, the operation load, and the maximum deflection in the middle of the span of the aircraft on the taxiway bridge in order to construct the quantitative relationship between the fatigue state and safe passage redundancy. By taking the maximum landing weight (2857.63 kN) of the standard aircraft type B747-400 as the operation load, according to the 35 flights per day of the taxiway bridge, about 255,500 operation sorties of the taxiway bridge are calculated within the specified design life of 20 years. Therefore, 0-255,500 is used as the operation time value to operate on the established FEM of the taxiway bridge. The maximum deflection value in the middle of the span of 0-255,500 operations is derived, and the correlation between the maximum deflection value in the middle of the span and the operation times is analyzed [34]. The relationship is as follows:  
\[Y=10^{-10}N_{t}{}^{2}+7\times 10^{-5}N_{t}+Y_{c} \tag{6}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Aircraft** & **Maximum Deflection Value** & **Allowable Maximum** \\
**Operation Times** & **in the Mid-Span/mm** & **Deflection/mm** \\ \hline
0 & 1.3715 & \\
12,775 & 3.41 & \\
63,875 & 6.87 & 26.03 \\
127,750 & 10.36 & \\
191,625 & 17.38 & \\
255,500 & 24.49 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The relationship between the taxiway bridge deflection and aircraft operation times. \(Y\) (mm) is the maximum deflection value of the bridge deck mid-span; \(N_{t}\) is the total number of aircraft sorties that can operate under the existing load state; and \(Y_{c}\) (mm) is the mid-span deflection caused by the weight of the taxiway bridge. The initial state of the taxiway bridge (load = 0, operation time = 0) is inputted into the finite element simulation software. The maximum deflection value in the middle of the span is 1.3715 mm, indicating that the deflection value caused by its own weight is 1.3715 mm. The curve is shown in Figure 7, with the dotted line representing the fitting curve:  
According to various calculations, the correlation coefficient \(R^{2}\) = 0.9919, indicating that the correlation degree of this curve to the data is as high as 99.19%, is very much in line with the prediction requirements [28]. Therefore, it can be concluded that the safe passage redundancy of the taxiway bridge under a standard aircraft load type is:  
\[N_{s}=N_{t}-N_{0} \tag{7}\]  
\(N_{s}\) is the safe passage (sorties) and \(N_{0}\) is the sorties that are now operated. According to the fatigue formula inferred from the above data, by substituting the allowable maximum deflection value of the bridge deck into 26.03 mm, it can be obtained that the difference between the maximum deflection value and the allowable maximum deflection value of the taxiway bridge under this fatigue state is 0.25 mm, and 2023 sorties B747-400 can still pass safely with the maximum landing weight [35]. Due to the small difference between 255,500 and 257,023, in the subsequent calculation, 255,500 can be taken as the maximum number of passes of the standard aircraft type under the maximum landing weight.