## 3 Theoretical Analysis
### Establishment of the Safe Passage Redundancy Index of the Taxiway Bridge  
The passage redundancy of the taxiway bridge is also studied under the fatigue accumulation state. Safe passage redundancy refers to the remaining times that the aircraft can safely pass through the taxiway bridge. Currently, the most widely used strength verification method in the field of bridge fatigue strength is the verification of the maximum deflection in the middle of the span. This verification method has the advantages of obvious change, strong regularity, and can be detected without on-site loading. Therefore, this method is used to quantitatively analyze the fatigue safety passage redundancy of the taxiway bridge. Article 4.2.3, titled \"Code for the design of highway reinforced concrete and prestressed concrete bridges and culverts\" (JTJ023-85), provides the design specifications for taxiway bridges, and points out that the maximum deflection of the upper bearing structure of the bridge with a reinforced concrete structure calculated by the operating load (excluding the impact force) shall not exceed the following values. In Table 4, \(L\) is the calculated span (mm) and \(L_{1}\) is the cantilever length (mm). According to the design drawing of the taxiway bridge, the bridge deck is composed of two spans simply supported beams, and the maximum deflection value of the bridge deck appears at the mid-span of each span. Therefore, it can be seen that the allowable maximum deflection value is \(1/600\)\(L\) = 26.03 mm, meaning that when the aircraft passes the taxiway bridge for the Nth time, if the maximum deflection value is generated by the action line between the wheel and the bridge deck at the mid-span (hereinafter referred to as the maximum deflection value at the mid-span) is greater than 26.03 mm, the bridge meets the fatigue end standard and no longer meets the needs of safe passage. According to statistics, the taxiway bridge studied in this study sees 35 aircraft every day on average. If the flight growth rate is not considered, the cumulative traffic sorties in the whole life cycle (20 years) can be calculated from this. Referring to the standard aircraft type of taxiway bridge operation of the airport, B747-400 is selected as the standard aircraft type, and the takeoff and landing structure type and load value (2857.63 kN are inputted \begin{table}
\begin{tabular}{c c} \hline \hline
**Position** & **Allowable Maximum Deflection** \\ \hline The mid-span of the girder of the beam bridge & \(1/600\)\(L\) \\ The cantilever end of the girder of the beam bridge & \(1/300\)\(L_{1}\) \\ The truss, arch & \(1/800\)\(L\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The allowable maximum deflection of each part of the bridge. Figure 6: The S–N curve of reinforcement and concrete. into the FEM to obtain the mid-span deflection values of the two spans of the taxiway bridge. Since the mid-span deflection values of the two spans of the taxiway bridge has little difference, the maximum mid-span deflection value of the two spans is selected as the maximum mid-span deflection value. The relationship between the maximum deflection value in the span and the number of aircraft operations is shown in Table 5.  
It can be observed from the table that with the increase in operation times, the maximum deflection value in the middle of the span increases, but it is less than the allowable maximum deflection value in the whole life cycle, and the absolute value of the difference between the two is 1.54 mm, indicating that the fatigue performance of the taxiway bridge still meets the requirements of safe passage after 255,500 sorties of the standard model under this loading state [33].