## 4 Construction of the Safety Passage Redundancy Evaluation Model for the Taxiway Bridge
### Fatigue Safe Passage Analysis of the Taxiiway Bridge Based on the Flight Growth Rate  
When studying its fatigue characteristics, the annual growth rate of flights is a factor that must be considered [36]. At this stage, the load of the taxiway bridge is controlled according to the maximum landing weight [37]. According to various statistics, the average number of passing aircraft is 35 per day, so the annual take-off and landing sorties reaches 12,775, and the number of operating sorties within 20 years of service life is about 255,500. Considering that the flight growth rate of the airport is affected by economic development, region, and other factors, the annual growth rate of flights is proposed to be 3%, 5%, 7%, and 9%, respectively [1]. The operational sorties of each year in the life cycle are calculated, as shown in Table 6.  
Based on the B747-400 standard operating at the maximum landing weight and 12,775 sorties per year, and considering the annual growth rates of 3%, 5%, 7%, and 9%, the change in the maximum deflection value in the mid-span after 20 years of operation of the taxiway bridge is shown in Table 7.  
Figure 10: Data validation curve. Figure 9: The relationship curve between the maximum deflection and the load value in mid-span. According to the correlation analysis, the calculation relationship is constructed as follows:  
\[Y=0.0305\alpha^{2}+0.0512\alpha+(Y_{max}-Y_{c}) \tag{9}\]  
In the formula, \(Y\) (mm) is the maximum deflection value of the bridge deck mid-span; \(\alpha\) is the value that removes the percentage sign of the annual growth rate of flights, i.e., 5% is recorded as \(\alpha=5\); and \(Y_{c}\) (mm) is the mid-span deflection caused by the weight of the taxiway bridge. The curve is shown in Figure 11, and the dotted line represents the fitting curve. After verification, the correlation coefficient \(R^{2}=0.999\), indicating that the correlation between the curve and the data is as high as 99.9%, which can be used to predict the maximum deflection value of the taxiway bridge under the fatigue state in relation to different flight growth rates, and safety redundancy analysis can be conducted [27]. It can be seen from the above figure that when the average annual growth rate of flights in that year is 6.3066%, the maximum deflection value in the middle span of the taxiway bridge reaches an allowable maximum deflection value of 26.03 mm after 20 years of operation. Therefore, the airport throughput must be strictly controlled, or the taxiway bridge must be regularly maintained, upgraded, and reconstructed to improve its bearing capacity. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Flight Growth Rate** & **3\%** & **5\%** & **7\%** & **9\%** \\ \hline Year 1 & 12,775 & 12,775 & 12,775 & 12,775 \\ Year 2 & 13,158 & 13,414 & 13,669 & 13,925 \\ Year 3 & 13,553 & 14,084 & 14,626 & 15,178 \\ Year 4 & 13,960 & 14,789 & 15,650 & 16,544 \\ Year 5 & 14,378 & 15,528 & 16,745 & 18,033 \\ Year 6 & 14,810 & 16,304 & 17,918 & 19,656 \\ Year 7 & 15,254 & 17,120 & 19,172 & 21,425 \\ Year 8 & 15,712 & 17,976 & 20,514 & 23,353 \\ Year 9 & 16,183 & 18,874 & 21,950 & 25,455 \\ Year 10 & 16,668 & 19,818 & 23,486 & 27,746 \\ Year 11 & 17,169 & 20,809 & 25,130 & 30,243 \\ Year 12 & 17,684 & 21,850 & 26,889 & 32,965 \\ Year 13 & 18,214 & 22,942 & 28,772 & 35,932 \\ Year 14 & 18,761 & 24,089 & 30,786 & 39,166 \\ Year 15 & 19,323 & 25,294 & 32,941 & 42,691 \\ Year16 & 19,903 & 26,558 & 35,247 & 46,533 \\ Year 17 & 20,500 & 27,886 & 37,714 & 50,721 \\ Year 18 & 21,115 & 29,281 & 40,354 & 55,286 \\ Year 19 & 21,749 & 30,745 & 43,179 & 60,261 \\ Year 20 & 22,401 & 32,282 & 46,201 & 65,685 \\ Total sorties & 343,269 & 422,418 & 523,717 & 653,571 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Operation sorties in 1–20 years at different growth rates.