# Corrosion Fatigue Assessment of Bridge Cables Based on Equivalent Initial Flaw Size Model
## 4 Corrosion Fatigue Lifespan Assessment of Parallel Wire Cable
### Service Environment Effect on Corrosion Fatigue Lifespan  
The corrosive environment in Section 4.3 is an industrial environment where a 24 \(\upmu\)m-thick pure zinc coating is corroded within 3.9 years. The corrosion rate in this environment is approximately 1.95 \(\times\) 10\({}^{-13}\) m/s. According to the experiments [26], the initial corrosion rate of bare steel wire is about 0.133 times that of zinc, which is approximately 2.59 \(\times\) 10\({}^{-14}\) m/s. This result is much lower than the corrosion rate of uncoated steel wire at the specified temperature and humidity provided in Table 3[52]. However, the actual environment is much more severe because the Runyang Suspension Bridge is located in the middle and lower reaches of the Yangtze River, where there is a long rainy and foggy season, and it is exposed to high humidity and high-temperature conditions throughout the year. [PERSON] et al. [53] provides statistics on the temperature and humidity annual profile of the Runyang Suspension Bridge, indicating that humidity exceeds 70% for approximately 77.4% of the year. To consider the influence of different environments on corrosion fatigue lifespan, the conversion coefficient (\(\tau\)) is adjusted to account for the severity of the environment. \[\tau=\tau_{0}\cdot\frac{v_{c}}{v_{c,0}} \tag{36}\]  
where \(\tau_{0}\) represents the conversion coefficient value of the industrial environment that can cause the 24 \(\upmu\)m-thick pure zinc coating to corrode completely within 3.9 years with respect to the experimental environment. \(v_{c,0}\) corresponds to the corrosion rate of bare steel wire in that industrial environment, and \(v_{c}\) corresponds to the corrosion rate of bare steel wire under different temperature and humidity conditions. Based on the average temperature of 20 \({}^{\circ}\)C as a reference, this study further calculated the fatigue lifespan of the steel wires in Runyang Suspension Bridge cable under five humidity environments: 70%, 75%, 80%, 85%, and 90%, with an equivalent stress amplitude of 23.65 MPa. The calculation method involves amplifying the conversion coefficient \(\tau\) based on the ratio of the corrosion rate provided in Table 3 to 2.59 \(\times\) 10\({}^{-14}\) m/s. As shown in Figure 19, the calculation results indicate that the fatigue lifespan of the steel wires gradually decreases with increasing humidity. The respective lifespan spans are 88, 72, 57, 37, and 34 years. An increase in humidity by 20% results in a reduction of approximately 54 years in lifespan. This demonstrates the significant impact of humidity on the fatigue lifespan. The corrosion condition of the main cable of a suspension bridge was analyzed by [PERSON] et al. [54], and it was found that the exterior of the cable undergoes a cycle of wet and dry conditions during day and night, while the interior and sides are consistently exposed to high humidity, and the bottom is immersed in water. When the protective sheath is cracked, a situation arises where the steel wires are exposed to high humidity or immersed in a water solution for an extended period, resulting in a severe corrosion environment for the wires. Therefore, this study further conducted a comparative analysis of the lifespan at a humidity of 90% under different temperatures ranging from 10 to 50 degrees Celsius. The results are shown in Figure 20. The calculated results demonstrate that in a high-humidity environment, the lifespan gradually decreases with increasing