# Corrosion Fatigue Assessment of Bridge Cables Based on Equivalent Initial Flaw Size Model
## 4 Corrosion Fatigue Lifespan Assessment of Parallel Wire Cable
### Load Effect on Corrosion Fatigue Lifespan
Hence, the time interval for each calculation (\(T_{i+1}-T_{i}\)) is set as 15 days. Currently, the live load on the service cables of bridges is approximately 5% to 12% of the total load [48]. Assuming a constant load of 500 MPa for the cable, the stress fluctuation caused by the live load on the cable wire is estimated to be around 26 to 68 MPa. With the transformation of urban industries, the increase in heavy vehicle traffic will significantly increase the stress fluctuation on the cable wires. In order to compare the effects of different load conditions on the corrosion fatigue lifespan, a baseline stress level of 23.65 MPa is considered. Further analysis is conducted to compare the fatigue lifespan under equivalent stress amplitudes of 40, 50, 60, and 70 MPa. All load conditions are exposed to the same corrosion environment, where the complete depletion of the 30 \(\upmu\)m thick galvanized coating in that environment takes approximately 4.9 years. The conversion coefficient \(\tau\) for this environment is assumed to be 0.1985. Figure 15 shows the variation of defect depth in the bridge wires under different stress amplitudes. Due to the relatively small stress amplitude caused by the load on the suspension ropes, it takes a long time for pitting corrosion to transition into cracks. When the equivalent stress amplitude is 23.65 MPa, the pitting depth needs to reach 1.179 mm before transitioning into a crack. However, due to the large depth, the converted crack will quickly propagate and fracture, with the crack propagation time estimated to be around 1-2 years. As the stress amplitude gradually increases, the transition depth decreases. When the stress amplitude reaches 70 MPa, the transition time falls within 100 years. With the increase in stress amplitude, the fatigue lifespan gradually decreases. The fatigue lifespan corresponding to 23.85 MPa is approximately 639 years, while it decreases to 73 years when the stress amplitude increases to 70 MPa. The calculation results indicate that within the 100-year reference period for bridge design, the wire will not experience corrosion fatigue fracture. However, this does not necessarily imply that the wire can still safely serve in practical conditions. The initiation mechanism of corrosion fatigue cracks includes four categories, and pitting-induced cracks are just one of them. Additionally,  
Figure 15: Evolution of defect depths under different stress amplitudes. multiple pits may grow together on this cross-section. Within the design reference period, plastic fracture caused by significant cross-section loss is prone to occur. Furthermore, considering the evolution of defect size within the internal strands of the cable when the equivalent stress amplitude is 70 MPa, the time for progressive fracture of each strand in a 109-strand wire cable under the current corrosion environment is calculated and presented in Figure 16. The fracture lives of the 2 nd, 4 th, 6 th, 8 th, and 10 th strands are estimated to be approximately 76, 93, 96, 107, 118, and 131 years, respectively. As shown in Figure 9, due to the symmetric nature of the corroed wire cross-section, when the 2 nd, 4 th, 6 th, 8 th, and 10 th strands fracture, the 3 rd, 5 th, 7 th, and 9 th strands will also fracture in a relatively short time. According to the Technical Specification for Maintenance of Urban Bridges (CJ) 99-2003) [49], when the cable reaches a 2% fracture rate, it is required to be replaced. For a 109-strand steel cable with an estimated operational lifespan of approximately 93 years, the cable will fail and reach the replacement criteria. In reality, the steel wires used in bridge cable strands are made from high-quality high-carbon steel round bars, which undergo isothermal quenching and drawing during the manufacturing process. However, they inevitably have processing defects and residual stresses along with construction scratches that occur during transportation and installation. Under the combined influence of corrosive media and stress, these defects are prone to initiate cracks.