## 7 Conclusions  
In this study, an elastic-plastic damage constitutive model and an elastic-plastic damage evolution model for high-strength steel wires were established based on continuum damage mechanics. The wire elements of a suspension rod in a certain cable-stayed bridge were taken as the research object. The finite element software ANSYS was used to analyze the damage evolution behavior under the coupling effects of traffic flow, bridge, and wind. Furthermore, the reliability of the simulation results was verified using experimental data from the literature. Considering the possibility of multiple pits in corroded steel wires in practical engineering, this study, based on the damage evolution model, explored the influence of the relative distribution of pits on the mechanical properties and fatigue life of the wire. The specific conclusions are as follows:  
Figure 16: The relationship between fatigue life of steel wire and corrosion pit distribution. (**a**) Along the \(X\)-axis; (**b**) Along the \(Z\)-axis.  
1. Based on the theory of continuous damage mechanics, the element birth and death technique was used to simulate the damage evolution process of pitted steel wire in ANSYS. This approach better accounts for the interaction between damage-induced pits and cracks as well as the effects of stress concentration. The model's calculated results demonstrated good agreement with experimental results under similar conditions, validating the rationality of this method.  
2. For single-pit steel wires, after the initiation of cracks, cracks at the pit site will rapidly propagate and accelerate the failure of the steel wire. The crack initiation life constitutes approximately 80% of the steel wire's fatigue life under high-cycle fatigue conditions. This indicates that under high-cycle fatigue, the crack initiation life dominates the majority of the fatigue life.  
3. Using the wind-traffic-bridge coupling system calculated stress-time history data as the load condition, we thoroughly discussed the influence of the relative distribution position of pits on the mechanical properties and fatigue life of steel wires. When pits are distributed along the \(X\)-axis of the wire, the intersection of pits leads to the overlap of stress concentration zones, resulting in the superposition of fatigue damage at the pit locations and ultimately accelerating the fatigue failure of the steel wire. Moreover, the fatigue life of the steel wire is minimized when the pits are tangential. When pits are distributed along the \(Z\)-axis of the wire, the pits formed by the intersection have a larger aspect ratio. This shape of pits, compared to semi-ellipsoidal pits, has a lower stress concentration, thereby slowing down the rate of damage accumulation at the pit locations. Therefore, even with a higher number of surface pits, the steel wire exhibits a higher fatigue life than a single-pit steel wire. When the distance between pits equals the pit radius, the steel wire achieves the maximum fatigue life. The above results indicate that different pit distribution states significantly affect the fatigue life of the steel wire, providing theoretical reference for the maintenance and normal operation of cable structures.  
Conceptualization, L.Y. and M.W.; methodology, L.Y. and M.W.; software, L.Y. and M.W.; validation, L.Y. and M.W.; formal analysis, L.Y. and M.W.; investigation, L.Y.; resources, L.Y. and M.W.; data curation, L.Y. and M.W.; writing--original draft preparation, L.Y.; funding acquisition, M.W.; writing--review and editing, L.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number [51708470] and Youth Science and Technology Innovation Team of Bridge Safety Assessment in Southwest Petroleum University, grant number [2019 CXTD07].  
The raw data supporting the conclusions of this article will be made available by authors on request.  
The authors declare no conflicts of interest.