## 1 Introduction  
Suspension bridges represent a bridge structure with the main cable under tension as the main load-bearing component. In the operation process, under the coupling effect of a dead load (such as a stiffening beam, main cable, and sling), live load (such as automobiles and railway trains), and wind load [1, 2], the main cable will generate time-varying dynamic loads on both sides of the main saddle, resulting in a force imbalance in the main cable on both sides of the middle tower [2, 3]. With the continuous action of the unbalanced force, dynamic contact and \"layered-slipping\" phenomena occur between the main cable wires in the main saddle [4], resulting in friction, wear, and fatigue between the steel wire and the saddle material. At the same time, due to the intrusion and retention of rain and water vapor, electrochemical corrosion will occur on the steel wire inside the main cable. Corrosion-fatigue damage will occur on the steel wire of the main cable when the corrosion accumulates to a certain extent [2, 3]. The main cable wires are subjected to both tribo- and corrosion-fatigue, resulting in tribo-corrosion-fatigue damage behaviors. The development of cumulative damage causes a deterioration in the wire wear and a decrease in the effective cross-sectional area, which leads to the gradual deterioration of the wire's load-bearing strength. A decrease in the wire load-bearing capacity seriously affects the load-bearing safety of the main cable [4; 5; 6; 7]. Therefore, it is of great significance to study the tribo-corrosion-fatigue deterioration behaviors of main cable wires to ensure the load-bearing safety of the main cable in suspension bridges. Numerous engineering practices and experimental studies have demonstrated that friction and corrosion interact in terms of the tribo-corrosion fatigue of steel wire [8; 9]. When fatigue and corrosion damage coexist, their effects are not simply superimposed. A steel wire's strength and toughness will deteriorate significantly as tribo-corrosion-fatigue behaviors worsen [10]. [PERSON] [11] studied the degradation of the mechanical properties of corroded wires and their relationship with different corrosion parameters through tensile tests. By introducing the damage variable d, the damage constitutive model of the corroded wire was established. [PERSON] [12] proposed a numerical simulation method to study the damage evolution and failure process of a high-strength bridge wire with precorrosion defects under fatigue loading. Based on the theory of continuous damage mechanics, a fatigue damage model for a steel wire with precorrosion defects was established. [PERSON] [13] established a continuous damage model and simulation algorithm to simulate the corrosion-fatigue process of high-strength bridge cable wires. [PERSON] [14] established a multiscale corrosion-fatigue damage model based on Faraday's law and the initiation and propagation rates of microcracks. The evolution of damage at the stages of pit growth and microcrack propagation was described. [PERSON] [15] chose the high-strength wires of cables or slings from actual bridges as the research object to explore corrosion-fatigue failure. The fatigue tests of the steel wire under different corrosion conditions were carried out, the S-N curves of the steel wire with different corrosion degrees were given, and a service life prediction model was put forward. [PERSON] [16] proposed an improved continuum damage mechanics model to predict the corrosion-fatigue life of high-strength steel wires by considering the influence of the corrosion environment and external forces. Many experimental studies were conducted using the replacement of old cable wire and salt fog acceleration corrosion or electrochemical corrosion of a steel wire to investigate the effect of corrosion on the fatigue and mechanical performance of the cable.