## 1 Introduction  
A cable-stayed bridge is a cable support system consisting of three basic components: cables, towers and a bridge deck. During the service period, the safety of the entire bridge is inextricably intertwined with the properties of the cable system [1, 2]. Just within the last 30 years, there have been many accidents caused by the damage and breakage of cables worldwide [3, 4, 5]. The average life of these cables is no more than 20 years, and compared with the 100-year designed life of the whole bridge, the life of the cable seems too short. The most commonly used material for bridge cables is hot-dip galvanized high-strength steel wire, which possesses good comprehensive mechanical properties: high strength, good plasticity and good toughness [6]. In addition, the undamaged steel wire possesses a strong ability to resist fatigue crack nucleation but a weak ability to resist fatigue crack propagation [7]. But it is well known that corrosion can significantly reduce the fatigue life of steel wires, mainly because corrosion damage greatly shortens the fatigue crack initiation life of the wire during the service period, thus reducing the service life and residual strength of the steel wire [8]. Therefore, an in-depth study of the influence of pre-corrosion damage on the fatigue behavior of steel wires plays an important role in developing the life-cycle design theory of bridge structures and ensuring bridge safety. At present, numerous experiments have been conducted, removing the barrier for life investigations of corroded steel wire. For example, [PERSON] and [PERSON] [9] conducted fatigue tests on steel wires with various corrosion degrees. The results show that the fatigue strength of corroded steel wires decreases greatly compared with the undamaged steel wire. After that, [PERSON] and [PERSON] [10] also investigated the pitting effect on steel wire fatigue properties. In addition, [PERSON] et al. [11] investigated the mechanical properties and fracture characteristics of in situ bridge wires by tensile and fatigue tests. The tests show that the ultimate strain of corroded wires decreased with an increase in the degree of corrosion, the fatigue properties of wires degraded significantly at the early corrosion stage and the degradation rate slowed down with further development of corrosion. [PERSON] et al. [12] conducted experimental research on the fatigue performance of corroded steel wires by using 3D profile measurements and then established an empirical formula for fatigue life calculation based on test results. Based on those experimental researches, some numerical methods were proposed to predict the fatigue life of corroded steel wires. For instance, [PERSON] et al. [13] based their work on the theory of critical distances to estimate the fatigue life of corroded bridge wires, in which the stress concentration factor is recommended to be estimation indicator of the residual life of wires. [PERSON] et al. [14] established a finite element (FE) model of steel wire with a hemi-spherical or bullet-shaped corrosive pit, simulated the growth of corrosive pits by removing units step-by-step, and then analyzed the distribution of the stress and strain fields around the corrosive pits at different stages. In addition, several calculational models are developed to predict the crack growth life of corroded steel wire based on fracture mechanics or damage mechanics [15; 16; 17], providing reference for the service safety performance and fatigue life evaluation of high-strength steel wire. In order to simplify the corrosion process, most studies introduced above presuppose the shape of the corrosion pit and assume that the pit evolves at the same rate in all directions. However, the actual morphology and distribution of corrosion pits are uncontrollable, and shapes of corrosion pits are various, such as the narrow-deep pit, the ellipsoid pit, the wide-shallow pit and so on [18].