1. Introduction
Cable-stayed bridges have become the first choice for long-span bridges due to their outstanding features such as aesthetics, large spans, well-defined forces, and high navigability. In the face of an extreme, treacherous, and complex service environment, the most important force transmission component of the bridge is facing huge challenges in its long-term performance [1,2,3].
Researchers continue to explore the mechanism of corrosion damage to study the long-term performance of the cable steel wire. John Matte et al. [4] believe that when the cable reaches the ultimate load capacity, the brittle steel wire has been completely broken, and the remaining ductile steel wire is regarded as an ideal elastic-plastic model. Nakamura et al. [5] accelerated corrosion tests and static tensile tests on the stay cable steel wire. The study showed that when the steel wire developed etch pits, their ductility was significantly reduced. Min [6] analyzed the electrochemical reaction caused by the corrosive medium entering the cable system and found that the reason for the insufficient durability of the stay cable is the imperfect corrosion protection system, such as defects in the production and installation quality and later management and maintenance. Sixiao et al. [7] enhanced the HDPE sheath to stabilize the macroscopic modulus of elasticity of the stay cable, reduce the impact of the cluster effect, extend the service life of the stay cable, and effectively improve the durability of the cable structure. Jingyu [8] conducted experimental studies on the long-term performance and fatigue strength of CFRP cable and found that the damage dispersion of fatigue failure specimens was low. Bo [9] concluded that the stress concentration in the anchorage zone is the main factor affecting the long-term performance of large-tonnage FRP cable anchorage systems. The stress concentration can lead to fatigue damage or the degradation of the local mechanical properties of the cable. Li et al. [10] conducted risk assessments on the durability of the stay cable, summarizing that the risks affecting the durability of the stay cable are environmental corrosion, vibration, material aging, sheath cracking, and construction errors. Jing [11] identified the production process and external environment as primary factors influencing the durability of the HDPE protection system for cables and further explored the mechanisms behind the damage to the HDPE sheath. Ying et al. [12] considered the durability of the bridge from four aspects of construction, management, maintenance, and transportation, aiming to ensure the service safety of Wuhan Qingshan Yangtze River Highway Bridge. Sheng [13] carried out static tensile tests on the removed tension cables of old bridges and analyzed the degradation patterns of the ultimate strength and ultimate strain of steel wire under different corrosion conditions. Bo [14] took Jinan Yellow River dual-purpose bridge as the project basis and used the MIDAS model to study the impact of cable force variation on the anchorage area. The study showed that there is an obvious stress concentration phenomenon in the cable-beam connection area and at the anchorage plate. Yafei et al. [15] found that short cables are more susceptible to damage by analyzing the mechanical properties of typical cables of the Hejiang Yangtze River Second Bridge in Sichuan.
In terms of the cable remaining life, A. Wöhler [16] conducted a systematic experimental study on fatigue failure. By using measured data, Wöhler proposed the use of the S-N curve to describe fatigue behavior and the concept of fatigue endurance limit, laying the foundation of the modern fatigue theory. Castillo E et al. [17], through parallel steel wire and strand experiments based on the distribution of the Weibull, proposed a statistical model of the fatigue life and fatigue strength of steel wire. James M. Stallings et al. [18] used a multi-probability distribution model to simulate the impact of steel wire quantity and strand length on the remaining life of the steel wire. It was shown that the remaining fatigue life of cables decreases as the number and length of steel wire increases. Chengming et al. [19] established an evaluation method for the load-carrying capacity of parallel steel wire based on the probability distribution of the strength of a single steel wire. Mingdian et al. [20] studied the impact of steel wire corrosion, established the relationship between steel wire rusting and load-carrying capacity, and concluded that the load-carrying capacity of steel wire continuously decreases with the deepening of corrosion. Wei [21] fitted the three-dimensional etch pit size by numerical simulation and analyzed the fatigue life of the steel wire using ANSYS. He proposed a formula for quickly calculating the load-carrying capacity and remaining service life of the steel wire. Combining corrosion fatigue experiments with the equivalent crack method theory based on finite element simulation can more convincingly assess the remaining fatigue life of steel wires [13]. Zhihong [22] studied the multi-pits on corroded steel wires, equating them to a state of multiple cracks, and investigated the stress concentration factor at the tip of etch pits and the stress intensity factor for groups of etch pits with different crack sizes and verified the impact of multiple cracks on the remaining life of steel wires through fatigue life experiments.
In summary, the cable systems of existing cable-stayed bridges all have varying degrees of corrosion damage. Currently, there is relatively little research on the evolution laws of corrosion damage to cable steel wires. This study takes this as an entry point to conduct accelerated corrosion experiments on cable-stayed steel wires. Based on the experimental measurement data, the dynamic model cellular automata is used to simulate the development process of etching pits. It is defined on the discrete space composed of finite units and evolves according to certain local evolution laws. Further establishes a finite element model of etch pits to analyze the impact of stress concentration effects on the mechanical properties of steel wires and deduces the evolution laws of corrosion damage to cables. This is expected to provide a reference for the design of long-term performance of similar bridges.
2. Accelerated Corrosion Test on In-Service Cable Wires
2.1. Experimental Pre-Processing
2.1.1. Electrified Accelerated Corrosion
An in-service cable-stayed bridge in Guangdong Province, China, was used as a research object to carry out corrosion damage evolution experiments on the cable steel wires of the replaced cables. The bridge is in an oceanic subtropical monsoon climate zone. The bridge service environment has a high Cl− content, and environmental factors have a typical impact on the long-term performance of the cables.
The corrosion of the cable steel wire is mainly due to direct contact with the atmospheric environment and is also influenced by the humidity and temperature of the air, as well as the promotional effects of corrosive media. Due to the long service life of cables under actual conditions, artificial accelerated corrosion methods have become widely applied and ideal corrosion test methods, provided that the corrosion mechanism is consistent with the actual situation. There are numerous artificial accelerated corrosion simulation methods, including cyclic immersion corrosion, electrified accelerated corrosion, and salt spray environment accelerated corrosion. Each method of accelerating corrosion has its own advantages and disadvantages. In different corrosive media, salt solution corrosion is the most common and most destructive. Cl− penetrates the surface oxide film of the steel wire and enters its interior to promote electrochemical reactions. At the same time, Cl− destroys metal passivation, accelerates the dissolution of anodic metal, and forms corrosion products. At the same time, the use of constant current to accelerate the corrosion of steel wire to further improve the experimental efficiency [23]. The cable steel wire used in the experiment was taken from a coastal cable-stayed bridge; hence, a 5% NaCl solution is used to simulate the Cl− corrosion, highlighting the influential factors. Ultimately, a dry-wet cycle of electrified accelerated corrosion solution was selected to conduct a study on the evolution of corrosion damage in cable steel wires.
2.1.2. Cable and Equipment Parameters
The technical parameters of the cable body and the steel wires inside the cable used in the experiment are shown in Table 1 and Table 2, and the equipment required for the experiment is shown in Table 3.
The force in the anchorage area of the cable is relatively complex, and the risk of damage under the combined action of corrosion and fatigue is extremely high. The experiment selects the steel wires from a section of the cable anchorage system, and the specific cutting sections selected are shown in Figure 1. First, the sheath and anchorage of the cable system removed from the actual bridge are cut as shown in Figure 2. It is specified that all steel wires used are the outermost circle of steel wires in the cross-section of this area, and the initial degree of corrosion is consistent. The separated steel wires are wiped clean with a cotton cloth, taken out, stored, and numbered. According to the specifications [24] for the dimensions of round cross-sectional test samples in metal material tensile tests, the corresponding length of steel wire is cut, and a 50 mm steel wire segment is taken for the experiment.
2.1.3. Experimental Design
In order to ensure the stability of the experimental results, a total of four different corrosion conditions are set up, with 3 steel wires in each group of experiments: The first group of experiments is set for the service steel wire after natural corrosion from real bridge dissection; the second group of experiments is set for the electro-corrosion for 24 h, static in the dry environment for 24 h, and one dry-wet cycle; the third group of experiments is set for the dry-wet cycle three times, a total of the electro-corrosion for 72 h, static in the dry environment for 72 h; the fourth group of experiments is set for the dry-wet cycle five times, a total of 120 h of corrosion and 120 h of static in the dry environment. The current density was selected as 2000 μA/cm2, corresponding to a current of 0.23 A. The design of accelerated corrosion experiments is shown in Figure 3. To ensure that the service environment of the cable is as similar as possible, the experimental process controls the temperature of 35 °C and the humidity of more than 75%. After the completion of the corresponding stages is completed, the macro- and micromorphologies of the steel wires in the four groups are recorded, and tensile fracture experiments are carried out on the corroded steel wires of each group.
2.2. Corrosion Process Analysis
2.2.1. Macro- and Micromorphologies
Figure 4 shows the micromorphology of the steel wires after corrosion in different corrosion conditions. Evidently, the surface of the naturally corroded steel wires has a dull metal luster, is no longer smooth, and appears grayish white; after a single cycle of dry-wet electrified accelerated corrosion, the surface of the steel wire appears white crystalline zinc oxide, and some areas have begun to exhibit rust. These rust spots are unevenly distributed over the surface of the steel wire; after three cycles of dry-wet electrified accelerated corrosion, the surface of the steel wire forms a significant amount of orange-red rust Fe2O3, and the white areas are Fe(OH)2 deposits on the surface of the steel wire. Clearly, the iron matrix of the steel wire has suffered damage. Compared to corrosion after one cycle of dry-wet accelerated corrosion, the degree of damage to the steel wire after three cycles is more severe. After five cycles of dry-wet accelerated corrosion, a significant amount of reddish-brown iron rust has formed on the surface of the steel wire, and the zinc coating has been completely consumed. The corrosion damage is the most severe among all corrosion conditions.
To further clarify the appearance of corrosion damage on the steel wire surface, a scanning electron microscope DM4 was used to capture the micromorphology of the corroded steel wire, as shown in Figure 5. Here, 1-1, 1-2, and 1-3 represent the numbers of three steel wires under the natural corrosion condition after dissection from the actual bridge, while 2-1, 2-2, and 2-3 represent the numbers of steel wires under the accelerated corrosion condition after a single cycle of dry-wet electrified accelerated corrosion and so on. Like the micromorphology, the surface of the naturally corroded steel wire showed varying degrees of damage to the galvanized layer, among which steel wires 1-1 and 1-2 had a small amount of red rust Fe2O3 at the damaged galvanized layers. Based on the corrosion products, it is inferred that the galvanized layer is consumed here, the iron matrix is exposed to a certain extent, and there are some oxidation products. Steel wire 1-3 had a lower degree of corrosion, only showing a reduction in the thickness of the galvanized layer. After a single cycle of dry-wet electrified accelerated corrosion, part of the black iron matrix of the steel wire has been significantly exposed, proving that the galvanized layer had been largely lost. Steel wire 2-1 shows obvious etch pits on the surface, and steel wire 2-3 has more severe corrosion damage compared to the other steel wires in the same group, with red rust spots appearing. Under the condition of three cycles of dry-wet electrified accelerated corrosion, the iron matrix of each steel wire is visible to the naked eye, and there is a large area of reddish-brown rust on the iron matrix of each steel wire. Steel wires 3-1 and 3-2 have multiple etch pits visible, and the rust on steel wire 3-3 is evenly distributed on the surface of the steel wire. When the number of dry-wet cycles reaches five times, steel wires 4-1 to 4-3 all have a large amount of reddish-brown rust, and some local areas have connected into patches. By magnifying the micro view, the orange-red rust is not dense, there are many pores in the rust layer, and some iron matrix that has not been completely rusted is also mixed in. This also well confirms the main reasons why the corrosion rate will increase when the iron matrix begins to corrode.
2.2.2. Analysis of Breakage Experiments
After the steel wire is corroded by the corrosive medium, the effective load-carrying area is reduced, and the stress concentration caused by etch pits leads to a sharp decline in the mechanical properties of the steel wire. Hence, it is necessary to analyze the mechanical properties of the damaged steel wire. A WDW-50 microcomputer-controlled electronic universal testing machine is used to conduct tensile fracture tests on steel wires that have naturally corroded after service and those after accelerated testing to analyze their mechanical properties. The experimental data obtained is shown in Table 4, and the load-displacement relationship of different steel wires is depicted in Figure 6.
The average tensile strength of steel wires under different corrosion conditions is shown in Figure 7. As corrosion time and the number of dry-wet cycles increase, the tensile strength of the steel wires exhibits a clear downward trend. After five dry-wet cycles, the average tensile strength of the steel wires is less than 1700 MPa, and the tensile strength of the corroded steel wires has decreased by nearly 5%. As corrosion advances, electrochemical reactions on the steel wire’s surface lead to roughening of the galvanized layer or iron matrix. Etch pits form in more severely corroded areas, offering an environment for corrosive media to accumulate. The common development, fusion, and penetration of these pits will produce a certain degree of stress concentration effect, and then the pits continue to expand. The interplay of corrosion by-products further accelerates the corrosion process, intensifying the steel wire’s damage and notably reducing its tensile strength.
During the tensile fracture process of steel wires, the form of the steel wire’s fracture surface is an important indicator reflecting whether the fracture is ductile or brittle. When necking occurs at the fracture part of the steel wire, it indicates that the fracture is ductile; when there is no necking at the fracture and the steel wire breaks directly, the fracture can be judged as brittle. Figure 8 shows the fracture morphology of the steel wires after tensile testing under different corrosion stages. After natural corrosion and one dry-wet cycle, obvious necking phenomena appear at the fracture of the steel wires; after three dry-wet cycles, partial necking occurs at the fracture of the steel wires; and after five dry-wet cycles, the necking at the fracture is not obvious, and the steel wire breaks directly during the tensile process, with two distinct extended cracks at the break. Overall, the fractures of the steel wires after natural corrosion, one dry-wet cycle, and three dry-wet cycles can clearly show necking phenomena, and the fracture form is chisel-like, which is a ductile fracture. However, after five dry-wet cycles, the fracture morphology of the steel wire tends to be split-chisel, and the fracture only shows a very low degree of necking. As a result, the ductility of the steel wire is significantly reduced.
2.3. Analysis of Etch Pit Morphology
As the steel wire is continuously loaded, stress concentration may occur at the site of the largest etch pit, which can lead to the expansion and rapid development of cracks. Once the number of broken steel wires reaches a threshold, the cable may be at risk of failure. Therefore, it is of great significance to study the distribution, geometric morphology, and dynamic development of corrosion etch pits after the damage of a single steel wire to prevent cable failure. The research samples are based on 5 cable steel wires that have been naturally corroded after steel wire replacement. First, the sections with more severe corrosion on each steel wire are identified. Then, observations are made using a scanning electron microscope (SEM) to find sections with more pronounced etch pits. Subsequently, an industrial electronic microscope (228SD) is used to measure the length and width of the etch pits, and a single-point micrometer is used to measure the depth of the etch pits. Etch pits with a depth range of d ≥ 0.001 mm are included in the statistical range. A total of 100 sets of geometric data for etch pit length, width, and depth are statistically analyzed, as shown in Figure 9, Figure 10 and Figure 11.
Using SPSS, normality tests were carried out on etch pit length, width, and depth, and the samples geometric dimensions of the etch pits all satisfied a right-skewed distribution. According to the statistical data, the length of the etch pits on the surface of the naturally corroded steel wire after service is mainly distributed in the range of 0.005 mm to 0.015 mm, the etch pit width is mainly distributed in the range of 0.005 mm to 0.02 mm, and the etch pit depth has a broader range distribution compared to the other two dimensions, mainly distributed in the range of 0 mm to 0.04 mm. The size development of etch pits along the width and depth directions shows a trend that shows a trend greater than that in the length direction. Combined with the analysis of the typical etch pit geometric morphology, as shown in Figure 12, the geometric morphology of the etch pits is generally dominated by shallow spherical etch pits and deep ellipsoidal etch pits. The shallow spherical etch pits have a roughly circular length-to-width ratio, and the etch pit depths are generally less than 0.1 mm, while the deep ellipsoidal etch pits have a length-to-width ratio of less than 1.5 and etch pit depths generally less than 0.15 mm.
The maximum etch pit depth of steel wires under different corrosion conditions was recorded. The area within 1 cm of the maximum etches pit depth of the steel wire under natural corrosion conditions was marked with color to facilitate location and then subjected to dry-wet cycle electrified corrosion along with the rest of the steel wires in the accelerated corrosion experiment. After reaching different stages of corrosion, the steel wire is removed, the rust is cleaned off the etch pit surface, and then it was measured with a digital micrometer. Finally, the maximum etch pit depth on the steel wire surface under natural corrosion and different dry-wet cycle electrified corrosion conditions was obtained. The geometric dimensions of the etch pits were also measured using an electron microscope and a pointed flathead electronic digital micrometer. The maximum etch pit depth was selected as the evaluation index for the accuracy of the subsequent cellular automaton simulation of steel wire etch pit evolution.
3. Cellular Automata-Based Characterization of Steel Wire Damage
3.1. Cellular Automata-Based Corrosion Process Simulation
Cellular automata were proposed by John von Neumann in the 1950s to simulate biological self-replication [25]. Compared with other dynamic simulation methods, cellular automata are not determined by strictly defined physical or functional equations but are composed of a series of model construction rules that can simulate the spatiotemporal evolution process of complex systems [26].
The five primary components of a cellular automaton are cells, cell states, cell neighborhoods, local rules, and boundary conditions. Cells are the most fundamental units, distributed at the lattice points of one-dimensional, two-dimensional, and three-dimensional grids, each possessing an independent state. Cell states are mainly categorized into one-dimensional and two-dimensional states. The one-dimensional cell state refers to an infinitely extending line segmented by equally spaced cells, as depicted in Figure 13. The two-dimensional cell state is extensively utilized in models, with states that can be divided into three grid arrangements: triangular, quadrilateral, and hexagonal, as illustrated in Figure 14. The neighborhood of one-dimensional cells is determined by radius, while the neighborhood of two-dimensional cells is commonly defined using a quadrilateral grid that is easy to visualize, typically divided into three types, with the central cell in the square lattice representing the central cell and the gray cells representing the cell neighbors, as shown in Figure 15.
Cellular automata simulations usually model real-world scenarios that involve spatially extensive or even infinite objects, necessitating the definition of appropriate boundary conditions prior to simulation. The three commonly used boundary conditions are periodic, reflective, and fixed-value boundaries. Periodic boundary conditions connect the two boundaries through certain specifications; reflective boundary conditions designate one boundary of the cellular space as a mirror axis of symmetry, mirroring the cell states from one side of this boundary to the other; fixed-value boundary conditions pertain to the states of cells outside the boundary of the cellular space. Local rules refer to the dynamic functions that determine the next state of a cell based on its current state and the states of its surrounding neighbors at a given moment. These are essentially state transition functions, which are typically categorized into three types: steady-state, periodic, and chaotic.
From a mesoscale perspective, the evolution of etch pits is simulated based on cellular automata [27,28]. When conducting cellular automata-based corrosion process simulation, the evolution of multiple fine etch pits that appear during the uniform corrosion process of steel wires is first simulated, making the development of multiple etch pits on the steel wire surface visible. Subsequently, the evolution of a larger single-etch pit is simulated according to the actual conditions of the cables in service. From this, the number of cells dissolved by each column of etch pits at every timestep Nd is extracted, and max (Nd) is taken as the maximum depth of the etch pit [29]. The program is continuously debugged to match the actual data.
Based on the principles of electrochemical corrosion of steel wires, the model classifies cell types as: metal cells M, corrosive solution cells C, non-corrosive solution cells N, galvanized layer cells Z, and passive film cells P. The Moore type, that is, the Von Neumann type of cell neighbors, is selected according to the evolutionary relationship between the central cell and its surrounding neighbors. The boundary conditions in the cellular automaton are determined by the specific physical properties of the system being simulated, and the dynamic process of steel wire corrosion development can be regarded as a diffusion process of corrosive factors within the steel wire. Therefore, this model employs periodic boundary conditions, considers the actual growth dynamics of steel wire corrosion, and sets local rules for the cellular automaton to establish a galvanized steel wire corrosion damage etch pit evolution model that considers the influence of the surface galvanized layer. The electrolyte concentration is defined as c = C/N, where C is the number of corrosive cells and N is the number of non-corrosive cells. In the model, c is taken as 0.4, Pd as 0.2, and Pp as 0.05. The initial model diagram is shown in Figure 16, where red represents corrosive cells C, gray represents non-corrosive cells N, yellow represents galvanized layer cells Z, and black represents the steel wire entity [30].
Figure 17 shows the uniform corrosion morphology of the galvanized layer on the steel wire surface at the initial stage of corrosion. Different characteristics of fine etch pits appear randomly and further develop. The galvanized layer corrodes first. However, due to the presence of a dense oxide film on the surface of the galvanized layer, the corrosion rate progresses more slowly at the initial stage. The microindicators in the upper right corner show that pitting corrosion has formed and begun to develop, with the geometric characteristics of the pitting being more pronounced in the longitudinal direction. The essence of the reduction in the mechanical properties of the corroded steel wire is due to the decrease in the effective cross-sectional area of the steel wire and the increase in surface roughness. Therefore, the load-carrying capacity and elongation of the steel wire decrease with the increase in the degree of rusting. As shown in the corrosion process of the iron matrix, the effective cross-sectional area of the steel wire gradually decreases, and the surface roughness increases. This change is the reason for the reduction in the steel wire’s load-carrying capacity and elongation. The blue part in the microindicators in the upper right corner of Figure 17b represents the oxide film. Since the reaction of the iron matrix with oxygen does not produce a dense oxide film like ZnO, the corrosion rate will continuously accelerate, the etch pit size expands rapidly, and as the corrosion process progresses, the etch pits of steel wires surface develop into typical etch pit shapes such as broad shallow type, narrow deep type, and elliptic type [31].
Figure 18 shows the trend of the simulated etch pit depth changes over time steps and the quadratic fitting curve. It should be particularly noted that since the results of the cellular automaton simulation are dimensionless, there is no need to label units on such graphs. The maximum depth of the etch pit increases with the increase in time steps, but the rate gradually tends to level off. This is because after the steel wire undergoes pitting corrosion, the etch pit first develops longitudinally. In the initial stage of corrosion, the corrosion rate of the etch pit towards the depth direction is relatively large, leading to significant geometric changes in the etch pit depth. Once the etch pit depth reaches a certain level, the trend of etch pit development along the lateral direction becomes more apparent, and the trend of etch pit depth changes becomes more moderate.
To meet the numerical fitting requirements of the cellular automaton experiment, the Moore type of cell neighbors was chosen [32,33]. The specific evolution process of the largest etch pit is shown in Figure 19, where black represents the steel wire entity and gray represents the simulated etch pit morphology. The electrolyte concentration c of the single-etch pit cellular automaton model was set to 0.7, and the time steps were taken as 230, 240, 260, and 280, respectively. The maximum depth of etch pits under the four time steps is shown in Figure 20.
The maximum depth of etch pits on the surface of naturally corroded steel wires inside the cables after replacement was 0.061 mm. After the accelerated corrosion experiment, the depth of the etch pits gradually evolved. The maximum etch pit depths obtained from the cellular automaton simulations at four different time steps were compared with the actual measured values, as shown in Table 5. It can be concluded that the error between the actual and simulated values is controlled within 10%. The simulation results based on the cellular automaton model of etch pit development are highly in line with the actual development patterns observed in the accelerated corrosion experiment.
Furthermore, the cellular automaton model was used to simulate the etch pit morphology and maximum depth after seven and nine cycles of dry-wet electrically accelerated corrosion in a corrosion solution with a NaCl concentration of 5%. The geometric appearance is shown in Figure 21, and the maximum etch pit depth is shown in Figure 22. The cross-sectional shape of the etch pit morphology gradually changed from semicircular to semi-elliptical, and the trend of etch pit depth growth is gradually becoming more moderate. The pits visually show a trend of gradually spreading to both sides, which is consistent with the actual pattern described earlier, where etch pits first develop vertically along the longitudinal direction perpendicular to the steel wire surface and then gradually expand horizontally.
3.2. Etch Pit Damage Stress Concentration
Based on the cellular automaton simulation of individual etch pits, the maximum etch pit depth of the steel wire at different time stages was obtained, and the stress concentration effect of different initial etch pits under load was analyzed. First, a steel wire entity model was established using ABAQUS, and an ellipsoidal etch pit was created on the surface of the steel wire, with the initial length and width dimensions both set at 0.2 mm. The etch pit depths were defined as 0.06 mm, 0.07 mm, and 0.08 mm, respectively, to study the stress changes in the steel wire at this time. Subsequently, the maximum etch pit depths were defined as 0.1 mm, 0.5 mm, and 1.0 mm to investigate the stress variation patterns of steel wires with different degrees of damage. According to Saint-Venant’s principle, to ensure that boundary conditions do not affect the stress distribution near the etch pit area, the steel wire model length was set at 30 cm to calculate the stress concentration factor KT for the steel wire cracks at different damage levels, which is the ratio of the maximum stress σmax to the nominal stress σnon [34].
During service, the cable steel wires are mainly subjected to tension. The model boundary conditions are set as fixed and tensioned ends, respectively. To ensure that the steel wire remains in an elastic state, the surface load is taken as 30% of the steel wire’s ultimate strength, which is 531 MPa. The mesh near the etch pit is refined to ensure the computational accuracy near the steel wire etch pit. A 0.02 mm mesh division is used near the etch pit. The solid finite element model of the steel wire and etch pit is shown in Figure 23, and the stress nephograms when the etch pit depths are 0.06 mm, 0.07 mm, and 0.08 mm are shown in Figure 24. Regardless of the size of the etch pit, the maximum stress appears at the bottom of the etch pit and then decreases outward, which can be explained by the fact that the derivation and development of cracks in basic fracture and damage mechanics [35] usually start from the bottom of the etch pit.
Figure 25 shows the stress distribution cloud diagram of the steel wire under axial tension when the etch pit depth ranges from 0.1 mm to 2.75 mm. The maximum stress and stress concentration factors corresponding to different etch pit sizes are shown in Figure 26.
As the depth of the etch pit increases, the stress concentration phenomenon causes the stress at the bottom of the etch pit to gradually increase. When the etch pit depth increases from 0.1 mm to 2.75 mm, the stress concentration factor increases from 1.71 to 3.34, more than doubling. The most significant changes in maximum stress and stress concentration factors occur during the phase where the etch pit depth develops from 0.1 mm to 0.5 mm. In the early stages of etch pit development, the maximum stress experienced by the steel wire can fluctuate by nearly 600 MPa. Subsequently, the rate of increase in maximum stress and stress concentration factor relative to etch pit size growth becomes relatively mild but remains positively correlated.
Considering the stress concentration effect, the corrosion damage index of the steel wire is investigated by taking the weight loss during the corrosion process as the index. Table 6 and Figure 27 show the tensile strength and corrosion damage index Di of the steel wire corresponding to etch pits of different sizes. As the depth of the etch pit increases, the tensile strength of the steel wire continuously decreases. With the smallest etch pit, the tensile strength of the steel wire is reduced from an initial 1770 MPa to 1739 MPa, and as the etch pit size develops from 0.06 mm to 2.75 mm, the tensile strength is reduced by more than 60%. This is consistent with the rule that the more severe the corrosion of the steel wire in the dry-wet cycle electrified accelerated corrosion experiment, the lower the tensile strength of the steel wire. In the actual use of the cable-stayed bridge, during the repeated tensile loading process of the cable, the stress concentration effect will increase the stress of the cable, resulting in stress redistribution of the steel wire inside the cable. The stress redistribution will act on the steel wire and aggravate the corrosion damage of the steel wire. The two are coupled and promote each other. The stress concentration effect at the bottom of the etch pit is highly likely to lead to the sudden fracture of the steel wire, which can lead to serious cable breakage and bridge collapse accidents. Therefore, in the early stage of the development of the etch pit, it is necessary to timely maintain the steel wire in the cable and even replace the cable to ensure the safe use of the bridge [36,37].
3.3. Cable Corrosion Damage Evolution
Based on the cellular automaton simulation of the corrosion process of steel wires and the stress concentration effect of etch pits of different sizes, it is known that brand new galvanized steel wires initially contact with corrosive media, and etch pits gradually form on the surface of the steel wires. As the etch pits further expand, the effective cross-sectional area of the steel wires decreases, and the stress on the steel wires increases rapidly with the reduction in the effective area. When the stress on the steel wires reaches the tensile strength of the steel wires, steel wire breaks occur. The process is the entire process of steel wire damage evolution.
The corrosion morphological process of steel wires can be divided into general corrosion and local corrosion, as depicted in Figure 28. General corrosion, also known as uniform corrosion, poses a minimal threat. When steel wires undergo only uniform corrosion, the galvanizing layer can effectively safeguard their service life. However, as the service duration of stay cables increases, most steel wires will develop more hazardous pitting corrosion, with the progression of pitting on galvanized steel wires illustrated in Figure 29.
In a humid atmosphere, when galvanized steel wires form a microbattery with Zn and Fe, Zn acts as the anode and dissolves, while Fe is protected as the cathode. Under the influence of stress and corrosive media, the surface oxide film of the steel wire is corroded and damaged. The corroded surface and the intact surface form the anode and cathode, respectively, with the metal at the anode dissolving into ions and generating an electric current that flows towards the cathode. Since the anode area is significantly smaller than the cathode, the current density at the anode is high, leading to further erosion of the steel wire surface. When the passive film on a section of the steel wire surface is no longer intact, it becomes a pitting source and forms a microbattery with the adjacent surface. The metal at the pitting site dissolves rapidly, leading to the gradual formation of a pit. As the external corrosive medium continues to dissolve, the interior of the pit becomes acidic, accelerating the dissolution of the metal anode within the pit and causing further corrosion. The presence of pits reduces the effective load-bearing area of the steel wire at that location, and stress concentration occurs near the pits, reducing the wire’s effective resistance. As the pits grow to a critical size, cracks gradually initiate near the pits, rapidly expanding from short to long cracks. The stress concentration effect intensifies, further deteriorating the long-term performance of the steel wire.
Furthermore, based on the damage to the individual steel wires, the corrosion damage process of the entire cable is deduced. The main reason for the corrosion damage of cable-stayed cables is due to leakage and water seepage in the anchorage system and the failure of the corrosion protection system, which leads to uniform corrosion, pitting, stress corrosion, and corrosion fatigue of the steel wires inside the cable body in the service environment, resulting in a reduction in their effective load-carrying area. The stress on the steel wires increases accordingly, until the stress on the weakest steel wire exceeds its tensile strength, causing a steel wire to break. Subsequently, the stress on the remaining steel wires is redistributed, further increasing the internal stress of the remaining steel wires. This cycle continues until the stress on all the unbroken steel wires reaches the nominal breaking force of the cable, leading to cable rupture.
The damage distribution across the cross-section of a cable is classified by the corrosion level of the cable steel wires, and a corrosion distribution cloud diagram of the cable body cross-section is drawn based on the actual location. This is used to characterize the distribution of rust on the cable steel wires and has a positive significance for analyzing the long-term degradation performance of the cable. Using the same cable anchorage system replaced by a cable-stayed bridge, corresponding to Figure 1 and Figure 2, a 44 cm section from left to right is numbered for each circle of steel wires, which often contains a threaded splice joint and is a high-risk area for corrosion damage to the steel wires inside the cable [38]. According to regulations and the relevant literature [39,40], the corrosion degree of the cable steel wires is divided into five levels, from level I to level V. The numbering and circle division of the steel wires inside the cable are shown in Figure 30, and the physical appearance of each circle of steel wires is shown in Figure 31. The surface of the first circle of steel wires has various colors of corrosion products, and as the steel wires develop towards the inner circle, the overall color of the steel wires tends to be more uniform, and the consumption of the galvanized layer is significantly reduced.
The corrosion grade distribution cloud diagram of the steel wires inside the cable cross-section, obtained through statistical analysis, is shown in Figure 32. Additionally, it illustrates the schematic of the corrosion medium diffusing from the damaged part of the cable into the interior. By combining the analysis of Figure 31 and Figure 32, the multi-age steel wires in the anchorage section did not experience steel wire breaks but suffered from varying degrees of corrosion damage. Looking at the damage distribution across the cable cross-section, the corrosion damage to the steel wires is not uniformly distributed. When the cable is damaged, the side of the steel wires that first contact with the external corrosion medium show more severe corrosion damage. Considering the position of each steel wire, the outer steel wires of the cable are more severely corroded, while the inner steel wires have less damage. Only after the outer steel wires contact with the corrosion medium and undergo electrochemical action do the inner steel wires gradually start to have electrochemical reactions. In the circumferential direction, the closer the steel wire is to the point of entry of the external corrosion medium, the more severe the damage; as the distance increases, the degree of damage decreases accordingly. In the radial direction, the degree of steel wire damage decreases from the outside to the inside.
Cables can be regarded as parallel steel wire bundle models composed of multiple parallel steel wires, and the damage to the cable is the sum of the damages to the individual steel wires within the cable [41]. To better represent the evolution law of cable damage, the radial damage ratio Rr is defined as the ratio of the damage degree Cn of the nth circle steel wire to the damage degree C1 of the first circle wire. Taking the average corrosion damage weight loss of the outermost circle of steel wires as the comparison scale, the outermost circle steel wires are set as Rr = 1. The larger the radial damage ratio Rr of the steel wires in the same circle, the more severe the corrosion damage to that section of the cable. According to the actual measurement data, the second circle steel wire has an Rr of 0.872. The radial damage ratio Rr of the wires from the second to the fifth circle changes little and remains stable, indicating that the corrosion damage suffered by the steel wires in this area is almost at the same level. Until the sixth and seventh circle wires, that is, the single steel wires at the center, the radial damage ratio Rr approaches 0, which further illustrates that when the cable anchorage system is in parts such as connecting cylinders and threaded splices where corrosion protection is more likely to fail, the outermost steel wires bear most of the corrosion effects, and the interior of the cable is less eroded by the corrosive medium.
4. Conclusions
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(1). Natural corrosion damages the surface galvanized layer of steel wire. As dry-wet cycles increase, the galvanized layer is consumed, iron rust appears, pores form in the rust layer, and tensile strength shows a downward trend. The fracture morphology is split chisel with low necking, indicating reduced ductility. The average tensile strength of corroded steel wire is less than 1700 MPa, a nearly 5% decrease.
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(2). Etch pit geometric dimensions in corroded bridge cable surfaces follow a right-skewed distribution. Depth range is broader than length and width. Shapes are mainly shallow spherical and deep ellipsoidal. Length: 0.005–0.015 mm. Width: 0.005–0.02 mm. Depth: 0–0.04 mm.
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(3). A cellular automata-based etch pit model for cable steel wires is established and verified. After galvanized layer consumption, iron matrix participates in electrochemical reactions, expanding etch pit size. Etch pit depth increases with time steps, but the rate flattens. Initially, the etch pit develops longitudinally, then laterally.
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(4). The maximum stress of the steel wire etch pit is at the bottom and decreases outward. As the depth increases, the stress concentration at the bottom grows, leading to increased maximum stress and stress concentration factors. Maximum stress approaches 1800 MPa, and the factor is above 3.0. The tensile strength continuously decreases. After corrosion, the average tensile strength is less than 1700 MPa, a nearly 5% drop.
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(5). In the circumferential direction, corrosion is more severe on the side contacting the corrosive medium first. In the radial direction, steel wire damage decreases from outside to inside. In vulnerable cable parts like connection sleeves and threaded splices, the outermost steel wires bear most corrosion while the interior is less eroded.
Conceptualization, G.Y., L.Z. and X.G.; methodology, L.Z.; software, G.Z., Z.H. and M.L.; validation, G.Y., L.Z. and G.Z.; formal analysis, G.Y., L.Z., G.Z. and M.L.; investigation, L.Z.; resources, L.Z. and Z.H.; data curation, G.Y., L.Z., G.Z. and X.H.; writing—original draft preparation, L.Z., X.G. and X.H.; writing—review and editing, L.Z. and X.H.; visualization, G.Y. and L.Z.; supervision, G.Y. All authors have read and agreed to the published version of the manuscript.
The data presented in this study are available on request from the corresponding author.
Author Liping Zhou was employed by the company Guizhou Transportation Planning Survey & Design Academe Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Footnotes
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Enlarge this image.Figure 3. Experimental design for accelerated corrosion: (a) experimental apparatus and (b) experimental circuit.
Enlarge this image.Figure 5. Micromorphology of steel wires after corrosion: (a) Steel wire 1-1, (b) Steel wire 1-2, (c) Steel wire 1-3, (d) Steel wire 2-1, (e) Steel wire 2-2, (f) Steel wire 2-3, (g) Steel wire 3-1, (h) Steel wire 3-2, (i) Steel wire 3-3, (j) Steel wire 4-1, (k) Steel wire 4-2, and (l) Steel wire 4-3.
Enlarge this image.Figure 6. Load-displacement relationship of damaged steel wire: (a) natural corrosion, (b) one wet-dry cycle, (c) three wet-dry cycles, and (d) five wet-dry cycles.
Enlarge this image.Figure 8. Steel wire fracture morphology: (a) natural corrosion, (b) one wet-dry cycle, (c) three wet-dry cycles, and (d) five wet-dry cycles.
Enlarge this image.Figure 14. Two-dimensional cellular state: (a) triangular grid, (b) square grid, and (c) hexagonal grid.
Enlarge this image.Figure 15. Two-dimensional cellular neighbor types: (a) Von. Neumann, (b) Moore, and (c) Moore extension.
Enlarge this image.Figure 17. Etch pit morphology of steel wire: (a) corrosion process of galvanized layer and (b) corrosion process of iron substrate.
Enlarge this image.Figure 21. Morphology of maximum etch pits after seven and nine cycles of dry-wet alternation: (a) seven wet-dry cycles and (b) nine wet-dry cycles.
Enlarge this image.Figure 22. The maximum depth of corrosion pits after seven and nine cycles of dry-wet alternation: (a) seven wet-dry cycles and (b) nine wet-dry cycles.
Enlarge this image.Figure 24. The stress distribution condition within etch pits: (a) etch pit depth of 0.06 mm, (b) etch pit depth of 0.07 mm, and (c) etch pit depth of 0.08 mm.
Enlarge this image.Figure 25. Comparison of stress cloud maps for different etch pits: (a) etch pit depth of 0.1 mm, (b) etch pit depth of 0.5 mm, (c) etch pit depth of 1.0 mm, (d) etch pit depth of 1.5 mm, (e) etch pit depth of 2.0 mm, (f) etch pit depth of 2.25 mm, (g) etch pit depth of 2.5 mm, and (h) etch pit depth of 2.75 mm.
Enlarge this image.Figure 25. Comparison of stress cloud maps for different etch pits: (a) etch pit depth of 0.1 mm, (b) etch pit depth of 0.5 mm, (c) etch pit depth of 1.0 mm, (d) etch pit depth of 1.5 mm, (e) etch pit depth of 2.0 mm, (f) etch pit depth of 2.25 mm, (g) etch pit depth of 2.5 mm, and (h) etch pit depth of 2.75 mm.
Enlarge this image.Figure 26. Stress concentration under different etch pit depths: (a) maximum stress and (b) stress concentration factor.
Enlarge this image.Figure 31. Physical appearance of steel wires in each circle: (a) Circle 1, (b) Circle 2, (c) Circle 3, (d) Circle 4, (e) Circle 5, and (f) Circle 6.
Enlarge this image.Figure 32. Cable cross-sectional corrosive medium diffusion and damage distribution.
Main technical parameters of the cable body.
| Model Number | Cable Body | Bare Cable (Wire Bundles) | Breaking Force | |||
|---|---|---|---|---|---|---|
| Outer Diameter (mm) | Unit Mass (kg/m) | Diameter (mm) | Area (mm2) | Unit Mass (kg/m) | ||
| LPES 1770-7-127-Zn | 109 | 41.1 | 91.0 | 4888 | 38.4 | 8651 |
Technical requirements for steel wire.
| Item | Nominal Diameter (mm) | Standard Tensile Strength (MPa) | Elongation (%) | Torsional Property | Relaxation Rate |
|---|---|---|---|---|---|
| Numerical value | 7.0 ± 0.07 | 1770 | ≥4 | ≥12 times | ≤2.5 |
Artificial accelerated corrosion test equipment.
| Number | Equipment Name | Specification Model | Technical Parameters | Quantity |
|---|---|---|---|---|
| 1 | Linear regulated DC power supply | KD3005D | Voltage Range/Current Range | 1 |
| 2 | Electronic balance | SL500ZN | Accuracy 0.01 g | 1 |
| 3 | Scale | / | Accuracy 0.01 m | 1 |
| 4 | Measuring cylinder | / | 5000 mL | 1 |
| 5 | Digital camera | CANON EOS | / | 1 |
| 6 | Electronic microscope | DM4 | Magnification 500/1000 | 1 |
Tensile strength of steel wires at different corrosion stages.
| Corrosion Stage | Steel Wire Number | Ultimate Tensile Load (kN) | Tensile Strength (MPa) | Average Tensile Strength (MPa) | Percentage Decrease in Average Tensile Strength (%) |
|---|---|---|---|---|---|
| Natural corrosion | 1-1 | 66.27 | 1722.86 | 1745.13 | 1.41 |
| 1-2 | 68.13 | 1771.22 | |||
| 1-3 | 66.98 | 1741.32 | |||
| One wet-dry cycle | 2-1 | 66.20 | 1721.10 | 1719.83 | 2.83 |
| 2-2 | 66.10 | 1718.45 | |||
| 2-3 | 66.16 | 1720.01 | |||
| Three wet-dry cycles | 3-1 | 65.94 | 1690.22 | 1695.78 | 4.19 |
| 3-2 | 64.96 | 1688.81 | |||
| 3-3 | 65.71 | 1708.31 | |||
| Five wet-dry cycles | 4-1 | 64.86 | 1686.21 | 1683.52 | 4.88 |
| 4-2 | 64.85 | 1685.95 | |||
| 4-3 | 64.56 | 1678.41 |
Comparison of actual and simulated values.
| Maximum Pit (mm) | Actual Value | Simulated Value | Simulation Error (%) |
|---|---|---|---|
| Natural corrosion | 0.061 | 0.059 | 3.27 |
| One wet-dry cycle | 0.065 | 0.062 | 4.61 |
| Three wet-dry cycles | 0.071 | 0.067 | 5.63 |
| Five wet-dry cycles | 0.080 | 0.073 | 9.85 |
Changes in tensile strength under different etch pits.
| Etch Pits Size (mm) | 0.06 | 0.07 | 0.08 | 0.1 | 0.5 | 1 | 1.5 | 2 | 2.25 | 2.5 | 2.75 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Di | 0.017 | 0.019 | 0.023 | 0.028 | 0.138 | 0.265 | 0.383 | 0.49 | 0.54 | 0.587 | 0.631 |
| Tensile strength (MPa) | 1739 | 1734 | 1730 | 1720 | 1526 | 1300 | 1092 | 903 | 815 | 731 | 653 |
References
1. Ma, J.; Sun, S.Z.; Yang, Q. Review on China’s bridge engineering research. China J. Highw. Transp.; 2021; 34, pp. 91-96.
2. He, X.; Guo, Z.; Xu, H. Vehicle impact effect suspender in half-through arch bridge considering vehicle-bridge coupled vibration. Noise Vib. Control; 2022; 42, pp. 206-213.
3. Feng, L.; Wu, K.; Lu, X.; Qiao, W. Research status and development tendency of ultra-high strength steel wire for bridge cables. Mater. China; 2020; 39, pp. 395-403.
4. Xu, J.; Chen, W. Behavior of wires in parallel wire stayed cable under general corrosion effects. Constr. Steel. Res.; 2013; 85, pp. 40-47. [DOI: https://dx.doi.org/10.1016/j.jcsr.2013.02.010]
5. Nakamura, S.-I.; Suzumura, K.; Tarui, T. Mechanical properties and remaining strength of corroded bridge wires. Struct. Eng. Int.; 2004; 14, pp. 50-54. [DOI: https://dx.doi.org/10.2749/101686604777964305]
6. Ling, M. The Exploring Research on Durability of Stayecable. Master’s Thesis; Beijing Jiaotong University: Beijing, China, 2010.
7. Chen, S.; Chen, K.; Zeng, Y.; Gao, H. Study on measures for durability of stay cable. High Speed Railw. Technol.; 2015; 6, pp. 60-64.
8. Wu, J. A Novel Anchorage System of CFRP Cables and Its Performance. Master’s Thesis; Harbin Institute of Technology: Harbin, China, 2018.
9. Feng, B. Study on Anchorage System and Its Long-Term Performance for Large Capacity FRP cable. Ph.D. Thesis; Southeast University: Nanjing, China, 2019.
10. Liang, L.; Xing, G.; Wu, F. Durability risk assessment of stay cables based on cloud theory. J. Northeast. Univ.; 2019; 40, pp. 425-429.
11. Chen, J. Experimental Study on Corrosion Damage of HDPE System of Stayed Cables Under Environment and Loading. Master’s Thesis; Chongqing Jiaotong University: Chongqing, China, 2020.
12. Chang, Y.; Li, S.; Hu, H. Structure durability for Qingshang Changjiang river highway bridge in Wuhan. Bridge Constr.; 2020; 50, 7.
13. Zhang, S. Experimental Research on Mechanical Properties of Naturally Corroded Cable. Master’s Thesis; Xiangtan University: Hunan, China, 2020.
14. Li, B. Research on mechanical properties of cable anchorage zone of extra-dosed cable-stayed bridge. High Speed Railw. Technol.; 2022; 3, 13.
15. Ma, Y.; Li, Z.; Peng, A.; Wang, L.; Zhang, J. Vulnerability evaluation of cable stayed bridge considering cable damage. J. Chang. Univ.; 2022; 42, pp. 101-109.
16. Suresh, S. Fatigue of Materials; 2nd ed. National Defense Industry Press: Beijing, China, 1999; pp. 25-32.
17. Castillo, E.; Fermandes-Canteli, A.; Esslinger, V.; Thürlimann, B. Statistical model for fatigue analysis of wires, strands and cables. IABSE Proc.; 1985; 82, pp. 1-40.
18. Stallings, J.M.; Frank, K.H. Stay-cable fatigue behavior. J. Struct. Eng.; 1991; 117, pp. 936-950.
19. Lan, C.; Li, H.; Jv, Y. Bearing capacity assessment for parallel wire cables. China Civ. Eng. J.; 2013; 46, 8.
20. Xie, M.; Xie, F.; Hu, X.; Ji, B. Study on the Bearing Capacity Evaluation Model of Stay Cables in Corrosion Environment. J. Transp. Sci. Eng.; 2017; 33, 7.
21. Bo, W. Residual Life Analysis of Parallel Wire Cable in Service. Master’s Thesis; Chongqing Jiaotong University: Chongqing, China, 2020.
22. Wang, Z. The Research on Stress Intensity Factor and Remaining Life of Cable Wire with Multiple Corrosion Holes. Master’s Thesis; Changsha University of Science and Technology: Changsha, China, 2021.
23. Feng, W. Experimental Research on the Electric Accelerated Corrosion Method and the Current Efficiency. Master’s Thesis; Shenzhen University: Shenzhen, China, 2015.
24.
25. Kyparissas, N.; Dollas, A. Large-scale Cellular Automata on FPGAs: A New Generic Architecture and a Framework. ACM Trans. Reconfigurable Technol. Syst.; 2020; 14, 5.
26. Ming, H. Elementary cellular automata and self-referential paradoxes. J. Log. Comput.; 2020; 30, pp. 745-763.
27. Guo, Z.; Chen, H.; Li, X.; Yu, J. Simulation of the Evolution Process of Stayed Cable Electrochemical Corrosion Based on Cellular Automata. J. Magnes. Alloys; 2019; 42, pp. 19-27.
28. Gu, P.; Rao, J.; Dong, H.; Jiang, Q. Research of Cellular Automata Based on Data Mining. Proceedings of the 22nd China Database Conference (Technical Reports Section); Hefei, China, 23–26 August 2005; pp. 177-179.
29. Wang, H.; Lv, G.; Zhang, Y. Cellular Automaton Simulations of Corrosion Pit Growth. Corros. Sci. Prot. Technol.; 2008; 20, pp. 472-475.
30. Saunier, J.; Dymitrowska, M.; Chausse, A.; Stafiej, J.; Badiali, J.P. Diffusion, interactions and universal behavior in a corrosion growth model. J. Electroanal. Chem.; 2005; 582, 267.
31. Liao, H. Corrosion Simulation and Stress Redistribution of Parallel Steel Cable Based Cellular Automata. Master’s Thesis; Harbin Institute of Technology: Harbin, China, 2021.
32. Chen, M.C.; Wen, Q.Q.; Zhu, Q.; Huang, H.; Xie, L. Simulation of corrosion process for concrete filled steel tubular columns with the cellular automata method. Eng. Fail. Anal.; 2017; 82, pp. 298-307.
33. Hayati, M.; Rezaei, A. Design of a New Optimized Universal Logic Gate for Quantum-Dot Cellular Automata. IETE J. Res.; 2019; 68, pp. 1141-1147.
34. Zhang, L.; Cheng, J.; Wang, A.; Liu, L.; Li, L. Research on High Fatigue Stress Amplitude Cables for400 MPa Bridges. Highway; 2024; 69, pp. 1-4.
35. Chen, J.; Ren, Y.; Lu, G. Damage in Quasi-Brittle Materials from a Two-Scale Perspective: From Geometric Discontinuity to Free Energy Reduction. Chin. J. Theor. Appl. Mech.; 2024; 9, pp. 1-11.
36. Zhou, Z.; Wang, S.; Gong, Z. Asymmetric Cable Replacement Technique for Cable-Stayed Bridges in Service. World Bridges; 2010; 1, pp. 56-58.
37. Hu, Z. Experimental Study on the Fatigue Properties and Time-Dependent Corrosion Model of Coastal Bridge Suspenders. Master’s Thesis; Chongqing Jiaotong University: Chongqing, China, 2020.
38. Wang, Q. Experimental Study on Corrosion Damage Mechanism of the Bridge Cable Anchorage System Under Service Environment. Master’s Thesis; Chongqing Jiaotong University: Chongqing, China, 2020.
39. He, X.; Yao, G.; Long, H.; Ying, L.; Guo, Z.; Zhao, L.; Tang, Y.; Huang, P. Corrosion protection failure test analysis of the initial damaged cable ICCP mechanism. Case Stud. Constr. Mater.; 2024; 20, e03227.
40.
41. Fan, C. A Multi-Scale Corrosion Fatigue Damage Model of High-Strength Wires and Fatigue Analysis of Bridge Cable. Master’s Thesis; Southeast University: Nanjing, China, 2022.
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; Zeng, Guiping 2 ; He, Zhiqiang 2 ; Gou, Xuetong 2 ; He, Xuanbo 2 ; Liu, Mingxu 2 1 State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China;
2 State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China;