**4. Corrosion Process**

## *4.1. Uniform Corrosion*

The development of the uniform corrosion of steel wire is mainly affected by two factors: the corrosion time, and the uniform corrosion rate. As the uniform corrosion depth is not easy to obtain directly, it is generally described using the volumetric method, weight-loss method, or other methods. In this study, the weight-loss method was used to describe the uniform corrosion of steel wire, which is given as Equation (1). With reference to the specification for removal of corrosion products, the chemical substances generated after steel wire corrosion can be removed without damaging the metal matrix, and the quality loss of metal in the corrosive environment can be accurately measured, to evaluate the degree of corrosion of steel wire.

$$
\psi = \frac{m\_0/l\_0 - m\_1/l\_1}{m\_0/l\_0} \times 100\% \tag{1}
$$

where *ψ* represents the loss rate of steel wire mass, *m*<sup>0</sup> represents the quality of steel wire before corrosion, *l*<sup>0</sup> represents the length of steel wire before corrosion, *m*<sup>1</sup> represents the quality of steel wire after corrosion, and *l*<sup>1</sup> represents the length of steel wire after corrosion.

Owing to the large slenderness ratio of the steel wire specimen, the sectional area of both ends of the steel wire is small and the calculation constant is large, so the length change caused by corrosion can be ignored. That is *l*<sup>0</sup> = *l*1. Therefore, Equation (1) can be rewritten as Equation (2):

$$
\psi = \frac{m\_0 - m\_1}{m\_0} \tag{2}
$$

According to Equation (3), the mass loss of steel wire is converted into the coating and corrosion depth of steel wire *du*.

$$d\mu = \frac{\psi}{A\rho} = \frac{m\_0 - m\_1}{\pi D \rho l\_0} \tag{3}$$

where *A* is the surface area of steel wire, *A* = *πDl*0, *D* is the initial diameter of steel wire, *ρ* is the material density, and *l*<sup>0</sup> is the length of steel wire.

Figures 4 and 5 show the average mass loss per unit length of all steel wire samples, indicating that the overall distribution of test results was relatively regular. The change of steel wire mass loss at each stage was stable, without obvious mutations, indicating that the test effect was good. The mass loss of Galfan steel wire increased obviously with the increase of corrosion time. During the entire corrosion period, the increasing trend of corrosion quality was close to an exponential change, and the corrosion rate gradually slowed down.

down.

down.

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Figures 4 and 5 show the average mass loss per unit length of all steel wire samples,

Figures 4 and 5 show the average mass loss per unit length of all steel wire samples,

indicating that the overall distribution of test results was relatively regular. The change of steel wire mass loss at each stage was stable, without obvious mutations, indicating that the test effect was good. The mass loss of Galfan steel wire increased obviously with the increase of corrosion time. During the entire corrosion period, the increasing trend of corrosion quality was close to an exponential change, and the corrosion rate gradually slowed

indicating that the overall distribution of test results was relatively regular. The change of steel wire mass loss at each stage was stable, without obvious mutations, indicating that the test effect was good. The mass loss of Galfan steel wire increased obviously with the increase of corrosion time. During the entire corrosion period, the increasing trend of corrosion quality was close to an exponential change, and the corrosion rate gradually slowed

**Figure 4.** Average mass loss per unit length of galvanized steel wire. **Figure 4.** Average mass loss per unit length of galvanized steel wire. **Figure 4.** Average mass loss per unit length of galvanized steel wire.

**Figure 5.** Average mass loss per unit length of Galfan steel wire. **Figure 5.** Average mass loss per unit length of Galfan steel wire. **Figure 5.** Average mass loss per unit length of Galfan steel wire.

Owing to the influence of the coating thickness and corrosion randomness, the corrosion rate of different steel wires varies, so the steel wire corrosion coefficient was introduced to describe the randomness. Figures 6 and 7 show the fit distribution law of the two kinds of steel wires. The corrosion coefficient of the galvanized steel wire conformed to the normal distribution N(*μ*, *σ*2) with *μ* = 1.00 and *σ* = 0.0483, whereas the Galfan steel wire Owing to the influence of the coating thickness and corrosion randomness, the corrosion rate of different steel wires varies, so the steel wire corrosion coefficient was introduced to describe the randomness. Figures 6 and 7 show the fit distribution law of the two kinds of steel wires. The corrosion coefficient of the galvanized steel wire conformed to the normal distribution N(*μ*, *σ*2) with *μ* = 1.00 and *σ* = 0.0483, whereas the Galfan steel wire Owing to the influence of the coating thickness and corrosion randomness, the corrosion rate of different steel wires varies, so the steel wire corrosion coefficient was introduced to describe the randomness. Figures 6 and 7 show the fit distribution law of the two kinds of steel wires. The corrosion coefficient of the galvanized steel wire conformed to the normal distribution N(*µ*, *σ* 2 ) with *µ* = 1.00 and *σ* = 0.0483, whereas the Galfan steel wire conformed to the Cauchy distribution C(*γ*, *x*0) with *x*<sup>0</sup> = 1.00 and *γ* = 0.0391.

conformed to the Cauchy distribution C(*γ*, *x*0) with *x*0 = 1.00 and *γ* = 0.0391.

conformed to the Cauchy distribution C(*γ*, *x*0) with *x*0 = 1.00 and *γ* = 0.0391.

Therefore, the uniform corrosion rate of the two kinds of steel wire can be expressed

Therefore, the uniform corrosion rate of the two kinds of steel wire can be expressed

as in Equation (4).

as in Equation (4).

ቊ

ቊ

1.00669, *γ* = 0.03908.

1.00669, *γ* = 0.03908.

() = ∗ (−43.97 ∗ (−/316.48) + 45.37)

() = ∗ (−43.97 ∗ (−/316.48) + 45.37)

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ீ() = ீ ∗ (−49.73 ∗ (−/1093.36) + 49.81) (4)

ீ() = ீ ∗ (−49.73 ∗ (−/1093.36) + 49.81) (4)

where *t* is the corrosion duration, conforms to the normal distribution N(*μ*, *σ<sup>2</sup>*) with *μ* = 1.00, *σ* = 0.04834, and conforms to the Cauchy distribution C(*γ*, *x*0) with *x*<sup>0</sup> =

where *t* is the corrosion duration, conforms to the normal distribution N(*μ*, *σ<sup>2</sup>*) with *μ* = 1.00, *σ* = 0.04834, and conforms to the Cauchy distribution C(*γ*, *x*0) with *x*<sup>0</sup> =

**Figure 6.** Corrosion coefficient distribution of galvanized steel wire. **Figure 6.** Corrosion coefficient distribution of galvanized steel wire. **Figure 6.** Corrosion coefficient distribution of galvanized steel wire.

**Figure 7.** Corrosion coefficient distribution of Galfan steel wire. **Figure 7.** Corrosion coefficient distribution of Galfan steel wire. **Figure 7.** Corrosion coefficient distribution of Galfan steel wire.

*4.2. Pitting Corrosion 4.2. Pitting Corrosion*  The key factor causing cracks in corrosion fatigue is pitting corrosion, which is ac-Therefore, the uniform corrosion rate of the two kinds of steel wire can be expressed as in Equation (4).

$$\begin{cases} du\_{Zn}(t) = \psi\_{Zn} \ast (-43.97 \ast \exp(-t/316.48) + 45.37) & \text{Galvantized steel wire} \\ du\_{Gd}(t) = \psi\_{Gd} \ast (-49.73 \ast \exp(-t/1093.36) + 49.81) & \text{Galfan steel wire} \end{cases} \tag{4}$$

tective layer is consumed. Owing to the stress concentration effect, the stress at the edge of the corrosion pit is far greater than the overall stress level. When the depth of the corrosion pit increases to a certain extent, it becomes a crack. A crack usually occurs at the of the corrosion pit is far greater than the overall stress level. When the depth of the corrosion pit increases to a certain extent, it becomes a crack. A crack usually occurs at the where *t* is the corrosion duration, *ψZn* conforms to the normal distribution N(*µ*, *σ 2* ) with *µ* = 1.00, *σ* = 0.04834, and *ψGal* conforms to the Cauchy distribution C(*γ*, *x*0) with *x*<sup>0</sup> = 1.00669, *γ* = 0.03908.

#### *4.2. Pitting Corrosion*

The key factor causing cracks in corrosion fatigue is pitting corrosion, which is accompanied by uniform corrosion. When a passivation or film forms on the metal material surface, a small and deep corrosion pit is generated on the substrate surface after the protective layer is consumed. Owing to the stress concentration effect, the stress at the edge of the corrosion pit is far greater than the overall stress level. When the depth of the corrosion pit increases to a certain extent, it becomes a crack. A crack usually occurs at the

position with the greatest pitting corrosion, so the deepest pitting corrosion determines the working state of the steel wire and is a key analysis point in corrosion fatigue analysis. position with the greatest pitting corrosion, so the deepest pitting corrosion determines the working state of the steel wire and is a key analysis point in corrosion fatigue analysis. position with the greatest pitting corrosion, so the deepest pitting corrosion determines the working state of the steel wire and is a key analysis point in corrosion fatigue analysis.

Figure 8 shows the surface morphology of the steel wire after cleaning. The pits on the surface of the steel wire are obvious. To further determine the distribution characteristics of the pitting corrosion of the different types of steel wire, the steel wire indication was detected using a 3D shape scanner, and a 3D model of the steel wire surface was established based on the regression of 2D scanning results. As the steel wire specimen was not completely straight, the surface profile presented an irregular curve shape as a whole. To eliminate the influence of the steel wire specimen's own curved shape on the test results, the small window moving average automatic baseline correction method was used to estimate the baseline corresponding to the measured profile. According to the difference between the measured contour coordinates and the baseline coordinates, the pitting depth on the axial length of the steel wire could be determined. Figure 8 shows the surface morphology of the steel wire after cleaning. The pits on the surface of the steel wire are obvious. To further determine the distribution characteristics of the pitting corrosion of the different types of steel wire, the steel wire indication was detected using a 3D shape scanner, and a 3D model of the steel wire surface was established based on the regression of 2D scanning results. As the steel wire specimen was not completely straight, the surface profile presented an irregular curve shape as a whole. To eliminate the influence of the steel wire specimen's own curved shape on the test results, the small window moving average automatic baseline correction method was used to estimate the baseline corresponding to the measured profile. According to the difference between the measured contour coordinates and the baseline coordinates, the pitting depth on the axial length of the steel wire could be determined. Figure 8 shows the surface morphology of the steel wire after cleaning. The pits on the surface of the steel wire are obvious. To further determine the distribution characteristics of the pitting corrosion of the different types of steel wire, the steel wire indication was detected using a 3D shape scanner, and a 3D model of the steel wire surface was established based on the regression of 2D scanning results. As the steel wire specimen was not completely straight, the surface profile presented an irregular curve shape as a whole. To eliminate the influence of the steel wire specimen's own curved shape on the test results, the small window moving average automatic baseline correction method was used to estimate the baseline corresponding to the measured profile. According to the difference between the measured contour coordinates and the baseline coordinates, the pitting depth on the axial length of the steel wire could be determined.

The pitting depth could be calculated using the uniform corrosion depth and maximum pitting factor [20]. Figures 9 and 10 show the 3D surface regression profile of the steel wire surface. According to the 40 measured surface profiles and regression analysis results, the block maximum value method was used to obtain a sample of the maximum pitting factor in each exposure period. The analysis accuracy of the block maximum method is directly affected by the selected block size, and the sample size of the block maximum should be sufficiently large. After comprehensive consideration, this study determined that the block size for calculating the pitting factor was 10 mm. The maximum pitting depth was taken every 10 mm along the length of the steel wire, and the maximum pitting factor was calculated according to Equation (5). The pitting depth could be calculated using the uniform corrosion depth and maximum pitting factor [20]. Figures 9 and 10 show the 3D surface regression profile of the steel wire surface. According to the 40 measured surface profiles and regression analysis results, the block maximum value method was used to obtain a sample of the maximum pitting factor in each exposure period. The analysis accuracy of the block maximum method is directly affected by the selected block size, and the sample size of the block maximum should be sufficiently large. After comprehensive consideration, this study determined that the block size for calculating the pitting factor was 10 mm. The maximum pitting depth was taken every 10 mm along the length of the steel wire, and the maximum pitting factor was calculated according to Equation (5). The pitting depth could be calculated using the uniform corrosion depth and maximum pitting factor [20]. Figures 9 and 10 show the 3D surface regression profile of the steel wire surface. According to the 40 measured surface profiles and regression analysis results, the block maximum value method was used to obtain a sample of the maximum pitting factor in each exposure period. The analysis accuracy of the block maximum method is directly affected by the selected block size, and the sample size of the block maximum should be sufficiently large. After comprehensive consideration, this study determined that the block size for calculating the pitting factor was 10 mm. The maximum pitting depth was taken every 10 mm along the length of the steel wire, and the maximum pitting factor was calculated according to Equation (5).

$$G(t) = da(t) / du(t) \tag{5}$$

where *G*(*t*) is the maximum pitting factor, *da*(*t*) is the maximum pitting depth, and *du*(*t*) is the uniform corrosion depth in the same period. where *G*(*t*) is the maximum pitting factor, *da*(*t*) is the maximum pitting depth, and *du*(*t*) is the uniform corrosion depth in the same period. where *G*(*t*) is the maximum pitting factor, *da*(*t*) is the maximum pitting depth, and *du*(*t*) is the uniform corrosion depth in the same period.

**Figure 9.** Regression of the 3D corrosion morphology of galvanized steel wire. **Figure 9. Figure 9.** Regression of the 3D corrosion morphology of galvanized steel wire. Regression of the 3D corrosion morphology of galvanized steel wire.

**Figure 10.** Regression of the 3D corrosion morphology of Galfan steel wire. **Figure 10.** Regression of the 3D corrosion morphology of Galfan steel wire.

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The existing research ignored the time-varying characteristics of the maximum pitting factor and posited that the maximum pitting factors in different periods have the same distribution characteristics. Figures 11 and 12 show the fitting results of the maximum pitting factor of steel wire in certain periods. The maximum pitting factor has obvious time-varying characteristics. Gumbel distribution was used to fit the maximum pitting factor. The relationship between the pitting system and location parameters, scale parameters, and corrosion time can be expressed as in Equation (6). The existing research ignored the time-varying characteristics of the maximum pitting factor and posited that the maximum pitting factors in different periods have the same distribution characteristics. Figures 11 and 12 show the fitting results of the maximum pitting factor of steel wire in certain periods. The maximum pitting factor has obvious timevarying characteristics. Gumbel distribution was used to fit the maximum pitting factor. The relationship between the pitting system and location parameters, scale parameters, and corrosion time can be expressed as in Equation (6). **Figure 10.** Regression of the 3D corrosion morphology of Galfan steel wire. The existing research ignored the time-varying characteristics of the maximum pitting factor and posited that the maximum pitting factors in different periods have the same distribution characteristics. Figures 11 and 12 show the fitting results of the maximum pitting factor of steel wire in certain periods. The maximum pitting factor has obvious time-varying characteristics. Gumbel distribution was used to fit the maximum pitting factor. The relationship between the pitting system and location parameters, scale parameters, and corrosion time can be expressed as in Equation (6).

$$Z\_p = \exp\left\{-\exp\left[-\left(\frac{\chi-\mu(t)}{\sigma(t)}\right)\right]\right\} \tag{6}$$

Relative frequency

 (h)

where () and () are the location parameters and scale parameters corresponding to the accelerated corrosion duration *t*, respectively. where *µ*(*t*) and *σ*(*t*) are the location parameters and scale parameters corresponding to the accelerated corrosion duration *t*, respectively. where () and () are the location parameters and scale parameters corresponding to the accelerated corrosion duration *t*, respectively.

Maximum pitting factor **Figure 11.** Fitting results of maximum pitting factor of galvanized steel wire. **Figure 11.** Fitting results of maximum pitting factor of galvanized steel wire. coating and Galfan coating corresponding to the accelerated corrosion duration *t*.

ቊ () = 1.3967 exp(−/58.0061) + 0.2190 (7) **Figure 12.** Fitting results of maximum pitting factor of Galfan steel wire. **Figure 12.** Fitting results of maximum pitting factor of Galfan steel wire.

water, salt, and other substances, the corrosion factors of the external environment enter the cable body and cause steel wire corrosion. The corrosion of steel wire generally goes through the following three stages [21]: (1) uniform corrosion and pitting corrosion, (2) pitting crack development, and (3) corrosion fatigue crack growth. Uniform corrosion refers to uniform corrosion and detachment of the steel wire surface, which belongs to pure chemical reaction and directly causes the reduction of the steel wire diameter. The reduction of diameter is approximately equal along the length of steel wire. Owing to the nonuniformity of the material, the diameter of the steel wire decreases, accompanied by pitting corrosion randomly distributed on the surface of the steel wire. Uniform corrosion includes the corrosion consumption of the steel wire coating and the time needed for uniform corrosion and pitting of the steel wire matrix. The specific development rules of uniform corrosion and pitting were obtained through accelerated corrosion tests in this study. On the basis of the unit area *A*0 of pitting calculation, Equation (9) can be used to obtain the maximum pitting coefficient distribution of *A*k in any area [22,23]. When estimating the maximum pitting coefficient per unit area, Saint Venant's principle must be considered. The minimum length of the analysis unit should be greater than twice the

= +

1 ( 

where is the surface area of the analysis target, and is the surface area of unit area. and are the location parameters and scale parameters of the corresponding fitting

Y. Kondo pointed out that the initiation of fatigue cracks is caused by pitting, and the transition from pitting depth to fatigue cracks is related to the stress amplitude of the steel wire. When the stress amplitude is large, the cracks easily occur in smaller pits, and vice

), = (9)

**5. Corrosion Fatigue of High-Strength Steel Wire** 

*5.1. Corrosion Fatigue Degradation Model* 

diameter of the steel wire.

analysis results by exponential function.

For galvanized steel wire, the pitting factor was larger at the early stage of corrosion; *µ* was 3.386 at 96 h. The pitting factor decreased significantly with the increase of time at the later stages; *µ* was 1.649 at 216 h. The change amplitude of Galfan steel wire was smaller than that of the galvanized steel wire but also decreased with the increase of time; *µ* was 1.778 at 606 h and 1.261 at 1088 h. The increase of the pitting depth was limited, and estimating the corrosion process of the degraded steel wire according to a single distribution law may underestimate the service state of steel wire. Furthermore, the fitting analysis of the location parameters and scale parameters of the pitting distribution function in different corrosion stages showed that the distribution parameters of the two coatings conformed to the exponential change law, which could be calculated according to Equations (7) and (8).


where *µZn*(*t*), *σZn*(*t*), *µGal*(*t*), and *σGal*(*t*), respectively, represent the location parameters and scale parameters of the maximum pitting coefficient distribution between the zinc coating and Galfan coating corresponding to the accelerated corrosion duration *t*.

#### **5. Corrosion Fatigue of High-Strength Steel Wire**

## *5.1. Corrosion Fatigue Degradation Model*

When the protection system of cable components is damaged because the air contains water, salt, and other substances, the corrosion factors of the external environment enter the cable body and cause steel wire corrosion. The corrosion of steel wire generally goes through the following three stages [21]: (1) uniform corrosion and pitting corrosion, (2) pitting crack development, and (3) corrosion fatigue crack growth. Uniform corrosion refers to uniform corrosion and detachment of the steel wire surface, which belongs to pure chemical reaction and directly causes the reduction of the steel wire diameter. The reduction of diameter is approximately equal along the length of steel wire. Owing to the non-uniformity of the material, the diameter of the steel wire decreases, accompanied by pitting corrosion randomly distributed on the surface of the steel wire. Uniform corrosion includes the corrosion consumption of the steel wire coating and the time needed for uniform corrosion and pitting of the steel wire matrix. The specific development rules of uniform corrosion and pitting were obtained through accelerated corrosion tests in this study.

On the basis of the unit area *A*<sup>0</sup> of pitting calculation, Equation (9) can be used to obtain the maximum pitting coefficient distribution of *A<sup>k</sup>* in any area [22,23]. When estimating the maximum pitting coefficient per unit area, Saint Venant's principle must be considered. The minimum length of the analysis unit should be greater than twice the diameter of the steel wire.

$$
\mu\_k = \mu\_0 + \frac{1}{\sigma\_0} \ln(\frac{A\_k}{A\_0}), \sigma\_k = \sigma\_0 \tag{9}
$$

where *A<sup>k</sup>* is the surface area of the analysis target, and *A*<sup>0</sup> is the surface area of unit area. *µ*<sup>0</sup> and *σ*<sup>0</sup> are the location parameters and scale parameters of the corresponding fitting analysis results by exponential function.

Y. Kondo pointed out that the initiation of fatigue cracks is caused by pitting, and the transition from pitting depth to fatigue cracks is related to the stress amplitude of the steel wire. When the stress amplitude is large, the cracks easily occur in smaller pits, and vice versa. The development of pitting pits into fatigue cracks can be described based on the theory of fracture mechanics. The stress intensity factor *K* is introduced to describe the strength of the stress field near the crack tip. The generation of cracks is mainly affected by the alternating stress field at this location. The amplitude of the stress intensity factor ∆*K* can be calculated according to Equation (10).

$$
\Delta K = F\_a \left(\frac{a}{b}\right) \Delta \sigma\_a \sqrt{\pi a} + F\_b \left(\frac{a}{b}\right) \Delta \sigma\_b \sqrt{\pi a} \tag{10}
$$

where *a* is the crack depth, *b* is the diameter of steel wire, ∆*σ<sup>a</sup>* is the equivalent axial stress amplitude, and ∆*σ<sup>b</sup>* is the equivalent axial stress amplitude. *F a b* is calculated using Equation (11) [24].

$$\begin{cases} F\_{\overline{a}} \left( \frac{a}{b} \right) = 0.92 \cdot \frac{2}{\pi} \cdot \sqrt{\frac{2b}{\pi a} \cdot \tan \frac{\pi a}{2b}} \cdot \frac{0.752 + 1.286 \left( \frac{a}{b} \right) + 0.37 \left( 1 - \sin \frac{\pi a}{2b} \right)^3}{\cos \frac{\pi a}{2b}}\\\ F\_{\overline{b}} \left( \frac{a}{b} \right) = 0.92 \cdot \frac{2}{\pi} \cdot \sqrt{\frac{2b}{\pi a} \cdot \tan \frac{\pi a}{2b}} \cdot \frac{0.923 + 0.199 \left( 1 - \sin \frac{\pi a}{2b} \right)^4}{\cos \frac{\pi a}{2b}} \end{cases} \tag{11}$$

where *F<sup>a</sup> a b* denotes axial stress, *F<sup>b</sup> a b* denotes bending stress, *a* is the crack depth, and *b* is the diameter of steel wire.

The corrosion cracking of steel wire is generated from pitting to cracks. When the stress intensity factor at the pitting reaches the threshold value for crack growth of 2.8 MPa·m1/2 [25], the pitting development is transformed into the crack development stage. The Paris formula is the most widely used method for the growth rate analysis of metal corrosion fatigue cracking, and the crack growth rate is expressed as the fatigue crack growth rate [26].

$$\frac{da}{dt} = \mathcal{C}(\Delta K)^m N \tag{12}$$

where ∆*K* is the effective stress intensity factor amplitude, and *C* and *m* are the parameters of the Paris criterion.

To comprehensively consider the impact of the daily traffic flow intensity level on the crack development rate, a crack depth development model was established based on the proportion of daily traffic flow operations, as given in Equation (13).

$$\begin{cases} a\_i = \Delta a + a\_{i-1} \\ \Delta a = \mathbb{C} \sum n\_q \left[ \sum e\_j (\Delta \mathcal{K}\_{qj})^m \mathcal{N}\_{qj} \right] \end{cases} \tag{13}$$

where *a<sup>i</sup>* is the depth of the crack at time *i*, ∆*a* is the increment of the crack, *e<sup>j</sup>* is the operating time of traffic flow with different intensities, ∑ *e<sup>j</sup>* = 24 h, and ∆*K<sup>j</sup>* and *N<sup>j</sup>* are the stress intensity factor range and the number of cycles.

Mayrbaurl pointed out that the critical relative crack depth conforms to the logarithmic normal distribution, with an average value of 0.390 and a coefficient of variation of 0.414. Based on the tests, the maximum critical relative depth was 0.5, which can be used as the judgment standard for steel wire failure.

#### *5.2. Protype Bridge and Traffic Load*

To further analyze the corrosion fatigue degradation of the two types of high-strength steel wire under a load, this study took a long-span suspension bridge as the research background and took high-strength steel wire suspenders as the research object, to investigate the corrosion fatigue degradation of galvanized and Galfan high-strength steel wire under the same conditions. The main bridge structure of the bridge is a single span 838 m steel concrete composite girder suspension bridge. The main cable span is (250 + 838 + 215) m. The vertical layout is shown in Figure 13. Steel concrete composite girders are used as stiffening girders, and the steel beams are combined with concrete bridge decks through shear studs. The section layout is shown in Figures 14 and 15. The full width of the stiffening girder is 33.2 m. The steel longitudinal beams on both sides are connected by steel cross beams. The center height is 2.8 m. The center distance between the webs of the longitudinal beams on both sides is 26.0 m. The bridge deck is a reinforced concrete bridge deck with a full width of 25.0 m and a thickness of 0.22 m. The standard spacing of suspender lifting

points is 16 m. There are two suspenders for each lifting point, with 204 suspenders in total for the whole bridge, and 151 *φ*5 mm high-strength steel wires included in each suspender. with 204 suspenders in total for the whole bridge, and 151 5 mm high-strength steel wires included in each suspender. with 204 suspenders in total for the whole bridge, and 151 5 mm high-strength steel wires included in each suspender. wires included in each suspender. 250m 838m 215m

are used as stiffening girders, and the steel beams are combined with concrete bridge decks through shear studs. The section layout is shown in Figures 14 and 15. The full width of the stiffening girder is 33.2 m. The steel longitudinal beams on both sides are connected by steel cross beams. The center height is 2.8 m. The center distance between the webs of the longitudinal beams on both sides is 26.0 m. The bridge deck is a reinforced concrete bridge deck with a full width of 25.0 m and a thickness of 0.22 m. The standard spacing of suspender lifting points is 16 m. There are two suspenders for each lifting point,

are used as stiffening girders, and the steel beams are combined with concrete bridge decks through shear studs. The section layout is shown in Figures 14 and 15. The full width of the stiffening girder is 33.2 m. The steel longitudinal beams on both sides are connected by steel cross beams. The center height is 2.8 m. The center distance between the webs of the longitudinal beams on both sides is 26.0 m. The bridge deck is a reinforced concrete bridge deck with a full width of 25.0 m and a thickness of 0.22 m. The standard spacing of suspender lifting points is 16 m. There are two suspenders for each lifting point,

are used as stiffening girders, and the steel beams are combined with concrete bridge decks through shear studs. The section layout is shown in Figures 14 and 15. The full width of the stiffening girder is 33.2 m. The steel longitudinal beams on both sides are connected by steel cross beams. The center height is 2.8 m. The center distance between the webs of the longitudinal beams on both sides is 26.0 m. The bridge deck is a reinforced concrete bridge deck with a full width of 25.0 m and a thickness of 0.22 m. The standard spacing of suspender lifting points is 16 m. There are two suspenders for each lifting point, with 204 suspenders in total for the whole bridge, and 151 5 mm high-strength steel

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**Figure 13.** Elevation Layout of the Bridge. **Figure 13.** Elevation Layout of the Bridge. **Figure 13.** Elevation Layout of the Bridge.

**Figure 14.** Schematic Diagram of a Suspender. **Figure 14.** Schematic Diagram of a Suspender. **Figure 14.** Schematic Diagram of a Suspender. **Figure 14.** Schematic Diagram of a Suspender.

**Figure 15.** Section of the Main Girder. **Figure 15.** Section of the Main Girder. **Figure 15.** Section of the Main Girder. **Figure 15.** Section of the Main Girder.

Stochastic traffic flow simulation is the mainstream method for long-span bridge operation evaluation. After the degradation of the suspender steel wire changes from pitting to cracking, it enters the main stage of crack development. The crack growth speed is mainly affected by the stress response of the suspender under the traffic load. Based on the measured traffic flow in a certain area, obtained by the traffic load monitoring system, Stochastic traffic flow simulation is the mainstream method for long-span bridge operation evaluation. After the degradation of the suspender steel wire changes from pitting to cracking, it enters the main stage of crack development. The crack growth speed is mainly affected by the stress response of the suspender under the traffic load. Based on the measured traffic flow in a certain area, obtained by the traffic load monitoring system, Stochastic traffic flow simulation is the mainstream method for long-span bridge operation evaluation. After the degradation of the suspender steel wire changes from pitting to cracking, it enters the main stage of crack development. The crack growth speed is mainly affected by the stress response of the suspender under the traffic load. Based on the measured traffic flow in a certain area, obtained by the traffic load monitoring system, Stochastic traffic flow simulation is the mainstream method for long-span bridge operation evaluation. After the degradation of the suspender steel wire changes from pitting to cracking, it enters the main stage of crack development. The crack growth speed is mainly affected by the stress response of the suspender under the traffic load. Based on the measured traffic flow in a certain area, obtained by the traffic load monitoring system, this study analyzed and selected the data of representative periods, to simulate theformation of traffic flow for loading, so as to obtain the corrosion fatigue degradation of suspender steel wire under different levels of traffic loading.

The traffic data collected by a weigh-in-motion system (WIM) included the vehicle data of the region from 1 March to 31 March 2015, including the vehicle wheelbase, axle load, vehicle speed, and other details [27]. Figure 16 shows the hourly traffic volume results obtained from the collected data by time and lane statistics. The daily traffic volume changed greatly. On the basis of the action area of the traffic flow with obvious changes in traffic volume, the traffic flow level was divided into three intensity levels: dense, moderate, and sparse. The traffic flow intensive periods were mainly concentrated at 9:00–11:00 and 13:00–17:00, and the sparse flow period was from 21:00 to 7:00. The vehicle traffic characteristics at different intensity levels were fitted to obtain the distribution characteristics of the traffic volume and vehicle flow speed under the three intensity levels, as shown in Figures 17 and 18. erate, and sparse. The traffic flow intensive periods were mainly concentrated at 9:00– 11:00 and 13:00–17:00, and the sparse flow period was from 21:00 to 7:00. The vehicle traffic characteristics at different intensity levels were fitted to obtain the distribution characteristics of the traffic volume and vehicle flow speed under the three intensity levels, as shown in Figures 17 and 18. erate, and sparse. The traffic flow intensive periods were mainly concentrated at 9:00– 11:00 and 13:00–17:00, and the sparse flow period was from 21:00 to 7:00. The vehicle traffic characteristics at different intensity levels were fitted to obtain the distribution characteristics of the traffic volume and vehicle flow speed under the three intensity levels, as shown in Figures 17 and 18.

this study analyzed and selected the data of representative periods, to simulate the formation of traffic flow for loading, so as to obtain the corrosion fatigue degradation of sus-

this study analyzed and selected the data of representative periods, to simulate the formation of traffic flow for loading, so as to obtain the corrosion fatigue degradation of sus-

The traffic data collected by a weigh-in-motion system (WIM) included the vehicle data of the region from 1 March to 31 March 2015, including the vehicle wheelbase, axle load, vehicle speed, and other details [27]. Figure 16 shows the hourly traffic volume results obtained from the collected data by time and lane statistics. The daily traffic volume changed greatly. On the basis of the action area of the traffic flow with obvious changes in traffic volume, the traffic flow level was divided into three intensity levels: dense, mod-

The traffic data collected by a weigh-in-motion system (WIM) included the vehicle data of the region from 1 March to 31 March 2015, including the vehicle wheelbase, axle load, vehicle speed, and other details [27]. Figure 16 shows the hourly traffic volume results obtained from the collected data by time and lane statistics. The daily traffic volume changed greatly. On the basis of the action area of the traffic flow with obvious changes in traffic volume, the traffic flow level was divided into three intensity levels: dense, mod-

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pender steel wire under different levels of traffic loading.

pender steel wire under different levels of traffic loading.

**Figure 16.** Change trend of daily average hourly traffic volume. **Figure 16.** Change trend of daily average hourly traffic volume. **Figure 16.** Change trend of daily average hourly traffic volume.

**Figure 17.** Traffic volume (moderate flow). **Figure 17.** Traffic volume (moderate flow). **Figure 17.** Traffic volume (moderate flow).

**Figure 18.** Vehicle flow speed (moderate flow). **Figure 18.** Vehicle flow speed (moderate flow).

flow simulation process is shown in Figure 19.

**Table 7.** Key parameters of traffic flow.

Based on the statistical results of traffic volume and traffic flow speed, the average spacing of vehicles could be determined according to Equation (14). The key parameters

=∙ (14)

based on the Monte Carlo method, vehicle samples were obtained [28], so as to select the traffic flow in typical representative periods for a load effect analysis. The specific traffic

where *Q* denotes traffic volume, *K* denotes traffic density, and *V* denotes traffic speed.

Dense flow Traffic volume (pcu/h) 572 474 209

Moderate flow Traffic volume (pcu/h) 451 378 184

Sparse flow Traffic volume (pcu/h) 175 186 132

**Key Parameter Passing Lane Carriage-Way Slow Lane** 

Traffic speed (km/h) 93.36 88.4 70.76

Traffic speed (km/h) 94.12 87.48 67.98

Traffic speed (km/h) 92.12 81.80 67.98

Based on the statistical results of traffic volume and traffic flow speed, the average spacing of vehicles could be determined according to Equation (14). The key parameters of traffic flow are given in the Table 7, and the characteristics of traffic flow parameters could then be determined. In combination with the random traffic flow sampling method based on the Monte Carlo method, vehicle samples were obtained [28], so as to select the traffic flow in typical representative periods for a load effect analysis. The specific traffic flow simulation process is shown in Figure 19. Based on the statistical results of traffic volume and traffic flow speed, the average spacing of vehicles could be determined according to Equation (14). The key parameters of traffic flow are given in the Table 7, and the characteristics of traffic flow parameters could then be determined. In combination with the random traffic flow sampling method based on the Monte Carlo method, vehicle samples were obtained [28], so as to select the traffic flow in typical representative periods for a load effect analysis. The specific traffic

 Moderate flow Fit curve

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$$Q = \mathbf{K} \cdot \mathbf{V} \tag{14}$$

where *Q* denotes traffic volume, *K* denotes traffic density, and *V* denotes traffic speed. where *Q* denotes traffic volume, *K* denotes traffic density, and *V* denotes traffic speed.


**Table 7.** Key parameters of traffic flow. **Table 7.** Key parameters of traffic flow.

**Figure 18.** Vehicle flow speed (moderate flow).

0.0

0.1

0.2

Relative frequency

0.3

0.4

80 85 90 95

Traffic speed (km/h)

**Figure 19.** Vehicle flow simulation.

## *5.3. Numerical Analysis*

Based on the above vehicle flow load simulation method, the dense, moderate, and sparse evacuation flows obtained from the sampling were loaded into the bridge finite element model. The vehicle bridge coupling analysis system established on the basis of finite element analysis software ANSYS in a previous study was used to obtain the bridge suspender response. For suspension bridges, short suspenders in the middle of the span are the most easily damaged suspenders, because of their short length and the large bending stress caused by the relative displacement between the main cable and the main girder. As the link element cannot directly give the bending stress, Wyatt's theoretical formula was introduced to calculate the bending stress, according to the axial stress of the suspender and the angle generated by the relative movement between the main cable and the stiffening girder [29].

$$
\sigma\_b = \tan \theta \cdot \sqrt{\sigma\_a E} \tag{15}
$$

where *σ<sup>a</sup>* is axial stress, *E* is elasticity modulus of steel wire, *θ* is the angle caused by the relative movement between the main cable and the stiffening girder. relative movement between the main cable and the stiffening girder. Figures 20 and 21 show the stress response results of short suspenders in the mid span. The response of the suspenders under the overall traffic flow is affected by the num-

where is axial stress, *E* is elasticity modulus of steel wire, is the angle caused by the

tan

 θσ

*b a* = ⋅ *E* (15)

σ

Based on the above vehicle flow load simulation method, the dense, moderate, and sparse evacuation flows obtained from the sampling were loaded into the bridge finite element model. The vehicle bridge coupling analysis system established on the basis of finite element analysis software ANSYS in a previous study was used to obtain the bridge suspender response. For suspension bridges, short suspenders in the middle of the span are the most easily damaged suspenders, because of their short length and the large bending stress caused by the relative displacement between the main cable and the main girder. As the link element cannot directly give the bending stress, Wyatt's theoretical formula was introduced to calculate the bending stress, according to the axial stress of the suspender and the angle generated by the relative movement between the main cable and the

Figures 20 and 21 show the stress response results of short suspenders in the mid span. The response of the suspenders under the overall traffic flow is affected by the number of vehicles and the distance between vehicles, and the response under a dense flow is most obvious. However, during driving, a driver spontaneously maintains a safe distance, to ensure safety requirements, which is usually greater than the distance between adjacent suspenders. Therefore, the extreme value of the axial force response of suspenders under sparse or moderate flow may exceed the extreme value of axial force under a dense flow, owing to the impact of single vehicle weight at the time of traffic flow. The bending stress is mainly affected by the continuous superposition of traffic flow effects, and the overall response level and extreme value of bending stress under a dense flow are the most obvious. ber of vehicles and the distance between vehicles, and the response under a dense flow is most obvious. However, during driving, a driver spontaneously maintains a safe distance, to ensure safety requirements, which is usually greater than the distance between adjacent suspenders. Therefore, the extreme value of the axial force response of suspenders under sparse or moderate flow may exceed the extreme value of axial force under a dense flow, owing to the impact of single vehicle weight at the time of traffic flow. The bending stress is mainly affected by the continuous superposition of traffic flow effects, and the overall response level and extreme value of bending stress under a dense flow are the most obvious.

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**Figure 19.** Vehicle flow simulation.

*5.3. Numerical Analysis* 

stiffening girder [29].

**Figure 20.** Axial stress response. **Figure 20.** Axial stress response.

**Figure 21.** Bending stress response. **Figure 21.** Bending stress response.

improving the service life of steel wire.

50

Development rate

100

0

**Figure 22.** Corrosion rate of galvanized steel wire.

0

500

1000

Development rate (um/year)

1500

2000

0 5 10 15 20

Operation time (year)

2.5 7.5 5.0

Operation time (year)

Crack Uniform corrosion Pitting

Basing on the obtained stress responses of suspender steel wires under different traffic flows, and combined with the uniform corrosion and pitting corrosion laws of steel wires obtained from the tests, the corrosion fatigue degradation of steel wires was analyzed. Based on the proportion of traffic flow at different levels determined from the traffic flow monitoring data, the corrosion fatigue of the two types of steel wire under the combined action of traffic flow was simulated by sampling. Figures 22 and 23 show the change rules of the uniform corrosion rate, pitting rate, and crack development rate of steel wire. The initial rate of uniform corrosion and pitting corrosion was fast and then Basing on the obtained stress responses of suspender steel wires under different traffic flows, and combined with the uniform corrosion and pitting corrosion laws of steel wires obtained from the tests, the corrosion fatigue degradation of steel wires was analyzed. Based on the proportion of traffic flow at different levels determined from the traffic flow monitoring data, the corrosion fatigue of the two types of steel wire under the combined action of traffic flow was simulated by sampling. Figures 22 and 23 show the change rules of the uniform corrosion rate, pitting rate, and crack development rate of steel wire. The initial rate of uniform corrosion and pitting corrosion was fast and then rapidly decreased. On the contrary, the crack

rapidly decreased. On the contrary, the crack growth rate gradually increased, and the rate increased with time. The crack growth rate of galvanized steel wire exceeded the cor-

exceeded the corrosion rate 10 years later. Although the time difference was small, the corrosion rate of galvanized aluminum steel wire was lower, the relative crack growth rate was also significantly lower than that of galvanized steel wire, which is conducive to

growth rate gradually increased, and the rate increased with time. The crack growth rate of galvanized steel wire exceeded the corrosion rate after seven years of corrosion, whereas that of galvanized aluminum steel wire exceeded the corrosion rate 10 years later. Although the time difference was small, the corrosion rate of galvanized aluminum steel wire was lower, the relative crack growth rate was also significantly lower than that of galvanized steel wire, which is conducive to improving the service life of steel wire. rosion rate after seven years of corrosion, whereas that of galvanized aluminum steel wire exceeded the corrosion rate 10 years later. Although the time difference was small, the corrosion rate of galvanized aluminum steel wire was lower, the relative crack growth rate was also significantly lower than that of galvanized steel wire, which is conducive to improving the service life of steel wire.

Basing on the obtained stress responses of suspender steel wires under different traffic flows, and combined with the uniform corrosion and pitting corrosion laws of steel wires obtained from the tests, the corrosion fatigue degradation of steel wires was analyzed. Based on the proportion of traffic flow at different levels determined from the traffic flow monitoring data, the corrosion fatigue of the two types of steel wire under the combined action of traffic flow was simulated by sampling. Figures 22 and 23 show the change rules of the uniform corrosion rate, pitting rate, and crack development rate of steel wire. The initial rate of uniform corrosion and pitting corrosion was fast and then rapidly decreased. On the contrary, the crack growth rate gradually increased, and the rate increased with time. The crack growth rate of galvanized steel wire exceeded the cor-

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**Figure 22.** Corrosion rate of galvanized steel wire. **Figure 22.** Corrosion rate of galvanized steel wire.

**Figure 21.** Bending stress response.

**Figure 23.** Corrosion rate of Galfan steel wire.

Mean STD

3 years

0

100

200

300

Distribution of crack depth(um)

400

500

600

4 years

Mean

0

200

400

600

Distribution of crack depth(um)

800

1000

1200

Figures 24 and 25 show the distribution law of steel wire crack depth at different stages. With the increase of service time, the average crack depth of the whole steel wire increased and the development rate increased, which is consistent with the analysis results in the above figure. However, owing to the randomness of the pitting corrosion and crack development, the STD value of crack distribution was large at the end of service, STD **Figure 23.** Corrosion rate of Galfan steel wire. Figures 24 and 25 show the distribution law of steel wire crack depth at different stages. With the increase of service time, the average crack depth of the whole steel wire increased and the development rate increased, which is consistent with the analysis results in the above figure. However, owing to the randomness of the pitting corrosion and crack development, the STD value of crack distribution was large at the end of service, and the discreteness of wire life became obvious.

6 years 9 years 12years

**Figure 24.** Crack depth distribution of galvanized suspender steel wire.

8 years 12 years 16 years

4 8 12 16 20

Operation time(year)

0

0

100

200

300

Mean value and STD(um)

400

500

600

200

400

Mean value and STD(um)

600

800

1000

3 6 9 12 15

Operation time(year)

and the discreteness of wire life became obvious.

Figures 24 and 25 show the distribution law of steel wire crack depth at different stages. With the increase of service time, the average crack depth of the whole steel wire increased and the development rate increased, which is consistent with the analysis results in the above figure. However, owing to the randomness of the pitting corrosion and crack development, the STD value of crack distribution was large at the end of service,

Figures 24 and 25 show the distribution law of steel wire crack depth at different stages. With the increase of service time, the average crack depth of the whole steel wire increased and the development rate increased, which is consistent with the analysis results in the above figure. However, owing to the randomness of the pitting corrosion and crack development, the STD value of crack distribution was large at the end of service,

0 5 10 15 20 25 30 35

Operation time (year)

0 5 10 15 20 25 30 35

Operation time (year)

2.5 7.5 5.0 10.0

Operation time (year)

2.5 7.5 5.0 10.0

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Operation time (year)

Crack Uniform corrosion Pitting

Crack Uniform corrosion Pitting

**Figure 23.** Corrosion rate of Galfan steel wire.

**Figure 23.** Corrosion rate of Galfan steel wire.

25

Development rate

Development rate

25

50

0

50

0

0

0

500

500

1000

Development rate (um/year)

Development rate (um/year)

1000

1500

2000

1500

2000

and the discreteness of wire life became obvious.

and the discreteness of wire life became obvious.

**Figure 24.** Crack depth distribution of galvanized suspender steel wire. **Figure 24.** Crack depth distribution of galvanized suspender steel wire. **Figure 24.** Crack depth distribution of galvanized suspender steel wire.

**Figure 25.** Crack depth distribution of Galfan suspender steel wire.

Figure 26 shows the life distribution of the two types of steel wire under a comprehensive traffic flow. The average life of Galfan steel wire was significantly higher than that of the galvanized steel wire, being 28.47 years and 17.24 years, respectively. Figures 27 and 28 show the corrosion fatigue life of the two kinds of coated steel wires under different strengths of traffic flow. The strength level of the traffic flow was the decisive factor affecting the steel wire degradation. The durability of Galfan steel wire was obviously better than that of galvanized steel wire, and the overall life of the steel wire was longer. Nevertheless, the average life of galvanized steel wire was 11.13 years, whereas that of the Galfan steel wire was 16.92 years under dense traffic flows. The corrosion fatigue life of steel wire was not significantly increased. Under a sparse traffic flow, the service life of steel wire was better than expected and was significantly higher than the design life of general cable structures (25 years). Under rarefaction flow, the average life of the two kinds of steel wires could reach 35 years and 55 years, respectively. When the proportion of sparse traffic flow and moderate traffic flow is relatively high during bridge operation, the slow corrosion fatigue degradation of Galfan steel wire at this stage could greatly improve the service life of steel wire. However, when the traffic flow intensity level is generally high, obtaining good results using Galfan steel wire would be difficult.

**Figure 25.** Crack depth distribution of Galfan suspender steel wire.

**Figure 25.** Crack depth distribution of Galfan suspender steel wire.

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Figure 26 shows the life distribution of the two types of steel wire under a comprehensive traffic flow. The average life of Galfan steel wire was significantly higher than that of the galvanized steel wire, being 28.47 years and 17.24 years, respectively. Figures 27 and 28 show the corrosion fatigue life of the two kinds of coated steel wires under different strengths of traffic flow. The strength level of the traffic flow was the decisive factor affecting the steel wire degradation. The durability of Galfan steel wire was obviously better than that of galvanized steel wire, and the overall life of the steel wire was longer. Nevertheless, the average life of galvanized steel wire was 11.13 years, whereas that of the Galfan steel wire was 16.92 years under dense traffic flows. The corrosion fatigue life of steel wire was not significantly increased. Under a sparse traffic flow, the service life of steel wire was better than expected and was significantly higher than the design life of general cable structures (25 years). Under rarefaction flow, the average life of the two kinds of steel wires could reach 35 years and 55 years, respectively. When the proportion of sparse traffic flow and moderate traffic flow is relatively high during bridge operation, the slow corrosion fatigue degradation of Galfan steel wire at this stage could greatly improve the service life of steel wire. However, when the traffic flow intensity level is generally high, obtaining good results using Galfan steel wire would be difficult.

Figure 26 shows the life distribution of the two types of steel wire under a comprehensive traffic flow. The average life of Galfan steel wire was significantly higher than that of the galvanized steel wire, being 28.47 years and 17.24 years, respectively. Figures 27 and 28 show the corrosion fatigue life of the two kinds of coated steel wires under different strengths of traffic flow. The strength level of the traffic flow was the decisive factor affecting the steel wire degradation. The durability of Galfan steel wire was obviously better than that of galvanized steel wire, and the overall life of the steel wire was longer. Nevertheless, the average life of galvanized steel wire was 11.13 years, whereas that of the Galfan steel wire was 16.92 years under dense traffic flows. The corrosion fatigue life of steel wire was not significantly increased. Under a sparse traffic flow, the service life of steel wire was better than expected and was significantly higher than the design life of general cable structures (25 years). Under rarefaction flow, the average life of the two kinds of steel wires could reach 35 years and 55 years, respectively. When the proportion of sparse traffic flow and moderate traffic flow is relatively high during bridge operation, the slow corrosion fatigue degradation of Galfan steel wire at this stage could greatly improve the service life of steel wire. However, when the traffic flow intensity level is generally high, obtaining good results using Galfan steel wire would be difficult.

**Figure 26.** Life distribution of steel wire under comprehensive traffic flow. **Figure 26.** Life distribution of steel wire under comprehensive traffic flow. **Figure 26.** Life distribution of steel wire under comprehensive traffic flow.

**Figure 27.** Service life of galvanized suspender wire. **Figure 27.** Service life of galvanized suspender wire. **Figure 27.** Service life of galvanized suspender wire.

**Figure 28.** Service life of Galfan suspender steel wire. **Figure 28.** Service life of Galfan suspender steel wire.

#### **6. Conclusions 6. Conclusions**

This paper took the difference in the corrosion fatigue degradation characteristics of galvanized and Galfan high-strength steel wire coatings as the research goal. It analyzed the difference of uniform corrosion and pitting corrosion of two coatings under the same conditions through an accelerated corrosion test. It then constructed a dynamic distribution model of uniform corrosion and pitting corrosion during coating corrosion. On the This paper took the difference in the corrosion fatigue degradation characteristics of galvanized and Galfan high-strength steel wire coatings as the research goal. It analyzed the difference of uniform corrosion and pitting corrosion of two coatings under the same conditions through an accelerated corrosion test. It then constructed a dynamic distribution model of uniform corrosion and pitting corrosion during coating corrosion. On the basis of an accelerated corrosion test and the traffic load monitoring data of a large bridge, the

basis of an accelerated corrosion test and the traffic load monitoring data of a large bridge, the corrosion fatigue degradation of two kinds of steel wires under traffic load during

(1) The macro morphology of the corrosion of high-strength steel wire had obvious stage change characteristics. At the early stage of corrosion, the steel wire coating could effectively protect the iron matrix, and the corrosion products were free of Fe oxides. When the corrosion developed to a certain stage, brown corrosion products began to appear; on the galvanized steel wire at 386 h and on the Galfan steel wire at 1016 h. The surface coating began to be consumed, and the steel wire Fe matrix started to corrode. At this time, the steel wire surface a reddish brown rust appeared. The corrosion of steel wire can be generally divided into two parts. The first part is the corrosion of the surface coating. When the corrosion depth exceeds the coating thickness, corrosion of the second part of the steel wire matrix starts. After the corrosion products are removed, uneven pits appeared on the steel wire surface. The corrosion resistance of Galfan steel wire is obviously better than that of galvanized steel wire. (2) The development law of steel wire corrosion depth was fitted and analyzed. In addition, a uniform corrosion development model and pitting corrosion probability model of galvanized and Galfan steel wire were established. With the extension of corrosion time, the uniform corrosion depth of zinc coating and Galfan coating conformed to the exponential increase trend. The development trend of the two coatings was similar, and the corrosion rate gradually slowed down with the increase of time. The corrosion coefficient of galvanized steel wire conformed to normal random distribution, whereas that of Galfan steel wire conformed to Cauchy distribution. The section distribution of the maximum pitting coefficient did not reject the Gumbel distribution. The location and scale parameters of the maximum pitting coefficient distribution in the two coating intervals showed an exponential downward trend with

(3) The early rate of uniform corrosion and pitting corrosion was fast, and then it decreased rapidly, whereas the crack growth rate gradually increased. With the increase of time, the rate increased. The average value of the overall crack depth of the steel wire also increased, and the development rate continued to increase. The STD value of the crack distribution in the late service period was large, and the discreteness of the steel wire life became obvious. Based on the analysis of the corrosion

the increase of corrosion duration.

corrosion fatigue degradation of two kinds of steel wires under traffic load during operation was investigated. The following conclusions were obtained:


It should be mentioned that the corrosion fatigue properties of coated steel wires were investigated through accelerated corrosion tests. However, the period of the accelerated corrosion test was relatively short, which is quite different from the real environment in service. In a subsequent study, the corrosion rate and characteristics of the steel wire need to be investigated using field exposure tests and cable components in service, which could better determine the corrosion characteristics and effects of traffic load on the corrosion performance of steel wire coatings.

**Author Contributions:** Conceptualization, Y.Z. (Yue Zhao); Methodology, Y.Z. (Yue Zhao); Software, X.F.; Validation, X.F.; Formal analysis, B.S.; Writing—original draft, B.S.; Writing—review & editing, Y.Z. (Yiyun Zhu); Supervision, Y.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Science Basic Research Program of Shaanxi (Program No. 2022JQ-336), and the open fund of Shaanxi Provincial Key Laboratory (Chang'an University) of Highway Bridges and Tunnels (Program No. 300102212509).

**Data Availability Statement:** Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.
