﻿ 桥梁缆索高强钢丝均匀腐蚀及点蚀的规律
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (12): 1615-1621.  DOI: 10.11908/j.issn.0253-374x.2018.12.001 0

### 引用本文

JIANG Chao, WU Chong, JIANG Xu. Experiment Research on Uniform Corrosion and Pitting Corrosion of High-Strength Bridge Wires[J]. Journal of Tongji University (Natural Science), 2018, 46(12): 1615-1621. DOI: 10.11908/j.issn.0253-374x.2018.12.001

### 文章历史

Experiment Research on Uniform Corrosion and Pitting Corrosion of High-Strength Bridge Wires
JIANG Chao , WU Chong , JIANG Xu
College of Civil Engineering, Tongji University, Shanghai 200092, China
Abstract: In order to study the uniform corrosion and pitting corrosion of high-strength bridge wires, a total of 30 steel wire specimens on six corrosion levels were prepared by using the acetic acid salt spray test. The variation of uniform corrosion depth and pitting depth was evaluated by using weight analysis and three dimension scanning. The results show that the measured uniform corrosion depth follows the power-law distribution. The coefficient of variation of uniform corrosion depth decrease with the corrosion time. The pitting depth follows the normal distribution and maximum pitting depth follows the extreme value distribution. Finally, the prediction models for uniform corrosion depth and maximum pitting depth were established and then applied to the real cables on the bridge.
Key words: high-strength bridge wires    uniform corrosion    pitting corrosion    maximum pitting depth

1 试验概况 1.1 试件设计

 图 1 预腐蚀钢丝试件样品 Fig.1 Samples of pre-corroded steel wires
1.2 质量损失与均匀腐蚀深度计算

 ${\eta _{nk}} = \frac{{{m_{n0}} - {m_{nk}} - \frac{1}{3}\sum\limits_{i = 1}^3 {\left[ {{m_{{\rm{c1}}}}\left( i \right) - {m_{{\rm{c2}}}}\left( i \right)} \right]} }}{{{m_{n0}}{l_{\rm{e}}}/{l_{\rm{n}}}}}$ (1)

 $\begin{array}{l} \Delta m = \rho {l_{\rm{e}}}\Delta A = \rho {l_{\rm{e}}}\frac{{\rm{ \mathsf{ π} }}}{4}\left[ {{D^2} - {{\left( {D - 2{d_{{\rm{u}},nk}}} \right)}^2}} \right] = \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{ \mathsf{ π} }}\rho {l_{\rm{e}}}\left[ {{d_{{\rm{u}},nk}}\left( {D - {d_{{\rm{u}},nk}}} \right)} \right] \end{array}$ (2)

 $\begin{array}{l} {d_{{\rm{u}},nk}} = \frac{{\Delta m}}{{{\rm{ \mathsf{ π} }}\rho {l_{\rm{e}}}D}} = \\ \;\;\;\;\;\;\;\frac{{{m_{n0}} - {m_{nk}} - \frac{1}{3}\sum\limits_{i = 1}^3 {\left[ {{m_{{\rm{c1}}}}\left( i \right) - {m_{{\rm{c2}}}}\left( i \right)} \right]} }}{{{\rm{ \mathsf{ π} }}\rho {l_{\rm{e}}}D}} = \\ \;\;\;\;\;\;\;{\eta _{nk}}\frac{{{m_{n0}}}}{{{\rm{ \mathsf{ π} }}\rho D{l_{\rm{n}}}}} \end{array}$ (3)
1.3 三维扫描及数据处理

 图 2 钢丝三维模型 Fig.2 3D model of steel wires

2 试验结果分析 2.1 均匀腐蚀深度

A~F组试件均匀腐蚀深度的统计特性如表 3所示.随着腐蚀时间的增加，钢丝均匀腐蚀深度的均值增大，变异系数减小.A组试件的变异系数远大于其他组，原因是一方面镀锌层尚未完全耗尽，部分钢丝基体与尚存的镀锌层同时受到腐蚀，腐蚀速率不稳定，腐蚀深度不确定性较大; 另一方面是钢丝均匀腐蚀深度较小，对腐蚀深度的波动更敏感.

 ${d_{\rm{u}}}\left( t \right) = 1.009{t^{0.764}}$ (4)
 图 3 均匀腐蚀深度随腐蚀时长变化关系 Fig.3 Uniform corrosion depth versus exposure time

2.2 点蚀深度

 图 4 试件不同角度下的表面轮廓线 Fig.4 Surface profiles

 图 5 试件C1腐蚀深度等高线 Fig.5 Contour of corrosion depth

 $f\left( x \right) = \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}$ (5)

 图 6 试件点蚀深度分布 Fig.6 Distribution of corrosion depth

 $\left. \begin{array}{l} \mu = 1\;963.52{\eta ^{1.021}}\\ \sigma = 895.88{\eta ^{1.306}} \end{array} \right\}$ (6)
 图 7 μ与质量损失率的关系 Fig.7 μ versus weight loss
 图 8 σ与质量损失率的关系 Fig.8 σ versus weight loss

3 最大点蚀深度模型 3.1 模型推导

 $F\left( x \right) = \int_{ - \infty }^x {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}{\rm{d}}x}$ (7)

 $\begin{array}{l} {\left[ {\frac{{1 - F\left( x \right)}}{{f\left( x \right)}}} \right]^\prime } = {\left[ {\frac{{\int_x^{ + \infty } {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}{\rm{d}}x} }}{{\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}}}} \right]^\prime } = \\ {\left[ {\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}\int_x^{ + \infty } {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}{\rm{d}}x} } \right]^\prime } = \\ \exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}\frac{{x - \mu }}{{{\sigma ^2}}}\int_x^{ + \infty } {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}{\rm{d}}x} - \\ \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }} = \frac{{\int_x^{ + \infty } {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}{\rm{d}}x} }}{{\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}\frac{{{\sigma ^2}}}{{x - \mu }}}} - \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }} \end{array}$ (8)

x→+∞时，

 $\begin{array}{l} \mathop {\lim }\limits_{x \to + \infty } {\left[ {\frac{{1 - F\left( x \right)}}{{f\left( x \right)}}} \right]^\prime } = \\ \mathop {\lim }\limits_{x \to + \infty } \frac{{\int_x^{ + \infty } {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}{\rm{d}}x} }}{{\exp \left\{ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right\}\frac{{{\sigma ^2}}}{{x - \mu }}}} - \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }} = \\ \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }}\mathop {\lim }\limits_{x \to + \infty } \frac{1}{{1 + \frac{{{\sigma ^2}}}{{{{\left( {x - \mu } \right)}^2}}}}} - \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} \sigma }} = 0 \end{array}$ (9)

 $F\left( x \right) = \exp \left\{ { - \exp \left( { - \frac{{x - b}}{a}} \right)} \right\}$ (10)

 $\begin{array}{*{20}{c}} {a = \frac{\sigma }{{\sqrt {2\ln n} }}}\\ {b = \mu - \sqrt {2\ln n} \sigma + \frac{{\left( {\ln \ln n + \ln 4{\rm{ \mathsf{ π} }}} \right)\sigma }}{{2\sqrt {2\ln n} }}} \end{array}$ (11)

 $n = \frac{{3L\left( { - 13\;717\eta + 5\;426.39} \right)}}{{10}}$ (12)

3.2 模型验证

3.3 实例分析

 $\begin{array}{*{20}{c}} {{d_{\rm{u}}}\left( t \right) = 1.009{{\left( {3.74k} \right)}^{0.764}} = 50\mu {\rm{m}}}\\ {k = 44.24\;{\rm{h}}} \end{array}$ (13)

 图 9 拉索钢丝均匀腐蚀深度 Fig.9 Uniform corrosion depth

 图 10 拉索钢丝最大点蚀深度分布 Fig.10 Distribution of maximum pitting depth
4 结论

(1) 缆索高强钢丝在腐蚀下均匀腐蚀深度随腐蚀时长的变化同样遵循幂函数规律，均匀腐蚀深度的变异系数随腐蚀时长减小.

(2) 明确了钢丝三维扫描的数据处理方法，钢丝的点蚀深度服从正态分布，建立了以质量损失率为变量的点蚀深度模型.

(3) 建立了钢丝最大点蚀深度预测模型，试验结果与预测值的对比验证了模型的准确性.

(4) 以实桥为例，分析了在实际腐蚀环境下拉索钢丝均匀腐蚀深度以及最大点蚀深度的变化，为定量研究拉索腐蚀后的使用寿命提供了参考.

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