﻿ 混凝土电化学沉积修复孔隙率演化及其近似表征

# 混凝土电化学沉积修复孔隙率演化及其近似表征Approximate Characterization of Porosity Evolution in Concrete Repaired by Electrochemical Deposition

Abstract: The process of electrochemical deposition restoration is influenced by many factors and even the restoration effect of the same batch of specimens presents a fluctuating feature. In this paper, the porous concrete specimens were used to simulate the damage specimen during the process of electrochemical deposition. To evaluate the repair effects, the porosity of all the specimens were measured. Gauss distribution, Extreme distribution and Laplace distribution were used to fit the evolution of the porosity and Bayesian Information Criterion (BIC criterion) and goodness of fit determination coefficient (R2) were used to evaluate the corresponding goodness of fit. The results showed that the porosity of the specimens decreased with the progress of the restoration process, but the restoration effect (evolution of the porosity) of the same batch of specimens presented random characteristics under the same electrochemical environment setting. The fitting degree showed that compared with the Extreme distribution and Laplace distribution, the Gauss distribution was more consistent with the probabilistic characterization of the concrete porosity evolution in the repair process.

1. 引言

2. 电化学沉积修复及其效果评价试验设计

2.1. 电化学试验设置

1) 在转换箱底部放入钛板，并加上3~5 cm的垫块；修复试件放在垫块之上；

2) 将钛板和电源正极相连，将试件内部钢筋(笼)和电源阴极相连，形成闭合回路；

3) 加入已配置好的电解质溶液，打开电源开关，进行电化学沉积修复试验。

Figure 1. Electrochemical deposition restoration device

2.2. 试件制备

Figure 2. Steel bar distribution

Table 1. Proportion of porous concrete materials (kg/m3)

2.3. 孔隙率测量试验原理

${P}_{T}=\frac{{\rho }_{a}-{\rho }_{d}}{{\rho }_{a}}×100%$ (1)

${P}_{T}=\left(1-\frac{B-A}{{\rho }_{w}V}\right)×100%$ (2)

3. 电化学沉积修复试验结果与分析

3.1. 修复前后试件孔隙率分布

Figure 3. Porosity evolution of 13 specimens during restoration

Figure 4. Average value of porosity during restoration

(1) Gauss分布 (2) Extreme分布 (3) Laplace分布

Figure 5. Fitting diagram of porosity evolution distribution function for the specimens to be repaired

3.2. 修复试件孔隙率演化近似合

4. 孔隙率演化表征函数拟合评价

4.1. 拟合函数评价指标

${R}^{2}=1-\frac{RSS}{TSS}=1-\frac{{\sum }_{i=1}^{n}{\left({y}_{i}-{Y}_{i}\right)}^{2}}{{\sum }_{i=1}^{n}{\left({Y}_{i}-{\stackrel{¯}{Y}}_{i}\right)}^{2}}$ (3)

${R}^{2}$ 的取值在0到1之间。 ${R}^{2}$ 愈接近于1，拟合函数的残差平方和愈小，拟合优度愈高。

BIC准则是指在不完全情报下，对部分未知的状态用主观概率估计，然后用贝叶斯公式对发生概率进行修正，最后再利用期望值和修正概率做出最优决策 [16] 。BIC指数愈小，拟合度愈高。BIC准则公式如下：

$BIC=q×In\left(n\right)+n×In\left(\frac{RSS}{n}\right)$ (4)

4.2. 函数模型拟合度评价

4.3. 电沉积修复混凝土超声波速表征评价分析

Figure 6. R2 distribution diagram

Figure 7. BIC coefficient distribution diagram

Figure 8. Gauss distribution of porosity over time

5. 结论

1) 孔隙率分布表明修复过程多孔混凝土试件的平均孔隙率呈下降趋势，沉积产物逐渐增多，混凝土修复过程中逐渐密实。

2) 混凝土同批次不同试件孔隙率差异较大，体现了混凝土自身的随机性；混凝土不同时间孔隙率随时间的下降幅度也各不相同，体现了电沉积修复过程的随机性。

3) 混凝土的孔隙率分布可通过经典概率密度函数回归拟合，比较Gauss分布、Extreme分布、Laplace分布，可发现Gauss分布更适用于修复混凝土的孔隙率分布。

NOTES

*通讯作者。

[1] Mehta, P.K. (1997) Durability—Critical Issues for the Future. Concrete International, 19, 1-12.

[2] Ryu, J.S. and Otsuki, N. (2005) Experimental Study on Repair of Concrete Structural Members by Electrochemical Method. Scripta Materialia, 52, 1123-1127.
https://doi.org/10.1016/j.scriptamat.2005.02.001

[3] Ryu, J.S. and Otsuki, N. (2002) Crack Closure of Reinforced Concrete by Electro Deposition Technique. Cement and Concrete Research, 32, 159-264.
https://doi.org/10.1016/S0008-8846(01)00650-0

[4] Chen, Q., Zhu, H.H., Ju, J.W., Jiang, Z.W., Yan, Z.G. and Li, H.X. (2018) Stochastic Micromechanical Predictions for the Effective Properties of Concrete Considering the In-terfacial Transition Zone Effects. International Journal of Damage Mechanics, 27, 1252-1271.
https://doi.org/10.1177/1056789517728501

[5] Chen, Q., Jiang, Z.W., Yang, Z.H., Zhu, H.H., Ju, J.W., Yan, Z.G. and Wang, Y.Q. (2017) Differential-Scheme Based Micromechanical Framework for Unsaturated Concrete Re-paired by the Electrochemical Deposition Method. Acta Mechanica, 228, 415-431.
https://doi.org/10.1007/s00707-016-1710-6

[6] Chen, Q., Jiang, Z.W., Zhu, H.H., Ju, J.W. and Yan, Z.G. (2017) Micromechanical Framework for Saturated Concrete Repaired by the Electrochemical Deposition Method with Inter-facial Transition Zone Effects. International Journal of Damage Mechanics, 26, 210-228.
https://doi.org/10.1177/1056789516672163

[7] Chen, Q., Mousavi Nezhad, M., Fisher, Q. and Zhu, H.H. (2016) Multi-Scale Approach for Modeling the Transversely Isotropic Elastic Properties of Shale Considering Mul-ti-Inclusions and Interfacial Transition Zone. International Journal of Rock Mechanics and Mining Sciences, 84, 95-104.
https://doi.org/10.1016/j.ijrmms.2016.02.007

[8] Mohankumar, G. (2005) Concrete Repair by Electrodeposition. Indian Concrete Journal, 79, 57-60.

[9] Monteiro, P. and Ryou, J.S. (2004) Electrodeposition as a Rehabilitation Method for Concrete Materials. Canadian Journal of Civil Enginereing, 31, 776-781.
https://doi.org/10.1139/l04-044

[10] Zhu, H.H., Chen, Q., Yan, Z.G., Ju, J.W. and Zhou, S. (2014) Microme-chanical Model for Saturated Concrete Repaired by Electrochemical Deposition Method. Materials and Structures, 47, 1067-1082.
https://doi.org/10.1617/s11527-013-0115-4

[11] Jiang, Z.W., Xing, F., Sun, Z.P. and Wang, P.M. (2008) Healing Effectiveness of Cracks Rehabilitation in Reinforced Concrete Using Electrodeposition Method. Journal of Wuhan University of Technology, 23, 917-922.
https://doi.org/10.1007/s11595-007-6917-x

[12] Chen, Q., Jiang, Z.W. and Yang, Z.H. (2015) An Experimental Study on the Repair of Deteriorated Concrete by Electrochemical Deposition Method. In: Environmental Sustainability in Transportation Infrastructure, American Society of Civil Engineers, Reston, 87-94.
https://doi.org/10.1061/9780784479285.008

[13] Kewalramani, G. (2006) Concrete Compressive Strength Pre-diction Using Ultrasonic Pulse Velocity through Artificial Neural Networks. Automation in Construction, 15, 374-379.
https://doi.org/10.1016/j.autcon.2005.07.003

[14] Braun, H., et al. (1980) A Simple Method for Testing Good-ness of Fit in the Presence of Nuisance Parameters. Journal of the Royal Statistical Society, 42, 53-63.
https://doi.org/10.1111/j.2517-6161.1980.tb01100.x

[15] Larntz, K. (1978) Small-Sample Comparisons of Exact Levels for Goodness of Fit Statistics. Journal of the American Statistical Association, 73, 253-263.
https://doi.org/10.1080/01621459.1978.10481567

[16] Constantinopoulos, C., Titsias, M.K. and Likas, A. (2006) Bayesian Feature and Model Selection for Gaussian Mixture Models. IEEE Transactions on Pattern Analysis and Ma-chine Intelligence, 28, 1013-1018.
https://doi.org/10.1109/TPAMI.2006.111

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