Probabilistic Generalization of a Comprehensive Model for the Deterioration Prediction of RC Structure under Extreme Corrosion Environments
Abstract
:1. Introduction
2. Review of the Reliability Model of Combined Deterioration
2.1. Governing Equation and Limit State Functions
2.2. Reduced Number of Random Variables
3. Other Further Improvements for the Probabilistic Model of Combined Durability
3.1. Single Limit State Function
3.2. Simplification for the Algorithm of Conventional Solution Procedure
3.3. Response Surface Method
- The probability of corrosion initiation of a reference specimen is calculated using the Monte Carlo method.
- The Monte Carlo result for the above reference specimen is used to build a response surface.
- By changing the mean value of reach random variable, the probabilities of corrosion initiation in other specimens can be calculated by the above mentioned response surface.
4. Semi-Empirical Approach for the Probabilistic Study of Combined Durability
4.1. Concentration Distribution of Free Chloride ions Considering Carbonation
4.2. Experimental Verification and Comparison with the Comprehensive Combined Model for the Semi-Empirical Solution
4.3. Probability Calculation
5. Illustrative Example and Parametric Study
5.1. Problem Description
5.2. Result Discussion
5.2.1. Probability
5.2.2. Effect of Reducing Limit State Functions
5.2.3. Effect of Simplified Solution Procedure
5.2.4. Application of the Response Surface Method
5.2.5. Discussion for the Semi-Empirical Probabilistic Model
5.2.6. Comparison with the Conventional One-Dimensional Solution
6. Conclusions
- A comprehensive model is reviewed to calculate the reliability of corrosion deterioration due to carbonation, chloride penetration, and their combined effect.
- Two simplified approaches for the solution procedure of this probabilistic model are provided.
- A semi-empirical method is developed to approximately predict the concentration distribution of chloride ions, and swiftly calculate the probability of combined deterioration.
- Comparison to the original non-simplified model shows that all of these improved approaches can greatly simplify the computational cost, and that the accuracies are acceptable.
Author Contributions
Funding
Conflicts of Interest
Appendix A. Mechanism of Chemical Link between Carbonation and Chloride Movement
Appendix B. Calculation of Average Error e
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Variable | Mean Value | COV | Distribution |
---|---|---|---|
Cfc,b | 0.75% binder w. t. | 0.2 | Log-Normal |
CCO2,b | 0.02 mol/m3 of pore air | 0.1 | Normal |
Cfc,th | 0.4% binder w. t. | 0.2 | Normal |
ct | 40 mm | 0.2 | Normal |
Dfc,ref | 6.5 × 10−12 m2/s | 0.2 | Log-Normal |
ϕhc,0 | 0.5 | 0.3 | Normal |
[CCaO]0 | 3000 mol/m3 of concrete | 0.05 | Normal |
d | 0.9 | 0.05 | Normal |
kϕ | 0.2 | 0.1 | Normal |
Mix Proportions | Specimen | |||||
---|---|---|---|---|---|---|
FAC-1 (Ref.) | OPC-1 | OPC-2 | OPC-3 | FAC-2 | FAC-3 | |
w/b | 0.45 | 0.35 | 0.35 | 0.55 | 0.45 | 0.45 |
a/b | 4 | 4 | 6 | 4 | 4 | 4 |
FA | 0.1 | 0 | 0 | 0 | 0.2 | 0.3 |
Variable | Mean Value | COV | Distribution |
---|---|---|---|
Cfc,b | 0.75% binder w. t. | 0.2 | Log-Normal |
CCO2,b | 0.02 mol/m3 of pore air | 0.1 | Normal |
Cfc,th | 0.4% binder w. t. | 0.2 | Normal |
ct | 40 mm | 0.2 | Normal |
Dfc,ref | 6.5 × 10−12 m2/s | 0.2 | Log-Normal |
DCO2 | 3 × 10−8 m2/s | 0.2 | Log-Normal |
[CCaO]0 | 3000 mol/m3 of concrete | 0.05 | Normal |
βc | 0.15 | 0.1 | Normal |
cpar | 15 mm | 0.05 | Normal |
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Zhu, X.; Chen, Z.; Wang, H.; Chen, Y.; Xu, L. Probabilistic Generalization of a Comprehensive Model for the Deterioration Prediction of RC Structure under Extreme Corrosion Environments. Sustainability 2018, 10, 3051. https://doi.org/10.3390/su10093051
Zhu X, Chen Z, Wang H, Chen Y, Xu L. Probabilistic Generalization of a Comprehensive Model for the Deterioration Prediction of RC Structure under Extreme Corrosion Environments. Sustainability. 2018; 10(9):3051. https://doi.org/10.3390/su10093051
Chicago/Turabian StyleZhu, Xingji, Zaixian Chen, Hao Wang, Yabin Chen, and Longjun Xu. 2018. "Probabilistic Generalization of a Comprehensive Model for the Deterioration Prediction of RC Structure under Extreme Corrosion Environments" Sustainability 10, no. 9: 3051. https://doi.org/10.3390/su10093051