Numerical Solutions for Chloride Diffusion Fluctuation in RC Elements from Corrosion Probability Assessments
Abstract
:1. Introduction
2. Mechanical Model
2.1. Problem Statement
2.2. Analytical Solution
2.3. Numerical Solution
2.4. Chloride Diffusion Coefficient
3. Probabilistic Approaches
4. General Methodology
5. Analyses and Results
5.1. Probabilistic Results
5.2. Numerical Results
5.2.1. The 2D Chloride Diffusion
5.2.2. The 3D Chloride Diffusion
6. Conclusions
- (1)
- Three different probabilistic techniques (i.e., MCS, FORM, DI) were used to estimate the probability of failure of steel bars by considering the time of corrosion initiation. The probabilistic analyses were carried out using several simulations for each variable. PDF functions were defined, which have a great importance in practical applications since they enable the analyst to know if the probability of failure is acceptable according to the parameters involved (Table 2 and Figure 2). MCS is a technique used to evaluate some functions using several random variables. For each sample, a random variable is assigned as a deterministic value from which several random numbers are generated. The results are treated as a distribution, and they are statistically determined. MCSs directly provide the t-variant failure probability. Results show a strong influence of the T variation. It was also noted that MCS provides high values in favor of safety, i.e., ~6.5 years (Figure 4 and Table 3) with relatively few samples. A very good agreement was achieved with DI and FORM.
- (2)
- Numerical solutions were developed to study the trend of Dcl under different loadings. Fick’s II law expressed by Equation (2) is a highly non-linear equation hard to accurately solve. Considering Dcl as a non-constant value means to assume the problem as non-linear. These disadvantages make this model less attractive in practice. For this reason, analytical solutions are usually used. In particular, a methodology was proposed where four types of functions are used (Table 4). Results show that, due to the oscillations of the generic function (e.g., sinusoidal and general), the chloride content C can assume lower values with respect to C values for constant diffusivity. The 3D analyses, accounting for the random variability and advanced solutions, show that chloride C can be higher than ~1.50 compared to C by traditional approaches.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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α [44] | β [44] | Dcl,ref [29] | w/c * | T0 [40] |
11.80 | 4.0 | 0.40 cm2/year | 0.50 a | 23.0 °C (296.0 K) |
R [40] | tref [43] | T * | tr [43] | hDcl [50] |
8.134 J/mol K | 28 days (0.076 years) | 25.0 years | 30.0 years | 0.75 |
Parameter | PDF Distribution | μ | ±σ a | CV (%) |
---|---|---|---|---|
Ea (kJ/mol) | Normal | 44.60 [40] b | 4.30 | 10.0 |
T (°C) | Normal | 23.0 *c | 8.0 | 35.0 |
Cf (kg/m3) | Log-normal | 1.50 [44] | 0.75 | 50.0 |
ωe | Beta (5, 1) | 0.83 * | 0.1408 | 17.0 |
m | Beta (1, 4) | 0.20 [48] | 0.1632 | 82.0 |
h | Beta (4, 1) | 0.80 * | 0.1632 | 20.0 |
n | Uniform (0, 12) | 6.0 [50] | 3.4641 | 58.0 |
xc (cm) | Log-normal | 5.0 *d | 1.50 | 30.0 |
C0 (kg/m3) | Uniform (0, 1) | 0.50 * | 0.2886 | 58.0 |
Cs (kg/m3) | Log-normal | 1.15 [7] e | 0.575 | 50.0 |
Scenario I a Dcl = 0.423 cm2/Year Cb = 3.31 × 10−6 kg/cm3 | Scenario II Dcl = 0.256 cm2/Year Cb = 3.31 × 10−6 kg/cm3 | Scenario III Dcl = 0.256 cm2/Year Cb = 4.51 × 10−6 kg/cm3 | ||||
---|---|---|---|---|---|---|
μtR (Year) | σtR (Year) | μtR (Year) | σtR (Year) | μtR (Year) | σtR (Year) | |
MCS | 21.44 (14.11) b | 14.95 (4.68) | 35.41 (23.39) | 24.96 (8.01) | 35.03 (23.31) | 24.58 (7.98) |
FORM | 14.82 | 4.21 | 24.36 | 6.92 | 24.36 | 6.36 |
DI | 14.87 | 5.20 | 24.41 | 8.54 | 24.41 | 8.54 |
Type | Dcl × fD(x,t) | Possible Applications |
---|---|---|
Constant | Dcl × constant |
|
Sinusoidal | Dcl × Sin(t) |
|
Gaussian |
| |
General | a |
|
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Zacchei, E.; Nogueira, C.G. Numerical Solutions for Chloride Diffusion Fluctuation in RC Elements from Corrosion Probability Assessments. Buildings 2022, 12, 1211. https://doi.org/10.3390/buildings12081211
Zacchei E, Nogueira CG. Numerical Solutions for Chloride Diffusion Fluctuation in RC Elements from Corrosion Probability Assessments. Buildings. 2022; 12(8):1211. https://doi.org/10.3390/buildings12081211
Chicago/Turabian StyleZacchei, Enrico, and Caio Gorla Nogueira. 2022. "Numerical Solutions for Chloride Diffusion Fluctuation in RC Elements from Corrosion Probability Assessments" Buildings 12, no. 8: 1211. https://doi.org/10.3390/buildings12081211
APA StyleZacchei, E., & Nogueira, C. G. (2022). Numerical Solutions for Chloride Diffusion Fluctuation in RC Elements from Corrosion Probability Assessments. Buildings, 12(8), 1211. https://doi.org/10.3390/buildings12081211