Study on the Effect of Cracking Parameters on the Migration Characteristics of Chloride Ions in Cracked Concrete
Abstract
:1. Introduction
2. Chloride Diffusion Theory
2.1. Homeostasis Studies
2.2. Transient Studies
3. Numerical Model of Cracked Concrete
3.1. Four-Phase Model versus Two-Phase Model
3.2. Validation of the Simulation Model
4. Simulation Results and Discussion
4.1. Crack Location Parameters
4.2. Crack Angle Parameters
4.3. Crack Width Coefficient and Crack Length Coefficient
4.4. The Aspect Ratio of the Crack and Crack Area Ratio
4.5. Dimensionless Crack Diffusion Coefficient
4.6. Crack Frequency
4.7. The Theoretical Solution for the Equivalent Diffusion Coefficient
4.7.1. Parallel Model and Series Model
4.7.2. Verification of Theoretical Solutions
5. Conclusions
- (1)
- When the crack position varies along the x-direction, the change in the equivalent diffusion coefficient in the middle portion of the concrete is gradual, while it rapidly increases near the left and right boundaries. When the crack position varies along the y-direction, the trend is opposite to that of the x-direction. In the middle portion, the equivalent diffusion coefficient changes gradually, while it rapidly decreases near the top and bottom boundaries. Generally, cracks pose the greatest threat to concrete when they are close to the inlet and outlet surfaces, and the least threat when they are close to the top and bottom boundaries. The impact on concrete is relatively small when cracks move in the middle positions.
- (2)
- Under the influence of the crack angle, when θ = 90° (i.e., the crack is perpendicular to the direction of chloride ion diffusion), the damage to concrete is minimized. However, when θ = 0° or θ = 180° (i.e., the crack is parallel to the direction of chloride ion diffusion), the damage to concrete is maximized.
- (3)
- When the crack length is about to penetrate the concrete, the equivalent diffusion coefficient of cracked concrete increases sharply. Under the condition of equal crack area, the thinner and longer the crack, and the greater the equivalent diffusion coefficient of cracked concrete. The increase in the equivalent diffusion coefficient of cracked concrete is non-linear with the increase in the crack diffusion coefficient, and the trend of increase gradually diminishes. Different crack structural parameters lead to different trends in the variation in the equivalent diffusion coefficient of cracked concrete with the crack diffusion coefficient.
- (4)
- Through studying multiple cracks, the following pattern is discovered. When the side length of concrete is B and the number of cracks is n (n ≥ 2), if the spacing between cracks is located at B/n, and the distance between the cracks at the top and bottom ends and the concrete edge is B/2n, the equivalent diffusion coefficient reaches its maximum value. At this point, the damage to the concrete is maximized.
- (5)
- Based on Fick’s diffusion law, a theoretical model for the equivalent diffusion coefficient of cracked concrete was established. A comparison between theoretical and numerical solutions shows that the maximum error in the equivalent diffusion coefficient calculated using the “parallel-then-series” model is 4.4%, while for the “series-then-parallel” model, it is 13.2%. Both models can effectively predict the equivalent diffusion coefficient of cracked concrete in real projects, with the “parallel-then-series” model exhibiting higher accuracy.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Four-Phase Model | Two-Phase Model | |
---|---|---|
Constitute | Mortar matrix, coarse aggregates, ITZ, cracks. | Mortar matrix, cracks. |
Advantages | The influences of the four phases on the diffusion properties of concrete can be considered. The study on ion transport can delve into a microscopic level, enabling analysis of the distribution and transport processes of ions in localized regions of concrete. | Only the influence of the two phases on the diffusion properties of concrete can be considered. The study of ion transport is limited to a macroscopic level, allowing analysis of the distribution and transport patterns of ions in the entirety of concrete. |
Disadvantages | Modeling complexity, large computational requirements, and required parameters are numerous and difficult to obtain. | Simple modeling, low computational effort, fewer parameters required. |
Four-Phase Model | Two-Phase Model | |
---|---|---|
Aggregate size range () | 5 mm–15 mm | |
Aggregate volume fraction () | 50% | |
Interface transition zone thickness () | 100 μm | |
Diffusion coefficient in the interfacial transition zone ) | ||
Mortar diffusion coefficient ) | ||
Crack diffusion coefficient ) |
Four-Phase Model | Two-Phase Model | |
---|---|---|
) |
Parameters | Connotation |
---|---|
Length of the concrete matrix | |
Width of the concrete matrix | |
Length of the crack | |
Width of the crack | |
Angle rotated counterclockwise from the positive x-axis to the major axis of the crack | |
Coordinates of the center of the crack | |
Maximum distances from the crack center to the y-axis and the x-axis | |
Diffusion coefficient of the concrete matrix | |
Diffusion coefficient of the crack | |
Equivalent diffusion coefficient in the x-direction for concrete containing cracks |
Dimensionless Parameters | Formulas |
---|---|
Crack location parameters | |
Crack angle | |
Crack width | |
Crack length coefficient | |
Aspect ratio of the crack | |
Crack area ratio | |
Dimensionless crack diffusion coefficient | |
Dimensionless equivalent diffusion coefficient |
Parallel Model | Series Model | ||||
---|---|---|---|---|---|
Theoretical Solution (m2/s) | Real Value (m2/s) | Errors (%) | Theoretical Solution (m2/s) | Real Value (m2/s) | Errors (%) |
5.8953 × 10−12 | 5.8953 × 10−12 | 0 | 4.70469 × 10−12 | 4.7047 × 10−12 | 2.92057 × 10−6 |
6.13436 × 10−12 | 6.1344 × 10−12 | 6.52061 × 10−6 | 4.70562 × 10−12 | 4.7056 × 10−12 | 5.23485 × 10−6 |
6.37342 × 10−12 | 6.3734 × 10−12 | 3.13804 × 10−6 | 4.70656 × 10−12 | 4.7066 × 10−12 | 7.78033 × 10−6 |
6.61248 × 10−12 | 6.6125 × 10−12 | 3.02457 × 10−6 | 4.7075 × 10−12 | 4.7075 × 10−12 | 5.31844 × 10−7 |
6.85154 × 10−12 | 6.8515 × 10−12 | 5.83814 × 10−6 | 4.70844 × 10−12 | 4.7084 × 10−12 | 8.92046 × 10−6 |
7.0906 × 10−12 | 7.0906 × 10−12 | 0 | 4.70938 × 10−12 | 4.7094 × 10−12 | 3.84899 × 10−6 |
Parallel-Then-Series Model | Series-Then-Parallel Model | ||||
---|---|---|---|---|---|
Theoretical Solution (m2/s) | Real Value (m2/s) | Errors (%) | Theoretical Solution (m2/s) | Real Value (m2/s) | Errors (%) |
5.29125 × 10−12 | 5.1988 × 10−12 | 1.778206 | 4.75076 × 10−12 | 5.1988 × 10−12 | 8.618147 |
5.38559 × 10−12 | 5.2649 × 10−12 | 2.292374 | 4.7517 × 10−12 | 5.2649 × 10−12 | 9.747541 |
5.47579 × 10−12 | 5.3255 × 10−12 | 2.822126 | 4.75264 × 10−12 | 5.3255 × 10−12 | 10.756855 |
5.56212 × 10−12 | 5.3814 × 10−12 | 3.35816 | 4.75359 × 10−12 | 5.3814 × 10−12 | 11.666376 |
5.64481 × 10−12 | 5.4331 × 10−12 | 3.896616 | 4.75453 × 10−12 | 5.4331 × 10−12 | 12.489599 |
5.72409 × 10−12 | 5.4811 × 10−12 | 4.433233 | 4.75547 × 10−12 | 5.4811 × 10−12 | 13.238774 |
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Huang, T.; Feng, S.; Wang, M.; Peng, Z. Study on the Effect of Cracking Parameters on the Migration Characteristics of Chloride Ions in Cracked Concrete. Buildings 2024, 14, 1738. https://doi.org/10.3390/buildings14061738
Huang T, Feng S, Wang M, Peng Z. Study on the Effect of Cracking Parameters on the Migration Characteristics of Chloride Ions in Cracked Concrete. Buildings. 2024; 14(6):1738. https://doi.org/10.3390/buildings14061738
Chicago/Turabian StyleHuang, Tao, Shuang Feng, Mengge Wang, and Zhongqi Peng. 2024. "Study on the Effect of Cracking Parameters on the Migration Characteristics of Chloride Ions in Cracked Concrete" Buildings 14, no. 6: 1738. https://doi.org/10.3390/buildings14061738