Experimental Investigation of the Relationship between Surface Crack of Concrete Cover and Corrosion Degree of Steel Bar Using Fractal Theory
Abstract
:1. Introduction
2. Experimental Program
3. Methodology
3.1. Box-Counting Method
3.2. Pixel-Covering Method
3.3. Fractal Dimension of Corrosion-Induced Cracks
4. Results and Discussion
4.1. Relationship between Corrosion Degree and the Fractal Dimension of Cracks
4.2. Verification of Proposed Relationship between Corrosion Rate and Fractal Dimension
5. Conclusions
- (1)
- Corrosion-induced cracks on the surface of the specimens exhibited clear fractal characteristics. For a uniform steel bar diameter, the fractal dimension and fitting line interception increased with the corrosion rate, which indicates a larger fractal dimension corresponding to more severe corrosion in the steel bar. Moreover, the smaller the steel bar diameter, the smaller the corresponding fractal dimension. However, as the corrosion rate increased, the fractal dimension increment of the specimens with a small steel bar diameter increased.
- (2)
- The scale coefficient of the corrosion-induced crack was sensitive to the corrosion rate. The scale coefficients increased by approximately 200% (176–268%) with every 5% increment in the corrosion rate, regardless of the steel bar diameter. In addition, the scale coefficient increased significantly with the increase in the steel bar diameter.
- (3)
- The relationship between the fractal dimension of the crack, the corrosion rate, and the steel bar diameter was established and the verification results are good. A new non-destructive detective method, based on this proposed relationship, can be developed to rapidly evaluate the corrosion behavior of a steel bar in deteriorated RC structures.
- (4)
- Finally, a relationship involving the fractal dimension of the crack, the corrosion rate, and the steel bar diameter was established, and verification results based on that relationship were favorable. A new non-destructive detection method based on this proposed relationship can be developed to rapidly evaluate the corrosion behavior of steel bars in deteriorated RC structures.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Reinforcement Diameter (mm) | Yield Strength (MPa) | Modulus of Elasticity (GPa) |
---|---|---|
6.5 | 326 | 218 |
8 | 321 | |
10 | 338 |
Specimen Label | Reinforcement Diameter (mm) | Theoretical Corrosion Rate (%) |
---|---|---|
A10 | 10 | 0 |
B6.5 | 6.5 | 5 |
B8 | 8 | 5 |
B10 | 10 | 5 |
C6.5 | 6.5 | 10 |
C8 | 8 | 10 |
C10 | 10 | 10 |
D6.5 | 6.5 | 15 |
D8 | 8 | 15 |
D10 | 10 | 15 |
E6.5 | 6.5 | 20 |
E8 | 8 | 20 |
E10 | 10 | 25 |
F6.5 | 6.5 | 25 |
F8 | 8 | 25 |
F10 | 10 | 25 |
G6.5 | 6.5 | 30 |
G8 | 8 | 30 |
G10 | 10 | 30 |
d = 6.5 mm | δ | N | d = 8 mm | δ | N | d = 10 mm | δ | N |
---|---|---|---|---|---|---|---|---|
C6.5-2 | 1 | 2634 | C8-3 | 1 | 4168 | C10-4 | 1 | 8052 |
2 | 1376 | 2 | 1972 | 2 | 3036 | |||
3 | 982 | 3 | 1355 | 3 | 1825 | |||
4 | 797 | 4 | 1043 | 4 | 1296 | |||
5 | 676 | 5 | 874 | 5 | 1037 | |||
D6.5-2 | 1 | 5083 | D8-2 | 1 | 7867 | D10-3 | 1 | 17,866 |
2 | 2267 | 2 | 3108 | 2 | 6449 | |||
3 | 1502 | 3 | 1974 | 3 | 3858 | |||
4 | 1136 | 4 | 1421 | 4 | 2460 | |||
5 | 934 | 5 | 1140 | 5 | 1980 | |||
E6.5-1 | 1 | 8952 | E8-3 | 1 | 14,950 | E10 | 1 | |
2 | 3401 | 2 | 5507 | 2 | ||||
3 | 2123 | 3 | 3350 | 3 | ||||
4 | 1537 | 4 | 2372 | 4 | ||||
5 | 1223 | 5 | 1881 | 5 | ||||
F6.5-2 | 1 | 24,048 | F8-1 | 1 | 36,094 | F10-1 | 1 | 42,763 |
2 | 8242 | 2 | 11,790 | 2 | 12,762 | |||
3 | 4515 | 3 | 6509 | 3 | 6531 | |||
4 | 3055 | 4 | 4400 | 4 | 4136 | |||
5 | 2256 | 5 | 3293 | 5 | 2916 | |||
G6.5-2 | 1 | 42,792 | G8-3 | 1 | 67,192 | G10-4 | 1 | 81,454 |
2 | 13,751 | 2 | 20,265 | 2 | 23,004 | |||
3 | 6886 | 3 | 10,422 | 3 | 11,394 | |||
4 | 4270 | 4 | 6562 | 4 | 6404 | |||
5 | 3029 | 5 | 4642 | 5 | 4824 |
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Li, W.; Wu, M.; Shi, T.; Yang, P.; Pan, Z.; Liu, W.; Liu, J.; Yang, X. Experimental Investigation of the Relationship between Surface Crack of Concrete Cover and Corrosion Degree of Steel Bar Using Fractal Theory. Fractal Fract. 2022, 6, 325. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6060325
Li W, Wu M, Shi T, Yang P, Pan Z, Liu W, Liu J, Yang X. Experimental Investigation of the Relationship between Surface Crack of Concrete Cover and Corrosion Degree of Steel Bar Using Fractal Theory. Fractal and Fractional. 2022; 6(6):325. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6060325
Chicago/Turabian StyleLi, Weiwen, Meizhong Wu, Tiansheng Shi, Pengfei Yang, Zejie Pan, Wei Liu, Jun Liu, and Xu Yang. 2022. "Experimental Investigation of the Relationship between Surface Crack of Concrete Cover and Corrosion Degree of Steel Bar Using Fractal Theory" Fractal and Fractional 6, no. 6: 325. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6060325