Evaluation of Irregular Concrete Cracks Using Fractal Geometry

Natural factors and disasters lead to various types of cracks in buildings. These cracks are irregular, and their paths cannot be accurately determined or predicted, especially those resulting from the corrosion of reinforcing steel. The use of fractal geometry offers new perspectives for understanding the mechanism of crack formation and its evolution. More importantly, this geometry describes irregular shapes that cannot be described by Euclidean geometry. Processing concrete crack images using fractal structures provides a new understanding of these cracks, their distribution, density, propagation mechanism within the concrete, and their length. This is achieved by identifying and approximating these shapes to known fractal structures using the parameters of the assumed fractal body. The results of the study showed that the indicators of the proposed fractal body were consistent with the results of the Box-Counting tests in terms of the shape of the crack and its indicators after applying several measures to the images taken. The fractal analysis showed that the more complex the crack path and the larger the area, the more the proposed structure of the fractal body would have a different dimension and an advanced stage in fragmentation. From a materials science perspective, this approach provides a quantitative and objective tool for diagnosing the condition of damaged concrete structures, thereby aiding in the assessment of maintenance or reinforcement requirements. Therefore, combining image processing and fractal analysis can be considered an effective and appropriate method for evaluating the reliability of damaged buildings without always requiring destructive laboratory testing.