Fractal and Complexity Analysis of Crack Patterns of Masonry Walls

In order to develop automatic image-based methods for damage evaluation after earthquakes, crack maps need to be evaluated using computer-based algorithms. A common method to link the crack map to a damage state is to compute the fractal dimension of the crack map by the box-counting method. In this paper, it is shown that determining the fractal dimension by the box-counting method can lead in some cases to erroneous interpretations of the level of the damage as an increase in the number of cracks does not necessarily lead to an increase in the fractal dimension. To tackle this issue, the fractal dimension is computed by another method, the extended box counting method. It is observed that this estimation of the fractal dimension can better capture the increase in the number of cracks. The method is applied to masonry walls and it is shown that a good correlation between the complexity dimension and the stiffness loss ratio exists.