Sensitivity analysis of fractal dimensions of crack maps on concrete and masonry walls

Assessing building damage after earthquakes requires a visual inspection of the damage, indicated by maps of the cracking pattern on walls, which could be standardized via automated algorithms. To quantitate this damage, fractal dimensions of these crack maps could be computed by the box-counting algorithm to capture the complexity and irregularity of the pattern. When using the box-counting method, however, the computed fractal dimensions depend on several parameters that can render the measurement ambiguous: the box size interval, the scale factor for the box sizes, the choice of breakpoint location, and the grid disposition and orientation. This paper, therefore, uses a literature search and an evaluation of crack map databases to investigate the sensitivity of the measured fractal dimensions of crack maps on reinforced concrete and unreinforced masonry walls to these four parameters. It then formulates recommendations for the choice of these factors. Because the value of the estimated fractal dimension varied by up to 0.5 depending on the assumed parameters, it is therefore important to use the same set of assumptions when comparing the fractal dimensions of crack patterns.