Topological data analysis-based damage indices for plastered stone masonry walls under cyclic loading

The qualitative aspect of visual inspection of damaged structures can be largely benefited by incorporating quantitative metrics. Moreover, automating this process requires the development of effective computational tools capable of making reliable assessments, appropriately calibrated to the mechanical and structural characteristics of the systems under analysis. In this paper, two damage indices are determined based on the topology of crack patterns. The results of an experimental campaign involving six plastered stone masonry walls are used to show that, for walls constructed with uncut limestone blocks and pebbles, these damage indices are correlated with strength degradation. To this end, topological data analysis is employed to estimate persistent diagrams and minimum spanning trees of crack patterns extracted from digital images using convolutional neural networks and signal processing techniques. The results show that the topological complexity of crack patterns is a strong indicator of the damage level in structures.