Phenomenological model for the damage diagnosis of masonry structures based on crack parameters

Abstract Assessment of the technical condition of historic buildings is a key task in ensuring their structural safety and long-term preservation, particularly in the presence of damage associated with crack formation. In contemporary engineering practice, such assessments are largely based on qualitative defect analysis and do not provide a unified quantitative interpretation of the condition of either individual structural elements or the building as a whole. This study proposes a phenomenological probabilistic approach for assessing the condition of load-bearing masonry walls based on crack-pattern parameters, including the crack width, crack length, and crack density, which are considered quantitative indicators of the structural condition associated with the structural loading level expressed by the axial load ratio (N/N u ), where N is the applied load, and N u is the ultimate failure load. A generalised condition index is introduced based on the normalised inspection data, while the weighting coefficients are determined by considering the statistical interrelationship between the parameters. A significant feature of the proposed model is its independence from the service life of the building, which enables direct rapid nondestructive assessment under field conditions. To account for the uncertainty and variability in crack-pattern parameters, the Monte Carlo method is employed to simulate their statistical structure. The proposed approach enables classification of the structural condition and facilitates the transition from qualitative defect description to quantitative probabilistic assessment. The model is intended for masonry buildings composed of small-unit elements, in which walls serve as the primary load-bearing structural components. Its application is particularly relevant for historic buildings and cultural heritage structures, where minimising intervention while ensuring the required level of structural safety is of primary importance. The proposed model was applied to a real building. The obtained results demonstrated that the identified structural condition is consistent with the observed damage pattern and adequately reflects the actual state of the structure. The proposed approach can be applied as an engineering diagnostic tool and as decision-support assistance in planning repair, strengthening, and preservation measures for buildings.