Multiscale procedure to assign structural damage levels in masonry buildings from observed or numerically simulated seismic performance

The damage level (DL) is a fundamental metric in earthquake engineering and is particularly effective for multiple purposes, such as correlating structural damage to consequences and losses (e.g. economic, casualties, etc.) as well as to physical and mechanical variables quantifiable from both experimental and numerical tests. Despite the relevance of the topic, the conversion of complex information on the damage spreading over a 3D building into a synthetic DL remains an open issue for which there are currently no agreed-upon scientific criteria in the literature. Within this context, the study focuses on unreinforced masonry (URM) buildings by providing an analytical multi-scale approach that integrates structural damage at the panel-scale and macro-element size (where the macro-element is intended as an assemblage of components, like vertical walls or diaphragms). The approach is specifically conceived to be applied consistently to both observed and numerically simulated damage. As a result, the method is particularly effective for supporting the validation of numerical models or synthetically interpreting the huge amount of results from nonlinear analyses as much as feasible using an objective basis. The paper proposes a comparison of DL interpretation arising from other approaches in the current literature, highlighting their pros and cons. The effectiveness of the proposed procedure is then assessed using four URM case studies, all of which exhibited primarily a 'box-like behaviour'. They were specifically chosen based on the extremely detailed documentation available for both the damage and geometric/mechanical features of the buildings as well as aiming to reduce the uncertainty in the seismic input, making them ideal candidates also for validation purposes. To this end, the applicability of the procedure also to the damage simulated by nonlinear dynamic analyses was proven by adopting equivalent frame models of the case studies, developed and calibrated in previous researches. Definitely, the results encourage the adoption of the proposed procedure to interpret as analytically as possible the real damage that occurred on URM building, when accurate damage observations from field surveys are available, as well as that coming from numerical simulations.