Optimal intensity measure and probabilistic seismic demand model for the assessment of historical masonry buildings: application to two case studies

This paper presents a probabilistic seismic demand model (PSDM) as a relationship between intensity measures (IMs) and engineering demand parameters (EDPs) for the seismic assessment of two case studies resembling historical masonry buildings. The first one is representative of stiff monumental buildings, and the second of tall and slender masonry buildings. Both structures are modelled in the OpenSees software using three-dimensional macroelements that consider both the in-plane and out-of-plane response of masonry walls. A set of 100 accelerograms are selected to represent the seismic excitation. After full characterization of the seismic input in terms of IMs, both buildings are subjected to the action of these accelerograms to study the maximum structural response in the context of cloud analysis. The most suitable IMs are determined subsequently under the notions of efficiency, practicability, proficiency, and sufficiency. In addition, a composed measure is proposed as a linear combination in logarithmic space of the IMs that exhibit the best coefficient of determination (R²) within the EDP vs. IM regression. This optimal composed measure is determined through machine learning-based Lasso regression. In the final stage of the study, fragility curves are derived to measure the likelihood of exceedance of certain levels of average roof displacement in terms of IM parameters.