Assessing unreinforced masonry structures subjected to seismic sequences using a pushover-based procedure

Seismic vulnerability assessments of historical masonry structures are particularly tricky, because of the geometric complexity and the highly nonlinear behaviour of the material. These challenges become even more critical when structures are subjected to multiple seismic events in a sequence. To address this issue, a novel assessment framework is proposed, combining nonlinear static (pushover, PO) analyses on Finite Element (FE) models with the N2-method -widely recognized in design codes worldwide as the standard. A key feature of the proposed methodology is its ability to capture the evolution of structural damage cumulated in consecutive earthquakes. For each event in the sequence, a capacity curve is obtained from the nonlinear static analysis of the FE model. The N2-method is then applied to quantify the resulting damage, which is incorporated into the model by updating the mechanical properties of the affected elements. This iterative approach enables the progressive simulation of cumulative damage effects induced by seismic sequences. To boost computational efficiency, FE models are also developed using elastic macroblocks and nonlinear contact-based interfaces, defined according to failure mechanisms identified through a Limit Analysis-based strategy. The methodology is benchmarked on three realistic examples: a masonry arch with buttresses, and two masonry frames with one and seven bays, respectively. The accuracy of the PO-based procedure is validated through comparisons with nonlinear time-history analysis results.