Seismic Vulnerability of Masonry Walls Damaged by Foundation Settlements: Development of Analytical Fragility Curves

Foundation settlements occur frequently in real structures and can substantially weaken a building’s earthquake resistance. Most studies in the literature either ignore settlements or treat them separately from seismic effects. This omission is especially critical for unreinforced masonry (URM) buildings, which are inherently brittle and vulnerable when settlements and seismic forces combine. In this work, the authors analyse the influence of differential settlements on the seismic capacity of typical URM facades using nonlinear static (pushover) analyses. Settlement parameters (plan extent, magnitude, and vertical profile) are varied alongside key wall characteristics (opening percentage and layout, and diaphragm stiffness), covering a range of case studies that emphasize the role of each parameter. Nonlinear static analyses are used to derive cumulative fragility curves, quantifying the increase in seismic vulnerability due to prior damage. The analyses show that even small differential settlements, on the order of a few millimetres, can trigger crack patterns that significantly reduce lateral load capacity and stiffness, altering failure mechanisms and increasing fragility. These results underscore the importance of incorporating settlement–seismic interaction in the assessment and retrofitting of URM buildings.