Cumulative fragility curves for seismic vulnerability assessment of damaged masonry buildings subjected to differential settlements

The seismic vulnerability of existing unreinforced masonry buildings is often assessed by considering a single external hazard. However, real-world scenarios frequently involve multiple hazards acting sequentially or simultaneously, leading to cumulative damage effects. Among these, differential foundation settlements and seismic actions, although moderate in intensity, can critically compromise structural performance when combined. This study investigates the influence of prior settlement-induced damage on the seismic capacity of unreinforced masonry façades. A comprehensive parametric analysis is performed using finite element modelling and nonlinear static analysis to develop fragility curves that capture the incremental seismic vulnerability associated with settlement damage. Various façade configurations are analysed under different geometric and structural conditions, considering a range of settlement scenarios in terms of intensity, location, and extent. The numerical framework is implemented through a Python-driven routine in Abaqus software, employing a homogenized model under plane-stress conditions. Each case studied involves two main analyses. First, a pushover analysis of the undamaged façade is performed to obtain the baseline capacity (i.e. without settlement). Subsequently, the same façade is subjected to foundation settlements and a second pushover analysis is carried out on the resulting damaged configuration, compared with the pushover response of the façade without settlements. The fragility curves for both intact and damaged façades allow for a quantitative assessment of seismic vulnerability degradation due to ground movement effects. The results indicate that even moderate settlements can substantially reduce seismic capacity, highlighting the interplay between settlement characteristics and façade properties and the importance of multi-hazard assessment for masonry structures.