Seismic rocking of masonry structures: nonlinear modelling and retrofit strategies with viscous dampers

This paper presents a comprehensive investigation of the nonlinear seismic response of masonry structures subjected to rocking phenomena, with particular reference to historical buildings. Masonry constructions are often characterized by poor connections between structural elements, leading to the activation of local out-of-plane mechanisms rather than a global box-like behavior under seismic actions. In such conditions, structural components can be effectively idealized as rigid blocks undergoing rocking motion. The study initially focuses on the development and validation of a nonlinear finite element (FEM) model implemented in SAP2000, calibrated against the classical analytical solution proposed by Housner. The comparison highlights the influence of foundation compliance, modeled through nonlinear springs, on the dynamic response, particularly in terms of oscillation period elongation. Subsequently, nonlinear time-history analyses are performed using both artificial and recorded seismic accelerograms, scaled to different intensity levels. The system response is evaluated in terms of rotations and displacements, and incremental dynamic analysis is carried out to investigate the relationship between seismic intensity and rocking demand. A case study involving the historic building of the Opificio delle Pietre Dure in Florence is then analyzed. The structure exhibits significant vulnerability to out-of-plane mechanisms due to the presence of slender masonry walls with inadequate transverse restraints. To mitigate such vulnerabilities, a retrofit solution based on steel portal frames equipped with fluid viscous dampers (VFDs) is proposed and numerically assessed. The results demonstrate that the introduction of VFDs significantly reduces both displacements and rotations, leading to an average reduction of approximately 32% in peak response. The study confirms the effectiveness of nonlinear dynamic analysis in capturing the complex behavior of rocking systems and highlights the potential of energy dissipation devices as a viable and compatible strategy for the seismic protection of historic masonry structures.