Pushover Analyses of Rocking-Sliding Masonry Walls using Macro-Element and Rigid Macro-Block Models

Historical and monumental masonry constructions are generally vulnerable to out-of-plane failures due to the absence of rigid floors and poor connections between orthogonal walls. This leads to activating rocking mechanisms of external walls or façades, whose ultimate force and displacement are affected by a complex dynamic structural behaviour between the rocking façade and transverse walls. This interaction is often neglected in the engineering practice. However, this simplified assumption may lead to significant approximations, as demonstrated by numerous experimental and numerical studies in the literature. This paper investigates the rocking capacity of unreinforced masonry walls interacting with adjacent transverse walls and subjected to out-of-plane loadings. Interlocking effects are simulated through frictional resistances according to the macro-block model (MBM) used for macro-limit analysis. Based on the equivalence of the contiunuous distribution of these forces and the discrete distribution of transversal elastic-plastic links, a numerical model is developed by using the discrete macro-element method (DMEM), starting from the onset of the failure mechanism and during its evolution. The results of the two models are compared in terms of both forcedisplacement and pushover curves, with reference to the case study of a front wall of a two-storey unreinforced masonry building. The presented preliminary results demonstrate the capability of the DMEM to describe the load and displacement capacities of rocking walls accounting for the contribution of lateral walls. Although the paper focuses on a specific case study, the presented results allow for assessing the contribution of lateral walls in the stage of activation and during the evolution of the rocking mechanism and can represent a base for the definition of more accurate procedures for assessing local failures of historic masonry buildings.