Numerical Simulation of the Dynamic Out-Of-Plane Two-Way Bending Seismic Behaviour of Unreinforced Masonry Walls Using Equivalent SDOF Systems

Damage and collapse of walls in the out-of-plane (OOP) direction are common failure modes in existing unreinforced masonry (URM) buildings when subjected to seismic excitation. These localized mechanisms also hinder the realisation of the complete in-plane seismic capacity of URM buildings. Among such OOP failures, a distinction can be made between (i) one-way bending which occurs in long walls and walls without side supports, and (ii) two-way bending which occurs in walls that have at least one vertical and one horizontal edge supported. This paper examines the suitability of a single-degree-of-freedom model for modelling the dynamic behaviour of URM walls subjected to OOP seismic excitation and undergoing two-way bending. The model operates in two phases: (i) initial elastic and (ii) post cracking, transitioning instantaneously between the phases once the force required to crack the wall is surpassed. Post cracking, the wall is treated as a system comprised of rigid blocks, and wall resistance is computed by combining three distinct contributions. These contributions are (i) bilinear elastic rigid block rocking, (ii) elastoplastic friction, and (iii) bilinear degrading component taking into account strength and stiffness degradation of walls. The model's complete behaviour in both phases is described by six independent parameters, which can be computed analytically. This paper explores the performance of the proposed model, especially when compared with and calibrated against experimental results from incremental dynamic testing of full-scale single leaf and cavity walls, for which the model demonstrates excellent agreement.