Modelling the Dynamic Out-of-Plane Two-Way Bending Seismic Response of Unreinforced Masonry Walls

Abstract

The collapse of walls in the out-of-plane (OOP) direction is a common failure mechanism in existing unreinforced masonry (URM) buildings when subjected to seismic excitation. Such local mechanisms also prevent the realisation of the full in-plane seismic capacity of URM buildings. Among OOP failures, a distinction can be made between (i) one-way bending which occurs 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 proposes 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 considers two distinct phases: (i) initial elastic and (ii) post cracking, transitioning instantaneously between the two once the force required to crack the wall has been exceeded. The model's complete behaviour (i.e. in both phases) is described by six independent parameters, which can be calculated analytically. Post cracking, the wall is treated as a system composed of rigid blocks, and the wall resistance is calculated as the superimposition of three separate contributions: (i) the bilinear elastic rigid block rocking, (ii) the elastoplastic friction, and (iii) a bilinear degrading component taking into account strength and stiffness degradation of the wall. The proposed model is then calibrated against experimental results from incremental dynamic testing of full-scale walls. For this, two walls with different failure modes under horizontal bending, i.e. line and stepped failure are considered. Calibration of the model shows excellent agreement with test results, successfully capturing their behaviour from cracking to collapse. The calibrated models were employed to evaluate behaviour factors under both natural and induced seismicity, resulting in values close to two for both walls.