Macroelement modelling based on a Bouc-Wen formulation with degradation for the dynamic analysis of masonry walls

The use of the equivalent frame approach for modelling the response of regular unreinforced masonry structures is a widespread practice especially in practitioners’ field, thanks to the combination of a low computational burden and the quite satisfactory accuracy of the results. The advantages are acknowledged mostly when the seismic or dynamic response of these buildings must be analysed, considering the complexity of the dynamic actions. In this framework, the complex hysteretic and degrading phenomena experienced by masonry during cyclic actions must be accurately considered. Hence, the in-plane flexural and shear behaviour of piers and spandrels, as well as the typical nonlinear mechanisms of masonry material, are properly described by means of a lumped hinge approach adopting a macroelement formulation. The proposed force-based macroelement is composed of an elastic beam in series with two flexural hinges lumped at the end nodes for the description of the flexural mechanisms and a shear hinge for the characterization of the shear mechanism. The constitutive relationship adopted to describe the nonlinear behaviour of masonry is based on a modified and enriched Bouc-Wen law. This latter has been enhanced with the introduction of two scalar parameters, representing damage and flexibility increase effects, respectively. While the first controls both strength and stiffness degradation, the second only regulates stiffness decay, permitting to independently drive the two phenomena. The model is used to study both the static and dynamic responses of masonry panels, considering different geometric configurations and loading conditions. In particular, the performances of the enriched Bouc–Wen model are accurately examined, with the aim of analysing the effect of the degradation on the global response of masonry.