A macro-element approach for modeling the nonlinear behaviour of monumental buildings under static and seismic loadings

The seismic assessment and subsequent rehabilitation of historical masonry structures constitutes a contemporary issue in most seismic regions and particularly in Europe in which the monumental buildings represent a huge cultural heritage that must be safeguarded. The different behaviour of masonry structures, compared to ordinary concrete and steel buildings, requires ad hoc algorithms capable of reproducing the nonlinear behaviour of masonry media and providing reliable numerical simulations. Refined finite element numerical models, such as the smeared cracked and discrete crack finite element models, able to predict the complex non-linear dynamic mechanical behaviour and the degradation of the masonry media, require sophisticated constitutive laws and a huge computational cost. As a consequence these methods are nowadays not suitable for practical application and extremely difficult to apply to large structures. In the past many authors developed simplified or alternative methodologies that, with a reduced computational effort, should be able to provide numerical results that can be considered sufficiently accurate for engineering practice purposes. However most of these methods are based on simplified hypotheses that make these approaches inappropriate for monumental buildings. In this paper a new modelling approach for the simulation of the seismic behaviour of monumental masonry buildings is presented. In particular a three dimensional discrete element model, able to predict the nonlinear behaviour of masonry shell elements, is presented as an extension of a previously introduced plane discrete-element conceived for the simulation of the in-plane behaviour of masonry plane elements. The proposed approach is based on the concept of macro-element discretization and has been conceived with the aim of capturing the nonlinear behaviour of a macro-portion of a masonry element and of the entire building, as an assemblage of several elements. The new macro-element enriches a larger computational framework, based on macro-element approach, devoted to the numerical simulation of the seismic behaviour of historical masonry structures.