## 1 Introduction  
During the last decades, different strong earthquake events occurred in Italy, e.g., 2009 (L'Aquila) [1; 2; 3], 2012 (Emilia-Romagna) [4], 2016 (Centro Italia) [5; 6] and 2017 (Ischia) [7] seismic events, where several historical buildings realized in ancient unreinforced masonry (URM) suffered serious damages. In fact, these constructions were designed to resist mainly the gravity loads: they are generally characterized by slender walls, flexible horizontal floors, bad quality of the masonry, bad interlocking among perpendicular walls and between walls and roof, absence of tie-beams used to absorb the thrusts of arches and vaults [8]. Considering their wide diffusion and their high seismic vulnerability, the structural safety of existing URM buildings is a very topical issue. In Italy, and more in general in the Mediterranean area, a huge amount of such buildings belongs to the historical architectural heritage, and their conservation is needed both for the importance of their cultural value as well as for the functions that they still perform up to now. Moreover, in many developing countries such structural typology is still adopted now and commonly used, so a huge amount of residential and civil buildings around the world are built in URM. For such reasons, in the last decades, much attention has been paid to URM buildings to assess their structural safety and to define appropriate intervention of retrofitting [9; 10; 11; 12]. Despite the important research works devoted to the study of the mechanical behavior of URM structures carried out by several researchers in the last few years--a complete overview of the different modelling strategies for the computational analysis of such structures has been provided in [13]--the correct evaluation of the seismic behavior of masonry structures, which is useful to define the retrofitting interventions, remains still an open issue. As it is well known, masonry is a composite structural material obtained by assembling natural or artificial blocks by means of mortar layers or dry joints. Difficulties in modeling are related to heterogeneity, anisotropy and to some peculiar features of masonry material, whose mechanical behavior depends on several parameters that are difficult to assess, such as mechanical properties of constituent materials, arrangement of units, thickness of joints, presence of internal filling with relative unknowns and difficulties in describing connections between external layers, manufacturing imperfections, state of conservation, etc. In order to take into account these characteristics, several methodologies have been proposed in the scientific literature [14]; however, the use of refined models is usually limited to the research field, while in the common practice simplified approaches are more diffused. Such approaches usually rely on the description of the structure as an assemblage of its structural elements modelled by means of macroelements, requiring a small number of mechanical parameters and low computational effort. Considering structural assessment of URM buildings, different approaches have been proposed for the evaluation of their seismic vulnerability, among which numerical analyses stand out for their diffusion and applicability to both monumental and so-called minor architectures [15; 16]. In particular, the implementation of appropriate Finite Element models (FEM) represents one of the most suitable approaches for their ability to analyze even complex structures. It must be noticed that, due to its complex inner microstructure, the masonry shows a different behavior in compression and tension, therefore, because of the very low tensile strength of masonry material, URM buildings exhibit a non-linear behavior even at early stages of seismic loading, calling for the adoption of nonlinear analyses.