PSI - Issue 11

Siro Casolo et al. / Procedia Structural Integrity 11 (2018) 20–27 Siro Casolo & Giuseppina Uva / Structural Integrity Procedia 00 (2018) 000–000

21

2

1. Introduction: Modelling the Mechanics of Masonry Structures

At the beginning of the Construction History, there were stones, sometimes bricks, and there was mortar, sometimes even nothing. And there was the rule of the thumb. The first concern of the ancient builders was to rise solid, monolithic walls out of sparse materials and they learnt by trial and error to wisely use the available materials and blocks’ shapes arranging them in the best possible pattern. Especially in earthquake prone areas, they did very well, passing down the art of masonry construction over the following generations. In his renowned work “ De Architectura” (Vitruvius, 35 25 a.C) , Marcus Vitruvius Pollio wrote: “There are two styles of walls: opus reticulatum (now used by everybody), and the ancient style called opus incertum. Of these, the reticulatum looks better, but its construction makes it likely to crack, because its beds and builds spread out in every direction. On the other hand, in the opus incertum, the rubble, lying in courses and imbricated, makes a wall which, though not beautiful, is stronger than the reticulatum”. Texture often makes the difference between the ruinous disintegration of a wall and the possibility of activating the global response of the building, as a preferred option, or at least partial mechanisms of damage, as a second chance. In the present mechanics of masonry, the awareness of this ancient art when modeling bond-texture has experienced different fortunes. Sometimes it led to sophisticated works of homogenization (e.g.: Uva & Salerno, 2006; Bacigalupo & Gambarotta, 2012; Petracca et al., 2017), but often almost completely disappeared, overpowered by the useful and captivating simplicity of kinematic approaches for the analysis of local mechanisms. Multi-leaf walls are extremely vulnerable to out-of-plane actions (Fig. 1) and the overall response strongly depends on: the shape and arrangement of the blocks and the effectiveness of the transversal interlocking (Giuffré, 1993; 1999). The rule of thumbs ascertained that a significant improvement of the seismic performance can be achieved by inserting headers, which enhance the monolithic response under out-of-plane loads. A rational computational approach requires, therefore, to properly consider the effects of the texture in masonry walls. At the same time, an effective vulnerability analysis of masonry structures should adopt “engineering” modelling approaches that can be easily implemented and managed into computer codes aimed at structural analysis, but are not simplistic (Casolo et al., 2000; Betti et al., 2010; Preciado et al., 2015). An effective approach that can be fruitfully adopted is the Rigid Body and Spring Modeling (RBSM). In the last few years, from the early developments and applications, full-discrete approaches have gained increasing popularity in the field of seismic analysis of masonry structures (Casolo, 1999; Casolo, 2000; Bertolesi et al, 2016; Bertolesi et al, 2017; Bertolesi et al. 2018; Pantò et al., 2017), and it seems that RBSM could be one of the promising alternative codes with respect to the commercial software based on the continuum approach.

Fig. 1. Left: global out-of plane mechanism (view after Messina Earthquake, 1908); center: partial out-of-plane mechanism of a church façade; right: weak masonry, separation of the wythes. 2. A heuristic approach to the modelling of multi-leaf masonry walls accounting for the texture It is authors’ opinion that, at present, the effective analysis of realistic case studies in the non-linear range (like the case of churches’ masonry façades that is here proposed) requires a macro-modelling approach strategy (Pietruszczak & Ushaksarei, 2003). However, the determination of the macroscopic mechanical properties to be utilized is a complex task and homogenization procedures might not be easily applied in the presence of irregular bond-textures and multi leaf walls, which are both very common situations. Moreover, they still require expensive non-linear FE computations.