PSI - Issue 44

Ylenia Di Lallo et al. / Procedia Structural Integrity 44 (2023) 488–495 Y. Di Lallo et al./ Structural Integrity Procedia 00 (2022) 000–000

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behaviour and possible damage occurrence due to a seismic event (Calderini at al. (2009), Tashkov et al. (2010), Facconi et al. (2018), Cocco et al. (2019), Brando et al. (2020)). In this regard, a crucial aspect is the choice of the most suitable modelling method, which depends both on the accuracy of the results to be achieved and the computational burden that can be afforded (Lourenço (2002), D’Altri et al. (2020), Masciotta and Lourenço (2022)). Within the FE (finite element) method, we can distinguish two main approaches: “macro-modelling” and “micro modelling”. The first group includes all modelling strategies in which the masonry wall system is represented by a continuous, homogeneous material, in which the mechanical behaviour of the whole masonry is identified through a single constitutive model. This type of modelling requires a smaller computational burden as it involves the creation of a model with simple geometries and few mechanical parameters of the materials. Some examples of macro-element modelling applied to masonry structures can be found in Berto et al. (2002), Pelà et al. (2011), Lopez et al. (1999). The latter group entails numerical modelling approaches that distinguish all individual masonry components: blocks, mortar, and unit-mortar interfaces. Micro-models can be detailed (Lourenço and Rots (1997), Petracca et al. (2017a)) or simplified (Lourenço (1997)). These methods make possible to obtain accurate results in terms of stresses, deformations, and damage mechanisms, but they require a relevant computational effort and a high level of knowledge of the mechanical characteristics of the different constituent materials. For this reason, their use becomes unwieldy when dealing with the analysis of complex structures (Roca et al. (2010)). To attain modelling approaches able to provide fairly accurate results while involving a reduced computational effort, several authors are trying to develop increasingly simplified models. An example is the DEM (discrete element method), initially developed by Cundall et al. (1971), which considers masonry as a system of discrete blocks connected via contact points along the edges. Since then, several DEM-based calculation techniques were developed, such as the NCSM, i.e., non-smooth contact dynamics method (Jean (1999), Beatini (2017), Malomo et al. (2021)), which essentially differ from one another for the type of employed contact surfaces. Although the computational burden is reduced with the use of DEMs as compared to micro-models, it is still necessary to model a large number of elements and contact surfaces to realistically discretize a structure. The present work falls within this line of research by describing a Multi-Unit Discretization (MUDis) approach aimed at improving the efficiency of simplified micro-models for the seismic analysis of masonry structures with periodic arrangement of units and mortar joints. The approach belongs to the category of D-FEM (discontinuum-finite element modelling) in which the masonry element is subdivided into grouped linear elastic units of predetermined geometry and shape, separated by non-linear interface elements. The geometry of the multi-unit modules was defined by the Authors in a previous work (Brando et al. (2022)) according to considerations on the potential in-plane failure surfaces of the masonry with periodic pattern subjected to lateral actions; the interface elements, on the other hand, were formulated on the basis of the CI (composite interface) model proposed by Lourenço and Rots (1997), which was appropriately modified and calibrated (Brando et al. (2022)). In this paper, the MUDis approach, successfully tested on masonry panels of different aspect ratio and subjected to diverse pre-compression loads (Brando et al. (2022)), is validated through the numerical simulation of a full-scale masonry façade belonging to a URM building mock-up experimentally tested in the facilities of the University of Pavia (Magenes et al. (1995)).

2. The proposed CI-based MUDis procedure 2.1. Description of the discretization approach

The modelling procedure herein proposed is designed to subdivide masonry walls with regular and periodic pattern into quadrangular multi-unit modules (MU) of predetermined geometry. As depicted in Fig. 1(a), the modules are formed by four linear elastic polygons that share the same mechanical characteristics of the bricks composing the investigated walls. The units are separated by interface surfaces representing potential crack planes along which failure is expected, and where all the non-linearities of the material are concentrated. The geometry of the modules was chosen following an engineering process aimed at reproducing the most common in-plane failure mechanisms observed in masonry walls subjected to horizontal and vertical actions (Brando et al. (2022)). The adopted subdivision derives therefrom, allowing to capture all the relevant collapse mechanisms of masonry, such us compressive crushing, sliding along the joints, diagonal cracking of the units, and contemporaneous diagonal cracking of the units and sliding