Micromodels for the in-plane failure analysis of masonry walls: Limit Analysis, FEM and FEM/DEM approaches

Abstract

In the last decades the modeling of masonry structures has become an argument particularly appealing for many researchers and a large variety of numerical techniques have been formulated with the aim to produce practical applications in civil engineering, with special reference to the preservation and restoration of cultural heritage. Nevertheless, the question appears today still far from being resolved in a general way. The characteristics of fragility, heterogeneity and anisotropy of masonry, as well as the extreme variety of the building/construction rules strongly compromise the possibility of a unified description of its mechanical behavior. In this work a comparison of different models and techniques for the assessment of the mechanical behavior of two-dimensional block masonry walls subjected to the static action of in-plane loads is presented. Different approaches and numerical models are considered: a Limit Analysis approach (LA), a FEM/DEM procedure and a non-linear heterogeneous Finite Element analysis (FE). Here a standard Limit Analysis is adopted via a homemade procedure based on Linear Mathematical Programming, considering friction at interfaces. Analyses are performed referring to benchmark examples from literature.

Limit analysis approach for the in-plane collapse of masonry arches

“…This work focus the attention on the study of the ultimate behaviour of masonry arches of different geometries and shape, considering the presence of friction, considered by several authors (Ferris and Tin-Loi, 2001;Mousavian and Casapulla, 2020;Portioli et al, 2014;Casapulla and Maione, 2020), and comparing results with several contributes present in literature (Brandonisio et al, 2017;Calderini and Lagomarsino, 2015;Como, 2015;Misseri et al, 2018;DeJong et al, 2008). In particular, starting from (Baggio and Trovalusci, 2000), a new version of the ALMA code (Analisi Limite Murature Attritive) has been developed based on the Limit Analysis (Pepe, 2020;Pepe et al, 2019Pepe et al, , 2020a namely ALMA 2.0. ALMA 2.0 has been implemented in recent coding language of Python TM permits an easy and fast scalability and improving of the code.…”

“…The position the critical joints is then obtained following a solved with a trial and error strategy by varying its position. (Pepe et al, 2019(Pepe et al, , 2020a overcome the limit in term of number of blocks respect to the original version (Baggio and Trovalusci, 2000) and it has been improved in order to take into account foundation settlement (Pepe et al, 2020b), cohesion between the joints and retrofitting cable (Pepe, 2020).…”

New insights on homogenization for hexagonal-shaped composites as Cosserat continua

“…Composite materials can be investigated by directly describing their constituents in a micromechanical discrete model or by homogenizing them as equivalent continua. In the former case, for example to study heterogeneous materials such as polycrystalline materials, jointed rock systems, and block masonry with periodic microstructures, the model involves a system with a large numbers degrees of freedom and as a consequence the computational costs is very high [1][2][3][4]; such cost increases by reducing the material scale [5]. In the latter case, by using homogenization techniques, the numerical analyses are faster and more efficient but it is fundamental to define equivalent continua that properly takes into account the influence of the microstructure on the macro-scale behaviour with particular reference to shape, size and texture of elements [6] and among them focus on those techniques developed for deriving scale-dependent models [7][8][9][10][11][12].…”

Discrete and Continuous Approaches for the Failure Analysis of Masonry Structures Subjected to Settlements

“…Equations governing systems of rigid blocks interacting though no tension and frictional interfaces formally correspond to those of perfect plastic systems with non-associative flow rule (Fichera, 1964). Limit Analysis, largely recognized as a very effective tool to estimate collapse load and collapse mechanisms for masonry structures (Baggio and Trovalusci, 2000;Milani, 2011;Portioli et al, 2014;Milani and Taliercio, 2016;Pavlovic et al, 2016;Cascini et al, 2018;Pepe et al, 2019b), is used to determine the failure configuration of dry joints masonry panels subjected to settlements, modeling the walls (according to the microscale approach) as an assemblage of rigid blocks in contact through frictional interfaces. It is important to underline that the Limit Analysis model presented here is based on the perfect plasticity hypothesis, and information about the ultimate displacement entities is thus not available.…”