Masonry Macro-block Analysis

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. Unreinforced masonry structures present low tensile strength, and the linear analyses seem to not be adequate for assessing their structural behavior. On the other hand, the static and dynamic nonlinear analyses are complex, since they involve large time computational requirements and advanced knowledge of the practitioner. The nonlinear analysis requires advanced knowledge on the material properties, analysis tools, and interpretation of results. The limit analysis with macro-blocks can be assumed as a more practical method in the estimation of maximum load capacity of structure. Furthermore, the limit analysis requires a reduced number of parameters, which is an advantage for the assessment of ancient and historical masonry structures, due to the difficulty in obtaining reliable data. The observation of the damage in masonry buildings caused by earthquakes in the past has been shown that the masonry structures can be discretized into several macro-blocks and interfaces. The macro-blocks are portions of a structure with similar material properties and structural behavior, to which the mechanical properties of the material can be assigned or, by simplification, they can be assumed to be infinitely rigid. The interfaces in a macro-modelling represent, in general, the cracks associated to the failure mechanisms. However, in a micro-modelling strategy applied to masonry, in which the units and the joints are individually considered, the interfaces simulate the behavior of the joints. Furthermore, different criteria for the strength parameters of macro-blocks and interfaces can be considered. The limit analysis (Fig. 1) with macro-blocks is a simplified and powerful structural analysis tool to evaluate the ultimate capacity of masonry structures by static models, involving the equilibrium of the macro-blocks through the limit analysis basic concepts.