Modeling of Masonry Structures at Multiple Scales

Masonry represents the material used in the great majority of the world-building heritage structures. Reliable tools for analysis of masonry structures are needed not only for seismic vulnerability assessment but also to properly design interventions to restore and strengthen existing buildings, which deserve to be preserved. Masonry is a nonlinear, heterogeneous, and anisotropic material whose properties strongly depend on its microstructure, typically composed of two phases, blocks and mortar, and on the way it is assembled. To simulate the mechanical behavior of masonry structures, numerous models have been developed, characterized by different detailing levels. For large structures, the need for computational efficiency leads to simplified models characterized by the subdivision of masonry walls in macro-elements. A notable example of this group of models is the equivalent-frame method, which consists of identifying the masonry wall with an ideal frame, where panels are modeled as beams characterized by proper mechanical behavior. The detailing level can be increased by considering each macro-element as a homogenized continuum, assuming that, at the scale of representation, masonry can be treated as a continuum having mechanical properties that reproduce the overall response of a certain portion of the heterogeneous microstructure. However, the formulation of a suitable constitutive law is not an easy task. It should phenomenologically reproduce the material mechanics, including tension cracking, shear sliding, compressive crushing, and many other aspects. Moreover, this approach requires a cumbersome identification of mechanical parameters that are not always easy to determine from basic experimental tests on the material. To consider the role of each constituent and the effects of their interactions, a microscale model can be set up, where blocks, mortar joints, and mortar-block interfaces are represented explicitly. In this work, masonry structures are studied at several detailing levels. An issue affecting equivalent-frame models, namely the presence of irregularity in the wall opening layout, is addressed by comparing equivalent-frame results with finite-element ones, which are assumed to better represent the actual behavior of irregular walls. A parametric analysis on masonry piers, modeled as a homogenized continuum, is carried out, aimed to assess the influence of the height-to-width ratio and the vertical compression load on the nonlinear static behavior. The focus is then shifted to finer scales. The localization analysis of an orthotropic macro-scale model in the framework of multi-surface plasticity is presented, deriving analytical localization conditions corroborated by finite element simulations. Finally, a microscale model for regular masonry is developed to analyze the localization properties of the representative volume element, also by investigating the role of its size and periodicity directions.