Abstract

A review of methods applicable to the study of masonry historical construction, encompassing both classical and advanced ones, is presented. Firstly, the paper offers a discussion on the main challenges posed by historical structures and the desirable conditions that approaches oriented to the modeling and analysis of this type of structures should accomplish. Secondly, the main available methods which are actually used for study masonry historical structures are referred to and discussed.

The main available strategies, including limit analysis, simplified methods, FEM macro- or micro-modeling and discrete element methods (DEM) are considered with regard to their realism, computer efficiency, data availability and real applicability to large structures. A set of final considerations are offered on the real possibility of carrying out realistic analysis of complex historic masonry structures. In spite of the modern developments, the study of historical buildings is still facing significant difficulties linked to computational effort, possibility of input data acquisition and limited realism of methods.

Abstract

Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr–Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second‐Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan‐type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two‐dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature.

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Reinforced brick masonry has experienced only scarce use as a fully structural material due to, among other reasons, the lack of design criteria and calculation tools allowing a scientific, but also practical, engineering approach to design and assessment. Aiming at contributing to a more widespread use of this material, a simplified method for the ultimate analysis of reinforced masonry arches and cylindrical vaults, based on the lower-bound theorem (or static approach) of plasticity, has been developed. This approach has been satisfactorily validated by comparison with experimental and numerical results obtained by more accurate numerical models.

Abstract

Masonry structures forming part of our historical heritage were often constructed using nonperiodic textures. In this case, unlike the situation for masonry with periodic textures, few methods are available to estimate wall strength and, moreover, available methods are often difficult to apply. In this work, Discontinuity Layout Optimization (DLO) is proposed as a method of estimating the failure load and associated mechanism of masonry walls constructed with non-periodic textures. In the first part three different textures are considered (periodic, quasi-periodic and chaotic) with a simplified scheme and a parametric analysis is undertaken, considering the variation of the height of the panel. A further classification for quasi-periodic textures is then provided and a DLO rigid block analysis is carried for square panels to show the influence of such textures. The results highlight the importance of the parameters considered in the analysis, and that DLO is a suitable method to investigate their influence.

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We formulate a linear programming approach to the limit analysis of discrete element models of masonry structures. Numerical results show the ability of the given procedure to predict the limit value of the multiplier of variable horizontal forces, which are applied to masonry walls in association with a fixed vertical loading.

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