Characterization of the response of quasi-periodic masonry: Geometrical investigation, homogenization and application to the Guimarães castle, Portugal.

In many countries, historical buildings were built with masonry walls constituted by random assemblages of stones of variable dimensions and shapes. The analysis of historic masonry structures requires often complex and expensive computational tools that in many cases are difficult to handle, given this large variability of masonry. The present paper validates a methodology for the characterization of the ultimate response of quasi periodic masonry. For this purpose, the behaviour at collapse of a wall at the Guimarães castle in Portugal is investigated by means of a rigid-plastic homogenization procedure, accounting for the actual disposition of the blocks constituting the walls and the texture irregularity given by the variability of dimensions in the blocks. A detailed geometric survey is conducted by means of the laser scanning technique, allowing for a precise characterization of dimensions and disposition of the blocks. After a simplification of the geometry and assuming mortar joints reduced to interfaces, homogenized masonry in- and out-of-plane strength domains are evaluated on a number of different Representing Elements of Volume (RVEs) having different sizes and sampled on the walls of the castle. Strength domains are obtained using a Finite Element (FE) limit analysis approach with a heterogeneous discretization of the RVEs with triangular elements representing units and interfaces (mortar joints), at different orientations of the principal actions with respect to the horizontal direction. The role played by vertical compression is also investigated, considering the case of masonry with weak and strong mortar. Finally, a series of limit analyses are carried out at structural level, using two different FE numerical models of the so-called Alcaçova wall, a representative perimeter wall of the caste. The first model is built with a heterogeneous material and the second model is built with a homogeneous material obtained through the homogenization procedure performed previously. The purpose is to determinate the reliability of results, in terms of limit load and failure mechanism, for the homogenized model and to compare these results to the ones obtained with the heterogeneous model.