Structural analysis of a quasi-random masonry wall: geometry details, homogenization and application

In many countries, historical buildings were built with masonry walls constituted by random assemblages of blocks and stones of variable dimensions. The analysis of historic masonry structures requires often complex and expensive computational tools that in many cases are difficult to handle, given this condition of large variability of masonry. The present paper addresses a methodology for the characterization of the response of rubble masonry. First, a brief state of the art regarding homogenization is presented. Then, the characterization of the masonry and statistical analysis of the dimensions of the stone units from the walls of Guimarães castle are carried out. This is followed by the homogenized limit analysis of representative volume elements (RVEs) from the Alcaçova wall in the Guimarães castle, in order to obtain its in-plane an out-of-plane failure surfaces at different orientations of a load and increasing compressive loads considering the case of masonry with weak and strong mortar independently. Finally, a safety for seismic loading was carried out in two numerical models of the Alcaçova wall, being the first one built with a heterogeneous material and the second one with a homogeneous material that was obtained by means of homogenized limit analysis of representative volume elements. The purpose is to determinate the reliability of results, in terms of limit load and failure mechanism, from the homogenized model, compared to the heterogeneous model.