A Multi-Pier-Macro MPM method for the progressive failure analysis of perforated masonry walls in-plane loaded

The aim of this paper is to present and put at disposal a reliable numerical procedure called MPM (Multi-Pier-Macro) method that can be used by unexperienced practitioners by means of a software equipped only with non-linear truss elements with softening for the progressive failure analysis of large scale perforated masonry walls in-plane loaded. The authors have a previous successful experience in the field, with a procedure proposed called MP Multi-Pier approach that relies into the substitution of a masonry wall in plane loaded with a composition of trusses, typically two vertical piers and braces. The intrinsic drawbacks of the MP method (mainly the large number of elements needed for the analyses) is here overcome, modeling each pier, spandrel and cross-joint belonging to a large and perforated wall with the minimum number of truss elements (piers and braces), having in mind to carry out very fast but reliable progressive failure analyses for large existing structures subjected to horizontal loads. To achieve such goal, for each single element used, suitable equivalent geometric and mechanical properties are assigned, assuring the equivalence element by element of the 1D mesh with the continuum in terms of elastic energy, behavior at peak and softening branch. MPM is benchmarked on two large scale perforated walls, where the results of several previous models are available from the literature, showing satisfactory accuracy in the reproduction of the global behavior and the activation of the mechanisms inducing the collapse.