Monte Carlo homogenized limit analysis model for randomly assembled blocks in-plane loaded

A simple rigid-plastic homogenization model for the limit analysis of masonry walls in-plane loaded and constituted by the random assemblage of blocks with variable dimensions is proposed. In the model, blocks constituting a masonry wall are supposed infinitely resistant with a Gaussian distribution of height and length, whereas joints are reduced to interfaces with frictional behavior and limited tensile and compressive strength. Block by block, a representative element of volume (REV) is considered, constituted by a central block interconnected with its neighbors by means of rigid-plastic interfaces. The model is characterized by a few material parameters, is numerically inexpensive and very stable. A sub-class of elementary deformation modes is a-priori chosen in the REV, mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating the power dissipated in the heterogeneous model with the power dissipated by a fictitious homogeneous macroscopic plate.Due to the inexpensiveness of the approach proposed, Monte Carlo simulations can be repeated on the REV in order to have a stochastic estimation of in-plane masonry strength at different orientations of the bed joints with respect to external loads accounting for the geometrical statistical variability of blocks dimensions. Two cases are discussed, the former consisting on full stochastic REV assemblages (obtained considering a random variability of both blocks height an length) and the latter assuming the presence of a horizontal alignment along bed joints, i.e. allowing blocks height variability only row by row. The case of deterministic blocks height (quasi-periodic texture) can be obtained as a subclass of this latter case. Masonry homogenized failure surfaces are finally implemented in an upper bound FE limit analysis code for the analysis at collapse of entire walls in-plane loaded. Two cases of engineering practice, consisting on the prediction of the failure load of a deep beam and a shear wall arranged with random texture are critically discussed. In particular, homogenization results are compared with those provided by a heterogeneous approach. Good agreement is found both on the failure mechanism and on the distribution of the collapse load.