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

Abstract

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.\ud Good agreement is found both on the failure mechanism and on the distribution of the collapse load

Quasi-analytical homogenization approach for the non-linear analysis of in-plane loaded masonry panels

“…Such a result is in perfect agreement with limit analysis considerations, as already shown by many authors, in e.g. [4][12][17] [19].…”

Simple homogenization model for the non-linear analysis of in-plane loaded masonry walls

“…In the first step, masonry is substituted with a macroscopic equivalent material through a simplified averaging procedure, in which the unit cell is subdivided into a few triangular plane stress elements (bricks) and interfaces (mortar joints and brick-brick interfaces). A particularly interesting preliminary lower bound limit analysis application [10,[13][14][15][16] of the model is also discussed, assuming that elements are constant stress triangles (CST). Afterwards, within the rough discretization of the REV assumed, the model is generalized to the non-linear case.…”

“…through FEs [8,9]. Recently, efficient models based on homogenization have been presented [10][11][12][13][14][15][16][17], which allow non-linear analyses of large scale structures, still considering both the real disposition of bricks and the actual mechanical properties of the constituent materials. Clearly, the numerical models to use at a structural level should be sufficiently simple, reliable and efficient to allow a quick evaluation of (a) collapse loads, (b) displacements near collapse and (c) post peak behavior of the structures.…”

Automatic Morphologic Analysis of Quasi‐Periodic Masonry Walls from LiDAR

“…() for a review. These techniques have been recently extended to random or quasi‐periodic masonry, e.g., Cluni and Gusella () or Milani and Lourenço ().…”