A simplified homogenized limit analysis model for randomly assembled blocks out-of-plane loaded

Abstract

A kinematic rigid-plastic homogenization model for the limit analysis of masonry walls arranged in random texture and out-of-plane loaded is proposed. The model is the continuation of a previous work by the authors in which masonry in-plane behavior was investigated. 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. Two different classes of problems are investigated, the first consisting of full stochastic REV assemblages without horizontal and vertical alignment of joints, the second assuming the presence of a horizontal alignment along bed joints, i.e. allowing block height variability only row by row. A sub-class of elementary deformation modes is a priori chosen in the REV, mimicking typical failures due to joint cracking and crushing. The model is characterized by a few material parameters and it is therefore particularly suited to perform large scale Monte Carlo simulations. Masonry strength domains are obtained equating the power dissipated in the heterogeneous model with the power dissipated by a fictitious homogeneous macroscopic plate. A stochastic estimation of out-of-plane masonry strength domains (both bending moments and torsion are considered) accounting for the geometrical statistical variability of block dimensions is obtained with the proposed model. The case of deterministic block height (quasi-periodic texture) can be obtained as a sub-class of this latter case. As an important benchmark, the case in which joints obey a Mohr-Coulomb failure criterion is also tested and compared with results obtained assuming a more complex interfacial behavior for mortar. Masonry homogenized failure surfaces are finally implemented in an upper bound Finite Element (FE) limit analysis code. Firstly, to validate the model proposed, two small scale structural examples of practical interest are considered, relying in masonry panels in two-way out-of-plane bending. In both cases, failure load distributions and failure mechanisms provided by the homogenization model are compared with those obtained through a heterogeneous approach. Finally, in order to show the capabilities of the approach proposed when dealing with large scale structures, the ultimate behavior prediction of a Romanesque masonry church facade located in Portugal and arranged in irregular texture is presented. Comparisons with Finite Element heterogeneous approaches and ''at hand'' calculations show that reliable predictions of the load bearing capacity of real large scale structures may be obtained with a very limited computational effort.