Blast analysis of enclosure masonry walls using homogenization approaches

Abstract

A simple rigid-plastic homogenization model for the analysis of enclosure masonry walls sub- jected to blast loads is presented. The model is characterized by a few material parameters, is numerically inexpensive and very stable, and allows full parametric studies of entire walls subject to blast pressures. With the aim of considering the actual brickwork strength along vertical and horizontal axes, masonry out-of-plane anisotropic failure surfaces are obtained by means of a compatible homogenized limit analysis approach. In the model, a 3D system of rigid infinitely strong bricks connected by joints reduced to interfaces is identified with a 2D Kirchhoff-Love plate. For the joints, which obey an associated flow rule, aMohr-Coulomb fail- ure criterion with a tension cutoff and a linearized elliptic compressive cap is considered. In this way, the macroscopic masonry failure surface is obtained as a function of the macroscopic bending, torque, and in-plane forces by means of a linear programming problem in which the internal power dissipated is minimized. Triangular Kirchhoff-Love elements with linear in- terpolation of the displacements field and constant moment within each element are used at a structural level. In this framework, a simple quadratic programming problem is obtained to analyze entire walls subjected to blast loads. The multiscale strategy presented is adopted to predict the behavior of a rectangular wall supported on three sides (left, bottom, and right) representing an envelope wall in a building and subjected to a standardized blast load. The top edge of the wall is assumed unconstrained due to an imperfect connection (often an inter- layer material is used to prevent damage in the in-fill wall). A comparison with a standard elastic-plastic heterogeneous 3D analysis conducted with a commercial FE code is also pro- vided for a preliminary verification of the procedure at a structural level. The good agreement found and the very limited computational effort required for the simulations conducted with the presented model indicate that the proposed simple tool can be used by practitioners for the safety assessment of out-of-plane loaded masonry panels subjected to blast loading. An ex- haustive parametric analysis is finally conducted with different wall thicknesses, joint tensile strengths, and dynamic pressures, corresponding to blast loads (in kilograms of TNT) ranging from small to large.