Fast Vulnerability Evaluation of Masonry Towers by Means of an Interactive and Adaptive 3D Kinematic Limit Analysis with Pre-assigned Failure Mechanisms

The paper presents an interactive kinematic limit analysis approach that can be handled also by inexperienced users for a reliable evaluation of the seismic vulnerability of masonry towers. The procedure requires only a 3D Computer-Aided Design CAD representation of the tower and the mechanical properties to assign to the different volumes. Five possible failure mechanisms are hypothesized, corresponding to those more frequently observed during post-earthquake surveys. They are all constituted by few macro-blocks mutually roto-translating and the code proposed automatically optimizes the shape of the selected failure mechanisms with a Genetic Algorithm GA approach, minimizing the failure multiplier—in agreement with the upper bound theorem of limit analysis—so furnishing quickly an estimation of the collapse acceleration and the crack pattern at collapse. The approach has several advantages, the most important being (1) the possibility to account for the actual geometry of the tower in an extremely detailed manner (so considering openings, irregularities, mass variation along the height, etc.), (2) the drastically reduced computational burden needed (only the recursive evaluation of the principle of virtual powers is required), (3) the adaptation of the failure mechanisms to the specificity of the problem treated, (4) the possibility to apply distributions of horizontal loads different from standard ones and finally (5) the possibility of utilization for all those practitioners not familiar with finite elements and computational limit analysis. The practical procedure proposed is validated against FE pushover computations and non-linear dynamic analyses conducted on two historical towers located in northern Italy, showing perfect agreement with results obtainable by means of complex procedures certainly not manageable at a common professional level.