UB-ALMANAC: An adaptive limit analysis NURBS-based program for the automatic assessment of partial failure mechanisms in masonry churches

As well known, masonry churches fail upon formation of partial failure mechanisms, usually activating at very low levels of horizontal accelerations, which are responsible for the collapse of specific macro-blocks, typically the facade, the apse, lateral naves long walls, etc. Such collapses are a sort of fingerprint for a church and are dependent on the peculiar geometric features of each structure. In order to cope with such unique behavior, the Italian Guidelines on Cultural Heritage for the safety assessment of historical masonry churches require the separate analysis of 28 preassigned failure mechanisms by means of the application of the upper bound theorem of limit analysis in presence of a no-tension material. The utilization of an arbitrary subset of mechanisms, whilst fully justified by past earthquakes experience, could in principle lead to an overestimation of the load carrying capacity and force practitioners to calculations that are still not fully automated. In this context, we present here an efficient and straightforward automatic Upper Bound Adaptive LiMit ANAlysis program for masonry Churches: UB-ALMANAC. The code proposed in this paper relies into a rough finite element discretization constituted by few NURBS rigid elements joined by elasto-plastic interfaces. The mesh is directly prepared within a CAD environment based on the 3D model of the whole church, thus being immediately conceived at architectural level. Limit analysis is then performed automatically under the desired horizontal loads distribution, using the kinematic theorem of limit analysis with dissipation allowed only along interfaces and progressive adaptation of the mesh through a Genetic Algorithm, leading to a quick estimation of the first activating failure mechanism and the most vulnerable macro-block. Three small-medium size churches damaged by the recent Emilia Romagna (2012) and Monti Sibillini (2016) seismic sequences are analyzed and results are compared with both alternative numerical approaches and the actual damages observed. Very good match is systematically found, meaning that the proposed tool could represent a breakthrough toward the full automation of the limit analysis assessment of partial failure mechanisms for churches.