Collapse behavior of masonry domes under seismic loads: An adaptive NURBS kinematic limit analysis approach

The ultimate limit state behavior of masonry domes under axisymmetric gravity loads is nowadays well known and it has been proved how a generalization of the thrush line method used successfully for arches is quite effective also in this case. However, the behavior of a dome under horizontal loads, which is important in case of seismic action, becomes incredibly hard to tackle and still remains an open issue. The present paper aims at presenting a fast and reliable automatized kinematic limit analysis approach able to accurately predict the actual behavior of masonry domes subjected to horizontal static loads. The model uses a rough discretization of the dome obtained by means of few rigid-infinitely resistant NURBS generated elements, adapting step by step the initial mesh in order to progressively overlap the element edges (where all dissipation is lumped) with the hinges forming the failure mechanism. The adoption of a rough mesh makes the code extremely fast, much more competitive than a standard FE model, allowing at the same time to approximate the actual geometry and load distributions in an extremely accurate way. The utilization of geometries obtained with laser scanner acquisitions is straightforward and the presence of pre-existing cracks can be accounted for as well. Three complex case studies are analyzed in detail to benchmark the approach proposed, relying into existing domes belonging to the Italian cultural heritage. The first example has the geometrical parameters of a typical late Renaissance dome, the Cathedral of Montepulciano, the second is the dome of Anime Sante church (collapsed during the L'Aquila 2009 earthquake with a paradigmatic failure mechanism) and the last is the dome of Caracalla baths, whose causes of collapse remain still unknown. In all cases inspected, the approach proposed quickly provides collapse accelerations and active failure mechanisms at a fraction of the time needed by non-linear FE analyses, providing interesting hints into the actual behavior of such kind of structures under horizontal loads.