Energy-based method for identifying vulnerable macro-elements in historic masonry churches

Seismic vulnerability of historic churches is a well known issue in earthquake engineering. The need of preserving these buildings encourages the development of reliable numerical methods to assess their seismic behavior. In this paper a new approach is presented, based on evaluating damage pattern obtained by non-linear dynamic analysis and the energy dissipated by each macro-element during earthquakes. A "hierarchy of dissipated energy'' concept emerges to give a scale of vulnerability of the parts that compose a church. By modifying masonry mechanical parameters or geometric features, the crack pattern and amount of energy dissipation density of each element is varied and calibrated to achieve the desired hierarchy. The structural designer can therefore estimate the effectiveness of strengthening devices by checking reduction and possibly migration of dissipated energy density from weaker structural elements to more resistant ones, together with a preferable damage pattern. The proposed strategy is applied to a single nave church, hit by the Emilia Romagna earthquake (Italy, 2012), first defining a scale of vulnerability of the macro-elements and then proposing a rehabilitation strategy, which improves the seismic response in terms of damages and dissipated energy. The strong vulnerability of the main dome vault is shown, due to the combination of its high dissipated energy density with its intrinsic weakness. Strengthening techniques are aimed to reduce the amount of dissipated energy of vulnerable macro-elements and to attenuate out-of-plane mechanisms.