Seismic vulnerability evaluation of historical masonry churches: Proposal for a general and comprehensive numerical approach to cross-check results

The seismic vulnerability evaluation of existing masonry churches is an important issue in earthquake engineering. The Italian Guidelines for the built heritage suggest a quantitative assessment of vulnerability by means of a technique that uses the upper bound theorem of limit analysis on 28 pre-assigned failure mechanisms, assuming masonry unable to withstand tensile stresses. In the framework of the kinematic theorem, the failure mechanism activating in reality is that associated to the lowest multiplier. Whilst the approach is very straightforward, it is intrinsically affected by possible inaccuracies, both because the real geometry of the church is accounted for only in an approximate way and the choice to limit the analysis to 28 mechanisms could exclude from computations the real mechanism occurring, with the consequent overestimation of the collapse acceleration.In this paper a general approach relying into the collection of different numerical procedures is proposed to all practitioners interested in a precise estimation of the seismic vulnerability of masonry churches, with an indication of all the steps to follow to predict with fair accuracy their load carrying capacity. The approach comprises the determination of eigen-frequencies and modes, spectral analyses (both assuming an elastic behavior for masonry), limit analyses with FEM and pre-assigned failure mechanisms, pushover and non-linear dynamic computations. A case study is discussed in order to calibrate the procedure and discuss the actual accuracy of the results obtained.