Non-Linear Static and Dynamic Analysis of Rocking Masonry Corners Using Rigid Macro-Block Modelling

The corner failure is one of the most typical local mechanisms in masonry buildings vulnerable to earthquakes. The seismic assessment of this mechanism is poorly studied in the literature and in this paper it is addressed by means of both nonlinear static and dynamic analyses of rocking rigid blocks. The static approach is based on the displacement-based method and is aimed at predicting the onset of the 3D failure mechanism and its evolution through incremental kinematic analysis. This approach also considers the presence of a thrusting roof and the stabilizing contribution of frictional resistances exerted within interlocked walls. The capacity in terms of both forces and displacements is compared with the seismic demand through the construction of acceleration–displacement response spectra, with some originality. The nonlinear dynamic approach is based on the seminal Housner’s work on rocking rigid blocks and considers the influence of transverse walls, roof overloads and outward thrust, all included in an updated equation of one-sided motion. In particular, the process of defining an equivalent prismatic block, representative of the original corner geometry, is presented to convert the 3D dynamic problem into a 2D rocking motion. The wide suitability and advantage of such modeling approaches to assess the seismic response of rocking masonry structures with reference to specific limit states are demonstrated through a real case study, i.e. the collapse of a corner in a masonry school building during the 2016–2017 Central Italy seismic sequence. The compared results provide a good agreement of predictions in terms of both onset and overturning conditions, for which the static model appears to be more conservative than the dynamic one.