A significant correlation between the in-plane (IP) and out-of-plane (OOP) damage propagation of masonry infills (MIs) is frequently observed after strong earthquakes, posing a serious problem as regards vulnerability of public buildings such as schools. The present work is aimed at identifying the effects of different IP and OOP modelling assumptions of MIs on their seismic damage. To this end, the state secondary school De Gasperi-Battaglia in Norcia (Italy), object of monitoring by the Department of Civil Protection since 2000, is investigated for the heterogeneity of infill typologies. The school is composed of a basement and three storeys above ground level, with a reinforced concrete (r.c.) framed structure having a long-shaped rectangular plan. Two typologies can be identified in terms of transverse layout of MIs: (i) double-leaf interior partitions, made of hollow clay bricks; (ii) double-leaf exterior infill walls, constituted by facade solid bricks paired with hollow clay bricks. In addition, partial height infills in the longitudinal direction, due to classroom windows, make the columns susceptible to short column effects. MIs are represented by a five-element macro-model predicting both in-plane (IP) and out-of-plane (OOP) behaviour through a horizontal nonlinear truss and four diagonal nonlinear beam elements, respectively. Stiffness and strength values in the OOP direction are also reduced considering the evolution of the IP damage. Three assumptions are investigated for the behaviour of structural MIs: i.e. elastic both IP and OOP; inelastic IP and elastic OOP; inelastic both IP and OOP. Bare and infilled test structures are subjected to biaxial spectrum-compatible accelerograms, to evaluate the IP and OOP damage levels and effectiveness of the OOP simplified verification proposed by seismic codes.

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The out-of-plane verification of unreinforced masonry infills (MIs) placed at different floor levels of a building is generally carried out through simplified methods, but seismic events in Italy (e.g. L'Aquila, 2009) and worldwide (e.g. Northridge, 1994) have highlighted that code provisions may result in wrong estimations of safety. The types of damage observed for MIs are usually a combination of, or an interaction between, in-plane (IP) and outof-plane (OOP) mechanisms. Specifically, the IP drift ratio is generally reduced at the upper storeys of buildings, where the OOP drift ratio increases due to an increase of seismic acceleration. Significant OOP damage may also take place at the lower storeys where the highest values of IP drift ratio are attained. The present work is aimed at identifying the effects of the IP and OOP nonlinear interaction of MIs on their seismic behaviour and acceleration demand. A five-element macro-model comprising four diagonal nonlinear beams and one (horizontal) central nonlinear truss for the prediction of the OOP and IP behaviour of MIs, respectively, is first implemented in a C++ computer code for the nonlinear dynamic analysis of r.c. infilled framed structures. The proposed algorithm addresses the issue of nonlinear interaction by modifying stiffness and strength values of the MI in the OOP direction on the basis of simultaneous or prior IP damage and vice versa. Moreover, a lumped plasticity model describes the inelastic behaviour of r.c. frame members, including a 26-flat surface modelling of the axial load-biaxial bending moment elastic domain at the end sections where inelastic deformations are expected. A spatial one-bay multi-storey shear-type model is considered as equivalent to infilled r.c. framed buildings. In particular, the dependence of the results on variation of the following design parameters is considered: i.e. number of storeys; bay length; aspect ratio of MIs, with two leaves of clay hollow bricks, defined as the ratio between the panel length and height; strength level of the r.c. framed structure. Biaxial spectrum-compatible accelerograms are considered at ultimate limit states. A review of the current Italian (NTC18), European (EC8) and American (FEMA356) code provisions is performed by means of comparison with analyses results.

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