The out-of-plane vulnerability of masonry walls plays a crucial role in the seismic response of existing structures. Depending upon mechanical properties and section morphology, collapse may occur by the onset of a mechanism or, as historic constructions often exhibit, leaf separation, disaggregation or sliding. In these latter cases, structural analyses based on rigid-body mechanics may overestimate the seismic capacity, thus resulting unconservative. The distinct element method (DEM), which represents masonry as an assembly of discrete blocks and nonlinear interfaces, could instead be used. Nevertheless, it is more complex and requires more input parameters, so it is still barely applied in engineering practice. In this paper, the seismic out-of-plane response of masonry walls was modelled with DEM. A shake table test on a two-leaf rubble stone masonry wall and a single-leaf wall in tuff blocks was simulated through nonlinear dynamic analyses. The mechanical properties of joints were calibrated on the basis of dynamic identification under low-intensity white noise input, leading to a good prediction of the seismic response. Then, they were further tuned based on the surveyed crack pattern for an improved matching between experimental results and numerical postdictions. Finally, the results provided by the limit analysis were discussed in the light of DEM simulations.

The destruction of Amatrice and the surrounding villages in Central Italy after the 2016 seismic sequence was so impressive that engineers, authorities and local communities started sharing the common feeling that historical stone masonry buildings were too below current safety standards. The severe damage caused by the earthquakes led to a general distrust of traditional building techniques, leading to the conclusion that there is nothing to do but demolish and rebuild, perhaps with a false antique. Is there an alternative? Is there a way to combine safety and preservation of architectural heritage? This paper aims contributing to the understanding of the seismic behaviour of stone masonry by reproducing, through simulation on a shake table, the progressive loss of compactness of a real scale rubble masonry wall up to the ruinous collapse with the separation between the two external leaves. The laboratory simulation allowed to evaluate the decrease of the fundamental frequency with increasing damage and estimate the maximum displacement profile and the amount of cracking that the wall is able to sustain before failing. Eventually, two modelling strategies based on finite and discrete element methods were proposed and applied to verify the capability of simulating the out‐of‐plane seismic response and the failure mechanisms of rubble masonry.

The out-of-plane collapse of the façade represents one of the major threats and the most frequent cause of damages of churches due to strong earthquakes. Due to the slenderness of the façade and the lack of adequate connections to the side walls and the wooden roof, the seismic action can trigger the overturning. A detailed assessment is therefore required to judge whether or not to intervene. This paper presents an approach for the seismic assessment of the stability of the façade, through a discrete element model based on a photographic survey, with the aim of representing the actual geometry and arrangement of the stone units and their effects on the kinematics of the overturning. The collapse mechanism is simulated with both, quasi-static pushover and dynamic pulse-based analyses and the results compared to those of conventional rigid-body kinematics. The proposed approach is then applied to seven masonry churches that suffered severe damages during the 2009 L’Aquila (Italy) earthquake and the failure mode provided by the analyses is compared to the damages caused by the earthquake. The method is able to give a reliable estimate of the expected failure mechanism, taking into account the quality of the masonry and the connections to the side walls, while also providing the seismic acceleration required to trigger the motion and the ultimate displacement beyond which collapse occurs.

The paper investigates the effectiveness of two-dimensional Discrete Element Method as a tool for structural analysis of arches provided with buttresses and backfill and strengthened with externally bonded reinforcement. Masonry vault and buttresses are modelled as an assembly of 2D rigid blocks interacting through non-linear contact joints, the backfill is discretized into deformable elastic-plastic triangular elements, while the reinforcement is modelled by means of truss elements bonded to the substrate through non-linear springs. A parametric analysis on the influence of material parameters and the effect of the discretization of the backfill is carried out, and the outcome of different reinforcement systems, consisting of Steel Reinforced Grout applied either at the intrados or at the extrados, are analysed. The comparison with experimental full-scale tests proved the ability of the numerical approach to capture hinges position, load bearing capability, as well as the increase in deflection and load capacity provided by the reinforcement.

The survey of damages after recent earthquakes have shown the fragility of masonry churches against the out-of-plane overturning of the façade. This failure mechanism is currently analyzed having recourse to a rigid body model, using either limit analysis with kinematic approach, or dynamic analysis under rocking motion. However, both the aforementioned methods neglect the interaction with the lateral walls, leading to an underestimation of the effective structural capacity under seismic action. The main goal of this work is therefore to investigate the effect of the interlocking between the façade and the transversal wall and the influence of the quality of masonry in out-of-plane overturning. For this purpose, a refined model of masonry through a Discrete Element Method is developed, based on a detailed recognition of masonry units. The acceleration and displacement capacity are estimated through quasi-static pushover and pulse-based dynamic analyses and compared to those calculated for the rigid body model. The proposed methodology is then applied to a sample of three single-nave masonry churches that suffered damages during the 2009 L’Aquila, Italy earthquake.

The out-of-plane collapse of the façade represents one of the major threats and the most frequent cause of damages of churches due to strong earthquakes. Due to the slenderness of the façade and the lack of adequate connections to the side walls and the wooden roof, the seismic action can trigger the overturning. A detailed assessment is therefore required to judge whether or not to intervene. This paper presents an approach for the seismic assessment of the stability of the façade, through a discrete element model based on a photographic survey, with the aim of representing the actual geometry and arrangement of the stone units and their effects on the kinematics of the overturning. The collapse mechanism is simulated with both, quasi-static pushover and dynamic pulse-based analyses and the results compared to those of conventional rigid-body kinematics. The proposed approach is then applied to seven masonry churches that suffered severe damages during the 2009 L’Aquila (Italy) earthquake and the failure mode provided by the analyses is compared to the damages caused by the earthquake. The method is able to give a reliable estimate of the expected failure mechanism, taking into account the quality of the masonry and the connections to the side walls, while also providing the seismic acceleration required to trigger the motion and the ultimate displacement beyond which collapse occurs.