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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 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. 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 surveyed crack pattern for an improved matching between experimental results and numerical postdictions. Finally, the results provided by limit analysis were discussed in the light of DEM simulations.