Issue 51

F. Clementi et alii, Frattura ed Integrità Strutturale, 51 (2020) 313-335; DOI: 10.3221/IGF-ESIS.51.24 322 9) and not considering (Fig. 10) steel chains in the bell cell. In this way, it was possible to study the effect of the interventions carried out in the 80s not only qualitatively but also quantitatively. The mortar dimension is modelled as well as the bricks into the rigid blocks, assuming the null value of the joints. For what concerns the mass density, it is related to the existing masonry and assumes specific values as indicated in the [26]. Moreover, looking to Fig. 11 it is clear that the wooden floor was modelled, while the masonry panels, the steel chains and the masonry stairs in the annex were recreated as truthful as possible in detail. Hence, in this perspective, comparing the real masonry of Amatrice in Fig. 5 with the numerical models in Fig. 9 and Fig. 10, it is possible to comprehend the level of detail used for the modelling. In fact, the dimensions used for the blocks correspond to the reliefs done on the masonry textures of the façades. However, the very small and irregular existing stones which characterise the panels of the annex and the upper part of the bell-cell were simplified, focusing on the complexity of the two-leaf masonry. For these reasons, the models are respectively defined by 4388 rigid blocks with different geometries for the models with steel chains and 4401 for the models without steel chains in the bell cell. Figure 10 : Views of the North façade (a), East façade (b), South façade (c), West façade (d) of the numerical model without steel chains of the civic clock tower of Amatrice (Rieti, Italy) with the NSCD method. To have a wider view of the damage induced by the 2016 seismic sequence (Fig. 6), in addition to past interventions, attention was paid to the choice of the value of the only material parameter that governs the NSCD method, namely the friction coefficient which is closely related to the quality of the masonry. In fact, the degradation of the mechanical characteristics over time [27], could influence the resistance of the masonry. Hence, for all the blocks along the elevation and of the annex, in both models with and without interventions, the fixed value of the friction was chosen equal to µ = 0.5, for simulating a quite good quality of masonry, also thanks to the observation of the damage actually recorded which is present but without clear collapses in these areas. Otherwise, for the modelling of the bell cell, highlighted with a yellow surface in Fig. 11, we used different values of the friction coefficient to investigate the sensitivity of the dynamic response by varying it. For these reasons, the values used are varied between 0.3 and 0.5 with a step of 0.05 to simulate all the possible conditions from bad to good masonry, as reported in Tab. 1. In the same way, these friction values were applied in both models (with and without the steel chains) pointing out a comparison between the bounding effect of the friction in the mortar and the resistant action of the chains on the typical failure mechanisms of the bell cell.