Issue 51

F. Clementi et alii, Frattura ed Integrità Strutturale, 51 (2020) 313-335; DOI: 10.3221/IGF-ESIS.51.24 334 Its simplicity comes from the following fundamental simplifying assumptions: (i) block rigidity; (ii) simple contact laws between blocks; (iii) absence of any damping. As a result, the mechanical behaviour of the masonry structures is influenced by only the friction coefficient, related to the quality of existing masonry of the analysed bell tower. This is a significant consequence for modelling cultural heritage since the determination of the mechanical properties is always uncertain and variable. Despite its simplicity, the model can predict a large variety of dynamical behaviours of historical structures and their seismic vulnerability. Different failure mechanisms may be found, depending on the value assigned to the friction coefficient. In this case study, the value of the friction of the bell cell was varied to represent the current state of the masonry walls and other probable future situations. Moreover, the resistant action of the steel chains was related to the action of different values of the friction, pointing out its relevance. Thus, it was possible to obtain coherent collapse mechanisms and good matching with the real state of the structure and also to predict other potential damages at varying of the masonry mechanical properties. Finally, the sensitivity of the result to the input parameters is pointed out as consequence of the model’s non-smoothness. This character is also present in real structures. Indeed, small irregularities in buildings (especially ancient buildings) affect the seismic response in a visible way. However, the overall behaviours (failure mechanisms) of the analysed macro-elements only gradually change along with the parameters. For instance, if the friction coefficient increased, the overturning mechanisms become gradually prevailing over sliding mechanisms. This represents the main outcomes to understand the behaviour of existing ancient structures. Another purpose of this work is to suggest retrofitting works according to NSCD numerical results and to highlight that sensitivity to data is less evident in the standard FEM continuum models and represents a further distinguishing feature of the proposed approach. Finally, the need of inserting steel chains is confirmed to be fundamental for medium-high values of friction coefficients as pointed out by numerical results, and furthermore the study shows how important it is to improve the performance of the mortar in order to ensure a monolithic behaviour under the action of sliding associated with medium- low mortar resistance values. Other sensitivity analyses are left for future works where the deformability of the blocks and the cohesive zone model should be used instead of rigid blocks and Coulomb’s friction law. R EFERENCES [1] Lagomarsino, S., Podesta`, S. (2004). Damage and Vulnerability Assessment of Churches after the 2002 Molise, Italy, Earthquake, Earthq. Spectra, 20(S1), pp. s271–283, DOI: 10.1193/1.1767161. [2] Milani, G. (2013). Lesson learned after the Emilia-Romagna, Italy, 20–29 May 2012 earthquakes: A limit analysis insight on three masonry churches, Eng. Fail. Anal., 34, pp. 761–778, DOI: 10.1016/j.engfailanal.2013.01.001. [3] Brandonisio, G., Lucibello, G., Mele, E., Luca, A. De. (2013). Damage and performance evaluation of masonry churches in the 2009 L’Aquila earthquake, Eng. Fail. Anal., 34, pp. 693–714, DOI: 10.1016/j.engfailanal.2013.01.021. [4] Valente, M., Milani, G. (2019). Damage assessment and collapse investigation of three historical masonry palaces under seismic actions, Eng. Fail. Anal., 98, pp. 10–37, DOI: 10.1016/j.engfailanal.2019.01.066. [5] Pellegrini, D., Girardi, M., Lourenço, P.B., Masciotta, M.G., Mendes, N., Padovani, C., Ramos, L.F. (2018). Modal analysis of historical masonry structures: Linear perturbation and software benchmarking, Constr. Build. Mater., 189, pp. 1232–1250, DOI: 10.1016/j.conbuildmat.2018.09.034. [6] Formisano, A., Vaiano, G., Fabbrocino, F., Milani, G. (2018). Seismic vulnerability of Italian masonry churches: The case of the Nativity of Blessed Virgin Mary in Stellata of Bondeno, J. Build. Eng., 20, pp. 179–200, DOI: 10.1016/j.jobe.2018.07.017. [7] Milani, G., Valente, M. (2015). Failure analysis of seven masonry churches severely damaged during the 2012 Emilia- Romagna (Italy) earthquake: Non-linear dynamic analyses vs conventional static approaches, Eng. Fail. Anal., 54, pp. 13–56, DOI: 10.1016/j.engfailanal.2015.03.016. [8] Clementi, F., Quagliarini, E., Monni, F., Giordano, E., Lenci, S. (2017). Cultural Heritage and Earthquake: The Case Study of in Ascoli Piceno, Open Civ. Eng. J., 11(Suppl-5, M5), pp. 1079–1105, DOI: 10.2174/1874149501711011079. [9] Quagliarini, E., Maracchini, G., Clementi, F. (2017). Uses and limits of the Equivalent Frame Model on existing unreinforced masonry buildings for assessing their seismic risk: A review, J. Build. Eng., 10, pp. 166–182, DOI: 10.1016/j.jobe.2017.03.004. [10] Clementi, F., Gazzani, V., Poiani, M., Mezzapelle, P.A., Lenci, S. (2018). Seismic Assessment of a Monumental Building through Nonlinear Analyses of a 3D Solid Model, J. Earthq. Eng., 22(sup1), pp. 35–61, DOI: 10.1080/13632469.2017.1297268.