Issue 51

F. Clementi et alii, Frattura ed Integrità Strutturale, 51 (2020) 313-335; DOI: 10.3221/IGF-ESIS.51.24 327 Figure 15 : Numerical cumulative damages of the civic clock tower of Amatrice (Rieti, Italy) under the four main shocks recorded in the village during the Central Italy seismic sequence of 2016 for both configurations, with and without the steel chains, at varying of the friction on the bell cell. For what concerns the displacements THs of the control point #2 (see Fig. 17), belonging to the upper part of the bell cell on the opposite side of the control point #1, the dynamic behaviour of the model with the steel chains is similar to the one with the previous control point. Otherwise, the models without the bounding due to the chains resist over time and introduce greater displacements for each friction value considered. On the other hand, the control point #3 (see Fig. 18) selected at the base of a masonry pier, presents relevant dislocations and early collapses for the model without the chains at increasing of the friction coefficient, as µ =0.40, µ =0.45 and µ =0.50. Instead, for the minor friction values, the blocks have important displacements over time, without collapses during the last heavy shock. Similarly, the models with the steel chains introduced lower values of displacements than the other, without final collapses for all friction values. In fact, by increasing the value of the friction coefficient it is observable that -in general- translation-like mechanisms are substituted with rotation-like mechanisms. Furthermore, the structure will present many sliding surfaces for small values of the friction coefficient, and as this increase, it is possible to note a clear activation of rotation-like mechanisms of the peripheral walls instead, which leads to major displacements and most localized damage along with the tower. Looking at the displacements THs of the control point #4, which is at the base of a masonry pier, plotted in Fig. 19, they introduced similar evolution over time, with values near each other. Differently from control points #1 to #3, the #4 presents displacements higher with steel chains and increasing of the friction coefficient, due to the overall behaviour of the bell cell. Lastly, during the final steps of the analyses, there is a change in the dynamic behaviour of the masonry, with an increase of displacements of the model without chains. For what concerns the THs of the control point #5 (see Fig. 20), belonging to the annex of the civic tower with fixed friction value equal to 0.50, they present comparable displacements for all the analyses, with the main values during the final shock of the 30 th October. Lastly, the dissipated energy is plotted for all the models in both configurations, with and without steel chains (respectively C with a solid line, and NC with a dotted line), and reported in Fig. 21 at varying of the friction coefficient of the bell cell under the four continuous shocks to investigate cumulative damages. Thus, in the cases of the two events of 24 th August 2016 and of 26 th October 2016, the higher values of the dissipation of energy belong to the models without the steel chains for all the friction coefficient used. Additionally, the dissipated energy raises at the decreasing of the friction values of the masonry cell bell. Otherwise, the response of the structures at the end of the analysis is different under the action of the strong event of 30 th October 2016. In fact, the dissipated energy with friction coefficients equal to 0.45 and 0.50 in this case is higher for the models with steel chains.