Issue 51

M.G. Masciotta et alii, Frattura ed Integrità Strutturale, 51 (2020) 423-441; DOI: 10.3221/IGF-ESIS.51.31 433 of freedom. Fig. 10 shows the FE mesh generated by the code, where the individual masonry components, bricks and mortar joints, are highlighted in cyan and red, respectively, while the parts loaded with lime bags are displayed in yellow. Figure 10: FE model of the experimental specimen generated by NOSA-ITACA for RS and RSW. A model updating [40] is performed on the FE model with the aim of estimating the Young’s moduli E of the two masonry components (mortar and brick). The algorithm used and implemented in the NOSA-ITACA code for model updating is based on the construction of local parametric reduced order models embedded in a trust-region scheme. The objective function to be minimized is the distance between experimental and numerical natural frequencies and mode shapes. The optimal mechanical characteristics of the two masonry components are estimated by using the first three experimental frequencies and mode shapes of the reference scenario (RS), assumed as undamaged configuration, because the parameters to be optimized are only two. This choice is based on the observation that in both reference scenarios (RS and RSW) no visible cracks were present, thus the arch behavior can be plausibly considered as linear elastic at this stage. The model updating is carried out considering the base of the concrete supports clumped and adding concentrated masses to the measurement points (black nodes in Fig. 10) to take the weight of the accelerometers into account. Tab. 4 summarizes the mechanical characteristics of the materials employed in the FE model: in bold the parameter values obtained via model updating (the others, including the Poisson’s ratios and mass densities, are kept fixed during the optimization process). It is interesting to note that the updated Young’s moduli obtained through the aforementioned procedure are consistent with the values reported in literature [41, 42]. The modal results of the calibrated numerical model are summarized in Tab. 5 along with the experimental counterpart. The relative errors in frequencies and MAC values are also reported to assess the degree of consistency between experimental and numerical mode shapes for RS. It is worth noting that the fourth and fifth numerical mode shapes are inverted with respect to the corresponding experimental modes, as clearly shown in Fig. 11. Furthermore, the MAC value relative to the second mode shape is quite low. This is likely due to the fact that the numerical mode shape, being the model clamped at the base of both concrete abutments, is characterized by a displacement in Y direction coupled with a torsion around the X axis, while the corresponding experimental mode shape (as visible in Fig. 11 for RS, and even better in Fig. 13 for RSW) seems to be characterized by a movement in Y direction and a torsion around the Z axis, even though the moving support is nominally kept blocked in the reference configurations. E [MPa] ν ρ [kg/m 3 ] Brick 2500 0.2 1653.3 Mortar 500 0.2 1750.0 Concrete 25000 0.2 2500.0 Table 4 : Materials properties adopted for the numerical model.