## 4 Estimation of Elastic Parameters on Masonry Panel  
### Experimental Tests Layout  
In this Section the application of impact tests to estimate the elastic properties of a masonry panel is described. The analyzed masonry wall belongs to the Basilica of Santa Maria degli Angeli, a monumental structure located near Assisi, in central Italy (Figure 8) mainly made from brickwork material [47]. The masonry panel analyzed consists of a slender pillar (about 1.95 \(\times\) 0.25 m) of a structural buttresses system above the vaults of the lateral aisles, with the function of withstanding the horizontal thrust and the inertial forces derived by the central nave (Figure 9a). The masonry is characterized by a regular pattern with bricks arranged on a double-leaf panel comprising headers and stretchers (Figure 9b). The generic block has dimensions of 25 \(\times\) 12 \(\times\) 5.5 cm and mortar joints with a thickness of about 1.1\(\sim\)1.3 cm. The sample was chosen as a typological element, in order to estimate the elastic parameters of the equivalent homogeneous media useful for reliable structural models. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Wall**} & \(\rho\) & \(\
u\) & \(d\) & \(N\) & \(V_{R}\) & \(\sigma_{V_{R}}\) & **Conf. Int.** & **E** \\  & [kg/m\({}^{3}\)] & [\(-\)] & [m] & **Samples** & **[m/s]** & **[m/s]** & **[m/s]** & **95\% [m/s]** & **[MPa]** \\ \hline CLS1 & 2400 & 0.2 & 0.20 & 14 & 2053 & 231 & \(\pm\)132 & 29,226 \(\pm\) 3886 \\ CLS2 & 2400 & 0.2 & 0.20 & 41 & 2131 & 621 & \(\pm\)196 & 31,464 \(\pm\) 6048 \\  & & & 0.40 & 37 & 1722 & 303 & \(\pm\)101 & 20,556 \(\pm\) 2477 \\  & & & 0.60 & 34 & 1475 & 210 & \(\pm\)73 & 15,076 \(\pm\) 1536 \\  & & & 0.80 & 29 & 1613 & 166 & \(\pm\)63 & 18,040 \(\pm\) 1441 \\  & & & 1.00 & 24 & 1576 & 188 & \(\pm\)79 & 17,216 \(\pm\) 1773 \\  & & & 1.20 & 19 & 1639 & 112 & \(\pm\)54 & 18,629 \(\pm\) 1241 \\  & & & 1.40 & 14 & 1428 & 134 & \(\pm\)77 & 14,125 \(\pm\) 1562 \\  & & & 1.60 & 5 & 1498 & 39 & \(\pm\)45 & 15,547 \(\pm\) 946 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of concrete walls CLS1 and CLS2 and impact tests results: mass density \(\rho\); Poisson ratio \(\
u\); distance between the measurements points \(d\); number of suitable samples used in the analysis; mean of R-waves velocity \(\overline{V}_{R}\); standard deviation of R-waves velocity \(\sigma_{V_{R}}\); Interval of R-waves velocity with a confidence level of 95%; Young modulus \(E\). Differently from the concrete case studies described in the previous section, it was possible to carry out both direct and indirect tests. The indirect tests were performed by positioning the accelerometers and the instrumented hammer on one side of the panel. The accelerometers were placed keeping the first in a fixed point, 20 cm apart from the impact point, and the second at a variable distance from the first, starting from a minimum of 20 cm to a maximum of 80 cm with constant steps of 20 cm (Figure 9c). More in detail, the impact point was placed at the center of the wall to avoid wave reflection effects, and the propagation velocity was detected both to the left and the right side of the impact point. As regards the direct tests, it was possible to perform two types of configurations: the first consisted of hitting the wall panel in the center of one of its short sides and measuring the propagated P-waves through its length, corresponding to 1.95 m, on the opposite side (Figure 8d); the second consisted of hitting the wall on one of its long sides to detect the wave in a point placed in the opposite side, evaluating the propagation within its thickness, corresponding to 25 cm in length (Figure 9d). In the second type of test, the hits were given in the same points indicated in the right and left directions, while the accelerometers were positioned precisely on the opposite side of the panel.