## 4 Estimation of Elastic Parameters on Masonry Panel
### Analysis of the Results  
The results derived by the indirect tests are summarized in Table 2, in which, as for the cases of concrete walls CLS1 and CLS2, the R-wave velocities obtained on several coupled positions of the accelerometers are reported, together with the statistical elaborations. The outcomes show values of the mean velocities that are quite stable for \(d\geq 0.40\) m owing to the periodicity of the texture. In fact, for \(d=0.20\) m the high value of standard deviation is due to the large range of measured velocities, characterized by lower values of about 300-400 m/s detected near the edges of the wall and maximum values higher than 900 m/s related to a couple of accelerometers placed on the same brick. Figure 10 shows typical signals recorded during the tests applied on the masonry panel. It should be noted as the time interval detected by the two accelerometers in which the passage of the R-wave occurs is greater in this type of material with respect to concrete. Figure 9: **(a)** Tested masonry wall: buttresses of the central nave located above the aisle reinforced with steel tie rods added in the latest restoration; **(b)** Schematic representation of the positioning of the accelerometers on the wall and point of impact of the instrumented hammer; **(c)** Schematic representation of indirect test configuration denoting the position of the accelerometers and the impact point of the instrumented hammer; **(d)** Schematic representation of direct test configuration denoting the directions of volume waves propagation. The second type of test investigated the P-waves propagation through the length/ thickness of the wall: as illustrated in Figure 9d, the impact points were fixed both in the shorter faces of the panel and in each numbered station of the larger face, as indicated in Figure 9c, with the related receiver accelerometer placed on the opposite side. The P-wave is the faster wave propagated in a solid and therefore the first signal on the recorded curve of the accelerometers gives information on this type of wave. In this test the distance of travel of the waves was the same for all hits and it was equal to 1.95 m for the greater side, and equal to 0.25 m for the test along the thickness. Figure 11 shows typical signals recorded during the tests, where the red circle indicates the instances in which the impact and the arrival of the P-wave were detected. Table 3 summarizes the results in terms of mean velocity of P-waves, standard deviation and range of velocities with a confidence interval of 95%. The results show consistent values of the mean velocity, but smaller distances determine a higher value of standard deviation, due to the heterogeneity and the uncertainties of the material. \begin{table}
\begin{tabular}{c c c c c} \hline
**d [m]** & **N Samples** & \(\overline{V}_{R}\) **[m/s]** & \(\sigma_{V_{R}}\) **[m/s]** & **Conf. Int. 95\% [m/s]** \\ \hline
0.20 & 35 & 626 & 295 & \(\pm 101\) \\
0.40 & 20 & 540 & 99 & \(\pm 46\) \\
0.60 & 11 & 548 & 60 & \(\pm 40\) \\
0.80 & 3 & 521 & 23 & \(\pm 43\) \\ \hline \end{tabular}
\end{table} 
Table 2: Indirect impact tests results: distance between the measurement 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%. Figure 10: Typical values recorded by the accelerometers in the indirect tests on the masonry panel. As previously asserted, the knowledge of the values of velocity of R- and P-waves gives more information on the elastic parameters of the medium, through which they were propagated.