# Application of Sonic Tests and Modal Identification in the Characterization of Masonry Walls
## 3 Sonic Tests
This process involved taking the moment when the wave was generated by the instrumented hammer and the moment when the accelerometer recorded the arrival of the wave and subtracting the values to obtain the arrival time. The arrival times taken from both tests were those corresponding to the P-waves, since they correlate better with the modulus of elasticity of the material. For calculation purposes, it was assumed that the masonry wall structures have a Poisson's ratio in the range of 0.2-0.3 based on the literature [23; 24], and without additional information, was assumed a Poisson coefficient of 0.25. A density of 1937 kg/m\({}^{3}\) was considered. The density value was based on simple measurements in the laboratory of small wallets considering the brick, mortar, and reinforcement. Table 1 presents the summary of the results obtained for the velocities of P-wave propagation for each wall, in each test. Figures 4-6 represent the velocities of propagation by a surface graphic in the tested area. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wall** & **Test** & \begin{tabular}{c} \(-\) \\ _V(m/s)_ \\ \end{tabular} & \begin{tabular}{c} **V\({}_{\text{min}}\) (m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **V\({}_{\text{max}}\) (m/s)** \\ \end{tabular} &
\begin{tabular}{c} **COV** \\ \end{tabular} \\ \hline \multirow{3}{*}{W1} & Direct & 2463.74 & 1766.02 & 3013.15 & 15\% \\ \cline{2-6}  & Indirect (vertical) & 1431.38 & 1065.81 & 2102.42 & 20\% \\ \cline{2-6}  & Indirect (horizontal) & 1422.71 & 1049.21 & 1872.09 & 19\% \\ \hline \multirow{3}{*}{W2} & Direct & 2468.05 & 2325.58 & 2560.81 & 5\% \\ \cline{2-6}  & Indirect (vertical) & 1442.03 & 1075.08 & 2500.00 & 26\% \\ \cline{2-6}  & Indirect (horizontal) & 1610.60 & 1209.01 & 1923.07 & 14\% \\ \hline \multirow{3}{*}{W3} & Direct & 2267.31 & 2049.18 & 2557.54 & 7\% \\ \cline{2-6}  & Indirect (vertical) & 1397.41 & 1208.02 & 2015.30 & 15\% \\ \cline{2-6}  & Indirect (horizontal) & 1500.47 & 1282.05 & 1923.07 & 12\% \\ \hline \end{tabular}
\end{table} 
Table 1: Velocity values for the direct and indirect sonic tests. Figure 3: Indirect tests grid configuration. Figure 4: Surface of the direct tests’ velocity data (m/s). From the surface analysis, it is possible to observe that, in most of the area tested, the walls present low variability (<15%), which reflects their material uniformity. Moreover, it is visible that the values obtained in the horizontal direction tests present higher values of velocities compared to the values obtained in the vertical tests, which indicates that there are less voids in the horizontal slope of the walls. By applying Equation (2), it was possible to reach the masonry dynamic elasticity modulus, which are gathered in Table 2. Considering the indirect tests values, the results obtained show that the dynamic elasticity modulus average varied between 3.03 and 4.52 GPa. Figure 5: Surface of the indirect tests (vertical slope) velocity data (m/s). Figure 6: Surface of the indirect tests (horizontal slope) velocity data (m/s). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wall** & **Test** & \
\begin{tabular}{c} **E\({}_{\text{average}}\)** \\ **(GPa)** \\ \end{tabular} & **E\({}_{\text{min}}\) (GPa)** &
\begin{tabular}{c} **E\({}_{\text{max}}\)** \\ **(GPa)** \\ \end{tabular} & \(\sigma\) \\ \hline \multirow{3}{*}{W1} & Direct & 9.79 & 5.03 & 14.65 & 2.79 \\ \cline{2-6}  & Indirect (vertical) & 3.30 & 1.83 & 7.13 & 0.23 \\ \cline{2-6}  & Indirect (horizontal) & 3.26 & 1.77 & 5.65 & 0.55 \\ \hline \multirow{3}{*}{W2} & Direct & 9.83 & 8.72 & 10.58 & 0.89 \\ \cline{2-6}  & Indirect (vertical) & 3.35 & 1.86 & 10.08 & 0.09 \\ \cline{2-6}  & Indirect (horizontal) & 4.18 & 2.35 & 5.96 & 0.79 \\ \hline \multirow{3}{*}{W3} & Direct & 8.29 & 6.77 & 10.55 & 1.12 \\ \cline{2-6}  & Indirect (vertical) & 3.15 & 2.35 & 6.55 & 0.06 \\ \cline{2-6}  & Indirect (horizontal) & 3.63 & 2.65 & 5.96 & 0.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Elasticity modulus values obtained from the sonic tests.