# Application of Sonic Tests and Modal Identification in the Characterization of Masonry Walls
## 6 Conclusions  
To the best of the author's understanding, in order to investigate the structural behavior of specimens of reinforced masonry walls of soil-cement compressed earth blocks, sonic tests were performed on six walls. The results of the tests enabled for the characterization of the walls as a regular and uniform masonry type, with an elasticity modulus that can vary between 3.03 and 3.35 GPa in the vertical direction and 3.14 and 4.84 GPa in the horizontal direction. The fact that the horizontal direction has higher values of elasticity modulus compared to the vertical indicates that it has lesser significant voids throughout the cross section. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Wall**} & \multicolumn{2}{c}{**1 st Mode**} & \multicolumn{2}{c}{**2 nd Mode**} & \multicolumn{2}{c}{**3 rd Mode**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} & \multirow{2}{*}{**(\%)**} \\  & \multicolumn{2}{c}{**(Hz)**} & & & & & & & & & & \\ \cline{2-11}  & **Num** & **Exp** & **Num** & **Exp** & **Num** & **Exp** & & & & \\ \hline W1 & 9.34 & 9.31 & 26.37 & 26.24 & 33.72 & 43.57 & 5.8 & 3.45 & 3.30 & 3.26 \\ \hline W2 & 9.16 & 9.17 & 26.34 & 25.86 & 33.86 & 42.93 & 5.7 & 3.35 & 3.35 & 4.18 \\ \hline W3 & 8.13 & 8.39 & 26.33 & 23.64 & 39.20 & 39.26 & 4.9 & 2.80 & 3.15 & 3.63 \\ \hline W4 & 9.57 & 9.52 & 26.30 & 26.81 & 39.45 & 44.51 & 3.3 & 3.60 & 3.08 & 4.52 \\ \hline W5 & 9.39 & 9.38 & 26.20 & 26.44 & 43.39 & 43.88 & 0.6 & 3.50 & 3.19 & 4.84 \\ \hline W6 & 9.38 & 9.38 & 26.29 & 26.44 & 43.53 & 43.88 & 0.3 & 3.50 & 3.03 & 3.14 \\ \hline \hline \end{tabular}  
* Num—Numerical frequencies obtained with numerical model. Exp—Frequencies obtained with the experimental tests (dynamic identification tests). E\({}_{\text{num}}\)—Young modulus considered in the numerical analysis. E\({}_{\text{exp},\text{ver}}\)—Average Young modulus obtained in the sonic tests in the vertical direction. E\({}_{\text{exp},\text{horz}}\)—Average Young modulus obtained in the sonic tests in the horizontal direction.  
\end{table} 
Table 4: Correlation between the measured and calculated frequencies. Figure 11: MAC correlation matrix. A numerical model of each wall was developed, and their mechanical properties were calibrated with the data obtained from the sonic tests analysis. The frequencies obtained from the numerical models of the walls were compared with the frequencies obtained from the environmental vibration tests, using the modal assurance criterion, and it allowed a good correlation in terms of frequencies in modes 1 and 3. In turn, mode 2, which corresponds to the torsional mode, presented a poor correlation. According to this correlation, it is possible to assume that the elasticity modulus obtained by the indirect tests in the vertical slope was the best approach. Nevertheless, the elasticity modulus obtained in the indirect tests in the horizontal slope has a 10-20% of overestimation. From this study, it is possible to conclude that sonic tests provide reliable data that can be used to characterize masonry structures, and that the indirect tests configuration is the one that is most likely to be carried out on existing structures as the emitter and the receiver are on the same face of the structure. Furthermore, the combined methodology of using sonic and environmental vibration tests allows the calibration and validation of numerical models of masonry structures and for the assessment of the state of conservation and structural safety. The approach for the indirect characterization of these materials has several limitations and the proposed relations seem to point to a good empirical relationship of some physical-mechanical properties, namely the Young modulus.