# Application of Sonic Tests and Modal Identification in the Characterization of Masonry Walls
## 3 Sonic Tests  
Sonic tests allow the characterization of a material by analyzing the propagation of acoustic waves produced by the percussion of an object. Acoustic waves are mechanical waves, which comprise a set of movements that occur in nature and which, by the action of forces of different types, end up being annulled, restoring the particles to their positions of equilibrium by means of elastic forces [20]. They can be classified according to their frequency of propagation as: sonic (20 Hz-20 kHz), infrasonic (<20 Hz), and ultrasonic (20 kHz-200 kHz). When using acoustic tests to characterize masonry, which is a heterogeneous material, the sonic test is the most suitable compared to the ultrasonic test because  
Figure 2: Masonry wall layout. it has lower frequencies and longer wavelengths that can complete the emitter-receiver path [21; 22]. The use of sonic tests [8] in the characterization of construction material are based on the propagation of acoustic waves and, depending on the configuration adopted in the test (the relative position of the emitter and receiver), it is possible to identify different types of waves. Direct tests aim to measure the velocity (VP) of primary waves (P-waves) by placing the hammer and accelerometer in line at opposite sides of the wall. Indirect tests can measure both the velocity of P- and R-waves (VR) [8]. It is possible to correlate the velocities with the physical and elastic properties of the analyzed solid [12], namely Poisson's ratio and dynamic modulus, through the following expressions:  
\[\frac{V_{p}}{V_{R}}=\sqrt{\frac{2(1-v)(1-v)^{2}}{\left(1-2v\right)\left(0.87- 1.12\right)^{2}}} \tag{1}\]  
\[V_{p}=\sqrt{\frac{E}{\rho}\frac{(1-v)}{(1+v)(1-2v)}} \tag{2}\]  
where \(v\) is the Poisson's ratio, \(E\) is the dynamic modulus and \(\rho\) is the density of the material. These expressions were developed for solid, elastic, isotropic, and homogeneous materials; however, it is adequate to use them in masonry structures, as they provide approximate estimations of their mechanical properties. Regarding the testing campaign, direct and indirect sonic tests and environmental vibration tests were carried out on the walls. The equipment used for the execution of the sonic tests was an instrumented hammer with a 1 kg mass and a nylon tip, an accelerometer, a data acquisition system from National Instruments, and a personal computer. With respect to the process of the dynamic characterization, tests were carried out on all walls. The equipment used thus included four accelerometers (PCB model 393B12), with a measurement range of \(\pm\)0.5 g and 10,000 mV/g, and a frequency range between 0.15 and 1000 Hz, a personal computer, cables, and a data acquisition system from National Instruments. In this experimental campaign, two test configurations were performed: direct and indirect (vertical and horizontal analysis). For the direct tests, the set used constituted nine rows, spaced by 20 cm in the vertical slope, and by 1 m in the horizontal slope. The instrumented hammer (emitter) and accelerometer (receiver) were placed on opposite sides of the specimen faces. Waves were generated by the impact of the instrumented hammer in each row and recorded by the data acquisition system. To perform the indirect tests, a grid of points was marked on each wall with a 7 \(\times\) 3 configuration, spaced by 30 cm, both in vertical and horizontal slopes (see Figure 3). To collect data corresponding to the horizontal slope, the accelerometer was fixed at position A1, and the instrumented hammer was struck at points A2 and A3, along the points of the vertical slope. In turn, to collect data corresponding to the vertical slope, the accelerometer was fixed in position A4, and the instrumented hammer was struck at points A5, A6, A7, A8, A9, and A10, along the points of the horizontal slope. For the data processing, the sonic analyzer tool was used to extract the arrival times of the waves.