# Onsite Testing for Nonlinear Analysis of an Earthquake Damaged Historical Church in Italy
## 3 Onsite Testing and Dynamic Monitoring
The qualitative inspection returned qualitatively a compact homogeneous brick masonry and few inclusions of fragmented bricks bonded well with lime mortar (Figure 8). Considering the results from the video borescope inspection, the material was assumed to be homogeneous and isotropic material and the well-known Equation (1) was applied. Equation (1) relates the velocity of the sonic impulse (\(V\)) to the dynamic modulus of elasticity (\(E_{d}\)) by considering an approximated average density of the masonry (\(\rho\)) equal to 1800 kg/m\({}^{3}\) according to the Italian Code [15] and a Poisson's ratio (\(\
u\)) of 0.26 according to double flat jack test M3 executed in the same location. \[E_{d}=V^{2}\rho\frac{(1+\
u)(1-2\
u)}{(1-\
u)} \tag{1}\]  
Figure 8: Video borescope inspection and derived reconstructed stratigraphy. Figure 7: Sonic tomography. The sonic tomography returned a homogeneous section with an average velocity of 1250 m/s, which respectively yields to [PERSON]'s moduli of 1674 MPa according to [PERSON] et al. [16] and 1945 MPa according to [PERSON] et al. [17]. It can be observed that the average value of these two estimations is the approximate value of test M3 (Table 1), thus the reliability of the double flat jack test on this type of masonry was confirmed. The modal parameters of the church were assessed with the ambient vibration test (AVT) [18], the response acceleration of the construction was recorded for about one hour by 16 ICP piezoelectric accelerometers (PCB 393 B12, 10 V/g sensitivity, \(\pm\)0.5 g range and 8 ug rms resolution) placed in seven points at two different levels: points A, B, C and D are located on the internal cornice of the drum at 16 m height and F, G, and C at 27.5 m height on the extrados of the dome in proximity of the lantern as shown in Figure 9.  
The data were processed according to the operational modal analysis (OMA), based on the assumption of white noise random vibrations. In this condition, it is sufficient to analyze the response of the structure (output-only modal identification) to extract the modal parameters of the building (natural frequencies, modal shape vectors and modal damping). The signals were recorded with a sample frequency of 200 Hz and later filtered with eighth order high-pass filter at 0.7 Hz to increase the signal-to-noise ratio. The cross-power spectra were computed with 0.049 Hz frequency resolution and 5% windowing and related to the reference measurements of node B and C. The polyreference least-squares complex frequency-domain method (PolyMAX [19; 20]) was applied to determine the stable poles of the approximating polynomial in correspondence of the modal parameters of the construction reported in Figure 10.  
Figure 9: Ambient vibration test setup. The experimental modal assurance criterion (MAC) [21] shows a slight interaction between the second and third mode (24%) and a relevant dependency between the first and fourth mode (41%), as expected the rotational modes (third and fourth modes) present partial common displacements with two main translational modes (first and second modes) as shown in Figure 11.  
Figure 5:0 Results of the operational modal analysis.