# Sonic and Impact Test for Structural Assessment of Historical Masonry
## 3 Results  
### Sonic and Endoscopy Tests  
A wall surface of 1 m \(\times\) 1 m was subdivided into a grid of equidistant points 20 cm, by removing the plaster around the points of application of the impact hammer (Figures 3b and 4a). Each single point of this grid consisted of a punctual sonic survey in order to obtain an average value of sonic velocity inside the analysed area of an highly inhomogeneous materials such as the masonry. At least three measurements were performed for each point, the average of which is shown in Table 1. The type of sonic survey was trasversal to the thickness (85 cm) of the masonry wall. Unfortunately, there were no surveys of the sonic wave before the mortar injections technique. Table 1 shows the sonic results of some significant points of the mesh, as the average of those of the entire test grid.  
The sonic speed (\(v\)) of crossing the material is proportional, in the case of a homogeneous and isotropic material [15], the dynamic elastic modulus (\(E_{d}\)), the Poisson's ratio (\(v\)) and the density (\(\rho\)) of the material, by Formula (1):  
\[E_{d}=\ v^{2}\ \rho\ \frac{(1+v)\ (1-2v)}{(1-v)} \tag{1}\]  
The Poisson's ratio (\(v\)) varies proportionally to the compression stress (\(\sigma\)) acting on the wall [16], according to the following report (2):  
\[v=0.15\div 0.30\ \text{for}\ 0.30\ f_{k}\leq\sigma\leq 0.8f_{k} \tag{2}\]  
where \(f_{k}\) is the compression strength derived from the double flat jacks test, which gave \(\sigma=\) 0,30 MPa, \(f_{k}=\) 1 MPa and elastic modulus \(E=\) 1220 MPa. According to (2), since the operating compression stress measured with the flat jack was just 0.30 MPa, the corresponding lower value of the Poisson's ratio equal to 0.15 was used for the calculation of \(E_{d}\) by Equation (1); the value of density of the unordered masonry stone used in (1) was 1900 Kg/m\({}^{3}\) in accordance with the values of the table C8.5.I of the italian technical code \"Circolare 21 gennaio 2019 n. 7\" [17] regarding the masonry type \"unordered masonry stone\".  
The presence of discontinuity, associated with phenomena of refraction of the wave, as well as the wavelength of the dominant frequency means that the masonry deviates from the ideal behaviour. All these aspects lead to the evaluation of the results mainly in terms of qualitative and not quantitative characteristics of the masonry. Despite this, interesting research [18] was conducted in order to correlate the mechanical characteristics of masonry with sonic velocity parameters.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Point** & **Average Speed (m/s)** & **E\({}_{d}\) (MPa)** \\ \hline P 2.5 & 419 & 316 \\ P 2.6 & 368 & 244 \\ P 3.3 & 1044 & 1959 \\ P 3.4 & 837 & 1260 \\ P 3.5 & 531 & 508 \\ P 3.6 & 409 & 301 \\ P 4.3 & 761 & 1041 \\ P 4.4 & 663 & 792 \\ P 4.5 & 549 & 542 \\ P 4.6 & 618 & 687 \\ P 5.4 & 11 The low sonic results also increased uncertainties about the presence of voids or cavities within the wall texture. Therefore, at one point of the sonic test mesh, a 48 cm long hole (half the thickness of the wall) was made for inserting the endoscope in order to visually investigate the masonry stratigraphy (Figure 5). In fact, the test shows, after an initial section of compact masonry, the presence of a first discontinuity. After the first layer of whole stone, the stratigraphy is characterized by the alternation of stones smaller than the first interspersed with discontinuities that are not entirely filled by the injections. Subsequently, there was a central discontinuity between two walls of equivalent thicknesses, the sum of which constitutes the thickness of the masonry. The acquired images also show the total absence of injections in the deeper layers of the masonry. The stratigraphy detected is the following:  
* 0-15 cm: compact stone (Figure 5b);
* 15-22 cm: first discontinuity (Figure 5c)
* 22-48 cm: stones interspersed with discontinuity (Figure 5d).