## 5 Discussion and Conclusions  
In this article, we showed the principles of a novel NDE method for concrete based on the propagation of highly nonlinear solitary waves along a metamaterial in contact with the concrete to \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cast Day**} & \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Top**} & \multicolumn{2}{c}{**Bottom**} \\ \cline{3-6}  & & \multicolumn{1}{c}{**TOF (ms)**} & \multicolumn{1}{c}{_E (GPa)_} & \multicolumn{1}{c}{**TOF (ms)**} & \multicolumn{1}{c}{_E (GPa)_} \\ \hline \multirow{4}{*}{Day 1} & \multirow{4}{*}{1} & 0.59608 & 24 & 0.57420 & 39 \\  & & 0.58260 & 31 & 0.57420 & 39 \\  & & 0.57944 & 35 & 0.57768 & 35 \\ \cline{2-6}  & & 0.59276 & 25 & 0.57644 & 37 \\  & & 0.58484 & 31 & 0.57668 & 37 \\  & & 0.59608 & 24 & 0.57420 & 39 \\ \hline \multirow{4}{*}{Day 2} & \multirow{4}{*}{3} & 0.57892 & 35 & 0.57401 & 39 \\  & & 0.57768 & 35 & 0.57200 & 42 \\  & & 0.58492 & 31 & 0.57800 & 35 \\ \cline{1-1} \cline{2-6}  & & 0.58932 & 28 & 0.57600 & 37 \\ \cline{1-1}  & & 0.58512 & 30 & 0.56740 & 48 \\ \cline{1-1}  & & 0.57172 & 42 & 0.57600 & 37 \\ \hline Average \(E\) (GPa) Short beam \(w/c=0.42\) & 30.92 \(\pm\) 5.107 (16.52\%) & 38.67 \(\pm\) 3.37 (8.73\%) \\ \hline Cylinder \(w/c=0.42\) & & 41.1 \(\pm\) 1.389 (3.38\%) & \\ \hline Cylinder \(w/c=0.45\) & & 37.6 \(\pm\) 1.815 (4.82\%) & \\ Cylinder \(w/c=0.50\) & & 31.8 \(\pm\) 1.907 (6.00\%) & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Time of flight and modulus of elasticity of the beams in which Condition 4 was imposed. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Condition** & _E (GPa)_ **Mean \(\pm\) Standard Deviation** & **RSD (\%)** \\ \hline
1 & 31.44 \(\pm\) 0.966 & 3.07 \\
2 & 31.13 \(\pm\) 1.558 & 5.00 \\
3 & 32.37 \(\pm\) 1.354 & 4.18 \\
4 & 29.42 \(\pm\) 2.660 & 9.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The modulus of elasticity of the beams in which different conditions are measured by UPV (ultrasonic pulse velocity) test. be evaluated. The method aimed at determining the modulus of hardened concrete, in particular to estimate the water-to-cement ratio in a concrete volume close to an HNSW transducer. We demonstrated that the transducers designed and assembled to exploit the principles offer sufficient repeatability and reliability to identify the differences in the amount of water purposely added to the beams in order to mimic rainfall situations. Owing to the nature of concrete material, it is acknowledged that the \(w/c\) ratio is likely not to be the only concrete parameter affecting the amplitude and the time of flight of the reflected solitary wave. Future studies should look at the effect of the aggregate size and overall any other factor that is known to influence the Young's modulus of concrete. Nonetheless, the study presented in this paper is the first attempt to prove that solitary waves can be used to measure water in excess in concrete surfaces. The advantages of the proposed HNSW-based method are the easy and fast implementation, the possibility to carry out a large number of tests simultaneously, and independence upon internal damage and/or the presence of reinforcing steels inside the concrete. Finally, being a local and contact method, the approach can be successfully applied to characterizing effects of finishing and curing conditions. Figure 5 showed that the measured values of \(E\) are on a part of the curve that is not extremely favorable for sensitivity. Future studies should redesign the metamaterial, such as different sized or different modulus balls, in order to shift the region of influence in a range where a large change in the TOF gives rise to small variation of the Young modulus. Such a region would consent to discriminate small differences in the Young modulus due to changes in the \(w/c\) ratio.