## 4 Results and Discussion
Based on the relationships \(A_{2}=\beta_{2}A_{1}{}^{2}\) and \(A_{3}=\beta_{3}A_{1}{}^{3}\), the nonlinearity parameters \(\beta_{2}\) and \(\beta_{3}\) were determined [47; 56; 57; 58; 59; 60]. Based on the above, it becomes obvious that \(A_{2}\) over \(A_{1}{}^{2}\) and \(A_{3}\) over \(A_{1}{}^{2}\) should have a linear slope, since other variables such as sample length and ultrasonic frequency remain constant during the test (Figure 7b,c). Recording harmonic oscillations during the fluid phase is very difficult due to high attenuation [2]. This issue was solved, using the high power pulser RPR-4000. During the hardening process, noticeable changes in the nonlinear parameter occurred that relate to microstructural changes in the material. The attenuation during the first few hours is too high, but the chemical activity within the material continues to develop. During this stage, a decrease in the nonlinear parameters occurs due to the micromechanical interconnection of the forming particles. Figure 8 presents the nonlinear parameters \(\beta_{2}\) and \(\beta_{3}\) as a function of time for the cement paste for the different CNT concentrations. Since the water to cement ratio is constant for all specimens, the changes in the nonlinear parameters for the different specimens are due to the different percentage of the carbon nanotubes. Figure 6: Difference in temperature for cement paste and mortar with absence of nanoinclusions. Figure 8: Nonlinear parameters for cement paste with **(a)** 0% CNTs, **(b)** 0.2% CNTs, **(c)** 0.4% CNTs and **(d)** 0.6 % CNTs. Figure 7: (**a**) Long-term stability test of the measurement system at room temperature, (**b**) Assessment of the system linearity for the second harmonic and (**c**) Assessment of the system linearity for the third harmonic. Figure 9 depicts a summary diagram of the nonlinear parameters \(\beta_{2}\) and \(\beta_{3}\) (Figure 9a,b, respectively) as a function of time for the CNT-reinforced cement paste samples. It can be observed that higher CNT concentrations correspond to higher relative nonlinear parameter values for both the second and third order nonlinear parameter. Furthermore, the third order nonlinear parameter \(\beta_{3}\) is more sensitive to microstructural modifications in the material during its hardening process. It was observed that, as the percentage of nanotubes in cement matrix increases, the values of nonlinear parameters also increase. During the first 18 h of the experiment, the nonlinear parameter values were higher in comparison to the following hours, when they reached a plateau. The changes were even more pronounced in the third harmonic parameter. This indicates that the third harmonic oscillation is much more sensitive to the material's microstructural changes. Microstructural changes during the first hours occur in the fresh cement paste. The chemical reactions in the material are rapid and the sample undergoes progressive mechanical setting. In addition, the carbon nanotube mesh is integrated into the cement matrix. These alterations are less dramatic after the first 18 h. Regarding the mortar samples with the different carbon nanotube concentrations, the results were similar to those obtained for the cement paste samples, as it is shown in Figure 10.  
Figure 10: Nonlinear parameters for mortar with **(a)** 0% CNTs, **(b)** 0.2% CNTs, **(c)** 0.4% CNTs and **(d)** 0.6 % CNTs. Figure 3:0 Nonlinear parameter (**a**) \(\beta_{2}\) and (**b**) \(\beta_{3}\) as a function of time for CNT-reinforced cement paste specimens. Figure 11 shows a summary diagram of the nonlinear parameters \(\beta_{2}\) and \(\beta_{3}\) (Figure 9a,b, respectively) as a function of time for the CNT-reinforced mortar specimens. It can be observed that higher CNT concentrations correspond to higher relative nonlinear parameter values for both the second and third order nonlinear parameter. The third order nonlinear parameter \(\beta_{3}\) is also found to be more sensitive to microstructural modifications in the material during its hardening process.