## 4 Experimental Results and Discussion  
### Intact Cement Mortar Specimens under Three-Point Bending  
For the specimen loaded at a constant rate equal to 66 N/s (specimen LR1), a number of N = 580 acoustic hits were recorded until the fracture instant. The temporal evolution of the load applied is plotted in Figure 2a, in juxtaposition to that of the amplitude of the acoustic hits. The fracture instant was detected at t\({}_{\text{f}}\) = 56.3 s. The respective evolution of these quantities in the Natural Time domain is plotted in Figure 2b. In this figure, each acoustic hit is located at a \"distance\" equal to \(\Delta\chi\) = 0.0017 from the two neighbor acoustic hits (i.e., the one at the left and the one at the right). Adopting now the methodology described in Section 2 (Table 1), the values of the F-function were calculated using a sliding window of n = 15 successive interevent times, and each value was associated to a unique value of the Natural Time X. In this way, it became possible to plot the evolution of the F-function and also, of the Load, versus the Natural Time parameter, X, as it is seen in Figure 3. In this figure the short, thick, blue, linear segment represents the very last value of the F-function, which corresponds to the width of the sliding window of the last n = 15 acoustic hits recorded before macroscopic fracture (i.e., from \(\chi_{\text{N}-\text{n}+1}\) to \(\chi_{\text{N}}\)). It is obvious from Figure 3, that, in the 0.72 \(<\) X \(<\) 0.92 interval (see the green-shaded rectangle), the F-function is almost perfectly governed by a power law of the form:  
\[\mathrm{F(X)}=\mathrm{A}\cdot\mathrm{X^{m}} \tag{5}\]  
The fitting procedure (red line in Figure 3) provides for the exponent m a numerical value equal to m = 8.0. It is worth noticing that, in this region of X-values, the load applied increases from about 95% to almost 99% of the maximum value attained before macroscopic fracture (Lmax\(\approx\)3.74 kN). As mentioned previously, fracture occurred at the instant t\({}_{\mathrm{f}}\) = 56.3 s and, therefore, the time interval 0.72 \(<\) X \(<\) 0.92 corresponds to the time interval 0.4 s \(<\) t\({}_{\mathrm{f}}\)-t \(<\) 2.9 s. As a first conclusion, it can be said that the rapid increase of the F-function, observed a few seconds before fracture, is described excellently by the power law given by Equation (5), which is identical to the law suggested in ref. [13] for a completely different material. This conclusion is in full accordance with the findings of [PERSON] et al. [10], who studied the response of concrete specimens and concluded that, at the stage of the accelerated growth of microcracks, the F-function starts increasing, rapidly attaining its maximum value. Moreover, it is quite interesting to note that, at the specific interval of X-values (i.e., the 0.72 \(<\) X \(<\) 0.92 interval), additional quantities (as for example the cumulative counts) appear being governed by a similar power law in case their evolution is described in the Natural Time domain. Further details concerning the evolution of the cumulative counts will be given in Section 5 (Discussion and Concluding remarks). The procedure adopted for the analysis of the data of the LR1 test is now applied for the study of the LR2 test, in which the specimen was loaded at a higher rate, equal to 80 N/s. In  
Figure 3: The evolution of the F-function versus the Natural Time X in juxtaposition to the respective evolution of the Load applied for the LR1 test. Figure 2: The temporal evolution of the load applied, in juxtaposition to that of the amplitude of the acoustic hits, in (**a**) the conventional- and (**b**) the Natural-Time domains, for the LR1 test. this test, N = 734 acoustic hits were recorded until the time instant of macroscopic fracture. The temporal evolution of the load applied is plotted in Figure 4a, again, in juxtaposition to the amplitude of the acoustic hits.