## 3 Results and Discussion
### Quasi-Static Mechanical Characterization  
Tables 3 and 4 include the quasi-static mechanical characterization carried out for both hydraulic lime concretes (with and without PVA fibers) at 28 and 156 days. The data is also depicted in three bar plots in Figure 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Slump [mm]** & **Density [kg/m\({}^{3}\)]** \\ \hline FFLC-0.0 & 65 & – \\ FFLC-0.3 & 53 & 2132 \\ FFLC-0.6 & 65 & 2130 \\ FFLC-0.9 & 50 & 2146 \\ FFLC-1.2 & 55 & 2164 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Slump in the Abrams cone test and density values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & \(f_{e}\) **[MPa] (28 Days)** & \(f_{e}\) **[MPa] (156 Days)** & \(E\) **[GPa] (28 Days)** \\ \hline FFLC-0.0 & 1.7 (0.2) & 1.5 (0.1) & 7.1 (1.1) \\ FFLC-0.3 & 1.8 (0.1) & 1.7 (0.1) & 3.9 (1.2) \\ FFLC-0.6 & 2.0 (0.1) & 2.2 (0.1) & 3.2 (0.8) \\ FFLC-0.9 & 2.2 (0.1) & 2.2 (0.0) & 4.3 (0.3) \\ FFLC-1.2 & 2.5 (0.1) & 2.5 (0.1) & 2.5 (0.3) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quasi-static mechanical tests characterization results: \(f_{c}\), compressive strength; \(E\), elastic modulus (mean values, standard deviation in parentheses). Figure 2: Configuration for a three-point bending test setup. By the initially established \(w/\ell\) ratio during the design of the base or matrix concrete, the expected compressive strength value is achieved in all cases. Table 3 reflects how the compressive strength increases as the fiber content rises (at 28 and 156 days). While the primary effect of fiber inclusion in concrete pertains to increased ductility and toughness [41], in these cases, high fiber quantities generate a confinement effect that substantially enhances compressive strength in this type of low-strength concrete. Furthermore, Table 3 and Figure 3 show that at 156 days of age, the compressive strength of the concretes approximately matches that of 28 days, confirming that the material no longer evolves in terms of its mechanical behavior. Regarding the modulus of elasticity, Table 3 and Figure 3 indicate variability in terms of its reduction as fiber is added, except for a fiber quantity of \(\phi_{f}=0.9\%\), where an increase is observed. This could result from the greater or lesser degree of matrix disintegration due to fiber addition, as well as a potential limit or optimum value beyond which the modulus undergoes a drastic reduction. In this research, we have drawn an analogy with flexural and residual flexural strengths since, instead of being defined for crack opening values, we refer to vertical displacement values here. In other words, \(\sigma_{R1}\) will denote the residual flexural strength value for 0.5 mm of vertical displacement of the load application point instead of 0.5 mm of crack opening. The same procedure is followed for the remaining flexural and residual flexural strengths. Figure 3: (a) \(f_{c}\) at 28 days, (b) \(f_{c}\) at 156 days, and (c) \(E_{c}\) at 28 days, in a quasi-static regime. Figure 4a compares the calculated values of \(\sigma_{N}\) under quasi-static and dynamic conditions, with loading rates \(v_{1}=4\times 10^{-4}\) mm/s and \(v_{2}=4\) mm/s, respectively. In the quasi-static regime, as \(\phi_{f}\) increases, so does \(\sigma_{N}\), reaching its maximum value at \(\phi_{f}=0.009\). In the dynamic regime, there is likewise an increasing trend for \(\sigma_{N}\) as \(\phi_{f}\) is augmented, except at \(\phi_{f}=0.006\), where it decreases relatively. Additionally, values of \(W_{F}\) have been measured at both loading rates for fiber-unreinforced concretes up to 0.5 mm of vertical