## 3 Results and Discussion
### Stress-Strain Model of the Compression Response for SFRC  
This section will study the influence that the factors \(\ell_{f}^{*}\), \(\lambda\), and \(\phi_{f}\) had on the SFRC compression model proposed by [PERSON] et al. [42]. The most important aspect that must be highlighted is the gain in the capacity of energy absorption that the addition of steel-fibers in the concrete provides. It may increase up to 45% in the segment prior to the peak load and reach almost three times more in the segment subsequent to the peak load in average values with respect to the concrete without fiber reinforcement. In addition, once the maximum load has been surpassed, \(W_{2f}\) may reach a maximum value five times greater than the matrix without fiber. This fact demonstrates the increase in ductility that a structural element of SFRC, requested at uniaxial compression, may exhibit. Table 4 shows the statistical values of each one of the analyzed responses of the compression strength of SFRC obtained from the tests included in the database. From the linear adjustment and the statistical analysis of the relationships between the defined variables, the \(\beta_{i}\) coefficients of the model were calculated. They are included in Table 5. Figures 6-9 represent the Pareto diagrams for the \(f_{c}^{\circ}\), \(\epsilon_{c}^{\circ}\), \(W_{1}^{\circ}\), and \(W_{2}^{\circ}\) responses, as well as the adjustment diagrams of their response surfaces with respect to the statistically significant factors. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \(\mathbf{\beta_{0}}\) & \(\frac{d_{a}}{\ell_{a}}\) & \(\frac{\ell_{f}}{\ell_{a}}\) & \(\frac{d_{f}}{\ell_{a}}\) & \(\lambda\) & \(\phi_{f}\) & \(\frac{\ell_{f}}{\ell_{a}}\) & \(\mathbf{R_{a}^{2}(\%)}\) \\ \hline \(f_{c}^{\circ}\) & \(1\) & \(0.259\) & \(\mathbf{0.1176}\) & \(-\mathbf{11.65}\) & \(-0.00178\) & \(\mathbf{3.75}\) & \(0.0223\) & \(10.7\) \\ \(E_{c}^{\circ}\) & \(--\) & \(--\) & \(--\) & \(--\) & \(--\) & \(--\) & \(--\) & \(--\) \\ \(e_{c}^{\circ}\) & \(1\) & \(0.254\) & \(-0.0089\) & \(-3.35\) & \(-0.00261\) & \(-\mathbf{13.94}\) & \(0.0363\) & \(40.0\) \\ \(W_{1}^{\circ}\) & \(1\) & \(-\mathbf{1.889}\) & \(\mathbf{0.437}\) & \(19.1\) & \(0.0085\) & \(\mathbf{48.62}\) & \(-0.253\) & \(35.2\) \\ \(W_{2}^{\circ}\) & \(0.98\) & \(-3.13\) & \(0.99\) & \(-13\) & \(0.0375\) & \(\mathbf{110.8}\) & \(-0.58\) & \(54.3\) \\ \hline \end{tabular}
\end{table} 
Table 3: Coefficients of \(\beta_{i}\) adjustment of the \(x_{i}\) factors in the linear models with non-dimensional responses (bold = statistically significant). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mean** & **(Std. dev.)** & **[Max.–Min.]** \\ \hline \(f_{c}^{\circ}\) & \(1.04\) & \((0.12)\) & \([0.69\)–\(1.34]\) \\ \(E_{c}^{\circ}\) & \(0.99\) & \((0.08)\) & \([0.76\)–\(1.21]\) \\ \(\epsilon_{c}^{\circ}\) & \(1.27\) & \((0.30)\) & \([0.93\)–\(2.51]\) \\ \(W_{1}^{\circ}\) & \(1.45\) & \((0.52)\) & \([0.91\)–\(3.73]\) \\ \(W_{2}^{\circ}\) & \(2.83\) & \((1.09)\) & \([1.12\)–\(5.49]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of the responses of the parameters of the \(\sigma\)-\(\epsilon\) model for SFRC proposed by [PERSON] et al. [42].