## 3 Results and Discussion
### Stress-Strain Model of the Compression Response for SFRC
Its corresponding characteristic value is:  
Figure 6:2  
It should be noted that Equations (13) and (14) are defined only for concretes with a minimum fiber content and thus, they do not provide negative values (indeed, all the SFRCs in the database yielded positive residual strengths since the minimum values in the database for \(\phi_{f}\) and \(\lambda\) were 0.0024 and 20, respectively). It should be reminded that \(\sigma_{R}^{*}\) can also be obtained from experimental \(\sigma\)-\(\epsilon\) records using Equation (8). It bears emphasizing that both \(f_{c}^{\circ}\) and \(\sigma_{R}^{*}\) were calculated in mean values since the database contained exclusively the tests' results. Nevertheless, in light of the concept of characteristic resistance (expressed as that corresponding to the quantile of 5% in the distribution of resistances obtained in a group of tests on similar specimens), Equations (11) and (14) were determined. They permit calculating the characteristic values of \(f_{c}^{\circ}\) and \(\sigma_{R}^{*}\), if one wishes to work with them. The residual compressive strength can also be related to the residual flexural strengths \(f_{R,\mathrm{1k}}\) and \(f_{R,\mathrm{3k}}\), which are the flexural strengths for crack mouth opening displacements of 0.5 mm and 2.5 mm. [PERSON] et al. [71] showed that the dimensional and non-dimensional expressions relating these parameters, on average and in characteristic fashion, are:  
Figure 6:3  
Figure 6:4  
Figure 6:5  
Figure 6:6 Linear adjustment with the average and characteristic values of \(f_{c}^{\circ}\). Figure 6:7  
The residual flexural strengths \(f_{\rm{R,1k}}\) and \(f_{\rm{R,3k}}\) in Equations (15)-(18) were introduced in MPa\({}_{2}\) the residual compression strengths \(\sigma_{R}\) and \(\sigma_{\rm{RK}}\) were obtained in MPa, whereas \(\sigma_{R}^{*}\) and \(\sigma_{\rm{RK}}^{*}\) were non-dimensional. Equations (15)-(18) were derived from an RSM study on a flexural database with experiments reported by [PERSON] et al. [72]. Note that non-dimensional values of the residual compressive strength depended only on \(f_{\rm{R,1k}}\) because the ratio \(f_{\rm{R,3k}}/f_{\rm{R,1k}}\) was not found to be significant for them [71]. It bears emphasizing that fibers greatly enhanced both flexural and compressive SFRC behavior as compared with the same values of the corresponding base concrete. However, so far, it was only the flexural behavior of SFRC that was accounted for by the standards in [68,69], to the extent that the characteristic residual flexural strengths \(f_{\rm{R,1k}}\) and \(f_{\rm{R,3k}}\) were taken as indices to perform an SFRC classification [69]. Consequently, as stated in [71], it is appropriate to relate the residual compressive strength \(\sigma_{R}\) to its flexural counterparts, not only to the fiber parameters. In the responses \(\epsilon_{c}^{\circ}\), \(W_{1}^{\circ}\), \(W_{2}^{\circ}\), and \(\sigma_{R}^{*}\), the \(\phi_{f}\) factor was statistically significant, and its effect was positive on their variation. \(\lambda\) was also significant on \(\epsilon_{c}^{\circ}\), \(W_{2}^{\circ}\), and \(\sigma_{R}^{*}\) with a positive effect on variability. This demonstrated that the ductility and capacity of energy absorption from the maximum strength in the phase subsequent to the cracking of the SFRC were governed by a parameter related to the geometry of the fiber, such as \(\lambda\), and for the fiber content, \(\phi_{f}\). This result was in line with that set forth by [PERSON] et al. [31,32] for SFRC and by [PERSON] et al. [31,33] for steel-fiber reinforced mortars. As previously explained, the importance of the statistical analysis lies with the determination of the significance of the factors and not with the \(R_{a}^{2}\) goodness adjustment coefficient since this permits determining if a factor has a real influence on the explanation of the response variability. The coefficients \(R_{a}^{2}\) only indicated the dispersion of the data around the mean adjustment surface of the selected linear model.