## 4 Conclusions  
This article studied the influence that a series of parameters, related to the concrete matrix and reinforcement of fiber, have on the compression behavior of SFRC. By means of an extensive search of the scientific literature, a database was compiled, which included a total of 197 uniaxial compression tests performed on \(150\times 300\) mm\({}^{2}\) (diameter \(\times\) height) cylinders. The database included the results of experimental campaigns developed with steel-fiber reinforced concrete with hooked end fibers and a single fold and their respective matrices without steel-fiber reinforcement. The data analysis was performed by means of the response surface methodology, which consisted of a set of statistical and mathematical techniques applied to the creation of data adjustment models, which enabled the optimization of parameters and the search for the interactions that occurred between them. The study  
Figure 11: Pareto diagram and response surface of \(\sigma_{R}^{*}\). was done with first and second degree polynomic adjustment models. The latter was eliminated for not correctly predicting the responses in the domain of the definition of the factors and for presenting strong multicollinearity. Firstly, the descriptive variables of the compression response of the SFRC (\(f_{cf}\), \(E_{cf}\), \(\epsilon_{cf}\), \(W_{1f}\), and \(W_{2f}\)) were selected and correlated with factors associated with the matrix without reinforcement (\(f_{c}\) and \(d_{m}\)), with factors that define the geometry of the fiber (\(\ell_{f}\), \(d_{f}\), and \(\lambda\)), with its content (\(\phi_{f}\)), and the relationship between the sizes of the fiber and aggregate (\(\ell_{f}/d_{m}\)). From the analysis performed, it was found that \(\phi_{f}\) was statistically significant for all the responses and that \(f_{c}\) was also significant, except for \(W_{2f}\), which corresponded to the work on post-crack volumetric deformation. In addition, both of them were the only factors in which multicollinearity was not present. The so-called fiber factor, \(\phi_{f}\lambda\), was not found to be significant. Subsequently, the responses and factors were analyzed in a non-dimensional manner. Only the fiber content, \(\phi_{f}\), was significant for all the responses and demonstrated moderate multicollinearity. The fiber length, \(\ell_{f}\), was the next factor that was shown to have a great influence on responses. Both factors, together with the aspect ratio, \(\lambda\), were chosen to analyze the compressive strength model of the SFRC of [PERSON] et al. [42] (it dealt with representative parameters of the geometry and fiber content, used in the majority of the models applied to the SFRC). The proposed model considered the increase of ductility and the energy absorption that the inclusion of fiber to the concrete provided. In particular, its curve, \(\sigma\)-\(\epsilon\), referring to the concrete with fibers, in the softening branch was calculated in such a manner that the subsequent consumption of energy after peak load was equal to the value of that same energy calculated in conformity with the data collected in the database. This softening branch was defined by a parameter, \(\sigma_{R}\), which was the compressive residual strength associated with \(\epsilon=3\,\epsilon_{cf}\). The factor \(\phi_{f}\) was statistically significant in all the responses, and \(\lambda\) was also in \(\epsilon_{cf}\), \(W_{2f}\) and \(\sigma_{R}\). This fact demonstrated that the ductility and the capacity of energy absorption from the maximum stress in the post-cracking phase of the SFRC was governed by the geometry of the fiber through the aspect ratio \(\lambda\) and by its content \(\phi_{f}\). Conceptualization, A.d.l.R. and G.R. ; methodology, A.d.l.R. and G.R. ; software, A.d.l.R. ; validation, A.d.l.R., G.R., and E.P. ; writing, original draft preparation, A.d.l.R. ; writing, review and editing, G.R. and E.P.