## 4 Conclusions
\begin{tabular}{l l} \(i\), \(j\) & Index assigned to factors and responses \\ \(k\) & Number of explanatory variables in an RSM adjustment \\ \(\ell_{f}\) & Fiber length \\ \(\ell_{0}=30\) mm & Coefficient to keep non-dimensionality \\ \(\ell_{f}^{*}=\frac{\ell_{f}}{\ell_{0}}\) & Non-dimensional fiber length \\ \(n\) & Number of factors or independent variables \\ \(p\)-value & Statistical parameter to determine statistical significance \\ \(R^{2}\) & Determination coefficient/multiple correlation coefficient \\ \(R_{a}^{2}\) & Adjusted determination coefficient \\ \(R_{f}^{2}\) & Determination coefficient corresponding to estimate \(\hat{\beta}_{j}\) \\ RSM & Response surface methodology \\ SFRC & Steel-fiber reinforced concrete \\ VIF & Variance inflation factor \\ \(W_{1}=\int_{0}^{c_{c}}\sigma dc\) & Volumetric deformation work in the pre-peak branch of unreinforced concrete matrix in \\ \(150\times 300\) mm\({}^{2}\) cylinders \\ \(W_{1f}=\int_{0}^{c_{f}}\sigma dc\) & Volumetric deformation work in pre-peak branch of SFRC in \(150\times 300\) mm\({}^{2}\) cylinders \\ \(W_{2}=\int_{c_{c}}^{3c_{c}}\sigma dc\) & Volumetric deformation work in post-peak branch of unreinforced concrete matrix in \\ \(W_{2f}=\int_{c_{f}}^{3c_{c}}\sigma dc\) & Volumetric deformation work in post-peak branch of SFRC in \(150\times 300\) mm\({}^{2}\) cylinders \\ \(W_{1}^{*}=W_{1f}/f_{c_{f}}\epsilon_{cf}\) & Non-dimensional volumetric deformation work in pre-peak branch of SFRC relative to \\ \(W_{2}^{*}=W_{2f}/f_{c_{f}}\epsilon_{cf}\) & Non-dimensional volumetric deformation work in post-peak branch of SFRC relative to \\ \(W_{1}^{\circ}=W_{1f}/W_{1}\) & Non-dimensional volumetric deformation work in pre-peak branch of SFRC relative to \\ \(W_{1}\) & \\ \(W_{2}^{\circ}=W_{2f}/W_{1}\) & Non-dimensional volumetric deformation work in post-peak branch of SFRC to relative to \\ \(w_{M}\) & Crack mouth opening displacement \\ \(x_{i},x_{j}\) & Factors or independent variables \\ \(y\) & Response or dependent variable \\ \(\beta_{j}\) & Mean value of \(y\) \\ \(g_{i}\) & Estimated value for \(y\) in observation \(i\) \\ \(y_{i}\) & Actual value for \(y\) in observation \(i\) \\ \(a\) & Non-dimensional coefficient \\ \(\beta_{0}\) & Adjusted constant \\ \(\beta_{i}\) & Adjusted coefficient for a linear term \\ \(\beta_{ii}\) & Adjusted coefficient for a quadratic term \\ \(\beta_{jj}\) & Adjusted coefficient for a combined term \\ \(\hat{\beta}_{j}\) & Value for the coefficient \(\beta_{j}\) estimated by the RSM model to obtain the VIF \\ \(\epsilon_{cf}\) & Critical strain at peak load of SFRC in \(150\times 300\) mm\({}^{2}\) cylinders \\ \(\epsilon_{c}\) & Critical strain at peak load of unreinforced concrete matrix in \(150\times 300\) mm\({}^{2}\) cylinders \\ \(\epsilon^{*}=\frac{\epsilon}{\epsilon_{cf}}\) & Strain relative to the critical strain at peak load of SFRC \\ \(\epsilon_{c}^{\circ}=\frac{\epsilon_{cf}}{\epsilon_{c}}\) & Critical strain at peak load of SFRC relative to the critical strain of the corresponding \\ \(\epsilon_{u}\) & Ultimate strain of SFRC in \(150\times 300\) mm\({}^{2}\) cylinders \\ \(\lambda=\frac{\ell_{f}}{\ell_{f}}\) & Fiber aspect ratio \\ \(\xi\) & Error observed in the response \\ \(\sigma\) & Stress \\ \(\sigma_{R}\) & Compressive residual strength; \(\sigma(3\,\epsilon_{cf})\) \\ \(\sigma^{*}=\frac{\sigma}{f_{cf}}\) & Non-dimensional stress \\ \(\sigma_{R}^{*}=\frac{\sigma_{R}}{f_{cf}}\) & Non-dimensional compressive residual strength; \(\sigma^{*}(3)\) \\ \(\phi_{f}\) & Volumetric fiber ratio (steel-fiber volume per m\({}^{3}\)) \\ \end{tabular}