## 5 Numerical Simulation  
### Suggestion of Compressive and Tensile Stress Blocks  
To predict the flexural behavior of plain concrete and SFRC pedestrian decks, a sectional analysis was conducted because this method can adopt actual compressive and tensile stress blocks based on RILEM TC 162-TDF recommendation [15]. Although several compressive stress-strain models were suggested for SFRCs and well summarized by [PERSON] and [PERSON] [33], we simply adopted a parabolic compressive stress-strain model for both plain concrete and SFRC, as recommended by the RILEM TC 162-TDF: the compressive stress parabolically increases with strains of up to 85% of the compressive strength and then it is assumed to be maintained up to a strain value of 0.0035 (Figure 12). This is caused by the fact that the parabolic model can be simply adopted, and it is a minor factor influencing the accuracy of section analysis for reinforced SFRC decks. In contrast, the tensile stress-strain model is different for the plain concrete and SFRC. It is assumed that there is no contribution of plain concrete beyond its tensile strength (after cracking), whereas the tensile force at the crack surface can be resisted by steel fibers up to a strain value of 0.025 for the case of SFRC. The characteristic parameters of the tensile stress-strain model for SFRC shown in Figure 12 are obtained from three-point bending test results of notched beams and formulae suggested by the RILEM recommendation [15]. Before reaching the tensile strength (\(\sigma_{1}\)), SFRC is assumed to exhibit a linear elastic behavior (\(\sigma=E_{c}\varepsilon\)), and its elastic modulus (\(E_{c}\)) is calculated based on the following equation given by [PERSON] et al. [34]: \(E_{c}=\left(-36\sigma_{V}\frac{l_{f}}{d_{f}}+5520\right)f_{c}^{0.41}\), where \(\sigma\) is the tensile stress, \(\varepsilon\) is the tensile strain, \(v_{f}\) is the fiber volume fraction, \(l_{f}\) is the fiber length, and \(d_{f}\) is the fiber diameter. The tensile strength (\(\sigma_{1}\)) and strain capacity (\(\epsilon_{1}\)) is also calculated by \(\sigma_{1}=0.7f_{f1}(1.6-d)\) and \(\epsilon_{1}=\sigma_{1}/E_{c}\), where \(f_{h}\) is the flexural strength and \(d\) is the effective depth. After the tensile strength, a bilinear softening curve was obtained until the ultimate strain value of 0.025. The characteristic tensile stresses and strains in the softening zone (\(\sigma_{2}\), \(\sigma_{3}\), \(\epsilon_{2}\), and \(\epsilon_{3}\)), as shown in Figure 12, can be calculated based on the following equation:  
\[\sigma_{2}=0.45f_{eq,2}k_{h} \tag{8}\]  
\[\sigma_{3}=0.37f_{eq,3}k_{h} \tag{9}\]  
\[\epsilon_{2}=\epsilon_{1}+0.0001 \tag{10}\]  
\[\epsilon_{3}=0.025 \tag{11}\]  
where \(f_{eq,2}\) and \(f_{eq,3}\) are equivalent strength parameters and \(k_{h}=1.0-0.6\frac{h-12.5}{47.5}|12.5\leq h\leq 60|\) (in cm). The equivalent strength parameters are calculated based on the three-point bending test and RILEM recommendation [15] as follows:  
\[f_{eq,2}=\frac{3}{2}\frac{D_{BZ,2}^{f}}{0.5}\frac{L}{b(h-a_{0})^{2}} \tag{12}\]  
\[f_{eq,3}=\frac{3}{2}\frac{D_{BZ,3}^{f}}{2.5}\frac{L}{b(h-a_{0})^{2}} \tag{13}\]  
where \(D_{BZ,2}^{f}\) and \(D_{BZ,3}^{f}\) are the energy absorption capacities up to the deflections of \(\delta_{2}\) and \(\delta_{3}\), respectively (\(\delta_{2}=\delta_{L}+0.65\) mm, \(\delta_{3}=\delta_{L}+2.65\) mm), \(\delta_{L}\) is the deflection corresponding to the flexural strength at the LOP (\(f_{L}\)), \(L\) is the clear span length, \(b\) is the beam width, \(h\) is the beam height, and \(a_{0}\) is the notch depth. In order to calculate the energy absorption capacities by the fibers only, the energy absorbed by matrix (\(D^{b}{}_{BZ}\)) was neglected from the values of \(D^{f}{}_{BZ,2}\) and \(D^{f}{}_{BZ,3}\) based on the values of \(f_{L}\) and \(\delta_{L}+0.3\) mm [5]. Therefore, the equivalent strength parameters and the characteristic tensile stresses in thesoftening zone are purely based on the fiber bridging capability of steel fibers.