## 5 Numerical Simulation
### Comparison of Experimental and Numerical Results  
Figure 13 shows the comparative flexural load versus deflection curves of all tested specimens from both the experiments and numerical simulations. In general, the numerical results overestimated the flexural strengths of SFRC pedestrian decks, and the difference between the experimental and numerical results increased with increasing fiber volume contents. The 3D hooked-end fiber specimens resulted in the lowest accuracy, whereas the 5D hooked-end fiber specimens provided the highest one. The flexural strength ratios of the experiment and simulation were found to be approximately 0.75, 0.81, and 0.93 for the 3D, 4D, and 5D hooked-end fiber specimens, respectively. The possible reason for increasing the inaccuracy of numerical results at higher volume contents of fibers is the poorer fiber dispersion and orientation. When we increased the amount of steel fibers, the slump flow values were generally reduced, deteriorating the workability. Furthermore, fiber balls are more easily formed and fiber alignment is easily disturbed at higher fiber volume fractions. Because the pedestrian deck has a  
Figure 12: Material model for sectional analysis.  
much greater width of 1000 mm than the notched beam with 150 mm width, such deteriorated fiber dispersion and orientation characteristics became more obvious, causing the increased inaccuracy of numerical results. The RILEM recommends to take into account the size effect using a section depth, \(d\), in the equation for tensile strength. However, it was insufficient to precisely consider the poorer fiber dispersion and orientation in a larger specimen since they were affected by numerous parameters, such as casting method, viscosity of cement matrix, type and amount of aggregate, etc. The differences between the numerical and experimental results increase with increasing the fiber volume fraction, meaning that the higher amount of fibers is more affected by the parameters. Therefore, a further study is required to take into account the deteriorated fiber dispersion and orientation by increasing the specimen size more accurately.  
Based on the sectional analysis results, the SFRC decks with 0.6% or lower fiber volume fraction exhibited the deflection-softening behavior, whereas that with 1.0% volume fraction provided the deflection-hardening behavior. These observations were very similar to the experimental results that the specimens with \(v_{f}\) of 0.37% and 1.0% provided the deflection-softening and deflection-hardening behaviors, respectively, and that with \(v_{f}\) of 0.6% showed a vague deflection-hardening or deflection-softening behavior.  
As shown in Figure 14, by increasing the amount of steel fibers, higher neutral axis depths were obtained at identical deflections regardless of the fiber type. This is because a higher number of steel fibers can more effectively limit the propagation of flexural cracks into the compressive zone. Moreover, because a greater area of tensile stress block was obtained with higher fiber volume contents, the area of compressive stress block needs to be increased based on the force equilibrium. Similar observations  
Figure 13: Comparative load versus deflection responses: (**a**) 3D fiber, (**b**) 4D fiber, (**c**) 5D fiber.  
were also reported by a previous study [6] for SFRC beams. Thus, it is noted that increasing the amount of hooked-end steel fibers can effectively limit the deep propagation of flexural cracks into the compressive zone.