## 2 Materials and Methods
### Prototype Simulation
#### 3.3.2 Results of Prototype Simulation  
Table 7 shows detailed results of runoff characteristics of the IRD system according to the various structures. The time of occurrence of the maximum infiltration was simulated to be 176 s and 112 s later, respectively. The peak of surface runoff exists at 587 and 600 s. When Pr-Pe4S10 designed as a multiple-structure was applied, the retention effect was demonstrated by slowing the time of maximum surface runoff through relatively fast maximum penetration compared to the cases of control group. It was found that the maximum infiltration flow rate was reduced by 81.21% compared to Pr-Pe0S10, an impervious drainage system. It can be concluded due to these changes in runoff characteristics, that when the IRD system with a multiple structure was applied to cities and watersheds, surface runoff decreases with retention effects by infiltration (Figure 17). The hydrograph of the various structure cases showed that the runoff characteristics of the initial rainfall duration of 600 s were significantly changed according to the surface slope. Table 8 shows the runoff characteristics for each case according to the cross-slope. The maximum penetration occurred at 2.1 \(\times\) 10\({}^{-3}\) m\({}^{3}\)/s, 112 s in the case Pr-Pe4S10 with 0% cross-slope. In addition, the maximum surface runoff reduction rate according to the slope was 69-81%, and the deviation according to the cross slope was about 12%. The cross slope was analyzed as a major design factor of the IRD system. The maximum surface runoff was simulated as 3.93 \(\times\) 10\({}^{-4}\) m\({}^{3}\)/s, 7.29 \(\times\) 10\({}^{-4}\) m\({}^{3}\)/s, and 7.99 \(\times\) 10\({}^{-4}\) m\({}^{3}\)/s, respectively, as the cross slope increased, indicating a proportional relationship between the slope and the maximum surface runoff. In case of total infiltration, 0.923 m\({}^{3}\), 0.742 m\({}^{3}\), and 0.756 m\({}^{3}\) were simulated. Thus, the design of an excessive cross slope may cause an increase in the burden on the drainage system during high-intensity heavy rain (Table 8). The surface runoff and infiltration of the IRD system with respect to the permeability of the pavement \begin{table}
\begin{tabular}{c c c c} \hline
**Case No.** & **\(\Delta t\) (Second)** & **\(\Delta x\) (mm)** & **Mass Error (\%)** \\ \hline \multirow{4}{*}{Pr-Pe0S10} & 0.10 & 3 & \(-2\) \\ \cline{2-4}  & 0.15 & 4 & \(-4\) \\ \cline{2-4}  & 0.03 & 2 & 3 \\ \hline \multirow{4}{*}{Pr-Pe1S10} & 0.07 & 3 & 17.7 \\ \cline{2-4}  & 0.10 & 5 & 16.3 \\ \cline{2-4}  & 0.10 & 4 & 17.2 \\ \cline{2-4}  & 0.20 & 3 & 17.5 \\ \cline{2-4}  & 0.50 & 5 & 12 \\ \hline Pr-Pe2S10 & 0.20 & 2 & 7.4 \\ \hline \multirow{4}{*}{Pr-Pe3S10} & 0.20 & 3 & 15.2 \\ \cline{2-4}  & 0.05 & 5 & 9.9 \\ \cline{2-4}  & 0.03 & 3 & 2 \\ \hline \multirow{4}{*}{Pr-Pe4S10} & 0.03 & 5 & 153 \\ \cline{2-4}  & 0.20 & 3 & 7 \\ \cline{2-4}  & 0.30 & 3 & 14 \\ \hline \multirow{4}{*}{Pr-Pe4S13} & 0.05 & 3 & 12 \\ \cline{2-4}  & 0.10 & 3 & 11 \\ \cline{1-1} \cline{2-4}  & 0.20 & 3 & 10 \\ \cline{1-1} \cline{2-4}  & 0.30 & 2 & 6 \\ \hline Pr-Pe4S15 & 0.10 & 3 & 8 \\ \hline \end{tabular}
\end{table} 
Table 6: Results of mass conservation error of prototype model (with respect to time and space interval). Table 9 shows the maximum surface runoff, infiltration, and the timing of each occurrence. The maximum permeability occurs in Pr-Pe2S10, which had the largest permeability, but the decrease in the maximum surface runoff occurred in Pr-Pe4S10, which had the least permeability. In the case of Pr-Pe3S10, the time at which the maximum surface runoff occurs increases by 20 s, so it can be concluded that the urban water circulation problem can be solved if the delay time was designed with the permeable design. Figure 16 shows the surface runoff and infiltration of permeable rainwater drainage systems with respect to the permeability of the pavement. When the IRD system was applied, it was simulated that the surface runoff was reduced significantly (Figure 19).