## 3 Results  
### Simulation Results  
The simulation using OpenFOAM for various flood cases for the model in full size instead of the 1/20 in the experiment for the underground station was performed for continuous inundation analysis. The original simulation discharge values were changed to  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Instability** & \(\mathbf{\alpha}\) & \(\mathbf{\beta}\) & \(\mathbf{a_{1}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{b_{2}}\) & **Ref.** \\ \hline \multirow{2}{*}{Toppling} & 3.472 & 0.188 & \multirow{2}{*}{0.633} & \multirow{2}{*}{0.367} & \multirow{2}{*}{0.00102} & \multirow{2}{*}{\(-0.0049\)} & [PERSON] et al. [15] \\  & 0.6952 & & \(-\)1.064 & & & & [PERSON] et al. [17] \\ \multirow{2}{*}{Sliding} & 7.975 & 0.018 & 0.633 & 0.367 & 0.00102 & \(-\)0.0049 & [PERSON] et al. [15] \\ \hline \end{tabular}
\end{table}
Table 1: Coefficients for the toppling and sliding critical velocities.  
0.67 m\({}^{3}\)/s as discharge Q1 by using the law of similitude, which was the original inflow discharge value of the prototype. Additional simulation conditions were set assuming inflow coming in through the ground stairs, and as the overflow depth of rainwater was assumed to be 0.4 and 0.5 m, the flowrate of 1.35 and 1.88 m\({}^{3}\)/s for discharge Q2 and Q3 was determined through the weir formula assuming a falling flow [23].  
\[Q=C_{d}b\sqrt{g}H^{1.5}. \tag{8}\]  
where \(C_{d}\) is the discharge coefficient, \(H\) is the overflow depth from the top stairs, and \(b\) is the width of the water flow from the stairs leading to B1F. Coefficient C\({}_{d}\) was assumed to be 0.85 using the coefficient values in situations where rainfall at the roads entered into the underground that were changed to discharge values [23]. The assumed maximum overflow depth of 0.5 m is at the knee height of an adult.  
To analyze the effect of flood inundation and its drag force on the human body, additional human models, which depicted 60-year-old females who would be considered feeble to inundation situations were employed in the numerical simulation. To find the flooding effect at the underground stations, the location of human models was placed in 3 locations, which were the middle of the stairs leading to B1F, a location right below the stairs, and a location which was positioned at a distance from the stairs (Figure 3).  
First, the simulation results depicting the entire model were analyzed. Figure 4 shows the depth-averaged velocity of the results of the simulation with discharge inflow of Q1 and Q2 which are 0.67 and 1.33 m\({}^{3}\)/s flowing through all the stairs. The results are shown from 20 to 40 s after the inflow starts from the four stairs, and the inundation level continues to rise as varying velocities of the fluid are shown as it flows around the stairs into the outflow area located at the center of the model. The non-simulated areas at the center would be where the stairs leading to B2F were located in the original experimental model. The highest velocity occurred at the bottom of the stairs with over 3 m/s up to 4 m/s velocity, and the central passage was flooded with high velocities up to 2.5 m/s. Since the flow came through all the stairs, the flow propagation would collide at the center of the model, and the inundation depth would show an instantaneous increase and then later decrease into a lower depth value, as the accumulated water flows to the outflow area in the center. This is displayed in Figure 5e,f as the inflow time changes from 30 s to 40 s where some areas show inundation depth decreasing as the flow continued to 40 s the water reached the outflow region out of the model.  
Figure 3: Model implementation of human figures into simulation.