## 3 Results
### Flow Analysis and Drag Force at Human Models  
When underground space is flooded, stairs can become a major evacuation facility but also can cause flood flow with strong momentum, which can affect walking stability. Therefore, we analyzed the effect on safety by analyzing the time change in drag force caused by flood flow for people trying to evacuate by stairs. For analysis using human models to specific areas near and on the stairs, the changes to the external force to the human body due to flow changes were investigated.  
Pressure changes occurring in the lower body of the human model according to changes in water depth and flow rate were analyzed. Figure 11 shows the pressure from the water flow applied to the lower legs of the human model in the various flood simulations of Q1, Q2, and Q3. The maximum pressure location is shown, which depends on the flowrate and depth of the water flow. Depending on the flowrate, the pressure from the inundation shows the pressure forming from the ankles to the calf area, and higher flowrate shows higher values that reach maximum values near the knee, as the inundation depth also increases in higher flow rates. Lower flowrates of Q1 with 0.67 m\({}^{3}\)/s showed maximum pressure occurring around 0.16 m in depth, while higher flowrates of Q3 with 1.88 m\({}^{3}\)/s had the maximum pressure at about 0.28 m in depth with higher inundation depth.  
Figure 10: Risk percentage changes of sliding and toppling by time of inflow.  
Figure 9: Result of estimation of sliding and toppling critical velocities.  
Then, the changes to the velocity and depth near the 3 models located in different places near and on the stairs were analyzed. Figure 12 shows the simulated velocity result and water surface near the 3 models each located below the stairs, middle of the stairs, and distance from the stairs. For the model right below the stairs in Figure 12a-c, the velocity reached up to 6.4 m/s, while the depth was about 0.4 m. Figure 12d shows the model in the middle of the stairs, where the nearby velocity was 4 m/s, and the depth was 0.1 m. The velocity would eventually increase up to 4.6 m/s and 0.37 m in depth in Figure 12f. Finally, in Figure 12g-i, the model located distance from the stairs showed the velocity increasing up to 2.9 m/s, and the depth was 0.65 m. This depicts the hydraulic changes near the models in different locations of the underground station.  
As a result of the pressure change in the lower body of the human model according to changes in the flowrate in Figure 13, the size of the drag force increased by approximately 304%, as the flow increased by about 176% on average. This shows the effect of flow rate conditions on the size of the drag force on the human model. Higher drag force values are seen below the stairs than the mid-stairs, which is due to the gravitational acceleration being applied to the flow coming downstairs. This conforms to former research where jet flow below stairs would affect human stability [29]. Also, the drag force changes timewise  
Figure 11: Result of calculation of pressure changes due to discharge.  
Figure 12: Simulated velocity near the human models.  
for different human model locations were analyzed. It showed that as the human model was located at a certain distance from the stairs, the drag force would increase accordingly to the time of inflow, but values of drag force at the center of stairs and below stairs did not have difference timewise, due to the fact that high flow would have instantaneous effect of drag force, as the flood flow propagation ended within 10 s within the stairs, so there was almost no change in drag force over time. On the other hand, for the model located at a distance from the stairs, the drag force gradually increased up to 40 s.