## 3 Derailment Simulation Using the Simplified FEA Model
### Model Validation through Comparisons with Real-World Accidents  
This study compared the simulated 2D level train derailment behaviour with a real-world accident that occurred on 22 April 2016, in Republic of Korea, which is known as the \"Yulchon Station Derailment\". This accident was caused by speeding when approaching a turnout, which resulted in a wheel-climb derailment. Although only a few passengers were on board, the accident could have resulted in a significant disaster under alternative circumstances. The first locomotive overturned approximately 150 m from the derailment point, and the second train stopped approximately 200 m from this point after rotating by 180\({}^{\circ}\) as shown in Figure 8[25]. The simulation was compared with the Yulchon Station Derailment accident to verify the total displacement and horizontal course of the first vehicle after derailment. Additionally, the possibility of vehicle overturning was confirmed by calculating the gravitational force at the centre of gravity of the train and the resultant force due to lateral acceleration [26; 27]. As shown in Figure 9, when a vehicle is travelling along a curved track or following a derailment event, gravitational acceleration continues to act in the direction of the ground at the centre of gravity of the vehicle, and a centrifugal or lateral force is generated. The load on the wheel is reduced depending on the location of the resultant force, causing tilting. Railway tracks generally use carts and slacks, while railway vehicles use dampers or tilting devices to prevent this phenomenon. However, this study simply assumes that derailment and rollover occur when the point of action of the vertical and lateral forces acting on the vehicle's centre of gravity deviates from the end points of the wheels. Therefore, the aforementioned characteristics were excluded, and the simulation was compared to a real-world accident. The rollover limit lateral velocity could be calculated using the height of the vehicle's centre of gravity, the distance between the wheel tips, and gravitational acceleration. Based on investigation reports, the analysis was carried out assuming a fixed speed of 117 km/h (32.5 m/s) at the time of derailment while considering the angular velocity and frictional state of the derailment [25]. In addition, the lateral acceleration limit for determining vehicle rollover was assumed to be 1.7 m, which is the centre of gravity height of KTX vehicles currently used in Korea [27], and the spacing of the wheel tips was set to 1.4 m. Gravitational acceleration was assumed to be 9.8 m/s\({}^{2}\), which is approximately  
Figure 8: Yulchon Station Derailment in Korea [25]. 4 m/s\({}^{2}\). The simulation behaviour was analysed at an angular velocity \(v_{R}\) of 0.20 rad/s and friction rate \(\mu_{B}\) of two. As shown in Figures 10 and 11 and Table 4, unlike the actual accident, the simulation showed that the second vehicle derailed, yawed, and collided with the third vehicle. In addition, it was confirmed that the displacements in the driving direction of the following cars from vehicle number four were more significant than the actual accident. This is because, due to the nature of this simplified model, structural friction and detailed characteristics, such as structural friction between vehicle wheels, rails, and components, and energy dissipation due to vehicle and connection failure, are not reflected in the actual railroad track environment [15; 16; 17; 18]. Furthermore, although the total displacement after the derailment of the first vehicle differed from that in the real accident, an analysis of lateral acceleration indicated that the possible moment of overturn occurred at 4.8 s in Figure 12, and the displacement of the first vehicle at that time was 136.78 m. This difference can be attributed to the characteristics of the model, which do not consider the sudden deceleration and behaviour due to overturning. Figure 10: Behaviour after derailment: real-world scenario.