## 9 Conclusions  
Comparing the theoretical impact force using the Olson model and impact simulations, the study draws the following conclusions:  
1. The Olson model did not consider the lateral stiffness of suspension, resulting in a large difference between the theoretical impact force and the simulated impact force when estimating the impact force of DCP Type \(1\) installed between the rails.
2. To estimate the load transmitted to the DCP, the lateral stiffnesses were considered as a spring-mass model using the wheelset, bogie frame, and bodies of a vehicle. The impact forces were estimated by solving the equations of motion. The calculated response of the dynamic equations showed that the average impact force was 55% of the original Olson model, and the maximum impact force was 75%.
3. To verify the theoretical impact forces estimated by the equations of motion, impact simulations were performed on the R3500, R5000, and R7000 of the curved tracks using the KTX. Two conditions were considered: the first is to derail along the tangential direction of the curve after derailment, and the second is to derail with additional angle due to the centrifugal effect. All simulation results showed relative deviations of less than 8%, confirming that the proposed method considering suspension stiffnesses in the Olson model can predict the impact force acting on the DCP well.  
This study presents a new approach to improving the analysis and design methodology for Derailment Containment Provisions (DCPs). The method is proposed by comparing the Olson model and dynamic simulations, taking into account the mass effect of vehicle bodies during collision. This is achieved by using a simplified spring-mass model to consider the lateral stiffness of suspension and its effect on the transfer of vehicle body mass during collision. The proposed method is shown to be effective through impact simulations performed on curved tracks using the KTX model. This enables a good estimation of the impact force of DCP, considering the effective mass transfer of the vehicle body during collision. The proposed method offers a more accurate and effective method for predicting the impact force acting on DCP Type 1 and can be used for the design of a new DCP Type 1, and the findings of this study can provide valuable information for DCP design and improve the safety of train derailment incidents.  
Conceptualization, I-H.S.; Data curation, I-H.S. and J.-S.S.; Funding acquisition, N.-H.L. and H.-U.B.; Investigation, I-H.S., J.-S., J.-S.K., H.-U.B. and N.-H.L.; Project administration, J.-S.S. and J.-S.K.; Supervision, J.-S.S.; Validation, J.-S.S. and J.-S.K.; Writing--original draft, I-H.S.; Writing--review & editing, J.-S.S., J.-S.K. and N.-H.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by a grant (RS-2021-KA163289) funded by the Ministry of Land, Infrastructure, and Transport of the Korean government.  
Not applicable.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Curve Radius** & **Additional Angle \(\beta\) (\({}^{\circ}\))** & **Olson Model Mean** & **Simulation Mean** & **Relative Deviations (\%)** & **Olson Model Maximum** & **Simulation Maximum** & **Relative Deviations (\%)** \\ \hline R3500 & 0 & 247.5 & 247.8 & 0.12 & 530.18 & 551.8 & 4.08 \\  & 0.893 & 350.2 & 339.2 & 3.14 & 750.12 & 779.7 & 3.94 \\ R5000 & 0 & 207.1 & 191.6 & 7.46 & 443.5 & 444.4 & 0.21 \\  & 0.747 & 292.9 & 271.3 & 7.89 & 627.4 & 578.0 & 7.87 \\ R7000 & 0 & 175 & 170.2 & 2.72 & 374.8 & 376.1 & 0.36 \\  & 0.631 & 247.5 & 232.3 & 6.13 & 530.2 & 493.4 & 6.93 \\ \hline \hline \end{tabular}
\end{table}
Table 9: The impact forces of final simulation results at 300 km/h on the six cases.