## 5 Comparison with Impact Simulation  
To verify the theoretical impact forces acting on DCP, the Virtual Testing Model (VTM) on the Korean high-speed train [30] was simulated using a commercial program, LS-DYNA [31]. The vehicle was modeled as only one power car with the highest mass considering excessive computing time. Basic parameters, such as the mass of the vehicle and the characteristics of the suspension devices, were referred to the previous study [32]. Table 2 represents the mass information of the KTX power car used in the simulation. The finite element vehicle model used in the simulation is shown on the left side of Figure 8. The body and bogies are composed of shell elements and the wheelsets are composed of 3D solid elements. The connections between the car body and bogie were modeled with beam elements. The DCP is shown on the right side of Figure 8. The DCP is a rectangular concrete structure with reinforced bars with a size of 140 mm in height and 500 mm in width. The bottom surface of the DCP was constrained on all degrees of freedom, and the automatic surface-to-surface contact condition was applied to the DCP and wheelsets. Table 3 shows the finite element information and properties of the vehicle used in the simulation model. To compare the theoretical impact force by the Olson model with the impact force numerically obtained, a simulation was carried out under the same condition as shown in Figure 9. The traveling speed is 300 km/h and the collision angle is 0.85\({}^{\circ}\). The weight of the power car is about 68 tons. Here, 0.85\({}^{\circ}\) is the largest impact angle on a straight track calculated by the geometric yaw angle between the rail and train. To shorten computing time, only the section where collision occurs was modeled as a concrete material, and the other section was modeled as a rigid one. \begin{table}
\begin{tabular}{c c} \hline
**Component** & **Weight (ton)** \\ \hline Car Body & 54.96 \\ Each Bogie Frame & 2.42 \\ Each Wheelset & 2.048 \\ \hline \end{tabular}
\end{table} 
Table 2: Masses of the high-speed train model. Figure 8: Finite element model for simulation. A concrete material in LS-DYNA was used to analyze the fracture behavior and failure plane shape of the DCPs due to impact force [33; 34; 35]. The Continuous Surface Cap Material (MAT159, CSCM Concrete) model was developed in the 1990s and has been widely applied in many studies. The CSCM model has a good advantage in effectively modeling concrete damage and is widely used because it can calculate the element's behavior with only a few variables. The impact force calculated by the collision simulation is shown in Figures 8-10. The red line represents the force curve of a 50 ms moving average. The moving average method applied to the data is used to simply analyze the data trend, and is also used to calculate the static equivalent force of an impacting structure for strength design. In general, when a 50 ms moving average method is applied, raw data are not excessively equalized and are not overestimated owing to the remaining noise signals [19; 36]. Based on raw data without filtering, collision is completed at about 520 ms because the contact force no longer occurs. The average and maximum forces on the DCP can be obtained, as shown in Table 4 and Figure 10. Relative deviations in Table 4 are the relative differences between theoretical impact forces and simulation impact force. Relative deviations are defined as the following equation. \[Relative\,deviation=\left|\frac{Impact\,force\,(Theory)-Impact\, force(Simulation)}{Impact\,force(Theory)}\times 100\right|\]