## 2 Limitations of the Existing Calculation Method for the Guardrail Interval Limit  
The concept of a guardrail interval is proposed based on the European Standard (EN) [36] and can be defined as the distance from the working edge of the end of the buffer segment of a guardrail to the working edge of the rail on the opposite side, as shown in Figure 2.  
The guardrail interval limit should be set to ensure that various types of trains can smoothly pass through the guardrail opening section without collision, as shown in Figure 3. The guardrail interval limit can be calculated using Equation (1):  
\[C_{r}<(T_{\text{min}}-\varepsilon)+d_{\text{min}}, \tag{1}\]  
where \(T_{\text{min}}\) is the minimum wheelset inner distance (i.e., 1350 mm), \(\varepsilon\) is the wheelset inner distance reduction under the vehicle load (i.e., 2 mm), and \(d_{\text{min}}\) is the minimum flange thickness (i.e., 22 mm). With these assumed values, the guardrail interval \(C_{r}\) should be less than 1370 mm. In the worst-case scenario, where the most adverse wheelset has its edge against the rail, this limit ensures that the wheel back on the other side will not touch the guardrail.  
A statistical analysis of the field data showed that none of the various turnout types resulted in a wheel-track impact in the opening section at the toe or heel end of the straight guardrail and the opening section at the heel end of the lateral guardrail. Wheel-track impact  
Figure 3: Calculation method for the guardrail interval limit.  
Figure 2: Guardrail interval.  
only occurred in the opening section at the toe end of the lateral guardrail. When a train passes through a turnout in trailing and straight-facing directions, it runs in a straight line before entering the guardrail. Only when a train passes through the turnout in the side-facing direction does it run along a curve before entering the guardrail. Therefore, when a train is running in a straight line before entering the guardrail, the current guardrail interval limit should ensure that the wheels will not hit the opening section of the guardrail. However, when the train is running along a curve before entering the guardrail, the current guardrail interval limit does not completely avoid a wheel-track impact at the opening section.  
The existing calculation method also does not consider the impact based on the vehicle running attitude and the wheelset angle of attack. Therefore, the worst-case conditions are not considered. When the vehicle crosses the turnout in a straight line, the wheel running direction is parallel to the rail, which ensures that the back of the wheel does not hit the opening section of the guardrail, as shown in Figure 3(a). When the vehicle crosses the turnout in the side-facing direction, the wheels are barely out of the lead curve or are still in the lead curve before entering the toe end of the guardrail. The bogie approaches or reaches the free inscribing state when running on a small-radius curve, and the wheel running direction and rail direction are at different angles. Under the worst-case condition, when a guiding wheelset with the smallest inner distance and thinnest flange enters the opening section of the guardrail, the wheels on the upper rail of the curve are in immediate contact with the rail, and the wheels on the lower rail of the curve are far from the rail. The twisting of the bogie and wheelset moves the lower wheels further from the rail, which causes the distance between the back of the lower wheel and the working edge of the upper rail to drop below the guardrail interval limit of 1370 mm. This causes a collision with the guardrail opening section, as shown in Figure 3(b).  
Figure 4: Vehicle running attitude when passing through the turnout.  
Therefore, to prevent the wheels from hitting the opening section of the guardrail when the vehicle crosses the turnout in the side-facing direction, the vehicle running attitude and the wheelset angle of attack need to be considered for the guardrail interval limit.