## 1 Introduction
[PERSON] and [PERSON] [28] and [PERSON] and [PERSON] [29] proposed a prediction algorithm for the derailment coefficient of a turnout that combines data from multiple sensors yet did not consider enough factors to evaluate the safety of wheel-track contact. [PERSON] et al. [30] suggested an analysis method for a track ballast-wheel interaction that could be further developed to model the interaction in a train-derailment event, based on the discrete-element method (DEM). [PERSON] and [PERSON] [31] studied the train derailments that occurred in China on some railway bridges due to insufficient lateral rigidity. [PERSON] et al. [32] and [PERSON] and [PERSON] [33] established an asymmetric vehicle-track coupled dynamics model to analyze the influence of rail fastener failure on derailment. [PERSON] et al. [34] conducted modeling and simulation of collision-causing derailment to design the derailment containment provision using a simplified vehicle model. [PERSON] et al. [35] conducted a full-scale train bogie derailment test and analyzed the post-derailment behavior of the casting bogie. Generally, existing research on double-slip turnouts has mainly focused on structural design and fault remediation and little on derailment. The studies focusing on derailment primarily concentrate on the mechanism of derailments occurring on curved tracks, bridge sections, and switch panels of turnouts with small frog numbers, and the preventive measures to avoid the derailment. There has been little research on derailment at the crossings where guardrails are placed at a turnout, especially for double-slip turnouts. Therefore, we analyzed recent derailment accidents at double-slip turnouts in China and focused on the derailment mechanism. When a train passes through the acute-angle crossing of a double-slip turnout in the facing direction, the wheels may hit the opening section of the guardrail. Gradually, the frequent wheel impact loosens, deforms, or even damages the rail support bolt at the front end of the guardrail, which causes the rail head of the guardrail opening section to tip over to the side of the stock rail. This reduces the height difference between the stock rail and guardrail; thus, when a train passes through, the wheel flange can impact and abrade the top surface of the rail head of the guardrail opening section. The abrasion and plastic deformation eventually cause the rail head to form a stepped structure, as shown in Figure 1. When a significant degree is reached, this stepped structure causes the wheel flange to climb the guardrail when a train passes, which eventually leads to train derailment. Under normal operating conditions, the train wheel impacting the guardrail opening section is the direct cause of derailments at double-slip turnouts. If the wheel contact with the guardrail opening section can be prevented, the occurrence of derailment at the guardrail can be effectively reduced or avoided. According to an analysis of derailment accidents by railways bureau, the following factors lead to wheel impact on the guardrail opening section:  
1. Track gage widening at the end of the buffer segment of the guardrail, and the flangeway not being widened by the same degree. 2. Abrasion at the upper rail of the curve, which increases the gage; however, the flangeway at the end of the buffer segment of the guardrail is kept the same. 3. During maintenance and repair, the restoring segment of gage widening of the lead curve moves backward, which increases the gage at the end of the buffer segment of the guardrail while the flangeway remains the same. 4. After the straight section of the guardrail experiences severe abrasion, adjusting pieces are continuously added at the end of the guardrail to maintain the check interval, which reduces the flangeway. 5. The guardrail bolts are not tightened in time after loosening and unloading, which causes the guardrail head to drop and reduces the flangeway.