## 6 Summary  
To address the derailment problem in recent years at the guardrail of the double-slip turnouts, this study focused on clarifying the derailment mechanism and discussed the feasibility of both the existing guardrail interval limit and its calculation method. A calculation method for the guardrail interval limit was proposed that considers the vehicle running attitude and wheelset angle of attack. It was verified against the actual measurement data of double-slip turnouts where derailment occurred. The proposed calculation method was used to determine the guardrail interval limits of the main types of single turnouts and double-slip turnouts in China and to analyze the main influencing factors and laws. The main conclusions are as follows.  
(1) Under the most unfavorable vehicle conditions, the turnout alignment determines the guardrail interval limit. According to the calculated results using the developed method, the guardrail interval limit should be 1365 mm, which meets the requirements of most turnouts and effectively avoids impact and wear as well as derailment at the opening section of the guardrail.  
(2) For single turnouts, the guardrail interval limit can be reduced by decreasing the frog number and the radius of the lead curve and gage widening. The guardrail interval limit can also be reduced by decreasing the distance from the end of the lead curve and the end of the gage widening to the buffer segment at the toe end of the guardrail. When the endpoint of the gage widening reaches or is deep into the end of the buffer segment, the adverse effects are aggravated. When the end of the lead curve reaches or enters the end of the buffer segment, adverse effects do not worsen. In the gage widening restoring segment, a straight-track design is more likely to increase the twisting angle of the bogie than a curved-track design, which will reduce the guardrail interval limit.  
(3) For double-slip turnouts, the guardrail interval limit can become smaller with the decrease of the frog number and the increase of the gage widening. A broken rail comprising the stock rail and switch rail in front of the guardrail will cause the bogie to approach or reach the inscribing state, which will cause adverse effects similar to those of a curved rail. The guardrail interval limit can decrease with the increase of the angle of attack at the tip of the switch rail, and the reduction in the distance from the tip of the switch rail and end of the gage widening to the buffer segment at the toe end of the guardrail. When the end of the gage widening reaches or enters the end of the buffer segment, the adverse effects continue to increase.  
In future, more field test data will be used to verify the method for calculating guardrail interval limits proposed in this paper as well as the feasibility of the recommended guardrail interval limit. This verified interval limit will effectively avoid wheel-rail impact and derailment at the opening section of the guardrail in turnout, thereby ensuring vehicle safety. Further, the optimization design of turnout will be conducted based on the results obtained in this research.  
Conceptualization, P.W. and S.W.; methodology, P.W. and Z.Z.; software, P.W. and Z.Z.; validation, P.W. and Z.Z.; formal analysis, P.W.; investigation, P.W. and S.W.; resources, S.W.; writing--original draft preparation, P.W.; writing--review and editing, S.W.; funding acquisition, P.W. and S.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China under Grant 51878661 and 51808557.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.