## 4 Discussion and Conclusions  
The proposed methodology for the prediction of RCF behavior was validated in real case studies thanks to the selection of the appropriate track section characteristics. The qualitative comparison of the predicted results with the experimental measurements shows a good relationship since for the first section a high density of cracks is obtained at similar locations, while for the second section only isolated cracks appear. Nevertheless, further consideration of the results is necessary. * In the first section under analysis, the predictions show clearly the same RCF pattern that is experimentally observed in the real track. The methodology assumes the existence of RCF problems at specific locations. The predicted results at straight lines and circular curves show a good relationship with measurements. On the other hand, although similar conclusions might be obtained for clothoids, relationship is not so accurate. Consequently, these transitions must be treated carefully, because the vehicle dynamic behavior is subjected to changes between different track sections. * In the second track section, only isolated cracks without a clear pattern are measured. The prediction of isolated cracks may be due to numerical effects owing to the MBS irregularities file. In this section, no RCF problems are predicted, since calculated cracks are few and very isolated. Nevertheless, the appearance of isolated cracks could be a sign of a potential breakage of the rail if preventive maintenance actions are not carried out on time. * Predictions are good for small depth values because the initiation and minimum crack size are well controlled. Therefore, the scheduling of grinding maintenance task can be improved to avoid the propagation of cracks that could lead to rail failure. * The difference in some crack growths could be due to different factors. First, a lack of information regarding the degradation state of the rails in the first measurement date. A second reason behind the difference for deeper cracks while the trend remains similar could be a lack of data to characterize the coefficients of the fourth-degree polynomial. Finally, the employed damage function was developed for normal grade rails but the material grade of installed rails could have small differences. * \(\Delta t\) and \(T_{\text{total}}\) have been considered equal. Smaller values of \(\Delta t\) with an updating of track irregularities or rail profiles may vary results in \(T_{\text{total}}\). * The methodology was implemented using models available in the literature. The database for crack propagation, i.e., \(a_{\text{min}}\) values and coefficients of fourth-degree can be updated by XFEM calculations [47]. This kind of numerical solution is suitable as has been proven by [PERSON] et al. [48]. Figure 13: Comparison of the trend-lines between measurements and predictions for three different sections. Assessment with one measured cross-section per yard: (**a**) Measurements; (**b**) Predictions. In this article, cracks on railway track systems are predicted using a methodology by means of MBS. Different engineering methods are coupled to obtain a global model. The comparison of predictions with experimental measurements proves that the proposed methodology is a promising strategy to predict RCF behavior:  
* The location of predicted cracks and their growth allow predicting RCF behavior. The track sections can then be sorted against the chance of failure, reducing the LCC with the adequate scheduling of the consequent maintenance programs. The high reliability in the prediction of the initiation of cracks makes possible a reduction of maintenance costs. * The track quality and the evolution of rail wear can be considered along with the assessment of cracks. In the same way, this methodology can be used to support the decision of changes in running conditions and the design of track sections. Conceptualization, B.R.-A. and J.N. ; methodology, B.R.-A. ; validation, B.R.-A. and A.S.E. ; investigation, B.R.-A. and A.S.E.