# A Fatigue Reliability Assessment for Rail Tension Clamps Based on Field Measurement Data
## 4 Conclusions  
This study identified the cause of the fracturing of tension clamps used in rail fastening systems for urban railways and performed reliability analyses on their fatigue failure based on actual measurement data. The stress range, which is the dominant factor in the fatigue failure of the tension clamps, was estimated from the measured strains on the tension clamps at locations where most of the fracturing occurred from repeated train operations. The field measurement data at seven MLs, on both the inner and outer rails and from both inside and outside track gauges, were used in the study.  
The statistical model of the stress ranges of the seven MLs was established using the field measurement data. The Kolmogorov-Smirnov goodness of fit test was employed to identify the fitness of the distributions for the stress ranges of five distribution types. The most fitted distribution for the stress range was selected by comparing the most likely values of the five distribution types. The statistical parameters of the fitted distribution were estimated by the linear regression of the empirical cumulative distribution functions plotted on the probability papers for the fitted distribution.  
The reliability analysis on the fatigue failure of the tension clamps was performed using the statistical models of the stress ranges based on the measured data. The limit state function was defined as a linear function of the critical and cumulative damage indexes. The random variables for the reliability analysis included the stress range, critical damage index, detail category constant, and error factor. The results of the reliability analysis were mainly dominated by the statistical parameters of the stress ranges. The reliability indexes for the inside track gauges, which had large means or standard deviations of the stress range, were smaller than those of the outside track gauges. Moreover, the reliability level of the inner rails was lower than that of the outer rails at the aforementioned specific MLs, which is consistent with the field observations of fatigue damage to the tension clamps.  
It is noteworthy that the reliability index of the tension clamps at all of the MLs decreased to less than half of the initial reliability within 10 years. Therefore, periodic inspection for fatigue damage to tension clamps is required. Furthermore, a system for the maintenance and replacement of the inner and outer rails and the inside and outside track gauges is necessary.  
Conceptualization--[PERSON]-H.K.; methodology--[PERSON]-H.K. and [PERSON]-C.P.; validation--H.-B.S. and [PERSON]-[PERSON]; formal analysis--J.-H.K.; investigation--[PERSON]-H.K., [PERSON]-C.P. and H.-B.S.; resources--H.-B.S. and M.K.; writing (original draft preparation)--J.-H.K.; writing (review and editing)--H.-B.S., [PERSON]-C.P. and M.K.; visualization--J.-H.K.; supervision--H.-B.S.; project administration--H.-B.S.;  
Figure 8: The variations in the reliability index with the accumulated number of stress cycles: (**a**) ML1 and ML2; (**b**) ML3 and ML4.  
funding acquisition--H.-B.S. and M.K. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Incheon National University (International Cooperative) Research Grant (2017-0212).  
The authors declare no conflict of interest.