Estimating Track Capacity Based on Rail Stresses and Metal Fatigue

This paper describes a framework to evaluate the structural capacity of railroad track to train-induced loads. The framework is applied to estimate structural performance in terms of allowable limits for crosstie spacing. Evaluation of the load-carrying capacity of track is conducted by examining the state of stress in the rail. Rail stresses are estimated by superimposing the contributions from different sources: (1) live-load stresses, (2) thermal stresses, and (3) residual stresses. Rail bending and thermal stresses are calculated based on assuming that the rail behaves as a beam supported by a linear elastic foundation. The classical beam on elastic foundation analysis is modified in the present work to account for crosstie spacing that exceeds the limits of the classical theory. Finite element methods are used to develop an amplification factor on the bending moment calculated from beam on elastic foundation theory, which is applied when the spacing between crossties becomes discrete and the foundation support is no longer considered as continuous. The rail stress analysis is then used in conjunction with a failure criterion based on the formation and growth of internal defects in rail due to the repeated passage of wheels, i.e. metal fatigue. A similar methodology was applied in previous work to estimate allowable limits for rail head wear in terms of vertical head-height loss and gage-face side wear. Moreover, allowable limits estimated from this methodology are inherently linked with the frequency of rail testing to detect internal rail head defects and mitigate the likelihood of accidents from broken rails. The analyses described in this paper depend on various assumptions regarding operational, structural and environmental factors. These factors include vehicle weight, train speed, rail size, foundation modulus, temperature differential (i.e. difference between the rail temperature and the stress-free or neutral temperature), and rail test interval (i.e. tonnage between rail tests). Sensitivity studies are conducted to examine the relative effect of these factors on the estimation of maximum free span between effective ties. In addition, results from applying the methodology described in this paper are compared to the limits specified in the current track safety regulations.