Heavy and frequent train loads generate large bending stresses in rail. These stresses contribute to the propagation of transverse fatigue defects, which are among the leading causes of broken rail derailments in North America. A thorough assessment of the rail structural condition requires reliable methods for estimating rail bending stresses. This is often challenging due to the many uncontrollable environmental, operational, and structural factors that affect the magnitude of rail bending stresses along the thousands of miles of track.
In this study, a new methodology was developed for estimating rail bending stresses over long distances using train-mounted vertical track deflection (VTD) measurements. Mathematical correlations between track modulus, rail deflection, rail stress, and applied load form the basis of the method. To develop the correlations, a new finite element modelling method was developed which allowed the simulation of a stochastically varying track modulus along the track. Track models with different track modulus distributions were developed and the resulting VTD and rail bending stresses under moving wheel loads were calculated. The mathematical correlations between the inputted track modulus, modelled VTD and rail bending stresses were quantified using statistical approaches.
Based on the results, equations were proposed to estimate the statistical properties of track modulus and rail bending stresses over track windows using the VTD measurements. A framework was also developed to estimate the probability distributions of maximum tensile and compressive bending stresses in the rail head and base, which are necessary for calculating the rail reliability under applied loading. The accuracy of the proposed equations was first verified using a numerical case study for which a random track modulus distribution was considered and artificial noise was added to the modelled VTD. Subsequently, datasets collected from a study site were used to validate the methodology for estimating rail bending stresses. The rail-mounted strain gauges and the wheel impact load detector system at the study site provided information about the rail bending strains under known applied loads. This allowed validation of the maximum bending stresses estimated using train-mounted VTD measurements.