The determination of rail yield strength levels to support increased wheel loads is usually based on empirical adjustments to the Hertzian equations for contact stresses. A formulation is given, based on reliability theory, which enables a more refined analysis to be carried out and incorporates the material property variations, provided these can be approximated as Gaussian normal distributions.

Application has been made to unit train operations and estimates made of strength levels required for mean wheel loads in excess of 150 kN. The results indicate the importance of rail/wheel tangential forces on rail damage in curves and show that, while variations in wheel loads about the mean have an influence on performance, the effects are not highly significant. Spread of steel strength also has only a marginal influence within the bounds of accepted steelmaking control.

A comparison has been made between the predicted strength level and service trials which indicates that the suggested procedure provides conservative results.