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Finite-element analysis of unsupported sleepers using three-dimensional wheel–rail contact formulation

Owing to repeated traffic loads, the ballast of a railroad track can become unevenly distributed, resulting in different settlements of adjacent sleepers and possibly to a sleeper–ballast loss of contact. The sleeper–ballast loss of contact can significantly change the stiffness properties and modes of deformation of the track. This in turn can cause damage to the structure and can lead to undesirable dynamic behaviour of the vehicles that negotiate this damaged track. The focus of this investigation is on developing a more comprehensive procedure that can be used to examine the effect produced by unsupported sleepers of a flexible track on the dynamics of railroad vehicle systems. The procedure used in this study is based on a validated non-linear multi-body railroad vehicle system formulation that takes into account the coupling between the elastic deformations of the track, the sleeper movements, and the three-dimensional contact parameters. The method used in this article allows for developing a detailed finite-element track model that accounts for non-periodic and asymmetrical mechanical defects. The finite-element equations of motion of the track that includes unsupported sleepers are integrated with the non-linear constrained dynamic equations of the multi-body railroad vehicle system. Component mode synthesis methods are used to reduce the number of the governing equations of motion and eliminate high-frequency modes. The dynamic coupling between the track modal co-ordinates and the wheel–rail contact parameters is considered in this investigation by using creepage and creep force expressions that depend on the track deformations and sleeper movements. In order to demonstrate the use of the procedure described in this article, a track model which has rails and sleepers modelled as beams rigidly connected at the intersection points is used. The effect of the ballast is considered using an elastic foundation. The results obtained in this investigation are used to compare between the responses of two tracks; one with no sleeper–ballast loss of support and the other with unsupported sleepers. The results are reported for different values of the forward velocities in order to have a better understanding of the effect of the sleeper loss of support on the system dynamics. The creepages that depend on the track deformations as well as the system frequencies are analysed. The results obtained in this investigation are found to be in good agreement with the results reported in the literature on unsupported sleepers.