In continuation of the authors’ previous published work, this paper presents improved models of relatively long railway tracks and discusses the new studies on their development and implementation. The proposed models address the through-the-soil interaction of ties in a long track segment and capture the traveling wave effects on ties located long distances from a loaded tie. These models are very computationally efficient, since they are expressed in a closed solution form. They are also very accurate and capture all the dynamic characteristics of the physical problem (e.g. frequency content), since they represent scaled characteristics responses of a reference response that is computed through rigorous analytical procedures. It is noted that the proposed models are developed for all vibration modes of ties due to wave propagation in linear, isotropic and homogeneous media. The models are verified through comparisons with other BEM solutions, and the accuracy and efficiency are established. Implementation of the proposed modes is demonstrated through a study on the critical train velocity and the effects on the system’s vibration response are quantified and discussed.

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