A procedure to develop scalable models for the transient response of sleepers in conventional and high-speed railway lines and implementation to the vertical vibration mode

This paper presents a procedure to develop scalable reduced models for the through-the soil interaction and traveling wave effects of distant sleepers in a long railway track. For development purposes, and, without loss of generality, the geometry of the sleepers is consistent with the UIC-60 track system commonly used in European high speed rail and the vertical vibration mode is considered. The ballast and the effects of soil layering are not considered in the present paper; however, it is the subject of ongoing research. The proposed reduced models are based on B-Spline impulse response functions (BIRF) of the sleepers only as computed through boundary element method (BEM) solutions of the full model, preserve the frequency content of the full models, and they are highly accurate within the assumptions of linear isotropic and homogeneous soil media. They are expressed in a scalable form with respect to soil properties and sleeper spacing. In particular, the BIRFs of distant sleepers can be accurately approximated by appropriate scaling operations of time and amplitude of a reference sleeper BIRF while retaining all dynamic characteristics of the full model. Three main scaling parameters are proposed: (i) the apparent propagation velocity, (ii) the geometric damping coefficient, and (iii) the soil properties of a reference soil (i.e., the shear modulus and shear wave velocity). The models are validated through comparisons with other BEM solutions, and the accuracy and efficiency are established. The proposed models are developed as part of an NSF funded research on vibrations induced by high-speed rail traffic and are consistent with the associated train and rail models and a multi-system interface coupling (MSIC) technique that were developed as a part of the project and presented in companion papers. The proposed procedure forms the framework for developing scaled reduced models for other vibration modes and different sleeper geometries and can be generalized to include any foundation type or layered soil profiles.