A unified analytical model for track deformation mapping and vehicle-track dynamic response induced by substructure deformation

Abstract

This study establishes a nonlinear vehicle–track coupled dynamic model that explicitly accounts for the effects of substructure deformation. Based on the vehicle–track coupled dynamics framework, the track structure is modeled using an energy-based approach, in which displacement functions of track layers are expanded into modified Fourier series. The static rail geometry and interlayer contact relations are derived through the principle of stationary potential energy. Considering the dynamic excitation from moving trains, a cross-iterative algorithm is employed to obtain the system responses, thereby enabling unified analysis of static track deformation and dynamic vehicle–track interactions. The results demonstrate that the proposed model effectively reveals the coupling mechanism between substructure deformation parameters, rail surface geometry, and system dynamics. The critical conditions for avoiding void formation under cosine-type and angular-type subgrade settlements follow power-law and linear relations, respectively. For a cosine-type settlement with a wavelength of 15m and amplitude exceeding 35mm, vehicle ride quality deteriorates significantly. Moreover, interlayer separation induced by substructure deformation leads to repeated “contact–separation–recontact” impacts, which may degrade long-term structural performance. This study provides a unified theoretical and computational framework for quantitatively assessing the effects of substructure deformation on high-speed train safety and track structure durability.

Keywords

high-speed railway / substructure deformation / energy method / voids between layers / mapping relationship / dynamic responses

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Central South University