Key Takeaways & Executive Findings
- •• A unified analytical model integrates static track deformation mapping and dynamic vehicle-track interactions under substructure deformation. • Critical conditions for avoiding void formation follow power-law and linear relations for cosine-type and angular-type subgrade settlements, respectively. • Cosine-type settlement with wavelength 15 m and amplitude >35 mm significantly deteriorates vehicle ride quality. • Interlayer separation causes repeated contact-separation-recontact impacts, potentially degrading long-term structural performance.
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 15 m and amplitude exceeding 35 mm, 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.
1. Introduction
China's high-speed railway (HSR) network is extensive, dense, and characterized by highly complex service environments. During long-term operation, substructure components such as bridges and subgrades inevitably undergo deformations induced by geological conditions, climatic variations, and time-dependent material properties [1]. These deformations, such as track slab warping, interlayer damage between track and substructure, and uneven pier settlements (as shown in Figure 1), can cause non-coordinated vertical displacements across track layers. Even minor substructure irregularities may lead to local stiffness discontinuities, including mortar debonding and baseplate voiding, which alter the static geometry of the rail surface and degrade structural integrity. With the ongoing development of 400 km/h high-speed trains in China, operational safety and stability now impose unprecedented requirements on track smoothness and geometric precision. Consequently, a comprehensive understanding of the coupled relationship among substructure deformation, rail geometry evolution, and vehicle-track dynamic behavior has become a crucial scientific and engineering challenge for ensuring the safety and durability of high-speed railway infrastructure.
Research on the mapping relationship between substructure deformation and rail geometry primarily falls into three methodological categories: 1) Analytical models based on beam and plate theory. CHEN et al [2, 3] theoretically derived expressions for the mapping relationship between pier settlements and rail deformations in unit-slab and longitudinally connected ballastless tracks. JIANG et al [4−9] developed simplified analytical or Ritz-based models to relate vertical and lateral deformations of bridges to rail geometry for CRTS II and III slab track systems. For subgrade settlements, GUO et al [10], and ZHONG et al [11] further proposed semi-analytical and spatial mapping models to characterize the coupling mechanisms between subgrade deformation and track geometry. 2) Commercial finite element software for mapping analysis of complex substructures. FENG et al [12] established a refined FEM model for a slab track-variable cross-section continuous beam system to investigate the deformation coordination mechanism among layers under nonuniform pier settlement. ALGIN et al [13], JIANG et al
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CHEN Yao, FENG Qing-song, ZHAO Lei, ZHANG Ling, YANG Zhou (2026). A unified analytical model for track deformation mapping and vehicle-track dynamic response induced by substructure deformation. Journal of Central South University. https://doi.org/10.1007/s11771-026-6289-z
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a unified analytical model that integrates static track deformation mapping and dynamic vehicle-track interactions under substructure deformation, using an energy-based approach and a cross-iterative algorithm.
How does the model handle substructure deformation?
The model explicitly accounts for substructure deformation by expanding displacement functions of track layers into modified Fourier series and deriving static rail geometry and interlayer contact relations via the principle of stationary potential energy.
What are the critical conditions for avoiding void formation?
For cosine-type subgrade settlements, the critical condition follows a power-law relation, while for angular-type settlements it follows a linear relation.
What is the impact of cosine-type settlement on vehicle ride quality?
For a cosine-type settlement with a wavelength of 15 m and amplitude exceeding 35 mm, vehicle ride quality deteriorates significantly.
What are the practical implications of interlayer separation?
Interlayer separation induced by substructure deformation leads to repeated 'contact-separation-recontact' impacts, which may degrade long-term structural performance.
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