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<p>The dynamic stress induced by high-speed trains directly affects the long-term settlement and dynamic stability of ballastless track subgrades, yet the absence of systematic analysis of disparate field data has hindered the development of a universally applicable design method. This study compiles an extensive database from field tests and literature, employs statistical analysis to investigate the magnitude and probability distribution of dynamic stress in ballastless track subgrades, and assesses the applicability of existing design formulas. The results show that the dynamic stress at the subgrade surface conforms to a normal distribution, with a mean of 13.63&#xa0;kPa and a standard deviation of 2.40&#xa0;kPa. A statistical transition speed of 150&#xa0;km/h is identified, below which the dynamic stress and corresponding dynamic amplification factor remain constant, while above it both increase linearly with a speed influence coefficient of 0.0011. Besides, the axle load coefficient is determined to be 0.08, and a new practical design formula is proposed to evaluate the subgrade surface dynamic stress via an upper envelope analysis. Additionally, the dynamic stress attenuates rapidly with subgrade depth, and the speed influence becomes negligible beyond a depth of 3.0&#xa0;m. Finally, a comprehensive formula integrating the effects of train axle load, speed, and subgrade depth is developed to predict the subgrade dynamic stress. Notably, the application of this formula suggests a required subgrade bed thickness of 1.9&#xa0;m, challenging the conservative code requirements. These findings provide a reliable data-driven basis for optimizing the design of ballastless track subgrades in high-speed railway systems.</p>

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Prediction of dynamic stress in ballastless track subgrade under high-speed trains

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Qi Yang,
  • Chao Qin,
  • Fang Xu,
  • Pengjiao Wang,
  • Rusong Nie,
  • Junping Zhang

摘要

The dynamic stress induced by high-speed trains directly affects the long-term settlement and dynamic stability of ballastless track subgrades, yet the absence of systematic analysis of disparate field data has hindered the development of a universally applicable design method. This study compiles an extensive database from field tests and literature, employs statistical analysis to investigate the magnitude and probability distribution of dynamic stress in ballastless track subgrades, and assesses the applicability of existing design formulas. The results show that the dynamic stress at the subgrade surface conforms to a normal distribution, with a mean of 13.63 kPa and a standard deviation of 2.40 kPa. A statistical transition speed of 150 km/h is identified, below which the dynamic stress and corresponding dynamic amplification factor remain constant, while above it both increase linearly with a speed influence coefficient of 0.0011. Besides, the axle load coefficient is determined to be 0.08, and a new practical design formula is proposed to evaluate the subgrade surface dynamic stress via an upper envelope analysis. Additionally, the dynamic stress attenuates rapidly with subgrade depth, and the speed influence becomes negligible beyond a depth of 3.0 m. Finally, a comprehensive formula integrating the effects of train axle load, speed, and subgrade depth is developed to predict the subgrade dynamic stress. Notably, the application of this formula suggests a required subgrade bed thickness of 1.9 m, challenging the conservative code requirements. These findings provide a reliable data-driven basis for optimizing the design of ballastless track subgrades in high-speed railway systems.