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<p>As urban rail transit networks become increasingly dense, new tunnels frequently undercross existing operational lines. The cyclic loads from existing double-track trains pose a threat to the structural safety of the underlying sections. This paper proposes a computationally efficient analytical model for the ‘double-track train–soil layer–underpass tunnel section’ system. In this model, the double-track train is represented as a moving two-degree-of-freedom (2-DOF) sprung mass system, the soil is modeled as a spring-damper system, and the underpass tunnel roof structure is treated as an Euler-Bernoulli simply supported beam. The system response is solved using the modal superposition method. Key parameters are calibrated via displacement back analysis, and the model’s predictive capability is validated against FLAC3D simulations and independent field measurement data. A systematic parametric study investigates the influence of train speed, tunnel beam length, overburden thickness, equivalent stiffness, and soil mechanical parameters. The analysis reveals the underlying mechanisms of system resonance and critical design parameters. For the specific case study, resonance peaks were observed at speeds around 48&#xa0;km/h and 72&#xa0;km/h, a dual-peak resonance phenomenon emerged at beam lengths of approximately 25&#xa0;m and 45&#xa0;m, and a vibration amplification effect was identified at a soil cover thickness near 5&#xa0;m. These findings highlight the resonance mechanisms that should be avoided in design, while the specific critical parameter values are case-dependent and should be re-calibrated for other projects. Increasing the equivalent beam stiffness can effectively suppress the vibration response, while grouting reinforcement modulated the system’s dynamic response. This study provides a theoretical framework and an efficient preliminary assessment tool for understanding vibration mechanisms and aiding early-stage design in similar projects.</p>

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An analytical approach for predicting vibrations in new tunnels undercrossing existing double-track railways

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  • 发表日期：

    2026年6月23日

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  • Yunsi Liu,
  • Yueyuan Huang

摘要

As urban rail transit networks become increasingly dense, new tunnels frequently undercross existing operational lines. The cyclic loads from existing double-track trains pose a threat to the structural safety of the underlying sections. This paper proposes a computationally efficient analytical model for the ‘double-track train–soil layer–underpass tunnel section’ system. In this model, the double-track train is represented as a moving two-degree-of-freedom (2-DOF) sprung mass system, the soil is modeled as a spring-damper system, and the underpass tunnel roof structure is treated as an Euler-Bernoulli simply supported beam. The system response is solved using the modal superposition method. Key parameters are calibrated via displacement back analysis, and the model’s predictive capability is validated against FLAC3D simulations and independent field measurement data. A systematic parametric study investigates the influence of train speed, tunnel beam length, overburden thickness, equivalent stiffness, and soil mechanical parameters. The analysis reveals the underlying mechanisms of system resonance and critical design parameters. For the specific case study, resonance peaks were observed at speeds around 48 km/h and 72 km/h, a dual-peak resonance phenomenon emerged at beam lengths of approximately 25 m and 45 m, and a vibration amplification effect was identified at a soil cover thickness near 5 m. These findings highlight the resonance mechanisms that should be avoided in design, while the specific critical parameter values are case-dependent and should be re-calibrated for other projects. Increasing the equivalent beam stiffness can effectively suppress the vibration response, while grouting reinforcement modulated the system’s dynamic response. This study provides a theoretical framework and an efficient preliminary assessment tool for understanding vibration mechanisms and aiding early-stage design in similar projects.