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Numerical analysis of soil vibrations due to trains moving at critical speed


High-speed train induced vibrations of track structure and underlying soils differ from that induced by low-speed train. Determining the critical speed of train operation remains difficult due to the complex properties of the track, embankment and ground. A dynamic analysis model comprising track, embankment and layered ground was presented based on the two-and-half-dimensional (2.5D) finite elements combining with thin-layer elements to predict vibrations generated by train moving loads. The track structure is modeled as an Euler–Bernoulli beam resting on embankment. The train is treated as a series of moving axle loads; the embankment and ground are modeled by the 2.5D finite elements. The dynamic responses of the track structure and the ground under constant and vibrating moving loads at various speeds are presented. The results show that the critical speed of a train moving on an embankment is higher than the Rayleigh wave velocity of the underlying soil, attributed to the presence of the track structure and the embankment. It is found that the dynamic response of ground induced by moving constant loads is mostly dominated by train speed. While for the moving load with vibration frequency, the ground response is mostly affected by the vibration frequency instead of train speed. Mach effect appears when the train speed exceeds the critical speed of the track–embankment–ground system.

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Financial support from the Natural Science Foundation of China (Grant Nos. 51178418 and 51222803) is gratefully acknowledged.

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Correspondence to Renpeng Chen.

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Invited Paper from the International Symposium on Geotechnical Engineering for High-speed Transportation Infrastructure (IS-GeoTrans 2012), October 26 to 28 2012, Hangzhou, China. Co-Editors Prof. Xiong (Bill) Yu, Case Western Reserve University, USA and Prof. Renpeng Chen, Zhejiang University, China.

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Bian, X., Cheng, C., Jiang, J. et al. Numerical analysis of soil vibrations due to trains moving at critical speed. Acta Geotech. 11, 281–294 (2016).

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  • Critical speed
  • 2.5D finite element method
  • High-speed train
  • Mach effect
  • Track–embankment–ground dynamic interaction