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On-line Access: 2022-06-24

Received: 2021-07-02

Revision Accepted: 2022-01-11

Crosschecked: 2022-06-24

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714


Xue-cheng BIAN


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Journal of Zhejiang University SCIENCE A 2022 Vol.23 No.6 P.443-457


Analysis of dynamic stresses in ballasted railway track due to train passages at high speeds

Author(s):  Jing HU, Xue-cheng BIAN

Affiliation(s):  Department of Civil Engineering, Fuzhou University, Fuzhou 350108, China; more

Corresponding email(s):   jingh@fzu.edu.cn

Key Words:  Ballasted railway, Stress analysis, Track irregularity, Stress path, High speed

Jing HU, Xue-cheng BIAN. Analysis of dynamic stresses in ballasted railway track due to train passages at high speeds[J]. Journal of Zhejiang University Science A, 2022, 23(6): 443-457.

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author="Jing HU, Xue-cheng BIAN",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Analysis of dynamic stresses in ballasted railway track due to train passages at high speeds
%A Jing HU
%A Xue-cheng BIAN
%J Journal of Zhejiang University SCIENCE A
%V 23
%N 6
%P 443-457
%@ 1673-565X
%D 2022
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2100305

T1 - Analysis of dynamic stresses in ballasted railway track due to train passages at high speeds
A1 - Jing HU
A1 - Xue-cheng BIAN
J0 - Journal of Zhejiang University Science A
VL - 23
IS - 6
SP - 443
EP - 457
%@ 1673-565X
Y1 - 2022
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2100305

Repeated train passages bring detrimental effects on train operations, especially at high speeds. In this study, a computational model consisting of moving train vehicles, track structure, and track foundation is used to investigate the stress distribution in the track substructure and underlying soil, particularly when the train speed approaches the critical speed via 2.5D finite element method. The numerical model has been validated by in-situ test results from a ballasted high-speed railway. The computational results reveal that the substructure is shown to be effective in reducing the stresses transmitted to the ground; however, a simple Boussinesq approximation is proved to be inaccurate because it cannot properly take account of the effect of multi-layered substructures and train speeds. It is acceptable to assume a simplified smooth track in the analysis model for determining the maximum stresses and displacements for a low-speed railway (≤100 km/h) but, for a high-speed one, the dynamic amplification effect of track irregularities must also be considered in subgrade design. Analysis of the stress paths revealed that the load speed and track irregularity increase the likelihood of failure for the subgrade; track irregularity can induce many times of principal stress rotations even under a simple single moving load.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]AREA (American Railway Engineering Association), 1996. Manual for Railway Engineering. AREA, Washington DC, USA.

[2]AuerschL, 2008. The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks. Journal of Sound and Vibration, 310(3):587-607.

[3]BianXC, ChaoC, JinWF, et al., 2011. A 2.5D finite element approach for predicting ground vibrations generated by vertical track irregularities. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 12(12):885-894.

[4]BianXC, JinWF, JiangHG, 2012. Ground-borne vibrations due to dynamic loadings from moving trains in subway tunnels. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 13(11):870-876.

[5]BianXC, JiangHG, ChangC, et al., 2015. Track and ground vibrations generated by high-speed train running on ballastless railway with excitation of vertical track irregularities. Soil Dynamics and Earthquake Engineering, 76:29-43.

[6]BianXC, ChengC, JiangJQ, et al., 2016. Numerical analysis of soil vibrations due to trains moving at critical speed. Acta Geotechnica, 11(2):281-294.

[7]BianXC, HuJ, ThompsonD, et al., 2019. Pore pressure generation in a poro-elastic soil under moving train loads. Soil Dynamics and Earthquake Engineering, 125:105711.

[8]BrennerSC, ScottLR, 2008. The Mathematical Theory of Finite Element Methods. Springer, New York, USA.

[9]CaiY, YuHS, WanatowskiD, et al., 2013. Noncoaxial behavior of sand under various stress paths. Journal of Geotechnical and Geoenvironmental Engineering, 139(8):1381-‍1395.

[10]CaiYQ, GuoL, JardineRJ, et al., 2017. Stress‍–‍strain response of soft clay to traffic loading. Géotechnique, 67(5):446-451.

[11]ChoiJ, 2014. Retracted: influence of track support stiffness of railway tracks on track impact factor. Journal of Engineering Mechanics, 140(8):04014052.

[12]DaiF, ThompsonDJ, ZhuY, et al., 2016. Vibration properties of slab track installed on a viaduct. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 230(1):235-252.

[13]GrabePJ, 2002. Resilient and Permanent Deformation of Railway Foundations under Principal Stress Rotation. PhD Thesis, University of Southampton, Southampton, UK.

[14]HeathDL, WatersJM, ShentonMJ, et al., 1972. Design of conventional rail track foundations. Proceedings of the Institution of Civil Engineers, 51(2):251-267.

[15]HuJ, BianXC, JiangJQ, 2016. Critical velocity of high-speed train running on soft soil and induced dynamic soil response. Procedia Engineering, 143:1034-1042.

[16]HuJ, BianXC, XuWC, et al., 2019. Investigation into the critical speed of ballastless track. Transportation Geotechnics, 18:142-148.

[17]IshiharaK, TowhataI, 1983. Sand response to cyclic rotation of principal stress directions as induced by wave loads. Soils and Foundations, 23(4):11-26.

[18]JinSH, ZengZP, ChenXF, et al., 2008. PSD analysis of slab track irregularity of Qinhuangdao-Shenyang dedicated passenger railway line. Journal of Railway Science and Engineering, 5(6):17-21 (in Chinese).

[19]JuSH, KuoHH, NiSH, 2018. Vibration induced by moving cranes in high-tech buildings due to rail pad materials. Shock and Vibration, 2018:8623913.

[20]KhajehdezfulyA, 2019. Effect of rail pad stiffness on the wheel/rail force intensity in a railway slab track with short-wave irregularity. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 233(10):1038-1049.

[21]LeiXY, ZhangB, 2011. Analysis of dynamic behavior for slab track of high-speed railway based on vehicle and track elements. Journal of Transportation Engineering, 137(4):227-240.

[22]LiDQ, SeligET, 1998a. Method for railroad track foundation design. I: development. Journal of Geotechnical and Geoenvironmental Engineering, 124(4):316-322.

[23]LiDQ, SeligET, 1998b. Method for railroad track foundation design. II: applications. Journal of Geotechnical and Geoenvironmental Engineering, 124(4):323-329.

[24]LiW, BianXC, DuanX, et al., 2018. Full-scale model testing on ballasted high-speed railway: dynamic responses and accumulated settlements. Transportation Research Record: Journal of the Transportation Research Board, 2672(10):125-135.

[25]LiuGR, JerrySSQ, 2003. A non-reflecting boundary for analyzing wave propagation using the finite element method. Finite Elements in Analysis and Design, 39(5-6):403-417.

[26]NgoNT, IndraratnaB, RujikiatkamjornC, 2017. Simulation ballasted track behavior: numerical treatment and field application. International Journal of Geomechanics, 17(6):04016130.

[27]NieZH, 2005. Study on Vertical Dynamic Response of the Track/Subgrade in High-Speed Railway. PhD Thesis, Central South University, Changsha, China(in Chinese).

[28]NieZH, LiL, LiuBC, et al., 2005. Testing and analysis on vibration of subgrade for Qinhuangdao-Shenyang railway. Chinese Journal of Rock Mechanics and Engineering, 24(6):1067-1071.

[29]NRA (National Railway Administration of the People’s Republic of China), 2014. Code for Design of High Speed Railway, TB 10621-2014. NRA, Beijing, China(in Chinese).

[30]NussbaumerHJ, 1981. The fast Fourier transform. In: Nussbaumer HJ (Ed.), Fast Fourier Transform and Convolution Algorithms. Springer, Berlin, Germany, p.80-111.

[31]PowrieW, YangLA, ClaytonCRI, 2007. Stress changes in the ground below ballasted railway track during train passage. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221(2):247-262.

[32]PowrieW, PriestJA, ClaytonCRI, 2008. Recent research on railway track sub-base behaviour. In: Ellis E, Yu HS, McDowell G (Eds.), Advances in Transportation Geotechnics. CRC Press, London, UK, p.37-46.

[33]RaymondGP, 1978. Design for railroad ballast and subgrade support. Journal of the Geotechnical Engineering Division, 104(1):45-60.

[34]SayeedA, ShahinMA, 2016. Three-dimensional numerical modelling of ballasted railway track foundations for high-speed trains with special reference to critical speed. Transportation Geotechnics, 6:55-65.

[35]SeligET, WatersJM, 1994. Track Geotechnology and Substructure Management. Thomas Telford, London, UK.

[36]ShengX, JonesCJC, PetytM, 1999. Ground vibration generated by a load moving along a railway track. Journal of Sound and Vibration, 228(1):129-156.

[37]ShinozukaM, 2005. Simulation of multivariate and multidimensional random processes. The Journal of the Acoustical Society of America, 49(1B):357-368.

[38]TakemiyaH, 2003. Simulation of track-ground vibrations due to a high-speed train: the case of X-2000 at Ledsgard. Journal of Sound and Vibration, 261(3):503-526.

[39]TakemiyaH, BianXC, 2005. Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage. Journal of Engineering Mechanics, 131(7):699-711.

[40]TanakaT, HiguchiT, BabaS, 2011. History of railway track maintenance of Japan from the viewpoint of regulations. Journal of Japan Society of Civil Engineers, Ser. D2 (Historical Studies in Civil Engineering), 67(1):38-48 (in Janpanese).

[41]VarandasJN, PaixãoA, FortunatoE, et al., 2016. A numerical study on the stress changes in the ballast due to train passages. Procedia Engineering, 143:1169-1176.

[42]XiaoJH, JuangCH, WeiK, et al., 2014. Effects of principal stress rotation on the cumulative deformation of normally consolidated soft clay under subway traffic loading. Journal of Geotechnical and Geoenvironmental Engineering, 140(4):04013046.

[43]YangLA, PowrieW, PriestJA, 2009. Dynamic stress analysis of a ballasted railway track bed during train passage. Journal of Geotechnical and Geoenvironmental Engineering, 135(5):680-689.

[44]YangYB, HungHH, 2001. A 2.5D finite/infinite element approach for modelling visco-elastic bodies subjected to moving loads. International Journal for Numerical Methods in Engineering, 51(11):1317-1336.

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