Review ArticleNo Access

Dynamic Factor of Suburban Railway Bridge Considering Random Vibration

Zenong Cheng

https://orcid.org/0000-0002-3532-182X

School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, P. R. China

Center of Urban Transportation and Rail Transit, China Academy of Transportation Sciences, Beijing 100029, P. R. China

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Yun Bai

https://orcid.org/0000-0002-2585-434X

School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, P. R. China

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Xinzheng Yang

Center of Urban Transportation and Rail Transit, China Academy of Transportation Sciences, Beijing 100029, P. R. China

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Xujie Feng

Center of Urban Transportation and Rail Transit, China Academy of Transportation Sciences, Beijing 100029, P. R. China

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, and

Nan Zhang

https://orcid.org/0000-0003-0215-2465

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, P. R. China

E-mail Address: nzhang@bjtu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0219455424300015Cited by:0 (Source: Crossref)

Abstract

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications.

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References

1. L. Peng, C. Wang and J. Wu , Study on the operation mode of suburban railway at home and abroad and the inspiration to Beijing, J. Phys.: Conf. Ser. 1187 (2019) 052066. Crossref, Google Scholar
2. R. Vávra and V. Janoš , Comparison of different conceptions of suburban railway transport, 2019 Smart City Symposium Prague (SCSP) (IEEE, 2019), pp. 1–5. Crossref, Google Scholar
3. Japan Railway Comprehensive Technology Research Institute, Design Standard and Explanation of Railway Structure Concrete Structure (Marusha Co., Ltd., Tokyo, 2004). Google Scholar
4. American Railway Engineering and Maintenance-of-way Association, AREMA Manual for Railway Engineering (AREMA, Lanham, 2010). Google Scholar
5. Council of Standards Australia, Bridge Design Part 2: Design Loads: AS 5100.2:2017 (SAI Global Limited, Sydney, 2017). Google Scholar
6. UIC, Load to be Considered in Railway Bridge Design: UIC CODE776-1 (UIC, Paris, 2006). Google Scholar
7. D. W. Jacobs and R. B. Malla , On live load impact factors for railroad bridges, Int. J. Rail Transp. 7(4) (2019) 262–278. Crossref, Web of Science, Google Scholar
8. National Railway Administration, Code for Design of Suburban Railway: TB 10624-2020 (China Railway Publishing House, Beijing, 2020). Google Scholar
9. National Railway Administration, Design Code for Railway Bridges and Culverts: TB10002.1-2017 (China Railway Publishing House, Beijing, 2017). Google Scholar
10. Y. B. Yang, J. D. Yau and L. C. Hsu , Vibration of simple beams due to trains moving at high speeds, Eng. Struct. 19(11) (1997) 936–944. Crossref, Web of Science, Google Scholar
11. H. Zeng and C. W. Bert , Dynamic amplification of bridge/vehicle interaction: A parametric study for a skewed bridge, Int. J. Struct. Stab. Dyn. 3(1) (2003) 71–90. Link, Web of Science, Google Scholar
12. L. Ding and H. Hao , Influence of vehicle and bridge properties on the dynamic amplification factor and dynamic load coefficient, International Symposium on Life-Cycle Performance of Bridges and Structures (2010), pp. 859–866. Google Scholar
13. L. Deng, Y. Yu, Q. Zou and C. S. Cai , State-of-the-art review of dynamic impact factors of highway bridges, J. Bridge Eng. 20(5) (2015) 04014080. Crossref, Web of Science, Google Scholar
14. Y. B. Yang, J. D. Yau, S. Urushdaze and T. Y. Lee , Historical review on resonance and cancellation of simply supported beams subjected to moving train loads: From theory to practice, Int. J. Struct. Stab. Dyn. 23 (2023) 2340008. Link, Web of Science, Google Scholar
15. Z. J. Liu, W. Liu and Y. B. Peng , Random function based spectral representation of stationary and non-stationary stochastic processes, Probabilistic Eng. Mech. 45 (2016) 115–126. Crossref, Web of Science, Google Scholar
16. J. Li, Q. Yan and J. B. Chen , Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures, Probabilistic Eng. Mech. 27(1) (2012) 19–28. Crossref, Web of Science, Google Scholar
17. H. Xiang, P. Tang, Y. Zhang and Y. Li , Random dynamic analysis of vertical train–bridge systems under small probability by surrogate model and subset simulation with splitting, Railw. Eng. Sci. 28(3) (2020) 305–315. Crossref, Google Scholar
18. N. Zhang, Z. J. Zhou and Z. Z. Wu , Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method, Railw. Eng. Sci. 30(1) (2022) 1–16. Crossref, Google Scholar
19. R. Calcada, A. Cunha and R. Delgado , Analysis of traffic-induced vibrations in a cable-stayed bridge. Part II: Numerical modeling and stochastic simulation, J. Bridge Eng. 10(4) (2005) 386–397. Crossref, Web of Science, Google Scholar
20. X. Yin, C. S. Cai, Y. Liu and Z. Fang , Experimental and numerical studies of nonstationary random vibrations for a high-pier bridge under vehicular loads, J. Bridge Eng. 18(10) (2013) 1005–1020. Crossref, Web of Science, Google Scholar
21. Z. Yu, P. Zhang, J. Mao, P. D. Spanos and Y. F. Chen , An efficient approach for stochastic vibration analysis of high-speed maglev vehicle-guideway system, Int. J. Struct. Stab. Dyn. 21(6) (2021) 2150080. Link, Web of Science, Google Scholar
22. H. W. Xie, Q. Luo, T. F. Wang, L. W. Jiang and P. D. Connolly , Stochastic analysis of dynamic stress amplification factors for slab track foundations, Int. J. Rail Transp. (2023), https://doi.org/10.1080/23248378.2023.2170286. Web of Science, Google Scholar
23. L. Song, H. B. Liu, L. Xu and Z. W. Yu , Random simulation method of track irregularities and its application in vehicle-track dynamic analysis, Int. J. Rail Transp. 5 (2022) 169–187. Google Scholar
24. N. Zhang and Z. N. Cheng , Dynamic design method of high speed railway bridge of common span, China Railway 2021(9) (2021) 6 (in Chinese). Google Scholar
25. Z. N. Cheng, N. Zhang, Q. K. Sun and X. Liu , Research on simplified calculation method of coupled vibration of vehicle-bridge system, Shock Vib. 2021(4) (2021) 1–14. Google Scholar
26. L. Xu, W. M. Zhai and J. M. Gao , A probabilistic model for track random irregularities in vehicle/track coupled dynamics, Appl. Math. Model. 51 (2017) 145–158. Crossref, Web of Science, Google Scholar
27. L. Xu and W. M. Zhai , Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities, Veh. Syst. Dyn. 56 (2018) 1552–1576. Crossref, Web of Science, Google Scholar
28. Z. J. Zhou, N. Zhang and Z. M. Wang , Probability distribution functions of maximum wheel unloading rate based on extremal index, Int. J. Struct. Stab. Dyn. 23(2) (2023) 2350015. Link, Google Scholar
29. National Railway Administration, PSD of Ballastless Track Irregularities of High Speed Railway: TB 3352-2014 (China Railway Publishing House, Beijing, 2014). Google Scholar
30. N. Zhang, W. W. Guo and H. Xia , Dynamic Interaction of Train-Bridge Systems in High-Speed Railway (Beijing Jiaotong University Press, 2018) (in Chinese). Google Scholar
31. Q. K. Sun, N. Zhang, X. Liu and Z. N. Cheng , Dynamic amplification factors of partial-interaction composite beams acted upon by the moving load, Int. J. Struct. Stab. Dyn. 23(1) (2023) 2350012. Link, Web of Science, Google Scholar
32. W. Guo, Y. Long, C. He, Y. Wang, Y. Zeng and J. Song , Off-line hybrid simulation method on train–track–bridge coupling vibration in high-speed railway, Int. J. Struct. Stab. Dyn. 22(10) (2022) 2241014. Link, Web of Science, Google Scholar
33. Research on Main Design Loads and Dynamic Coefficients of Railway Bridges and Culverts Part 1: Research on Vertical Dynamic Action of Trains (China Academy of Railway Sciences, 2020) (in Chinese). Google Scholar