A prediction model for field vibrations induced by urban trains of ground line

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1 JOURNAL OF EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol. 32 No. 6 Dec TB533. 2P A A prediction model for field vibrations induced by urban trains of ground line WEI Pengbo 1 XIA He 2 CAO Yanmei 2 1. Xi an Metro Co. ltd Xi an China2. School of Civil EngineeringBeijing Jiaotong UniversityBeijing China AbstractA prediction model for field vibrations induced by urban trains of ground line is proposed by establishing an analytical model and influence factor analysis. The analytical model is composed of two models the source model and the path modelwhich are linked by the force on ballasts. The influence factors include rail type rail irregulation train speed train arrangement train load and ground soil properties. The analytical model is validated by the in situ field measured data obtained at the Beijing-Guangzhou railway line. Together with the correlation degree of statistical software the vibration prediction model is validated. The results show that the prediction model is suitable to predict the vibration induced by urban trains of ground line. Key wordsground lineurban trainenvironmental vibrationprediction modelexperimentfactor analysis JB pbwei@ 163. com

2 Ansys Hertz Fig. 1 1 Train model Lagrange M i Z i + C i Z i + K i Z i = P i t 1 Z i i P i t i M i K i C i i Fig. 2 2 Rail supporting system model of ground line 3 Fig. 3 Force analysis for rail beam 2 1 Euler-Bern-oulli 2 - k rs C rs 3 - k sb c sb

3 k bg c bg 5 m s m p N + 1 Pt V 3 Euler-Bernoulli E * r 4 w r x t 2 w r x t I r + m x 4 r = Ptδx - x 0 t 2 p - Vt- Σ N m = -N f m tδx - x m w r x t r E * r = E r 1 + 2ζ r i E r ζ r I r m r x 0 p Pt f m t Pt m Hertz 3 ~ Fig. 5 Ballast model 4 Fig. 4 Path model for train-induced vibrations of ground line 4 5 SOLID m 98 m 3 m 6 m s 1 Rayleigh

4 E kpa Table1 Model parameters for soil and ballast γ kn /m 3 υ kn /m kn s /m VL z = 20 lga max /a ref 3 a max a ref a ref = 10-6 ms ~ Fig. 6 Rail type effects on ground vibration Fig Rail irregulation amplitude effects on ground vibration Fig. 8 Rail irregulation wavelength effects on ground vibration Fig Train speed effects on ground vibration Fig. 10 Train group effects on ground vibration SPSS curve estimation SPSS

5 Fig. 11 Train load effects on ground vibration Fig. 12 Ground parameters effects on ground vibration 4 4 VL = ρ E -5 ρ 2 r N e Zr e0. 012r 1 -v/ A w 4 VL dbμ ζ v r A w VL g = fr+ X v + X B 5 fr= A 1 + A 2 lnr rm A 1 = e 0. 5T A 2 = T Ts X v = r V /70-1 Vkm /h X B SPSS Fig. 13 Sensor installation and recording equipment 14 LD-98-ⅡP Fig. 14 LD-98-ⅡP radar speed detecting equipment

6 m 10 m 5 m INV303 / IV / 13a 13b LD-98-ⅡP m 15 Fig. 15 Train passing and measuring 3. 2 point at 20m 9 13# 1# Fig. 16 Validation of train-induced Fig. 17 Validation of train-induced ground vibrationpassenger ground vibrationfreight m SPSS 1. M XIA He. Dynamic interaction of vehicles and structuresm. BeijingScience Press2005. in Chinese 2YAU J DWU Y SYANG Y B. Impact response of bridges with elastic bearings to moving loadsj. Journal of Sound and Vibration WU Yean-Seng YANG Yeong-Bin. A semi-analytical approach for analyzing ground vibrations caused by trains moving over elevated bridges J.

7 44 32 Soil Dynamics and Earthquake Engineering JU S H LIN H T. Resonance characteristics of high-speed trains passing simply supported bridgesj. Journal of Sound and Vibration Chen YJJu SHNi SH et al. Prediction methodology for ground vibration induced by passing trains on bridge structuresj. Journal of Sound and Vibration D WEI Pengbo. Prediction and assessment for urban train-induced environmental vibrationsd. BeijingBeijing Jiaotong University in Chinese 7XIA HZHANG NCAO Y M. Experimental study of train-induced vibrations of environments and buildings J. Journal of Sound and Vibration JU S HLIN H T. Experimentally investigating finite element accuracy for ground vibrations induced by high-speed trains J. Engineering Structures J CAO YanmeiXIA He. Vibration of high-rise buildings induced by running trains J. Engineering Mechanics in Chinese 10. SPSS M XUE Wei. statistical analysis and application of SPSSM. BeijingChina Renmin University Press2005. in Chinese

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