Abstract: In this study, we propose a novel coupled periodic tunnel–soil analytical model for predicting ground-borne vibrations caused by vibration sources in tunnels. The problem of a multilayered soil overlying a semi-infinite half-space was solved using the transfer matrix method. To account for the interactions between the soil layer and tunnel structure, the transformation characteristics between cylindrical waves and plane waves were considered and used to convert the corresponding wave potentials into forms in terms of the Cartesian or cylindrical coordinate system. The induced ground-borne vibration was obtained analytically by applying a spatially periodic harmonic moving load to the tunnel invert. The accuracy and efficiency of the proposed model were verified by comparing the results under a moving constant and harmonic load with those from previous studies. Subsequently, the response characteristics under a spatially periodic harmonic moving load were identified, and the effects of a wide range of factors on the responses were systematically investigated. The numerical results showed that moving and Doppler effects can be caused by a spatially periodic harmonic moving load. The critical frequency and frequency bandwidth of the response are affected by the load type, frequency, velocity, and wavenumber in one periodicity length. Increasing the tunnel depth is an efficient way to reduce ground-borne vibrations. The effect of vibration amplification on the free surface should be considered to avoid excessive vibration levels that disturb residents.

隧道结构作用移动周期简谐荷载时的地表振动响应解析解

[1]BoströmA, KristenssonG, StrömS, 1991. Transformation properties of plane, spherical and cylindrical scalar and vector wave functions. In: Varadan VV, Lakhtakia A, Varadan VK (Eds.), Acoustic, Electromagnetic and Elastic Wave Scattering, Field Representations and Introduction to Scattering. Elsevier, Amsterdam, the Netherlands, p.165-210.

[2]ClouteauD, ArnstM, Al-HussainiTM, et al., 2005. Freefield vibrations due to dynamic loading on a tunnel embedded in a stratified medium. Journal of Sound and Vibration, 283(1-2):173-199.

[3]DegrandeG, ClouteauD, OthmanR, et al., 2006. A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element–boundary element formulation. Journal of Sound and Vibration, 293(3-5):645-666.

[4]DoyleJF, 1997. Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, 2nd Edition. Springer, New York, USA.

[5]ForrestJA, HuntHEM, 2006a. A three-dimensional tunnel model for calculation of train-induced ground vibration. Journal of Sound and Vibration, 294(4-5):678-705.

[6]ForrestJA, HuntHEM, 2006b. Ground vibration generated by trains in underground tunnels. Journal of Sound and Vibration, 294(4-5):706-736.

[7]FrançoisS, SchevenelsM, GalvínP, et al., 2010. A 2.5D coupled FE–BE methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace. Computer Methods in Applied Mechanics and Engineering, 199(23-24):1536-1548.

[8]GaoGY, HeJF, YangCB, et al., 2011. Ground vibration induced by trains moving on saturated ground using 2.5D FEM. Chinese Journal of Geotechnical Engineering, 33(2):234-241 (in Chinese).

[9]HeC, ZhouSH, DiHG, et al., 2018. Analytical method for calculation of ground vibration from a tunnel embedded in a multi-layered half-space. Computers and Geotechnics, 99:149-164.

[10]HeC, ZhouSH, GuoPJ, et al., 2019. Theoretical modelling of the dynamic interaction between twin tunnels in a multi-layered half-space. Journal of Sound and Vibration, 456:65-85.

[11]HusseinMFM, HuntHEM, 2009. A numerical model for calculating vibration due to a harmonic moving load on a floating-slab track with discontinuous slabs in an underground railway tunnel. Journal of Sound and Vibration, 321(1-2):363-374.

[12]HusseinMFM, FrançoisS, SchevenelsM, et al., 2014. The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space. Journal of Sound and Vibration, 333(25):6996-7018.

[13]JinH, TianQR, LiZ, et al., 2022. Ability of vibration control using rubberized concrete for tunnel invert-filling. Construction and Building Materials, 317:125932.

[14]KouroussisG, ConnollyDP, VerlindenO, 2014. Railway-induced ground vibrations–a review of vehicle effects. International Journal of Rail Transportation, 2(2):69-110.

[15]LinKC, HungHH, YangJP, et al., 2016. Seismic analysis of underground tunnels by the 2.5D finite/infinite element approach. Soil Dynamics and Earthquake Engineering, 85:31-43.

[16]LiuWF, WuZZ, LiCY, et al., 2022. Prediction of ground-borne vibration induced by a moving underground train based on excitation experiments. Journal of Sound and Vibration, 523:116728.

[17]LombaertG, DegrandeG, FrançoisS, et al., 2015. Ground-borne vibration due to railway traffic: a review of excitation mechanisms, prediction methods and mitigation measures. In: Nielsen JCO, Anderson D, Gautier PE, et al. (Eds.), Noise and Vibration Mitigation for Rail Transportation Systems. Springer, Heidelberg, Germany, p.253-287.

[18]LopesP, RuizJF, Alves CostaP, et al., 2016. Vibrations inside buildings due to subway railway traffic. Experimental validation of a comprehensive prediction model. Science of the Total Environment, 568:1333-1343.

[19]MaLX, LiuWN, 2018. A numerical train–floating slab track coupling model based on the periodic-Fourier-modal method. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 232(1):315-334.

[20]MaLX, LiuWN, JiangYJ, et al., 2017. Metro train-induced vibration influences on surrounding environments based on sliced finite element-infinite element coupled model. Journal of Vibration and Shock, 36(15):111-117 (in Chinese).

[21]MaLX, ZhangC, OuyangHJ, et al., 2021. 2.5D modelling of wave propagation in longitudinally curved viscoelastic structure using a coupled FEM-PML approach. Engineering Structures, 226:111337.

[22]MaM, LiuWN, QianCY, et al., 2016. Study of the train-induced vibration impact on a historic bell tower above two spatially overlapping metro lines. Soil Dynamics and Earthquake Engineering, 81:58-74.

[23]MaM, LiuWN, LiuWF, 2020. Research progresses of prediction method and uncertainty of train-induced environmental vibration. Journal of Traffic and Transportation Engineering, 20(3):1-16 (in Chinese).

[24]MaM, LiMH, QuXY, et al., 2022. Effect of passing metro trains on uncertainty of vibration source intensity: monitoring tests. Measurement, 193:110992.

[25]MetrikineAV, VrouwenvelderACWM, 2000. Surface ground vibration due to a moving train in a tunnel: two-dimensional model. Journal of Sound and Vibration, 234(1):43-66.

[26]PilantWL, 1979. Elastic Waves in the Earth. Elsevier, New York, USA.

[27]ShengX, JonesCJC, ThompsonDJ, 2002. Moving Green’s Functions for a Layered Circular Cylinder of Infinite Length. ISVR Technical Memorandum No. 885, University of Southampton, Southampton, UK.

[28]ShengX, JonesCJC, ThompsonDJ, 2005. Modelling ground vibration from railways using wavenumber finite- and boundary-element methods. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2059):2043-2070.

[29]XuLH, MaM, 2020. Study of the characteristics of train-induced dynamic SIFs of tunnel lining cracks based on the modal superposition approach. Engineering Fracture Mechanics, 233:107069.

[30]XuLH, MaM, 2022. Dynamic response of the multilayered half-space medium due to the spatially periodic harmonic moving load. Soil Dynamics and Earthquake Engineering, 157:107246.

[31]XuLH, MaM, CaoRN, et al., 2022. Effect of longitudinally varying characteristics of soil on metro train-induced ground vibrations based on wave propagation analysis. Soil Dynamics and Earthquake Engineering, 152:107020.

[32]YangYB, LiJ, 2022. 2.5D prediction of soil vibrations due to railway loads by the isogeometric analysis with scaled boundary. Engineering Analysis with Boundary Elements, 134:341-359.

[33]YangYB, LiangXJ, HungHH, et al., 2017. Comparative study of 2D and 2.5D responses of long underground tunnels to moving train loads. Soil Dynamics and Earthquake Engineering, 97:86-100.

[34]YangYB, LiuSJ, ChenW, et al., 2021. Half-space response to trains moving along curved paths by 2.5D finite/infinite element approach. Soil Dynamics and Earthquake Engineering, 145:106740.

[35]YuanZH, BoströmA, CaiYQ, 2017. Benchmark solution for vibrations from a moving point source in a tunnel embedded in a half-space. Journal of Sound and Vibration, 387:177-193.

[36]YuanZH, CaoZG, TangH, et al., 2021. Analytical layer element with a circular cavity and its application in predicting ground vibrations from surface and underground moving sources. Computers and Geotechnics, 137:104262.

[37]ZhangZH, ZhangXD, TangY, et al., 2018. Discrete element analysis of a cross-river tunnel under random vibration levels induced by trains operating during the flood season. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 19(5):346-366.

[38]ZhouSH, HeC, GuoPJ, et al., 2019. Dynamic response of a segmented tunnel in saturated soil using a 2.5D FE-BE methodology. Soil Dynamics and Earthquake Engineering, 120:386-397.

[39]ZouC, MooreJA, SanayeiM, et al., 2022. Impedance model of train-induced vibration transmission across a transfer structure into an over track building in a metro depot. Journal of Structural Engineering, 148(11):04022187.