Full Text:   <694>

Summary:  <220>

Suppl. Mater.: 

CLC number: 

On-line Access: 2023-07-20

Received: 2022-08-11

Revision Accepted: 2022-12-16

Crosschecked: 2023-07-20

Cited: 0

Clicked: 948

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2023 Vol.24 No.7 P.637-652

http://doi.org/10.1631/jzus.A2200385


Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil


Author(s):  Lihui XU, Meng MA

Affiliation(s):  Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China; more

Corresponding email(s):   mameng@bjtu.edu.cn

Key Words:  Coupled tunnel‍, –, ‍, soil model, Spatially periodic load, Transfer matrix method, Wave transformation, Parametric analysis


Share this article to: More <<< Previous Article|

Lihui XU, Meng MA. Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil[J]. Journal of Zhejiang University Science A, 2023, 24(7): 637-652.

@article{title="Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil",
author="Lihui XU, Meng MA",
journal="Journal of Zhejiang University Science A",
volume="24",
number="7",
pages="637-652",
year="2023",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A2200385"
}

%0 Journal Article
%T Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil
%A Lihui XU
%A Meng MA
%J Journal of Zhejiang University SCIENCE A
%V 24
%N 7
%P 637-652
%@ 1673-565X
%D 2023
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2200385

TY - JOUR
T1 - Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil
A1 - Lihui XU
A1 - Meng MA
J0 - Journal of Zhejiang University Science A
VL - 24
IS - 7
SP - 637
EP - 652
%@ 1673-565X
Y1 - 2023
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2200385


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

作者:徐利辉1,2,马蒙1,2
机构:1北京交通大学,城市地下工程教育部重点实验室,中国北京,100044;2北京交通大学,土木建筑工程学院,中国北京,100044
目的:地铁列车运行时诱发的振动会对周围环境造成不利影响。本文旨在提出适用于振动预测的周期性隧道-地层耦合解析模型,探讨各种参数(地层参数、隧道参数、荷载参数等)对振动响应的影响,研究振动的传播规律,为减振设计提供理论依据。
创新点:1.根据平面波与柱面波之间的转换关系,推导适用于环境振动预测的周期性隧道-地层耦合解析模型;2.通过参数分析,明确移动周期简谐荷载下振动响应的规律及各种参数的影响。
方法:1.通过理论推导和考虑隧道结构与层状土间的动力相互作用,获得移动周期简谐荷载下动力响应的计算方法(公式(19));2.通过对比验证,以及根据现有移动常力及移动简谐荷载的动力响应结果,验证所提模型的准确性及高效性(图4~6);3.通过参数分析,设置工程常见的参数(地层参数、隧道参数和荷载参数等),得到移动周期简谐荷载下的振动响应规律及各种参数的影响(图7~16)。
结论:1.所提周期性隧道-地层耦合解析模型的计算效率高,预测结果准确,可用于地铁列车振动环境影响预测。2.由于荷载移动效应及多普勒效应,荷载参数影响振动响应主频及频率分布带宽,但地层参数及隧道参数的影响较小。3.增加隧道埋深是降低地表振动水平的有效措施。4.地表一定距离处的振动水平高于隧道正上方,即出现振动放大区;环评时应当重点关注放大区内的振动水平,避免不利影响。

关键词:隧道-地层耦合模型;周期荷载;传递矩阵法;波转换关系;参数分析

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

Reference

[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 elementboundary 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.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE