Abstract
The vibration caused due to underground metro trains in densely populated urban areas and its adverse effect on the nearby structures and occupants is a growing concern for the policymakers and government bodies, demanding its rapid and correct assessment. Metro bodies in India use Research Designs and Standards Organisation guidelines similar to Federal Transit Administration guidelines for vibration assessment. However, in the guidelines, there is limited discussion on soil geotechnical properties, tunnel depth and axle load, which considerably affect the magnitude of train-induced ground vibration. This study focuses on developing easily comprehendible empirical relations to predict metro train-induced ground vibrations considering the effect of these parameters. Multiple non-linear regression is used to establish the empirical relations utilising the datasets generated from a two-dimensional train-track-tunnel-soil dynamic interaction (TTTSDI) finite element model. The TTTSDI model is based on the two-step methodology available in the literature and is validated with field measurement results of the Delhi metro sites. The developed empirical relations predicted the ground vibrations with maximum and minimum errors of 2.66% and 0.84%, respectively.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- \({{\dot a}_v},{{\dot a}_v}\) and a v :
-
Acceleration, velocity, and displacement vectors of the vehicle system, respectively
- ä t, \({{\dot a}_t}\) and a t :
-
Acceleration, velocity and displacement vectors of the track system, respectively
- M t, C t, and K t :
-
Global mass, damping and stiffness matrix of the track system, respectively
- M v, C v, and K v :
-
Mass, damping and stiffness matrix of the vehicle system, respectively
- N :
-
Number of degrees of freedom of track-tunnel subsystem
- P t :
-
Slab track force vector
- P v :
-
Vehicle force vector
- vl :
-
Vibration level
- V rms :
-
Root mean square velocity
References
ABAQUS 2019 (2019) Vélizy-Villacoublay, France.: Dassault Systemes, https://www.simulia.com
Anbazhagan P, Sitharam TG (2008) Seismic microzonation of Bangalore, India. Journal of Earth System Science 117:833–852, DOI: https://doi.org/10.1007/s12040-008-0071-5
Avillez J, Frost M, Cawser S, Skinner C, El-Hamalawi A, Shields P (2012) Procedures for estimating environmental impact from railway induced vibration: A review, ASME 2012 Noise Control and Acoustics Division Conference. American Society of Mechanical Engineers 381–392, DOI: https://doi.org/10.1115/NCAD2012-1083
Bathe KJ (2014) Finite element procedures, Second. Ed, Englewood Cliffs New Jersey. KJ Bathe, Watertown, MA, Watertown, MA
Chakrabortty P, Kumar U, Puri V (2018) Seismic site classification and liquefaction hazard assessment of jaipur city, India. Indian Geotech. Journal 48:768–779, DOI: https://doi.org/10.1007/s40098-017-0287-x
Chandar KR, Sastry VR, Hegde C (2017) A critical comparison of regression models and artificial neural networks to predict ground vibrations. Geotechnical and Geological Engineering 35:573–583, DOI: https://doi.org/10.1007/s10706-016-0126-3
Chatterjee K, Choudhury D (2013) Variations in shear wave velocity and soil site class in Kolkata city using regression and sensitivity analysis. Natural Hazards 69:2057–2082, DOI: https://doi.org/10.1007/s11069-013-0795-7
Connolly D, Giannopoulos A, Forde MC (2013) Numerical modelling of ground borne vibrations from high speed rail lines on embankments. Soil Dynamics and Earthquake. Engineering 46:13–19, DOI: https://doi.org/10.1016/j.soildyn.2012.12.003
Cuevas A, Febrero M, Fraiman R (2004) An anova test for functional data. Computational Statistics & Data Analysis 47:111–122, DOI:https://doi.org/10.1016/j.csda.2003.10.021
Deeks AJ, Randolph MF (1994) Axisymmetric time-domain transmitting boundaries. Journal of Engineering Mechanics 120:25–42, DOI:https://doi.org/10.1061/(ASCE)0733-9399(1994)120:1(25)
DMRC (2019) Outline design specifications for phase-IV. Delhi metro rail corporation Ltd., New Delhi
Fan C, Ding Y (2019) Cooling load prediction and optimal operation of HVAC systems using a multiple nonlinear regression model. Energy and Buildings 197:7–17, DOI: https://doi.org/10.1016/j.enbuild.2019.05.043
Ghangale D, Arcos R, Clot A, Cayero J, Romeu J (2020) A methodology based on 2.5D FEM-BEM for the evaluation of the vibration energy flow radiated by underground railway infrastructures. Tunnelling and Underground Space Technology 101:103392, DOI: https://doi.org/10.1016/j.tust.2020.103392
Gjelstrup H, Alcover IF, Andersen JE, Larsen A (2016) Probabilistic empirical model for train-induced vibrations. Proceedings of the Institution of Civil Engineers: Structures and Buildings 169:563–573, DOI: https://doi.org/10.1680/jstbu.15.00010
Hanumantharao C, Ramana GV (2008) Dynamic soil properties for microzonation of Delhi, India. Journal of Earth System Science 117: 719–730, DOI: https://doi.org/10.1007/s12040-008-0066-2
Heidary R, Esmaeili M, Gharouni Nik M (2020) Effects of train operational parameters on ground-borne vibrations induced by twin metro tunnels. International. Journal of Rail Transportation 1–13, DOI: https://doi.org/10.1080/23248378.2020.1749901
Krishna S (2013) Report of the sub-committee on rolling stock for metro railways. New Delhi
Kuhlemeyer RL, Lysmer J (1973) Finite element method accuracy for wave propagation problems. Journal of the Soil Mechanics and Foundation Divison 99:421–427
Kuppelwieser H, Ziegler A (1996) A tool for predicting vibration and structure-borne noise immissions caused by railways. Journal of Sound and Vibration 193:261–267, DOI: https://doi.org/10.1006/jsvi.1996.0266
Lei X (2017) High speed railway track dynamics, high speed railway track dynamics: Models, algorithms and applications. Springer Singapore, Singapore, DOI: https://doi.org/10.1007/978-981-10-2039-1
Ma M, Liu W, Qian C, Deng G, Li Y (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, DOI: https://doi.org/10.1016/j.soildyn.2015.11.007
Maheswari RU, Boominathan A, Dodagoudar GR (2010) Use of surface waves in statistical correlations of shear wave velocity and penetration resistance of Chennai soils. Geotechnical and Geological Engineering 28:119–137, DOI: https://doi.org/10.1007/s10706-009-9285-9
MATLAB R2020a (2020) Mathworks, California
Mhaske SY, Choudhury D (2011) Geospatial contour mapping of shear wave velocity for Mumbai city. Natural Hazards 59:317–327, DOI:https://doi.org/10.1007/s11069-011-9758-z
Nejati HR, Ahmadi M, Hashemolhosseini H, Hayati M (2012) Probabilistic analysis of ground surface vibration due to train movement, a Case study on tehran metro Line 4. Geotechnical and Geological Engineering 30:1137–1146, DOI: https://doi.org/10.1007/s10706-012-9528-z
Powrie W, Le Pen L, Milne D, Thompson D (2019) Train loading effects in railway geotechnical engineering: Ground response, analysis, measurement and interpretation. Transportation Geotechnics 21: 100261, DOI: https://doi.org/10.1016/j.trgeo.2019.100261
Quagliata A, Ahearn M, Boeker E, Roof C, Meister L, Singleton H (2018) Transit noise and vibration impact assessment manual. Cambridge, MA
Real T, Zamorano C, Ribes F, Real JI (2015) Train-induced vibration prediction in tunnels using 2D and 3D FEM models in time domain. Tunnelling and Underground Space Technology 49:376–383, DOI: https://doi.org/10.1016/j.tust.2015.05.004
Sadegheslam G, Mikaeil R, Rooki R, Ghadernejad S, Ataei M (2013) Predicting the production rate of diamond wire saws using multiple nonlinear regression analysis. Geosystem Engineering 16:275–285, DOI: https://doi.org/10.1080/12269328.2013.856276
Sharma ML, Singh Y, Gupta SC, Dubey RN, Sen A, Raj DMB (2017) Delhi metro induced vibartion measurement on various buildings. IIT Roorkee, Roorkee
Verbraken H, Eysermans H, Dechief E, François S, Lombaert G, Degrande G (2012) Verification of an empirical prediction method for railway induced vibration. In: Noise and Vibration Mitigation for Rail Transportation Systems 239–247, DOI: https://doi.org/10.1007/978-4-431-53927-8_28
Villot M, Bailhache S, Guigou C, Jean P (2015) Prediction of railway induced vibration and ground borne noise exposure in building and associated annoyance. In: Noise and Vibration Mitigation for Rail Transportation Systems 289–296, DOI: https://doi.org/10.1007/978-3-662-44832-8_34
Vogiatzis K, Zafiropoulou V, Mouzakis H (2018) Monitoring and assessing the effects from Metro networks construction on the urban acoustic environment: The athens metro Line 3 Extension. Sci. Total Environ. 639:1360–1380, DOI: https://doi.org/10.1016/j.scitotenv.2018.05.143
Xing M, Zhao C, Wang P, Lu J, Yi Q (2019) A numerical analysis of ground vibration induced by typical rail corrugation of underground subway. Shock and Vibration 2019:1–16, DOI: https://doi.org/10.1155/2019/8406813
Xu Q, Xiao Z, Liu T, Lou P, Song X (2015) Comparison of 2D and 3D prediction models for environmental vibration induced by underground railway with two types of tracks. Computers and Geotechnics 68: 169–183, DOI: https://doi.org/10.1016/j.compgeo.2015.04.011
Yang Y, Bin Hung HH (2001) A 2.5D finite/infinite element approach for modelling visco-elastic bodies subjected to moving loads. International Journal of Numerical. Methods Eng. 51:1317–1336, DOI: https://doi.org/10.1002/nme.208
Yang F, Fonder GA (1996) An iterative solution method for dynamic response O F bridge-vehicles systems. Earthquake Engineering and Structural Dynamics 25:195–215
Yang J, Zhu S, Zhai W, Kouroussis G, Wang Y, Wang K, Lan K, Xu F (2019) Prediction and mitigation of train-induced vibrations of large-scale building constructed on subway tunnel. Science of the Total Environment 668:485–499, DOI: https://doi.org/10.1016/j.scitotenv.2019.02.397
Zhai W-M (1996) Two simple fast integration methods for large-scale dynamic problems in engineering. Methods Eng. 39:1.
Lou, P., Zhong, X. G., Tang, J. F. & Zeng, Q. Y., DOI: https://doi.org/10.1002/(SICI)1097-0207(19961230)39
Zhai W, Cai Z (1997) Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track. Computers and Structures 63:987–997, DOI: https://doi.org/10.1016/S0045-7949(96)00401-4
Zhai W, Xia H, Cai C, Gao M, Li X, Guo X, Zhang N, Wang K (2013) High-speed train-track-bridge dynamic interactions — Part I: Theoretical model and numerical simulation. International Journal of Rail Transportation 1:3–24, DOI: https://doi.org/10.1080/23248378.2013.791498
Zhang J, Yan Q, Sun M, Li B, Chen W, Chen H (2021) Experimental study on the vibration damping of two parallel shield tunnels connected by an assembled transverse passage. Tunnelling and Underground Space Technology 107:103659, DOI: https://doi.org/10.1016/j.tust.2020.103659
Zhu Z, Wang L, Costa PA, Bai Y, Yu Z (2019) An efficient approach for prediction of subway train-induced ground vibrations considering random track unevenness. Journal of Sound and Vibration 455: 359–379, DOI: https://doi.org/10.1016/j.jsv.2019.05.031
Zou C, Wang Y, Tao Z (2020) Train-induced building vibration and radiated noise by considering soil properties. Sustainability 12:1–17, DOI: https://doi.org/10.3390/su12030937
Acknowledgments
The first author received a doctoral fellowship from the Ministry of Education, Government of India, to carry out the research work and is grateful for the same. The author(s) are thankful to the Delhi Metro Rail Corporation Ltd., New Delhi (India), for sharing the necessary information for this research.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kedia, N.K., Kumar, A. & Singh, Y. Development of Empirical Relations to Predict Ground Vibrations due to Underground Metro Trains. KSCE J Civ Eng 27, 251–260 (2023). https://doi.org/10.1007/s12205-022-0529-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-0529-z