Assessing the impact of building foundations located in the transmission path on train-induced ground vibration using a hybrid computational model

Abstract

Train-induced ground vibration impacts the environment and has attracted increased attention. Prediction of this vibration is subject to considerable uncertainty and is affected by many factors, particularly when building foundations are situated within the transmission path between the vibration source and the target building. A hybrid computational model for predicting ground vibration has been developed to assess the impact of building foundations of various types located in the transmission path. The model is used to investigate four types of foundations: raft, strip, pile, and box. The ground responses are determined by combining the semi-analytical model ‘modelling of train-induced vibration’ (MOTIV) for train-induced vibration with a finite element model of the ground including the building. MOTIV is used to determine the excitation in terms of the force density for a train running either on a surface railway or in a tunnel. The finite element model is used to determine line source transfer mobilities in the presence of the building foundations by applying a set of incoherent unit loads to the ground. The results indicate that building foundations in the transmission path can mitigate ground vibration, particularly for excitation at the ground surface, for which reductions in overall vibration level of between 4 and 8 dB are found. Deep foundations provide greater vibration reduction than shallow foundations, notably in cases involving surface railways. The underground railway case demonstrates less significant insertion loss than the surface railway case, with values based on overall velocity level between −2 and 2 dB, rising to 4 dB for the box foundation. Furthermore, it is observed that ground vibration mitigation is more pronounced in the near field than in areas further from the building.

Keywords

Train-induced vibration / Ground vibration / Hybrid model / Finite element model / Building foundation

References

[1] Thompson DJ, Kouroussis G, Ntotsios E. Modelling, simulation and evaluation of ground vibration caused by rail vehicles. Veh Syst Dyn, 2019, 57(7): 936-983

[2] With C, Bahrekazemi M, Bodare A. Validation of an empirical model for prediction of train-induced ground vibrations. Soil Dyn Earthq Eng, 2006, 26(11): 983-990

[3] Gjelstrup H, Alcover IF, Andersen JE, et al.. Probabilistic empirical model for train-induced vibrations. Proc Inst Civ Eng-Struct Build, 2016, 169(8): 563-573

[4] Kouroussis G, Vogiatzis KE, Connolly DP. Assessment of railway ground vibration in urban area using in situ transfer mobilities and simulated vehicle-track interaction. Int J Rail Transp, 2018, 6(2): 113-130

[5] Alsharo A, Douier K, Hussein MFM, et al.. Investigating the effect of using softer rail-pads on ground-borne vibration from underground railways. Int J Rail Transp, 2024, 12(5): 803-826

[6] International Organization for Standardization (2005) Mechanical vibration—ground-borne noise and vibration arising from rail systems. ISO 14837–1. Geneva

[7] Hanson CE, Ross JC, Towers DA et al (2012) High-speed ground transportation noise and vibration impact assessment. United States Federal Railroad Administration. Office of Railroad Policy and Development.

[8] Hanson CE, Towers DA, Meister L (2006) Transit noise and vibration impact assessment. US Department of Transportation, Federal Transit Administration

[9] Sheng X, Jones CJC, Thompson DJ. A theoretical model for ground vibration from trains generated by vertical track irregularities. J Sound Vib, 2004, 272(3–5): 937-965

[10] Hussein MFM, Hunt HEM. A numerical model for calculating vibration from a railway tunnel embedded in a full-space. J Sound Vib, 2007, 305(3): 401-431

[11] Yang J, Zhu S, Li Q, et al.. A spatial train-track-tunnel coupled dynamics model for assessing influences of curved railway line on circular tunnel vibrations. Appl Math Model, 2025, 140 115892

[12] Yang J, Zhu S, Xu L, et al.. A 3D train-track-tunnel-soil coupled dynamics model based on semi-analytical cylindrical layer element. Comput Geotech, 2025, 179 106966

[13] Jin Q, Thompson DJ, Lurcock DEJ, et al.. A 2.5d finite element and boundary element model for the ground vibration from trains in tunnels and validation using measurement data. J Sound Vib, 2018, 422: 373-389

[14] Li Z, Xu L, Wang D, et al.. 2D and 3D soil finite/infinite element models: modelling, comparison and application in vehicle–track dynamic interaction. Int J Rail Transp, 2023, 11(3): 339-363

[15] Xu L, Wu L, Li Z, et al.. Further research of multi-scale assemble and matrix reassemble method for efficient analysis of railway track–substructure system subjected to a moving train. Railw Eng Sci, 2025, 33(2): 271-289

[16] Sheng X, Jones CJC, Thompson DJ. Prediction of ground vibration from trains using the wavenumber finite and boundary element methods. J Sound Vib, 2006, 293(3–5): 575-586

[17] Degrande G, Clouteau D, Othman R, et al.. A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element–boundary element formulation. J Sound Vib, 2006, 293(3–5): 645-666

[18] François S, Schevenels M, Galvín P, et al.. A 2.5D coupled FE–BE methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace. Comput Methods Appl Mech Eng, 2010, 199(23–24): 1536-1548

[19] Xu Q, Xiao Z, Liu T, et al.. Comparison of 2D and 3D prediction models for environmental vibration induced by underground railway with two types of tracks. Comput Geotech, 2015, 68: 169-183

[20] Auersch L. Simple and fast prediction of train-induced track forces, ground and building vibrations. Railw Eng Sci, 2020, 28(3): 232-250

[21] Kuo KA, Jones S, Hunt HEM et al (2008). Applications of PiP: vibration of embedded foundations near a railway tunnel. In: 7th European Conference on Structural Dynamics. Southampton, pp E322

[22] Auersch L. Dynamic stiffness of foundations on inhomogeneous soils for a realistic prediction of vertical building resonance. J Geotech Geoenviron Eng, 2008, 134(3): 328-340

[23] Hussein M, Hunt H, Kuo K, et al.. The use of sub-modelling technique to calculate vibration in buildings from underground railways. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2015, 229(3): 303-314

[24] He C, Zhou S, Guo P. An efficient three-dimensional method for the prediction of building vibrations from underground railway networks. Soil Dyn Earthq Eng, 2020, 139 106269

[25] Clot A, Arcos R, Romeu J. Efficient three-dimensional building-soil model for the prediction of ground-borne vibrations in buildings. J Struct Eng, 2017, 143(9): 04017098

[26] Yang J, Zhu S, Zhai W, et al.. Prediction and mitigation of train-induced vibrations of large-scale building constructed on subway tunnel. Sci Total Environ, 2019, 668: 485-499

[27] Ropars P, Vuylsteke X, Augis E (2018) Vibrations induced by metro in sensitive buildings; experimental and numerical comparisons. In: EURONOISE 2018 Conference. Heraklion, pp 1381–1386

[28] Bucinskas P, Ntotsios E, Thompson DJ, et al.. Modelling train-induced vibration of structures using a mixed-frame-of-reference approach. J Sound Vib, 2021, 491 115575

[29] Lopes P, Costa PA, Ferraz M, et al.. Numerical modeling of vibrations induced by railway traffic in tunnels: from the source to the nearby buildings. Soil Dyn Earthq Eng, 2014, 61: 269-285

[30] Lopes P, Alves Costa P, Calçada R, et al.. Influence of soil stiffness on building vibrations due to railway traffic in tunnels: numerical study. Comput Geotech, 2014, 61: 277-291

[31] Colaço A, Alves Costa P, Amado-Mendes P, et al.. Vibrations induced by railway traffic in buildings: Experimental validation of a sub-structuring methodology based on 2.5D FEM-MFS and 3D FEM. Eng Struct, 2021, 240 112381

[32] Villot M, Ropars P, Jean P, et al.. Modeling the influence of structural modifications on the response of a building to railway vibration. Noise Control Eng J, 2011, 59(6641

[33] Coulier P, François S, Lombaert G, et al.. Application of hierarchical matrices to boundary element methods for elastodynamics based on Green’s functions for a horizontally layered halfspace. Eng Anal Bound Elem, 2013, 37(121745-1758

[34] Çelebi E, Fırat S, Çankaya İ. The evaluation of impedance functions in the analysis of foundations vibrations using boundary element method. Appl Math Comput, 2006, 173(1): 636-667

[35] Edirisinghe TL, Talbot JP. The significance of source-receiver interaction in the response of piled foundations to ground-borne vibration from underground railways. J Sound Vib, 2021, 506 116178

[36] Verbraken H, Lombaert G, Degrande G. Verification of an empirical prediction method for railway induced vibrations by means of numerical simulations. J Sound Vib, 2011, 330(8): 1692-1703

[37] Kuo KA, Verbraken H, Degrande G, et al.. Hybrid predictions of railway induced ground vibration using a combination of experimental measurements and numerical modelling. J Sound Vib, 2016, 373: 263-284

[38] Kouroussis G, Vogiatzis KE, Connolly DP. A combined numerical/experimental prediction method for urban railway vibration. Soil Dyn Earthq Eng, 2017, 97: 377-386

[39] Colaço A, Castanheira-Pinto A, Alves Costa P, et al.. Combination of experimental measurements and numerical modelling for prediction of ground-borne vibrations induced by railway traffic. Constr Build Mater, 2022, 343 127928

[40] Reumers P, Degrande G, Lombaert G, et al.. Integration of a hybrid vibration prediction model for railways into noise mapping software: methodology, assumptions and demonstration. Railw Eng Sci, 2025, 33(1): 1-26

[41] Lai CG, Callerio A, Faccioli E, et al.. Prediction of railway-induced ground vibrations in tunnels. J Vib Acoust, 2005, 127(5): 503-514

[42] Liu W, Wu Z, Li C, et al.. Prediction of ground-borne vibration induced by a moving underground train based on excitation experiments. J Sound Vib, 2022, 523 116728

[43] Li Z, Ma M, Li M, et al.. Hybrid method combining numerical modelling and experimental measurements for predicting ground-borne vibrations induced by underground trains. Soil Dyn Earthq Eng, 2024, 187 108959

[44] Ntotsios E, Thompson DJ, Hussein MFM. A comparison of ground vibration due to ballasted and slab tracks. Transp Geotech, 2019, 21 100256

[45] Ntotsios E, Thompson D, Hussein M. The effect of track load correlation on ground-borne vibration from railways. J Sound Vib, 2017, 402: 142-163

[46] Forrest JA, Hunt HEM. A three-dimensional tunnel model for calculation of train-induced ground vibration. J Sound Vib, 2006, 294(4–5): 678-705

[47] Forrest JA, Hunt HEM. Ground vibration generated by trains in underground tunnels. J Sound Vib, 2006, 294(4/5): 706-736

[48] Hussein MFM, François S, Schevenels M, et al.. The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space. J Sound Vib, 2014, 333(25): 6996-7018

[49] Ntotsios E, Thompson DJ, Reumers P, et al.. A track-independent vehicle indicator for ground-borne noise and vibration emission classification. Transp Geotech, 2024, 45 101215

[50] Thompson D, Ntotsios E, Degrande G et al (2022) Database for vibration emission, ground transmission and building transfer functions. SILVARSTAR project GA 101015442, Deliverable D2.1

[51] Thompson D. Railway noise and vibration: mechanisms, modelling and means of control, 20242Amsterdam, Elsevier

[52] Lurcock D (2018) Predicting groundborne noise and vibration in buildings from railway. Dissertation, University of Southampton

Funding

China Scholarship Council(202007090012)

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