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A comparison of two numerical models for the prediction of vibrations from underground railway traffic

A comparison of two numerical models for the prediction of vibrations from underground railway traffic
A comparison of two numerical models for the prediction of vibrations from underground railway traffic
Two prediction models for calculating vibration from underground railways are developed: the pipe-in-pipe model and the coupled periodic finite element–boundary element (FE–BE) model.

The pipe-in-pipe model is a semi-analytical three-dimensional model that accounts for the dynamic interaction between the track, the tunnel and the soil. The continuum theory of elasticity in cylindrical coordinates is used to model two concentric pipes: an inner pipe to represent the tunnel wall and an outer pipe to represent the surrounding soil. The tunnel and soil are coupled accounting for equilibrium of stresses and compatibility of displacements at the tunnel–soil interface. This method assumes that the tunnel is invariant in the longitudinal direction and the problem is formulated in the frequency–wavenumber domain using a Fourier transformation. A track, formulated as an Euler–Bernoulli beam, is then coupled to this model. Results are transformed to the space domain using the inverse Fourier transform.

The coupled periodic FE–BE model is based on a subdomain formulation, where a boundary element method is used for the soil and a finite element method for the tunnel. The Craig–Bampton substructuring technique is used to efficiently incorporate the track in the tunnel. The periodicity of the tunnel is exploited using the Floquet transformation to formulate the track–tunnel–soil interaction problem in the frequency–wavenumber domain and to compute the wave field radiated into the soil.

An invariant concrete tunnel, embedded in a homogeneous full space is analyzed using both approaches. The pipe-in-pipe model offers an exact solution to this problem, which is used to validate the coupled periodic FE–BE model. The free field response due to a harmonic load in the tunnel is predicted and results obtained with both models are compared. The advantages and limitations of both models are highlighted. The coupled periodic FE–BE model has a greater potential as it can account for the complex periodic geometry of the tunnel and the layering in a soil medium. The effect of coupling a floating slab to the tunnel–soil system is also studied with both models by calculating the insertion gain.

periodic fe–be method, pipe-in-pipe model, floating slabs, ground vibrations, dynamic track–tunnel–soil interaction
0267-7261
608-624
Gupta, S.
32658b41-cb78-4f2d-8848-f4b2e92e4fc5
Hussein, M.F.M.
3535c131-1710-4edc-a4a1-8fe67dee3f67
Degrande, G.
c79408b0-fe8a-4b0c-a2e2-347ccd2e052a
Hunt, H.E.M.
00743f03-05d5-4a74-bd25-96cd0679f808
Clouteau, D.
ce589a5f-517e-42ea-81b8-8a631340d999
Gupta, S.
32658b41-cb78-4f2d-8848-f4b2e92e4fc5
Hussein, M.F.M.
3535c131-1710-4edc-a4a1-8fe67dee3f67
Degrande, G.
c79408b0-fe8a-4b0c-a2e2-347ccd2e052a
Hunt, H.E.M.
00743f03-05d5-4a74-bd25-96cd0679f808
Clouteau, D.
ce589a5f-517e-42ea-81b8-8a631340d999

Gupta, S., Hussein, M.F.M., Degrande, G., Hunt, H.E.M. and Clouteau, D. (2007) A comparison of two numerical models for the prediction of vibrations from underground railway traffic. Soil Dynamics and Earthquake Engineering, 27 (7), 608-624. (doi:10.1016/j.soildyn.2006.12.007).

Record type: Article

Abstract

Two prediction models for calculating vibration from underground railways are developed: the pipe-in-pipe model and the coupled periodic finite element–boundary element (FE–BE) model.

The pipe-in-pipe model is a semi-analytical three-dimensional model that accounts for the dynamic interaction between the track, the tunnel and the soil. The continuum theory of elasticity in cylindrical coordinates is used to model two concentric pipes: an inner pipe to represent the tunnel wall and an outer pipe to represent the surrounding soil. The tunnel and soil are coupled accounting for equilibrium of stresses and compatibility of displacements at the tunnel–soil interface. This method assumes that the tunnel is invariant in the longitudinal direction and the problem is formulated in the frequency–wavenumber domain using a Fourier transformation. A track, formulated as an Euler–Bernoulli beam, is then coupled to this model. Results are transformed to the space domain using the inverse Fourier transform.

The coupled periodic FE–BE model is based on a subdomain formulation, where a boundary element method is used for the soil and a finite element method for the tunnel. The Craig–Bampton substructuring technique is used to efficiently incorporate the track in the tunnel. The periodicity of the tunnel is exploited using the Floquet transformation to formulate the track–tunnel–soil interaction problem in the frequency–wavenumber domain and to compute the wave field radiated into the soil.

An invariant concrete tunnel, embedded in a homogeneous full space is analyzed using both approaches. The pipe-in-pipe model offers an exact solution to this problem, which is used to validate the coupled periodic FE–BE model. The free field response due to a harmonic load in the tunnel is predicted and results obtained with both models are compared. The advantages and limitations of both models are highlighted. The coupled periodic FE–BE model has a greater potential as it can account for the complex periodic geometry of the tunnel and the layering in a soil medium. The effect of coupling a floating slab to the tunnel–soil system is also studied with both models by calculating the insertion gain.

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More information

Published date: July 2007
Keywords: periodic fe–be method, pipe-in-pipe model, floating slabs, ground vibrations, dynamic track–tunnel–soil interaction
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 354582
URI: http://eprints.soton.ac.uk/id/eprint/354582
ISSN: 0267-7261
PURE UUID: 6de45334-ced7-408d-9924-07530c515e95

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Date deposited: 21 Oct 2013 11:06
Last modified: 08 Jan 2022 15:08

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Contributors

Author: S. Gupta
Author: M.F.M. Hussein
Author: G. Degrande
Author: H.E.M. Hunt
Author: D. Clouteau

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