Simple and fast prediction of train-induced track forces, ground and building vibrations
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Simple and fast prediction of train-induced track forces, ground and building vibrations Lutz Auersch1
Received: 25 May 2020 / Revised: 30 July 2020 / Accepted: 6 August 2020 The Author(s) 2020
Abstract A simple and fast prediction scheme is presented for train-induced ground and building vibrations. Simple models such as (one-dimensional) transfer matrices are used for the vehicle–track–soil interaction and for the building–soil interaction. The wave propagation through layered soils is approximated by a frequency-dependent homogeneous half-space. The prediction is divided into the parts ‘‘emission’’ (excitation by railway traffic), ‘‘transmission’’ (wave propagation through the soil) and ‘‘immission’’ (transfer into a building). The link between the modules is made by the excitation force between emission and transmission, and by the free-field vibration between transmission and immission. All formula for the simple vehicle–track, soil and building models are given in this article. The behaviour of the models is demonstrated by typical examples, including the mitigation of train vibrations by elastic track elements, the low- and high-frequency cut-offs characteristic for layered soils, and the interacting soil, wall and floor resonances of multi-storey buildings. It is shown that the results of the simple prediction models can well represent the behaviour of the more time-consuming detailed models, the finite-element boundary-element models of the track, the wavenumber integrals for the soil and the three-dimensional finite-element models of the building. In addition, measurement examples are given for each part of the prediction, confirming that the methods provide reasonable results. As the prediction models are fast in calculation, many predictions can be done, for example to assess the environmental effect along a new & Lutz Auersch [email protected] 1
Federal Institute of Materials Research and Testing, D-12200 Berlin, Germany
railway line. The simple models have the additional advantage that the user needs to know only a minimum of parameters. So, the prediction is fast and user-friendly, but also theoretically and experimentally well-founded. Keywords Railway-induced vibration Ground vibration Layered soil Building response Excitation forces Track and vehicle irregularities List of symbols A Amplitude AL Layer amplitude AH Half-space amplitude AS Soil area under the foundation AW Cross-area of the wall b Track width b* Normalised track width c Damping of the soil under the foundation C0 Damping matrix dC Thickness of the column dW Thickness of the wall dF Thickness of the floor D Material damping ratio of track or building material EC Elasticity modulus of concrete EM Elasticity modulus of masonry e1,e2 Base vectors EI Bending stiffness EI Bending stiffness matrix f Frequency f0 Basic resonance frequency of the building f1 Layer frequency fC Resonance frequency of the wall/column fF Eigenfrequency of the floor F Force (point load)
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FS FT FW F* FT G h h1 hB H HP
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