Simple and fast prediction of train-induced track forces,ground and building vibrations

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 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.

Dynamic track-soil interaction——calculations and measurements of slab and ballast tracks

The dynamic behaviour of slab and ballast tracks was investigated using measurements and calculations.Hammer impacts and train passages were analysed and measurements were made using geophones(velocity transducers)which had been time-integrated to displacements.The calculations were carried out in the frequency-wavenumber domain for multi-beamon-continuous soil models.The characteristics of the different tracks and track elements were established in theory and by experiment.The frequency-dependent compliances(displacement transfer functions)showed clear rail-on-railpad resonances or highly damped track-soil resonances.Compared to the rail and sleeper,the track slab had much lower amplitudes.The slab track usually had the highest rail amplitudes due to soft railpads.Train passage yielded track displacements which were a superposition of the axle loads from the two neighbouring axles of a bogie and from the two bogies of two neighbouring carriages.This global behaviour was characteristic of the track slab of the slab track,whereas the rails of the slab and the ballast tracks behaved more locally with only one bogie of influence.The measurements agreed very well with the theory of continuous soil in the case of the six measured slab tracks and acceptably well for the six measured ballast tracks.The measurements allowed us to find appropriate model parameters and to check the models.For example,the Winkler model of the soil was found to be less appropriate because it reacted more locally.