Ground Vibrations from High-Speed Railways Krylov, V V ISBN 978-0-7277-6379-2 https://doi.org/10.1680/gvfhsr.63792 ICE Publishing: All rights reserved Chapter 2 Fast trains and isolating tracks on inhomogeneous soils Lutz Auersch Federal Institute for Materials Research and Testing, Berlin, Germany 2.1. Introduction The main topic of this chapter is the influence of the homogeneous or inhomogeneous soil model on the prediction of train-induced ground vibrations. The homogeneous half-space is the simplest but also the most extreme soil model. The homogeneous soil model has often been used by the German Federal Institute for Materials Research and Testing (BAM) for Berlin soil, which consists of the same material down to great depths. It was observed in early measurements by BAM that certain soil behaviours can be explained only by the presence of inhomogeneous soils (Holzlo¨hner and Auersch, 1984). Inhomogeneous soils were analysed first by the two-dimensional (2D) finite-element method and thin-layer boundaries (Auersch, 1983; Ru¨cker, 1979) and later by wavenumber integrals (Auersch, 1994). The layering of the soil also has an important influence on train-induced ground vibration. This was clearly demonstrated in early test runs by the Institution of Civil Engineers (ICE) (Auersch, 1988, 2012) (Figure 2.1). Detailed and simplified methods have been developed for the careful analysis and approximate predic- tion of all aspects of railway-induced vibrations. The wavenumber method yields the dynamic soil and track behaviour, including infinitely long tracks and trans-Rayleigh trains. The combined finite- element boundary element method uses the Green’s functions from the wavenumber method to calculate the track–soil and the building–soil interaction. A variety of explicit formulas have been derived from the results of the detailed models to predict the emission, transmission and immission of train-induced ground vibrations. The methods used in this chapter will be described in full detail. Results will be presented to illustrate the special impact of inhomogeneous soils on railway vibration. Layered soils, namely a soft layer on a stiffer half-space, yield a quite specific transmission behaviour. The low-frequency and sometimes also high-frequency cut-off of the transfer function of the soil is demonstrated in theory and by experiments at some sites, for which the soil model is approximated from dispersion and transfer function measurements. In addition to the dynamic axle loads, the passage of static loads can also cause ground vibrations. Whereas for normal trains the static axle loads have only minor ground vibration effects, their contri- bution could be more important for high-speed trains. A particular effect arises when the train runs at the Rayleigh wave speed of the soil or even faster. The strongest effects are for homogeneous soils. It is still to be determined which Rayleigh train effects remain for realistic inhomogeneous soils. This question will be analysed in detail in this chapter. COPYRIGHTED MATERIAL. DO NOT DISTRIBUTE