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Excitation force spectra are necessary for a realistic prediction of railway-induced ground vibration. The excitation forces cause the ground vibration and they are themselves a result of irregularities passed by the train. The methods of the related analyses - the wavenumber integration for the wave propagation in homogeneous or layered soils, the combined finite-element boundary-element method for the vehicle-track-soil interaction - have already been presented and are the base for the advanced topic of this contribution. This contribution determines excitation force spectra of railway traffic by two completely different methods. The forward analysis starts with vehicle, track and soil irregularities, which are taken from literature and axle-box measurements, calculates the vehicle-track interaction and gets theoretical force spectra as the result. The second method is a backward analysis from the measured ground vibration of railway traffic. A calculated or measured transfer function of the soil is used to determine the excitation force spectrum of the train. A number of measurements of different soils and different trains with different speeds are analysed in that way. Forward and backward analysis yield the same approximate force spectra with values around 1 kN for each axle and third of octave.
The attenuation of the amplitudes with distance of technically induced surface wave fields is analyzed in theory and experiments. Experimental results of technically induced ground vibration are presented and collected from literature, which show a power-low attenuation A ~ r–q of amplitudes A with distance r and exponents q > 0.5 higher than for elastic surface waves. Additional attenuation effects are analyzed theoretically. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as A ~ exp(–kr), but for a broadband excitation, the sum of the exponential laws yields a power law with a higher exponent. Some more effects are discussed, for example the dispersion of the Rayleigh wave due to the layering of the soil, which yields a stronger attenuation A ~ r–q–dq, including an additional exponent of dq = 0.5 in case of an impulsive loading.
The attenuation of technically induced surface waves is studied theoretically and experimentally. In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation ν ~ r -q where the exponents q are in the range of 0.5 to 2.0 and depend on the source types. Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected. Some potential effects on ground vibration attenuation are theoretically analyzed. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as exp(-kr), but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent. Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.
Construction work, such as pile driving and soil compaction, or road and railway traffic excite nearby buildings, and the perceptible or audible vibration can be a nuisance for nearby inhabitants. A simplified building model has been created for these situations, which includes the effects of soil-structure interaction, the low-frequency amplification along the height of the building as well as the high-frequency reduction and the floor resonances. The model consists of one wall for all supporting structures (walls and columns) and one floor for each storey. The effect of different floor resonance frequencies is included in a stochastic procedure. The soil is modelled by a spring and a viscous damper, and the free-field amplitudes of the soil are applied under this soil element.
The model can be calculated by transfer matrices or in a continuous wave-type version where an analytical solution can be evaluated numerically. The building response in the high-frequency (acoustic) region is calculated as mean values over wider frequency bands. The approach to an infinite building model can be found for these high frequencies and the corresponding soil-structure transfer can be described by the ratio of impedances at foundation level.
The rules for choosing the parameters to obtain realistic results are derived from complex calculations for example, for the stiffness and damping of building foundations and many measurements as for the damping of floor resonances. The influences on the floor resonance from the soil (damping) and the supporting structure (detuning) are important. Some more effects will be discussed by the simplified and detailed models and by measurements to establish a good understanding of ground-induced building vibrations.
The dynamics of slab tracks and floating slab tracks are analyzed by multibeam models for the track and by integration in the wave-number domain for the soil, which is modeled as a layered half-space. Frequency-dependent compliances and force transfers are calculated for a great variety of track and soil parameters. The distribution of the load and the displacements along the track is investigated as well as the wave propagation perpendicular to the track and the ground vibration amplitudes. The floating slab track has a dominating plate-mat resonance and a strong high-frequency reduction. A track-soil resonance can also be recognized for an unisolated slab track in the case of layered soils. Generally, there is a strong damping of the track by the soil. The reduction effect of the slab mat is mainly owing to the elimination of this strong damping. The continuous soil yields slightly different rules for the displacements and force densities than those of a Winkler support. The total force transfer from the rail to the soil is the best criterion to judge the effectiveness of a floating slab track in reducing the ground vibration at some distance from the railway line. The total force transfer is easier to calculate than the double Fourier integrals of the ground vibration amplitudes, namely in the far field, and it has the best correlation with the reduction of the ground vibration.
Vehicle, track and ground vibration as well as their interaction are considered in a combined finite-element boundary-element (FEBEM) approach. The layered soil is calculated in frequency wavenumber domain and the solution for fixed or moving point or track loads follow as wavenumber integrals. The soil results from the measurements and the detailed models are approximated by simple formula which are used for the prediction of train-induced ground vibration. The influence of the track and the soil on the train induced ground vibration is analysed by the detailed models. The ground vibrations strongly depend on the regular and random inhomogeneity of the soil. The regular layering of the soil yields a cut-on and resonance phenomenon while the random inhomogeneity yields a scattering of the axle impulses which proved to be important for high-speed trains. The attenuation with distance of the ground vibration due to the point-like excitations such as vibrator or hammer excitations and the train-track excitation are investigated and compared. All theoretical results are compared with measurements at conventional and high-speed railway lines.