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#### Erscheinungsjahr

- 2015 (9) (entfernen)

#### Dokumenttyp

#### Sprache

- Englisch (9) (entfernen)

#### Schlagworte

- Elastic track elements (1)
- Force transfer (1)
- Geometric trackbed irregularities (1)
- Ground vibration (1)
- Multi-beam-on-support model (1)
- Parametric excitation (1)
- Rail pad (1)
- Railway (1)
- Reduction (1)
- Sleeper pad (1)

#### Organisationseinheit der BAM

- 7.2 Ingenieurbau (9) (entfernen)

The maintenance of the transport infrastructures and their further development are going to remain focal points for investment and research in Germany in future. According to the latest development forecasts made by both the federal government and Deutsche Bahn, even if rail´s percentage share of the market were to remain unchanged, growth of around 50% would be expected in the next ten years, especially in freight traffic. This growth is necessitating considerable development both in the technical design of the tracks and in the abatement of the noise and vibration caused by railway traffic.

The reduction of train-induced ground vibration by elastic elements such as rail pads and sleeper pads has been analyzed by a combined finite-element boundary-element method. The dynamic compliance of the track, the transfer function of the total force on the ground and the ground vibration ratios have been calculated for a variety of isolated and un-isolated track systems. It has been found that the soil force transfer, which describes the excitation force of the soil, is an appropriate quantity to predict the reduction of the ground vibration and the effectiveness of isolated tracks. All force transfer functions of isolated tracks display a vehicletrack resonance where the wheelset on the compliant track is excited by wheel and track irregularities. At higher frequencies, considerable reductions of the amplitudes are observed as the benefit of the resilient element. The influence of the stiffness of the rail or sleeper pads, the ballast and the soil, and the mass of the sleeper and the wheelset on the resonance frequency and the reduction has been investigated. Sleeper pads are advantageous due to the higher mass that is elastically supported compared to the rail-pad track system. The combination of elastic rail and sleeper pads has been found to be disadvantageous, as the second resonance occurs in the frequency range of intended reduction.

The computation of the wave propagation in homogeneous and layered soils can be performed by a numerical integration in wavenumber domain. The numerical difficulties of an infinite integral and an integrand with poles can be solved. But if this computation must be repeated for many distances, many frequencies, many loads, or many soil models, it becomes a time consuming task which is not acceptable for a user-friendly prediction tool for railway induced ground vibration. Therefore, an approximate method for the computation of the wave field has been developed. The computation consists of several steps. At first, an approximate dispersion profile is calculated according to rules which have been derived from exact solutions. Secondly, the dispersion is used to achieve the amplitude for a certain frequency and a certain distance by calculating the approximate solution of a corresponding homogeneous half-space. Thirdly, three layer corrections are added which include lowfrequency near-field effects, high-frequency far-field effects, and a resonance amplification around the layer frequency. This procedure yields the wave field due to a point load. For a train load, many of these point-load responses have to be summed up, and a frequencydependant reduction factor has to be multiplied to incorporate the effect of the load distribution along and across the track. - The prediction method is applied to real sites, and the appropriate soil models are identified by approximating the measured transfer functions (frequency-dependant amplitudes) which is presented as an alternative to the approximation of the dispersion (frequency-dependant wave velocities). These examples demonstrate the general behavior of layered soils: the low amplitudes of the stiff half-space at low frequencies, the high amplitudes of the softer layer at high frequencies, the strong increase of amplitudes and a possible resonance amplification at mid frequencies. The material damping of the layer yields a strong attenuation of the amplitudes with the distance for high frequencies. The response depends strongly on the resonance or layer frequency which is shown for different layer depths and velocities always in good agreement with measurements. The layer frequency can be of immense influence if train-speed effects are analysed in a layered soil. The good agreement with many measurements in this contribution as well as in the references validates the prediction of ground vibration based on the theory of a layered half-space.

Train-induced ground vibration can be excited by wheel and track irregularities and by two kinds of irregularities of the soil, by geometric irregularities or by the spatially varying soil stiffness. For both types of irregularities, the effective track irregularity on top of the track is calculated in wavenumber domain and with wavenumber integrals. For a general multi-beam track model, the wavenumber integrals are solved numerically. The irregularities of the soil are filtered by the track when transferred from the bottom to the top of the track. The high-wavenumber irregularities are strongly reduced due to the bending stiffness of the track and the compliance of the support. In addition, soft track elements reduce directly the stiffness variation of the support. Therefore, the mitigation effect of elastic track elements for these excitation components seems to be important. For under-sleeper pads and slab tracks, calculation and measurements are presented including additional excitation components and the dynamic vehicle–track interaction, and the relevance of the excitation mechanisms is discussed based on the dynamic forces which are acting on the ground. Due to the restricted amplitudes, the parametric excitation by the stiffness variation seems to be less important than the geometric irregularities. The calculations yield the correct trends of the measurements and many details of the measured ballast, slab, and under-sleeper-pad tracks.

A survey of the phenomena and methods for floor vibrations is presented. Experimental results of floor vibrations are shown for many floors in six different buildings. The signals have been evaluated for waves and modes by simple procedures. General rules have been established between the material and the area of a specific floor, and its local eigenfrequency. The damping values of the floor vibrations have been found between D = 1 and 10 % where somewhat higher values have been measured for wooden floors, and a weak correlation with the eigenfrequency has been established. The velocities of bending waves propagating in a storey and the attenuation with distance in the building have been analysed. A considerable transfer of vibration from one room to far away parts of the building has been found in the studied buildings with concrete and wooden floors. An example building has been analysed for modes of coupled floor bays. The strong coupling of similar neighbouring floor bays would yield a wide band of global resonance frequencies. The measured wooden floor exhibits a weak coupling of the neighbouring floor bays and a narrower band of eigenfrequencies. A special method has been tested with the impulse measurements to estimate the coupled eigenmodes in presence of the high damping. From the ambient measurement, a low-frequency vibration mode has been detected which includes the vibration of the whole building and the soil. The coupling of floors to other floors and the whole building is an important phenomenon of structural dynamics which should be observed for the prediction of vibration due to internal and external sources.

Train-induced ground vibrations are generated by static and dynamic axle loads which can be calculated by vehicle-track-soil models and the vehicle and track irregularities. A fast prediction method has been developed which uses approximate transfer functions of layered soils. In the present contribution, this prediction method is used for the inverse calculation of the axle-load spectra from the measured ground vibration. The layered soils of some measuring sites show very differing ground vibration spectra in the amplitude range of 0.0001–1.0 mm/s as a consequence of the soft layer and stiff half-space, differing layer frequencies, as well as the far- and near-field measuring points. The back-calculation, however, yields axle-load spectra within a single order of magnitude around 1 kN. Axle-box measurements confirm the amplitude level of the axle loads. This standard axle-load spectrum can be used for a basic prediction at a new site. The separation of train and site-specific components allows a better evaluation of railway vibrations, for example, of different trains and different tracks. By eliminating the effects of differing soil characteristics, an important mid-frequency component has been found which lies between 8 and 32 Hz depending on the train speed. The origin of this dominant mid-frequency component is discussed using advanced prediction methods like moving constant loads, scattered axle impulses and axle-sequence spectra.

Ground vibrations due to different technical sources are analysed in theory and experiment for the dispersion of Rayleigh waves and the admittance spectra. Both tasks are theoretically based on the same concept: The admittance function in frequencywavenumber domain yields the dispersion as its maxima, and the admittance function in space domain is obtained by integrating it over the wavenumbers. On the experimental side, many signal processing methods have been applied to many sites and have been developed by the authors in the last 35 years, i.e., time-domain methods, including the cross-correlation method, and frequency-domain methods such as the spectral analysis of surface waves with two or multiple sensors, the wavenumber-transform method, and the spatial autocorrelation method. All methods are presented by their basic formula and by at least one example site. Different sensor arrays and deterministic and stochastic sources have been tested for the spatial autocorrelation method and the wavenumber-transform method at several sites. In addition, all frequency-domain methods are presented for a specific layered site comparing their quality. The evaluated dispersion curves are very similar, but a somewhat higher frequency range has been found for the fastest method, i.e., the multi-sensor spectral-analysis-of-surface-waves method. The theoretical solutions have been used for the inversion of the measured dispersion to the soil profile of the specific layered soil. The theoretical soil model has subsequently been used to predict the ground vibration spectra of hammer and railway excitation that exhibit a good agreement with the corresponding measurements. Thus, the contribution shows the benefit of active and passive seismic methods for the prediction of railway vibration, including a new version of the spatial autocorrelation method for technical vibrations. On the other hand, technical and namely railway vibrations are considered a seismic source for the exploration of near surface soils.

Train passages induce static and dynamic forces on the track, the train-induced vibrations propagate through the soil and excite neighbouring buildings. The problem of train vibrations is divided into the parts emission, which is the excitation by railway traffic (the present contribution), transmission, which is the wave propagation through the soil, and immission, which is the transfer into a building, - The calculation of the axle loads are based on the vehicle-track-soil interaction. This interaction uses the dynamic stiffness of the vehicle (the inertia of the wheelset) and the dynamic stiffness of the track-soil System. Based on various time consuming finite-element boundary-element calculations, an approximate track-soil model has been established. The vehicle-track-soil analysis yields several transfer functions between the various geometric or stiffness irregularities and the axle loads of the train. Geometric irregularities of the vehicle (the wheels) and the track (rail surface and track alignment) are the simplest components. Geometric irregularities of the subsoil (trackbed irregularities) have to be transferred to effective irregularities at rail level. The bending stiffness of the track is filtering out the short-wavelength contribution. Stiffness irregularities occur due to random variations in the bailast or the subsoil, which must also be transferred to effective track irregularities, and due to the discrete rail support on sleepers. The axle loads due to the effective track errors from stiffness variations have their specific vehicle-track transfer function. - All necessary formula for the prediction of axle-load spectra will be presented. The prediction method is compared with axle-box measurements at a Standard ballasted track. Moreover, ground Vibration measurements at numerous sites are exploited for the axle-load spectra and the Validation of the prediction method.

The ground vibrations, which are generated by trains on different tracks, have been calculated by finite-element boundary-element models. The ballasted track is modelled in detail by the finite element method. The infinite soil is modelled by the boundary element method as a homogeneous or layered half-space. The track-soil system is coupled to a simple rigid mass model of the vehicle so that the vehicle-track interaction is completely included. Transfer functions are calculated in frequency domain without and with vehicle-track interaction, the compliance of the track and the mobilities of the soil at different distances from the track. Finally, the ratios between the ground vibration amplitudes with and without mitigation measures are calculated to quantify the effectiveness of the mitigation measures.
Tracks with under-sleeper pads have been investigated in a wide parameter study for the RIVAS project. The main parameters that influence the reduction of ground vibration are the stiffness of the under-sleeper pad, the mass and the width of the sleeper. The softest sleeper pad yields the best reduction of the ground vibration. The influence of the sleeper mass is not so strong, as the characteristic frequency is ruled by the mass of the sleeper and the mass of the wheelset as well.