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- Ground vibration (38)
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- Vehicle-track interaction (9)
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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.
The reduction in train-induced ground vibrations by different railway lines and by mitigation measures in the propagation path was analysed in a unified approach by two-dimensional finite element calculations. In general, there was no reduction at low frequencies, and the reduction be-came stronger with increasing frequencies. A maximum reduction of 0.1 at high frequencies was established with an open trench. Reductions between 0.7 and 0.2 have been found for the other sit-uations, filled trenches, walls, plates, and blocks, as well as for railway lines on dams, in cuts and in a tunnel. Bridges can produce amplifications due to their resonance frequencies, but also strong reductions due to massive bridge piers. The influence of some parameters has been analysed, such as the bridge span, the inclination of the dam and the cut, the stiffness of the soil, and the tunnel structure. The dynamic track stiffnesses of a surface, bridge, and tunnel track have been calculated using the 3D finite-element boundary-element method for comparison with corresponding meas-urements.
In this article, the passage of different trains over different bridges will be studied for resonant excitation. The intensity of the resonance will be estimated in frequency domain by using three separated spectra. At first, the excitation spectrum of the modal forces is built by the mode shape and the passage time of the train over the bridge. The second spectrum is the frequency response function of the bridge which include the modal frequency, damping and mass. The third part is the spectrum of the axle sequence of the train. The influences of train speed, bridge length, bridge support, track irregularities, and train type on the resonance amplitudes will be analysed for each of these spectra separately for getting a better insight. A variety of axle-sequence spectra and corresponding rules will be presented for different vehicles and trains. As examples, the passage of a slow freight train over a long-span bridge, a normal passenger train over a medium-span bridge, and a high-speed train over a short bridge will be analysed. Corresponding measurements show the amplification, but also the cancellation of the subsequent axle responses. Namely in one of the measurement examples, the first mode of the bridge was amplified and the second mode was cancelled at a low speed of the train and vice versa at a higher speed.
The soilstructure interaction of elastic plates on homogeneous or layered soils excited by horizontally propagating waves is analysed. Large plates are modelled by a combined finite-element boundary-element method (FEBEM), whereas the response of infinitely long plates is calculated by a numerical integration in the frequencywavenumber domain. The finite-element boundary-element method yields the complete soilplate transfer function of frequency and distance whereas the frequencywavenumber solution of the infinitely long plate can serve as an approximation for long distances on a finitely long plate. The soilplate transfer function starts to decrease strongly at the coincidence frequency, where the bending stiffness equals the plate inertia. A strong decrease follows at mid frequencies and a strong reduction of less than 0.1 of the ground vibration is reached at high frequencies. Rules for the characteristic frequencies are derived from the numerical results clearly indicating the strongest influence of the soil stiffness and the weaker influence of the bending stiffness of the plate. The influence of the mass, length and width of the plate are shown to be limited in case of realistic parameters, but it should be noted that the reduction effects are less effective for layered soils and for nearer observation points.
Two measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results. The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and forces.
Seismic reponse of three-dimensional structures using a Green's function approach to the soil
(1986)
Seismic response of three-dimensional structures using a green's function approach to the soil
(1986)
Simple and advanced boundary-element method for the soil and its application to railway dynamics
(2007)
Simple and advanced boundary-element method for the soil and its application to railway dynamics
(2007)
A simple and fast prediction scheme is presented for train induced ground and building vibrations. Simple models such as (1-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, that is 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.
A complex measuring campaign has been performed including the simultaneous measurement of vehicle, track, and soil vibrations during train runs at 16, 25, 40, 63, 80, 100, 125, 140, 160 km/h, and impulse measurements of the passenger car, three track sections and the soil. A ballast track on the soil surface and on a concrete bridge have been investigated as well as a slab track in a tunnel. The evaluation and comparison of all these data shows a generally good agreement for all components if the strong low- and high-frequency cut-off characteristics of the layered and damped soil are incorporated. There is a strong causal correlation between the vehicle and the soil by the dynamic excitation forces and a weak relation between the track and the soil by the axle-sequence spectrum of the train. However, the similarity between the axle-impulse spectrum observed at the track and the spectra of the ground vibration lead to the special excitation component of “scattered axle impulses” which is pre-dominant at the far-field points of the soil.
The propagation of ground vibrations is theoretically analysed with frequency-wavenumber and simplified methods. Experimental methods are presented which can characterise the site-specific ground vibrations by wave velocities, stiffness and damping. Measurements with hammer and train excitation have been performed at several sites. The one-third octave spectra show the stiffness-dependent amplitudes and the low- and high-frequency filter effects due to the layering and the damping of the soil. Specific train effects, an additional high-frequency filter, the sleeper passage frequency, and an amplified mid-frequency component can be clearly found. The attenuation with distance is analysed in detail where the theoretical exponential and the empirical frequency-dependent power law are considered. Hammer and train excitation show the same site-specific effects which are mainly due to the stronger or weaker damping of the soil. The train attenuation is generally weaker than the hammer attenuation. The attenuation exponent of the power law, which is strongly dependent on the site and the frequency, is reduced for the train vibration by 0.3 to 0.5 in agreement with the theory. Reasons are discussed for the overall power law and for the dominating mid-frequency component.
This contribution intends to give an overview on the vibration behaviour of slab tracks in comparison of measurements and calculations and also by comparison of different track types at more than ten different measuring sites.
In theory, tracks on continuous soil are calculated by the frequency-wavenumber domain method. In experiment, geophone measurements are transformed to displacement results. Two aspects of track behaviour are considered, the frequency-dependant compliance of the track, measured by hammer impact, and the deflection under a passing axle load. In theory, the response to a single axle can be calculated, whereas in experiment, only the passage of the whole train can be measured. For comparison of theory and experiment, the calculated deflection under a single axle is superposed to get the response of the whole train. As a result, the slab track characteristics are completely different from the ballast track characteristics where each axle can be seen in the time histories. The slab track has a more global behaviour where only a whole bogie can be found in the track response and moreover, the two neighbouring bogies are not completely separated. The measurement of the different track elements (rail, sleeper, track plate, base layer) and the frequency-dependant compliances with possible resonances yield further information About the properties of the track elements. The calculations show that the soil has the dominant influence on the amplitudes and the width of the track-plate displacements. In the measurement results, the following
parameters are analysed: slab track vs. ballast track, different types of slab tracks, damaged slab tracks, different trains, switches at different measuring points, voided sleepers, an elastic layer, the mortar layer, and different soils at different places. Finally, a good agreement between measured and calculated results is found for the normal and some special (damaged, floating) slab tracks.
The soil-foundation-structure interaction is always important when building vibrations due to train passages have to be considered. The frequency range for train vibrations is up to 100 Hz. Normally, soft surface soils are crucial so that the wavelength can be much smaller than the foundation dimensions. Three topics are of interest for the prediction and the under-standing of building vibrations. 1. The „kinematic interaction“ or the „added foundation ef-fect“, which is calculated either by the combined boundary-element finite-element method or by the wavenumber domain method, results in a reduction of the free-field vibration. The stiff-ness of the foundation resists the wave deformation, plates and walls for horizontally propa-gating waves or piles for vertically incident waves. 2. The „inertial interaction“ or the „added building effect“ yields an amplification around the vertical building resonance, which may be a rigid mode on the compliant soil or a flexible mode for high-rise buildings, and a reduction at higher frequencies. This has been analysed by detailed finite element models of apartment and office buildings. 3. Base isolation is a method to further reduce building vibrations. It is important to know the soil-foundation impedance for the possible reduction, as well as the correct building impedance. A high-rise building cannot be considered as a rigid mass model. It has a frequency-dependent behaviour with longitudinal waves travelling from the founda-tion to the top of the building which include the effect of floor vibrations. Experiences from building projects in Vienna, Frankfort and Berlin will give some additional results for the ex-citation from tunnel lines, the kinematic response of pile foundations, and the inertial re-sponse of the flexible multi-storey buildings.
The soil-foundation-structure interaction is always important when building vibrations due to train passages have to be considered. The frequency range for train vibrations is up to 100 Hz. Normally, soft surface soils are crucial so that the wavelength can be much smaller than the foundation dimensions. Three topics are of interest for the prediction and the under-standing of building vibrations. 1. The „kinematic interaction“ or the „added foundation ef-fect“, which is calculated either by the combined boundary-element finite-element method or by the wavenumber domain method, results in a reduction of the free-field vibration. The stiff-ness of the foundation resists the wave deformation, plates and walls for horizontally propa-gating waves or piles for vertically incident waves. 2. The „inertial interaction“ or the „added building effect“ yields an amplification around the vertical building resonance, which may be a rigid mode on the compliant soil or a flexible mode for high-rise buildings, and a reduction at higher frequencies. This has been analysed by detailed finite element models of apartment and office buildings. 3. Base isolation is a method to further reduce building vibrations. It is important to know the soil-foundation impedance for the possible reduction, as well as the correct building impedance. A high-rise building cannot be considered as a rigid mass model. It has a frequency-dependent behaviour with longitudinal waves travelling from the founda-tion to the top of the building which include the effect of floor vibrations. Experiences from building projects in Vienna, Frankfort and Berlin will give some additional results for the ex-citation from tunnel lines, the kinematic response of pile foundations, and the inertial re-sponse of the flexible multi-storey buildings.
The resonances of railway bridges have often been analysed for short bridges under periodical high-speed trains, for simply supported one-span bridges, for the fundamental bridge mode, and by time-domain analyses. Many time-consuming calculations have been performed to establish simplified rules for standards. In this contribution, the passage of different (existing, new and hypothetic) trains over different bridges will be analysed in frequency domain by using three separated spectra with the purpose to get a better physical insight in the phenomena. At first, the excitation spectrum of the modal forces is built by the mode shape and the passage time of the train over the bridge. The second spectrum is the frequency response function of the bridge which include the modal frequency, damping and mass. The third part is the spectrum of the axle sequence of an arbitrary train which is not limited to periodical or specific (conventional, articulated, regular or standard) trains and which does not include any bridge parameters. The final solution in frequency domain is obtained as the product of these three complex, strongly varying spectra for the dominating bridge mode or in general as the sum of these products over all relevant bridge modes. The time domain solution is obtained via the inverse Fourier transform, and the resulting time histories have been successfully compared with some measurement results. The method is applied to the vertical and torsional modes of a mid-long 1-span bridge on elastomeric bearings under standard train speeds, and to a long multi-span integral bridge under long periodical freight trains. Different resonance and cancellation effects have been found for systematically varied train speeds according to the axle sequence of the whole train which is dominated by the two locomotives in that case. To be more specific, the first torsional mode of the mid-span bridge is excited for a train speed of 100 km/h whereas the second bending mode is excited for a train speed of 160 km/h. In both cases, the other mode is suppressed by the minima of the axle-distance spectra. In addition, the case of the German high-speed train ICE4 and the very high-speed hyperloop case will be discussed briefly. In general, it is shown that resonance effects are also worth to be studied for freight and passenger trains with lower speeds.
The resonances of railway bridges have often been analysed for short bridges under periodical high-speed trains, for simply supported one-span bridges, for the fundamental bridge mode, and by time-domain analyses. Many time-consuming calculations have been performed to establish simplified rules for standards. In this contribution, the passage of different (existing, new and hypothetic) trains over different bridges will be analysed in frequency domain by using three separated spectra with the purpose to get a better physical insight in the phenomena. At first, the excitation spectrum of the modal forces is built by the mode shape and the passage time of the train over the bridge. The second spectrum is the frequency response function of the bridge which include the modal frequency, damping and mass. The third part is the spectrum of the axle sequence of an arbitrary train which is not limited to periodical or specific (conventional, articulated, regular or standard) trains and which does not include any bridge parameters. The final solution in frequency domain is obtained as the product of these three complex, strongly varying spectra for the dominating bridge mode or in general as the sum of these products over all relevant bridge modes. The time domain solution is obtained via the inverse Fourier transform, and the resulting time histories have been successfully compared with some measurement results. The method is applied to the vertical and torsional modes of a mid-long 1-span bridge on elastomeric bearings under standard train speeds, and to a long multi-span integral bridge under long periodical freight trains. Different resonance and cancellation effects have been found for systematically varied train speeds according to the axle sequence of the whole train which is dominated by the two locomotives in that case. To be more specific, the first torsional mode of the mid-span bridge is excited for a train speed of 100 km/h whereas the second bending mode is excited for a train speed of 160 km/h. In both cases, the other mode is suppressed by the minima of the axle-distance spectra. In addition, the case of the German high-speed train ICE4 and the very high-speed hyperloop case will be discussed briefly. In general, it is shown that resonance effects are also worth to be studied for freight and passenger trains with lower speeds.
Offshore wind energy towers are dynamically loaded by waves and wind. Pile foundations provide stiffness and damping and should be properly calculated. A combined finite-element boundary-element method for the dynamic interaction of flexible structures and the soil has been developed. The flexible structures such as single piles or complete wind energy towers are modeled by the finite element method whereas the homogeneous or layered soil is modeled by the boundary element method which uses the Green’s functions for interior loads in the layered half-space to establish the dynamic stiffness matrix of the soil. Soils with a stiffness that is continuously increasing with depth can be modeled as multi-layer soils with step-wise increasing stiffness. The effects of different parameters such as the stiffness of the soil, the axial and bending stiffness of the pile, and the radius of the cylindrical contact area will be analysed for the different components of excitation (vertical, horizontal, rotation and coupling). The results can be determined as specific power laws which are different for the different load cases and for the different soil models (Winkler support, homogeneous continuum, continuum with increasing stiffness). The dynamic effect of radiation damping will be analysed by the frequency-dependent compliance functions. A clear layering of the soil can cause noticeable changes in the dynamic compliances as reductions of the stiffness and the damping in certain frequency ranges (below and around layer resonance frequencies). The distribution of the displacements along the pile help to explain the observed laws. An example of an offshore wind energy tower has been modeled and calculated for wind, wave and weight loads. The resonances of the tower are usually limited by the radiation damping which is strongest for a soft soil.
Offshore wind energy towers are dynamically loaded by waves and wind. Pile foundations provide stiffness and damping and should be properly calculated. A combined finite-element boundary-element method for the dynamic interaction of flexible structures and the soil has been developed. The flexible structures such as single piles or complete wind energy towers are modeled by the finite element method whereas the homogeneous or layered soil is modeled by the boundary element method which uses the Green’s functions for interior loads in the layered half-space to establish the dynamic stiffness matrix of the soil. Soils with a stiffness that is continuously increasing with depth can be modeled as multi-layer soils with step-wise increasing stiffness. The effects of different parameters such as the stiffness of the soil, the axial and bending stiffness of the pile, and the radius of the cylindrical contact area will be analysed for the different components of excitation (vertical, horizontal, rotation and coupling). The results can be determined as specific power laws which are different for the different load cases and for the different soil models (Winkler support, homogeneous continuum, continuum with increasing stiffness). The dynamic effect of radiation damping will be analysed by the frequency-dependent compliance functions. A clear layering of the soil can cause noticeable changes in the dynamic compliances as reductions of the stiffness and the damping in certain frequency ranges (below and around layer resonance frequencies). The distribution of the displacements along the pile help to explain the observed laws. An example of an offshore wind energy tower has been modeled and calculated for wind, wave and weight loads. The resonances of the tower are usually limited by the radiation damping which is strongest for a soft soil.
The dynamics of un-isolated and isolated ballast tracks have been analysed by multi-beam models for the track and by a layered half-space model for the soil. The solution is calculated in frequency-wavenumber domain and transformed back to space domain by a wavenumber integral. This is a faster method compared to other detailed track-soil interaction methods and almost as fast as the widely used Winkler-soil method, especially if the compliances of the soil have been stored for repeated use. Frequency-dependent compliances and force transfer functions have been calculated for a variety of track and soil parameters. The ballast has a clear influence on the high-frequency behaviour whereas the soil is dominating the low-frequency behaviour of the track. A layering of the soil may cause a moderate track-soil resonance whereas more pronounced vehicle-track resonances occur with elastic track elements like rail pads, sleeper pads and ballast mats. Above these resonant frequencies, a reduction of the excitation forces follows as a consequence. The track deformation along the track has been analysed for the most interesting track systems. The track deformation is strongly influenced by the resonances due to layering or elastic elements. The attenuation of amplitudes and the velocity of the track-soil waves change considerably around the resonant frequencies. The track deformation due to complete trains have been calculated for different continuous and Winkler soils and compared with the measurement of a train passage showing a good agreement for the continuous soil and clear deviations for the Winkler soil model.
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.
Transfer admittance spectra of technically induced surface wave fields are analyzed in theory and experiments. Theoretical admittance spectra of layered soils are obtained by integration in wavenumber domain and compared with experimental admittances due to hammer or vibrator excitation. The admittance spectra are strongly influenced by the layering and damping of the soil. Deep stiff-soil layers yield a low-frequency cutoff, whereas a strong damping yields a high-frequency cutoff. A sharp cutoff in a narrow frequency band, which is measured at some sites, can be explained by a damping that increases with frequency, such as viscous material or scattering damping.
A variety of isolation measures exists to reduce the vibration in the neighbourhood of railway lines. They can be roughly classified as elastic or stiffening systems. There are the following elastic elements, rail pads or resilient fixation systems between rail and sleeper, under sleeper pads or sleeper shoes under the sleepers, and ballast mats under the ballast. Stiffening systems (plates) are used as slab tracks, floating slab tracks, or mass-spring systems. In the EU project “Railway induced vibration abatement solutions (RIVAS)”, elastic under sleeper pads have been investigated. The dynamic behaviour of the track and the surrounding soil has been calculated by the combined finite-element boundary-element method in a systematic parameter study. It has been shown that the mitigation effect can be improved by soft under sleeper pads or by heavy sleepers. Consequently, such track elements (soft under sleeper pads and heavy sleepers) have been thoroughly investigated in laboratory tests to establish the static and dynamic parameters as well as their serviceability. Finally, field tests at and near railway tracks with and without under sleeper pads have been performed. To determine the reduction effect of the isolated track, the ground vibrations excited by trains or artificial sources have been measured. The soil properties at the different sites have also been measured so that the comparison of the isolated and un-isolated track can take into account possible differences of the soil parameters. The contribution shows how the different (numerical, laboratory and field) methods and results can be combined to achieve an improved mitigation solution with soft under sleeper pads and heavy sleepers for ballasted and slab tracks.
The vehicle–track interaction generates forces and consequently vibrations in the environment. The interaction has been analysed by the simultaneous measurements of vehicle, track and ground vibrations during test runs with varied train speeds. The special effects of the passage over a bridge and through a tunnel are studied and compared with the measurements on a conventional ballasted surface line. The maximum amplitudes, narrow band and one-third octave band spectra are presented for the axle-box accelerations and for the track, bridge and ground vibrations. The different frequencies and frequency bands are related to wheel out-of-roundness, track alignment errors, the sleeper passage and the wheelset–track resonance. An axle impulse component has been observed at the track, at the near-field soil and as a scattered version in the far field. Specific results can be found for the bridge track, where clearly speed-dependent bridge resonances occur due to the axle sequence of the train, and for the tunnel track where soft rail pads are responsible for a strong amplification around the wheelset–track resonance. On the other hand, the axle impulses are strongly reduced by the tunnel track, and the scattered axle impulse component is not as relevant as for the surface track. As a consequence, a strong mid-frequency amplitude reduction of the tunnel compared to the surface line has been measured for low and high train speeds by the Federal Institute of Material Research and Testing (BAM) and by other institutes.
The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks
(2008)
The dynamic response of the railway track is strongly influenced by the underlying soil. For a soft soil and very high train speeds or for a very soft soil and regular train speeds, the train speed can be close to the speed of elastic waves in the soil. This paper presents a detailed study of the so-called moving-load effect, i.e. an amplification of the dynamic response due to the load movement, for the tracks on soft soil. The analysis is carried out by evaluating the related integrals in the wavenumber domain. The influence of the load speed is quantified for a large set of parameters, showing that the effect on the soil vibration is reduced with increase of the frequency, track width and inverse wave velocity. Therefore, the moving-load effect associated with vibratory train loads is negligible whereas the amplification associated with the moving dead weight of the train can be significant. The strong moving-load effect on a perfectly homogeneous soil, however, can be strongly diminished by a layered or randomly varying soil situation. This theoretical result is affirmed by measurements at a test site in Germany where the trains run on a very soft soil at a near-critical speed. The results for soft soils are compared with experimental and theoretical results for a stiff soil. It is found that the influence of the stiffness of the soil is much stronger than the moving-load effect. This holds for the soil vibration as well as for the track vibration which both show a minor dependence on the load speed but a considerable dependence on the soil stiffness in theory and experiment.
Railway tracks can include soft isolation elements such as rail pads, sleeper shoes and ballast mats. For these types of isolation elements and normal soil conditions, the influence of the load speed is usually negligible. There is only one isolation measure for which the moving load may be effective: a track which is constructed as a heavy massspring system. The resonance of this track system is shifted to lower frequencies and amplitudes for increasing train speed. A critical train speed can be reached if the massspring system has a marginal bending stiffness along the track.
This article presents an integrated model for the computation of vehicletrack interaction and the ground vibrations of passing trains. A combined finite element and boundary element method is used to calculate the dynamic compliance of the track on realistic soil whereas multi-body models are used for the vehicle. The dynamic stiffness of the vehicle and that of the track are combined to calculate the dynamic axle loads due to the irregularities of the vehicle and the track as well as those due to sleeper passing excitation. These loads serve as input for the calculation of ground vibration near railway lines in the time and frequency domains.
The theoretical methods and results have been proven by experiments in several respects and at several instances. First, on the occasion of the test and record runs of the Intercity Experimental, there was a very good quality of the vehicle and of the newly built track so that the deterministic parts of the excitationthe static load and the sleeper-passing componentcould clearly be identified, the first being of minor importance apart from the track. Second, simultaneous measurements of the vehicle, the track and the soil at three different track situations were performed where we could verify the different parts of the stochastic excitation and their importance for the ground vibrations. The irregularities of the vehicle are dominant at high frequencies whereas the irregularities of the track are more important at lower frequencies. The comparison of the theory and the measurements also points to the phenomena of the vehicletrack resonance and the scattering of the quasi-static axle impulses by randomly varying soil.
A study on building vibrations has been performed by finite element calculations. Family houses, multi-storey residential buildings, office buildings and office towers have been modelled in detail. The frequency-dependent response due to a free-field excitation has been evaluated for walls, columns and floors. The ratio of building amplitudes to free-field amplitudes starts with uB/u0 = 1 at zero frequency and is usually lower than 1 at 50 Hz, the end of the frequency range considered here. In between, amplifications occur due to several reasons. There are „soil resonances“ where the whole building is vibrating on the compliant soil, “column resonances” where the upper storeys are vibrating on the compliant columns, and the “floor resonances” where the floors are vibrating excited by their supports. Results are presented for all building types, but a special focus is set on office buildings. A parameter study shows the influence of the stiffness of the soil, the number of storeys, and the width of the building. It has been found that the “soil resonance” is strongly modified by the low-frequency floor resonances for the normal office building. The main resonance of a twenty-storey office tower is determined equally by the “soil mode” and the “column mode”. It is an important observation for these office buildings that the resonances can differ for different parts of the building such as the centre, the edge, the corner, and the core of the building. This leads to non-uniform vibration modes across the building, which look like another type of “floor resonance” and which have been observed in several real building projects. Experimental results will be shown which can confirm the calculated phenomena.
A study on building vibrations has been performed by finite element calculations. Family houses, multi-storey residential buildings, office buildings and office towers have been modelled in detail. The frequency-dependent response due to a free-field excitation has been evaluated for walls, columns and floors. The ratio of building amplitudes to free-field amplitudes starts with uB/u0 = 1 at zero frequency and is usually lower than 1 at 50 Hz, the end of the frequency range considered here. In between, amplifications occur due to several reasons. There are „soil resonances“ where the whole building is vibrating on the compliant soil, “column resonances” where the upper storeys are vibrating on the compliant columns, and the “floor resonances” where the floors are vibrating excited by their supports. Results are presented for all building types, but a special focus is set on office buildings. A parameter study shows the influence of the stiffness of the soil, the number of storeys, and the width of the building. It has been found that the “soil resonance” is strongly modified by the low-frequency floor resonances for the normal office building. The main resonance of a twenty-storey office tower is determined equally by the “soil mode” and the “column mode”. It is an important observation for these office buildings that the resonances can differ for different parts of the building such as the centre, the edge, the corner, and the core of the building. This leads to non-uniform vibration modes across the building, which look like another type of “floor resonance” and which have been observed in several real building projects. Experimental results will be shown which can confirm the calculated phenomena.
Train-induced ground vibrations are all generated by the vehicle, by static or dynamic vehicle loads. The most important and most accepted excitation are the dynamic wheel loads from the passage over track irregularities. Dynamic wheel loads will be compared from parallel axle-box and ground vibration measurements at more than seven sites. Some low-frequency excitation of ground vibrations, typically between 10 and 30 Hz, cannot be found in the axle-box measurements. Therefore, other vehicle modes, such as rigid bogie modes, flexible carriage modes, rigid and flexible wheelset modes, have been analysed for additional excitation forces. These vehicle dynamics analyses give an explanation for higher axle-box results at high frequencies, but not for the excitation of the higher low-frequency ground-vibration component. Finally, the effect of the moving static train loads will be analysed. For a regular track and soil, the moving static train loads yield the quasi-static response which exists only in the low-frequency nearfield of the track. If the support stiffness is randomly varying along the track, the pulses on the track generate an additional low-frequency component which is called the irregular pulse responses.
This component will be demonstrated by numerical analysis where all axle pulses are superposed in frequency domain.
The layered soil is calculated in the frequency wavenumber domain and the solutions for fixed or moving point or track loads follow as wavenumber integrals. The resulting point load solutions can be approximated by simple formula. Measurements yield the specific soil parameters for the theoretical or approximate solutions, but they can also directly provide the point-load solution (the transfer function of that site). A prediction method for the train-induced ground vibration has been developed, based on one of these site-specific transfer functions. The ground vibrations strongly depend on the regular and irregular inhomogeneity of the soil. The regular layering of the soil yields a cut-on and a resonance phenomenon, while the irregular inhomogeneity seems to be important for high-speed trains. The attenuations with the distance of the ground vibration, due to point-like excitations such as vibrator, hammer, or train-track excitations, were investigated and compared. All theoretical results were compared with measurements at conventional and high-speed railway lines, validating the approximate prediction method.
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 damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany. The loss of contact between the sleeper and the track plate, between the track plate and the base plate, and between the base plate and the base layer have been analysed. The soil properties of each site have been measured and have been used to establish realistic track-soil models. Theoretical results of the wavenumber domain and the finite-element boundary element method have been compared with the experimental results. The observed experimental and theoretical results, changes in the time histories of displacements and velocities due to train passages and in the transfer functions (receptances) due to hammer impacts, are encouraging that these measurements can be used to detect track damage.
Experiments have been performed at a test site with six different tracks with under-ballast plates. Hammer excitations of the soil and the tracks as well as train passages have been measured. The experimental observations are as follows. 1. The natural soil is stiff gravel whereas the railway dam consists of softer material. 2. The track compliance indicates a soft ballast if no train is present to provide a confining pressure. 3. The track response to the train passages can be split into a low-frequency region which is ruled by the static loads and a high-frequency region which is ruled by dynamic loads. 4. The track responses to hammer and track excitation indicate the presence of many voids between the sleepers and the ballast. 5. The ground vibrations are highly influenced by the soil. Due to the stiff soil at the site, the hammer and train induced spectra have a considerable high-frequency content. 6. A reduction of the ground vibration has been observed in a low-frequency range. The mitigation effects of an under-ballast plate are also investigated by calculations of a wavenumber domain model. The under-ballast plate has an effect at low frequencies where it distributes the static load over a longer track section. The impulse of the axle passage is longer and the frequencies are lower due to the plate stiffness. The axle impulses could yield a low-frequency ground vibration in an irregular soil with a randomly varying stiffness. This low-frequency part of the ground vibration (the scattered axle impulses) seem to be reduced by the under-ballast plate.
Experiments have been performed at a test site with six different tracks with under-ballast plates. Hammer excitations of the soil and the tracks as well as train passages have been measured. The experimental observations are as follows. 1. The natural soil is stiff gravel whereas the railway dam consists of softer material. 2. The track compliance indicates a soft ballast if no train is present to provide a confining pressure. 3. The track response to the train passages can be split into a low-frequency region which is ruled by the static loads and a high-frequency region which is ruled by dynamic loads. 4. The track responses to hammer and track excitation indicate the presence of many voids between the sleepers and the ballast. 5. The ground vibrations are highly influenced by the soil. Due to the stiff soil at the site, the hammer and train induced spectra have a considerable high-frequency content. 6. A reduction of the ground vibration has been observed in a low-frequency range. The mitigation effects of an under-ballast plate are also investigated by calculations of a wavenumber domain model. The under-ballast plate has an effect at low frequencies where it distributes the static load over a longer track section. The impulse of the axle passage is longer and the frequencies are lower due to the plate stiffness. The axle impulses could yield a low-frequency ground vibration in an irregular soil with a randomly varying stiffness. This low-frequency part of the ground vibration (the scattered axle impulses) seem to be reduced by the under-ballast plate.
Ground vibrations created by running high-speed trains at speeds between 100 and 320 km/h are calculated in detail using transfer functions to model the effects of the moving loads. These transfer functions for layered soils are obtained by integration in the wavenumber domain. The train-induced vibrations in a soil that is considered to consist of single layers of two slightly different soils are analysed for different excitations: for their spectra, attenuation laws and amplitude-speed relations. An important mid-frequency component is shifted through the cut-on region of the layered soil with an increase in the train speed. The cut-on frequency divides the response of the layered soil into a low-frequency low-amplitude range and a high-frequency high-amplitude range. This leads to completely different train speed dependencies for the two soil layers with strongly increasing amplitudes around the cut-on frequency and almost constant amplitudes beyond this frequency. All calculated results closely agree with ground vibration measurements at two corresponding sites, especially if the mid-frequency component is calculated by axle impulses.
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.
Many measurements of train induced ground vibrations show high amplitudes for a certain mid-frequency range. This ground vibration component cannot be well explained by dynamic loads of the train. Many characteristics indicate that the axle impulses, which are scattered by an irregular soil, are the excitation. This new understanding of railway-induced ground vibration is verified by numerical analysis. The response of the regular homogeneous and irregular inhomogeneous soils has been calculated by the finite-element method in frequency domain. A specific superposition of the impulse responses has been invented including time shift, axle sequence, track filter and hanning filter. The superposition yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil of which the stiffness varies randomly in space, the superposition yields a mid-frequency ground vibration component from the scattering of the axle impulses. The existence and the importance of this component can thus be demonstrated by the calculations. Some rules of the influence of distance, train speed, soil stiffness, strength and width of the stiffness variation have been derived from the calculations. Many measurements show the unique explanation of the mid-frequency ground vibration component by the scattered axle impulses.
Train-induced ground vibrations - the emission and transmission from tunnel and surface lines
(2023)
Train-induced ground vibrations are quite different for tunnel and surface lines. The excitation of the track and ground vibration by the vehicle-track-soil interaction maybe influenced by the stiffer track support of the tunnel invert. The excited waves are propagating on a different path compared to the surface line. The wave propagation in the interior of the soil is calculated by a wavenumber integral in a similar way as the propagation along the surface and a general reduction of < 0.5 has been found. An additional reduction has been found because of the missing Rayleigh wave. The different excitation of tunnel lines is analysed theoretically by the combined finite-element boundary-element method and some results about the influencing tunnel and soil parameters will be shown. Measurements have been made at the Mühlberg-Tunnel in Germany. The vibrations of the train, the track and the soil have been measured simultaneously at the tunnel and a nearby surface line. Spectra will be shown for different train speeds between 60 and 160 km/h. A clear reduction effect for the tunnel line compared to the surface line has been observed in a specific (train-speed-dependent) frequency range. This agrees well with the observations of other research institutes. The mid-frequency tunnel-surface reduction seems to be a consequence of the stiffer track structure which leads to a wider distribution of the axle loads. Therefore, the axle impulses due to the train passage are longer and have a lower frequency content. This will have an effect on the ground vibrations at some distance which are present in case of an irregular transmission path through a ballast and soil with varying stiffness. A similar reduction effect can also be found for other track forms where the axle impulses are distributed on a longer track segment, for example slab tracks, tracks with under ballast plates, under ballast mats or under sleeper pads.
Train-induced ground vibrations – The emission and transmission from tunnel and surface lines
(2023)
Train-induced ground vibrations are quite different for tunnel and surface lines. The excitation of the track and ground vibration by the vehicle-track-soil interaction maybe influenced by the stiffer track support of the tunnel invert. The excited waves are propagating on a different path compared to the surface line. The wave propagation in the interior of the soil is calculated by a wavenumber integral in a similar way as the propagation along the surface and a general reduction of < 0.5 has been found. An additional reduction has been found because of the missing Rayleigh wave. The different excitation of tunnel lines is analysed theoretically by the combined finite-element boundary-element method and some results about the influencing tunnel and soil parameters will be shown. Measurements have been made at the Mühlberg-Tunnel in Germany. The vibrations of the train, the track and the soil have been measured simultaneously at the tunnel and a nearby surface line. Spectra will be shown for different train speeds between 60 and 160 km/h. A clear reduction effect for the tunnel line compared to the surface line has been observed in a specific (train-speed-dependent) frequency range. This agrees well with the observations of other research institutes. The mid-frequency tunnel-surface reduction seems to be a consequence of the stiffer track structure which leads to a wider distribution of the axle loads. Therefore, the axle impulses due to the train passage are longer and have a lower frequency content. This will have an effect on the ground vibrations at some distance which are present in case of an irregular transmission path through a ballast and soil with varying stiffness. A similar reduction effect can also be found for other track forms where the axle impulses are distributed on a longer track segment, for example slab tracks, tracks with under ballast plates, under ballast mats or under sleeper pads.
Ground vibrations near railway lines are generated by the forces that are acting between wheel and rail. It seems to be a straight forward assumption that the vehicle dynamics are important for the level and the frequencies of the excitation forces. Different vehicle dynamics phenomena are analysed for their role in the excitation of ground vibrations: rigid body modes of the bogies, elastic (bending) modes of the car body, and elastic modes of the wheelset. The theoretical analyses use rigid body models, simplified elastic models, and detailed elastic models. Some of these problems are vehicle–track interaction problems where 3D finite‑element boundary‑element models have been used for the track and soil. It is shown that the rigid or flexible vehicle modes are well in the frequency range of ground vibrations (4 to 100 Hz). They have an influence on the excitation force but the additional forces are rather small and can be neglected in ground vibration prediction. The theoretical results are checked by experimental results of a simultaneous measurement of vehicle,
track, and ground vibrations.
The dynamic compliance of different railway tracks on different layered soils have been calculated using a combined finite-element and boundary-element method:
conventional track on homogeneous soil with different stiffness,
extreme normal and inverse layering of the soil,
plates in and on top of the soil (slab track on various soils),
conventional track with elastic rail pads.
Three measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results. The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and forces.
Three measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results.
The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and forces.
Three measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results. The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and Forces.
Abstract. Three measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results.
The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and forces.
A combined finite element boundary element method has been developed to calculate the dynamic interaction of the railway track and the underlying soil. The track-soil results are coupled with a simple vehicle model to establish the force transfer function of the vehicle-track-soil system. Mitigation measures at the track, namely three different tracks with under-sleeper pads, are analysed. The un-sprung vehicle and heavy track masses on soft track elements yield a lower vehicle-tracksoil resonant frequency and a better reduction of the excitation forces at higher frequencies. If the effectiveness of the mitigation is measured as a vibration ratio between the isolated and an un-isolated reference track, the vehicle-track-soil resonance of the reference track has an important influence on the mitigation effectiveness. Therefore, different un-isolated reference tracks are analysed. It is shown how the frequency and amplitude of the vehicle-track resonance are influenced by the stiffness of the rail pads (strongest), the ballast (medium) and the soil (weakest). The reference track models have been compared with shaker tests on two railway tracks with strong resonances. The damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany and compared with the theoretical behaviour of intact and damaged tracks.
A combined finite element boundary element method has been developed to calculate the dynamic interaction of the railway track and the underlying soil. The track-soil results are coupled with a simple vehicle model to establish the force transfer function of the vehicle-track-soil system. Mitigation measures at the track, namely three different tracks with under-sleeper pads, are analysed. The un-sprung vehicle and heavy track masses on soft track elements yield a lower vehicle-tracksoil resonant frequency and a better reduction of the excitation forces at higher frequencies. If the effectiveness of the mitigation is measured as a vibration ratio between the isolated and an un-isolated reference track, the vehicle-track-soil resonance of the reference track has an important influence on the mitigation effectiveness. Therefore, different un-isolated reference tracks are analysed. It is shown how the frequency and amplitude of the vehicle-track resonance are influenced by the stiffness of the rail pads (strongest), the ballast (medium) and the soil (weakest). The reference track models have been compared with shaker tests on two railway tracks with strong resonances. The damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany and compared with the theoretical behaviour of intact and damaged tracks.
This article deals with two topics of vehicle-track-soil interaction, the mitigation of railway induced ground vibration by soft track elements, and the identification of track damage. Theoretical results have been achieved by a combined finite-element boundary-element method (FEBEM). The theoretical results are confronted with measurements at four sites. Improved mitigation effects have been found for soft rail pads under heavy sleepers. The insertion loss, however, can be too optimistic if a strong vehicle track resonance occurs for the un-isolated reference track. Two measurement sites show this strong vehicle-track resonance at about 80 Hz, which has been approximated by using the results of a wide parameter study including the rail pad, ballast, and soil stiffness, as well as the ballast model and the soil layering. – The detection of slab track damage is mainly based on the differences of the receptance or compliance functions. Theoretical results have been confirmed by measurements at one site where a loss of contact between track plate and base layer was visible. Measurements at a second site with a hidden damage have been compared with the theoretical results of a loose sleeper. The differences between intact (or repaired) and damaged tracks are strong enough to encourage the further development of this method for the identification of track damages.
There is a strong need for cost-effective mitigation measures for
turnouts. SBB has initiated a series of examinations using different methodologies to gain a deeper understanding of the excitation mechanisms at low frequencies, in addition to that obtained in the RIVAS project. To date it is not yet clear what constitutes a complete measurement data set that would enable understanding most of the vibration excitation mechanisms in turnouts. Increasing vibration at turnouts in comparison to normal track is observed for all measured frequencies.
The different methodologies are presented in the paper. Under-sleeper pads (USP) are a cost-effective method to reduce vibration at frequencies above 63 Hz (1/3 octave), but there is probably no improvement for frequencies below 63 Hz. A first test of new frog geometry did not show relevant improvements in Vibration emission in comparison to a reference frog geometry. Axle box acceleration measurements are an interesting method to identify defects in a turnout. A specialized measurement system of rail roughness could identify certain geometry Problem areas for some frogs. Noise increases also are observed at turnouts for frequencies ranging between 80 to 1000 Hz. The use of railway source models to calculate
contact forces for ballasted track and turnouts seems promising, in particular for understanding the influence of ground.
The damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany with slab tracks and ballast tracks and compared with the theoretical behaviour of intact and damaged tracks. The loss of contact between the sleeper and the plate, between the plate and the base layer, and some problems with soft or weakened soil have been analysed. The observed results, changes in the time histories of displacements and velocities due to train passages and in the transfer functions (compliances) due to hammer impacts, are encouraging that these measurements can be used to detect track damage. In addition, calculations with the combined finite-element boundary-element method have been used to confirm the conclusions about intact or damaged railway tracks.
This contribution presents experimental methods to detect track damage. At BAM (Federal Institute of Material Research and Testing), a measuring car with a measuring system of 72 channels, geophones, mountings, cables, harmonic and impulsive exciters is used for dynamic measurements of the track, the soil and buildings. An instrumented hammer allows force measurements and to evaluate transfer functions of the track, and the soil. Wave measurements are used to identify the soil characteristics. Train passages are measured at the track and for the train induced ground vibrations. In addition to these in situ options, tests of tracks or track elements can be performed in a large laboratory.
A finite-element boundary-element software for the dynamic interaction of flexible structures and the soil has been extended for pile foundation. The boundary element method for the soil uses the Green´s functions of the layered half-space which have been generalised for interior loads. Pile groups of 10 to 20 piles of different arrays are analysed and compared with single piles. Simplified models have been developed for a user-friendly, practice oriented prediction software for railway induced ground and building vibration.
The vibrations of soil and foundations are demonstrated for different types of loading. Train-induced ground vibrations are studied in a measurement campaign where a test train has run with regularly varied speeds. The measured train-induced soil vibration at 2 to 100 m distance from the track is compared with the wave propagation due to hammer excitation and with the theoretical wave field. The strong influence of the soil and the train speed on the amplitudes and frequencies of the vibration has been analysed for passages of the locomotive and the carriages. - The generation of ground vibration by strong explosions has been studied on a large testing area with sandy soil. The propagating waves were measured in a regular grid of measuring points in 10 to 1000 m. Therefore, the dominance of certain waves at certain distances and the changes of compressional waves and Rayleigh waves could clearly be observed. The results are compared with impulse hammer measurements in the range of 5 to 50 m. - A drop test facility has been built on the testing area of the Federal Institute of Materials Research and Testing (BAM). Heavy masses (containers) of up to 200 t can be dropped from 10 m height on a big reinforced concrete foundation. The foundation was instrumented by accelerometers, strain gauges and pressure cells to give information about the loading condition and by geophones to measure the vibration of the surrounding soil and building. Both excitation processes, the release of the mass and the impact, produce high vibration amplitudes. On a smaller drop foundation, the influence of the drop height and the target stiffness has been studied more systematically.
The attenuation of wave amplitudes is ruled by the planar, cylindrical or spherical geometry of the wave front (the geometric or power-law attenuation) but also by the damping of the soil (an exponential attenuation). Several low- and high-frequency filter effects are derived for the layering and the damping of the soil, for the moving static and the distributed train loads and for a homogeneous or randomly heterogeneous soil. Measurements of hammer- and train-induced vibrations at five sites have been analysed for these attenuation and filter effects. The measured attenuation with distance can be discribed by generalised power laws and some reasons will be discussed. The theoretical filter effects can well be found in the measurements.
The attenuation of wave amplitudes is ruled by the planar, cylindrical or spher-ical geometry of the wave front (the geometric or power-law attenuation) but also by the damping of the soil (an exponential attenuation). Several low- and high-frequency filter effects are derived for the layering and the damping of the soil, for the moving static and the distributed train loads and for a homoge-neous or randomly heterogeneous soil. Measurements of hammer- and train-induced vibrations at five sites have been analysed for these attenuation and filter effects. The measured attenuation with distance can be discribed by gen-eralised power laws and some reasons will be discussed. The theoretical filter effects can well be found in the measurements.
A method is presented which allows to calculate the wave-field in a homogeneous or layered soil in case of a dynamic interior load. The wave propagation along the surface, the distribution of the response over the depth, the horizontal propagation at different depths and the vertical downward propagation are shown and compared with the simpler surface solution of the half-space and the interior solution of the full-space. The complete wave-field (Green's function) is applied to the dynamic behaviour of piles and pile groups by use of a boundary element formulation. The stiffness, damping and – typically for piles – mass of different groups of piles are presented. Different group effects occur for lines, circles, grids, parallels and crosses of piles, which can be regarded as oscillations around average values. Moreover, the piles and pile groups behave almost like a damper for most of the frequencies. A building on a pile group that is excited by ground vibration due to surface or interior loads shows a reduction of the wave-field due to kinematic and inertial soil–building interaction effects. The results presented lead to simplified descriptions of the wave-field due to interior loads and of the soil–pile–building interaction which can be used for the prediction of technically induced vibration.