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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.
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.
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.
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.
Explosion-induced ground vibrations have been measured at several places. Results about the wave propagation are shown in this contribution. The particle velocities of the soil have been measured at up to 1000 m distance from the explosion and are presented as time records (seismograms) and one-third octave band spectra (transfer functions). The results are compared with the results of hammer impacts. The seismograms clearly show different wave types, compressional waves of the air, the water and the soil, and the Rayleigh wave. The hammer impacts yield good results up to 100 m and incorporate higher frequencies at about 50 Hz, whereas the explosion results in a ground vibration with frequencies around 10 Hz and a longer range of influence. Explosion and hammer excitations are evaluated for the wave velocities of the soil by using the wavenumber and the spatial auto-correlation method. The attenuation of the ground vibration amplitudes A with distance r can well be presented by a power law A ~ r -q. This type of amplitude-distance law and the corresponding power q > 1 are substantiated in the contribution. The influence of the charge weight W is evaluated as an additional power law A ~ W -p for each measuring site. The power is found quite similarly around q 0.6 as all sites have a medium soft soil such as sand and clay. The obtained amplitude-charge-distance law can be used to predict the explosion-induced ground and building vibrations at other sites.
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.
A combined finite-element boundary-element method for the dynamic interaction of the soil with flexible structures such as single piles or complete wind energy towers has been developed. Flexible piles in different soils are analysed in frequency domain. The different parameters such as the stiffness of the soil, the bending stiffness and the radius of the hollow pile are analysed for their influence on the complex compliances. The results have been determined as specific power laws which are different for the different load cases (horizontal, rocking, coupling) and for the different soil models (Winkler, continuum with constant, root-parabolic and proportional-linear stiffness variation). The strongest influence of the soil stiffness can be found for the homogeneous soil and the horizontal component. Winkler soils have a weaker influence than the corresponding continuous soils. An offshore wind energy tower has been modeled and calculated for wind and wave loads.
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.
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.
Train passages induce forces on the track, train-induced vibrations propagate through the soil and excite neighbouring buildings. The emission, which is the first part of the prediction of vibrations near railway lines, is presented by focusing on the dynamic axle loads. The calculation of the axle loads is based on the vehicle-track-soil interaction. This interaction calculus utilises 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 ballast or the subsoil, which must also be transferred to effective track irregularities, and due to the discrete rail support on sleepers. All necessary transfer functions for the prediction of axle-load spectra are presented as general formula and as specific graphs for differing vehicle and track parameters. The prediction method is applied to a ballast track and a slab track and compared with corresponding axle-box measurements. Moreover, ground vibration measurements at numerous sites are exploited for the axle-load spectra and the validation of the prediction method. All theoretical and experimental results confirm that the dynamic axle-load spectra have an approximate value of 1 kN per third of octave and increase with train speed, track stiffness and around the vehicle-track resonance.
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.
Vibration of normal apartment, office and production buildings, which are excited by technically induced ground vibrations are considered. Many wavelengths of the Rayleigh waves of the soil fit into the foundation dimensions. The related high discretization effort can nowadays be realized with detailed soil-structure interaction method. The combined finite-element boundary-element method is used here as a detatiled method. Simplified method can be used with less computation time, but these methods must be calibrated by exact results. One simplification is to extent the structure to infinity and to solve the problem by wavenumber domain methods. Another simplification is the use of a Winkler soil instead of the continuous soil. Usually, the Winkler parameters are not only soil parameters but depend also on the rigid or flexible foundation structure. Substructure methods use commercial FEM software for the building part. The contribution will show some detailed and some simplified results on large structural elements such as foundation plates, walls, storey plates on columns as well as results on complete buildings. The reduction of the ground vibration by stiff elements and the amplification due to floor or building resonances are discussed which are the most important phenomena of the soil-building interaction.
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.
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.
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.
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.
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.
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 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.
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.
Long wooden floor beams above a ball room in an old historical palace have been analysed experimentally. The eleven beams are weakly coupled by three layers of floor boards. It has been investigated if the state (the stiffness) of the wooden beams can be determined by vibration measurements of global or preferably local modes. Hammer, heel-drop and ambient excitations have been used. The vibration modes of the structure show dominating local deformations if an impact excitation is applied. This is understood as the positive superposition of several modes which yield the maximum at the excitation point but a cancellation at more distant points. Natural modes have been estimated from these vibration modes by standard and special methods which were necessary for the high damping of the wooden floor. It has been found that all floor beams contribute to each natural mode even for a weak coupling of the beams. In addition to the modal discussion, the impact tests have also been analysed for the wave propagation and amplitude attenuation with distance. The coupling of floor beams has been studied theoretically by an analytic multiple-beam model where the coupling by translational or rotational springs and by a common support motion has been assumed.
Long wooden floor beams above a ball room in an old historical palace have been analysed experimentally. The eleven beams are weakly coupled by three layers of floor boards. It has been investigated if the state (the stiffness) of the wooden beams can be determined by vibration measurements of global or preferably local modes. Hammer, heel-drop and ambient excitations have been used. The vibration modes of the structure show dominating local deformations if an impact excitation is applied. This is understood as the positive superposition of several modes which yield the maximum at the excitation point but a cancellation at more distant points. Natural modes have been estimated from these vibration modes by standard and special methods which were necessary for the high damping of the wooden floor. It has been found that all floor beams contribute to each natural mode even for a weak coupling of the beams. In addition to the modal discussion, the impact tests have also been analysed for the wave propagation and amplitude attenuation with distance. The coupling of floor beams has been studied theoretically by an analytic multiple-beam model where the coupling by translational or rotational springs and by a common support motion has been assumed.
The present contribution evaluates four measuring series made by the Federal Institute of Material Research and Testing for the relations between train speed and ground vibration amplitudes. This experimental evaluation is supported by the simulation of the train passages at the different sites by using appropriate excitation mechanisms and forces as well as layered soil models which have been derived from impact measurements at each site.
The present contribution evaluates four measuring series made by the Federal Institute of Material Research and Testing for the relations between train speed and ground vibration amplitudes. This experimental evaluation is supported by the simulation of the train passages at the different sites by using appropriate excitation mechanisms and forces as well as layered soil models which have been derived from impact measurements at each site.
Mitigation measures of railway induced vibration have been demonstrated at the emission, transmission and immission part. It must be carefully observed that the correct masses and stiffnesses are used.
Typical mistakes have been shown,
- 1D models for vehicle-track interaction,
- impedance instead of stiffness for the infill material of a trench,
- rigid buildings or neglecting the soil-building interaction.
The dominant mid-frequency part of the ground vibration is due to the irregular soil.
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.
Irregularities of the track are a main cause of train-induced ground vibration, and track maintenance is of great importance. Although geometric irregularities at the wheel-rail contact are widely used, other types of irregularities, such as stiffness irregularities, irregularities from different track positions and irregularities in the wave propagation, were analysed in the present study. The track behaviour was investigated by a multi-beam-on-soil model. This track model is coupled with a vehicle model to calculate the vehicle–track interaction. The track model was also used for the track filtering, which transfers a track support error to the equivalent rail irregularity or, conversely, the sharp axle pulse on the rail to a smoother pulse on the soil. In the case in which this filtering varies randomly along the track, the pulses of the moving static load induce a certain ground Vibration component (“the scatter of axle pulses”). This effect was calculated by the superposition of axle pulses in the frequency domain and by a stochastic simulation. Simultaneous vehicle, track and soil measurements at a certain site were used to evaluate the different excitation and ground Vibration components. The agreement between calculations and axle-box and soil measurements is good. The ground vibrations calculated from rail irregularities and corresponding dynamic loads, however, clearly underestimate the measured ground vibration amplitudes. Only the static load that is moving over a varying track support stiffness can produce the important mid-frequency ground Vibration component by the scatter of axle pulses.
The passage of the train is dominated by the impulses of the static axle loads. The response of the regular homogeneous and irregular soils has been calculated by the finite-element method in frequency domain. The superposition of the impulse responses 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 or ballast of which the stiffness varies randomly in space, a mid-frequency ground vibration component is generated by the scattering of the axle impulses. Measurements will be shown which prove the existence of the mid-frequency ground vibration component and the unique explanation by the scattered axle impulses: many international measurements with a raised mid-frequency component, axle-box measurements with a too low mid-frequency dynamic load, amplitude-speed dependencies which are incompatible with irregularity-induced dynamic loads, and ground vibration reductions due to stiff track elements.
In the last three decades, the vibrations of many floors and bridges have been measured. The contribution shows some evaluation methods, experimental results and some modelling and theoretical results. Simple evaluation methods have been developed for single and coupled floors. Two coupled beams have been measured in good agreement with the theory. A more complex coupling model has been found for a large wooden floor in a castle consisting of six floor bays which correlates well with the measurements. Damaged and intact poles have been tested by their natural frequencies and damping values, and a fair correlation between the degree of damage and the shift of the frequency. Road bridges have been analysed in detail and some examples are presented. Railway bridges and trains are studied for resonant excitation. The risk of resonance can be estimated in frequency domain by using axle-sequence spectra of the train and the natural frequencies of the bridge. A measurement example shows the amplification, but even stronger the cancellation of the subsequent axle responses. Several high-speed trains and freight trains have been analysed for their potential resonance amplification.
The passage of the train is dominated by the impulses of the static axle loads. The response of the regular homogeneous and irregular soils has been calculated by the finite-element method in frequency domain. The superposition of the impulse responses 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 or ballast of which the stiffness varies randomly in space, a mid-frequency ground vibration component is generated by the scattering of the axle impulses. Measurements will be shown which prove the existence of the mid-frequency ground vibration component and the unique explanation by the scattered axle impulses: many international measurements with a raised mid-frequency component, axle-box measurements with a too low mid-frequency dynamic load, amplitude-speed dependencies which are incompatible with irregularity-induced dynamic loads, and ground vibration reductions due to stiff track elements.
In the last three decades, the vibrations of many floors and bridges have been measured. The contribution shows some evaluation methods, experimental results and some modelling and theoretical results. Simple evaluation methods have been developed for single and coupled floors. Two coupled beams have been measured in good agreement with the theory. A more complex coupling model has been found for a large wooden floor in a castle consisting of six floor bays which correlates well with the measurements. Damaged and intact poles have been tested by their natural frequencies and damping values, and a fair correlation between the degree of damage and the shift of the frequency. Road bridges have been analysed in detail and some examples are presented. Railway bridges and trains are studied for resonant excitation. The risk of resonance can be estimated in frequency domain by using axle-sequence spectra of the train and the natural frequencies of the bridge. A measurement example shows the amplification, but even stronger the cancellation of the subsequent axle responses. Several high-speed trains and freight trains have been analysed for their potential resonance amplification.
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.
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.
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 train passages over intact or damaged slab tracks on different soils have been calculated by the finite-element boundary-element or the wavenumber-domain method. The influence of track and soil parameters on the distribution of the track displacements and the soil forces has been analysed. The measured and calculated displacement time histories of train passages could be used to identify track damages such as lose sleepers or a lose track plate. The time histories and spectra of the soil forces can explain the measured ground vibration reduction of slab tracks. The calculated displacement and force distributions of slab tracks on continuous soils do not fulfil the Winkler hypothesis and Winkler models should not be used for track analysis.
The dynamic behaviour of slab and ballast tracks has been investigated by measurements and calculations. Hammer impacts and train passages have been analysed. Measurements have been performed by geophones (velocity transducers) which have been time-integrated to displacements. The calculations are done in frequency-wavenumber domain for multi-beam-on-continuous soil models. The characteristics of the different tracks and track elements have been established in theory and experiment. The frequency-dependent compliances (displacement transfer functions) show clear rail-on-rail-pad resonances or highly damped track-soil resonances. Compared to the rail and sleeper, the track plate has much lower amplitudes. The slab track has usually the highest rail amplitudes due to soft rail pads. The train passage yields track displacements which are a superposition of the axle loads from the two neighbouring axles of a bogie and from the two bogies of two neighbouring carriages. This global behaviour is characteristic for the track plate of the slab track whereas the rails of the slab and the ballast track behave more local with only one bogie of influence. The measurements agree very well with the theory of the continuous soil in case of the six measured slab tracks and acceptably well for the six measured ballast tracks. The measurements allow to find appropriate model parameters and to check the models, for example the Winkler model of the soil has been found less appropriate as it reacts more locally.