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Schlagworte
- Ground vibration (10)
- Track-soil interaction (5)
- Vehicle-track interaction (5)
- Layered soil (4)
- Railway track (4)
- Slab track (4)
- Train passage (4)
- Force transfer (3)
- Hammer impact (3)
- Mitigation (3)
- Railway (3)
- Axle impulses (2)
- Axle sequence (2)
- Field tests (2)
- Finite-element boundary-element method (2)
- Irregular soil (2)
- Rail roughness (2)
- Rayleigh wave (2)
- Resonance (2)
- Soil-building interaction (2)
- Static axle loads (2)
- Track vibration (2)
- Train-induced ground vibration (2)
- Vehicle–track interaction (2)
- Wavenumber integrals (2)
- Achsfolgespektren (1)
- Acoplamiento Método de los Elementos de Contorno-Método de los Elementos Finitos (1)
- Attenuation (1)
- Axle box measurements (1)
- Axle-load spectra (1)
- Ballast mat (1)
- Ballast track (1)
- Base isolation (1)
- Bauteile (1)
- Bauwerke (1)
- Beam dynamics (1)
- Beam-soil interaction (1)
- Bending waves (1)
- Boundary Element Method-Finite Element Method coupling (1)
- Boundary element (1)
- Bridge (1)
- Bridge resonance (1)
- Bridge vibration (1)
- Brücken (1)
- Cancellation (1)
- Compliance function (1)
- Continuous soil (1)
- Continuously inhomogeneous soils (1)
- Dynamic axle loads (1)
- Dynamic pile and pile group stiffness (1)
- Dynamic soil-structure interaction (1)
- Elastic length (1)
- Elastic track elements (1)
- Elastische Gebäudelagerung (1)
- Emission (1)
- Environmental vibrations (1)
- Excitation forces (1)
- Experimental verification (1)
- FEBEM and simplified methods (1)
- Fequency domain (1)
- Filter effects (1)
- Finite element (1)
- Finite-element method (1)
- Flexible plate (1)
- Floating slab track (1)
- Floor amplification (1)
- Foundation reduction (1)
- Foundations (1)
- Frequency-wavenumber method (1)
- Geometric trackbed irregularities (1)
- Geometric vehicle and track irregularities (1)
- High-speed trains (1)
- Insertion loss (1)
- Interacción dinámica suelo-estructura (1)
- Interaction (1)
- Interior load (1)
- Irregular ballast (1)
- Irregularities (1)
- Kinematic and inertial soil-pile-building (1)
- Laboratory tests (1)
- Layered soils (1)
- Material damping (1)
- Measured railway vibrations (1)
- Measurements (1)
- Modal analysis (1)
- Modalanalyse (1)
- Moving load (1)
- Multi-beam model (1)
- Multi-beam track model (1)
- Multi-beam-on-support model (1)
- Obstacles (1)
- Parametric excitation (1)
- Pile bending stiffness (1)
- Pile foundation (1)
- Plate-soil interaction (1)
- Prediction (1)
- Predictions (1)
- Quasi-static response; (1)
- Rail pad (1)
- Railway bridge (1)
- Railway forces (1)
- Railway measurement campaign (1)
- Railway track vibration (1)
- Random dynamics and vibrations (1)
- Random stiffness variation (1)
- Randomly heterogeneous soil (1)
- Rechenmodelle (1)
- Reduction (1)
- Resonancia en edificaciones (1)
- Resonant response (1)
- Scattered axle impulses (1)
- Scattering (1)
- Scattering damping (1)
- Sleeper pad (1)
- Soil forces (1)
- Soil stiffness (1)
- Soil transfer function (1)
- Stiffness (1)
- Stiffness variation (1)
- Track (1)
- Track alignment (1)
- Track deflection (1)
- Track deformation (1)
- Track displacements (1)
- Track dynamic (1)
- Track filter (1)
- Track filtering (1)
- Track-soil and vehicle-track resonances (1)
- Train induced ground vibration (1)
- Train-induced vibration (1)
- Trench (1)
- Tunnel (1)
- Tunnel-to-surface reduction (1)
- Under sleeper pads (1)
- Varying track stiffness (1)
- Vibration (1)
- Vibration isolation (1)
- Vibration reduction (1)
- Wave attenuation (1)
- Wave excitation (1)
- Wave propagation (1)
- Wavenumber domain (1)
- Wavenumber method (1)
- Wheel out-of-roundness (1)
- Wheelset (1)
- Wind energy tower (1)
- floor vibration (1)
- layered soil (1)
- modal analysis (1)
- wave analysis (1)
Organisationseinheit der BAM
- 7 Bauwerkssicherheit (14)
- 7.2 Ingenieurbau (14)
Die diskrete Stützung der Schiene auf Schwellen in regelmäßigem Abstand ergibt für den fahrenden Zug eine Parametererregung. Die Berechnung der parametererregten Schwingungen und der zugehörigen dynamischen Radlasten erfordert die Analyse des Gesamtsystems Fahrzeug-Fahrweg-Untergrund. Es wird eine Substrukturmethode vorgestellt, bei der Fahrzeug, Fahrweg und Untergrund jeweils mit geeigneten Methoden (Mehrkörperdynamik, Finite Elemente, Randelemente) berechnet werden. Das Verfahren wird auf eine Situation angewandt, die auch mehrfach experimentell untersucht wurde, die Hochgeschwindigkeitsversuchsfahrten des Intercity Experimental (ICE) auf der Neubaustrecke bei Würzburg. Es werden die Ergebnisse der Teilsysteme und des Gesamtsystems und schließlich die dynamische Radlast für verschiedene Fahrgeschwindigkeiten dargestellt. Die dynamische Radlast nimmt bei Steigerung der Fahrgeschwindigkeit bis 200 km/h zu, bleibt bei höheren Fahrgeschwindigkeiten jedoch ungefähr konstant. Eine ähnliche Tendenz wird bei den Erschütterungen in der Umgebung bemerkt. Mit den berechneten Radlasten werden die ICE-Vorbeifahrten sehr detailliert simuliert und die berechneten Erschütterungen mit den gemessenen verglichen. Es zeigt sich eine gute Übereinstimmung, so daß der wichtige Fahrgeschwindigkeitseffekt als theoretisch und experimentell abgesichert angesehen werden kann.
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.
An integral method to calculate the solution of a homogeneous or layered soil due to a harmonic point load is described. An infinite plate at the surface of the soil can be introduced in this integration in wavenumber domain, too. Finite structures on the soil are calculated by a combined finite element and boundary element method, which makes use of the point load solution of the soil. The compliance functions for a vertical point load and some vibration modes are calculated for realistic parameters of the plate and the soil and for a wide range of frequencies. The influence of the stiffness of the soil and the foundation is investigated, showing that the soil mainly affects the low-frequent response whereas the structural properties are more important at higher frequencies. A rigid approximation of flexible plates is only found at low frequencies, if the elastic length is used as the radius of a rigid disk. At higher frequencies, a characteristic behaviour of the flexible plate of approximately is observed, what is in clear contrast to the compliance of rigid foundations. A plate on a visco-elastic support (Winkler soil) shows similar displacements as a plate on a homogeneous half-space, but the maximal stresses between the plate and the soil are considerably smaller which is found to be more realistic for a plate on a layered soil. For practical applications, a normalized diagram and some explicit formulas of the exact and the approximate solutions of an infinite plate on a homogeneous half-space are given, which is a useful model to represent the soil-structure interaction of flexible foundations.
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.
Excitation force spectra are necessary for a realistic prediction of railway-induced ground vibration. The excitation forces cause the ground vibration and they are themselves a result of irregularities passed by the train. The methods of the related analyses - the wavenumber integration for the wave propagation in homogeneous or layered soils, the combined finite-element boundary-element method for the vehicle-track-soil interaction - have already been presented and are the base for the advanced topic of this contribution. This contribution determines excitation force spectra of railway traffic by two completely different methods. The forward analysis starts with vehicle, track and soil irregularities, which are taken from literature and axle-box measurements, calculates the vehicle-track interaction and gets theoretical force spectra as the result. The second method is a backward analysis from the measured ground vibration of railway traffic. A calculated or measured transfer function of the soil is used to determine the excitation force spectrum of the train. A number of measurements of different soils and different trains with different speeds are analysed in that way. Forward and backward analysis yield the same approximate force spectra with values around 1 kN for each axle and third of octave.
The attenuation of the amplitudes with distance of technically induced surface wave fields is analyzed in theory and experiments. Experimental results of technically induced ground vibration are presented and collected from literature, which show a power-low attenuation A ~ r–q of amplitudes A with distance r and exponents q > 0.5 higher than for elastic surface waves. Additional attenuation effects are analyzed theoretically. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as A ~ exp(–kr), but for a broadband excitation, the sum of the exponential laws yields a power law with a higher exponent. Some more effects are discussed, for example the dispersion of the Rayleigh wave due to the layering of the soil, which yields a stronger attenuation A ~ r–q–dq, including an additional exponent of dq = 0.5 in case of an impulsive loading.
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.
The aim of this contribution is a practice-oriented prediction of environmental building vibrations. A Green's functions method for layered soils is used to build the dynamic stiffness matrix of the soil area that is covered by the foundation. A simple building model is proposed by adding a building mass to the dynamic stiffness of the soil. The vertical soil-building transfer functions with building-soil resonances are calculated and compared with a number of measurements of technically induced vibrations of residential buildings. In a parametrical study, realistic foundation geometries are modeled and the influence of incompressible soil, deep stiff soil layering, soft top layers, and increasing soil stiffness with depth is analyzed. All these special soil models reduce the resonant frequency compared to a standard homogeneous soil. A physically motivated model of a naturally sedimented soil has a stiffness increasing with the square root of the depth and yields a foundation stiffness that decreases with foundation area considerably stronger than the relatively insensitive homogeneous soil. This soil model is suited for the Berlin measuring sites and reproduces satisfactorily the experimental results.
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.
The attenuation of technically induced surface waves is studied theoretically and experimentally. In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation ν ~ r -q where the exponents q are in the range of 0.5 to 2.0 and depend on the source types. Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected. Some potential effects on ground vibration attenuation are theoretically analyzed. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as exp(-kr), but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent. Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.
Ballast mats are an efficient measure to reduce the vibrations near railway lines. The vehicle-track system gets a low eigenfrequency due to the insertion of an elastic ballast mat under the ballast. For frequencies higher than this low vehicle-track eigenfrequency, the forces, which are generating the vibration of the soil, are considerably reduced. In this contribution, a combined finite-element boundary-matrix method is used to calculate a number of completely three-dimensional track models with and without ballast mats. The influence of the important parameters such as the stiffness of the ballast mat, the unsprung vehicle mass, the mass of the track, and the stiffness of the subsoil is investigated. The numerical results are presented as the transfer functions of the total force that is acting on the soil and generating the vibration of the environment. The effectiveness of ballast mats is achieved by division of two of these force functions. The general tendencies for this insertion loss are discussed and a comparison with measurements is given. To come to an improved practical tool for the design of ballast-mat tracks, the finite-element method results are approximated by a simple two-dimensional model of which the solution is given explicitly.
The propagation of waves through homogeneous or layered soil is calculated based on half-space theory. The moving dynamic loads of a train are approximated by fixed dynamic loads and the wave field can be calculated if the spectrum of the dynamic train loads is known. In addition to this dynamic wave field, there are three different components at three different frequency ranges which are caused by the passage of the static loads:
the regular static component at low frequencies,
the irregular static component at medium frequencies,
the sleeper-passing component at high frequencies.
For each of these components, an approximate solution is presented. The calculated wave field is compared with measurements of different trains at different sites. The measurement of impulse and harmonic point load excitation verifies the soil dynamic base of the method.
Train-induced ground vibration can be excited by wheel and track irregularities and by two kinds of irregularities of the soil, by geometric irregularities or by the spatially varying soil stiffness. For both types of irregularities, the effective track irregularity on top of the track is calculated in wavenumber domain and with wavenumber integrals. For a general multi-beam track model, the wavenumber integrals are solved numerically. The irregularities of the soil are filtered by the track when transferred from the bottom to the top of the track. The high-wavenumber irregularities are strongly reduced due to the bending stiffness of the track and the compliance of the support. In addition, soft track elements reduce directly the stiffness variation of the support. Therefore, the mitigation effect of elastic track elements for these excitation components seems to be important. For under-sleeper pads and slab tracks, calculation and measurements are presented including additional excitation components and the dynamic vehicle–track interaction, and the relevance of the excitation mechanisms is discussed based on the dynamic forces which are acting on the ground. Due to the restricted amplitudes, the parametric excitation by the stiffness variation seems to be less important than the geometric irregularities. The calculations yield the correct trends of the measurements and many details of the measured ballast, slab, and under-sleeper-pad tracks.
The reduction of train-induced ground vibration by elastic elements such as rail pads and sleeper pads has been analyzed by a combined finite-element boundary-element method. The dynamic compliance of the track, the transfer function of the total force on the ground and the ground vibration ratios have been calculated for a variety of isolated and un-isolated track systems. It has been found that the soil force transfer, which describes the excitation force of the soil, is an appropriate quantity to predict the reduction of the ground vibration and the effectiveness of isolated tracks. All force transfer functions of isolated tracks display a vehicletrack resonance where the wheelset on the compliant track is excited by wheel and track irregularities. At higher frequencies, considerable reductions of the amplitudes are observed as the benefit of the resilient element. The influence of the stiffness of the rail or sleeper pads, the ballast and the soil, and the mass of the sleeper and the wheelset on the resonance frequency and the reduction has been investigated. Sleeper pads are advantageous due to the higher mass that is elastically supported compared to the rail-pad track system. The combination of elastic rail and sleeper pads has been found to be disadvantageous, as the second resonance occurs in the frequency range of intended reduction.
The 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.
This contribution presents some principles and some examples of the mitigation of railway-induced ground vibrations. The principles are different for the mitigation measures at the track, in the soil or at the building. Force transfer functions of isolated and un-isolated track-soil systems, reflected and transmitted wave amplitudes at walls and trenches in the soil, and the transfer of the (free-field) vibration amplitudes to the foundation amplitudes of the building are analysed. The mitigation effect can be calculated by exact or simplified formulas. Some examples with 3D (finite-element boundary-element), 2D (beam-on-support), and 1D track models, 2D and 1D soil models, detailed 3D building models and finite or infinite 1D wall-floor models are investigated to find out if simple models can be used for a satisfactory prediction of the mitigation effect. The 1D track examples show that the force transfer of the track without vehicle can be exactly calculated, whereas the total force transfer can be calculated approximately if appropriate wheelset masses per track length are used for the isolated and the un-isolated track. The mitigation effect of a filled trench is calculated by a 2D finite element model and the results compare with simple transmission formula if the stiffness per area rather than the wave impedances are used for the infill material. The base isolation of a building is analysed by a detailed 3D model and the results are similar to the analytic results of a single wall with floors on the soil. Other reduction measures as different floor and column dimensions are usually less effective so that the clearly best mitigation solution at a building is a partly or a complete base isolation.
Measurements on the vehicle-track interaction and the excitation of railway-induced ground vibration
(2017)
Two railway measurement campaigns have been performed in Germany and Switzerland which yield insight in the vehicle-track-soil interaction. The campaign in Germany has included simultaneous measurement of vehicle, track, and soil vibrations during train runs with 16, 25, 40, 63, 80, 100, 125, 140, 160 km/h, and impulse measurements of the passenger car, three track sections and the soil. Two ballast tracks, one on the soil surface and one on a concrete bridge, have been investigated as well as a slab track in a tunnel. Ten different sites in Switzerland have been measured for soil properties and train-induced ground vibrations, which allow to determine the excitation forces of the railway traffic. New axle-box measurements at some of the Swiss sites have been analysed to get further experimental evidence. All these measurements have been evaluated to characterize the excitation processes. Relations between vehicle vibration and ground vibration can be observed. The vehicle vibrations, namely the accelerations of the wheelsets, yield the dynamic forces due to the passage over the irregularities of the vehicle and the track. The ground vibrations are correlated to these dynamic forces to a certain extent. Some mid-frequency ground vibration amplitudes, however, are higher than expected from the dynamic excitation forces. The experimental observations can be explained by an irregular response to the passage of the static loads, that means the passage of the static loads over an irregular ballast or soil. This correct understanding of the excitation processes is important for the prediction as well as for the mitigation of railway induced ground vibrations.
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.
Die Grundidee einer Schwingungsminderung ist es eine tiefe Eigenfrequenz der Struktur zu erreichen, so dass höhere Frequenzen abgemindert werden. Das gilt für die Minderung an der Quelle, zum Beispiel einem Eisenbahngleis, und für die Minderung am Empfänger, dem Gebäude. Die Eigenfrequenz ermittelt man aus dem Verhältnis der Auflagersteifigkeit und der Masse. Wie ist die Masse bei einem Gebäude zu wählen? Und wie ist die Untergrundsteifigkeit zu berücksichtigen? Als Referenzsituation ohne Minderungsmaßnahme? Der Beitrag bringt Rechenergebnisse zu abgefederten Gebäuden mit einfachen und komplexen (FE-) Modellen, Mess- und Rechenergebnisse zur Schwingungsübertragung von unabgefederten Gebäuden. Es wird der Einfluss der Abstimmfrequenz, der Bodensteifigkeit und der „starren“ Gebäudemasse untersucht. Die komplexen Gebäudemodelle erlauben, neben der Berechnung einer elastischen Gebäudelagerung, auch die Variation von Gebäudeparametern zur Reduktion der Deckenschwingungen. Den Ergebnissen bei der Erschütterungs-übertragung in Gebäude werden zwei ähnliche Beispiele zur elastischen Maschinenlagerung und zur elastischen Gleislagerung gegenübergestellt.
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.
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.
En este artículo se presentan 2 metodologías basadas en las formulaciones del Método de los Elementos de Contorno y del Método de los Elementos Finitos para estudiar el efecto de la interacción suelo-estructura en el comportamiento dinámico de edificaciones. Se ha estudiado la respuesta de un edificio de 3 plantas producida por un campo de ondas incidente con los 2 métodos propuestos. Los resultados obtenidos presentan un buen grado de acuerdo entre ellos. A partir de estos resultados se ha validado un modelo aproximado para estudiar este tipo de problemas y se han examinado diferentes tipologías de edificaciones. Las conclusiones alcanzadas muestran que la respuesta global de las estructuras se debe a la deformación de los forjados y depende de su superficie, de las condiciones de apoyo y del acoplamiento con los forjados de la misma planta. Del mismo modo, se ha observado un acoplamiento del comportamiento de pilares y forjados cuando las rigideces de ambos son similares.----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- This paper presents 2 methodologies based on the Boundary Element Method and the Finite Element Method to study soil-structure interaction effect on building behaviour. A 3-story building response induced by an incident wave field is studied using both methods. The results obtained show a good agreement. Then, a simplified model is validated from these methods and several buildings are analysed. Conclusions show that structural responses are due to floor deformation, and depend on their area, support conditions and coupling. A coupling between floors and columns when both elements have similar stiffness is also observed.
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.
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.
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.
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.
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.
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.
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.
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.
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.