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Organisationseinheit der BAM
- 7 Bauwerkssicherheit (82)
- 7.2 Ingenieurbau (82)
Eingeladener Vortrag
- nein (134)
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.
Es wurden Elemente zusammengetragen, die für die Prognose der Deckenschwingungen von Bedeutung sind. Das umfasst Formeln für die Deckeneigenfrequenzen, Rechenergebnisse zu einfachen und mehrfeldrigen Decken sowie vielfältige Messerfahrungen.
Die Berechnungen zeigen die verschiedenen Einflüsse auf die Deckeneigenfrequenzen. Die Eigenfrequenzen berechnen sich aus den Abmessungen, dem Material und den Auflagerbedingungen der Decken. Es wurde auch der Einfluss von Unterzügen und von auskragenden Rändern untersucht. Bei Mehrfelddecken stellt man eine Häufung von Eigenfrequenzen in Frequenzbändern fest. Solche Fälle sollten sinnvollerweise nur mit Mittelwertaussagen erfasst werden. Die Berechnung einiger Gesamtgebäudemodelle führt zu vielfältigen Schwingantworten der verschiedenen Gebäudeteile, die ebenfalls Mittelungsgesetze notwendig erscheinen lassen. Die Nachgiebigkeit der Wände und Stützen führt zu einer Verringerung der rotatorischen und vertikalen Auflagersteifigkeit und damit der Deckeneigenfrequenzen. Die Festlegung der Eigenfrequenzen allein aus den Eigenschaften eines Deckenfeldes erscheint deshalb als nicht vernünftig. Es werden Mittelungsgesetze genannt und entwickelt, neben Mittelungsgesetzen für das Gesamtgebäude insbesondere eine Mittelung für die Berücksichtigung verschiedener Decken in einem Gebäude.
Wesentliche Erkenntnisse werden aus den Messergebnissen gewonnen. Es wurden 18 Gebäude und insgesamt 55 Decken untersucht. Die Deckeneigenfrequenzen liegen zwischen 5 und 50 Hz. Es wurden empirische Formeln für die Eigenfrequenzen in Abhängigkeit von der Deckenfläche getrennt für Holz- und Stein/Betondecken aufgestellt.
Ein weiterer wichtiger experimenteller Befund ist die Dämpfung der Decken, die im Bereich 1 % < D < 5 % ermittelt wurde. Dieser Dämpfungsbereich sollte für die Erschütterungsprognosen verwendet werden, wobei für eine konservative Prognose ein geringer Dämpfungswert einzusetzen wäre. Schließlich wurden Resonanzüberhöhungen der Decken gegenüber den Freifeldamplituden des Bodens gemessen. Mit diesen Messergebnissen kann dann das fertige Prognosemodell abgeglichen werden.
Somit sind ausreichend Erkenntnisse über das Deckenverhalten zusammengetragen, die in das Prognosemodell für das gesamte Gebäude eingebaut werden können.
Schwingungsminderung an der Quelle und beim Empfänger - FEBEM-Berechnung von Gleisen und Gebäuden.
(2006)
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.
Seit 30 Jahren betreibt die Bundesanstalt für Materialprüfung intensive Forschung auf dem Gebiet der Eisenbahndynamik unter Einbeziehung aller Systemkomponenten. Das umfasst theoretisch/numerische Arbeiten, Feldmessungen und Laborversuche zu Fragen wie die Erschütterungs- und Körperschallweiterleitung durch den natürlichen Boden, das Schwingungsverhalten der verschiedenen Fahrwege auf dem Untergrund, die dynamischen Kräfte aus der Wechselwirkung zwischen dem Fahrzeug und dem Fahrweg sowie die Gleislageentwicklung unter dieser Belastung bei verschiedenen Fahrwegen. Es werden Ergebnisse zu den dynamischen Kräften bei Geschwindigkeiten von 40 bis 300 km/h [1] und zum Vergleich der Festen Fahrbahn mit dem Schottergleis [2] vorgestellt.
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.
Schwingungsminderung zwischen Quelle und Empfänger - FEM-Berechnung der Wellenausbreitung im Boden
(2006)
Im Forschungsvorhaben „Praxisgerechtes Prognoseverfahren für Schienenverkehrserschütterungen“ wurde ein Prognoseprogramm entwickelt, das die Erschütterungsemission, -transmission und –immission für verschiedene Bahnen, verschiedene Böden, verschiedene Gebäude und verschiedene Minderungsmaßnahmen prognostizieren und bewerten kann. Es ist gelungen, ein Prognoseverfahren zusammenzustellen, das sowohl wissenschaftlich fundiert als auch einfach handhabbar ist. Die besonderen Merkmale des Prognoseverfahrens sind folgende:
- Das Prognoseprogramm basiert auf physikalischen Modellen.
- Das Programm besitzt klar definierten Schnittstellen zwischen der Emission und der Transmission und zwischen der Transmission und der Immission. Im ersten Fall sind es die auf den Untergrund wirkenden Erregerkräfte von Fahrzeug und Fahrweg, im zweiten Fall sind es die Freifeldamplituden des Bodens.
- Das Prognoseprogramm erlaubt es, Messdaten einzulesen und in physikalisch sinnvoller Weise weiter zu verarbeiten.
Damit sind die gesetzten Ziele für das Prognoseverfahren erfüllt und mit der Implementierung in einem benutzerorientierten Programm übertroffen worden.
Es ist gelungen, ausgehend von komplexen Modellen einfache Modelle zu finden und anzupassen. Hier ist einerseits die vereinfachte Berechnung der Wellenausbreitung im Boden zu nennen, die sowohl für kontinuierlich steifer werdende Böden als auch für geschichtete Böden zutreffende Ergebnisse liefert. Andererseits war die vereinfachte Berechnung der Fahrweg-Boden-Wechselwirkung ein besonderer Erfolg, da sowohl Standardgleise als auch Bundesanstalt für Materialforschung und –prüfung (BAM) Seite 24 Praxisgerechtes Prognoseverfahren für Schienenverkehrserschütterungen Gleise mit Minderungsmaßnahmen (zum Beispiel mit Unterschottermatten) durch allgemeine Gesetzmäßigkeiten erfasst werden konnten.
In diesem Bericht werden die Berechnungsmethoden für die Transmission der Erschütterungen dargelegt. Da es sich um die Wellenausbreitung im Boden handelt, sind drei große Abschnitte dem Einfluss und den Berechnungsmöglichkeiten verschiedener homogener und geschichteter Böden gewidmet. Dabei kommt ein exaktes aufwändiges Rechenverfahren und daraus abgeleitete einfachere Näherungsverfahren zum Einsatz.
Zum Bodeneinfluss wurden verschiedene homogene und geschichtete Böden exakt berechnet. Daraus wird ein Näherungsverfahren abgeleitet, dass auf der Dispersionsbeziehung v(f) beruht. Die Dispersion einiger Fälle wird exakt berechnet und ein Näherungsverfahren gefunden, mit dem man aus dem Tiefenprofil v(z) die Dispersion v(f) ermitteln kann. Mitden Näherungsverfahren werden die Wellenfelder der verschiedenen Böden nachgerechnet. Es ergeben sich sehr gute Übereinstimmungen mit den exakten Ergebnissen.
Die Zuganregung wird in erster Linie mit ortsfesten dynamischen Achslasten erfasst. Mit der Lastverteilung über die gesamte Zuglänge ergibt sich eine deutlich andere, nämlich schwächere Abnahmegesetzmäßigkeit als für die elementare Punktlast.
Für die Prognose von Schienenverkehrserschütterungen wurden verschiedene Verfahren vorgestellt, die die theoretischen Methoden zur Wellenausbreitung im Boden auf der experimentellen Seite ergänzen.
Dies beginnt bei der notwendigen Ermittlung der Bodenkennwerte für den Prognoseort, das führt weiter zur sehr hilfreichen Bestimmung der Übertragungsfunktion am Prognoseort, und schließlich zur kritischen Verwendung von gemessenen Spektren als Emissionsgröße. Die verschiedenen Verfahren werden anhand der Messungen der ICE 3-und Thalys-Versuchsfahrten bei Gardelegen vorgeführt.
Die wichtigsten Aussagen dieser Untersuchung sind:
– Die Ergebnisse der Schwinger- und Impulsmessungen, die Bodenkennwerte und die Übertragungsfunktionen, Theorie und Messungen stimmen alle sehr gut miteinander überein.
– Es sind gute Prognosen der Schienenverkehrserschütterungen sowohl mit den theoretischen als auch den experimentellen Übertragungsfunktionen möglich (s. Bild 39 im Vergleich zu Bild 40).
– Die Verwendung von gemessenen Schienenverkehrserschütterungen als Emissionsspektrum wird ermöglicht. Sie ist aber an die Kenntnis der Bodenkennwerte am Messort gekoppelt. Mit den Bodenkennwerten am Messort können dann bodenunabhängige Lastspektren als Emissionsgröße berechnet werden.
Damit steht eine Vielfalt von theoretischen und messtechnischen Varianten für die Prognose der Erschütterungsausbreitung im Boden zur Verfügung.
Es wurde ein Prognosemodell für die Bauwerksschwingungen entwickelt.
Es besteht aus einer Gesamtbauwerkswand, die alle Wände und Stützen eines Bauwerks repräsentiert, und aus den Decken in den einzelnen Stockwerken. Das Modell wird stockwerkweise mit Übertragungsmatrizen berechnet.
Hinsichtlich der Decken besteht im Programm die Möglichkeit, die Deckeneigenfrequenz aus den Abmessungen und den Auflagerbedingungen berechnen zu lassen. Die Decken werden dann im Rechenprogramm als Modalmodelle realisiert und an den Deckenauflagern in die Übertragungsmatrizenkette eingebaut.
Aus diesem Komplexmodell des Gebäudes wurde entsprechend den Messerfahrungen ein praxisnäheres Standardmodell abgeleitet. Dazu werden die Wandamplituden aller Stockwerke gemittelt und bei den Decken wird eine gewisse Bandbreite der vorhandenen Deckeneigenfrequenzen unterstellt.
Entsprechend der hohen Bedeutung, den experimentelle Ergebnisse für die Prognose der Erschütterungsimmission haben, wurden sehr viele in der BAM vorhandene Messdaten erneut ausgewertet und darüber hinaus neue Gebäudemessungen durchgeführt. Die Messergebnisse wurden bei der Definition des Standardmodells herangezogen. Außerdem wurde die Auswahl der Fundamentparameter mit den Messerfahrungen abgeglichen. Schließlich geben die Messdaten von etwa 80 Decken wichtige Hinweise auf die richtige Wahl der Deckenparameter Eigenfrequenz und Dämpfung.
Eine Parameterstudie gibt Auskunft über die praktisch vorkommende Bandbreite der einzelnen Parameter und deren Auswirkung auf die Bauwerksamplituden. Die wichtigsten Parameter sind die Bodensteifigkeit und die Deckeneigenfrequenz, die die Abminderung der Gesamtbauwerksamplituden einerseits und die Amplitudenverstärkungen in der Deckenresonanzen andererseits bestimmen. Für diese beiden Parameter ergaben die Untersuchungen wesentliche Hinweise:
Für die Gebäudegründung sind die weicheren oberen Bodenschichten maßgeblich, und die Deckeneigenfrequenzen lassen sich in erster Näherung gut durch eine allseitig gelenkige Lagerung abbilden.
Mit den theoretischen und experimentellen Arbeiten konnte somit ein praxisgerechter Immissionsteil für die Erschütterungsprognose erstellt werden.
Simple and advanced boundary-element method for the soil and its application to railway dynamics
(2007)
Simple and advanced boundary-element method for the soil and its application to railway dynamics
(2007)
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.
A finite-element boundary-element software for the dynamic interaction of flexible structures and the soil has been extended for pile foundation. The boundary element method for the soil uses the Green´s functions of the layered half-space which have been generalised for interior loads. Pile groups of 10 to 20 piles of different arrays are analysed and compared with single piles. Simplified models have been developed for a user-friendly, practice oriented prediction software for railway induced ground and building vibration.
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.
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.
Excitation force spectra are necessary for a realistic prediction of railway-induced ground vibration. The excitation forces cause the ground vibration and they are themselves a result of irregularities passed by the train. The methods of the related analyses - the wavenumber integration for the wave propagation in homogeneous or layered soils, the combined finite-element boundary-element method for the vehicle-track-soil interaction - have already been presented and are the base for the advanced topic of this contribution. This contribution determines excitation force spectra of railway traffic by two completely different methods. The forward analysis starts with vehicle, track and soil irregularities, which are taken from literature and axle-box measurements, calculates the vehicle-track interaction and gets theoretical force spectra as the result. The second method is a backward analysis from the measured ground vibration of railway traffic. A calculated or measured transfer function of the soil is used to determine the excitation force spectrum of the train. A number of measurements of different soils and different trains with different speeds are analysed in that way. Forward and backward analysis yield the same approximate force spectra with values around 1 kN for each axle and third of octave.
The attenuation of the amplitudes with distance of technically induced surface wave fields is analyzed in theory and experiments. Experimental results of technically induced ground vibration are presented and collected from literature, which show a power-low attenuation A ~ r–q of amplitudes A with distance r and exponents q > 0.5 higher than for elastic surface waves. Additional attenuation effects are analyzed theoretically. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as A ~ exp(–kr), but for a broadband excitation, the sum of the exponential laws yields a power law with a higher exponent. Some more effects are discussed, for example the dispersion of the Rayleigh wave due to the layering of the soil, which yields a stronger attenuation A ~ r–q–dq, including an additional exponent of dq = 0.5 in case of an impulsive loading.
The attenuation of technically induced surface waves is studied theoretically and experimentally. In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation ν ~ r -q where the exponents q are in the range of 0.5 to 2.0 and depend on the source types. Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected. Some potential effects on ground vibration attenuation are theoretically analyzed. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as exp(-kr), but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent. Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.
Construction work, such as pile driving and soil compaction, or road and railway traffic excite nearby buildings, and the perceptible or audible vibration can be a nuisance for nearby inhabitants. A simplified building model has been created for these situations, which includes the effects of soil-structure interaction, the low-frequency amplification along the height of the building as well as the high-frequency reduction and the floor resonances. The model consists of one wall for all supporting structures (walls and columns) and one floor for each storey. The effect of different floor resonance frequencies is included in a stochastic procedure. The soil is modelled by a spring and a viscous damper, and the free-field amplitudes of the soil are applied under this soil element.
The model can be calculated by transfer matrices or in a continuous wave-type version where an analytical solution can be evaluated numerically. The building response in the high-frequency (acoustic) region is calculated as mean values over wider frequency bands. The approach to an infinite building model can be found for these high frequencies and the corresponding soil-structure transfer can be described by the ratio of impedances at foundation level.
The rules for choosing the parameters to obtain realistic results are derived from complex calculations for example, for the stiffness and damping of building foundations and many measurements as for the damping of floor resonances. The influences on the floor resonance from the soil (damping) and the supporting structure (detuning) are important. Some more effects will be discussed by the simplified and detailed models and by measurements to establish a good understanding of ground-induced building vibrations.
Cet article présente plusieurs modèles numériques pour létude des phénomènes vibratoires lors du passage dun train. Les modèles permettent destimer la propagation des ondes et les réceptances pour le sol et la voie. Le sol multicouche et le couplage voie-sol sont traités par une (double) intégration sur les nombres donde. Les raideurs dynamiques de la voie et du véhicule sont combinées et les forces dexcitation roue-rail dues aux irrégularités de la voie et des roues sont calculées. Ces forces dexcitation permettent de simuler les vibrations du sol lors du passage dun train. Les modèles sont validés par comparaison avec des mesures sur deux sites, en France et en Allemagne. Les vibrations calculées correspondent bien aux vibrations mesurées. ----------------------------------------------------------------------------------------------------
This contribution presents models that are necessary to calculate the vibrations due to the passage of a train. The models allow to calculate the propagation of the waves and the receptances of the soil and the track. The layered soil and the coupling with the track are treated by a (double) integration in wavenumber domain. The dynamic stiffnesses of the track and vehicle are combined and the excitation forces due to the irregularities of the track and the wheel are calculated. Finally, these excitation forces are used to simulate the ground vibration of a passing train. All these models are validated by a number of different measurements at two sites in France and Germany.
The ground vibrations, which are generated by trains on different tracks, have been calculated by finite-element boundary-element models. The ballasted track is modelled in detail by the finite element method. The infinite soil is modelled by the boundary element method as a homogeneous or layered half-space. The track-soil system is coupled with a simple rigid mass model of the vehicle so that the vehicle-track interaction is completely included. Transfer functions are calculated in frequency domain without and with vehicle-track interaction, the compliance of the track and the mobilities of the soil at different distances from the track. Finally, the ratios between the ground vibration amplitudes with and without mitigation measure are calculated to quantify the effectiveness of the mitigation measure.
Tracks with under sleeper pads have been investigated in a wide parameter study. The main parameters that influence the reduction of ground vibration are the stiffness of the under sleeper pad, the mass and the width of the sleeper. The softest sleeper pad yields the best reduction of the ground vibration. The influence of the sleeper mass is not as strong as the characteristic frequency is ruled by the mass of the sleeper and the mass of the wheelset as well.
The influence of other parameters has been examined. The stiffness of the rail pads, the bending stiffness of the track, the stiffness of the ballast, the sub-soil, and the soil, and the layering of the soil. All these parameters show no or only a minor influence on the mitigation effect.
As the standard isolated track, a track with an under sleeper pad of a stiffness of kS = 5 107 N/m has been chosen, which can also be expressed as a stiffness per area of kS ’’ = 7.4 107 N/m3 = 0.074 N/mm3.
The resonance frequency for this pad stiffness is observed between 32 and 40 Hz. The reduction of the ground vibration is about vi,I /vi,U = 0.2 and 0.1 at 100 Hz. The reduction can be improved by softer sleeper pads. But the compliance of the track gets higher than tolerable. A possibility to use softer sleeper pads without increasing the static compliance of the track is their combination with wide sleepers. The softer sleeper pads under wider sleepers yield the same compliance of the track and a better reduction of the ground vibration.
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.
Um die Erschütterungen infolge von Schienenverkehr zu reduzieren, werden elastische Elemente in den Eisenbahnfahrweg eingebaut: elastische Zwischenlagen zwischen Schiene und Schwelle, elastische Schwellensohlen zwischen Schwelle und Schotter und Unterschottermatten unterhalb des Schotters. Das elastische Element führt zu einer ausgeprägten Eigenfrequenz des Gesamtsystems bestehend aus Fahrzeug, Fahrweg und Untergrund. Die Wirkung der elastischen Elemente beruht darauf, dass die Frequenzen oberhalb dieser Eigenfrequenz abgemindert werden. Für die Ermittlung der Wirksamkeit der Minderungsmaßnahme werden das Gleis mit elastischem Element und das Gleis ohne elastisches Element berechnet. Beide Eisenbahnfahrwege werden mit der kombinierten Finite-Element- Randelement-Methode berechnet, wobei das Gleis einschließlich des Schotters mit der Finite-Element-Methode berechnet wird, der Gleisuntergrund hingegen mit der Randelementmethode. Für die erschütterungsmindernden Gleise erweist es sich als vorteilhaft, spezielle Gleisendelemente an den Seiten des FE-Modells anzufügen. Dadurch wird zusätzlich zur Unendlichkeit des Untergrundes auch die unendliche Länge des Gleises berücksichtigt. Für die Ermittlung der Minderungswirkung werden die frequenzabhängige Nachgiebigkeit des Gleise, die Kraftübertragung des Gleises, und die Fahrzeug-Fahrweg-Wechselwirkung berechnet. Schließlich werden die Kraftminderungen verschiedener Eisenbahnfahrwege dargestellt und der Einfluss der wesentlichen Parameter untersucht.
Erschütterungsminderung der besohlten Schwelle, Rechenergebnisse zur Auswahl einer Teststruktur
(2012)
The ground vibrations, which are generated by trains on different slab tracks, have been calculated by finite-element boundary-element models. The slab track is modelled in detail by the finite element method.
The infinite soil is modelled by the boundary element method as a homogeneous half-space. The track-soil system is coupled with a simple rigid mass model of the vehicle so that the vehicle-track interaction is completely included. Transfer functions are calculated in frequency domain without and with vehicle-track interaction, the compliance of the track and the mobilities of the soil at different distances from the track.
Finally, the ratios between the ground vibration amplitudes with and without mitigation measure are calculated to quantify the effectiveness of the mitigation measure.
Tracks with under sleeper pads have been investigated in a parameter study. The main parameter that influences the reduction of ground vibration is the stiffness of the under sleeper pad. The softest sleeper pad yields the best reduction of the ground vibration.
The influence of other parameters has been examined. The stiffness of the rail pads, the stiffness of the slab material, the stiffness of the sleeper material, and the distance of the sleepers. All these parameters show no or only a minor influence on the mitigation effect.
As the standard isolated track, a track with an under sleeper pad of a stiffness of kS = 5 107 N/m has been chosen, which can also be expressed as a stiffness per area of kS ’’ = 3.7 107 N/m3 = 0.037 N/mm3.
The resonance frequency for this pad stiffness is observed between 32 and 40 Hz. The reduction of the ground vibration is about vi,I /vi,U = 0.1 at 100 Hz.
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.
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.
Durch Schienenverkehr angeregte Wellenausbreitung durch den Boden - Stand der Simulationsmethoden
(2014)
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.
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.
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.