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Organisationseinheit der BAM
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Eingeladener Vortrag
- nein (134)
Seismic response of three-dimensional structures using a green's function approach to the soil
(1986)
Simple and advanced boundary-element method for the soil and its application to railway dynamics
(2007)
Simple and advanced boundary-element method for the soil and its application to railway dynamics
(2007)
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.
Fahrzeug-Fahrweg-Untergrund-Umgebung: theoretische, rechnen- und meßtechnische Untersuchungen
(1987)
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.
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)
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.
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 attenuation of wave amplitudes is ruled by the planar, cylindrical or spher-ical geometry of the wave front (the geometric or power-law attenuation) but also by the damping of the soil (an exponential attenuation). Several low- and high-frequency filter effects are derived for the layering and the damping of the soil, for the moving static and the distributed train loads and for a homoge-neous or randomly heterogeneous soil. Measurements of hammer- and train-induced vibrations at five sites have been analysed for these attenuation and filter effects. The measured attenuation with distance can be discribed by gen-eralised power laws and some reasons will be discussed. The theoretical filter effects can well be found in the measurements.
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.
Train-induced ground vibrations are all generated by the vehicle, by static or dynamic vehicle loads. The most important and most accepted excitation are the dynamic wheel loads from the passage over track irregularities. Dynamic wheel loads will be compared from parallel axle-box and ground vibration measurements at more than seven sites. Some low-frequency excitation of ground vibrations, typically between 10 and 30 Hz, cannot be found in the axle-box measurements. Therefore, other vehicle modes, such as rigid bogie modes, flexible carriage modes, rigid and flexible wheelset modes, have been analysed for additional excitation forces. These vehicle dynamics analyses give an explanation for higher axle-box results at high frequencies, but not for the excitation of the higher low-frequency ground-vibration component. Finally, the effect of the moving static train loads will be analysed. For a regular track and soil, the moving static train loads yield the quasi-static response which exists only in the low-frequency nearfield of the track. If the support stiffness is randomly varying along the track, the pulses on the track generate an additional low-frequency component which is called the irregular pulse responses.
This component will be demonstrated by numerical analysis where all axle pulses are superposed in frequency domain.
The train passages over intact or damaged slab tracks on different soils have been calculated by two methods. The finite element method (FEM) uses a Winkler soil under the track model by adding a thin “soil layer”. The combined finite element boundary element method has a continuous soil model which is included by the boundary element method. The basic results are the distributions of the track (rail, track plate, and base layer) displacements along the track for a single axle laod. These solutions are superposed to a complete train load and transformed to time histories. The influence of track and soil parameters has been analysed. The main interest is the influence of the track damage. A gap between track plate and base layer of different lengths has been studied for changes in amplitudes and widths of deflection. A best fit to measured track displacements has been found so that the track damage can be identified and quantified. The FEM model with Winkler soil cannot be fitted to the amplitude and width with the same soil parameters. Therefore, the FEBEM model is preferable for these railway track problems.
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.
The attenuation of wave amplitudes is ruled by the planar, cylindrical or spherical geometry of the wave front (the geometric or power-law attenuation) but also by the damping of the soil (an exponential attenuation). Several low- and high-frequency filter effects are derived for the layering and the damping of the soil, for the moving static and the distributed train loads and for a homogeneous or randomly heterogeneous soil. Measurements of hammer- and train-induced vibrations at five sites have been analysed for these attenuation and filter effects. The measured attenuation with distance can be discribed by generalised power laws and some reasons will be discussed. The theoretical filter effects can well be found in the measurements.
Vibration measurements have many causes and many technical and natural sources. Problems can sometimes be solved by short-term measurements, but in many cases, a long-term measurement is necessary. In long-term measurements of days, weeks, months and even years, it is easy to collect a huge quantity of raw data, but at the end, the post-processing of these data can be exhausting (for example one-year vibration data of a wind energy tower). A software has been developed which con-sists of measuring and evaluation routines where the measuring routines can operate different meas-uring systems and different measuring cards. The main advantage of this software is the fact that the interesting evaluations can be integrated in the measuring process so that the characteristics of the vibration can be extracted without storing all the raw data. Only important time segments are stored, for example train passages. The overall concept of the software and the main evaluation routines will be described in some details. Examples of our measurement experience will illustrate the capabilities of the software. 1) Surveying construction work in nearby sensitive buildings (for example an old wind tunnel), including a stable alarm system and meaningful vibration limits. 2) Prediction of train-induced vibration for a planned building to prevent annoyance and to improve the building design. 3) Modal analysis and long term measurements of several single- or multi-span, concrete or steel bridges 4) Modal and wave analysis of coupled floors in a historical building (“Neues Palais” at Potsdam). 5) Soil properties of various measurement sites (different routines to evaluate the dispersion). Moreover, from many projects, amplitudes, frequencies, and attenuation laws have been collected and analysed for the different sources such as vibratory or impact pile driving and ground compaction, demolition work with different machines, blasting in quarries and in tunnel works, bomb and mine clearing.
Usually, geometric irregularities are considered as the main cause of ground vibrations from trains. A varying stiffness of the track, the track support and the soil can also generate ground vibrations. The regular stiffness variation of the track on and between the sleepers results in a deterministic dynamic axle load. The random stiffness variation of the track support yields also dynamic axle loads. The dynamic axle loads are generated by the varying wheel displacements under the static axle load by the acceleration of the unsprung mass of the rail vehicle. The random stiffness variation has a second effect. The pulses from the passage of the static axle loads are superposed regularly to the quasi-static response, but also irregularly to yield a “scattered” part of the axle pulses. The same holds for a random variation of the soil stiffness. All these effects of stiffness variations have been calculated by wavenumber-domain multi-beam track models, a random finite-element soil model and the superposition of axle impulses in a stochastic simulation. The results are confronted with many measurements at different sites. It is concluded that the stiffness variation of the track and the soil generate an important ground vibration component near railway lines.
A simple and fast prediction scheme is presented for train-induced ground and building vibrations. For the emission, finite-element boundary-element or multiple-beam-on-continuous-soil models of the track have been analysed and approximated by faster track-on-Winkler-soil models. The vehicle-track interaction due to irregularities yields the excitation forces. For the transmission of waves in the soil, the wavenumber integral of the compliance of layered soils has been evaluated. The calculation time is reduced for the prediction by using the solution of a homogeneous half-space with a frequency-dependent wave velocity (the dispersion) of the soil. For the immision, many 2 and 3-dimenisonal finite-element building models have been investigated, and a good approximation has been established by a 1-dimensional soil-wall-floor model. In addition, the axle sequence of the train, the quasi-static and the “scattered” response of the soil, and the wave propagation from a tunnel to a pile foundation of a building have been included.
Es wird eine gekoppelte Finite-Element-Randelementmethode zur Berechnung von Pfahlgrün-dungen in inhomogenen (geschichteten) Böden vorgestellt. Sie beruht auf den Greenschen Funktionen (Punktlastlösungen) für inhomogene Böden. Diese Lösungen können auch für die Wellenausbreitung in der Tiefe, zum Beispiel von einem Bahntunnel zu einem eingebetteten Gebäude, dem Kellergeschoss benutzt werden. Die Punktlastlösungen in der Tiefe werden mit der Halbraumlösung an der Bodenoberfläche und mit der Vollraumlösung verglichen und Gesetzmäßigkeiten für geschichtete Böden abgeleitet. Zu den Pfahlgründungen werden die Horizontalnachgiebigkeiten von Pfählen in geschichteten Böden dargestellt. Für den homogenen und den kontinuierlich steifer werdenden Boden werden Potenzgesetze für den Boden- und Pfahleinfluss aufgestellt. Der Vergleich mit dem Winkler-Modell der rein lokalen Bodenreaktion zeigt, dass die Winkler-Bettung in allen Fällen einen zu kleinen Bodeneinfluss ergibt.
Es wird eine gekoppelte Finite-Element-Randelementmethode zur Berechnung von Pfahlgrün-dungen in inhomogenen (geschichteten) Böden vorgestellt. Sie beruht auf den Greenschen Funktionen (Punktlastlösungen) für inhomogene Böden. Diese Lösungen können auch für die Wellenausbreitung in der Tiefe, zum Beispiel von einem Bahntunnel zu einem eingebetteten Gebäude, dem Kellergeschoss benutzt werden. Die Punktlastlösungen in der Tiefe werden mit der Halbraumlösung an der Bodenoberfläche und mit der Vollraumlösung verglichen und Gesetzmäßigkeiten für geschichtete Böden abgeleitet. Zu den Pfahlgründungen werden die Horizontalnachgiebigkeiten von Pfählen in geschichteten Böden dargestellt. Für den homoge-nen und den kontinuierlich steifer werdenden Boden werden Potenzgesetze für den Boden- und Pfahleinfluss aufgestellt. Der Vergleich mit dem Winkler-Modell der rein lokalen Boden-reaktion zeigt, dass die Winkler-Bettung in allen Fällen einen zu kleinen Bodeneinfluss ergibt.
Die Definition und Beschreibung der Einfügedämmung im Normentwurf DIN 45673-4 ist noch nicht richtig. Es wird die Beschreibung aus DIN 45673-3 herangezogen, die für Messungen gilt. Für die drei Rechenverfahren gibt es jeweils eine passende Beschreibung. Mit diesen Vorlagen ist eine vernünftige Definition der Einfügungsdämmung zu finden. Es bedarf einer Abgrenzung gegenüber anderen (falschen) Möglichkeiten. Des Weiteren ist der Anhang 2 erweitert und der Parametersatz im Anhang 1 auf das Wesentliche reduziert worden.
Vibration measurements have many causes and many technical and natural sources. Problems can sometimes be solved by short-term measurements, but in many cases, a long-term measurement is necessary. In long-term measurements of days, weeks, months and even years, it is easy to collect a huge quantity of raw data, but at the end, the post-processing of these data can be exhausting (for example one-year vibration data of a wind energy tower). A software has been developed which con-sists of measuring and evaluation routines where the measuring routines can operate different meas-uring systems and different measuring cards. The main advantage of this software is the fact that the interesting evaluations can be integrated in the measuring process so that the characteristics of the vibration can be extracted without storing all the raw data. Only important time segments are stored, for example train passages. The overall concept of the software and the main evaluation routines will be described in some details. Examples of our measurement experience will illustrate the capabilities of the software. 1) Surveying construction work in nearby sensitive buildings (for example an old wind tunnel), including a stable alarm system and meaningful vibration limits. 2) Prediction of train-induced vibration for a planned building to prevent annoyance and to improve the building design. 3) Modal analysis and long term measurements of several single- or multi-span, concrete or steel bridges 4) Modal and wave analysis of coupled floors in a historical building (“Neues Palais” at Potsdam). 5) Soil properties of various measurement sites (different routines to evaluate the dispersion). Moreover, from many projects, amplitudes, frequencies, and attenuation laws have been collected and analysed for the different sources such as vibratory or impact pile driving and ground compaction, demolition work with different machines, blasting in quarries and in tunnel works, bomb and mine clearing.
A simple and fast prediction scheme is presented for train-induced ground and building vibrations. For the emission, finite-element boundary-element or multiple-beam-on-continuous-soil models of the track have been analysed and approximated by faster track-on-Winkler-soil models. The vehicle-track interaction due to irregularities yields the excitation forces. For the transmission of waves in the soil, the wavenumber integral of the compliance of layered soils has been evaluated. The calculation time is reduced for the prediction by using the solution of a homogeneous half-space with a frequency-dependent wave velocity (the dispersion) of the soil. For the immision, many 2 and 3-dimenisonal finite-element building models have been investigated, and a good approximation has been established by a 1-dimensional soil-wall-floor model. In addition, the axle sequence of the train, the quasi-static and the “scattered” response of the soil, and the wave propagation from a tunnel to a pile foundation of a building have been included.
Usually, geometric irregularities are considered as the main cause of ground vibrations from trains. A varying stiffness of the track, the track support and the soil can also generate ground vibrations. The regular stiffness variation of the track on and between the sleepers results in a deterministic dynamic axle load. The random stiffness variation of the track support yields also dynamic axle loads which are generated by the acceleration of the unsprung mass (from the varying wheel displacements under the static axle load). The random stiffness variation has a second effect. The pulses from the passage of the static axle loads are superposed regularly to the quasi-static response, but also irregularly to yield a “scattered” part of the axle pulses. The same holds for a random variation of the soil stiffness. All these effects of stiffness variations have been calculated by wavenumber-domain multi-beam track models, a random finite-element soil model and the superposition of axle impulses in a stochastic simulation. The results are confronted with many measurements at different sites. It is concluded that the stiffness variation of the track and the soil generate an important ground vibration component near railway lines.
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 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.
Prognosen zur Erschütterungsausbreitung und zur Immissionssituation in der Umgebung von Bahntrassen sind wegen der Vielfalt der Einflussfaktoren oft mit erheblichen Unsicherheiten behaftet. Ziel der Arbeit war es, die Bedingungen für die Ausbreitung von Körperschall und Erschütterungen genauer zu erfassen und in ein für Prognosezwecke geeignetes Rechenmodell umzusetzen. Aufbauend auf theoretischen Untersuchungen zum Übertragungsverhalten des Bodens und von Gebäuden wurden Erschütterungsmessungen an Trassen verschiedener Bahnen des Stadtverkehrs Erregerspektren sowie mit besonderen Messverfahren Bodenkennwerte ermittelt. Diese dienen als Grundlage für die Modellrechnungen über die Ausbreitung von Erschütterungen. Durch Kontrollmessungen wurde die Anwendbarkeit des Modells überprüft. Es zeigten sich z.T. gute Übereinstimmungen, jedoch wurde auch die Notwendigkeit einer weiteren Verbesserung deutlich. Die Möglichkeiten der Minderung der Erschütterungen wurden umfassend behandelt.
Das Ziel der Untersuchungen ist ein Prognosemodell für Erschütterungen infolge Schiennahverkehr. Ergänzend zu Bericht 9 wird insbesondere der dreidimensionale, instationäre und zufällige Charakter der Erschütterungsquelle und dessen Auswirkungen auf die Ausbreitung durch den Boden und auf die Schwingungen benachbarter Gebäude untersucht. Es werden jeweils theoretisch/numerisch und experimentell/messtechnisch
- Amplituden-Abstands-Gesetze,
- Freifeld-Bauwerks-Übertragungsverhältnisse und
- Deckenresonanzüberhöhungen
ermittelt, die zusammen mit den Ergebnissen des Berichts 9 eine realistische Prognose von Erschütterungen ermöglichen. Die Ergebnisse sind in einem einfachen Prognoseprogramm zusammengefasst, mit dem im konkreten Anwendungsfall der Einfluss einer Reihe von Quell-, Boden- und Bauwerkseigenschaften erfasst wird.
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.
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.
Dieser Vortrag präsentiert einige Prinzipien und einige Beispiele zur Minderung von Eisenbahnerschütterungen. Die Prinzipien unterscheiden sich für die Minderungsmaßnahmen im Gleis, im Boden und bei Gebäuden. Kraftübertragungsfunktionen isolierter und nicht isolierter Gleissysteme, reflektierte und durchgelassene Wellenamplituden bei gefüllten Bodenschlitzen und die Übertragung der Freifeldschwingungen ins Gebäude werden analysiert. Bei den einfachen Gleismodellen muss der richtige Anteil der unabgefederte Fahrzeugmasse zum eindimensionalen Gleismodell hinzugefügt werden. Der Minderungseffekt eines gefüllten Bodenschlitzes ist von der Steifigkeit und nicht von der Impedanz des Schichtmaterials bestimmt. Bei einer elastischen Gebäudelagerung muss die Minderungswirkung mit der richtigen Boden- (Fundament-) Steifigkeit berechnet werden, und das abgeminderte Gebäudeverhalten hängt wesentlich von der effektiven Gebäudemasse ab, die mit zunehmender Frequenz deutlich kleiner als die starre Gebäudemasse ist.
Prediction of building noise and vibration – 3D finite element and 1D wave propagation models
(2021)
Construction work or traffic excite nearby buildings, and the perceptible or audible vibration can be a nuisance for the inhabitants. The transfer of the vibration from the free field to the building has been calculated by the finite element method for many models in consultancy and research work. The analysis for all storeys of certain building points such as walls, columns and floors unveiled some rules, some typical modes, and some wavetype responses. A simplified building-soil model has been created, which includes well these effects of building-soil resonance, wall/column resonance, floor resonances, and the high-frequency reduction. The model consists of one wall for a wall-type apartment building or a column for each specific part (mid, side or corner) of a column-type office building. The building response in the high-frequency (acoustic) region is calculated as mean values over all storeys and over wider frequency bands, by wave-type asymptotes of an infinitely tall building, and by the soil to wall ratio of impedances. The secondary noise is predicted by Transfer values between the building vibration (center of floors, walls at a room corner) and the sound pressure.
Prediction of building noise and vibration – 3D finite element and 1D wave propagation models
(2021)
Construction work or traffic excite nearby buildings, and the perceptible or audible vibration can be a nuisance for the inhabitants. The transfer of the vibration from the free field to the building has been calculated by the finite element method for many models in consultancy and research work. The analysis for all storeys of certain building points such as walls, columns and floors unveiled some rules, some typical modes, and some wavetype responses. A simplified building-soil model has been created, which includes well these effects of building-soil resonance, wall/column resonance, floor resonances, and the high-frequency reduction. The model consists of one wall for a wall-type apartment building or a column for each specific part (mid, side or corner) of a column-type office building. The building response in the high-frequency (acoustic) region is calculated as mean values over all storeys and over wider frequency bands, by wave-type asymptotes of an infinitely tall building, and by the soil to wall ratio of impedances. The secondary noise is predicted by Transfer values between the building vibration (center of floors, walls at a room corner) and the sound pressure.
Die Linienlastgesetzmäßigkeit gilt nicht für Zuganregung. Die Punktlastgesetzmäßigkeit wird bei kurzen Zügen in größeren Entfernungen erreicht. Bei langen Zügen reduziert sich die Abnahme um r-0,3 für die theoretische exponentielle Dämpfungsabnahme, um r-0,5 für die vereinfachte potentielle Dämpfungsabnahme. Die gemessenen Abnahmereduktionen liegen in diesem Bereich.
Zur Erschütterungsausbreitung an oberirdischen Bahnlinien gibt es gute Übereinstimmungen zwischen Messungen und der Theorie geschichteter Böden. Bei der Interpretation der Ergebnisse spielt die Rayleigh-Welle eine große Rolle. Je nach Frequenz und Wellenlänge hat die Rayleigh-Welle eine bestimmte Eindringtiefe und erreicht damit mehr oder weniger steife Bodenschichten. Damit bekommt man eine frequenzabhängige Bodensteifigkeit für die Erschütterungsprognose. Für die Wellenausbreitung in der Tiefe statt an der Bodenoberfläche müssen eigene Gesetzmäßigkeiten gefunden werden. Es werden die Punktlastlösungen im Frequenz-Wellenzahlbereich und durch Integration über die Wellenzahlen berechnet. Man erhält die Wellenfelder, die Terzspektren für verschiedene Entfernungen und Frequenzen. Es wird die Tiefenlage und das Bodenmodell (homogen, geschichtet und kontinuierlich zunehmende Steifigkeit) variiert. Die Rayleigh-Welle verliert ihre Bedeutung und stattdessen kann die Vollraumlösung zur Interpretation und Prognose verwendet werden. Es werden die Halbraumlösung mit und ohne Rayleigh-Welle und die Vollraumlösung in der Tiefe diskutiert und verglichen. Neben der Wellenausbreitung (der Transmission) werden auch Effekte der Erschütterungsanregung (der Emission) und der Übertragung in Gebäude (der Immission) mit Hilfe der Finite-Element-Randelement-Methode berechnet. Die Verteilung der dynamischen Achslast durch die Tunnelsohle ergibt eine Minderung gegenüber der Punktlastanregung. Bei der Immission hat man keine Freifeldanregung wie an der Bodenoberfläche. Man muss entweder neben der Wellenamplitude (Verschiebung oder Schwinggeschwindigkeit) in der Tiefe auch die Spannung der ankommenden Welle berücksichtigen, oder man muss die Freifeldamplituden nach Bodenaushub berechnen. Die Rechenergebnisse deuten darauf hin, dass man als Freifeldanregung die zweifache Vollraumlösung ansetzen kann.
The present contribution evaluates four measuring series made by the Federal Institute of Material Research and Testing for the relations between train speed and ground vibration amplitudes. This experimental evaluation is supported by the simulation of the train passages at the different sites by using appropriate excitation mechanisms and forces as well as layered soil models which have been derived from impact measurements at each site.
There is a strong need for cost-effective mitigation measures for
turnouts. SBB has initiated a series of examinations using different methodologies to gain a deeper understanding of the excitation mechanisms at low frequencies, in addition to that obtained in the RIVAS project. To date it is not yet clear what constitutes a complete measurement data set that would enable understanding most of the vibration excitation mechanisms in turnouts. Increasing vibration at turnouts in comparison to normal track is observed for all measured frequencies.
The different methodologies are presented in the paper. Under-sleeper pads (USP) are a cost-effective method to reduce vibration at frequencies above 63 Hz (1/3 octave), but there is probably no improvement for frequencies below 63 Hz. A first test of new frog geometry did not show relevant improvements in Vibration emission in comparison to a reference frog geometry. Axle box acceleration measurements are an interesting method to identify defects in a turnout. A specialized measurement system of rail roughness could identify certain geometry Problem areas for some frogs. Noise increases also are observed at turnouts for frequencies ranging between 80 to 1000 Hz. The use of railway source models to calculate
contact forces for ballasted track and turnouts seems promising, in particular for understanding the influence of ground.
Zur Erschütterungsausbreitung an oberirdischen Bahnlinien gibt es gute Übereinstimmungen zwischen Messungen und der Theorie geschichteter Böden. Bei der Interpretation der Ergebnisse spielt die Rayleigh-Welle eine große Rolle. Je nach Frequenz und Wellenlänge hat die Rayleigh-Welle eine bestimmte Eindringtiefe und erreicht damit mehr oder weniger steife Bodenschichten. Damit bekommt man eine frequenzabhängige Bodensteifigkeit für die Erschütterungsprognose. Für die Wellenausbreitung in der Tiefe statt an der Bodenoberfläche müssen eigene Gesetzmäßigkeiten gefunden werden. Es werden die Punktlastlösungen im Frequenz-Wellenzahlbereich und durch Integration über die Wellenzahlen berechnet. Man erhält die Wellenfelder, die Terzspektren für verschiedene Entfernungen und Frequenzen. Es wird die Tiefenlage und das Bodenmodell (homogen, geschichtet und kontinuierlich zunehmende Steifigkeit) variiert. Die Rayleigh-Welle verliert ihre Bedeutung und stattdessen kann die Vollraumlösung zur Interpretation und Prognose verwendet werden. Es werden die Halbraumlösung mit und ohne Rayleigh-Welle und die Vollraumlösung in der Tiefe diskutiert und verglichen. Neben der Wellenausbreitung (der Transmission) werden auch Effekte der Erschütterungsanregung (der Emission) und der Übertragung in Gebäude (der Immission) mit Hilfe der Finite-Element-Randelement-Methode berechnet. Die Verteilung der dynamischen Achslast durch die Tunnelsohle ergibt eine Minderung gegenüber der Punktlastanregung. Bei der Immission hat man keine Freifeldanregung wie an der Bodenoberfläche. Man muss entweder neben der Wellenamplitude (Verschiebung oder Schwinggeschwindigkeit) in der Tiefe auch die Spannung der ankommenden Welle berücksichtigen, oder man muss die Freifeldamplituden nach Bodenaushub berechnen. Die Rechenergebnisse deuten darauf hin, dass man als Freifeldanregung die zweifache Vollraumlösung ansetzen kann.
Measurements at the foundation, the surrounding soil and nearby buildings have been done during several drop tests of different containers on different foundations. The first measurements have been done on a big foundation where it should be guaranteed that the foundation is rigid and the container is tested properly. It was controlled that the foundation does not absorb more than 2 percent of the energy of the container. Most of the drop energy is lost in shock absorbers. Later on, a smaller drop test facility has been built on the ground but inside an existing building. It had to be controlled by prediction and measurements that the drop test will not damage the building. Tests from different heights on soft, medium, and stiff targets have been done to find out rules which allow to identify acceptable and unacceptable drop tests. Later on, the biggest drop test facility has been built for masses up to 200 t. It was necessary for the design of the foundation to estimate the forces which occur during the drop tests. On the other hand, the acceptable tests should be selected and controlled by measurements where the impact duration is important. Different sensors, accelerometers, accelerometers with mechanical filters, geophones (velocity transducers), strain gauges, and pressure cells have been applied for these tasks. The signals have been transformed to displacements which proved to be best suited for the interpretation of the impact mechanism. Modell calculations have been used to check and understand the dynamic measurements. The simplest law is the conservation of the momentum which is a good approximation if the impact is short. If the soil under the foundation has an influence on the deceleration of the container, the maximum foundation velocity is lower than the simple estimation. The amplitudes of the foundation could also be estimated from the ground vibrations and their amplitude-distance law.
Measurements at the foundation, the surrounding soil and nearby buildings have been done during several drop tests of different containers on different foundations. The first measurements have been done on a big foundation where it should be guaranteed that the foundation is rigid and the container is tested properly. It was controlled that the foundation does not absorb more than 2 percent of the energy of the container. Most of the drop energy is lost in shock absorbers. Later on, a smaller drop test facility has been built on the ground but inside an existing building. It had to be controlled by prediction and measurements that the drop test will not damage the building. Tests from different heights on soft, medium, and stiff targets have been done to find out rules which allow to identify acceptable and unacceptable drop tests. Later on, the biggest drop test facility has been built for masses up to 200 t. It was necessary for the design of the foundation to estimate the forces which occur during the drop tests. On the other hand, the acceptable tests should be selected and controlled by measurements where the impact duration is important. Different sensors, accelerometers, accelerometers with mechanical filters, geophones (velocity transducers), strain gauges, and pressure cells have been applied for these tasks. The signals have been transformed to displacements which proved to be best suited for the interpretation of the impact mechanism. Modell calculations have been used to check and understand the dynamic measurements. The simplest law is the conservation of the momentum which is a good approximation if the impact is short. If the soil under the foundation has an influence on the deceleration of the container, the maximum foundation velocity is lower than the simple estimation. The amplitudes of the foundation could also be estimated from the ground vibrations and their amplitude-distance law.
Erschütterungen, die durch Eisenbahnverkehr erzeugt werden, breiten sich durch den Erdboden aus und regen benachbarte Gebäude zu Schwingungen an. Es wurde ein Prognoseverfahren für Bahnerschütterungen ent-wickelt, das mit einfachen Modellen schnell Ergebnisse liefert. Dies sind physikalische Modelle, zum Beispiel 1-dimensionale Modelle mit Übertragungsmatrizen für die Fahrzeug-Fahrweg-Boden-Wechselwirkung und für die Gebäude-Boden Wechselwirkung. Damit werden die komplexen Verhältnisse bei der Emission (dem Zusammen¬wirken von Fahrzeug und Fahrweg), bei der Transmission durch den homogenen oder geschichteten Boden und bei der Immission in Gebäuden näherungsweise erfasst. In (Auersch, 2020) wird gezeigt, dass diese einfachen Prognosemodelle die Ergebnisse von detaillierten Modellen wie der Finite-Element-Randelement-Methode für das Gleis, die Wellenzahlintegrale für den Boden und 3-dimensionale Finite-Element-Modelle für das Gebäude gut wiedergeben können. Dies entspricht auch der Absicht, die Prognosemodelle aus den Ergebnissen der Detailmodelle abzuleiten. Die drei Prognoseteile werden getrennt berechnet, aber es werden physikalisch sinn¬volle Schnittstellen verwendet. Für die Emission und Transmission sind es die auf den Untergrund wirkenden Erregerkräfte von Fahrzeug und Fahrweg, für die Transmission und Immission sind es die Freifeldamplituden des Bodens.
Erschütterungen, die durch Eisenbahnverkehr erzeugt werden, breiten sich durch den Erdboden aus und regen benachbarte Gebäude zu Schwingungen an. Es wurde ein Prognoseverfahren für Bahnerschütterungen ent-wickelt, das mit einfachen Modellen schnell Ergebnisse liefert. Dies sind physikalische Modelle, zum Beispiel 1-dimensionale Modelle mit Übertragungsmatrizen für die Fahrzeug-Fahrweg-Boden-Wechselwirkung und für die Gebäude-Boden Wechselwirkung. Damit werden die komplexen Verhältnisse bei der Emission (dem Zusammen¬wirken von Fahrzeug und Fahrweg), bei der Transmission durch den homogenen oder geschichteten Boden und bei der Immission in Gebäuden näherungsweise erfasst. In (Auersch, 2020) wird gezeigt, dass diese einfachen Prognosemodelle die Ergebnisse von detaillierten Modellen wie der Finite-Element-Randelement-Methode für das Gleis, die Wellenzahlintegrale für den Boden und 3-dimensionale Finite-Element-Modelle für das Gebäude gut wiedergeben können. Dies entspricht auch der Absicht, die Prognosemodelle aus den Ergebnissen der Detailmodelle abzuleiten. Die drei Prognoseteile werden getrennt berechnet, aber es werden physikalisch sinn¬volle Schnittstellen verwendet. Für die Emission und Transmission sind es die auf den Untergrund wirkenden Erregerkräfte von Fahrzeug und Fahrweg, für die Transmission und Immission sind es die Freifeldamplituden des Bodens.
A combined finite element boundary element method has been developed to calculate the dynamic interaction of the railway track and the underlying soil. The track-soil results are coupled with a simple vehicle model to establish the force transfer function of the vehicle-track-soil system. Mitigation measures at the track, namely three different tracks with under-sleeper pads, are analysed. The un-sprung vehicle and heavy track masses on soft track elements yield a lower vehicle-tracksoil resonant frequency and a better reduction of the excitation forces at higher frequencies. If the effectiveness of the mitigation is measured as a vibration ratio between the isolated and an un-isolated reference track, the vehicle-track-soil resonance of the reference track has an important influence on the mitigation effectiveness. Therefore, different un-isolated reference tracks are analysed. It is shown how the frequency and amplitude of the vehicle-track resonance are influenced by the stiffness of the rail pads (strongest), the ballast (medium) and the soil (weakest). The reference track models have been compared with shaker tests on two railway tracks with strong resonances. The damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany and compared with the theoretical behaviour of intact and damaged tracks.
A combined finite element boundary element method has been developed to calculate the dynamic interaction of the railway track and the underlying soil. The track-soil results are coupled with a simple vehicle model to establish the force transfer function of the vehicle-track-soil system. Mitigation measures at the track, namely three different tracks with under-sleeper pads, are analysed. The un-sprung vehicle and heavy track masses on soft track elements yield a lower vehicle-tracksoil resonant frequency and a better reduction of the excitation forces at higher frequencies. If the effectiveness of the mitigation is measured as a vibration ratio between the isolated and an un-isolated reference track, the vehicle-track-soil resonance of the reference track has an important influence on the mitigation effectiveness. Therefore, different un-isolated reference tracks are analysed. It is shown how the frequency and amplitude of the vehicle-track resonance are influenced by the stiffness of the rail pads (strongest), the ballast (medium) and the soil (weakest). The reference track models have been compared with shaker tests on two railway tracks with strong resonances. The damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany and compared with the theoretical behaviour of intact and damaged tracks.
Long wooden floor beams above a ball room in an old historical palace have been analysed experimentally. The eleven beams are weakly coupled by three layers of floor boards. It has been investigated if the state (the stiffness) of the wooden beams can be determined by vibration measurements of global or preferably local modes. Hammer, heel-drop and ambient excitations have been used. The vibration modes of the structure show dominating local deformations if an impact excitation is applied. This is understood as the positive superposition of several modes which yield the maximum at the excitation point but a cancellation at more distant points. Natural modes have been estimated from these vibration modes by standard and special methods which were necessary for the high damping of the wooden floor. It has been found that all floor beams contribute to each natural mode even for a weak coupling of the beams. In addition to the modal discussion, the impact tests have also been analysed for the wave propagation and amplitude attenuation with distance. The coupling of floor beams has been studied theoretically by an analytic multiple-beam model where the coupling by translational or rotational springs and by a common support motion has been assumed.
Long wooden floor beams above a ball room in an old historical palace have been analysed experimentally. The eleven beams are weakly coupled by three layers of floor boards. It has been investigated if the state (the stiffness) of the wooden beams can be determined by vibration measurements of global or preferably local modes. Hammer, heel-drop and ambient excitations have been used. The vibration modes of the structure show dominating local deformations if an impact excitation is applied. This is understood as the positive superposition of several modes which yield the maximum at the excitation point but a cancellation at more distant points. Natural modes have been estimated from these vibration modes by standard and special methods which were necessary for the high damping of the wooden floor. It has been found that all floor beams contribute to each natural mode even for a weak coupling of the beams. In addition to the modal discussion, the impact tests have also been analysed for the wave propagation and amplitude attenuation with distance. The coupling of floor beams has been studied theoretically by an analytic multiple-beam model where the coupling by translational or rotational springs and by a common support motion has been assumed.