7.2 Ingenieurbau
Filtern
Dokumenttyp
- Vortrag (37)
- Beitrag zu einem Tagungsband (21)
- Zeitschriftenartikel (5)
- Beitrag zu einem Sammelband (3)
- Buchkapitel (1)
- Posterpräsentation (1)
Referierte Publikation
- nein (68) (entfernen)
Schlagworte
- Ground vibration (18)
- Building vibration (7)
- Bahnerschütterungen (6)
- Layered soil (6)
- Vibration measurements (6)
- Hammer impact (5)
- Train-induced ground vibration (5)
- Container loading (4)
- Drop test (4)
- Erschütterungsminderung (4)
- Excitation forces (4)
- Foundation load (4)
- Layered soils (4)
- Train passage (4)
- Vehicle-track-soil interaction (4)
- Dispersionsmessung (3)
- Elastische Gleiselemente (3)
- Emission (3)
- Erschütterungen (3)
- Erschütterungsprognose (3)
- Mitigation (3)
- Slab track (3)
- Train speed (3)
- Tunnel (3)
- Wellengeschwindigkeit (3)
- 2-span bridge (2)
- Apartment building (2)
- Attenuation (2)
- Axle-sequence spectrum (2)
- Bodenübertragungsfunktion (2)
- Displacements (2)
- Elastische Elemente (2)
- Erschütterungsausbreitung (2)
- Evaluation (2)
- Filter effects (2)
- Finite element models (2)
- Freight train (2)
- Gleiströge (2)
- Ground vibration measurements (2)
- Halbraum (2)
- High-speed train (2)
- Immission (2)
- Irregularities (2)
- Measurement (2)
- Measurements (2)
- Office tower (2)
- Passenger train (2)
- Prediction (2)
- Railway bridge (2)
- Railway tunnel (2)
- Railways (2)
- Randomly heterogeneous soil (2)
- Scattering (2)
- Soil-wall-floor model (2)
- Surface-tunnel reduction (2)
- Train excitation (2)
- Transmission (2)
- Vehicle-track interaction (2)
- Vibration measurement (2)
- Vollraum (2)
- Wellenausbreitung in der Tiefe (2)
- Zuggeschwindigkeit (2)
- Achsfolgespektren (1)
- Achsimpulse (1)
- Amplitude-charge weight laws (1)
- Amplitude-distance laws (1)
- Amplituden-Abstands-Gesetze (1)
- Axle impulses (1)
- Axle loads (1)
- Axle pulses (1)
- Bahngleis (1)
- Ballast track (1)
- Base isolation (1)
- Bauteile (1)
- Bauwerk-Boden-Wechselwirkung (1)
- Bauwerke (1)
- Bodenschlitz (1)
- Brücken (1)
- Building response (1)
- Cars (1)
- Column/wall resonance (1)
- Combined finite-element boundary-element method (1)
- Components of excitation (1)
- Damage detection (1)
- Deckeneigenfrequenzen (1)
- Deckenschwingungen (1)
- Dynamic loads (1)
- Dämpfung (1)
- Einfügungsdämmung (1)
- Elastische Gebäudelagerung (1)
- Erschütterungen im Fernfeld (1)
- Explosion-induced ground vibrations (1)
- Fahrzeug-Fahrweg-Boden-Wechselwirkung (1)
- Finite element method (1)
- Flexibility (1)
- Flexible car body (1)
- Flexible wheelset (1)
- Floor resonance (1)
- Floors (1)
- Footbridge (1)
- Foundations (1)
- Frequency response function (1)
- Gebäudelagerung (1)
- Gebäudemodelle (1)
- Gebäudeschwingungen (1)
- Geometrie (1)
- High-Rise Building (1)
- High-rise buildings (1)
- Impedanzmethode (1)
- Inertial Interaction (1)
- Inertial interaction (1)
- Inhomogeneous soils (1)
- Irregular ballast (1)
- Irregular soil (1)
- Kinematic Interaction (1)
- Kinematic interaction (1)
- Kraft auf den Boden (1)
- Long-span bridge (1)
- Measurement campaigns (1)
- Modal force spectrum (1)
- Modal load spectrum (1)
- Modalanalyse (1)
- Modes (1)
- Modes and waves (1)
- Movin load test (1)
- Multi-beam method (1)
- Nachgiebigkeiten (1)
- Normung (1)
- Office building (1)
- Pfahlnachgiebigkeiten (1)
- Pile Foundation (1)
- Pile groups (1)
- Prediction of explosion induced ground and building vibration (1)
- Prognose (1)
- Propagation from a tunnel (1)
- Railbridge (1)
- Railway (1)
- Railway induced vibration (1)
- Railway track (1)
- Railway tracks (1)
- Railway trafiic (1)
- Randelementmethode (1)
- Rayleighwellendispersion (1)
- Rechenmodelle (1)
- Rechenverfahren (1)
- Residential building (1)
- Richtige Fahrzeugmasse (1)
- Rigid vehicle model (1)
- Scattered axle impulses (1)
- Schienenfahrweg (1)
- Schienenfahrwege (1)
- Simple and fast prediction (1)
- Simple prediction (1)
- Soft track elements (1)
- Soil properties (1)
- Soil-building interaction (1)
- Soil-building resonance (1)
- Soil-pile interaction (1)
- Soil-wall floor model (1)
- Spektralanalyse (1)
- Störgrößen (1)
- Surface Foundation (1)
- Surface line (1)
- Switch (1)
- Track and vehicle irregularities (1)
- Track beam (1)
- Track damage (1)
- Track damage monitoring (1)
- Track damage quantification (1)
- Track vibration (1)
- Track-soil interaction (1)
- Train configuration (1)
- Train passages (1)
- Tran speed (1)
- Transfer fuction (1)
- Transfer function (1)
- Tunnel line (1)
- Tunnel-pile transfer (1)
- Tunnelstrecke (1)
- Turnout (1)
- Under-sleeper pads (1)
- Varying soil stiffness (1)
- Varying stiffness (1)
- Varying track stiffness (1)
- Vibration excitation (1)
- Wavenumber integrals (1)
- Wavenumber method (1)
- Waves (1)
- Wellenausbreitung (1)
- Wellenfeldberechnung (1)
- Wheelset accelerations (1)
- Windenergieanlagen (1)
- Zerstreute Achsimpulse (1)
- elastische Gebäudelagerungen (1)
- zerstreute Achslastimpulse (1)
- Übertragungsmatrizen (1)
Organisationseinheit der BAM
- 7.2 Ingenieurbau (68) (entfernen)
Eingeladener Vortrag
- nein (37)
The passage of the train is dominated by the impulses of the static axle loads. The response of the regular homogeneous and irregular soils has been calculated by the finite-element method in frequency domain. The superposition of the impulse responses yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil or ballast of which the stiffness varies randomly in space, a mid-frequency ground vibration component is generated by the scattering of the axle impulses. Measurements will be shown which prove the existence of the mid-frequency ground vibration component and the unique explanation by the scattered axle impulses: many international measurements with a raised mid-frequency component, axle-box measurements with a too low mid-frequency dynamic load, amplitude-speed dependencies which are incompatible with irregularity-induced dynamic loads, and ground vibration reductions due to stiff track elements.
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.
Die Bundesanstalt für Materialforschung und -prüfung hat in den letzten 30 Jahren an vielen Orten Bahnerschütterungen gemessen. Dabei wurden immer auch Versuche zur Bestimmung der Bodeneigen-schaften durchgeführt, meist mit Hammeranregung, gelegentlich auch mit Schwingeranregung. Es werden verschiedene Auswertemethoden wie Seismogramm-Montage, Spektrale Analyse (SASW), Multistation Analysis of Surface Waves (MASW), f,v-Analyse (Dispersion aus zweifacher Fourier-Analyse), Spatial AutoCorrelation (SPAC, hier auch für deterministische Quellen) vorgestellt. Durch Approximation der frequenzabhängigen Wellengeschwindigkeiten (Dispersion) oder der gemessenen Übertragungsfunktionen erhält man ein passendes Bodenmodell. Zu diesem Bodenmodell kann man dann die Übertragungsfunktionen für Hammer- und Zuganregung berechnen. Mit allgemeinen oder spezifischen Achslastspektren werden dann die Bahnerschütterungen prognostiziert und mit den Messergebnissen verglichen. Bei etlichen Messorten, insbesondere in der Schweiz, wurden deutliche Merkmale einer Bodenschichtung beobachtet. Es ergibt sich eine deutliche Reduktion der tiefen Frequenzanteile durch den steifen unterliegenden Halbraum. Die weiche Deckschicht bestimmt das hochfrequente Verhalten. Hier bewirkt die Materialdämpfung des Bodens oft einen starken Amplitudenabfall, sowohl mit der Entfernung als auch mit der Frequenz. Für den verbleibenden mittelfrequenten Anteil wurde an mehreren Messorten die Amplituden-Fahrgeschwindigkeits-Gesetzmäßigkeiten untersucht. Es gibt konstante bis stark ansteigende Amplituden, und es zeigt sich auch hier, dass der geschichtete Boden von entscheidender Bedeutung ist.
Die Bundesanstalt für Materialforschung und -prüfung hat in den letzten 30 Jahren an vielen Orten Bahnerschütterungen gemessen. Dabei wurden immer auch Versuche zur Bestimmung der Bodeneigen-schaften durchgeführt, meist mit Hammeranregung, gelegentlich auch mit Schwingeranregung. Es werden verschiedene Auswertemethoden wie Seismogramm-Montage, Spektrale Analyse (SASW), Multistation Analysis of Surface Waves (MASW), f,v-Analyse (Dispersion aus zweifacher Fourier-Analyse), Spatial AutoCorrelation (SPAC, hier auch für deterministische Quellen) vorgestellt. Durch Approximation der frequenzabhängigen Wellengeschwindigkeiten (Dispersion) oder der gemessenen Übertragungsfunktionen erhält man ein passendes Bodenmodell. Zu diesem Bodenmodell kann man dann die Übertragungsfunktionen für Hammer- und Zuganregung berechnen. Mit allgemeinen oder spezifischen Achslastspektren werden dann die Bahnerschütterungen prognostiziert und mit den Messergebnissen verglichen. Bei etlichen Messorten, insbesondere in der Schweiz, wurden deutliche Merkmale einer Bodenschichtung beobachtet. Es ergibt sich eine deutliche Reduktion der tiefen Frequenzanteile durch den steifen unterliegenden Halbraum. Die weiche Deckschicht bestimmt das hochfrequente Verhalten. Hier bewirkt die Materialdämpfung des Bodens oft einen starken Amplitudenabfall, sowohl mit der Entfernung als auch mit der Frequenz. Für den verbleibenden mittelfrequenten Anteil wurde an mehreren Messorten die Amplituden-Fahrgeschwindigkeits-Gesetzmäßigkeiten untersucht. Es gibt konstante bis stark ansteigende Amplituden, und es zeigt sich auch hier, dass der geschichtete Boden von entscheidender Bedeutung ist.
A prediction software has been developed by BAM. The following topics have still be solved. A realistic irregularity spectrum can be derived from axle-box measurements. It agrees wel with the spectrum used for the high-speed 2 project in the United Kingdom. In addition, the scattering of axle pulses should be included. This mid-frequency component can also be found in the HS2 procedure. Finally, the reduction in case of a tunnel line compared to a surface line should be included. Some measurement results of BAM, HS2 and other institutes show a certain mid-frequency reduction. This is due to the load distribution of the tunnel which yields softer axle pulses and the scattered axle impulses are reduced.
Measurements of ground and track vibrations have been performed at a high-speed line in northern Germany. Impacts on the track and the ground, and passages of different trains with different speeds on different tracks have been measured. Transfer functions of the soil are presented and approximated by theoretical soil models. By using these transfer functions, the measured ground vibration between 2 to 64 m distance from the track can be transformed into a load spectrum which can be used for predictions at other sites. The method is compared to the soil-dependent method of an emission spectrum at a certain distance (8 m for example). The influence of train type, speed and track type is discussed on the base of the different emission quantities and the original measurements. The strong influence of the track, ballast track and slab track, is analysed by a theoretical model in wavenumber domain. The response of the track to the passage of the static load is reduced by the stiffness of the slab, the deformation of the track as well as the impulse acting on the soil. Usually, the impulse on the soil should result in a slow quasi-static movement of the soil, slower at further distances. In a heterogeneous soil, however, the impulses from the static loads scatter and keep parts of the higher impulse frequency band. In this case the reduced impulse spectra of the slab track will yield reduced ground vibration in a certain frequency band. Additional (BAM and international) measurements will be used to discuss this and possible other explanations for the different ground vibration differences.
The contribution shows measurement examples of cars, floors, foundations, railway tracks, a footbridge, and a railbridge. Vibrations may include modes and waves. Namely in soil-structure interaction, modes are damped, shifted and prevented so that alternatives for the modal analysis are necessary: The approximation of the whole spectrum (flexibility function) and of the whole train passage (moving-load response).
Die gesamte Prognose wurde rechnerisch erfasst. Die Rechenverfahren sind einfach und schnell. Die Emission und die Immission verwendet Übertragungsmatrizen. Die Transmissionsrechnung beruht auf der Dispersion der Rayleighwelle. Die Verknüpfung erfolgt über die Anregungskraft auf den Boden und über die Freifeldamplitude am Gebäude.
Es sind viele Eingabemöglichkeiten für Messdaten vorgesehen. Messungen können von einem Ort auf einen anderen Ort übertragen werden.
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.
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.
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.
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.
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.
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.
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.
Methods have been presented for detailed studies of railway vibration and for the fast prediction of train-induced ground vibration. The ground vibration is generated by static or dynamic loads. The main purpose of this contribution was to show the influence of inhomogeneous soils on the different vibration components.
Layered soils, namely a soft layer on a stiffer half-space, yield a quite specific transmission behavior. The low-frequency and sometimes also high-frequency cut-off of the transfer function of the soil is demonstrated in theory and by experiments at many sites of which the soil model is approximated from dispersion and transfer function measurements. The layer frequency divides the frequency range in a low-frequency range, where the stiff half-space rules the low amplitudes, and a high amplitude high-frequency range which is mainly determined by the softer top layer. A thick soft layer yields a very low layer frequency, so that the higher soft soil amplitudes have a wider range down to low frequencies. A thin layer yields a high layer frequency, so that the high frequencies above this layer frequency are dominant. The higher the contrast between the stiff half-space and the soft layer is, the stronger the increase between the half-space and layer amplitudes, the more characteristic are the spectra of the soil transfer function. The range of measured soils has been from vS1 down to 125 m/s, vS2 up to 1000 m/s and the layer frequencies are within 10 Hz < f0 < 75 Hz. Moreover, during this measuring campaign in Switzerland, all 11 sites showed clearly the layer-on-half-space behaviour. The transfer functions of inhomogeneous soils have been used to predict the ground vibration due to dynamic axle loads which is usually thought to be the most important component.
The passage of static loads, in the contrary, results in very small vibration amplitudes for low train speeds, which can only be found at near distances and at low frequencies. They attenuate very rapidly with distance and lose very rapidly the higher frequency content. The passage of static axle loads can be included in the prediction of railway vibration just for completeness.
Special attention should be given to the case if the train runs with the Rayleigh-wave speed of the soil (Rayleigh train). The Rayleigh-train effect is strongest for a homogeneous half-space: At the near-field of the track the amplitudes are raised strongly compared to normal trains, and in addition, little attenuation with distance is observed. In case of a layered soil, the low-frequency cut-off reduces the frequency range and the amplitudes of the homogeneous quasi-static ground vibrations. Therefore, the Rayleigh-train effects are clearly reduced by a layered soil and they disappear if the layer frequency (for example for a thin layer) is higher than the frequency band of the axle impulse. The Rayleigh-train effect could completely disappear in a randomly inhomogeneous soil, but this has not been analysed so far.
The axle impulses from static loads can have an additional, quite different effect. They can be scattered by a randomly inhomogeneous soil so that a part (the scattered part) of the axle impulse can reach further distances from the track. This can establish a certain mid-frequency component of the ground vibration which becomes dominant in the far-field, and this important component exists for all train speeds. Experimental results from BAM and international measurements show the importance of the corresponding frequency range.
The mitigation of train induced ground vibration by elastic and stiff track elements has been analysed threefold. The vehicle-track interaction yields the reduction at high frequencies above the vehicle-track resonance. This is the standard effect. The filtering of trackbed errors by the bending stiffness of the track yields a certain mid-frequency effect. An even stronger mid-frequency effect is predicted for the mitigation of the scattered axle impulses by the bending stiffness and elastic elements of the track.