## 7.2 Ingenieurbau

### Filtern

#### Erscheinungsjahr

- 2015 (37) (entfernen)

#### Dokumenttyp

- Beitrag zu einem Tagungsband (13)
- Zeitschriftenartikel (12)
- Vortrag (11)
- Beitrag zu einem Sammelband (1)

#### Schlagworte

- Structural health monitoring (3)
- Automated operational modal analysis (2)
- Resonance (2)
- Sommerfeld effect (2)
- Vibration (2)
- Wind turbine (2)
- Aberfan flowslide (1)
- Aerodynamic damping (1)
- Ambient vibration (1)
- Clay fill (1)
- Compression (1)
- Conductor cables (1)
- Constitutive modeling (1)
- Covariance analysis (1)
- Damage detection (1)
- Damage localization (1)
- Elastic track elements (1)
- Environmental/operational effects (1)
- Ermüdung (1)
- Evolutionary computing (1)
- Fatigue (1)
- Fluidised geomaterials (1)
- Force transfer (1)
- Geometric trackbed irregularities (1)
- Ground vibration (1)
- Inverse problem (1)
- Load vectors (1)
- Modal properties (1)
- Multi-beam-on-support model (1)
- Multimodal solution (1)
- Nonlinear finite element simulation (1)
- Normal strength concrete (1)
- Novelty analysis (1)
- Numerical modelling (1)
- Offshore-Windenergieanlagen (1)
- Overhead transmission lines (1)
- Parametric excitation (1)
- Physical model testing (1)
- Pile monitoring (1)
- Principal Component Analysis (1)
- Rail pad (1)
- Railway (1)
- Railway embankment (1)
- Reduction (1)
- Rissdetektion (1)
- Rissüberwachung (1)
- SPH (1)
- Schadensdetektion (1)
- Sleeper pad (1)
- Smoothed particle hydrodynamics (1)
- Subspace methods (1)
- System identification (1)
- Track (1)
- Varying track stiffness (1)
- Westend bridge (1)
- Wind tunnel experiments (1)

#### Organisationseinheit der BAM

- 7.2 Ingenieurbau (37) (entfernen)

Most railway embankments in the UK were built in the Victorian era and are of end-tipped construction using materials (usually cohesive) excavated from adjacent cuttings, resulting in a clod-and-matrix structure. Historically, there has been a lack in understanding of the mechanical behaviour of such railway embankments. In the next decade railway traffic in the UK, particularly freight, is forecast to grow considerably. Consequently, there is a need to improve the understanding of how increases in rail traffic loading may influence the mechanical behaviour of railway embankments and thus track performance. The Rail Safety and Standards Board in conjunction with Network Rail is currently undertaking a programme of applied research into this topic. As part of these studies a programme of physical model tests has been carried out. Physical model tests can provide high quality data on system performance under a large range of loading conditions and geometrical configurations. The data can be generated rapidly, with test periods of weeks or months rather than years or decades. Additionally, boundary conditions are well-defined and controlled, compared with the complex situations encountered in full scale embankments in the field. This paper summarises the physical model test programme, the development of the test set-up, the tests themselves and the conclusions drawn.

Aerodynamic damping of nonlinear movement of conductor cables in laminar and turbulent wind flow
(2015)

It is widely accepted that aerodynamic damping is a decisive parameter influencing the dynamic response of overhead transmission line conductors in turbulent wind flow. But anyway, methods of how to account for the effects of aerodynamic damping differ significantly and so might do the results. In this work, the source of aerodynamic damping shall be revised leading to the well-known formulation for a linear pendulum being the result of the relative velocity between the structure and wind flow. Based on wind tunnel tests and validated by simulations, the differences to a pendulum movement of a sagging cable are shown. The reasons for that deviation are the large deflections, resulting in a movement non parallel to the acting wind flow. For some analysis, in particular those in frequency domain, it is practically not possible to incorporate aerodynamic damping implicitly by fluid structure interaction. If the dynamic movement can be linearized at a working point of the mean deflection, a modification to the linear approach is suggested. This approach is validated by simulation with a finite element model of an existing overhead transmission line, calibrated with onsite measurements for wind velocities at lower levels. Further accent is put on the different possibilities to incorporate aerodynamic damping in time step analysis, such as Rayleigh damping or modal damping. The differences between both approaches are emphasized and modal damping is shown to be the most adequate representation of aerodynamic damping.

Der folgende Beitrag befasst sich mit der analytischen Herleitung eines sog. Spannweitenfaktors zur Berücksichtigung der Korrelation der Windeinwirkung auf weitgespannte Freileitungsseile. Insbesondere zur Abschätzung der Windlast auf Maste trägt dieser Lastfall maßgebend zur Bemessung bei. Mithilfe von Naturmessungen und Simulationen werden zugrunde gelegte Annahmen überprüft und validiert. Die Ergebnisse werden schließlich anhand der einschlägigen Regelwerke verglichen und bewertet.

Aerodynamic damping of nonlinear movement of conductor cables in laminar and turbulent wind flow
(2015)

A software prototype is developed for assessing and updating the reliability of single-cell prestressed concrete box girders subjected to chloride-induced reinforcement corrosion. The underlying system model consists of two integrated sub-models: a condition model for predicting the deterioration state of the box girder and a structural model for evaluating the overall system reliability. The condition model is based on a dynamic Bayesian network (DBN) model which considers the spatial variation of the corrosion process. Inspection data are included in the calculation of the system reliability through Bayesian updating on the basis of the DBN model. To demonstrate the effect of partial inspections, the software prototype is applied to a case study of a typical highway bridge with six spans. The case study illustrates that it is possible to infer the condition of uninspected parts of the structure due to the spatial correlation of the corrosion process.

Brückenmonitoring 7.2
(2015)

The maintenance of the transport infrastructures and their further development are going to remain focal points for investment and research in Germany in future. According to the latest development forecasts made by both the federal government and Deutsche Bahn, even if rail´s percentage share of the market were to remain unchanged, growth of around 50% would be expected in the next ten years, especially in freight traffic. This growth is necessitating considerable development both in the technical design of the tracks and in the abatement of the noise and vibration caused by railway traffic.

Der Erhalt und die Weiterentwicklung der Verkehrsinfrastrukturen werden auch zukünftig einen Investitions- und Forschungsschwerpunkt in Deutschland bilden. Gemäß den aktuellen Entwicklungsprognosen sowohl der Bundesregierung als auch der Deutschen Bahn wäre bei unveränderten Marktanteilen der Bahn eine Zunahme insbesondere des Güterverkehrs in den kommenden 10 Jahren um ca. 50% zu erwarten. Dieser Zuwachs erfordert erhebliche Entwicklungen sowohl in der technischen Konstruktion der Fahrwege als auch im Erschütterungs- und Lärmschutz infolge des Schienenverkehrs.

Risslumineszenz ist eine neue Erfindung, mit der Ermüdungsrisse unter laufendem Betrieb ohne weiteres Zutun leicht detektiert werden können, indem sie leuchten. Die Bedeutung liegt in der allgemeinen Problematik ermüdungsbeanspruchter Konstruktionen. Risse begrenzen ihre Lebensdauer. Das betrifft zum Beispiel Verkehrsinfrastrukturbauwerke oder allgemein Tragwerke unter nicht ruhender Beanspruchung, auch Maschinen, Baufahrzeuge, Kräne, Zentrifugen und Schiffe. Bei dem Risslumineszenzverfahren leuchten die Risse unter UVLicht.

The stochastic dynamic damage locating vector approach is a vibration-based damage localization method based on a finite element model of a structure and output-only measurements in both reference and damaged states. A stress field is computed for loads in the null space of a surrogate of the change in the transfer matrix at the sensor positions for some values in the Laplace domain. Then, the damage location is related to positions where the stress is close to zero. Robustness of the localization information can be achieved by aggregating results at different values in the Laplace domain. So far, this approach, and in particular the aggregation, is deterministic and does not take the uncertainty in the stress estimates into account. In this paper, the damage localization method is extended with a statistical framework. The uncertainty in the output-only measurements is propagated to the stress estimates at different values of the Laplace variable, and these estimates are aggregated based on statistical principles. The performance of the new statistical approach is demonstrated both in a numerical application and a lab experiment, showing a significant improvement of the robustness of the method due to the statistical evaluation of the localization information.

Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression
(2015)

Conventional approaches to model fatigue failure are based on a characterization of the lifetime as a function of the loading amplitude. The Wöhler diagram in combination with a linear damage accumulation assumption predicts the lifetime for different loading regimes. Using this phenomenological approach, the evolution of damage and inelastic strains and a redistribution of stresses cannot be modeled. The gradual degration of the material is assumed to not alter the stress state. Using the Palmgren–Miner rule for damage accumulation, order effects resulting from the non-linear response are generally neglected.
In this work, a constitutive model for concrete using continuum damage mechanics is developed. The model includes rate-dependent effects and realistically reproduces gradual performance degradation of normal strength concrete under compressive static, creep and cyclic loading in a unified framework. The damage evolution is driven by inelastic deformations and captures strain rate effects observed experimentally. Implementation details are discussed. Finally, the model is validated by comparing simulation and experimental data for creep, fatigue and triaxial compression.

This paper deals with the system identification of a mechanical structure supported by nonlinear springs subjected to an external load. If all mechanical parameters of the system were known, the displacement of the system subjected to this load could be easily calculated. However, the monitoring applications often deal with the inverse problem. The loads and displacements of the system are known and certain mechanical Parameters of the system are sought. The solution of such inverse problems can be difficult, especially when they have a nonlinear and multimodal character, which often makes them appear intractable at first sight. However, evolutionary computing can be applied to solve this inverse, nonlinear and multimodal problem. Sometimes a prior knowledge exists on certain system properties, which is difficult to implement into analytical or numerical solvers. This knowledge can play a decisive role in identifying the System properties and it can be easily included as a boundary condition when applying evolutionary algorithms.
This article discusses how and under what conditions the unknown spring resistances can be identified. The practical application of this procedure is exemplified here with the mechanical system of a pile foundation.

Vibration-based structural health monitoring of a wind turbine system. Part I: Resonance phenomenon
(2015)

This paper is focused on a resonance phenomenon of a wind turbine system in 5 MW class, on the basis of dynamic signals acquired continuously from the tubular tower under normal operational conditions during two years.
Firstly, technique specifications of the wind turbine system are introduced and a finite element model is developed to characterize the structural dynamic properties. The following part describes the continuous dynamic monitoring system integrated with an automated operational modal analysis procedure using the poly-reference Least Squares Complex Frequency domain (p-LSCF) method. Subsequently, variations and mutual relationships of environmental/operational factors such as vibration amplitude, temperature, wind speed, rotation speed of blades, pitch angle and nacelle direction are also presented. Finally, significant resonance is observed due to the fundamental frequency of the tower matching with the harmonic frequency induced by the rotation of three blades. As the rotation speed of rotor approaches to 8 rpm, the vibration amplitude of the tower increases significantly and the corresponding damping value decreases. With the further rising wind velocity, the rotation speed of blades stops increasing and the input energy just contribute to accumulate the vibration amplitude of tower. Such observation indicates the Sommerfeld effect that aggravates the resonance phenomenon. A vibration control device is necessary to minimize the excessive structural responses.
A companion paper will further discuss the environmental/operational effects on dynamic properties of the wind turbine system under the operational conditions.

The second part of these companion papers mainly researches environmental/operational influences on structural dynamic properties under normal operational conditions during two years, in order to extract a statistical based damage-sensitive indicator for health monitoring of a wind turbine system.
The correlation analyses between experimental identified frequencies, damping values as well as mode shapes and environmental/operational factors such as rotation speed of blades, wind speed, pitch angle, temperature and nacelle direction are presented. It is observed that the frequency estimates are influenced by the nacelle position, the activation of rotor, the rotation speed of blades and the wind speed as well as the temperature. Regarding to the damping estimates, they are mainly associated with variation of the aerodynamic damping due to the increasing wind speed. Besides, the resonance phenomenon is also observed in higher modes. The harmonic frequencies due to blades passing by tower are found and the corresponding damping value decreases. Moreover, the mode shapes in some modes are strongly affected by the position of the nacelle.
Subsequently, two types of simulated damage including the reduction of stiffness in both the rotor blade and the tubular tower are successfully detected by applying the Principal Component Analysis (PCA) based methods to these temperature-sensitive frequency estimates. Comparison of change of the extracted health features indicates that they are more sensitive with the tower damage.

This paper presents the continuous dynamic measurements of an aging prestressed box-beam bridge during the period from 2000 to 2013, which consists of dynamic properties and environmental/operational factors, as well as the Variation of the extracted health features after removing the environmental/operational effects. Firstly, the variations of frequency estimates, temperatures and traffic loads from 2000 to 2013 are described. Subsequently, correlation analysis between them indicates the nonlinear influences of the temperature on the frequency estimates. The Multiple Linear Regression (MLR) method is used to remove the environmental/operational effects and the health index is proposed by performing the Novelty Detection analysis of the residual errors. Finally, the variations of the health index may indicate clear structural modifications that can be also characterized by the long term monitoring of the dynamic strain in the prestressed cable.

Mit dem generellen Ziel, die Anwendbarkeit und Funktionalität des Verfahrens der stochastischen subspace-basierten Schadensdetektion für Strukturen von Offshore-Windenergieanlagen nachzuweisen, wurden experimentelle und numerische Untersuchungen an einer Laborstruktur sowie anschließend numerische Untersuchungen an einer OWEA-Gründungsstruktur durchgeführt.
Das zugrundeliegende Verfahren verwendet einen Ansatz, in weder modale Kenngrößen noch andere benutzerdefinierte Eingaben erfordert, nachdem einmalig der Referenzzustand aufgenommen wurde. Dabei werden ausschließlich dem Belastungsprozess inhärente stochastische Anregungen der betrachteten Struktur genutzt.
Auf der Basis experimentell erzielter Detektionsergebnisse aus einem Ermüdungsversuch an einer Laborstruktur aus Stahl wurden numerische Modelle und Berechnungsalgorithmen entwickelt und getestet. In einem zweiten Schritt wird diese Analysemethodik auf eine fiktive OWEA-Jacketstruktur realer Größe angewendet. An den simulierten Strukturantworten im Ungeschädigten und geschädigten Zustand wird der Detektionsalgorithmus angewendet, um den Einfluss von Sensorposition und Abtastrate auf die Schadensdetektion festzustellen. Unter Berücksichtigung einzelner vereinfachender Annahmen zeigten die Ergebnisse der Anwendung der vorgestellten Detektionsmethodik an den numerisch erzeugte Antwortdatensätzen eine beachtliche Empfindlichkeit des x2-Testwert basierten Schadensindikators. Obwohl nicht unter allen Umständen in einem frühen Stadium nachweisbar, typische Ermüdungsrisse in Schweißverbindungen von aufgelösten Tragwerken haben ab einer Restbiegesteifigkeit von ca. 80% einen signifikanten und detektierbaren Einfluss auf den Schadensindikator.
Künftige Forschungsaktivitäten in diesem Bereich sollten neben der Erkennung von Schäden auch die Lokalisierung und ggf. auch die Quantifizierung zum Ziel haben. Erforderlich dazu ist die Berücksichtigung und Verarbeitung der strukturellen Parameter und ihrer Sensitivitäten im zugrunde liegenden mathematischen Modell.

Landslides can cause major economic damage and a large number of casualities as it is possible to see from past events occurred all over the world. Being able to predict these kind of hazards would then suppose the achievement of great benefits. Here a model that combines a depth integrated description of the soil-pore fluid mixture together with a set of 1D models dealing with pore pressure evolution within the soil mass is presented. The mathematical model is based on the Biot-Zienkiewicz equations, from where a depth averaged model is derived. Concerning the material behaviour, the approach used is the one suggested by the Perzyna viscoplasticity, which has been extensively used in the past to model solid behaviour prior to failure. In this framework, a simple shear rheological model is derived, providing the basal friction needed in depth integrated models. The Smoothed Particle Hydrodynamics (SPH) has been the numerical technique chosen to spatially discretised the depth integrated equations of the mathematical model. The purpose of this work is to apply the SPH depth integrated numerical model, together with the sub-model that predicts the evolution of the pore water pressure inside the landslide, to simulate the propagation phase of the Aberfan flowslide occurred in 1966.

In diesem Artikel wird ein 3D FE-Modell für den Brückenübergangsbereich vorgestellt, das eine Bewertung hinsichtlich des Langzeitverhaltens ermöglicht und an dem Optimierungsmaßnahmen diskutiert werden können. Bestandteile des numerischen Modells sind das Fahrzeug-Fahrwegmodell mit Brückenstruktur und eine Randformulierung mit der SBFEM. Die hier diskutierten Optimierungsmaßnahmen fokussieren sich auf eine reine Anpassung der Fahrwegsteifigkeit durch elastische Elemente auf der Brückenstruktur.

An drei Straßenbrücken unterschiedlicher Länge und Bauart wurden vor Inbetriebnahme ambiente Schwingungsmessungen mit bis zu 350 Messpunkten durchgeführt, um auch höhere Eigenformen detaillierter zu ermitteln. An einer Eisenbahnbrücke der Strecke Hannover-Würzburg wurden bei Testzugfahrten mit definierten Geschwindigkeiten verschiedene Resonanzanregungen beobachtet. Dies wird mit dem Achsfolgespektrum des ganzen Zuges erklärt, wobei eher spezifische Frequenzauslöschungen als Resonanzanregungen maßgeblich sind.

A survey of the phenomena and methods for floor vibrations is presented. Experimental results of floor vibrations are shown for many floors in six different buildings. The signals have been evaluated for waves and modes by simple procedures. General rules have been established between the material and the area of a specific floor, and its local eigenfrequency. The damping values of the floor vibrations have been found between D = 1 and 10 % where somewhat higher values have been measured for wooden floors, and a weak correlation with the eigenfrequency has been established. The velocities of bending waves propagating in a storey and the attenuation with distance in the building have been analysed. A considerable transfer of vibration from one room to far away parts of the building has been found in the studied buildings with concrete and wooden floors. An example building has been analysed for modes of coupled floor bays. The strong coupling of similar neighbouring floor bays would yield a wide band of global resonance frequencies. The measured wooden floor exhibits a weak coupling of the neighbouring floor bays and a narrower band of eigenfrequencies. A special method has been tested with the impulse measurements to estimate the coupled eigenmodes in presence of the high damping. From the ambient measurement, a low-frequency vibration mode has been detected which includes the vibration of the whole building and the soil. The coupling of floors to other floors and the whole building is an important phenomenon of structural dynamics which should be observed for the prediction of vibration due to internal and external sources.

Ground vibrations due to different technical sources are analysed in theory and experiment for the dispersion of Rayleigh waves and the admittance spectra. Both tasks are theoretically based on the same concept: The admittance function in frequencywavenumber domain yields the dispersion as its maxima, and the admittance function in space domain is obtained by integrating it over the wavenumbers. On the experimental side, many signal processing methods have been applied to many sites and have been developed by the authors in the last 35 years, i.e., time-domain methods, including the cross-correlation method, and frequency-domain methods such as the spectral analysis of surface waves with two or multiple sensors, the wavenumber-transform method, and the spatial autocorrelation method. All methods are presented by their basic formula and by at least one example site. Different sensor arrays and deterministic and stochastic sources have been tested for the spatial autocorrelation method and the wavenumber-transform method at several sites. In addition, all frequency-domain methods are presented for a specific layered site comparing their quality. The evaluated dispersion curves are very similar, but a somewhat higher frequency range has been found for the fastest method, i.e., the multi-sensor spectral-analysis-of-surface-waves method. The theoretical solutions have been used for the inversion of the measured dispersion to the soil profile of the specific layered soil. The theoretical soil model has subsequently been used to predict the ground vibration spectra of hammer and railway excitation that exhibit a good agreement with the corresponding measurements. Thus, the contribution shows the benefit of active and passive seismic methods for the prediction of railway vibration, including a new version of the spatial autocorrelation method for technical vibrations. On the other hand, technical and namely railway vibrations are considered a seismic source for the exploration of near surface soils.

The 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 to 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 measures are calculated to quantify the effectiveness of the mitigation measures.
Tracks with under-sleeper pads have been investigated in a wide parameter study for the RIVAS project. 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 so strong, as the characteristic frequency is ruled by the mass of the sleeper and the mass of the wheelset as well.

The reduction of train-induced ground vibration by elastic elements such as rail pads and sleeper pads has been analyzed by a combined finite-element boundary-element method. The dynamic compliance of the track, the transfer function of the total force on the ground and the ground vibration ratios have been calculated for a variety of isolated and un-isolated track systems. It has been found that the soil force transfer, which describes the excitation force of the soil, is an appropriate quantity to predict the reduction of the ground vibration and the effectiveness of isolated tracks. All force transfer functions of isolated tracks display a vehicletrack resonance where the wheelset on the compliant track is excited by wheel and track irregularities. At higher frequencies, considerable reductions of the amplitudes are observed as the benefit of the resilient element. The influence of the stiffness of the rail or sleeper pads, the ballast and the soil, and the mass of the sleeper and the wheelset on the resonance frequency and the reduction has been investigated. Sleeper pads are advantageous due to the higher mass that is elastically supported compared to the rail-pad track system. The combination of elastic rail and sleeper pads has been found to be disadvantageous, as the second resonance occurs in the frequency range of intended reduction.

Deckenschwingungen stellen in der Regel das größte Problem bei Erschütterungsgutachten dar. In diesem Übersichtsbeitrag werden folgende Aspekte der Deckenschwingungen mit einfachen bis komplexen Rechenmodellen dargestellt.
Die Resonanzanregung der Decken hängt von der Phasenlage der Auflagerschwingungen ab. Der Wellenlauf der anregenden Freifeldbodenschwingungen kann die Resonanzstärke deutlich verringern. - Der Wellenlauf kann bei Pfahl- oder Plattengründungen zu Abminderungen der Freifeldamplituden führen (kinematische Bauwerk-Boden-Wechselwirkung). - Die Steifigkeit des Untergrundes hat einen starken Einfluss auf die Resonanzstärke. Dies hat einerseits mit der Abstrahlungsdämpfung zu tun, andererseits auch mit einer Schwingungstilgung. Die Tilgung kann in einem vereinfachten Wand-Decken-Modell mit einer einheitlichen Deckeneigenfrequenz oder realistischer mit einem Eigenfrequenzband berechnet werden. In einem schmalen Frequenzband vor der Deckeneigenfrequenz können weitere (Wand-) Eigenfrequenzen und nach der Deckeneigenfrequenz eine Frequenzlücke auftreten. Normalerweise nehmen die Deckenamplituden mit der Höhe im Gebäude zu. In der Frequenzlücke hingegen nehmen die Amplituden mit der Höhe ab. - Benachbarte Deckenfelder können gemeinsame Deckeneigenfrequenzen besitzen, vor allem wenn sie die gleichen Abmessungen haben. Man bekommt dann ein Band von Deckeneigenfrequenzen. - Bei einer Schwingungsanregung im Gebäude auf einer Decke schwingen auch die benachbarten Deckenfelder mit. Im Frequenzbereich lassen sich Übertragungsfunktionen darstellen, im Zeitbereich können Amplituden-Abstandsgesetze betrachtet werden. - Bei großen Stützenbauwerken treten häufig Kopplungen der Decken verschiedener Stockwerke auf. - Mit den verschiedenen Methoden lassen sich typische Gesetzmäßigkeiten für die Amplituden und Frequenzen der Deckenschwingungen ableiten.

The computation of the wave propagation in homogeneous and layered soils can be performed by a numerical integration in wavenumber domain. The numerical difficulties of an infinite integral and an integrand with poles can be solved. But if this computation must be repeated for many distances, many frequencies, many loads, or many soil models, it becomes a time consuming task which is not acceptable for a user-friendly prediction tool for railway induced ground vibration. Therefore, an approximate method for the computation of the wave field has been developed. The computation consists of several steps. At first, an approximate dispersion profile is calculated according to rules which have been derived from exact solutions. Secondly, the dispersion is used to achieve the amplitude for a certain frequency and a certain distance by calculating the approximate solution of a corresponding homogeneous half-space. Thirdly, three layer corrections are added which include lowfrequency near-field effects, high-frequency far-field effects, and a resonance amplification around the layer frequency. This procedure yields the wave field due to a point load. For a train load, many of these point-load responses have to be summed up, and a frequencydependant reduction factor has to be multiplied to incorporate the effect of the load distribution along and across the track. - The prediction method is applied to real sites, and the appropriate soil models are identified by approximating the measured transfer functions (frequency-dependant amplitudes) which is presented as an alternative to the approximation of the dispersion (frequency-dependant wave velocities). These examples demonstrate the general behavior of layered soils: the low amplitudes of the stiff half-space at low frequencies, the high amplitudes of the softer layer at high frequencies, the strong increase of amplitudes and a possible resonance amplification at mid frequencies. The material damping of the layer yields a strong attenuation of the amplitudes with the distance for high frequencies. The response depends strongly on the resonance or layer frequency which is shown for different layer depths and velocities always in good agreement with measurements. The layer frequency can be of immense influence if train-speed effects are analysed in a layered soil. The good agreement with many measurements in this contribution as well as in the references validates the prediction of ground vibration based on the theory of a layered half-space.

Train-induced ground vibrations are generated by static and dynamic axle loads which can be calculated by vehicle-track-soil models and the vehicle and track irregularities. A fast prediction method has been developed which uses approximate transfer functions of layered soils. In the present contribution, this prediction method is used for the inverse calculation of the axle-load spectra from the measured ground vibration. The layered soils of some measuring sites show very differing ground vibration spectra in the amplitude range of 0.0001–1.0 mm/s as a consequence of the soft layer and stiff half-space, differing layer frequencies, as well as the far- and near-field measuring points. The back-calculation, however, yields axle-load spectra within a single order of magnitude around 1 kN. Axle-box measurements confirm the amplitude level of the axle loads. This standard axle-load spectrum can be used for a basic prediction at a new site. The separation of train and site-specific components allows a better evaluation of railway vibrations, for example, of different trains and different tracks. By eliminating the effects of differing soil characteristics, an important mid-frequency component has been found which lies between 8 and 32 Hz depending on the train speed. The origin of this dominant mid-frequency component is discussed using advanced prediction methods like moving constant loads, scattered axle impulses and axle-sequence spectra.

Train passages induce static and dynamic forces on the track, the train-induced vibrations propagate through the soil and excite neighbouring buildings. The problem of train vibrations is divided into the parts emission, which is the excitation by railway traffic (the present contribution), transmission, which is the wave propagation through the soil, and immission, which is the transfer into a building, - The calculation of the axle loads are based on the vehicle-track-soil interaction. This interaction uses the dynamic stiffness of the vehicle (the inertia of the wheelset) and the dynamic stiffness of the track-soil System. Based on various time consuming finite-element boundary-element calculations, an approximate track-soil model has been established. The vehicle-track-soil analysis yields several transfer functions between the various geometric or stiffness irregularities and the axle loads of the train. Geometric irregularities of the vehicle (the wheels) and the track (rail surface and track alignment) are the simplest components. Geometric irregularities of the subsoil (trackbed irregularities) have to be transferred to effective irregularities at rail level. The bending stiffness of the track is filtering out the short-wavelength contribution. Stiffness irregularities occur due to random variations in the bailast or the subsoil, which must also be transferred to effective track irregularities, and due to the discrete rail support on sleepers. The axle loads due to the effective track errors from stiffness variations have their specific vehicle-track transfer function. - All necessary formula for the prediction of axle-load spectra will be presented. The prediction method is compared with axle-box measurements at a Standard ballasted track. Moreover, ground Vibration measurements at numerous sites are exploited for the axle-load spectra and the Validation of the prediction method.

Train-induced ground vibration can be excited by wheel and track irregularities and by two kinds of irregularities of the soil, by geometric irregularities or by the spatially varying soil stiffness. For both types of irregularities, the effective track irregularity on top of the track is calculated in wavenumber domain and with wavenumber integrals. For a general multi-beam track model, the wavenumber integrals are solved numerically. The irregularities of the soil are filtered by the track when transferred from the bottom to the top of the track. The high-wavenumber irregularities are strongly reduced due to the bending stiffness of the track and the compliance of the support. In addition, soft track elements reduce directly the stiffness variation of the support. Therefore, the mitigation effect of elastic track elements for these excitation components seems to be important. For under-sleeper pads and slab tracks, calculation and measurements are presented including additional excitation components and the dynamic vehicle–track interaction, and the relevance of the excitation mechanisms is discussed based on the dynamic forces which are acting on the ground. Due to the restricted amplitudes, the parametric excitation by the stiffness variation seems to be less important than the geometric irregularities. The calculations yield the correct trends of the measurements and many details of the measured ballast, slab, and under-sleeper-pad tracks.