TY - JOUR A1 - Auersch, Lutz T1 - Vehicle Dynamics and Train‑Induced Ground Vibration—Theoretical Analyses and Simultaneous Vehicle, Track, and Soil Measurements N2 - Ground vibrations near railway lines are generated by the forces that are acting between wheel and rail. It seems to be a straight forward assumption that the vehicle dynamics are important for the level and the frequencies of the excitation forces. Different vehicle dynamics phenomena are analysed for their role in the excitation of ground vibrations: rigid body modes of the bogies, elastic (bending) modes of the car body, and elastic modes of the wheelset. The theoretical analyses use rigid body models, simplified elastic models, and detailed elastic models. Some of these problems are vehicle–track interaction problems where 3D finite‑element boundary‑element models have been used for the track and soil. It is shown that the rigid or flexible vehicle modes are well in the frequency range of ground vibrations (4 to 100 Hz). They have an influence on the excitation force but the additional forces are rather small and can be neglected in ground vibration prediction. The theoretical results are checked by experimental results of a simultaneous measurement of vehicle, track, and ground vibrations. KW - Rigid vehicle model KW - Flexible car body KW - Flexible wheelset KW - Dynamic loads KW - Ground vibration PY - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-569796 VL - 5 IS - 1 SP - 223 EP - 247 PB - MDPI CY - Basel AN - OPUS4-56979 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - The dynamic train-track interaction on a bridge and in a tunnel compared with the simultaneous vehicle, track, and ground vibration measurements at a surface line N2 - The vehicle–track interaction generates forces and consequently vibrations in the environment. The interaction has been analysed by the simultaneous measurements of vehicle, track and ground vibrations during test runs with varied train speeds. The special effects of the passage over a bridge and through a tunnel are studied and compared with the measurements on a conventional ballasted surface line. The maximum amplitudes, narrow band and one-third octave band spectra are presented for the axle-box accelerations and for the track, bridge and ground vibrations. The different frequencies and frequency bands are related to wheel out-of-roundness, track alignment errors, the sleeper passage and the wheelset–track resonance. An axle impulse component has been observed at the track, at the near-field soil and as a scattered version in the far field. Specific results can be found for the bridge track, where clearly speed-dependent bridge resonances occur due to the axle sequence of the train, and for the tunnel track where soft rail pads are responsible for a strong amplification around the wheelset–track resonance. On the other hand, the axle impulses are strongly reduced by the tunnel track, and the scattered axle impulse component is not as relevant as for the surface track. As a consequence, a strong mid-frequency amplitude reduction of the tunnel compared to the surface line has been measured for low and high train speeds by the Federal Institute of Material Research and Testing (BAM) and by other institutes. KW - Vehicle–track interaction KW - Ground vibration KW - Tunnel-to-surface reduction KW - Bridge resonance KW - Axle sequence PY - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-585139 VL - 13 IS - 19 SP - 1 EP - 23 PB - MDPI CY - Basel, Schweiz AN - OPUS4-58513 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Site-specific amplitude-distance laws, wave velocities, damping, and transfer functions of the soil from hammer impacts and application to railway-induced ground vibration – Similarities and mid-frequency differences N2 - The propagation of ground vibrations is theoretically analysed with frequency-wavenumber and simplified methods. Experimental methods are presented which can characterise the site-specific ground vibrations by wave velocities, stiffness and damping. Measurements with hammer and train excitation have been performed at several sites. The one-third octave spectra show the stiffness-dependent amplitudes and the low- and high-frequency filter effects due to the layering and the damping of the soil. Specific train effects, an additional high-frequency filter, the sleeper passage frequency, and an amplified mid-frequency component can be clearly found. The attenuation with distance is analysed in detail where the theoretical exponential and the empirical frequency-dependent power law are considered. Hammer and train excitation show the same site-specific effects which are mainly due to the stronger or weaker damping of the soil. The train attenuation is generally weaker than the hammer attenuation. The attenuation exponent of the power law, which is strongly dependent on the site and the frequency, is reduced for the train vibration by 0.3 to 0.5 in agreement with the theory. Reasons are discussed for the overall power law and for the dominating mid-frequency component. KW - Hammer impact KW - Train passage KW - Layered soil KW - Attenuation KW - Filter effects KW - Randomly heterogeneous soil KW - Scattering PY - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-585020 SN - 2366-2557 SP - 1 EP - 17 PB - Springer AN - OPUS4-58502 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Reduction in Train-Induced Vibrations—Calculations of Different Railway Lines and Mitigation Measures in the Transmission Path N2 - The reduction in train-induced ground vibrations by different railway lines and by mitigation measures in the propagation path was analysed in a unified approach by two-dimensional finite element calculations. In general, there was no reduction at low frequencies, and the reduction be-came stronger with increasing frequencies. A maximum reduction of 0.1 at high frequencies was established with an open trench. Reductions between 0.7 and 0.2 have been found for the other sit-uations, filled trenches, walls, plates, and blocks, as well as for railway lines on dams, in cuts and in a tunnel. Bridges can produce amplifications due to their resonance frequencies, but also strong reductions due to massive bridge piers. The influence of some parameters has been analysed, such as the bridge span, the inclination of the dam and the cut, the stiffness of the soil, and the tunnel structure. The dynamic track stiffnesses of a surface, bridge, and tunnel track have been calculated using the 3D finite-element boundary-element method for comparison with corresponding meas-urements. KW - Train-induced vibration KW - Mitigation KW - Trench KW - Obstacles KW - Tunnel KW - Bridge KW - Finite element KW - Boundary element PY - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-579573 VL - 13 IS - 11 SP - 1 EP - 19 PB - MDPI CY - Basel AN - OPUS4-57957 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - The role of vehicle dynamics in train-induced ground vibrations and the detection of irregular axle-pulse responses due to a varying track support stiffness N2 - 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. KW - Wheelset KW - Vehicle-track interaction KW - Rail roughness KW - Random dynamics and vibrations KW - Modal analysis PY - 2022 U6 - https://doi.org/10.1177/09544097221086064 SN - 0954-4097 VL - 236 IS - 10 SP - 1218 EP - 1233 PB - Sage CY - London AN - OPUS4-55000 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz A1 - Song, Jiaojiao T1 - Dynamic damage detection of slab tracks – finite element models on Winkler soil and finite-element boundary-element models on continuous soil N2 - 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. KW - Track damage quantification KW - Finite element method KW - Combined finite-element boundary-element method PY - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-562207 SN - 2673-4109 VL - 3 IS - 4 SP - 979 EP - 997 PB - MDPI CY - Basel AN - OPUS4-56220 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Different types of continuous track irregularities as sources of train-induced ground vibration and the importance of the random variation of the track support N2 - 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. KW - Train-induced ground vibration KW - Geometric vehicle and track irregularities KW - Stiffness variation KW - Multi-beam track model KW - Track filtering KW - Dynamic axle loads KW - Static axle loads KW - layered soil PY - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-543846 SN - 2076-3417 VL - 12 IS - 3 SP - 1 EP - 22 PB - MDPI CY - Basel AN - OPUS4-54384 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Resonances of railway bridges analysed in frequency domain by the modal-force-excitation, bridge-transfer and axle-sequence spectra N2 - 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. KW - Railway bridge KW - Bridge vibration KW - Train passage KW - Axle sequence KW - Resonance KW - Cancellation KW - Fequency domain PY - 2021 U6 - https://doi.org/10.1016/j.engstruct.2021.113282 SN - 0141-0296 VL - 249 SP - 1 EP - 9 PB - Elsevier Ltd. CY - London AN - OPUS4-53766 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz A1 - Said, Samir T1 - Dynamic track-soil interaction – calculations and measurements about slab and ballast tracks N2 - The dynamic behaviour of slab and ballast tracks has been investigated by measurements and calculations. Hammer impacts and train passages have been analysed. Measurements have been performed by geophones (velocity transducers) which have been time-integrated to displacements. The calculations are done in frequency-wavenumber domain for multi-beam-on-continuous soil models. The characteristics of the different tracks and track elements have been established in theory and experiment. The frequency-dependent compliances (displacement transfer functions) show clear rail-on-rail-pad resonances or highly damped track-soil resonances. Compared to the rail and sleeper, the track plate has much lower amplitudes. The slab track has usually the highest rail amplitudes due to soft rail pads. The train passage yields track displacements which are a superposition of the axle loads from the two neighbouring axles of a bogie and from the two bogies of two neighbouring carriages. This global behaviour is characteristic for the track plate of the slab track whereas the rails of the slab and the ballast track behave more local with only one bogie of influence. The measurements agree very well with the theory of the continuous soil in case of the six measured slab tracks and acceptably well for the six measured ballast tracks. The measurements allow to find appropriate model parameters and to check the models, for example the Winkler model of the soil has been found less appropriate as it reacts more locally. KW - Slab track KW - Ballast track KW - Train passage KW - Hammer impact KW - Track-soil interaction PY - 2021 U6 - https://doi.org/10.1631/jzus.A1900651 SN - 1673-565X VL - 22 IS - 1 SP - 21 EP - 36 PB - Zhejiang University Press CY - Hangzhou AN - OPUS4-52107 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Train-induced ground vibration due to the irregularities of the soil N2 - Many measurements of train induced ground vibrations show high amplitudes for a certain mid-frequency range. This ground vibration component cannot be well explained by dynamic loads of the train. Many characteristics indicate that the axle impulses, which are scattered by an irregular soil, are the excitation. This new understanding of railway-induced ground vibration is verified by numerical analysis. The response of the regular homogeneous and irregular inhomogeneous soils has been calculated by the finite-element method in frequency domain. A specific superposition of the impulse responses has been invented including time shift, axle sequence, track filter and hanning filter. The superposition yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil of which the stiffness varies randomly in space, the superposition yields a mid-frequency ground vibration component from the scattering of the axle impulses. The existence and the importance of this component can thus be demonstrated by the calculations. Some rules of the influence of distance, train speed, soil stiffness, strength and width of the stiffness variation have been derived from the calculations. Many measurements show the unique explanation of the mid-frequency ground vibration component by the scattered axle impulses. KW - Train-induced ground vibration KW - Static axle loads KW - Quasi-static response; KW - Axle impulses KW - Irregular soil KW - Random stiffness variation KW - Scattered axle impulses PY - 2021 U6 - https://doi.org/10.1016/j.soildyn.2020.106438 SN - 0267-7261 VL - 140 SP - 106438 PB - Elsevier Ltd. CY - London AN - OPUS4-52006 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Simple and fast prediction of train-induced track forces, ground and building vibrations N2 - A simple and fast prediction scheme is presented for train induced ground and building vibrations. Simple models such as (1-dimensional) transfer matrices are used for the vehicle-track-soil interaction and for the building-soil interaction. The wave propagation through layered soils is approximated by a frequency-dependent homogeneous half-space. The prediction is divided into the parts “emission” (excitation by railway traffic), “transmission” (wave propagation through the soil) and “immission” (transfer into a building). The link between the modules is made by the excitation force between emission and transmission, and by the free-field vibration between transmission and immission. All formula for the simple vehicle-track, soil and building models are given in this article. The behaviour of the models is demonstrated by typical examples, that is the mitigation of train vibrations by elastic track elements, the low- and high-frequency cut-offs characteristic for layered soils, and the interacting soil, wall and floor resonances of multi-storey buildings. It is shown that the results of the simple prediction models can well represent the behaviour of the more time-consuming detailed models, the finite-element boundary-element models of the track, the wavenumber integrals for the soil, and the three-dimensional finite-element models of the building. In addition, measurement examples are given for each part of the prediction confirming that the methods provide reasonable results. As the prediction models are fast in calculation, many predictions can be done, for example to assess the environmental effect along a new railway line. The simple models have the additional advantage that the user needs to know only a minimum of parameters. So, the prediction is fast and user-friendly, but also theoretically and experimentally well-founded. KW - Railway induced vibration KW - Ground vibration KW - Layered soil KW - Building response KW - Excitation forces KW - Track and vehicle irregularities PY - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-513340 SN - 2662-4745 VL - 28 IS - 3 SP - 232 EP - 250 PB - Springer AN - OPUS4-51334 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz A1 - Said, Samir T1 - Slab track behaviour under train passage and hammer impact – Measurements at different sites and calculated track interaction with continuous soils N2 - This contribution intends to give an overview on the vibration behaviour of slab tracks in comparison of measurements and calculations and also by comparison of different track types at more than ten different measuring sites. In theory, tracks on continuous soil are calculated by the frequency-wavenumber domain method. In experiment, geophone measurements are transformed to displacement results. Two aspects of track behaviour are considered, the frequency-dependant compliance of the track, measured by hammer impact, and the deflection under a passing axle load. In theory, the response to a single axle can be calculated, whereas in experiment, only the passage of the whole train can be measured. For comparison of theory and experiment, the calculated deflection under a single axle is superposed to get the response of the whole train. As a result, the slab track characteristics are completely different from the ballast track characteristics where each axle can be seen in the time histories. The slab track has a more global behaviour where only a whole bogie can be found in the track response and moreover, the two neighbouring bogies are not completely separated. The measurement of the different track elements (rail, sleeper, track plate, base layer) and the frequency-dependant compliances with possible resonances yield further information About the properties of the track elements. The calculations show that the soil has the dominant influence on the amplitudes and the width of the track-plate displacements. In the measurement results, the following parameters are analysed: slab track vs. ballast track, different types of slab tracks, damaged slab tracks, different trains, switches at different measuring points, voided sleepers, an elastic layer, the mortar layer, and different soils at different places. Finally, a good agreement between measured and calculated results is found for the normal and some special (damaged, floating) slab tracks. KW - Slab track KW - Train passage KW - Hammer impact KW - Compliance function KW - Track deflection PY - 2020 UR - https://iiav.org/ijav/index.php?va=viewpage&vaid=177&id_number=95 U6 - https://doi.org/10.20855/ijav.2020.25.31622 SN - 1027-5851 VL - 25 IS - 3 SP - 341 EP - 354 PB - International Institute of Acoustics and Vibration CY - Gliwice AN - OPUS4-51346 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Vehicle-Track-Soil Interaction of Isolated, Un-isolated and Damaged Railway Tracks N2 - This article deals with two topics of vehicle-track-soil interaction, the mitigation of railway induced ground vibration by soft track elements, and the identification of track damage. Theoretical results have been achieved by a combined finite-element boundary-element method (FEBEM). The theoretical results are confronted with measurements at four sites. Improved mitigation effects have been found for soft rail pads under heavy sleepers. The insertion loss, however, can be too optimistic if a strong vehicle track resonance occurs for the un-isolated reference track. Two measurement sites show this strong vehicle-track resonance at about 80 Hz, which has been approximated by using the results of a wide parameter study including the rail pad, ballast, and soil stiffness, as well as the ballast model and the soil layering. – The detection of slab track damage is mainly based on the differences of the receptance or compliance functions. Theoretical results have been confirmed by measurements at one site where a loss of contact between track plate and base layer was visible. Measurements at a second site with a hidden damage have been compared with the theoretical results of a loose sleeper. The differences between intact (or repaired) and damaged tracks are strong enough to encourage the further development of this method for the identification of track damages. KW - Railway track KW - Track-soil interaction KW - Ground vibration KW - Mitigation KW - Under-sleeper pads KW - Track damage monitoring PY - 2020 U6 - https://doi.org/10.4203/ijrt.6.3.2 SN - 2049-5358 VL - 2 IS - 20 SP - 21 EP - 49 PB - Saxe-Coburg Publications CY - London AN - OPUS4-51257 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Characteristics of train passages over slab tracks from measurements and different track-soil models - Damage detection and ground vibration reduction N2 - The train passages over intact or damaged slab tracks on different soils have been calculated by the finite-element boundary-element or the wavenumber-domain method. The influence of track and soil parameters on the distribution of the track displacements and the soil forces has been analysed. The measured and calculated displacement time histories of train passages could be used to identify track damages such as lose sleepers or a lose track plate. The time histories and spectra of the soil forces can explain the measured ground vibration reduction of slab tracks. The calculated displacement and force distributions of slab tracks on continuous soils do not fulfil the Winkler hypothesis and Winkler models should not be used for track analysis. KW - Wavenumber domain KW - Continuous soil KW - Slab track KW - Soil forces KW - Track displacements KW - Track filter KW - Vehicle–track interaction PY - 2020 U6 - https://doi.org/10.1177/0954409719835036 SN - 0954-4097 VL - 234 IS - 2 SP - 142 EP - 160 PB - Sage CY - London AN - OPUS4-50266 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Vehicle-track-soil interaction and train-induced ground vibration – Theory and measurements in Germany, Switzerland and France N2 - Three measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results. The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and forces. KW - Vehicle-track-soil interaction KW - Train-induced ground vibration KW - Measurement campaigns KW - Wavenumber integrals KW - Components of excitation KW - Wheelset accelerations PY - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-486702 SN - 1742-6596 SN - 1742-6588 VL - 1264 SP - Artikel 012034-1 EP - 12 PB - IOP Publishing Ltd AN - OPUS4-48670 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Compliance and damping of piles for wind tower foundation in nonhomogeneous soils by the finite-element boundary-element method N2 - A combined finite-element boundary-element method for the dynamic interaction of the soil with flexible structures such as single piles or complete wind energy towers has been developed. Flexible piles in different soils are analysed in frequency domain. The different parameters such as the stiffness of the soil, the bending stiffness and the radius of the hollow pile are analysed for their influence on the complex compliances. The results have been determined as specific power laws which are different for the different load cases (horizontal, rocking, coupling) and for the different soil models (Winkler, continuum with constant, root-parabolic and proportional-linear stiffness variation). The strongest influence of the soil stiffness can be found for the homogeneous soil and the horizontal component. Winkler soils have a weaker influence than the corresponding continuous soils. An offshore wind energy tower has been modeled and calculated for wind and wave loads. KW - Pile foundation KW - Finite-element boundary-element method KW - Pile bending stiffness KW - Soil stiffness KW - Continuously inhomogeneous soils KW - Layered soils KW - Wind energy tower PY - 2019 U6 - https://doi.org/10.1016/j.soildyn.2018.12.005 SN - 0267-7261 VL - 120 IS - 5 SP - 228 EP - 244 PB - Elsevier CY - London AN - OPUS4-47891 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -