TY - CONF A1 - Auersch, Lutz ED - Papadrakakis, Manolis T1 - Frequency-wavenumber method for the wave propagation through the soil and the soil-structure interaction of railway tracks and building foundations near railway lines N2 - In soil-structure interaction, the soil and the (flexible) structures are modelled as elastic continua. The partial differential equations of elasticity can be transformed to algebraic equations in frequency-wavenumber domain where they can be solved by matrix methods. The results for the soil and a structure can be coupled in frequency-wavenumber domain, and the solution in space domain is obtained by an infinite wavenumber integral (the back-transformation). This method has several applications for the prediction of the emission, transmission and immission of railway-induced vibrations. The wave propagation in homogeneous or layered soils is calculated for surface and tunnel lines by a single wavenumber integration (transmission). The response of ballast or slab tracks (for the emission problem) and the foundation stiffness (for the immission problem) need an additional integration across the track or foundation width. In wavenumber domain, tracks and foundations of infinite length are analysed. Finite structures can be calculated by finite element models where the soil is calculated by the boundary element method. The Green’s functions for the boundary element method are calculated by a wavenumber integration as for the transmission problem. Some example results for all these tasks will be shown. The immission into buildings will be analysed in detail, and the effect of stiff slab foundations and (basement) walls on the incoming wavefield is quantified in a parameter study. The transfer function (the amplitude ratio) structure to free field usually starts with 1 at 0 Hz and decreases continuously with frequency. The reduction is due to the structural stiffness against wave deformation which turns to be higher than the stiffness of the soil, for example above the structure-soil coincidence frequency of the slab foundation. The reduction is better for a high structural stiffness and for a low soil stiffness. Walls are stiffer than plates for the relevant frequency range, but even walls and especially low basement walls are not infinitely rigid and can follow the wave deformation to a certain extent. These basic rules from frequency-wavenumber analysis can well be used for real building projects near railway lines where stiff foundations can be an alternative reduction method to the commonly used base isolation by elastic elements. T2 - COMPDYN 2025 CY - Rhodos, Greece DA - 15.06.2025 KW - Frequency-wavenumber method KW - Wave propagation KW - Soil-structure interaction KW - Building foundations KW - Mitigation measures PY - 2025 SP - 1 EP - 15 PB - NTUA CY - Athen AN - OPUS4-63470 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Auersch, Lutz T1 - Frequency-wavenumber method for the wave propagation through the soil and the soil-structure interaction of railway tracks and building foundations near railway lines N2 - In soil-structure interaction, the soil and the (flexible) structures are modelled as elastic continua. The partial differential equations of elasticity can be transformed to algebraic equations in frequency-wavenumber domain where they can be solved by matrix methods. The results for the soil and a structure can be coupled in frequency-wavenumber domain, and the solution in space domain is obtained by an infinite wavenumber integral (the back-transformation). This method has several applications for the prediction of the emission, transmission and immission of railway-induced vibrations. The wave propagation in homogeneous or layered soils is calculated for surface and tunnel lines by a single wavenumber integration (transmission). The response of ballast or slab tracks (for the emission problem) and the foundation stiffness (for the immission problem) need an additional integration across the track or foundation width. In wavenumber domain, tracks and foundations of infinite length are analysed. Finite structures can be calculated by finite element models where the soil is calculated by the boundary element method. The Green’s functions for the boundary element method are calculated by a wavenumber integration as for the transmission problem. Some example results for all these tasks will be shown. The immission into buildings will be analysed in detail, and the effect of stiff slab foundations and (basement) walls on the incoming wavefield is quantified in a parameter study. The transfer function (the amplitude ratio) structure to free field usually starts with 1 at 0 Hz and decreases continuously with frequency. The reduction is due to the structural stiffness against wave deformation which turns to be higher than the stiffness of the soil, for example above the structure-soil coincidence frequency of the slab foundation. The reduction is better for a high structural stiffness and for a low soil stiffness. Walls are stiffer than plates for the relevant frequency range, but even walls and especially low basement walls are not infinitely rigid and can follow the wave deformation to a certain extent. These basic rules from frequency-wavenumber analysis can well be used for real building projects near railway lines where stiff foundations can be an alternative reduction method to the commonly used base isolation by elastic elements. T2 - COMPDYN 2025 CY - Rhodos, Greece DA - 15.06.2025 KW - Frequency-wavenumber method KW - Wave propagation KW - Soil-structure interaction KW - Building foundations KW - Mitigation measures PY - 2025 AN - OPUS4-63468 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Auersch, Lutz T1 - Railway vibration – fast physics-based models for the prediction of ground vibration and the identification of track damage N2 - The following applications of machine learning will be discussed: 1. The prediction of the wave propagation from a railway line (completely physics based for surface lines, physics-based machine learning for tunnel lines) 2. The track behaviour for the emission of train-induced ground vibration (physics based for homogeneous soil, machine learning for layered soil) 3. Track damage detection and quantification from frequency response functions and moving load responses 4. Bridge damage detection and localisation from modal analysis and moving load 5. The use of axle-box acceleration for the identification of track/sub-soil condition and bridge resonances. The prediction of railway vibration usually needs time-consuming finite element, boundary element and wavenumber domain calculations. For a user-friendly prediction software however, fast calculations are needed. Several time-consuming detailed calculations have been used to develop simpler and fast models for the surface railway lines. The more challenging prediction from tunnel lines will be attacked by purely mathematical and by physics-informed machine learning. The dynamic stiffnesses of isolated or un-isolated railway tracks from detailed calculations with a continuous soil have been approximated with the simpler Winkler soil. The vehicle-track resonance (P2 resonance) rules the effect of the mitigation measures, and it can also be used for the on-board monitoring of the track and sub-soil condition. For the identification of track damage such as gaps between sleepers, track slabs and layers, detailed models with a continuous soil have been updated to get the best fit to the measured frequency response functions from hammer tests and the deformation pattern from the moving load response. Whereas the track damage can be locally identified, this is more difficult for bridges where the modal analysis gives mainly global information. The influence lines of the inclination for statically passing vehicles (locomotive, truck, compaction roller) have been used to localise bridge damage (stiffness variations). The on-board monitoring of rail bridges needs special conditions (regular trains with special speeds) to excite and measure the bridge resonance. T2 - 11th European Workshop on Structural Health Monitoring (EWSHM 2024) CY - Potsdam, Germany DA - 10.06.2024 KW - Vibration prediction KW - Track damage detection KW - Human and machine learning KW - Wave propagation KW - Surface line KW - Tunnel KW - Bridge resonance PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-612462 DO - https://doi.org/10.58286/29865 SN - 1435-4934 SP - 1 EP - 9 PB - NDT.net CY - Kirchwald AN - OPUS4-61246 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Auersch, Lutz T1 - Prediction of ground vibrations from rail tunnels –finite-element, boundary-element and wavenumber calculations N2 - The prediction of ground and building vibrations has been established for surface lines and has now been extended to tunnel lines. The wave propagation in homogeneous or layered soils (the transmission) is calculated by an integration in wavenumber domain. The wave amplitudes at different distances and for different frequencies will be analysed for the following situations. 1. The horizontal propagation from a surface point to a surface point constitutes the basic rules. 2. The horizontal propagation from a source point at depth to a receiver point at depth which is related to a building with a deep basement or on a pile foundation. 3. The propagation from depth to the surface, which is the normal case for free-field measurements, has some different characteristics, for example a weaker attenuation with the horizontal distance from the source, which can be approximated by the full-space solution and the reflection rules for incident waves. The emission from a tunnel structure has been calculated by a finite-element model of the tunnel combined with a boundary-element model of the soil giving the reduction compared to a point-load excitation. The immission has been analysed by finite-element models of tunnel-soil-building systems for examples of research and consultancy work. Measurement results from a high-speed and a metro line confirm some of the established rules. Figure T2 - Int. Conf. RASD, Recent Advance in Structural Dynamics CY - Southampton, GB DA - 01.07.2024 KW - Ground vibration KW - Tunnel line KW - Wave propagation KW - Wavenumber method KW - Building vibration KW - Thin layer method PY - 2024 SP - 1 EP - 12 CY - Southampton AN - OPUS4-61266 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Auersch, Lutz T1 - Railway vibration fast physics based models for the prediction of ground vibration and the identification of track damage N2 - The following applications of machine learning will be discussed: 1. The prediction of the wave propagation from a railway line (completely physics based for surface lines, physics-based machine learning for tunnel lines) 2. The track behaviour for the emission of train-induced ground vibration (physics based for homogeneous soil, machine learning for layered soil) 3. Track damage detection and quantification from frequency response functions and moving load responses 4. Bridge damage detection and localisation from modal analysis and moving load 5. The use of axle-box acceleration for the identification of track/sub-soil condition and bridge resonances. The prediction of railway vibration usually needs time-consuming finite element, boundary element and wavenumber domain calculations. For a user-friendly prediction software however, fast calculations are needed. Several time-consuming detailed calculations have been used to develop simpler and fast models for the surface railway lines. The more challenging prediction from tunnel lines will be attacked by purely mathematical and by physics-informed machine learning. The dynamic stiffnesses of isolated or un-isolated railway tracks from detailed calculations with a continuous soil have been approximated with the simpler Winkler soil. The vehicle-track resonance (P2 resonance) rules the effect of the mitigation measures, and it can also be used for the on-board monitoring of the track and sub-soil condition. For the identification of track damage such as gaps between sleepers, track slabs and layers, detailed models with a continuous soil have been updated to get the best fit to the measured frequency response functions from hammer tests and the deformation pattern from the moving load response. Whereas the track damage can be locally identified, this is more difficult for bridges where the modal analysis gives mainly global information. The influence lines of the inclination for statically passing vehicles (locomotive, truck, compaction roller) have been used to localise bridge damage (stiffness variations). The on-board monitoring of rail bridges needs special conditions (regular trains with special speeds) to excite and measure the bridge resonance. T2 - 11th European Workshop on Structural Health Monitoring (EWSHM) CY - Potsdam, Germany DA - 10.06.2024 KW - Vibration prediction KW - Track damage detection KW - Human and machine learning KW - Wave propagation KW - Surface line KW - Tunnel KW - Bridge resonance PY - 2024 AN - OPUS4-61231 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz A1 - Maldonado, M. T1 - Interaction véhicule-voie-sol et vibrations dues aux trains - Modélisations et vérifications expérimentales N2 - Cet article présente plusieurs modèles numériques pour l’étude des phénomènes vibratoires lors du passage d’un train. Les modèles permettent d’estimer la propagation des ondes et les réceptances pour le sol et la voie. Le sol multicouche et le couplage voie-sol sont traités par une (double) intégration sur les nombres d’onde. Les raideurs dynamiques de la voie et du véhicule sont combinées et les forces d’excitation roue-rail dues aux irrégularités de la voie et des roues sont calculées. Ces forces d’excitation permettent de simuler les vibrations du sol lors du passage d’un train. Les modèles sont validés par comparaison avec des mesures sur deux sites, en France et en Allemagne. Les vibrations calculées correspondent bien aux vibrations mesurées. ---------------------------------------------------------------------------------------------------- This contribution presents models that are necessary to calculate the vibrations due to the passage of a train. The models allow to calculate the propagation of the waves and the receptances of the soil and the track. The layered soil and the coupling with the track are treated by a (double) integration in wavenumber domain. The dynamic stiffnesses of the track and vehicle are combined and the excitation forces due to the irregularities of the track and the wheel are calculated. Finally, these excitation forces are used to simulate the ground vibration of a passing train. All these models are validated by a number of different measurements at two sites in France and Germany. KW - Ondes du sol multicouche KW - Irrégularités et forces roue-rail KW - Wave propagation KW - Layered soil KW - Wheel-rail irregularities and forces PY - 2011 DO - https://doi.org/10.3166/EJCM.20.257-280 SN - 1779-7179 VL - 20 IS - 5-6 SP - 257 EP - 280 PB - Hermès Science : Lavoisier CY - Paris AN - OPUS4-24557 LA - fra AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Auersch, Lutz T1 - Wave propagation in the elastic half-space due to an interior load and its application to ground vibration problems and buildings on pile foundations N2 - A method is presented which allows to calculate the wave-field in a homogeneous or layered soil in case of a dynamic interior load. The wave propagation along the surface, the distribution of the response over the depth, the horizontal propagation at different depths and the vertical downward propagation are shown and compared with the simpler surface solution of the half-space and the interior solution of the full-space. The complete wave-field (Green's function) is applied to the dynamic behaviour of piles and pile groups by use of a boundary element formulation. The stiffness, damping and – typically for piles – mass of different groups of piles are presented. Different group effects occur for lines, circles, grids, parallels and crosses of piles, which can be regarded as oscillations around average values. Moreover, the piles and pile groups behave almost like a damper for most of the frequencies. A building on a pile group that is excited by ground vibration due to surface or interior loads shows a reduction of the wave-field due to kinematic and inertial soil–building interaction effects. The results presented lead to simplified descriptions of the wave-field due to interior loads and of the soil–pile–building interaction which can be used for the prediction of technically induced vibration. KW - Wave propagation KW - Interior load KW - Dynamic pile and pile group stiffness KW - Kinematic and inertial soil-pile-building KW - Interaction PY - 2010 DO - https://doi.org/10.1016/j.soildyn.2010.04.003 SN - 0261-7277 SN - 0267-7261 VL - 30 IS - 10 SP - 925 EP - 936 PB - Elsevier Science CY - Amsterdam AN - OPUS4-21833 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -