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- Ground vibration (5)
- Finite-element boundary-element method (2)
- Force transfer (2)
- Layered soil (2)
- Mitigation (2)
- Railway (2)
- Railway track (2)
- Soil-building interaction (2)
- Track-soil interaction (2)
- Vehicle-track interaction (2)

#### Organisationseinheit der BAM

- 7.2 Ingenieurbau (16) (entfernen)

The soilstructure interaction of elastic plates on homogeneous or layered soils excited by horizontally propagating waves is analysed. Large plates are modelled by a combined finite-element boundary-element method (FEBEM), whereas the response of infinitely long plates is calculated by a numerical integration in the frequencywavenumber domain. The finite-element boundary-element method yields the complete soilplate transfer function of frequency and distance whereas the frequencywavenumber solution of the infinitely long plate can serve as an approximation for long distances on a finitely long plate. The soilplate transfer function starts to decrease strongly at the coincidence frequency, where the bending stiffness equals the plate inertia. A strong decrease follows at mid frequencies and a strong reduction of less than 0.1 of the ground vibration is reached at high frequencies. Rules for the characteristic frequencies are derived from the numerical results clearly indicating the strongest influence of the soil stiffness and the weaker influence of the bending stiffness of the plate. The influence of the mass, length and width of the plate are shown to be limited in case of realistic parameters, but it should be noted that the reduction effects are less effective for layered soils and for nearer observation points.

Vibration of normal apartment, office and production buildings, which are excited by technically induced ground vibrations are considered. Many wavelengths of the Rayleigh waves of the soil fit into the foundation dimensions. The related high discretization effort can nowadays be realized with detailed soil-structure interaction method. The combined finite-element boundary-element method is used here as a detatiled method. Simplified method can be used with less computation time, but these methods must be calibrated by exact results. One simplification is to extent the structure to infinity and to solve the problem by wavenumber domain methods. Another simplification is the use of a Winkler soil instead of the continuous soil. Usually, the Winkler parameters are not only soil parameters but depend also on the rigid or flexible foundation structure. Substructure methods use commercial FEM software for the building part. The contribution will show some detailed and some simplified results on large structural elements such as foundation plates, walls, storey plates on columns as well as results on complete buildings. The reduction of the ground vibration by stiff elements and the amplification due to floor or building resonances are discussed which are the most important phenomena of the soil-building interaction.

Train passages induce forces on the track, train-induced vibrations propagate through the soil and excite neighbouring buildings. The emission, which is the first part of the prediction of vibrations near railway lines, is presented by focusing on the dynamic axle loads. The calculation of the axle loads is based on the vehicle-track-soil interaction. This interaction calculus utilises 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 ballast or the subsoil, which must also be transferred to effective track irregularities, and due to the discrete rail support on sleepers. All necessary transfer functions for the prediction of axle-load spectra are presented as general formula and as specific graphs for differing vehicle and track parameters. The prediction method is applied to a ballast track and a slab track and compared with corresponding axle-box measurements. Moreover, ground vibration measurements at numerous sites are exploited for the axle-load spectra and the validation of the prediction method. All theoretical and experimental results confirm that the dynamic axle-load spectra have an approximate value of 1 kN per third of octave and increase with train speed, track stiffness and around the vehicle-track resonance.

The dynamics of un-isolated and isolated ballast tracks have been analysed by multi-beam models for the track and by a layered half-space model for the soil. The solution is calculated in frequency-wavenumber domain and transformed back to space domain by a wavenumber integral. This is a faster method compared to other detailed track-soil interaction methods and almost as fast as the widely used Winkler-soil method, especially if the compliances of the soil have been stored for repeated use. Frequency-dependent compliances and force transfer functions have been calculated for a variety of track and soil parameters. The ballast has a clear influence on the high-frequency behaviour whereas the soil is dominating the low-frequency behaviour of the track. A layering of the soil may cause a moderate track-soil resonance whereas more pronounced vehicle-track resonances occur with elastic track elements like rail pads, sleeper pads and ballast mats. Above these resonant frequencies, a reduction of the excitation forces follows as a consequence. The track deformation along the track has been analysed for the most interesting track systems. The track deformation is strongly influenced by the resonances due to layering or elastic elements. The attenuation of amplitudes and the velocity of the track-soil waves change considerably around the resonant frequencies. The track deformation due to complete trains have been calculated for different continuous and Winkler soils and compared with the measurement of a train passage showing a good agreement for the continuous soil and clear deviations for the Winkler soil model.

A complex measuring campaign has been performed including the simultaneous measurement of vehicle, track, and soil vibrations during train runs at 16, 25, 40, 63, 80, 100, 125, 140, 160 km/h, and impulse measurements of the passenger car, three track sections and the soil. A ballast track on the soil surface and on a concrete bridge have been investigated as well as a slab track in a tunnel. The evaluation and comparison of all these data shows a generally good agreement for all components if the strong low- and high-frequency cut-off characteristics of the layered and damped soil are incorporated. There is a strong causal correlation between the vehicle and the soil by the dynamic excitation forces and a weak relation between the track and the soil by the axle-sequence spectrum of the train. However, the similarity between the axle-impulse spectrum observed at the track and the spectra of the ground vibration lead to the special excitation component of “scattered axle impulses” which is pre-dominant at the far-field points of the soil.

Long wooden floor beams above a ball room in an old historical palace have been analysed experimentally. The eleven beams are weakly coupled by three layers of floor boards. It has been investigated if the state (the stiffness) of the wooden beams can be determined by vibration measurements of global or preferably local modes. Hammer, heel-drop and ambient excitations have been used. The vibration modes of the structure show dominating local deformations if an impact excitation is applied. This is understood as the positive superposition of several modes which yield the maximum at the excitation point but a cancellation at more distant points. Natural modes have been estimated from these vibration modes by standard and special methods which were necessary for the high damping of the wooden floor. It has been found that all floor beams contribute to each natural mode even for a weak coupling of the beams. In addition to the modal discussion, the impact tests have also been analysed for the wave propagation and amplitude attenuation with distance. The coupling of floor beams has been studied theoretically by an analytic multiple-beam model where the coupling by translational or rotational springs and by a common support motion has been assumed.

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.

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.

This contribution presents some principles and some examples of the mitigation of railway-induced ground vibrations. The principles are different for the mitigation measures at the track, in the soil or at the building. Force transfer functions of isolated and un-isolated track-soil systems, reflected and transmitted wave amplitudes at walls and trenches in the soil, and the transfer of the (free-field) vibration amplitudes to the foundation amplitudes of the building are analysed. The mitigation effect can be calculated by exact or simplified formulas. Some examples with 3D (finite-element boundary-element), 2D (beam-on-support), and 1D track models, 2D and 1D soil models, detailed 3D building models and finite or infinite 1D wall-floor models are investigated to find out if simple models can be used for a satisfactory prediction of the mitigation effect. The 1D track examples show that the force transfer of the track without vehicle can be exactly calculated, whereas the total force transfer can be calculated approximately if appropriate wheelset masses per track length are used for the isolated and the un-isolated track. The mitigation effect of a filled trench is calculated by a 2D finite element model and the results compare with simple transmission formula if the stiffness per area rather than the wave impedances are used for the infill material. The base isolation of a building is analysed by a detailed 3D model and the results are similar to the analytic results of a single wall with floors on the soil. Other reduction measures as different floor and column dimensions are usually less effective so that the clearly best mitigation solution at a building is a partly or a complete base isolation.

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.