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The passage of the train is dominated by the impulses of the static axle loads. The response of the regular homogeneous and irregular soils has been calculated by the finite-element method in frequency domain. The superposition of the impulse responses yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil or ballast of which the stiffness varies randomly in space, a mid-frequency ground vibration component is generated by the scattering of the axle impulses. Measurements will be shown which prove the existence of the mid-frequency ground vibration component and the unique explanation by the scattered axle impulses: many international measurements with a raised mid-frequency component, axle-box measurements with a too low mid-frequency dynamic load, amplitude-speed dependencies which are incompatible with irregularity-induced dynamic loads, and ground vibration reductions due to stiff track elements.
The passage of the train is dominated by the impulses of the static axle loads. The response of the regular homogeneous and irregular soils has been calculated by the finite-element method in frequency domain. The superposition of the impulse responses yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil or ballast of which the stiffness varies randomly in space, a mid-frequency ground vibration component is generated by the scattering of the axle impulses. Measurements will be shown which prove the existence of the mid-frequency ground vibration component and the unique explanation by the scattered axle impulses: many international measurements with a raised mid-frequency component, axle-box measurements with a too low mid-frequency dynamic load, amplitude-speed dependencies which are incompatible with irregularity-induced dynamic loads, and ground vibration reductions due to stiff track elements.
A prediction software has been developed by BAM. The following topics have still be solved. A realistic irregularity spectrum can be derived from axle-box measurements. It agrees wel with the spectrum used for the high-speed 2 project in the United Kingdom. In addition, the scattering of axle pulses should be included. This mid-frequency component can also be found in the HS2 procedure. Finally, the reduction in case of a tunnel line compared to a surface line should be included. Some measurement results of BAM, HS2 and other institutes show a certain mid-frequency reduction. This is due to the load distribution of the tunnel which yields softer axle pulses and the scattered axle impulses are reduced.
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.
Measurements of ground and track vibrations have been performed at a high-speed line in northern Germany. Impacts on the track and the ground, and passages of different trains with different speeds on different tracks have been measured. Transfer functions of the soil are presented and approximated by theoretical soil models. By using these transfer functions, the measured ground vibration between 2 to 64 m distance from the track can be transformed into a load spectrum which can be used for predictions at other sites. The method is compared to the soil-dependent method of an emission spectrum at a certain distance (8 m for example). The influence of train type, speed and track type is discussed on the base of the different emission quantities and the original measurements. The strong influence of the track, ballast track and slab track, is analysed by a theoretical model in wavenumber domain. The response of the track to the passage of the static load is reduced by the stiffness of the slab, the deformation of the track as well as the impulse acting on the soil. Usually, the impulse on the soil should result in a slow quasi-static movement of the soil, slower at further distances. In a heterogeneous soil, however, the impulses from the static loads scatter and keep parts of the higher impulse frequency band. In this case the reduced impulse spectra of the slab track will yield reduced ground vibration in a certain frequency band. Additional (BAM and international) measurements will be used to discuss this and possible other explanations for the different ground vibration differences.
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.
The contribution shows measurement examples of cars, floors, foundations, railway tracks, a footbridge, and a railbridge. Vibrations may include modes and waves. Namely in soil-structure interaction, modes are damped, shifted and prevented so that alternatives for the modal analysis are necessary: The approximation of the whole spectrum (flexibility function) and of the whole train passage (moving-load response).
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.
The train passages over intact or damaged slab tracks on different soils have been calculated by two methods. The finite element method (FEM) uses a Winkler soil under the track model by adding a thin “soil layer”. The combined finite element boundary element method has a continuous soil model which is included by the boundary element method. The basic results are the distributions of the track (rail, track plate, and base layer) displacements along the track for a single axle laod. These solutions are superposed to a complete train load and transformed to time histories. The influence of track and soil parameters has been analysed. The main interest is the influence of the track damage. A gap between track plate and base layer of different lengths has been studied for changes in amplitudes and widths of deflection. A best fit to measured track displacements has been found so that the track damage can be identified and quantified. The FEM model with Winkler soil cannot be fitted to the amplitude and width with the same soil parameters. Therefore, the FEBEM model is preferable for these railway track problems.
Measurements at the foundation, the surrounding soil and nearby buildings have been done during several drop tests of different containers on different foundations. The first measurements have been done on a big foundation where it should be guaranteed that the foundation is rigid and the container is tested properly. It was controlled that the foundation does not absorb more than 2 percent of the energy of the container. Most of the drop energy is lost in shock absorbers. Later on, a smaller drop test facility has been built on the ground but inside an existing building. It had to be controlled by prediction and measurements that the drop test will not damage the building. Tests from different heights on soft, medium, and stiff targets have been done to find out rules which allow to identify acceptable and unacceptable drop tests. Later on, the biggest drop test facility has been built for masses up to 200 t. It was necessary for the design of the foundation to estimate the forces which occur during the drop tests. On the other hand, the acceptable tests should be selected and controlled by measurements where the impact duration is important. Different sensors, accelerometers, accelerometers with mechanical filters, geophones (velocity transducers), strain gauges, and pressure cells have been applied for these tasks. The signals have been transformed to displacements which proved to be best suited for the interpretation of the impact mechanism. Modell calculations have been used to check and understand the dynamic measurements. The simplest law is the conservation of the momentum which is a good approximation if the impact is short. If the soil under the foundation has an influence on the deceleration of the container, the maximum foundation velocity is lower than the simple estimation. The amplitudes of the foundation could also be estimated from the ground vibrations and their amplitude-distance law.