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- Track-soil interaction (6)
- Layered soil (5)
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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.
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.
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 damage detection and repair control have become important tasks for ballast and slab tracks. Measurements which compare the damaged and the repaired status of the same track section at different times, or which compare a damaged and an intact track section at the same time, have been successfully performed at some sites in Germany. The loss of contact between the sleeper and the track plate, between the track plate and the base plate, and between the base plate and the base layer have been analysed. The soil properties of each site have been measured and have been used to establish realistic track-soil models. Theoretical results of the wavenumber domain and the finite-element boundary element method have been compared with the experimental results. The observed experimental and theoretical results, changes in the time histories of displacements and velocities due to train passages and in the transfer functions (receptances) due to hammer impacts, are encouraging that these measurements can be used to detect track damage.
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.
Measurements on the vehicle-track interaction and the excitation of railway-induced ground vibration
(2017)
Two railway measurement campaigns have been performed in Germany and Switzerland which yield insight in the vehicle-track-soil interaction. The campaign in Germany has included simultaneous measurement of vehicle, track, and soil vibrations during train runs with 16, 25, 40, 63, 80, 100, 125, 140, 160 km/h, and impulse measurements of the passenger car, three track sections and the soil. Two ballast tracks, one on the soil surface and one on a concrete bridge, have been investigated as well as a slab track in a tunnel. Ten different sites in Switzerland have been measured for soil properties and train-induced ground vibrations, which allow to determine the excitation forces of the railway traffic. New axle-box measurements at some of the Swiss sites have been analysed to get further experimental evidence. All these measurements have been evaluated to characterize the excitation processes. Relations between vehicle vibration and ground vibration can be observed. The vehicle vibrations, namely the accelerations of the wheelsets, yield the dynamic forces due to the passage over the irregularities of the vehicle and the track. The ground vibrations are correlated to these dynamic forces to a certain extent. Some mid-frequency ground vibration amplitudes, however, are higher than expected from the dynamic excitation forces. The experimental observations can be explained by an irregular response to the passage of the static loads, that means the passage of the static loads over an irregular ballast or soil. This correct understanding of the excitation processes is important for the prediction as well as for the mitigation of railway induced ground vibrations.
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.
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 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.
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.
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.
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.