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Prediction of building noise and vibration – 3D finite element and 1D wave propagation models
(2021)
Construction work or traffic excite nearby buildings, and the perceptible or audible vibration can be a nuisance for the inhabitants. The transfer of the vibration from the free field to the building has been calculated by the finite element method for many models in consultancy and research work. The analysis for all storeys of certain building points such as walls, columns and floors unveiled some rules, some typical modes, and some wavetype responses. A simplified building-soil model has been created, which includes well these effects of building-soil resonance, wall/column resonance, floor resonances, and the high-frequency reduction. The model consists of one wall for a wall-type apartment building or a column for each specific part (mid, side or corner) of a column-type office building. The building response in the high-frequency (acoustic) region is calculated as mean values over all storeys and over wider frequency bands, by wave-type asymptotes of an infinitely tall building, and by the soil to wall ratio of impedances. The secondary noise is predicted by Transfer values between the building vibration (center of floors, walls at a room corner) and the sound pressure.
Prediction of building noise and vibration – 3D finite element and 1D wave propagation models
(2021)
Construction work or traffic excite nearby buildings, and the perceptible or audible vibration can be a nuisance for the inhabitants. The transfer of the vibration from the free field to the building has been calculated by the finite element method for many models in consultancy and research work. The analysis for all storeys of certain building points such as walls, columns and floors unveiled some rules, some typical modes, and some wavetype responses. A simplified building-soil model has been created, which includes well these effects of building-soil resonance, wall/column resonance, floor resonances, and the high-frequency reduction. The model consists of one wall for a wall-type apartment building or a column for each specific part (mid, side or corner) of a column-type office building. The building response in the high-frequency (acoustic) region is calculated as mean values over all storeys and over wider frequency bands, by wave-type asymptotes of an infinitely tall building, and by the soil to wall ratio of impedances. The secondary noise is predicted by Transfer values between the building vibration (center of floors, walls at a room corner) and the sound pressure.
The present contribution evaluates four measuring series made by the Federal Institute of Material Research and Testing for the relations between train speed and ground vibration amplitudes. This experimental evaluation is supported by the simulation of the train passages at the different sites by using appropriate excitation mechanisms and forces as well as layered soil models which have been derived from impact measurements at each site.
There is a strong need for cost-effective mitigation measures for
turnouts. SBB has initiated a series of examinations using different methodologies to gain a deeper understanding of the excitation mechanisms at low frequencies, in addition to that obtained in the RIVAS project. To date it is not yet clear what constitutes a complete measurement data set that would enable understanding most of the vibration excitation mechanisms in turnouts. Increasing vibration at turnouts in comparison to normal track is observed for all measured frequencies.
The different methodologies are presented in the paper. Under-sleeper pads (USP) are a cost-effective method to reduce vibration at frequencies above 63 Hz (1/3 octave), but there is probably no improvement for frequencies below 63 Hz. A first test of new frog geometry did not show relevant improvements in Vibration emission in comparison to a reference frog geometry. Axle box acceleration measurements are an interesting method to identify defects in a turnout. A specialized measurement system of rail roughness could identify certain geometry Problem areas for some frogs. Noise increases also are observed at turnouts for frequencies ranging between 80 to 1000 Hz. The use of railway source models to calculate
contact forces for ballasted track and turnouts seems promising, in particular for understanding the influence of ground.
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.
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.
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.
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.
In the last three decades, the vibrations of many floors and bridges have been measured. The contribution shows some evaluation methods, experimental results and some modelling and theoretical results. Simple evaluation methods have been developed for single and coupled floors. Two coupled beams have been measured in good agreement with the theory. A more complex coupling model has been found for a large wooden floor in a castle consisting of six floor bays which correlates well with the measurements. Damaged and intact poles have been tested by their natural frequencies and damping values, and a fair correlation between the degree of damage and the shift of the frequency. Road bridges have been analysed in detail and some examples are presented. Railway bridges and trains are studied for resonant excitation. The risk of resonance can be estimated in frequency domain by using axle-sequence spectra of the train and the natural frequencies of the bridge. A measurement example shows the amplification, but even stronger the cancellation of the subsequent axle responses. Several high-speed trains and freight trains have been analysed for their potential resonance amplification.
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.
A study on building vibrations has been performed by finite element calculations. Family houses, multi-storey residential buildings, office buildings and office towers have been modelled in detail. The frequency-dependent response due to a free-field excitation has been evaluated for walls, columns and floors. The ratio of building amplitudes to free-field amplitudes starts with uB/u0 = 1 at zero frequency and is usually lower than 1 at 50 Hz, the end of the frequency range considered here. In between, amplifications occur due to several reasons. There are „soil resonances“ where the whole building is vibrating on the compliant soil, “column resonances” where the upper storeys are vibrating on the compliant columns, and the “floor resonances” where the floors are vibrating excited by their supports. Results are presented for all building types, but a special focus is set on office buildings. A parameter study shows the influence of the stiffness of the soil, the number of storeys, and the width of the building. It has been found that the “soil resonance” is strongly modified by the low-frequency floor resonances for the normal office building. The main resonance of a twenty-storey office tower is determined equally by the “soil mode” and the “column mode”. It is an important observation for these office buildings that the resonances can differ for different parts of the building such as the centre, the edge, the corner, and the core of the building. This leads to non-uniform vibration modes across the building, which look like another type of “floor resonance” and which have been observed in several real building projects. Experimental results will be shown which can confirm the calculated phenomena.
A study on building vibrations has been performed by finite element calculations. Family houses, multi-storey residential buildings, office buildings and office towers have been modelled in detail. The frequency-dependent response due to a free-field excitation has been evaluated for walls, columns and floors. The ratio of building amplitudes to free-field amplitudes starts with uB/u0 = 1 at zero frequency and is usually lower than 1 at 50 Hz, the end of the frequency range considered here. In between, amplifications occur due to several reasons. There are „soil resonances“ where the whole building is vibrating on the compliant soil, “column resonances” where the upper storeys are vibrating on the compliant columns, and the “floor resonances” where the floors are vibrating excited by their supports. Results are presented for all building types, but a special focus is set on office buildings. A parameter study shows the influence of the stiffness of the soil, the number of storeys, and the width of the building. It has been found that the “soil resonance” is strongly modified by the low-frequency floor resonances for the normal office building. The main resonance of a twenty-storey office tower is determined equally by the “soil mode” and the “column mode”. It is an important observation for these office buildings that the resonances can differ for different parts of the building such as the centre, the edge, the corner, and the core of the building. This leads to non-uniform vibration modes across the building, which look like another type of “floor resonance” and which have been observed in several real building projects. Experimental results will be shown which can confirm the calculated phenomena.
Methods have been presented for detailed studies of railway vibration and for the fast prediction of train-induced ground vibration. The ground vibration is generated by static or dynamic loads. The main purpose of this contribution was to show the influence of inhomogeneous soils on the different vibration components.
Layered soils, namely a soft layer on a stiffer half-space, yield a quite specific transmission behavior. The low-frequency and sometimes also high-frequency cut-off of the transfer function of the soil is demonstrated in theory and by experiments at many sites of which the soil model is approximated from dispersion and transfer function measurements. The layer frequency divides the frequency range in a low-frequency range, where the stiff half-space rules the low amplitudes, and a high amplitude high-frequency range which is mainly determined by the softer top layer. A thick soft layer yields a very low layer frequency, so that the higher soft soil amplitudes have a wider range down to low frequencies. A thin layer yields a high layer frequency, so that the high frequencies above this layer frequency are dominant. The higher the contrast between the stiff half-space and the soft layer is, the stronger the increase between the half-space and layer amplitudes, the more characteristic are the spectra of the soil transfer function. The range of measured soils has been from vS1 down to 125 m/s, vS2 up to 1000 m/s and the layer frequencies are within 10 Hz < f0 < 75 Hz. Moreover, during this measuring campaign in Switzerland, all 11 sites showed clearly the layer-on-half-space behaviour. The transfer functions of inhomogeneous soils have been used to predict the ground vibration due to dynamic axle loads which is usually thought to be the most important component.
The passage of static loads, in the contrary, results in very small vibration amplitudes for low train speeds, which can only be found at near distances and at low frequencies. They attenuate very rapidly with distance and lose very rapidly the higher frequency content. The passage of static axle loads can be included in the prediction of railway vibration just for completeness.
Special attention should be given to the case if the train runs with the Rayleigh-wave speed of the soil (Rayleigh train). The Rayleigh-train effect is strongest for a homogeneous half-space: At the near-field of the track the amplitudes are raised strongly compared to normal trains, and in addition, little attenuation with distance is observed. In case of a layered soil, the low-frequency cut-off reduces the frequency range and the amplitudes of the homogeneous quasi-static ground vibrations. Therefore, the Rayleigh-train effects are clearly reduced by a layered soil and they disappear if the layer frequency (for example for a thin layer) is higher than the frequency band of the axle impulse. The Rayleigh-train effect could completely disappear in a randomly inhomogeneous soil, but this has not been analysed so far.
The axle impulses from static loads can have an additional, quite different effect. They can be scattered by a randomly inhomogeneous soil so that a part (the scattered part) of the axle impulse can reach further distances from the track. This can establish a certain mid-frequency component of the ground vibration which becomes dominant in the far-field, and this important component exists for all train speeds. Experimental results from BAM and international measurements show the importance of the corresponding frequency range.
The mitigation of train induced ground vibration by elastic and stiff track elements has been analysed threefold. The vehicle-track interaction yields the reduction at high frequencies above the vehicle-track resonance. This is the standard effect. The filtering of trackbed errors by the bending stiffness of the track yields a certain mid-frequency effect. An even stronger mid-frequency effect is predicted for the mitigation of the scattered axle impulses by the bending stiffness and elastic elements of the track.
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.
Measured train passages and hammer impacts in combination with track-soil calculation have been successfully used for the detection of damaged slab tracks. This approach is now extended to intact slab and ballast tracks. The vibrations of many tracks have been measured at several levels from rail, sleeper, track plate, base plate, base layer to the subsoil by velocity or acceleration sensors. The time histories have to be integrated once or twice to get the displacements. The displacement signals include an arbitrary time-dependent shift which must be eliminated or respected in the interpretation. On the other hand, the calculation of slab and ballast tracks have been done in frequency-wavenumber domain. The displacements along the track and the frequency-dependent compliance transfer functions can be calculated. The latter can be compared with the results of the hammer impacts on the track. The deformation of the track can be transformed to time histories for a whole train and compared to the measured train passages. Many slab (and ballast) tracks have been measured at different sites. The displacements of the tracks are presented, and the following parameters have been analysed in the measurement results: slab track vs. ballast track, different types of slab tracks, damaged slab tracks, different trains, switches at different measuring points, an elastic layer, the mortar layer, different soils at different places. The soil should have the dominant influence on the track-plate displacements. Slab and ballast track yield also big differences in maximum displacement and width of deformation. Some of the preceding aspects will be analysed in comparison of measurement and theory.
Measured train passages and hammer impacts in combination with track-soil calculation have been successfully used for the detection of damaged slab tracks. This approach is now extended to intact slab and ballast tracks. The vibrations of many tracks have been measured at several levels from rail, sleeper, track plate, base plate, base layer to the subsoil by velocity or acceleration sensors. The time histories have to be integrated once or twice to get the displacements. The displacement signals include an arbitrary time-dependent shift which must be eliminated or respected in the interpretation. On the other hand, the calculation of slab and ballast tracks have been done in frequency-wavenumber domain. The displacements along the track and the frequency-dependent compliance transfer functions can be calculated. The latter can be compared with the results of the hammer impacts on the track. The deformation of the track can be transformed to time histories for a whole train and compared to the measured train passages. Many slab (and ballast) tracks have been measured at different sites. The displacements of the tracks are presented, and the following parameters have been analysed in the measurement results: slab track vs. ballast track, different types of slab tracks, damaged slab tracks, different trains, switches at different measuring points, an elastic layer, the mortar layer, different soils at different places. The soil should have the dominant influence on the track-plate displacements. Slab and ballast track yield also big differences in maximum displacement and width of deformation. Some of the preceding aspects will be analysed in comparison of measurement and theory.
Abstract. 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.
The present contribution evaluates four measuring series made by the Federal Institute of Material Research and Testing for the relations between train speed and ground vibration amplitudes. This experimental evaluation is supported by the simulation of the train passages at the different sites by using appropriate excitation mechanisms and forces as well as layered soil models which have been derived from impact measurements at each site.
The present contribution evaluates four measuring series made by the Federal Institute of Material Research and Testing for the relations between train speed and ground vibration amplitudes. This experimental evaluation is supported by the simulation of the train passages at the different sites by using appropriate excitation mechanisms and forces as well as layered soil models which have been derived from impact measurements at each site.
Mitigation measures of railway induced vibration have been demonstrated at the emission, transmission and immission part. It must be carefully observed that the correct masses and stiffnesses are used.
Typical mistakes have been shown,
- 1D models for vehicle-track interaction,
- impedance instead of stiffness for the infill material of a trench,
- rigid buildings or neglecting the soil-building interaction.
The dominant mid-frequency part of the ground vibration is due to the irregular soil.