MS19.2 - Traffic Induced Vibrations

Technological advances in recent years have allowed the emergence of high-speed train (HST) transport. However, high speeds have the potential to cause excessive ground vibrations that can affect the track structure and the surrounding area. This can potentially cause passenger discomfort and in the worst case severe track damage. The transmission of ground vibrations from a moving train to the ground is a complex dynamic problem, which depends on various key parameters. The Quasi-static excitation, which is the dominant factor of the track response occurs due to the static component of the axle load and contributes to the lower frequency excitations. The dynamic component of the excitation, contributes to the higher frequency excitations and occurs due to the irregularities in the contact between the wheel and the rail. The dynamic excitations are involved with the far-field response. Furthermore, the ballast tracks resting on soft subgrade are difficult to meet the demands of HST due to low vertical stiffness, low shear strength and high deformability. Despite the current advances in computational engineering, the study of HST crossing regions of soft soils is still a challenge. In the present paper a numerical approach for the prediction of vibrations induced by HST is developed, verified and validated. The proposed numerical method is based on a sub-structuring approach, where first the dynamic response of the rail-track system is computed and then the wave propagation along the ground surface is calculated. The dynamic load, which is the combination of high and low frequency excitations, on the track bed is calculated using mechanical models for rail-track interactions considering the train type, speed, track structure and the properties of underground. For the low frequency component, model based on flexible beam resting on continuous spring - dashpot elements are applied in time domain. Spring-dashpot elements represents the soil dynamic properties, where the properties determined using simplified analytical calculation-cone model for heterogeneous soil. For the high frequency component, a track dynamic model is utilized. The resultant combined dynamic force consisting of the quasi-static and dynamic component due to HST transit is applied on the FEM soil dynamic model in time domain on the ballast, which is the interface of the two models. In an attempt to capture the inelastic behavior of the soil, we consider in the present study a linear-equivalent analysis based on an iterative procedure. Moreover, an iteration is also applied in order to ensure the coupling between the rail-track system with the subgrade. The computed results are verified with existing numerical results from the literature and validated with available in-situ measurements. The dynamic stability of the system is evaluated based on the computed strain level of the soil. Extensive parametric study is conducted considering material heterogeneity and variation in train speed. Critical and subcritical speeds of the train and resultant ground vibration amplification effects are thoroughly studied. All simulation results demonstrate the accuracy and the good performance of the proposed numerical approach.

In the field of railway ground-borne noise and vibration, emission levels are strongly dependent on the track and ground properties so that measurements at different sites cannot be directly compared. Therefore, to compare the ground-borne noise and vibration performance of different vehicles, it is desirable to define a vehicle indicator that is track independent. The SILVARSTAR project aims to provide the railway community with proven software tools and methodologies to assess the ground-borne noise and vibration environmental impact of railway traffic on a system level. Within the project, a track-independent vehicle indicator (TVI) is proposed, based on the SILVARSTAR modelling approach, that can be used to identify railway vehicles which generate low ground-borne vibration and noise levels. The proposed TVI is based on applying a frequency weighting to the force density obtained at a site from the measured ground vibration velocity levels due to train passages and the measured line source transfer mobility. Unlike the vibration levels during train passages, the force density is relatively independent of the track and ground properties and the distance from the track at which it is calculated, and hence it is suitable to be used for the track-independent classification of railway vehicles. Two different formulations of TVI are proposed; one related to ground-borne vibration and the other to ground-borne noise. For both formulations, it is assumed that the starting point is the force density determined from the measured vibration response. Each TVI is a single number quantity, defined as a sum over all frequency bands of the frequency-weighted force density levels. The selected weighting functions are chosen to represent the vibration for a nominal track, ground and building. Nonetheless, they are shown to be representative of the changes in vibration and ground-borne noise that will occur when changing from one vehicle type to another, even when the track, ground, building and receiver distance do not correspond to the chosen nominal conditions. The proposed performance classification of different vehicles can be achieved by comparing the relative differences of their TVIs. A series of test cases is devised to demonstrate the calculation of the TVIs and the TVI-based classification of different vehicles at the same site. To replicate practical situations, the TVIs for each vehicle are calculated from force density levels obtained by numerical models. The simulations are performed using generic models of passenger and freight trains and the most important parameters of the vehicle that affect ground vibration and noise are investigated: wheel unevenness, unsprung mass, primary and secondary suspension stiffness, train speed and the number of axles per unit length and axle spacing. The study shows that although the values of the TVIs for each vehicle may vary due to the different modelling approaches and detail or due to the limited knowledge of the input parameters used for the target site, the TVI-based classification of different vehicles is insensitive to this model and parameter uncertainty.

Abstract. Train-induced vibration is a growing concern in China for tracks in close proximity to buildings, in particular, for over track building in metro depots. Over-track buildings generally include heavy transfer structures due to irregular spacings between ground columns in between the tracks. Ground-borne vibration transmits up the ground columns into the transfer structures then into over-track buildings where residents may experience feelable vibration at levels above those permitted by codes for human comfort and at levels that are potentially excessive in laboratories and manufacturing plants with sensitive equipment. Predictions of train-induced vibration levels are needed for comparison with serviceability limits. An analytical prediction method based on impedance modeling of building components has been developed that accounts for transmission through the transfer structures in the buildings. It includes impedance expressions that characterize the vibration transmission in structural components including columns, beams, and floors. Train-induced ground vibration generates axial wave transmission in ground columns, which transmits bending waves into the horizontal transfer structures, and then axial waves in the over-track building columns and bending in its floors. Model predictions closely matched measured levels in a metro depot in Shenzhen, China. The model was used to assess the potential effectiveness of reducing vibration transmission into the over track building by a heavy, high impedance, blocking floor at lower elevation.

Although rail is a sustainable and climate-friendly means of transport, vibration remains a particular environmental concern as it may cause annoyance to people and disturbance of sensitive equipment. Inspired by promising results obtained with seismic metamaterials to protect civil infrastructure from earthquakes [1], we aim to investigate how seismic metamaterials can mitigate railway induced vibration in a wide frequency band (1 – 80 Hz). This can be accomplished by placing resonators on the transmission path between track and buildings [2,3]. Attenuating vibration induced by moving dynamic axle loads remains challenging. Furthermore, vibration reduction is required in a broad frequency range. The challenge is also aggravated by considering layered soils, in which vibration is mainly propagating as a superposition of dispersive surface waves. Detailed models based on 3D coupled finite element - boundary element (FE-BE) formulations are developed to analyze the effect of seismic metasurfaces on railway induced vibration in a broad frequency band. Fixed loads applied on the surface of the soil and moving loads are considered. The resonators are modeled as a single degree of freedom systems on top of square concrete foundations. The soil is represented as a homogeneous halfspace or a horizontally layered medium. A uniform metasurface consisting of identical resonators on a homogeneous halfspace is considered first. The wavenumber-frequency spectrum and transfer function show a clear narrow band gap around the resonance frequency of the oscillators. This band gap is widened over a broader range of frequencies (40 – 70 Hz) using so-called classical and inverse metawedges, evoking rainbow trapping or conversion of surface waves into bulk shear waves, respectively [4]. For layered soil conditions, a uniform metasurface creates a partial band gap where mainly the fundamental mode is affected. The transfer function at a receiver behind the metasurface shows a shift in frequency. At a single frequency, non-uniform attenuation is found behind the metasurface, in contrast to the uniform attenuation observed in a homogeneous halfspace. Vibration mitigation in a wide frequency band still emerges using metawedges. Their efficiency, however, is reduced and the surface-to-shear wave conversion evoked by inverse metawedges in homogeneous media is no longer observed. We are presently performing analyses for moving loads on layered media with seismic metasurfaces. [1] S. Brûlé, E.H. Javelaud, S. Enoch, and S. Guenneau. Experiments on seismic metamaterials: molding surface waves. Physical Review Letters, 112(13):133901, 2014. [2] A. Palermo, S. Krödel, K.H. Matlack, R. Zaccherini, V.K. Dertimanis, E.N. Chatzi, A. Marzani, and C. Daraio. Hybridization of guided surface acoustic modes in unconsolidated granular media by a resonant metasurface. Physical Review Applied, 8:054026, 2018. [3] P.-R. Wagner, V.K. Dertimanis, I.A. Antoniadis, and E.N. Chatzi. On the feasibility of structural metamaterials for seismic-induced vibration mitigation. International Journal of Earthquake and Impact Engineering, 1(1-2):20–56, 2016. [4] A. Colombi, D. Colquitt, P. Roux, S. Guenneau, and R.V. Craster. A seismic metamaterial: The resonant metawedge. Scientific Reports, 6:27717, 2016.