paper ID: 284/p.1
Development and Experimental Validation of a Prediction Model to Assess Railway Traffic Induced Vibrations M. Crispino a , M. D’Apuzzo b and R. Lambertic a
DIIAR, Polytechnic of Milan, Via G. Di Biasio, 43, 03043 Cassino (FR), Italy,
[email protected] b DIMSAT, University of Cassino, Via G. Di Biasio, 43, 03043 Cassino (FR), Italy,
[email protected] c DIT, University of Naples, Via Claudio, 21, 80125 Napoli, Italy,
[email protected]
Railway traffic undoubtedly represents one of major sources of vibration. Within the Environmental Impact Assessment (EIA) procedures, quantitative and qualitative evaluation of vibration level is needed. In the present paper a vibration level prediction model for a railway superstructure on an embankment has been developed. The generation of vibration due to the dynamic interaction between the wheel and the railway superstructures is modelled assuming a lumped mass parameter model describing the railway superstructure and an excitation due to a spatial Power Spectral Density (PSD) function of rail profile defects, whereas the propagation of vibrations through the underlying soil is modelled by means of a Finite Element (FE) model. This model, that has been also validated through field test, can be effectively used to study construction solutions, within railway superstructure, aimed at mitigating vibration annoyance.
1. INTRODUCTION Among the environmental factors related to the management of railway which are to be taken into account at the design level, vibrations play a critical role. Vibrations are cyclic phenomena that are mainly transmitted through a solid medium, in the form of volumetric, shear and Rayleigh waves. Those are responsible for an energy transfer along the space and the adsorption of this energy by physically (buildings) and physiologically (human beings) sensitive receptors represents a relevant problem for the deterioration of the environment and the associated quality of life. On a phenomenological point of view, the problem of railway traffic induced vibrations can be divided into three main phases: the generation phase, the transmission phase through the railway superstructure and the underlying soils up to the foundation of the buildings nearby and the reception phase. The generation of vibration induced by railway traffic is related to the dynamic interaction between the vehicle and the railway superstructure that, in turn, is affected by the unevenness of the surfaces coming into contact (due to the undulations of rail profiles and the wear of tyres) and the irregularities of vehicle motion (side motions). These latter are responsible for the generation of interaction horizontal forces that can affect the vehicle handling stability but the associated ground vibrations are not much significant for the environmental point of view and therefore will be not examined in the followings. Within the propagation phase, reflection, refraction, and diffraction of vibrations waves may take place due to the presence of surface discontinuities. In addition, overall and/or frequencydependent attenuation phenomena may occur making the analysis of the problem extremely complex. As far as the reception phase is concerned, nuisance level is affected by the entity, type and the duration of prevailing effects, on one hand, and, on the other, by the sensitivity of the receptor
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paper ID: 284/p.2
itself with respect to the several parameters characterising the vibration input (amplitude, frequency content, etc.). The quantitative prediction of the impact due to railway traffic vibration can be tackled by employing several models available in literature or by developing specific new ones. However, an experimental on-site calibration phase is often necessary in order to improve the prediction. On a methodological point of view, it worthwhile to separate the analysis of the problem into the three aforementioned stages by defining three main sub-systems: a generation model, a transmission model and finally a reception model. In present work, a combined generation and propagation mathematical model to assess vibration level induced by a railway line on an embankment has been developed. This model, that has been also experimentally validated, may be successfully employed in the study of the effectiveness of countermeasures, conceived within the railway superstructures, aimed at mitigating the vibration level.
2. DESCRIPTION OF THE MODEL 2.1. Generation model. As already stated, the source of vibration generated by the transit of a train is located at the wheel-rail interface and it is due to the dynamic interaction between the rail and the wheel and to the irregular components of vehicle motion. The unevenness of wheel-rail contact is due to two main factors: the rail-wheel wear process and the track structure degradation. According to former, due to the localised sliding phenomena occurring in the rolling motion, the surface of rail head, initially almost even, gradually becomes undulated and irregular and, on the other side, the circular wheel surface progressively becomes partially flattened and ovalized. As regards the track degradation, the variation of both the dynamic vertical overloads and the material mechanical properties along the line is responsible for the differential permanent settlements in the railway superstructure due to creep behaviour of ballast and sub-ballast layers and of subgrade materials. It can be easily understood that the process of vibration generation is selfexciting and increasing with time (i.e. with the cumulated traffic), furthermore, it is amplified by the little misalignments in the axle configuration [1-2]. In order to study the vertical dynamic vehicle-track interaction, it is worth to detect three main sub-systems: 1) the vehicle with its body, bogies and axles; 2) the wheel-rail contact and the description of the input excitation 3) the railway superstructure itself with rail, rail-sleepers connection elements (rail-pads), the sleepers and the sleepers’ support (from the ballast layer up to the subgrade). As far as the dynamic behaviour of the vehicle-railway track system is concerned, each of these sub-system is characterised by a typical vibration frequency range. As a matter of fact, it has been observed that oscillation of the sprung masses of the vehicle are mainly located in the 0-10 Hz range whereas oscillations of vehicle’s unsprung masses and of the overall track masses (these latter assumed to be connected to a continuous elastic support) can be found from 20 to 125 Hz. The natural vibrations of the intermediate elastic links of the track can be located in the 200-2000 Hz range. The three sub-systems are dynamically uncoupled and therefore can be separately analysed [2-3]. In this specific case study, it has to be underlined that, as the train travelling speed is rather low (40-70 Km/h), the contribution of the vehicle sprung mass modes to the overall vertical dynamic
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paper ID: 284/p.3
overloads transmitted by the vehicle axles, can be easily neglected. Similarly, the role of the higher vibration modes of the railway structure is significant only in the dynamics of high speed railways with velocity of 250-300 Km/h. Basing on these premises, a lumped mass parameter model in order to describe the dynamics of railway superstructure has been employed (Fig. 1a). Relevant track masses are connected in the vertical direction by means of complex springs taking into account both elastic and hysteretic behaviour. Detail of model parameter are reported elsewhere [3]. Several studies [2, 4] have shown that this approach, although rather simplified may provide reasonable good results.
WHEELS M 1 (Rail + Wheel mass) RAIL K 1*(Rail-Pad vertical Complex stiffness) RAIL-PAD M 2 (Sleeper + Ballast mass)
SLEEPER
K 2*(Ballast vertical complex stiffness)
BALLAST
(a)
(b)
Figure 1. Railway superstructure model (a); propagation FE sub-model (b). As a results of the wheel-rail wear process and the track profile degradation previously mentioned, the rail surface profile, after a certain time, can be described by a superposition of wave of variable amplitude and length. Several studies have highlighted that the rail profile can be conveniently described as a stochastic process that can be assumed stationary and ergodic and therefore can be synthetically represented by means of a Power Spectrum Density (PSD) Function of the vertical defects [1]. The PSD of rail defects assumed in this study is that proposed by French Railways (SNFC): GD ( f ) =
GD ( Ω ) = V
A
(1)
f V ( b + 2π ) 3 V
where GD(f) (in m2 /(cycles/s)) is the PSD of rail defects as a function of temporal frequency; GD(Ω) (in m2 /(cycles/m)) is the PSD of rail defects as a function of spatial frequency; f is the temporal frequency of rail defects, in cycles/s; Ω is the spatial frequency of rail defects in cycles/m; A is a parameter dependent on the age of the track, generally it is assumed A = 1E-6 or 2E-6 for new and old railway tracks respectively; b is equal to 0.36; V is the travelling speed on the line in m/s.
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paper ID: 284/p.4
2.2. Propagation model. As regards the propagation phase, two main modelling approaches exist in literature: the analytical one [5] and that employing the Finite Element method [6-7]. In this study, the latter approach has been chosen as although it provides less accurate results with respect to the former, nevertheless it allows a more refined modelling of on-site layout and soil stratification (Fig. 1b). The embankment and the underlying soil have been described by means of a two-dimensional plane strain model as for the specific near field vibration conditions, the vibration source can be assumed to be linear. Mesh discretisation has been selected basing on on-site soil mechanical properties, that have been derived from on-site geotechnical investigations, and maximum frequency of interest [3]. Model’s geometrical dimensions, in terms of lateral extension and vertical depth, have been chosen in order to detect an area into which most of the vibration phenomenon is supposed to be exhausted due to the radiation and material damping effects. The railway superstructure model has been mounted on the FEM propagation model and dynamic eigenvalue analysis has been performed taking into account the first 1000 modes occurring in the frequency range of interest, in order to derive the transfer function in the frequency domain between the dynamic force exerted on the rail and the vertical vibration velocity at a specific distance from the railway line.
3. VIBRATION MEASUREMENTS In the site examined, formerly known as the “Bargellino” area, there is a 500 m long section of the Milan-Bologna by-pass railway line. In this area the railway is on a 6 m high embankment, and several high precision work activities are close to the railway infrastructure. Vibration measurement have been carried out at variable distance far from the embankment base by means of four vertical geophones and a DATA-6000 digital acquisition system connected to a laptop with a 500 Hz sampling frequency. Vibration are reported in terms of Root Mean Square (RMS) of vertical velocity in third octave frequency band.
4. ANALYSIS CARRIED OUT AND RESULTS As some of model parameter undergo to some degree of uncertainty, a sensitivity analysis has been performed in order to better match theoretical and measured response. Different values of mechanical properties of embankment materials have been chosen with respect to the soil properties that were already known due to on-site geotechnical investigation. In detail, the dynamic response in the frequency domain has been computed according to different values of the ratio between the Young modulus Eemb of the embankment material and of the soil material Esoil (Fig. 2a). In addition, the frequency response has been evaluated by varying the participating mass, M2 , of the sleeper-ballast system in the lumped parameter model describing the railway superstructure (Fig. 2b). The lowest value of M2 has been chosen by assuming only the sleeper mass whereas the higher value by supposing the whole ballast and sleeper mass participating to the vertical track dynamics.
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paper ID: 284/p.5
RMS of Vertical Velocity at 10 m from embankment base
RMS of Vertical Velocity at 10 m from embankment base
0.1
RMS Vz [mm/s]
Eemb/Esoil =1.2 0.08 Eemb/Esoil =1.5 0.06 0.04 0.02
RMS of Vz [mm/s]
Eemb/Esoil =1
0.12
M2 = 2600 kg
0.1
M2 = 1640 kg
0.08
M2 = 440 kg
0.06 0.04 0.02 0
0 0
10
20 30 40 3rd Octave frequency band [Hz]
50
0
10
20
30
40
50
3rd Octave Frequency Band [Hz]
(b)
(a)
Figure 2. Influence of embankment material properties on the dynamic response (a); influence of the participating mass of the sleeper-ballast system, M2 , on the dynamic response (b). As it can be observed from the diagram depicted in the figure, the influence of the embankment material properties is rather negligible, whereas the value of the ballast-sleeper system is responsible for a frequency shift of the peak response: with increasing of M2 value the frequency of the peak RMS is decreasing as the first natural frequency of the track decreases. Therefore, this parameter plays a key role in the calibration of the theoretical model with respect to the experimental measurements. Furthermore, the influence of track age and train speed have been investigated (Fig. 3a). As it can be derived from the figure, doubling the A parameter or increasing the velocity from 50 to 70 km/h, induces a dramatic increase of the dynamic response in the whole frequency range of interest. Therefore an inaccurate evaluation of train speed or track age may result in a poor fit between the amplitude of the theoretical and experimental response. Basing on these premises, calibration has been carried out in order to improve the comparison between the predicted and the measured values. Final results have been conveniently depicted in the figure 3b. As it can be observed, the match between the predicted and the measured response, expressed in terms of RMS of vertical velocity for third octave frequency band, seems reasonably good. Although more measurements are needed in order to fully validate the model, the capability of describing the railway superstructure and the underlying soils in a more detailed manner seems to promote the use in the evaluation of vibration mitigation techniques within the railway track or located nearby (such as trenches).
5. CONCLUSIONS A coupled generation and propagation model to predict vibration level induced by railways has been developed. The model that has been experimentally validated, allows to take into account the dynamic interaction between the railway superstructure and the underlying soils. An additional experimental campaign is necessary to verify the model effectiveness in different contexts. However, by making use of this model, it may be possible to evaluate the effectiveness of anti-vibrating solutions aimed at mitigating the vibration level transmitted in the surroundings such as anti-vibrating railway superstructures, longitudinal trenches or combined solutions.
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paper ID: 284/p.6 RMS of Vertical Velocity at 2 m from embankment base
0.1
0.12
0.08
0.1
RMS of Vz [mm/s]
RMS of Vz [mm/s]
RMS of Vertical Velocity at 10 m from embankment base
0.06 0.04
A=1E-6 V= 50 km/h 0.02
A=2E-6 V= 50 Km/h
Predicted Measured
0.08 0.06 0.04 0.02
A=1E-6 V = 70 Km/h
0
0 0
10
20
30
40
50
0
3rd Octave Frequency Band [Hz]
20
40 60 80 3rd Octave Frequency Band [Hz]
(a)
100
120
(b)
Figure 3. Influence of rail age and train traveling velocity on the dynamic response (a); Comparison between the predicted and the measured response (b).
ACKNOWLEDGEMENTS Authors wish to thank Prof. Eng. Francesco Saverio Marulo and Eng. Bruno Maia for carrying out the vibration measurements.
REFERENCES 1.
R. Panagin, La dinamica del veicolo ferroviario, Libreria Editrice Levrotto e Bella, Torino, 1990.
2.
M. Crispino, Sovrastrutture ferroviarie per alta velocità: sviluppo di una metodologia di calcolo ed analisi teorico-sperimentale sul subballast per il miglioramento delle prestazioni, Tesi di Dottorato in Ingegneria dei Trasporti, Napoli, Febbraio, 1996.
3.
M. Crispino, M. D’Apuzzo, R. Lamberti, Sviluppo e validazione sperimentale di un modello di generazione e trasmissione delle vibrazioni indotte dal traffico ferroviario, Quaderni del Dipartimento di Ingegneria dei Trasporti, 104 Napoli (2000).
4.
K. L. Knothe, S. L. Grassie, Modelling of Railway Track and Vehicle/Track interaction at high frequencies Vehicle System Dynamics, 22, Ed. Swets & Zeitlinger (1993).
5.
L. Auersh, Wave propagation in layered soils: theoretical solution in wavenumber domain and experimental results of hammer and railway traffic excitation, Journal of Sound and Vibration, 173(2), pp. 233-264, (1994).
6.
H. Chua, Groundborne Vibrations due to trains in tunnel, Earthquake Engineering and Structural Dynamics, 21, pp. 445-489, (1992).
7.
R. Lamberti, M. Crispino, F. Ruocco, A finite elements model for investigation of screening effects for reduction of vibration from railway infrastructures, in 12-th International FASE Symposium "Transport Noise and Vibration", St. Petersburg, RUSSIA, September 23-25, 1996.
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