Deriving parameters for the characterisation of the railway track quality in relation to environmental vibration Hielke Zandberg 1 ProRail Moreelsepark 3, Utrecht Agnes van Uitert 2 ProRail Moreelsepark 3, Utrecht Arnold Koopman 3 Level Acoustics & Vibration De Rondom 10, Eindhoven ABSTRACT Unevenness in track geometry, like longitudinal waves, track stiffness variations in transitions zones near bridges or culverts and irregularities like welds, insulated joints, switches and crossings, etc. induce dynamic forces into the wheel-rail interface of train and track. They are an important source for ground-borne vibrations. In the Netherlands, track unevenness is monitored to facilitate maintenance management using a Track Recording Car (TRC). Data of the TRC measuring campaigns is stored and available for stakeholders working in the field of rail maintenance or railway engineering. A database has been build using historical data of the TRC measurements dating back to 2013, together with meta data of track components such as insulated joints, switches, crossings, culverts, etc. To analyse the data, new parameters were defined how to best summarise PSD (Power Spectral Density) diagrams for characterising the track quality concerning environmental vibrations. This paper will show how these parameters can be used to compare track quality and quality of track components regarding environmental vibrations. The study analyses differences in track quality near transition zones like bridges, crossings and culverts in relation to vibration values. Results show that these parameters can give insight to railway professionals how to assess track quality and quality of track components in relation to vibration levels in dwellings nearby the track. 1. INTRODUCTION

Surfaces of railway tracks are not entirely smooth. Irregularities like welds, insulated joints, switches and crossings, and track stiffness variations in transitions zones near bridges or culverts, induce dynamic forces into the wheel-rail interface. In the long run these forces introduce unevenness in track geometry like longitudinal waves. In the Netherlands and many other countries track (and

1 Hielke.Zandberg@prorail.nl 2 Agnes.vanUitert@prorail.nl 3 Arnold.Koopman@ levelav.nl

sl 4) inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS GLASGOW

rail) unevenness is monitored to facilitate maintenance management using a Track Recording Car (TRC), mainly to determine the need for maintenance such as tamping of the track ballast. Wavelengths down to 3 m are measured according EN standard 13848 every six months. In this paper two of three expressed wavelengths ( λ ) ranges are considered: D1: 3 m < λ < 25 m, and D2: 25 m < λ < 70 m. Since 2021 also the D0 wavelength range D0: 1 m < λ < 5 m is measured. Data of these TRC measuring campaigns is stored and available for stakeholders working in field of rail maintenance or railway engineering. Railway traffic is an important source of ground-borne vibrations. Frequencies between 2 and 80 Hz are important for the human perception of vibrations. This corresponds with wavelength between 20 cm and 20 m for train speeds between 40 and 140 km/h. To characterise the quality of the track in more detail often power spectral density (PSD) estimation techniques are applied, which calculates the energy of a signal in relation to frequency (see i.e. Esveld [4], paragraph 16.12.3). In this case in relation to wavelength for a given track section. When complaints about rail vibrations are received from dwellings nearby a railway track, PSD diagrams are also produced from the TRC data to analyse track quality. There is a need to characterise track quality in relation to environmental vibration levels caused by passing trains on a larger scale. TRC data could then also be used to determine locations with possible risks for complaints. Different type of track components could also be compared in relation to the vibration emission. Therefore a study was conceived to develop parameters how to best summarise PSD diagrams of TRC data. These parameters should also be able to describe track unevenness and quality of track components in relation to environmental vibrations. Track components like crossings, bridgeheads, insulation joint, etc. contain track stiffness variations in longitudinal direction causing dynamic forces in the rail wheel interface and over time track unevenness, which will in turn emphasise dynamic forces and thus in time cause a further increase of the track unevenness. When vibration quality parameters are applied to historical TRC data, track quality and quality of different track components can more easily be analysed in relation to vibration emission. Vibration quality parameters can also be used as output in vibration emission models for railway tracks. This will help to get a better insight the vibration emission of track components or help to improve track design or track maintenance in relation to vibrations. Last but not least, vibration quality parameters can also be used as input for vibration propagation models, like those used for environmental assessment studies. 2. DESCRIPTION OF THE DATABASE

For this study a database was built merging historical data of the TRC measurements back to 2013 with Prorail meta data of track components such as: insulated joints, switches, crossings, culverts, bridgeheads, etc. These meta data consists of, next to coordinates, information such as: brand, type, year of installation, etc. TRC data in the EN 13848 D1 and D2 wavelength range were collected in the database. Due to a spatial resolution of 25 cm and 7000 4 km of measured track, this resulted in approximately 28 million datapoints for each measuring campaign. In total, data from 13 measuring campaigns could be stored in a database covering 7 years of measurements. This data could be merged with metadata of track components using a ProRail unique identifier earmarking each track branch between two switches together with GPS data. The data structure was build using MatLab. The database consists nearly 49,000 insulation joints, 6704 railway crossings,

4 The total route length of the Dutch railway infrastructure is nearly 3500 km. Part of it is double track or multiple track, the combined total track length is 7079 km

4622 culverts, 1545 steel bridges and 2251 concrete bridges. Data of switches could not be merged properly regarding its complexity with its stiffened frog points, turnout radius and insulated joints. 2.1 Designing parameters in the wavelength domain The EN 13848 distinguishes four principal geometric parameters; Longitudinal level (difference in height), alignment (deviation or shift in the horizontal plane),gauge (distance between the two rails), and twist or cant ( the rate of change in elevation between the two rails of a track). With increasing wavelength the amplitude of track irregularities increases. It is common practice to use power spectral density functions to analyse track quality in more detail. Environmental vibrations are strongly spectral related due to resonance effects in the track train interface or in different parts of a building. For instance, resonance effects of light-weight floors. For the vibration quality descriptor, the wavelength range representing geometrical irregularities between 1.6 m < λ < 12.5 m was divided into nine 1/3 octave bands. This gives us on the one hand detailed spectral information but on the other hand limits the number of additional fields in the database. Since the maximum train speed in the Netherlands is 140 km/h for most routes, wavelengths up to 12.5 m represent vibration frequencies down to 4 Hz. Ntosios [1] et. al. show that the axial rotation of wheelsets (roll) due to uncorrelated unevenness of the two rails is of a secondary effect for frequencies below 50 Hz. For the definition of vibration quality therefore only longitudinal level and alignment data were used for vertical respectively horizontal vibrations. The TRC data of the two rails were averaged, using the averaged Longitudinal Level

 and averaged Alignment Level 
 similar to track quality indicator (TQI) described in 5.4.1 (EN 13848-6). Ntosios et.al. also conclude that unevenness wavelengths of two rails can be considered strongly correlated for wavelength longer than 3 m. However, to simplify the track vibration quality parameter TRC data for wavelengths shorter than 3 m were also averaged. Figure 1: An example of a PSD (thin blue line) and its integration towards a 1/3-octave (dark blue bares) and octave (light blue bars) spectra

white noise

second derivative is white noise

107 11. (1/m]

For practical reasons, the descriptor applies a PSD over a 200 m track segment giving a sufficient number of waves in the defined sample length for the longer wavelengths up to 12.5 m. A 200 m track segment neglects the influence of the bogies at both ends of trains longer than 200 m. This seems a reasonable assumption since typical situations with perceived nuisance are found in dwellings within a range of 50 m from the track. Moreover the maximum length of freight trains is 740 m but only a limited number of bogies will add to the perceived vibration in the vicinity of a railway track. In the 3 to 10 meter wavelength range there is a steep slope in the PSD spectrum (see figure 1). Any integration towards broad bands will weigh the contribution of the longer wavelengths within the band stronger than the shorter ones. For the purpose of the sought for descriptor, which mostly comes down to comparison of sites, this weighing is unwanted. To overcome it, this part of the spectrum is double differentiated in the space domain first, before integrated, in the wavelength domain, to broad bands. Another justification of the double differentiation comes from information theory. Any truly random system, so containing no information, having maximum entropy, has a “white noise” spectrum. Any information, such as the influence of a discrete rail support, appears as a divergence from that baseline. The first three 1/3-octaves (describing the longest wave lengths) indeed follow the slope of white noise. For the other six, it is the second derivative that provides the white noise baseline. Finally, it should be noted that double differentiation in the space domain is equivalent to double differentiation in the time domain, given a certain (train) speed. That implies that the result is equivalent to acceleration, such as the one that is often measured on the axle. Combined with the inertial masses of a train and Newton's second law, this in turn relates to forces on the track. There is a sharp drop in the signal for the wavelengths shorter than 3 m due to the low pass filter in the equipment of the TRC for wavelength shorter than the D1 range (3 m < λ < 25 m). The 9 values of each 1/3-octave band is also summarized in one single RMS value for the whole wavelength range. 2.2 Designing parameters in the space domain Measurement guidelines for assessing vibrations annoyance often use indices based on RMS values over a defined time frame, like the British standard BS 6841 or indices based on a maximum value over a time frame, like the German DIN 4150-2 or the Dutch SBR-B guideline. Similar two parameters were defined for the vibration quality descriptor: RMS and Max fast describing an average wavelength value respectively a peak value of a 200 m track segment: − The "RMS" value representing the average quality of the segment based on the PSD. For every 1/3-octave band the RMS value of a 200 m segment was calculated. The RMS value was chosen to represent the line source of a passing train because only a limited number of bogies will add to the perceived vibration in the vicinity of a railway track. (see formule 1) − The "Max fast", representing the maximum value in the middle 1 meter of the 200 m track segment using an exponential window with a decay ( Λ ) of 2 meters (see also formule 1). The choice for 2 meters is based on the following consideration. For common train speeds the exponential spacial window should coincide as much as possible with the exponential time window used in the Dutch metric for vibration annoyance (Vmax) while enough data points should be available for a meaningful convolution integration. An optimum was found at 2 meters, coinciding with 1/8 seconds at 60 km/h and 8 datapoints given the current spatial sampling at a rate of 25 cm. Track components like culverts, railway crossings, joints, etc. can be regarded as a point source. Due to poor maintenance, one might expect sharp irregularities over time in rail geometry near these components.

D = function of aberrations x in the wavelength domain D0, D1 or D2 Δ = 200 m segment

   =   



(1)





Λ = window parameter 2 m ,    =  1



    .   −

(2)

!

2.3 The track vibration quality descriptor and its parameters In total the descriptor for the track vibration contains 40 parameters: 4 parameters for each 1/3-octave band over a 200 m window: - H RMS , the RMS value (height) of the longitudinal level LL over a 200 m window - H MAX fast, the maximum value (height) of the longitudinal level LL in a 200 m window - S RMS, the RMS value (shift) of the alignment AL in a 200 m window - S MAX fast , the maximum value (shift) of the alignment AL in a 200 m window Nine 1/3-octave bands times four parameters yields 36 parameters, plus 4 parameters representing the RMS and the Max fast value for the whole wavelength range for height and shift.

1/3 octave wavelength band (m)

RMS 11 9 7 5,5 4,5 3,7 3,1 2,6 2,2

H RMS height 0,40 0,41 0,39 0,36 0,34 0,33 0,15 - -

S RMS shift 0,22 0,19 0,15 0,13 0,15 0,22 0,13 - -

1/3 octave wavelength band (m)

Max 11 9 7 5,5 4,5 3,7 3,1 2,6 2,2

H Max height 0,36 0,36 0,37 0,26 0,16 0,09 0,03 - -

S Max shift 0,21 0,17 0,14 0,09 0,07 0,06 0,02 - -

Table 1: Normalised 5 RMS and Max track unevenness values for a sliding 200 m segments in 2020 for the Dutch railway network Table 1 shows the calculated RMS and Max fast parameters of the Dutch railway network for a sliding 200 m segment with a 1 m step size of the 2020 measuring campaign. The two 1/3-octave bands 2.6 and 2,2 are left blank due to the low pass filter in the TRC. The Max values represent an average over the whole network calculated from the max values in every 1/3-octave band for each 200 m segment of the Dutch track. The Max values in table 1 are lower compared to the presented RMS values due to a different treatment of the data. Therefore the RMS and Max values have no clear dimension. (see also footnote 5 below).

5 The reference value for the 1/3-octave bands 11, 9 and 7 is 1 mm, the reference value for the 1/3 octave bands 5,5 to 2,2 is 1 mm/s 2 due to the double differentiation of these wavelengths.

3. SOME BRIEF RESULTS

Specific parts of the network, for instance crossings and bridges, show increased values. To demonstrate this, figure 2 shows H RMS values of table 1 representing the average vibration quality over a sliding 200 m track segment of the Dutch railway network (black line in bold) compared to the values for various assets (other colours). The graph shows a relatively smooth spectrum across the left six 1/3-octave bands but is declining sharply for wavelengths shorter than 3 m due the low pass filter. The calculated PSD values for these wavelengths ( λ < 3 m) are much smaller. The plotted error bar in the figure represents the standard deviation.

─┼─ all track total network

┼ steel bridges

┼ crossings

┼ culverts

┼ concrete bridges

Figure 2: Average normalised H RMS in 2020 of the Dutch railway network per 1/3-octave band. The coloured lines in the graph represent the deviation of H RMS values of different track components for each 1/3-octave band. As expected, track segments which include a component like a crossing (green error bars) or culvert (blue error bars) vary statistically more in regard to regular track segments (bold black line and error bars). Segments containing steel bridges (red error bars) however vary even beyond the average of the network. Apparently, irregularities in the vicinity of a bridge spread over time and over a longer distance resulting in a higher H RMS values of these 200 m segments. 3. COMPARING RAIL COMPONENTS WITH AVERAGE RAIL QUALITY

RMS [-] | 06 04 02 5.5 45 37 wavelength [m]

Variation in track stiffness can be observed at rail components like switches, joints or crossings. In urban areas these track components can be regarded as a point source of railway vibrations for dwelling nearby the track. Over time differences in soil or ballast compacting near these points will occur due to the dynamic forces of rail traffic running over the component which leads to enhanced unevenness of the track. The H max value of a 200 m segment represents this effect. The black line in figure 4 shows the variation of the H max parameter in the Dutch railway network. Compared to the graph in figure 3, the H max value is declining more strongly in the 1/3-octave wavelength bands shorter than 5.5 m. This stronger decline is due to the fact that the double differentiation that is used for RMS had not been implemented for Max,fast in this study. Double differentiation also for Max,fast will be implemented in the future though.

─┼─ all track total network

┼ steel bridges

┼ crossings

┼ culverts

┼ concrete bridges

Figure 3: Normalised H max values in 2020 of the Dutch railway network per 1/3-octave band The H max value of steel bridges (red error bars) and crossing (green error bars) show more variation compared to the H max of regular 200m rail segments in the network without a specific track component. This is as expected for that uneven track is commonly observed near crossings and bridges. The H max value of culverts (blue error bars) also shows more variation compared to the average value of the network, but not as prominent. In the Netherlands, a different type of railway crossing has been applied for several years, based on solid rubber panels resting on sleepers. It is assumed that this concept leads to less track unevenness level over time. In this study the H max value in the 4.5 1/3-octave wavelength band was more closely analysed for railway crossings. Figure 5 shows the H max distribution in the 4.5 1/3 octave band of the Dutch railway network, railway crossing with a traditional design based on concrete plates and a crossing based on a concept of solid rubber panels.

Max [- 05 55 45 wavelength [m]

number [#] 05 crossings, rubber 1 15 Hays 5¢* third octave [-] ref 1 mm/s 25

Figure 4: H max distribution of the 4.5 1/3-octave wavelength band of regular track, railway crossing and railway crossings with solid rubber panels.

number [#] 10° 7000 km of track 7000 km of track nenecince netmisbes |

The distribution of H max of regular track has all the features of a log-normal distribution function, hence the long tail in the right half of the graph. The H max of railway crossings also seems to be a log-normal distribution. The P50 values (blue vertical lines in the graph) of railway crossings with concrete plates are almost three times the P50 value of regular track. Instead, the P50 value of railway crossing based on a design with solid rubber plates is a little higher. The difference of the P90 values in the graphs are more prominent. The same analysis was applied to various types of insulation joints but no clear differences between insulation joints could be distinguished. 4. COMPARISON WITH THE EN 13848-6 TRACK QUALITY INDEX.

In this study the correlation between the above newly defined descriptor and the EN 13848-6 track quality indicators (TQI's) based on standard deviation was investigated. A poor correlation was found between, on one hand, the track vibration quality parameters Hmax, H RMS, Smax, S RMS and, on the other, the often used chord of the corresponding longitudinal level

 respectively alignment level 
 values . This demonstrates that the track vibration quality parameters contain different, so extra, information. 5. CONCLUSIONS

The vibration track quality descriptor contains new additional parameters to analyse rail track and rail components in relation to environmental vibrations. The vibration track quality descriptor summarises track unevenness for wavelengths in the range from 2 to 12.5 m. The RMS values represent the overall unevenness of 200 m rail segments. The Max values represent local track stiffness discontinuities that can act as point sources in urban situations, like crossings and insulation joints. The newly defined parameters can be used for assessment of track maintenance levels over a long- time span when historical TRC data from various measurement campaigns is stored in a database. With help of the defined parameters for height and shift aberrations, TRC data can easily be merged with meta data of track components in a database. This enables new analyses of track components in urban areas with potential risk of environmental vibrations. The vibration quality descriptor and its containing parameters RMS and Max give an additional insight in track quality compared to the EN 14848-6 track quality indices which is demonstrated by the poor correlation that was found between the RMS and Max parameters on the one hand and defined TQI's for longitudinal level

 and alignment level 
 on the other hand. The parameters RMS and Max are suitable to be used as input parameters for vibration calculation models. Vibration prediction models for railway vibrations, like the Dutch model OURS or the Shift2Rail Silvarstar model, use track quality parameters to describe wavelength unevenness of railway tracks. The parameters discussed in this paper can also be used as an output parameter for calculation models which describe the degradation of railway track over time. The output can be used to assess the risk of vibration annoyance in relation to maintenance levels. Examples of track degradation which will effect vibration emission can be found near stiffness variations, e.g. track segments with components like railway crossings, insulation joints and other components with stiffness variations commonly found nearby dwellings close to the track. 6. REFERENCES

[1] Evangelos Ntotsios, David Thompson, Mohammed Hussein.(2017). The effect of track load correlation on ground- borne vibration from railways, Journal of Sound and Vibration 402 (2017) p142-163 [2] EN 13848-5, Geometric quality levels - plain line, switches and crossings [3] EN 13848-6, Characterisation of track geometry quality [4] Coenraad Esveld, Modern Railway Track - Second Edition, Delft 2001