1. Introduction
A prerequisite for safe and reliable rail system operation is an adequate assessment of rail-track quality based on the detected track geometry deviations or irregularities. Longitudinal level, horizontal alignment, gauge, cross-level, and twist are the five track geometry parameters used to effectively describe the track condition [
1]. Track quality is defined by calculating the track quality index (TQI) on both high-speed and conventional standard gauge rail-track systems. This numerical value represents the relative condition of the abovementioned track geometries [
2] over a track segment of a specific length.
Segments on which the TQIs are calculated are defined as linear track geometry datasets with homogeneous characteristics of track-geometry degradation influential factors [
3]. These factors can be classified into three groups: influential factors of designed alignment; influential factors of track structure; and influential factors of rail traffic [
4]. The degradation of the track geometry is primarily due to the action of dynamic vehicle loads caused by irregularities on the contact surface of the wheels and rails or in the horizontal track alignment. Higher track-exploitation intensity and the speed of rail vehicles result in a higher degradation rate [
5,
6]. In terms of structure, using rails with a higher steel hardness and its elastic fastening can slow down the degradation process [
7,
8]. The design of the horizontal track alignment also has a significant effect, especially the track curvature—the degradation of the track geometry on horizontal curves is faster than on the straight parts of the route [
9,
10,
11]. In addition, one must not ignore the elements that could influence the overall track geometry condition on a segment, such as switches, stops, bridges, or level crossings.
According to [
3], the first studies of the conventional track geometry degradation analyses began during the 1980s and 1990s, when the track data availability, especially in a digital format suitable for thorough analysis, was very modest. Historically, the data were collected with track-recording cars, which produced statistically processed data (e.g., standard deviations) for fixed 100 m, 200 m, or 1 km long segments. This “fixed segment” was too rigid to demonstrate the actual degradation of the geometry along the track. Consequently, more sophisticated segmentation processes were developed. Today, track-recording cars can collect and store high-resolution track data, ensuring that identified individual segments behave as uniformly as possible throughout the track exploitation process.
There are different procedures for TQI calculation adopted in railway systems around the world. Most of them use longitudinal level and horizontal alignment at least to represent the condition of the track [
12]. TQIs calculated on segmented rail networks can be sorted into two main categories: (1) objective or single TQIs, which are expressed separately for each geometry parameter; and (2) artificial or synthetic TQIs, which combine and merge different track geometry parameters into a single index [
13,
14]. The main difference between them is the base on which the TQI is calculated: as a standard deviation, an average value, or a weighted value over a track segment [
15]. Once calculated, TQIs are compared to maximum permitted values, most often depending on the rail line speed, and then the decision on track maintenance is made.
In addition to different calculation approaches, different TQIs are expressed for different track segment lengths, usually 3–25, 25–70, and 70–200m long [
16]. The 200m long segment is used most often, but in some cases, a particular track or entire network is evaluated based on only one TQI value [
14]. Recent studies of tram track quality used different techniques for determining the track segment: based on the type of track construction [
17] or based on the horizontal elements of track alignment (straight, curve, and curve with transition curve segments) [
18]. Both approaches resulted in segments of variable length along the network. Newer studies have suggested that the decision on track segment length needs to be based not only on the track technical parameters but also on the economic and operational aspects of track maintenance [
19].
Many cities worldwide that have retained the traditional tram systems dating back to before the First World War are trying to upgrade their maintenance procedures by introducing TQIs. However, they are facing several problems. The main one is documenting the tram infrastructure in digital databases, which is the prerequisite for any effective track segmentation, geometry evaluation, and maintenance planning. In addition, the actual knowledge of the track condition is limited to a small number of maintenance employees, and most of them do not have any tools for collecting, systemizing, and integrating the data covering the design, construction, operation, and further maintenance of the tracks. Such data could be stored in databases which would provide data for conducting the assessment of the track quality and maintenance needs [
20,
21]. Operators of most European urban rail systems carry out the track geometry quality assessment based on controlling the individual measured values of track geometry parameters concerning the permissible values prescribed by internal regulations [
22]. Such is the case with tram operators in the Republic of Croatia, ZET in the City of Zagreb, and GPP in the City of Osijek. Both operators control the quality of the tram track by using the same internal regulations, where only the most significant permissible deviations of track geometry parameters immediately after track construction and before reconstruction are defined [
23].
Applying the best practices of the track quality evaluation established for classic ballasted rail on tram networks would be most desirable. However, the procedures described in the literature [
13,
14,
15,
24] cannot be applied to tram tracks. The main reason for this is the questionable cost-effectiveness of procuring sophisticated track-recording cars for small tram networks consisting of only a few tens of kilometers of tracks. If the measurements are executed with manual tools, such as measuring rods or by manually operated track geometry trolleys, i.e., in unloaded track conditions, the maximum permitted values of the TQIs cannot be utilized. The other reasons are significant differences in track design requirements and exploitation conditions (the track location, geometry design parameters, construction elements, vehicles, and traffic characteristics) between the tram and conventional ballasted rail tracks [
22], defined as the critical geometry degradation influential factors [
5,
6]. These differences are primarily the consequence of small distances between the tram tracks and the surrounding facilities and requirements for the rational use of urban traffic areas. These requirements often include narrow-gauge tracks, tight horizontal curves of only 18(20) meters’ radius, and a lack of transition curves and cant.
For this reason, the tram vehicles are of smaller dimensions and weight (the tram axle load is usually twice as small) and with different undercarriages than conventional trains. The latter is particularly pronounced in the case of modern low-floor trams. The differences are also reflected in the tram traffic-flow characteristics given the movement priority and speed. Tram speed is low and very variable along the route due to the small stop distance. Such distances usually vary from 250 to 500 (800) meters, and include crossings where tram vehicles do not have priority to pass. Additionally, due to a lack of space in the densely built-up urban centers, trams often must share the lanes with road vehicles and therefore adjust (primarily reduce) their speed [
25].
For the same reason, the tram tracks’ superstructure is often built on continuously reinforced concrete slabs, with continuously welded grooved rails enclosed in pavement construction [
26]. The tram networks are usually upgraded over long periods, so the homogeneity of the geometry degradation influential parameters along the tram tracks is very low. In addition, they are deeply rooted in the urban fabric, which complicates track geometry measurement, maintenance, and reconstruction, especially in large tram–road intersection zones. This concludes that due to the differences in the track geometry data collection process, track design, and operational requirements of conventional and tram tracks and vehicles, the track quality analysis of narrow-gauge tram networks should be performed on shorter analytical segments [
14], by using a holistic TQI calculation approach with adjusted limit values.
The research presented in this paper had two main objectives: (1) to assess the narrow-gauge tram-track geometry quality through the application of established synthesized TQI by using geometry measurements collected in unloaded track conditions; and (2) to analyze how a change in the analytical segment length affects the track geometry assessment. The research was conducted using tram network data (alignment, structure, and exploitation conditions) and five geometry parameter values measured by a trolley, manually operated along the 27.5 km of tram tracks in the City of Osijek. To avoid possible misconceptions, two different synthesized TQIs established for conventional rail systems—one based on a weighted value and the other based on standard deviation—were calculated on consecutive 200-, 100-, 50- and 25m long analytical tram-track segments. The conducted comparative analysis of the TQIs calculation results demonstrated and quantified the effectiveness of the analyzed segmentation concepts in the tram-track quality assessment and provided further insights for establishing TQIs implementation at a broader scale by the owners of tram infrastructure.
3. Results
The five-number descriptive statistics for the calculated values of W and J indices by lengths of the analytical segment are given in
Table 5. The values of the W index on the analytical segments range between 0 and 1, where the value of the median, depending on the length of the analytical segment, is between 0.33 and 0.42. The values of the J index calculated on the same analytical segments range between 0.00 mm and 5.52 mm, where the value of the median, depending on the length of the analytical segment, is between 0.73 mm and 1.40 mm.
The distributions of the calculated W and J indices according to the track sections and analytical segment lengths are presented in
Figure 7. Each row presents the distribution of the synthesized index on L1, L2A, and L2B track sections calculated on consecutive segments, from top to bottom: 200-, 100-, 50-, and 25m long segments.
One can see in
Figure 7 that there is a certain regularity in the distribution of both TQI calculated values, i.e., that the calculated TQI values for the analytical segments are proportional. Furthermore, reducing the analytical segment length in the case of the W index leads to a redistribution of the W index on shorter analytical segments while retaining the value level in relative terms. In the case of the J index, reducing the analytical segment length reduces the value of the J index on shorter analytical segments.
The distribution of the W and J indices calculated for different analytical segment lengths is presented in
Figure 8. Their values are displayed as stacked bar lines. The bar line closest to the center line presents track geometry quality calculated for the 200m long analytical segment. Calculated W index values are categorized using different colors, where the green color indicates good quality (W < 0.2), the yellow color indicates satisfactory quality (W < 0.6), and the red color indicates insufficient quality (W ≥ 0.6) of the track geometry in operation. The distribution of the J index values is presented in a similar way, where the J index values are classified according to colors with a step of 2 mm.
Table 6 presents the share of W and J index limit values calculated for different segment lengths regarding the length of the entire network. Reducing the analytical segment length increases slightly the share of tracks with a good track quality W < 0.2 while the share of tracks with unsatisfactory track quality W > 0.6 decreases. On the other hand, reducing the analytical segment length significantly increases the share of segments with J < 2 mm and reduces the share of tracks with J > 4 mm.
4. Discussion
The distribution of calculated values of the W and J indices along the Osijek tram network confirmed that the tram-track geometry quality depends on exploitation intensity and is significantly influenced by the type of rail fastening, curvature of the alignment, and position of the tracks in the urban network. Most of the analytical track segments not constructed with the discrete double-elastic rail fastenings showed insufficient track geometry quality. Furthermore, on sections with the same tram-track construction type and exploitation intensity, the tram-track geometry quality was poorer on the analytical segments in the curves of small radii than the ones located in the straight line. Finally, the analytical segments along intersections or stops showed faster track-quality degradation than those not affected by road traffic.
By comparing distributions of W and J values over track sections for the same analytical segment length, similarities in the behavior of both indices were observed (
Figure 9).
The relations between the W and J index values calculated for the same analytical segment are presented in
Figure 10. The decrease in the analytical segment length causes the grouping of segments with extreme values of the W (0.0 and 1.0), while at the same time, the J value uniformly decreases.
By analyzing the change in the track geometry quality depending on the analytical segment length, it was noticed that the change in the segment length has a different effect on the value of the calculated W index than on the value of the calculated J index (
Figure 7 and
Figure 8). Track geometry quality defined by the W index changes as the length of the analytical segment decreases. For example, individual shorter analytical sub-segments, which belong to the same 200m analytical segment, progressed to poorer track quality (larger W value). In contrast, the remaining sub-segments progressed to better track geometry quality (smaller W value) than the corresponding 200m analytical segment. However, by reducing the analytical segment length relative to the 200m length of the segment, the value of the J index on individual shorter sub-segments was less than or equal to the value of the J index of the corresponding 200m analytical segment. To obtain more information on what happens to the W and the J indices values with the change in the analytical segment length, the average, maximum, and minimum values of the calculated indices, depending on the length of the analytical segment, were compared to the value of the corresponding calculated index values for the 200m-long analytical segment. The results are shown in
Figure 11.
Compared to the W value of the corresponding 200m long segment, the average value of the W index on shorter sub-segments remains unchanged. On the other hand, reducing the analytical segment length increases the maximum W value while the minimum W value decreases. In other words, a decrease in the length of the analytical segment along 200 m of tracks will increase the value of the W index on a few sub-segments, while on the remaining sub-segments, there will be a decrease in the value of the W. The average value of the W on the short sub-segments will be relatively equal to the W value on the corresponding 200m-long segment. The same analysis shows that decreasing the analytical segment length causes the average and minimum J index values to decrease while the maximum value of the J index stays the same relative to the value of J for the corresponding, more significant 200m segment.
Calculated J index values for all analyzed analytical segments did not exceed 5 mm. By comparing the calculated to the prescribed allowable J value of 12 mm for a speed of 30 km/h, it could be concluded that the tram tracks in the City of Osijek are in good condition. However, considering that the tram track was measured in unloaded conditions and that the tram tracks constructed on the concrete slab showed very small deviations of horizontal alignment and longitudinal level, the correctness of applying the synthetic J index (or its allowable values) in assessing the tram track geometry quality is questionable. Future research should explore the possibility of modifying the J index calculation, as well as re-defining the allowable values of horizontal alignment and longitudinal level for tram track geometry measured in unloaded track conditions.
5. Conclusions
The track geometry quality assessment can be performed in two ways, by comparing the individual measured values of the track geometry parameters concerning the allowable tolerances or by calculating the TQI along the track segment of a specific length. The established TQIs are mainly intended to assess the track geometry quality for high-speed and conventional standard-gauge railways and broad-gauge railways, where track geometry data are collected by track recording vehicles in loaded track conditions. They are commonly calculated as standard deviations or average or weighted values over a 200m long track segment. A comparison of the five narrow-gauge tram-track geometry parameters recorded on the Osijek tram network with a manually operated trolley in unloaded track conditions with the prescribed permissible tolerances defined for measured values collected in loaded track conditions showed that the measured values of individual tram-track geometry parameters are significantly lower. This is especially true for horizontal alignment and longitudinal levels, where the application of prescribed tolerances in track quality assessments could lead to the conclusion that the track quality is good or that these parameters do not affect the calculated value of TQI. Additionally, the heterogeneity of tram-track geometry degradation influential factors cannot be adequately considered by analyzing the fixed 200m long track segments. From the above, several questions arose: (1) how to assess the tram-track geometry quality by using measurements collected in unloaded track conditions; and (2) whether and how a change of the analytical segment length affects the track geometry assessment.
The goal of the investigation presented here was to answer these questions by performing the track quality assessment on the Osijek tram network using two essentially different TQIs, W and J indices. The calculation of the W index was based on the ratio of geometric values that exceeded permissible tolerances. Permissible tolerances (explicitly defined for this investigation as Alert Limits) were established in coordination with the tram track manager and considering the experience gained with track geometry quality analysis of tram networks with similar characteristics. The calculation of the J index was based on weighted standard deviations of track geometry parameters. Both TQIs were calculated for the entire 27.5 km of operational narrow-gauge tram track on consecutive 200-, 100-, 50-, and 25m-long analytical track segments. The following conclusions were made:
Track segmentation has a significant role in assessing the tram track quality based on track geometry deviations or irregularities and planning track maintenance or reconstruction;
By reducing the length of the analytical segment, the resolution of the tram-track geometry quality analysis grows, which means that it is possible to determine the sections of the tracks with insufficient quality more precisely by increasing the number of the analytical segments;
Both TQIs can be effectively used for tram-track geometry quality assessment. However, the W index, based on a weighted value of geometry deviations over an analytical segment, is less sensitive to a reduction in the segment length than the J index based on the standard deviation of geometric parameters–the decrease in the analytical segment length enlarges the number of segments with extreme values of W. At the same time, the J value uniformly decreases;
The segmentation process must be aligned with the tram track maintenance and reconstruction procedures. It should consider the following aspects affecting the choice of analytical segment length: which track repair/reconstruction technology will be applied; the allocated funds; and how the planned work will impact public and personal traffic along with the track segments.
Once the segments are defined throughout the entire tram network, it will be possible to develop models of track quality degradation (based on the results of geometry monitoring), which is essential for establishing more efficient, predictive tram track maintenance.