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Optimisation of track stiffness on the UK railways AUTHORS: Dr Mohamed Wehbi PhD, MSc, BSc, MPWI Senior Design Engineer Network Rail Peter Musgrave IEng, MICE, FPWI Lead Track Bed Design Engineer Network Rail The aim of this paper is to develop bespoke optimum value for track stiffness, with the aid of numerical modelling, for the UK railways to facilitate efficient and effective design and maintenance. INTRODUCTION The railway track is considered to be a structural system which is designed to withstand the combined effects of traffic and environment so that the maintenance cost and passengers safety are kept within acceptable limits and the subgrade is adequately protected (Burrow et al., 2009). If appropriate and timely maintenance is not carried out, speed restrictions may be imposed on the routes affected resulting in associated financial penalties and delays for customers. In order to develop robust railway track maintenance and design solutions it is necessary to adopt the use of appropriate measures of railway track performance. Generally, two types of measurements are carried out to determine track performance, namely; functional and structural. Functional measurements are associated with the way in which the track performs from the point of view of the user. Relevant measures include track geometry and ride comfort. The measurements of structural condition are associated with the structural integrity of the track system and include track deflection and stiffness, and are concerned with the long-term performance of the track (Tzanakakis, 2013). The effect of track stiffness on track performance can be categorised into two groups which relate to either deterioration due to the high value of track stiffness or deterioration due to low value of track stiffness. To control and manage track stiffness effectively, an optimum value for track stiffness is essential to support design and maintenance standards. There were a number of previous attempts to develop an optimum value for track stiffness; however, recent studies (Puzavace et al., 2012) have concluded that the optimum value for track stiffness is dependent on line specifications and a universally agreed value is not applicable. Therefore, the aim of this paper is to develop bespoke optimum value for track stiffness, with the aid of numerical modelling, for the UK railways to facilitate efficient and effective design and maintenance. TRACK STIFFNESS DEFINITIONS Vertical track stiffness is a function of the modulus of elasticity of different layers and components in the railway track system. There are a number of methods which can be used to represent track stiffness mathematically, depending on different factors such as isolating the stiffness of some components, frequency excitations and track stiffness non-linearity. In general, global track stiffness is the ratio of dynamic load applied over top rail deflection; however, it is difficult to determine the applied dynamic loads. Therefore, to overcome this problem, the global track stiffness can also be expressed, in a simplistic approach in terms of: track bed modulus, rail pad modulus and rail flexural bending as shown in equations 1 and 2 (Powrie & Le Pen, 2016). SIGNIFICANCE OF TRACK STIFFNESS THE EFFECT OF LOW TRACK STIFFNESS Equations 1 and 2 Low track stiffness leads to high track deflection which in turn generates high bending stresses (see figure 1) at the bottom of the rail, rapid rate of geometry deterioration (see figure 2) and high strain on rail clips (Berggen, 2009) (Powrie & Le Pen, 2016). One of the early studies on the effect of track stiffness on track geometry was carried out by British Rail (BR) in 1990 (Jenkins et al, 1990). The BR study analysed a site where approximately 10% of the route had low track stiffness and remainder had high track stiffness. The study concluded that the sections with low track stiffness had 50 % more deterioration compared to stiffer tracks sections. Another study by Ebersohn et al (1993) to determine the effect of low stiffness 24
on the structural and functional condition of the track system used several performance indicators to compare the performance of tracks with low track stiffness against tracks with relatively higher track stiffness. The analysis was normalised in respect to traffic and the results are shown in table 1. Table 1 THE EFFECT OF HIGH TRACK STIFFNESS Previous studies by Berggen (2009) and Hunt (2005) have shown that when track stiffness is high, lower displacements and bending stresses will be occur, however, the load is distributed over fewer sleepers (see figure 3) which increases the dynamic forces applied on the track resulting in ballast attrition and contact fatigue. TRACK STIFFNESS OPTIMISATION Various studies have been undertaken to determine the optimum global track stiffness value so the track would neither be too stiff to cause contact fatigue and ballast attrition nor too soft to cause rail bending fatigues and ballast settlement. A study by Pita et al (2004) examined the relationship between track stiffness and the total cost (construction and maintenance of tracks) and estimated that the optimum global track stiffness, at which the total asset cost is minimal, is between 70kN/ mm and 80kN/mm. However, later studies have concluded that the optimum global track stiffness can vary depending on line specifications (Puzavace et al, 2012). It is also important to note that most of the previous studies have ignored the effect of track stiffness on trains, i.e. wheel damage. Therefore, in order to develop a bespoke optimum global track stiffness value for the UK railways, the effect on wheel damage should be considered in the optimisation process. One potential approach to achieve this is through examining the total cost, of track construction and maintenance of track and trains, against different global track stiffnesses. Unfortunately, this approach is not feasible to adopt as it is very difficult to estimate the maintenance cost for tracks and trains. Figure 1: Rail bending stress for soft and stiff track for typical wheel load travelling at 100mph An alternative approach to find the optimum global track stiffness would be through the concept of the total elastic strain energy. The elastic strain energy is defined as the energy released when materials are deformed (Gavin, 2015) and it is a function of stress, strain and material volume, as shown in equation 3. Studies suggest that the strain energy generated in the material is highly associated with material damage and fatigue (Ellyin, 1989 and Kujawski, 1989); therefore, examining the effect of track stiffness on the total strain energy in the entire train-track system can serve as a good optimisation function. Minimising the strain energy for the entire train-track system would minimise the overall damage due to stress, hence maximising the lifespan of trains and tracks as a function of global track stiffness (see equation 4). To estimate the optimum global track stiffness, Finite Element Modelling (FEM) is used to calculate the total strain energy for the train-track system at different global track stiffnesses and loading conditions. The global track stiffness is varied by changing the subgrade Young s modulus and explained further in the following subsection. Figure 2: Rapid rate of geometry deterioration as a result of low track stiffness 25
FINITE ELEMENT MODELLING Figure 3: Sleeper/rail seat load for soft and stiff track for typical wheel load (70kN) travelling at 100mph Equations 3 and 4 To find the optimum global track stiffness at which the total strain energy of the train-track system is minimal, a 3D FEM was developed using ABAQUS standard software package and was used to calculate the total strain energy for different global track stiffnesses (generated from changing the stiffness of the subgrade). The model consists of four wheel sets, representing the rear and front of two coaches, interacting with the track through Hertezian contact (Fischer, 1999). Both the wheels and the track are modelled as elastic deformable elements, as illustrated in the idealisation in figure 4. To simplify the modelling and improve computational efficiency, the wheel load cases for different track qualities are imported from a previous study by Burrow et al (2017) rather than self-generating the dynamic loads and modelling the rail top and vehicle characteristics. As for the track, it consists of two rails fastened to rail pads and sleepers. This assembly is resting on a track bed which consists of different trackbed layers such as the ballast and natural subgrade supported by non-reflective boundary conditions to avoid stress reflections, see figure 5. The specifications and design of the track are selected to represent a typical UK railway track construction, see Table 2. It should be noted that the appropriate mesh size for each component is determined through a convergence analysis. OPTIMISATION FRAMEWORK To achieve the aim of this paper, a parametric study was carried out to determine the total strain energy for the train-track system with different global stiffnesses and loading characteristics. The global track stiffness was varied by changing the subgrade stiffness and the loading characteristics were varied by changing the travel speed and wheel loads (passenger or freight trains). Figure 6 shows a summary of the optimisation scope. OPTIMISATION RESULTS Based on the discussed optimisation scope shown in figure 6, the total strain energy is calculated for the different scenarios. Figure 7 shows the elastic strain energy levels for the entire train-track system for different global track stiffnesses for passenger trains travelling at 100mph on good track quality (FRA6). It can be noted from the figure that the total strain energy decreases with the increase in global track stiffness and the system would only achieve minimal total strain energy when the graph approaches 160kN/mm; however, it can be argued that this value is uneconomical to be considered as an optimum value for global track stiffness. Figure 4: Model idealisation Alternatively, if figure 7 is examined more carefully, it can be seen that the decreases of the total strain energy with increase in global 26
1. Stress in wheel: with the increase of global track stiffness, the stress levels within the wheel seem to increase because of the decrease of the wheelrail contact area. However, the increase appears to be small and therefore can be considered insignificant for the tested range of global track stiffnesses (see figure 10). 2. Stress in rail: with the increase of global track stiffness, the stress levels within the rail seem to decrease because the rail is experiencing less bending with the decrease in vertical track deflection (see figure 11). Figure 5: 3D model visualisation Table 2: Model specifications track stiffness is non-linear and there is a point, between 35kN/mm and 60kN/mm, at which the rate of decrease in the total strain energy is less significant. From an economical view, this point is considered to be a more viable optimum value for global track stiffness. This optimum point (inflection point) can be identified accurately by double differentiating the graphs in figure 7 and checking where the differentiated graph is intersecting with the x-axis, as shown in figure 8. From figure 8, the inflection point is at about 45kN/mm for both passenger and freight trains. This exercise was repeated for different track qualities, lines speeds and axle loads which all produced the same optimum value of global track stiffness, 45kN/mm. To understand the effect and contribution of each individual component on the total strain energy in the train-track system for different global track stiffnesses, the Von Mise stress in each component was investigated as shown in figure 9. The Von Mise was selected for this exercise because it is resultant of combining different stresses in different planes and can provide a general understanding of the stress state in the component (see Equation 5) (Kazimi, 2001). It should be noted that the Von Mise outputs for each component is normalised by the Young s modulus of the component s material. According to figure 9, a number of observations can be made as follows: 3. Stress in rail pad: with the increase of global track stiffness, the stress levels within the rail pad appear to increase. This is because the rail pad is being compressed and sandwiched, as the track bed stiffness increases. 4. Stress in sleeper: when global track stiffness is less than 50kN/mm, the stress levels within the sleeper appear to decrease with the increase of global track stiffness. On the other hand, when global track stiffness is more than 50kN/mm, the stress levels within the sleeper appear to increase with increased of global track stiffness. This is because when the global track stiffness is less than 50kN/mm, the bending stress within the sleeper is the dominant stress state in the resulting Von Mise stress. However, when the global track stiffness is more than 50kN/mm, the shear stress within the sleeper becomes the more dominant stress state in the resulting Von Mise stress. 5. Stress in ballast: when global track stiffness is less than 73kN/mm, the stress levels within the ballast appear to decrease with the increase of global track stiffness. On the other hand, when global track stiffness is more than 73kN/ mm, the stress levels within the ballast appear to increase with increased global track stiffness. This is because when the global track stiffness is less than 73kN/ mm, the soft subgrade results in the Figure 6: Optimisation scope 27
ballast experiencing a punching shear effect from the sleeper (see figure 12a). However, when the global track stiffness is more than 73kN/mm, the ballast starts to be crushed between the stiff subgrade and the sleepers (see figure 12b). 6. Stress in subgrade: with the increase of global track stiffness, the normalised stress on the subgrade decreases. This is because of the track ability to dissipate stress on the subgrade surface is higher with higher global track stiffness, hence more protection for the subgrade and lower normalised stress. OPTIMUM TRACK STIFFNESS IN THE UK Directly using the proposed optimum global track stiffness value in the UK may be considered difficult as it is a not common practice to express and measure track elasticity in terms of global track stiffness. There are two parameters that are used to quantify track elasticity, namely: 1. Track bed stiffness, which is measured using the Falling Weight Deflectometer (FWD) (Govan, 2011) 2. Dynamic track deflection, which is measured using sensors attached to the track (Wilk et al, 2015 and Powrie & Priest, 2011) To facilitate the use of the proposed optimum global track stiffness value in the UK, it is important to equate it to parameters commonly used in practice. To translate the optimum global track stiffness value found in the previous subsection (45kN/ mm) to FWD track bed stiffness, the UK track bed design standard can be utilised (Network Rail, 2015). The 45kN/mm optimum value was generated in the modelling using 300mm ballast and a subgrade with a modulus of 30MPa. If these parameters are used in the standard UK track bed design chart, the resulting track bed stiffness would be around 41kN/mm/sleeper end (see figure 13). It should be noted that this is only valid when using a rail pad with a stiffness of 150kN/mm. Figure 7: Total strain energy for different global track stiffnesses on good and poor track qualities On the other hand, to translate the optimum value of global track stiffness to dynamic rail deflection, the process is more complicated because the dynamic deflection is also a function of static and dynamic load (which varies depending on track quality and speed). Therefore, the optimum value of global track stiffness should translate into multiple dynamic deflection values that correspond to different axle loads, track qualities and speeds as shown in figures 14 and 15. It can be noted from the figures that with the increase of speed and decrease in track quality, the generated rail deflection increases. This is because increasing the speed and worsening track quality will increase the vertical dynamic loading generated from the train (Burrow et al, 2017). Since it is difficult to determine or measure the dynamic load at a specific point of interest, it would be difficult to choose the appropriate optimum deflection curve (poor or good track quality). Therefore, for practicality, it is may be better to target the deflection envelope bounded between poor and good track quality as highlighted in green in figures 14 and 15. It should be noted that depending on the dynamic load casings used for different speeds and track qualities, the generated rail deflection may vary. Figure 8: 2nd derivative of strain energy for different global track stiffnesses on good and poor track qualities Since the graphs in figures 14 and 15 relate to physical measurements, they provide the opportunity to validate the proposed deflection optimum limits by comparing them with deflection measurements from existing sites in the UK. Figure 16 shows rail deflection measurements, due to passenger trains passing on different existing tracks, superimposed on the optimum deflection envelope from figure 14. The performance for each site is assessed based on a number of performance criteria such as rate of deterioration of geometry, sleeper voiding and damage to track components. Equation 5 28
Figure 9: normalised Von Mise stress for different components and global stiffnesses (heavy freight travelling at N100mph on poor track quality) Figure 10: Wheel stress due to Hertezian contact with the rail Figure 11: Rail stress and deflection due to wheel loads 29
II - Guidance to maintenance: With the aid of track stiffness measurement devices, figures 14 and 15 can help track maintainers to identify hotspot locations where damage is more likely to happen as a result of inadequate track stiffness. This will allow maintainers to carry out preventative maintenance rather than corrective maintenance which can reduce the long-term cost for maintenance and minimise disruptions. Figure 12a: Ballast deformation due to shear stress (punching effect) III - Assurance to handback speeds: After the construction/renewal of railway lines, handback engineers can use figures 14 and 15, with the aid of track stiffness measurement devices, to determine the maximum allowable speed for running trains based on track elasticity to ensure the safe operation of the railway lines. CONCLUSIONS The aim of this paper was to develop a bespoke optimum track stiffness value for the UK railways. This aim was achieved using means of numerical modelling to correlate the total strain energy of the train-track system with the global stiffness of the track system. To this end, the study has concluded the following: Figure 12b: Ballast deformation due to normal stress (squashing effect) From figure 16, it can be observed that the deflection measurements from these sites appear to be in line with the optimum deflection envelope where poorly performing sites are located outside envelope and good performing sites are located inside the envelope. It should be noted that sites with drainage and subgrade erosion problems are excluded from the validation in figure 16. This is because those problems are not stiffness related although they manifest with similar symptoms as stiffness related problems if only stiffness data is examined without looking at other data such as Ground Penetrating Radar (GPR). Including these sites would skew the results with their unpredictable behaviour. From a practical point of view, figures 14 and 15 can be used in three different ways that can benefit the railway administrator, such as the following: I Guidance to design: Can help track designers to determine the appropriate combination of track bed layers and rail pad type to achieve the optimum stiffness of the system and maximise asset life by design. 1. Previously recognised the importance of track stiffness on the train-track system and identified that there is an optimum track stiffness value which is dependent on line specifications. 2. The concept of the total strain energy can be used to determine the optimum track stiffness value. 3. Engineering economy needs to be considered in the optimisation process to produce a feasible optimum value for track stiffness. 4. Depending on the value of the global track stiffness, the failure mode of each component may vary. 5. The effect of global track stiffness, within the tested range, on wheel damage may not be considered significant. 6. The generated rail deflection optimum envelope, which is associated with proposed optimum global track stiffness, correlate with measured field data. 7. Further research is required to investigate and test the sensitivity of results found based the assumptions made throughout the analysis and carry out further validations. REFERENCES Berggren, E., 2009. Railway track stiffness, Stockholm: Royal Institute of Technology. Burrow, M., Chan, A. & Shein, A., 2007. Deflectometer-based analysis of ballasted railway tracks. Proceedings of the Institution of Civil Engineers: Geotechnical Engineering, 160(GE3), p. 169 177. Figure 13: UK track bed design standards (after Network Rail, 2016) Burrow, M., Shi, J., Wehbi, M. & Ghatoara, G., 2017. Assessing the Damaging Effects of Railway Dynamic Axle Loads. TRB, Volume Accepted in Feb 2017. 30
Burrow, M., Teixeira, P. & Dahlberg, T., 2009. Track Stiffness Considerations for High Speed Railway Lines. In: N. P. Scott, ed. Railway Transportation: Policies, Technology and Perspectives. UK: Nova Science, pp. 303-354. D, K., 1989. Fatigue Failure Criterion Based on Strain Energy Density. Mechanika Teoretyczna I Stosowana, 27(1). Ebersohn, W., Trevizo, M. & Selig, E., 1993. Effect of low track modulus on track performance. China, Fifth international heavy haul railway conference. F, E., 1989. Cyclic Strain Energy Density as a Criterion for Multiaxial Fatigue Failure. In: B. M & M. K, eds. Biaxial and Multiaxial Fatigue. London: Mechnical Engineering Publications, pp. 571-583. Figure 14: rail deflection based on optimum global stiffness value for a passenger train Fischer-Cripps, A., 1999. The Hertzian contact surface. Journal of Materials Science, 34(1), pp. 129-137. Gavin, H. P., 2015. Strain Energy in Linear Elastic Solids, North Carolina: Department of Civil and Environmental Engineering in Duke University. Govan, C., 2013. The Use of Falling-Weight Deflectometers in Determining Critical Velocity Problems. Paris, Railway Track Science & Engineering Workshop, UIC. Hunt, G., 2001. EUROBALT II final report to railtrack: optimisation of ballast track, AEATR- TCE-2001-RR-311: European commission. Jenkins, K. & Wiseman, P., 1990. A statistical investigation of the effect of subgrade stiffness on rate of track, Derby: British Rail. Kazimi, S., 2001. Solid Mechanics. s.l.:tata McGraw-Hill Education. Network Rail, 2016. Formation Treatments standards, London: Network Rail. Figure 15: Rail deflection based on optimum global stiffness value for a freight train Pita, A., Robust, F. & Teixeira, P., 2003. High speed and track deterioration: The role of vertical stiffness of the. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. Plotkin, D. & Davis, D., 2008. Bridge Approaches and Track Stiffness, Washington DC: Federal Railroad Administration. Powrie, W. & Le Pen, L., 2016. A Guide to Track Stiffness, Milton Keyns: The Permanent Way Institution. Powrie, W. & Priest, J., 2011. Behaviour of ballasted track during high speed train passage. London, Railways Day. Puzavac, L., Popović, Z. & Lazarević, L., 2012. Influence of track stiffness on track behaviour under vertical load. Promet Traffic&Transportation, 24(5), pp. 405-412. Tazanakakis, K., 2013. The Railway Track and Its Long Term Behaviour: A Handbook for a Railway Track of High Quality. Berlin: Springer Science & Business Media. Wilk, S., Stark, T. & Rose, J., 2015. Non-Invasive Techniques for Measuring Vertical Transient Track Displacements. TRB, Volume 95. Figure 16: rail deflection based on optimum global stiffness value for a passenger train (with real deflection measurements) 31
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