Improvement of train-track interaction in transition zones via reduction of ballast damage

Transition zones in railway tracks are locations with considerable changes in the vertical stiffness of the rail support. Typically they are located near engineering structures, such as bridges, culverts, tunnels and level crossings. In such locations, the differential settlement always exists and continually grows without proper maintenance. Due to the effect of the differential settlement and bending stiffness of the rails, hanging sleepers may exist, which are invisible under ordinary circumstances, but generate high displacements and impact during train passages. Therefore, a method to detect the differential settlement (Or hanging sleepers) of track transition zones is presented, which is combined with numerical simulations and field measurements. The numerical model of the track transition zone developed here uses contact elements for modelling the connection between the sleepers and the ballast, bilinear springs for fastening system and Hertzian spring for wheel-rail interaction. The model is capable for simulating the dynamic behaviour of the transition zones with differential settlement or hanging sleepers. Using the model, the dynamic responses such as the vertical displacement of rail, the dynamic wheel load, the axial stress in rail and the vertical stress of ballast has been be obtained and analysed. The field measurements were performed as well. Using Video Gauge System (VGS) the vertical displacements of rail in the vicinity of a track transition zone were measured. The differential settlement of the measured transition zone was analysed by comparing the measurement and numerical results. Finally, based on the obtained findings and the simulation results some track design improvements and suggestions for maintenance actions are given. Figure 1. A track transition in Netherlands. In such locations, the vertical stiffness of the track support varies, resulting in amplification of the dynamic forces acting on the track, which ultimately leads to deterioration of the vertical track geometry. Also, differential settlement of the track sub-structure on the both sides of the transition contributes to the deterioration of the vertical geometry. The deterioration process is accelerated with increase of the operational velocities of the passing trains. Finally, all these result in tremendous increase of the maintenance efforts on correction of the track geometry in the transition zones (Li, 2005). Usually, the track transition zones require more maintenance (like tamping and adding ballast) than regular tracks. For instance, the maintenance on track transition zones is performed up to four to eight times more often than on the regular track in the Netherlands (Varandas, 2011). In the US $200 million is spent annually on maintenance of the track transition zones (Sasaoka, 2005). When such maintenance is neglected the transition zones deteriorate at an accelerated rate (Kerr, 1993; Dahlberg, 2001; Dahlberg, 2010), which may lead to pumping ballast, ballast penetration into the subgrade, hanging sleepers (void space under the sleepers), permanent rail deformations and breakage, fasteners damage, loss of gauge, cracking of the concrete sleeper or slab-track (Kerr, 1993; Li, 2005; Banimahd, 2008). Also, this can result in deterioration of the passenger’s comfort and even create a potential for derailment. Due to the different properties of ballast tracks on soil and tracks on concrete structures, the ballast and soil tend to settle more, which results in appearance of differential settlement after short time of operation. Without maintenance, the differential settlement increases gradually. In addition, due to the effect of the differential settlement and relatively high bending stiffness of the rails, voids under the sleepers may appear which is known as hanging sleepers. Such hanging sleepers cannot be noticed under ordinary circumstances, but they can have high vertical displacements and cause impact to ballast during train passages. To investigate the differential settlement of track transition zones, a method combined with numerical simulations and field measurements has been developed, which intends to provide guidance for the maintenance of track transitions, shown in Figure 2. The relationship between differential settlements and track responses could be calculated by the validated numerical model, among them the rail displacement is used as a representative index. Therefore, the differential settlement and other responses of a transition zone could be obtained by comparing the measured rail displacements to the anlysed results. The developed 3-D Finite Element (explicit integration) model of track transition zones is introduced in Section 2. The measurement tool Video Gauge System (VGS) used in this study is introduced in Section 3. In addition, the numerical and measurement results are compared to tune the numerical model and final comparison is given in Section 3. The dynamic responses of the transition zone model under various differential settlement levels are analysed in Section 4. A group of measurement results of a track transition zone used as an example for comparison with the numerical results are discussed in Section 5. Finally, some conclusions and recommendations are given in Section 6. Figure 2. Inspection procedure of track transition zones. 2 MODEL OF TRACK TRANSITION ZONES In this section the numerical model used for the analysis of the dynamic responses in transition zones is presented. The Finite Element model of the track consists of 3 parts, namely two ballast tracks (further to be referred to as Ballast Track 1 and Ballast Track 2) and a slab track on a bridge (further to be referred to as Bridge) in the middle, as shown in Figure 3. Therefore, using one model it is possible to analyze two typical track transitions: from soft to hard support and from hard to soft support. Figure 3. FE model of track transition zones: (a) full view, (b) cross-section of ballast track. The lengths of each Track and the Bridge are 48m and 24m respectively, so that the total length of the model is 120m. The components of the ballast tracks are rails, fasteners, sleepers, ballast and subgrade. The rails are modelled by beam elements with the cross-sectional and mass properties of the UIC54 rails. Spring and damper elements between the rails and sleepers are used to simulate the fasteners. In the vertical direction these springs have bilinear properties, so that in compression they have the stiffness of the rail pads and in tension the stiffness is much higher to simulate the clamping effect of the fasteners. Ballast, sleepers and subgrade are modelled using the fully integrated solid elements with the elastic material properties. The thickness of ballast and subgrade is 0.3m and 2m, respectively. The material properties of the model’s elements are collected in Table 1 and Table 2. Table 1. Material properties of solid elements. Elastic Modulus (Pa) Poisson ratio Sleeper 3.65E+10 0.167 Ballast 1.20E+08 0.25 Concrete slab 3.50E+10 0.167 Mortar layer 2.00E+08 0.167 Support layer 3.30E+08 0.25 Subgrade 1.80E+08 0.25 Table 2. Material properties of spring-damping elements. Horizontal Vertical Longitudinal Stiffness (N/m) 1.5E6 1.20E8, 1.20E11* 1.5E6 Damping 5.00E4 5.00E4 5.00E4 *1.20E8 in compression; 1.20E11 in tension. The contact between the wheels and rails is modelled using the Hertzian spring, which connects a group of nodes of the wheels and all the nodes of rail. The silent boundaries are applied on both ends of the model in order to reduce the wave reflection effect. Moreover, due to the relatively big length of the track model the boundary reflection effect has already been significantly reduced. All the nodes on the bottom of the subgrade are fixed both transnationally and rotationally. The vehicle consists of a car body, 2 bogies and 4 wheelsets connected by suspensions, which are modelled using rigid bogies and spring-damper elements. The distance between two wheels of a bogie is 2.2m and between two bogies of a vehicle is 12.6m. The axle load of the vehicle is 14.5t, which is a common value for passenger trains. The vertical connection between the sleepers and ballast in the model is important for modeling of the degradation mechanism of ballast. Therefore, the contact elements are applied between the sleepers and ballast. According to the penalty algorithm employed in the contact elements the search for penetrations between the bottom surface of the sleepers and the top surface of the ballast is made every time step during the calculation. When the penetration has been found, a force proportional to the penetration depth is applied to resist and ultimately eliminate the penetration. This method allows simulating the impact on ballast, which is proportional to the downward acceleration of the sleepers. To simulate the differential settlement, a downward displacement is applied to the ballast and subgrade of Ballast Track 1 and Ballast Track 2, while the vertical geometry of Bridge remains unchanged. Due to contact modelling of the connection between the sleepers and ballast as well as the clamping effect of the fasteners, voids between the sleepers and ballast in Ballast Track 1 and Ballast Track 2 will occur at the beginning of the calculation. During the stabilization phase, the model reaches the equilibrium state at 0.4s under the gravity load. At the equilibrium state, most of the sleepers are in contact with the ballast, while the sleepers in the vicinity of the transitions are hanging due to the bending resistance of the rails. Together with the effect of the gravity and resistance of the ballast, it is possible to simulate the realistic hanging state of the sleepers. The vertical displacements of the sleepers in the vicinity of Transition 1 after the model has reached the equilibrium are shown in Figure 4a. It has been observed that the differential settlement here is 2mm and the vertical displacements of rail are different with other differential settlement value. The vertical coordinates of sleepers and ballast are shown in Figure 4b. The horizontal axis at 48m represents the positions on the track where the Transition 1 is situated. In addition, the sleepers on Ballast Track 1 and Ballast Track 2 are numbered from Bridge to the other ends, while the sleepers on Ballast Track 1are negative number and on Ballast Track 1are positive number. The sleepers on Bridge are not numbered, since they are not considered in this study. Figure 4. FE model of track transition zones: (a) full view, (b) cross-section of ballast track. Figure 4a shows that ten sleepers in the vicinity of the track transition are hanging. In addition, the rail on bridge close to Transition 1 is settled during to the bending stiffness of rail. The hanging value of sleepers can be seen from the space between the vertical coordinates of sleepers and ballast in Figure 4b. It also shows that the hanging value of the sleepers is highest at Sleeper 1 and gradually reduces as the distance between the sleepers and the bridge increases. After the ten-sleeper distance, the hanging value is almost 0mm. The same situation is observed 40 42 44 46 48 50 -2.0 -1.5 -1.0 -0.5 0.0 Above Sleeper No. -2 R ai l d is pl ac em en t ( m m ) Rail displacement (mm) Bridge -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 Sleeper No. -16 -14 -12 -10 -8 -6 -4 -2 0 -0.4420 -0.4416 -0.4412 -0.4408 -0.4404