Concept of Thermal Shrinkage-Resistant Railroad Rail for Use in Continuous Welded Rail Track

Highlights

• The paper concerns the possibility of using an innovative railway rail structure in a contactless track:
  • The correct operation of CWR track, due to the occurrence of additional thermal stresses with a value dependent on changes in rail temperature, requires a systematic diagnosis of its condition;
  • The paper presents the research of longitudinal force load tests for a classic rail and for two cases of an innovative railway rail solution.
• The research presented in the paper shows that:
  • The proposed proprietary design of the rail used for the railroad track can enable the reduction in the longitudinal force occurring as a result of high ambient temperatures;
  • The use of an innovative rail conception will allow for less steel consumption, which means less emissions into the atmosphere during its production (lower carbon footprint).

Abstract

This paper presents the concept of a modified 60E1 rail dedicated to continuous welded rail (CWR) track. The presented solution is the subject of a patent application by the authors of the publication. The paper describes problems associated with the operation of CWR track and the phenomena of so-called “rail stressing”, i.e., stresses created in the rail due to thermal shrinkage that, in extreme cases, can lead to the buckling of the rail track. Simulation calculations of longitudinal track loads to represent the occurrence of thermal force as a result of the occurrence of high air temperatures were carried out for the constructed conventional model of the railroad track as well as the track with the proposed solutions. A discussion of the simulation results is presented, indicating the possibility for the wider application of both varieties of modified rail.

1. Introduction

The correct operation of a railroad means maintaining its operational capacity, as well as the safety of rail traffic. CWR track, which is increasingly replacing conventional track, provides great savings in materials by eliminating rail joints, which are replaced by the welding or thermite welding of the rail ends. It also provides better ride comfort, along with reduced sound wave emissions associated with train passage. The design of modern CWR track is being adapted to increasingly difficult operating conditions. Compared with the conventional track used, the use of this type of CWR track structure has entailed a number of operational problems affecting the safety of vehicle traffic. The savings that have been achieved with respect to conventional track are the elimination of conventional joints, greater durability, and having no maintenance of joints involving the maintenance of the fishplate spaces or the tamping of contacts. One of the main problems encountered in CWR track is the development of high stresses in the rails during its operation. These stresses can have a major impact on the formation of the buckling of the CWR track, which translates into railroad safety. The phenomenon of rail stressing, which is the stress created in the rail due to thermal shrinkage, can lead to the phenomenon of buckled rail, which in turn can lead to the phenomenon of track buckling, also known as track creep in the literature. The occurrence of the causal sequence of rail stressing–buckled rail–track buckling is currently a phenomenon observed on the tracks (especially CWR tracks) of most railroads on Earth. Naturally, the intensity of this phenomenon increases with the amplitude of the ambient temperatures in which the railroad track operates. Material losses due to track buckling are difficult to estimate, although ref. [1] reports that they amounted to USD 17 million in the US in 2002. According to [2], “The buckling wave usually is from 0.3 to 0.5 m, and it appears in a section of 8–20 m, although there have been cases recorded of it reaching even 1 m”. Unfortunately, there is also a history of human casualties caused by this phenomenon. Moreover, taking into account persistent climate trends (global warming), it is possible to predict a future increase in the track buckling phenomenon [3].

Such great interest in the problem of continuous welded track involves, among other things, a change in the operating conditions of railway transport. This is determined by increasing speeds in passenger traffic, which, in European conditions, is expressed via the construction of new—and the expansion of existing—high-speed lines and in freight traffic via increasing axle loads and travel speeds. A peculiarity of continuous welded track is the thermal stresses that occur in the rails when the length of the rail cannot be changed. According to [4], the magnitude of these stresses σ may be calculated from Relation (1):

$$\sigma =\alpha ·E·∆T_p\left[\mathrm{M}\mathrm{P}\mathrm{a}\right]$$

(1)

where

• α—thermal expansion coefficient of the rail steel [1/°C];
• E—Young modulus of steel [MPa];
• ΔT_p—temperature difference in the rail about the neutral temperature (the temperature at which there is no thermal stress in the rail) [°C].

The magnitude of the longitudinal thermal force in the track, depending on the rail type, is given by Expression (2):

$$F_p=\alpha ·E·A·∆T_p=\sigma ·A\left[\mathrm{k}\mathrm{N}\right]$$

(2)

where

• A—rail cross-section area [m²];
• Other symbols are defined as in Formula (1).

Under European climatic conditions, for extreme values of ΔT, the compressive or tensile strength in the central part of the continuous welded track—where changing the length of the rails is not possible—may reach 1600 kN in both rails, and the stresses in the rail may exceed 100 MPa. With temperature changes, rail movements (lengthening or shortening) are possible only at both ends of the continuous welded track section, at a length that balances longitudinal forces with longitudinal track resistance. Beyond the end sections, the phenomena observed during operation in the central zone of the continuous welded track are primarily longitudinal displacements (creeping) of the rails and the increasing local horizontal and vertical deformations of the track over time. These phenomena of a rheological nature may lead to a reduction in or even loss of stability in the continuous welded track. Increasingly, such tests are performed using the FEM.

This paper presents the concept of radially cut rail, the use of which in a CWR track will reduce the probability of the causal sequence of rail stressing–buckled rail–track buckling as compared to the probability of the aforementioned sequence occurring with the rails used today. This concept is based on two patent applications [5,6] filed with the Patent Office in December 2023.

2. Literature Review

The causal sequence of rail stressing–buckled rail–track buckling has been described and formalized in the form of a mathematical model in a fundamental way, for example, in [1,7,8]. Laboratory studies of the rail–sleeper system in terms of the rail stressing phenomenon are presented, for example, in [9,10]. When it comes to rail stressing, no publications have been found proposing an analytically supported approach to reducing this phenomenon by changing the shape of the rail during production. One exception to this is patent [11], which proposes a rail that has horizontal cutouts in the shape of holes made to reduce the weight of the rail. This solution is characterized by the presence of horizontal cutouts that interfere with the structure of the rail to a significant degree, which can lead to the formation of the notch phenomenon, significantly reducing the strength of rails made according to this description. Moreover, this solution does not take into account the dimensions of railroad sleepers in the placement of horizontal cutouts in the rail.

In [12], an improvement of the rail manufacturing process resulting in a reduction in the inherent stresses in the rail was proposed. One of the trends in countering track buckling found in the literature is the development of methods and tools for the early detection of stresses in the rails, enabling action to be taken to pre-empt track buckling. This approach is presented in scientific and research papers [13,14] and patents [15,16,17,18,19,20,21].

An interesting idea is to counteract the buckling of the track by modifying the “sleeper–ballast” system. Publication [22] proposes the use of newly shaped railroad sleepers and an upgraded railroad ballast to reduce track buckling. A special case of a track buckling study, in which wooden and reinforced concrete sleepers are used alternately, was considered in [4], where the beneficial effect of alternating the use of different types of sleepers on track buckling was found on the basis of a 3D finite element analysis of models. In [23], an evaluation of the effect of the shape of the railroad sleeper on ballasted track resistance is presented using discrete element modeling (DEM). In [24], improved sleeper resistance was demonstrated in the ballast when using sleepers fitted with additional anchors versus conventional sleepers.

Studies to determine the preferred temperature for rail installation in CWR track are presented in [25,26]. Patent [27] presents an active way to counteract track buckling by reheating or cooling the rails, depending on their current temperature. There are also numerous coatings used to envelop the rail that are aimed at lowering its temperature when exposed to sunlight. According to [28], ”Some coatings are able to reduce the temperature of the rail by up to 10 degrees”.

A major problem is controlling track buckling on railroad track curves. In [29], a FEM-based model of the behavior of continuous welded rail (CWR) on a small radius curve (250 m) is presented. Patent [30] presents a solution to the problem of track buckling on a curve by specifically reinforcing the subgrade.

Patents [31,32] propose to counteract track buckling using a special attachment of the rail to the sleeper to allow for the controlled lateral movement of the rail with respect to the track axis.

The track buckling phenomenon is particularly dangerous in the area of bridges. The track structure used on bridges is less resistant to lateral loads and more prone to buckling. There are publications [33,34] describing methods to reduce the buckling of railroad track on bridges, including ones involving different rail profiles [35]. Patent [36] presents a device for reducing future track buckling while the track is still under construction.

Publications [37,38] present analytical methods for determining the buckling of structures in objects with a specific shape and specific surroundings. Publication [39] presents an example of using the FEM-based simulation tool to determine the buckling of such objects.

3. Concept of Thermal Shrinkage-Resistant Railroad Rail

The basic concept resulting in the inventions described in [5,6] is the result of the analysis of recorded video footage of the track buckling phenomenon. As a result of this analysis, a conjecture was made that the element initiating the buckling of the track is a rail foot subjected to longitudinal thermal stress. Thus, modifying the shape of the rail to reduce the proportion of its foot without significantly degrading the strength parameters of the rail could be beneficial due to the increased resistance of such a rail to “rail stressing”, which would consequently translate into the increased resistance of the rail track to buckling. The aforementioned reduction in the proportion of the foot was accomplished by subtracting (e.g., using cutting) an arched section of the rail, as shown in Figure 1 (horizontal cutting) or in Figure 2 (vertical cutting). In both cases, it is important to maintain the inter-relationship between sleeper spacing and cutting radius, as shown in Figure 1 and Figure 2. The curved shape of the subtracted rail section was chosen so as to not provoke the formation of the notch phenomenon in the rail.

4. Research Method

In order to verify the theoretical assumptions of the radially cut rail, which is the subject of the authors’ invention, it is necessary to carry out simulation studies in the first instance and experimental studies in the longer term. However, experimental studies require the production of specimens as a first step, followed by their installation in the railroad track (test section), or possibly the conducting of laboratory tests on a scale of 1:1. Full-scale experimental research requires significant financial resources, as well as the establishment of cooperation with a manufacturer of the steel components of the track structure (steelworks). Consideration should also be given to working with an infrastructure manager who may be interested in such a solution in the future. Simulation studies in the initial phase of work on such a design solution are the most advantageous and are the least costly solution to verify theoretical assumptions, allowing at the same time the obtaining of information on the behavior, in this case, of the developed numerical model during its loading. Any successful simulation studies would provide an important premise for testing full-scale prototypes.

4.1. Simulation Studies

Simulation studies were performed on new models of previously built railroad rails and railroad track structures. They are to be used to determine the values of stresses and deformations occurring in the analyzed object under different horizontal (simulating, for example, the values of longitudinal forces) or vertical loads applied. For the numerical analysis, the program SIMULA ABAQUS was used, which is software employed, among other things, for nonlinear analysis in physical problems, including regarding the mechanics of deformable solids. The first stage of the study was a model of the rail currently in use (conventional) with modified rails, namely the horizontally–radially cut rail described in [5] and the vertically–radially cut rail described in [6]. Subsequent cases of simulation studies included a section of railroad track on prestressed concrete sleepers using both conventional rail and both types of modified rail. During the simulation tests, a horizontal load (longitudinal forces) corresponding to the thermal forces in the CWR track was inflicted. The elongation of the rails and the resulting stresses in them were also determined.

4.2. Material Model

For numerical calculations, the relevant material properties of the railroad track structure elements used were assumed. In the case of the presented models, this includes only sleepers and rail tracks.

Table 1. Stiffness and damping parameters of railroad track in simulation studies.

Parameter	Value	Unit
Modulus of elasticity of the rail 60E1	210,000	MPa
Modulus of elasticity of the sleeper	30,200	MPa
Rail density 60E1	7850	kg/m3
Sleeper density	2400	kg/m3
Poisson’s ratio of a rail 60E1 Poisson’s ratio of the sleeper	0.30 0.20	- -
Damping of the railway sleeper	250	kNs/m

shows the selected strength parameters of the materials used, necessary for correct simulation studies.

Studies on built simulation models also take into consideration the parameters of stiffness and damping elements included in the track construction. The presented parameters were accepted as the results of experimental tests and taken from scientific publications.

4.3. Numerical Model of the Track–Boundary Conditions and Loading

Numerical models of the railroad rails (Figure 3a–c) and the railroad grate (Figure 4a–c) were created. A solution in the form of half a railroad track (track grate) was proposed to reduce the time of the simulation calculations. The rail length adopted for simulation calculations in both cases was 3.6 m; in addition, in the rail calculation variants, the rails were founded on 6 standard prestressed concrete sleepers with 0.6 m spacing.

Due to the complex shape of the modeled objects, models of the track consisting of 6 sleepers (solid model) were built. At this stage of the research, only straight sections of the track were modeled; other variants, such as sections of the track located in a circular curve, will be developed in the further phase of research and development. Longitudinal forces acting on rails or rail tracks were taken as the main loads of the models. The increase in the applied force is meant to simulate the increase in rail temperature. In the case of one end of the track, by setting the values of the simulation parameters accordingly, the possibility of its movement was excluded. As a result, movement of the entire track grate may occur.

The geometry of the numerical model was defined in the form of a grid of nodes defining the location and size of finite elements. Three-dimensional, solid elements were selected. Square elements are considered more suitable to describe issues in which bending prevails. They better describe stress concentration and allow for a better approximation of curved shapes with fewer elements. Figure 5 presents a cross-section of a needle profile model with six- and eight-node elements.

The support mode employed during the experiment was replaced in the numerical model by idealized boundary conditions (Figure 6). The longitudinal force axially loading the rail was applied to simulate thermal changes loading the rail tracks. The load was applied gradually (incrementally), and for each step, a system of equations was solved to determine the incremental stresses, strains, and displacements of the track grate. Support conditions were determined in the model by taking away the corresponding degrees of freedom, preventing the model from moving in certain directions in the nodes.

From a geometric point of view, the interface (contact) is the place that connects two adjacent mesh segments with different mesh densities to maintain model continuity. This allows you to properly distribute the pressure on both meshes to maintain the homogeneity of the 3D model (Figure 7).

5. Results of Simulation Studies

Selected results of numerical calculations obtained using numerical models of the railroad track structure in different configurations are shown in the graphs depicting Huber–Mises equivalent stress contours (σ_max^HM), internal stresses (σ₁₁), and deformation (U). The obtained results of the numerical calculations are visualized in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13.

6. Evaluation of Simulation Studies

Table 2. Summary of the maximum values, stresses, and deformations for selected cases of simulation calculations on the created models.

Applied Longitudinal Force FT [kN]	Track Model—Straight Section, Standard Rail			Track Model—Straight Section, Modified Rail (Horizontally Cut)			Track Model—Straight Section, Modified Rail (Vertically Cut)
	σmaxHM [MPa]	σ11 [MPa]	U [mm]	σmaxHM [MPa]	σ11 [MPa]	U [mm]	σmaxHM [MPa]	σ11 [MPa]	U [mm]
279 kN (temperature increase by 15 °C)	148.9	20.01	2.05	52.1	12.65	0.86	31.3	7.47	2.90
372 kN (temperature increase by 20 °C)	198.6	27.31	2.74	70.1	16.87	1.07	41.8	9.96	3.87
465 kN (temperature increase by 25 °C)	248.0	34.11	3.42	87.7	21.08	1.34	52.2	12.46	4.84

presents a summary of the maximum values, stresses, and deformations for selected cases of simulation calculations on the created models.

Figure 14, Figure 15 and Figure 16 present a graphical summary of the results obtained for various load cases.

The numerical models built made it possible to simulate the deformation of the track grate under various applied loads. Only selected cases of loads—those corresponding to rail temperature increments of 15 °C, 20 °C, and 25 °C and those generating forces corresponding to the longitudinal forces—are presented here. The maximum equivalent stresses σ^HM for the conventional rail was 248.0 MPa, whereas for the modified rail at the same boundary conditions, the values were 87.7 MPa and 52.2 MPa. It can be noted that the Huber–Mises stresses (σ_max^HM) in both cases of modified rails are about 2.8–4.7 times smaller than in the case of the conventional solution. Concentration for both modified rail and conventional rail occurs at the point of application of longitudinal force. In the case of both rails modified at the cutouts, the stresses do not exceed 20 MPa. At the bottom of the foot of the standard rail, one can see an even distribution of stresses not exceeding 63 MPa. Analyzing the magnitude of deformations obtained from simulations, for the maximum longitudinal force adopted, the difference between the conventional solution and the modified rail (horizontally sliced) is 2.5 times smaller in favor of the new rail solution. An interesting, near-paradoxical result was obtained for the vertically machined modified rail, as the increase in deformation was almost 1.4 times greater than the conventional solution, while a 20 °C increase in rail temperature resulted in a 1.6–2.7 times smaller increase in the internal stresses σ₁₁ in both cases of the tested track models compared to the conventional solution.

7. Conclusions

The simulation studies of the new railroad rail design presented in this paper show that despite the modification made by subtracting a section of the railroad rail, it is still suitable for use in railroad track. This is shown in the results obtained from simulation studies, which, for the solutions proposed in the patent applications [5,6], are slightly more favorable than in the conventional solution. The main objective of the authors was to develop such a rail solution so as to minimize the phenomenon of rail stressing, i.e., stresses created in the rail due to thermal shrinkage occurring in the rails of a CWR track. The results obtained are promising; however, they still require the consideration of other variants (different types of rail or sleepers), as well as their validation. This can be achieved, among other ways, either by using a different computer tool or by performing an experimental study.

In the near term, the following is planned:

• Simulation studies for other cases such as a different rail profile (49E1);
• Simulation studies of a track variant located in a circular curve with different radii;
• Simulation studies of dynamic loads from a railroad vehicle.
• In the long term, the following is planned.
• Establishing cooperation with a steel mill producing steel components (including rails);
• Obtaining funding to conduct experimental research on real objects.

The proposed solution of the modified rail (horizontally and vertically cut) in the case of preserving its strength properties in relation to the conventional solution can lead to the lower consumption of steel materials used for this type of construction, causing a reduction of 1 running meter of 60E1 rail from 60.21 kg to 55 kg (horizontally cut rail) and 46 kg (vertically cut rail). For 1 km of two-rail track, it would represent savings of 10,420 kg of steel, or about 9% less steel consumption, for horizontally cut rail, and savings of 28,420 kg of steel, or about 24% less steel consumption, for vertically cut rail. This can provide significant financial and environmental benefits in the manufacture of railroads. Reducing steel consumption means fewer emissions into the atmosphere during its production, including a smaller carbon footprint.