SAFETY ENGINEERING OF ANTHROPOGENIC OBJECTS INFLUENCE OF THE BALLAST RESISTANCE ON THE STABILITY OF CONTINUOUS WELDED RAIL

The article is about the issue of the influence of ballast resistance on the stability of the Continuous Welded Rail. The ballast resistance affects both the longitudinal and transverse displacements. It depends on the quality of the ballast, the degree of its compaction and contamination. The article contains an analysis of the impact of ballast resistance on the track based on the Finite Difference Method. The calculations showed that the resistance value directly affects the allowable critical force and the maximum temperature rise in the rail that does not endanger the safety of railway traffic.


INTRODUCTION
The development of rail transport creates new challenges in relation to this mode of transport. A big step towards improving the quality of transports is the widespread use of the Continuous Welded Rail (CWR). However, this solution also has some disadvantages besides advantages. The main problem is the occurrence of high thermal stresses which may cause the rail to break in winter or buckle in summer. For this reason, diagnostics of the contactless track is carried out to ensure safety. The analyzes described in the literature have shown that each of the pavement elements has an impact on the track stability. Nevertheless, the most important element is the ballast -its compaction, pollution and scattering of sleepers. The article shows the relationship between the ballast resistance and the longitudinal displacement and the maximum temperature rise in the rail.

Ballast as a factor influencing track stability
The resistance to the displacement of the track is very much dependent on the ballast.
It depends on many parameters, especially the type and size of stone. The stability of the non-contact track is also dependent on the degree of compaction, layer thickness and maintenance condition. An important parameter is also the degree of scattering of the sleepers and the ambient temperature, especially whether the ballast is frozen.
The diameter of the aggregate grains used for the ballast ranges from 22.4 mm to 63 mm.
Most often it is a 30 cm thick layer and, depending on the train speed, the width of pouring the sleepers is 40 cm for speed between 160 km/h and 50 cm speed more than 160 km/h. The side resistance of the ballast was determined on the basis of many years of measurements.
They largely depend on the maintenance condition of the surface [1].
The resistance of the ballast affects the distribution of longitudinal forces in the track and the formation of stresses. It should be noted what influence the manufacturing technology has on the ballast resistance. In the studies carried out so far, it has been noticed that a clean and poorly compacted ballast has 2 to 3 times less resistance than a compacted ballast with noticeable contamination.

Model of longitudinal track displacement
The analysis covers the case of rails creep, i.e. their displacements along the track axis.
The values of these displacements depended on the braking force of the rolling stock moving along the section in question [2]. The analyzes are limited only to longitudinal displacements along the track axis [3].   [1] For this model, in the longitudinal direction, the equilibrium equations take the following form [5]: (1) The displacement values resulting from the rolling stock load and the thermal load can be added together. Their value may not exceed the limit of elastic path displacement beyond which a permanent displacement will occur [1]. (4) where: displacement due to rolling stock load, displacement caused by thermal forces, maximal displacement where there is no permanent displacement.
Based on the specified values of displacements, a criterion can be developed that determines the risk of track creep. They can be represented by the following formula [6]: The phenomenon of creep may occur when d k ≥1.

Lateral displacement
When the ballast and sleepers do not ensure full track stability, the track grate buckling occurs.
The design model treats the path as a beam whose ends are points of change in the nature of the buckling curve. The beam rests on a resilient ground and its ends are free to move. Figure 3 shows the scheme that was adopted for further analysis. The inflection points between which the analyzed section is located are marked as "inflection point" [7].   To determine the value of the resistance β(x), use the formula [8]: (6) where: H -track height, d -sleeper bedding height, l -track section length, k 0 -unit ballast resistance.
The critical buckling force can be represented by the following relationship:: Finally, based on the principle of minimum potential energy, the critical force can be written as [9]: Based on the theory of elasticity and the theory of small deformations, an algorithm has been developed to determine the values of forces at lateral displacement of the track for the is not able to regain its operational capacity by itself without human intervention [10].
The ballast resistance β depends on [11]: • the height of pouring sleepers, • precision of covering the head of sleepers, • the state of contamination of the ballast, • condition of railway sleepers, • type and condition of fastenings.
The described equation of the non-contact track was used for further analyzes.

Analysis of longitudinal displacement
To perform the analysis using the finite difference method, the track was divided into sections of short length. The longitudinal displacement of the track was described by differential equations of the following form: (9) Based on the Finite Difference Method, this equation can be written into a system of n equations for each node of the rail track under consideration.
For the i-th node, the written equations have the following form [12]: (10) For the sake of simplicity, the following symbols have been adopted: (11) and: (12) On the basis of the above-described method of determining the deflection value in individual nodes, a matrix of numerical coefficients was developed.

Analysis of lateral displacement
The value of the critical force for transverse track displacement can be described using the equation [9]: (13) where: β conditions. However, it should be remembered that even in the absence of the stabilizer passage, after a certain period of operation, the track becomes compacted and the ballast resistance increases, resulting in an increase in the value of ΔT 0 [13]. -264 -also the length of the train whose maneuvers cause creeping. Here, however, the change of the parameter did not show such a drastic increase or decrease in longitudinal displacements.
In the case of lateral displacement, the critical forces in the rails and the maximum temperature changes of the rails were calculated. The relationship between the ballast resistance and the calculated values is visible. For contaminated crushed stone, the maximum temperature change is only 23,4°C, which indicates a high risk of railway track buckling. The highest value of the maximum temperature increase was calculated for the track after the boost and stabilization of DGS. It amounts to 54,8°C, which guarantees the safe use of the railway line despite changing climatic conditions.
It can be stated that the parameter determining the value of the longitudinal displacement is the ballast resistance.ratio For this reason, it is very important to control the state of contamination, drainage and quality of backfilling of railway sleepers.