Longitudinal Track-Ballast Resistance of Railroad Tracks Considering Four Different Types of Sleepers

Rudney C. Queiroz

São Paulo State University, Bauru (SP), Brazil

Abstract

This paper aims at studying the behavior of a railroad track concerning the action of longitudinal forces, targeting the determination of the track-ballast resistance, in a real scale standard track model. This research, was developed at the São Paulo State University, and consisted of a comparative study of track- ballast resistance for railroad tracks built with four different types of sleepers. The first set of sleepers was made of steel, the second one was made of wood, the third one of prestressed-concrete and the fourth one of two-block concrete. In order to carry out this research, four 1600 mm gauge models were built with two TR-68 rails, fastened to seven sleepers by means of elastic fasteners and base plates. The sleepers, all of the same type for each model, were embedded in 0.35 m thick ballast, which was supported by a layer of 30 cm thick compacted soil. The computerized data acquisition system allowed displacement and force values to be obtained in real time. By convention, the maximum longitudinal track-ballast resistance corresponds to a displacement of 15 mm. The prestressed-concrete sleeper setup showed the greatest longitudinal track-ballast resistance per sleeper. The second best performance was obtained by the two- block concrete sleeper setup, followed by the wooden and the steel sleeper setups. The force- displacement curves showed an exponential rise to a maximum shape. The displacement corresponding to the maximum track-ballast resistances were different for each kind of sleeper setup. Correlations between forces and displacements (N= f (d)) were obtained for each type of sleeper. The relative displacements between the rails and sleepers were negligible, showing that the adopted elastic fasteners can bear the forces originated from the displacements of the track setup embedded in the ballast. The measured and analyzed data provided unpublished important parameters for the project of modern and permanent railroads using welded long rails.

Introduction

This paper is the result of the research developed in the Department of Civil Engineering at the São Paulo State University, Bauru (SP) Brazil. The work aimed mainly at obtaining values of horizontal resistances of the railway track, supplying parameters of longitudinal resistance for railway track on the length of the extremity free from the long welded rail, and joint spacing with the temperature variation. Each element of a railroad's permanent way experiences deformations due to continuous loading- unloading-reloading cycles from rail temperature variation and traffic. If excessive, these deformations can detrimentally affect the performance and operation of the rail system. The rails are structural elements in their essence and can be considered as beams on elasto-plastic foundations with varying mechanical properties. On the other hand, the study of the ballast, composed of course granular material (usually crushed stone), does not suffer equitable deformations as the other components of a railroad system. Although the behaviour of the ballast track is relatively known by the professional literature, as [1], [2], [3], and [4], an approximation made in the calculations has to be mentioned. As it is actually known, the longitudinal resistance of the ballast track has been gradually developed [5]. [6], [7], and [8] the elastic behaviour of continuously embedded rail systems studied in laboratory tests. This study expounds a new fastening in rail system. Very few studies of deformation under temperature variation and behavior of railway systems are part of the technical literature.

Traction and compression stress in the rail with temperature variation

The temperature measurement, in the railroad, is performed directly in the rail. Such temperature is different from the environmental one, usually larger because of the energy absorption by the steel. Due to the importance of the subject, the rail administration keeps permanent control in order to obtain the temperatures of the rails in several places, at several times of the year and hours of the day. For the study of implantation of a railroad, the maximum variations, averages and the temperature fall of the rail should be obtained. Such values will be used in theoretical calculations of the efforts and variations in the length of the rail. In practical applications, as in the establishment of a new rail, its temperature should be obtained in the assembly moment, in order to calculate the value of the joint spacing, considering the maximum and minimum temperatures. The temperature of the rail seating, when the bar has not begun to suffer stress variations yet, due to expansion or contraction, it is denominated "neutral temperature", because at this time, the rail is not subject to internal stress yet, due to the variations of the temperature and reaction in the fastener and sleepers. The rail steel supports the traction and compression stress due to temperature variation. Brazilian railroads variation of adopted temperature is around 60o C.

Being:

N Dl s = = E = Ex (1) S l

N: Axial forces; S: Traverse section of the rail; s : Stress in the rail; E: Elasticity Module of the steel (AND = 210.000.000 kN/m2); l: Length of the rail; Δl: Length increase due to temperature variation; x: Unitary deformation; t: Temperature variation; a: Thermal dilation coefficient of the rail steel (a= 0,0000105) oC-1.

D l = l .a .D t (2)

Dl x = = a.Dt = 0 ,0000105 x60 (3) máx l

2 s máx = E.x = 2.100.000x0,00063 = 132.300 kN/m

2 smax = 132.300 kN/m or 132,3 MPa

This stress is absorbed by the rail, even considering the stress increase due to traffic. The elasticity module of the rails is around 400 MPa.

The problem is restricted to the resistance of the railway track rupture due to temperature increase and compression between the extremities of the rails and rupture of the rail or splint under traction due to temperature decrease.

Limited Dilation Theory

When a long welded rail is submitted under temperature variations, in the track, two extreme areas of displacement and an immobile central area will be developed, as shown in Figure 1.

FREE EXTREMITY NO DISPLACEMENT

VARIABLE STRESS CONSTANT STRESS

Figure 1. Free extremity of displacement and immobile area in a long welded rail.

Considering:

N: Total forces due to dilation; R: Resistance offered by the junction splints; r: Unitary resistance of the rail-railway sleeper/ballast; l : Total length of the rail; ld: Length of the extremity of the rail, submitted to displacement.

Therefore:

ld N = R + r.dx (4) ò0

In which: N = R + ld . r (5)

N - R ld = (6) r

Being: N = S . E . a . Dt (7)

S.E.a.Dt - R ld = (8) r

The condition of the long rail will be satisfied:

l > 2 . ld (9)

Being: l > 2 . ld the fixed lenght, without dilation.

It is verified, therefore, that some of the main parameters are the unitary longitudinal resistance offered by the rails group, sleepers and ballast. The larger this resistance, the smaller the lengths of the extremities of the rails which expand.

Materials and Methods

The following devices were used in this research: a) Systems of horizontal and vertical reaction set on soil, b) Reaction beams and application of the loads, c) Jacks, electronic system for deformation measurement, and load cells, d) Railway tracks composed by seven sleepers, TR-68 rails, elastic fastener "Pandrol", ballast composed by crushed stone (basalt), and base in compacted soil, e) Wood, steel, prestressed concrete monoblock, and concrete bi-block sleepers, f) Technological rehearsals of the ballast material and of the soil, electronic reading system and data acquisition.

Four experimental models were built, with seven sleepers of each type, spaced by 60 cm, fastened in TR- 68 rails with elastic system “Pandrol”, gauge of 1600 mm. The sleepers are embedded in 30 cm of standard ballast on soil platform compacted with 40 cm in thickness.

Results

The results of the longitudinal displacements are characterized as the main researched parameters. Therefore, the main objective of this research is to obtain the longitudinal resistance for sleepers. Considering the values of these resistances and the conditions of railway track pattern used, it can be determined the length free from long rails welded displacement. Consequently, it is necessary to define the joint size for a given neutral temperature to lay the rail in the railway track. This research adopted 40mm as maximum total size and 10mm as minimum, allowing a maximum displacement of 15 mm among the head rails.

The displacement in function of the longitudinal maximum loads was:

Wooden slepeers: 28 mm,

Prestressed concrete monoblock sleepers: 15 mm,

Concrete bi-block sleepers: 21 mm,

Steel sleepers: 29 mm.

For the set of seven sleepers and the two rails submitted to longitudinal loads. By comparing the several curve loads versus displacements, it is obtained (Figure 2).

Loads versus Displacements Horizontal Loads - Longitudinal for 4 types of ties 80

70 (1) (2) 60 (3) 50 (4) 40

Loads (kN) 30

20

10

0 0 5 10 15 20 25 30 35 Displacements (mm) (1) Prestressed concrete monoblock (2) Concrete bi-block (3) Wood (4) Steel

Figure 2. Comparison among the curve loads versus longitudinal displacements for the four types of sleepers

It was verified that the sleepers of prestressed concrete monoblock sleepers and the concrete bi-block sleepers behavioured better than all the others. The prestressed concrete monoblock sleepers reached the maximum resistance around 69 kN, for a displacement of 10 mm.

Conclusions

Considering 15 mm limitation of the rail joint displacements, it was verified that the concrete bi-block sleepers reached value around 62 kN, against the prestressed concrete monoblock, around 69 kN, resistance. For 15 mm of rail joint displacement, the wooden sleepers reached around 53 kN and the steel sleepers, value around 45 kN. Table 1 shows the maximum resistance value for the four types of the sleepers studied, all of them related to 15 mm displacement.

Load per each sleeper (kN) for Sleepers displacement of 15mm. Wood 7,57 Concrete pre-stressed monoblock 9,86 Concrete Bi-block 8,86 Steel 6,43

Table 1. Comparison between the forces and displacements for the studied sleepers.

In this context it was verified that:

The research has contributed to estimate the values of longitudinal resistances for each type of the studied sleepers submitted to similar condition of a railway track to the adopted model. This research also has contributed to estimate the behavior of the extremities of long welded rails related to displacement joint size.

Acknowledgments

The authors would like to express their sincere thanks to Fapesp (Fundação de Amparo à Pesquisa do Estado de São Paulo) for the financial support that made possible the preparation of this article, and to the Department of Civil Engineering of São Paulo State University, Unesp, Bauru (SP), Brazil.

References

[1] K. Klugar. “Eisenbahn-und verkehrswesen I”. Technische Universität Graz. Germany. pp. 208-214. 1977.

[2] J. Megyeri. “Railway engineering” Müegyetemi Kiadó. Budapest. pp. 185-194. 1997.

[3] E. Nemesdy. “Railway superstructure”. Tankönyvkiadó. Budapest. pp. 242-313. 1966.

[4] B. Vásárhelyi. “Welded railway tracks”. Müszaki Könyvkiadó. Budapest. pp. 182-245. 1960. (1960),

[5] G. Kormos. “Longitudinal behaviour of rail embedded in elastic material”. 2002). Periodica Polytechnica Ser. Civ. Eng. Vol. 46. NO. 1. pp 115 – 124. (2002).

[6] E. Ludvigh. “Elastic behaviour of continuously embedded rail systems” Periodica Polytechnica Ser. Civ. Eng. Vol. 46. NO. 1. pp 103 – 114. (2002).

[7] B. Indraratna, W. Salim. “Mechanics of ballasted rail tracks – a geotechnical perspective” Taylor & Francis Group. London – UK. 226 pp. 2005.

[8] R. C. Queiroz. “Method for estimating railroad track settlements due to dynamic traffic loads”. Proceeding of the 16th International Conference on Soil Mechanics and Geotechnical Engineering (16ICSMGE). Osaka, Japan. pp. 1769-1772.