Investigation on the Effect of Railway Track Support

System Characteristics on the Values of Track Modulus

Mohammad Worya Khordehbinan

Master of Civil Engineering, University of Tehran, Iran, mkhordebinan@ut.ac.ir; Phone+98-871-3228257

Abstract

In this research, the variation of railway track modulus as a function of ballast layer thickness

and subgrade characteristics is investigated using numerical modeling. Track modulus plays an

essential role in the analysis of railway track systems and is regarded as a basic index of track

response to the train loads. Based on its definition, track modulus is related to the amount of

track vertical deflection. Therefore, it could be expected that the characteristics of track support

system greatly influence the magnitude of the track modulus. Although the importance of the

effect of track modulus on the railway track structural behavior is well recognized, this parameter

has not been investigated thoroughly. The current research is a response to this need. In this

paper, railway track support system is modeled using the finite element approach. The effect of

ballast layer thickness as well as subgrade stiffness on the values of track modulus is evaluated.

Based on the results obtained, discussions are made and suggestions are proposed to improve the

current understanding of track modulus.

Keywords: Track Modulus, Ballast, Subgrade, Railway

INTRODUCTION

Railway track performance is influenced by its components so that it is possible to gain higher

performance by understanding constituent parameters of tracks and modifying them. The most

important factor in analysis of a railway track is estimation of track modulus. In 1994, Cai et al,

described track modulus as proportion factor between rail vertical displacement and vertical

contact pressure between rail bed and foundation beam (underlying components of rail track)

(Boresi, et. al.- 2003)[1, 2]. The same year Selig and Li used more simplified definition as rail

bed module in their calculation and defined it as support force imposing on rail length unit per

rail unit displacement in vertical direction (Selig, et. al.- 1994). In technical text track modulus is

indicated by k and is measured in N/mm, while rail bed modulus is represented by u and is

measured in Pa. In addition to above mentioned difference, the main difference between track

modulus and rail bed modulus is that track modulus (k) takes effects of rail dimensions and

material, i.e., flexural stiffness indicating by EI, into consideration, while u depends on other

components of superstructure (such as rail joints to sleeper as well as sleeper itself) and

underlayment (ballast and sub-ballast and their underlying soil layer) and in whatever underlying

the rail and being considered as its support subgrade, and is independent from rail type. Rail bed

modulus is very important and has a direct relationship with performance level, rail track safety,

and amount of needed repair and maintenance. If rail bed modulus is low and/or its change in a

given length of track is excessive, it leads to undesired consequences. Ebersohn et al, (1993)

concluded that, if rail bed modulus is low, it leads to different settlement along track, and

therefore the need for maintenance operations increases (Ebersohn et al, 1993)[3]. On the other

hand, Zarembski and Palese (2003) argued that if the variation of rail bed modulus is too high, as

in bridges vicinity and slab tracks, dynamic forces imposed on track increase (Zarembski et. al.-

2003) [4]. Increasing dynamic forces leads to track component lifetime reduction and

subsequently, maintenance periods reduce. It is proven that reduction of rail bed modulus

variation in railway and road level crossing results in railway performance improvement and

maintenance operation reduction. Quality level of passengers and comfort specified by vertical

acceleration is another factor which is highly dependent to rail bed modulus quality. The above

mentioned discussion indicates the importance of accurate track stiffness determination and rail

bed modulus estimation. Different methods have been proposed by authors for measurement and

calculation of rail bed modulus. Generally, as it is shown in Fig.1 they can be classified into 3

major groups: theoretical, theoretical-exprimental and experimental. Hay (1953), Birmann and

Luber (1965- 1966) in Germany, Prause et al, (1974), Ahlf (1975) and West Australia Railway

(Westrail) (1976) performed some research in order to analyze track stiffness by theoretical and

experimental methods. All these researches on track stiffness and track modulus specification are

limited to case studies. So far, in all research, different levels of thickness of ballast layer role

and railway track subgrade condition have been considered generally [5]. Understanding rail

behavior and its bed modulus are important for track control and operation. (In this paper, it is

given for different possible kinds of single rail track systems.) Various factors are involved in

determining track modulus, thus regarding variability of these factors and their interaction as

well as dynamic nature of forces, determining rail bed modulus is difficult and complex and

requires extensive study. Therefore, it is necessary to find a technique for estimation bed

modulus which includes all factors. In this paper, track modulus is determined via field test in

Tehran-Mashhad railway track (in Iranian railways) performed by Railway Research Center.

Then, by use of finite element as an effective method in mechanical analysis of each component

of railway system, an optimal model of railway track is designed and is calibrated using field

test. Track modulus is analyzed under different thickness levels of ballast layer, different types of

bed, passing speed and axial load. Results of analysis are studied by Ansys software in order to

determine track modulus. Finally the following diagram is presented for various types of railway

tracks under ballast layer thickness and bed type in order to determine bed modulus and control

vertical displacement of railway track.

Fig.1. Classification of methods for measurement of rail bed stiffness and Track Modulus

TRACK SYSTEM ANALYSIS METHODS

Field test and numerical analysis by finite element method is used in order to track behavior

analysis. Field test is performed by Railway Research Center of Iran under leadership of Dr.

Mohammadzade, and results of this test are used by authors for further study. In numerical

analysis, the model having the most consistency with field test data is obtained based on finite

element method by using trial and error process. Then, modeling and analysis by software is

performed for various conditions of track. Sensitivity is also analyzed. Then a clear

conclusion is represented on the extent and amount of effects of different parameters on rail

bed modulus by drawing a diagram and appropriated tables

Methods of measurement of rail bed modulus

Theoretical methods Theoretical-experimental methods

experimental methods

Pyramid model AREMA bylaw model

Method proposed by Talbot

Beam on elastic subgarde model

Method of Academy of Railway Science of China

Method Nebraska University

Method of Technical University of Delft

Method USA Transportation Technology Center

Field Test Method

Field test was performed in track 4 of Bahram station (between Rey and Varamin stations in

Tehran-Mashhad railway line) which has subgrade of sandy soil type with high quality. Track

system was loaded by 20-ton axle load and passing velocities of 3.4 km/h and 6.88 km/h before

and after track tamping and stabilization.

Tests were performed in two stages by placing 7 force measuring tools and 6 displacement meter

sensors in three track sleepers in order to record forces imposed on rail bed and track vertical

displacement. In the first stage, track response was recorded by 6-axle diesel and 4-axle wagon

passing. Then, stabilization and tamping operations were performed in railway track, and by

reloading track by diesel and loaded wagon, track response was assessed. Figure (3) indicates

sensors evaluation of three sleeper’s vertical displacement under different rail supporting system

and track loading conditions.

b. base placed in track for performing test

a. Test location

d. Track stabilizer machine

c. Track tamping machine

e. six -axle diesel with wagon for track loading

Fig 2: Field test details

a. Before tamping (Train speed = 3/4 km/h)

b. After tamping and stabilization (Train speed = 6/88 km/h)

Fig 3: sleeper vertical displacement under diesel passing

Numerical Analysis Method

"Catia" and "Ansys" software were used in this study for modeling and model sensitivity

analysis. Dimensions of initial model were changed by using trial and error process so that the

method with lowest results discrepancy with track superstructure system in field study is

selected. Technical and general characteristics of track system constituents were specified based

on international standards so that they can be used as input data for modeling. Thus, mechanical

characteristics and behavior of system elements were studied and then track system was modeled

based on obtained data. Model accuracy is controlled by field test results as well as track

elements’ geometric characteristics. Sub-ballast layer thickness is assumed constant and as 10

cm in this study. B70 single-block prestressed concrete sleeper is selected with 260 cm length, 24

cm width and 15 cm height. Sleeper effective length is the modeling basis. Sleepers spacing and

their compressive strength is considered as 60cm and 600 kg/cm2 respectively. Rail type in

modeling is UIC60 characteristics.

Technical and general characteristics of ballasted railway track system components which are

used as basic parameters in modeling are classified according to table (1) [5, 6].

Table 1. Mechanical characteristics of ballasted track Components [5]

Materials Type Elasticity modulus

(kg/cm2) Poisson’s ratio

Adhesion

(kg/cm2) Friction angle

poor Subgrade (S1) 125 0.4 0.15 10

Fair Subgrade (S2) 250 0.3 0.1 20

good Subgrade (S3) 800 0.3 0 30

Rocky subgrage (R) 30000 0.2 15 20

Ballast 1300 0.2 0 45

Sandy subballast 2000 0.3 0 35

After modeling and analysis, model is calibrated in order to agree with railway track field test

state. Then developed models are analyzed and the model having lowest discrepancy with field

test state is selected as the main model for numerical analysis. Table (2) indicates section

characteristics of track tested for theory modeling [3, 5, 6].

Table 2. Track system parameter values with regard to field study in modeling

Parameter Track system Parameter Track system

Sleeper moment of inertia (cm4) 24200 Elastic modulus of bed (kg/cm2) 1240

Rail moment of inertia (cm4) 3950 Elastic modulus of Subballast (kg/cm2) 1260

Ballast thickness (cm) 38 Elastic modulus of ballast (kg/cm2) 2490

Subballast thickness (cm) 15.2 Elastic modulus of Sleeper (kg/cm2) 2.07×105

Wheel load (Ton) 14.2 Elastic modulus of rail (kg/cm2) 2.07×106

Sleeper length(cm) 259 Bed Poisson’s ratio 0.4

Sleeper width(mm) 229 Ballast layer Poisson’s ratio 0.4

Sleepers spacing (cm) 61 Sleeper Poisson’s ratio 0.3

Rail area (cm2) 86.5 Rail Poisson’s ratio 0.25

Sub-ballast Poisson’s ratio 0.3

Results of field study and theoretical model analyses have discrepancy. Model having lowest

acceptable discrepancy in data output with real state is presented in figure (4). Track length is

determined in model by considering load distribution principle. if wheel load is directly put on

one sleeper, that sleeper tolerates 40% of load and first adjacent sleepers and second adjacent

sleepers each tolerate 23% and 7% of the load, respectively. Thus the impact on third and fourth

and nth sleeper would be insignificant. Therefore, in each wheel load, 5 sleepers with perfect

symmetry have impact along rail. Regarding the model design condition, adjacent loads’ overlap

effect under good safety factor is ignored in modeling. Sleeper length in model is one third of

total sleeper length. Model boundary condition is assumed with regard to the fact that model has

symmetry along rail and sleeper, thus symmetry principle is assumed in mentioned directions. In

two other directions, one in track shoulder model is thoroughly free and in rail direction, model

plane lacks any displacement in direction vertical to plane. Degree of freedom is considered as

zero in lower plate.

Fig 4: Simulated Track System Model

There is 1 to 6 percent discrepancy between results of model analysis and field test

measurements which is justified regarding to field condition.

Table 3. Comparing result of field study and theoretical modeling [5]

Ballast surface strain

Bed surfaceModel

displacement(mm)Stress (kPa) 0.001550.8570Field state 0.001440.8971Theoretical state

6 4.71.4Discrepancy percent (%)

Axle and traffic load passing over the track are among critical factors of track and bed fatigue.

Based on track equipment, different amounts of axle load would be applied on different tracks.

Axle loads are 16 and 18 tons respectively for passenger tracks with maximum speed of 160

km/h and 20 and 25 tones for freight tracks with maximum speed of 100 km/h. Forces which are

imposed on railway track are mainly dynamic in nature. However, precise prediction of dynamic

forces imposing on railway tracks is difficult. On the other hand, more simplification of railway

track analysis and design process is necessary. Thus for design purpose, static vertical force

imposing from the wheel is multiplied by a factor termed as dynamic impact factor and quasi

static force used in railway track design is obtained. By applying dynamic impact factor in static

loads, effects of factors which have not been considered in simplifications are taken into account.

Some of these effects include track geometric characteristics, its quality, stiffness and

components, railway vehicle characteristic such as wheels type, load magnitude, and finally

speed, braking and vehicle acceleration increase and decrease. Different relations have been

proposed for calculating dynamic impact factor by different institutes and researchers based on

above mentioned factors. Regarding dominant condition of operation (including speed and axial

load) load factor of each axle is calculated independently for different loads by AREMA method.

Wheel diameter is assumed 920 mm in this study. Axle load on railway tracks is calculated for

each wheel (P) based on wagons condition in Iran and by selecting appropriate impact factor

( ). In this study, loading is performed by gradual method and pre-loading of 17.5% of imposed

load.

ANALYSIS OF RAILWAY TRACK MODULUS

Analysis of Field Test Result

Results of field test in stabilized sandy subgrade condition (high quality) for rail supporting

system in track 4 of Bahram station (between Rey and Varamin stations in Tehran-Mashhad

railway track) is given in table (4).

Result analysis in field test shows that under axle load of 20 tons, the maximum change in

sleeper vertical settlement and track modulus before tamping shows 54% decrease and

337.5% increase, respectively, compared to after track tamping and stabilization, and more

than 3 times increase respectively compared to after track tamping and stabilization.

According to researches on Iran railway tracks, track mechanical parameters become

heterogonous and track stiffness reduces due to track deterioration and track behavior departs

from beam behavior on Elastic bed and sleeper vertical displacement may increase threefold,

which by tamping and track stabilization track shows uniform behavior as its stiffness

increases [7, 8].

Table 4. Rail bed modulus in Field Test

Rail bed Modulus (MPa) Track system characteristics

Sleeper 3 Sleeper 2 Sleeper 1

35.06 23.964 17.20 Before tamping

54.78 53.62 57.24 After tamping and stabilization of track

Analysis of Finite Element Method Result

By model analysis based on rail displacement result in vertical direction, track modulus

values in terms of ballast layer thickness, subgrade quality and under different loadings which

is shown diagrammatically in figure (5).

Fig 5: Rail bed Modulus in terms of ballast layer thickness and loading condition

Analysis result of track modulus shows that the type of passenger and freight tracks do not

have effect in specifying this important design parameter, and has direct relationship with

ballast layer thickness in constant condition. Regarding the fact that subgrade type changes

along railway track line, impact of subgrade type change is expressed by four qualities (S1,

S2, S3 and R) as track modulus increase percent in table (5).

Table 5. Effect of change in type of bed on track modulus value

Type of subgrade change Track modulus increase

percent Type of subgrade change

Track modulus increase percent

Subgrade 1 to subgrade 2 11.81 Subgrade 1 to subgrade 3 44.1 Subgrade 2 to subgrade 3 28.86 Subgrade 2 to subgrade 4 59.3 Subgrade 3 to subgrade 4 23.62 Subgrade 1 to subgrade 4 78.11

Table 5 indicates that improving quality of subgrade can increase bed modulus by 12 to 78

percent. Regarding dependency of rail bed modulus to ballast layer thickness, percent of

increase in bed modulus due to change in this parameter is given in table 6.

Table 6. Percent of increase in rail bed modulus with additional in ballast layer thickness

Extent of increase in ballast layer thickness +5cm +10cm +15cm +20cm

20

30

40

50

60

70

25 30 35 40 45 50

Ballast layer Thickness (cm)

Tra

ck

mo

du

lus

(M

Pa

)

Axial load: 16 Tons Axial load: 18 Tons

Axial load: 20 Tons Axial load: 25 Tons

R

S3

s1

s2

Percent average of increase in rail bed modulus 0.93 1.72 2.6 3.77

In order to determine track modulus in terms of ballast layer thickness and bed Elasticity

modulus in general condition of Iran railway tracks some curves are represented in figure (6).

In order to maintain good railway track performance under traffic load and with regard to

field test performed in Iran railway tracks (in Tehran-Mashhad railway line), rail bed modulus

level may change to 70% in ballast layer retamping and restabilaztion interval which should

be accounted.

Fig 6: Rail bed modulus in terms of bed modulus of elasticity and ballast layer thickness

Track modulus as average for one loading cycle and subgrade condition with four classified

qualities (S1, S2, S3 and R) is obtained as follows:

subgrade type ONE: 32 MPa, subgrade type TWO: 36 MPa, subgrade type THREE: 46MPa,

subgrade type FOUR: 57MPa; these values decrease with regard to field traffic condition and

track repair and maintenance interval (tamping and stabilization). Table 7 gives effect of rail

bed modulus on maximum rail vertical displacement.

30

35

40

45

50

55

60

100 1000 10000 100000

Bed Elastic Modulus (kg/cm2)

Tra

ck M

od

ulu

s (M

Pa)

Ballast thickness: 30 cm

Ballast thickness: 35 cm

Ballast thickness: 40 cm

Ballast thickness: 45 cm

Ballast thickness: 50 cm

Table 7. Effect of change in track modulus on maximum vertical displacement of rail

Track modulus

Percent of track modulus increase

maximum vertical displacement of rail (mm)

Percent of decrease in maximum vertical displacement of rail

Speed: 160km/h Speed: 100km/h Speed: 160km/h Speed: 100km/h Maximum axial passing load (ton)

16 18 20 25 16 18 20 25 32 0 1.27 1.54 1.41 1.76 0 0 0 0 36 12.5 1.23 1.28 1.26 1.57 10.26 10.29 10.16 10.07 46 42.75 0.99 1.11 1.02 1.27 27.69 27.69 27.72 27.72 57 78.125 0.84 0.95 0.78 1.09 38.24 38.18 38.17 38.08

According to this table it can be said that increase in track modulus leads to decrease in

vertical displacement due to imposing load of vehicles’ wheels in rail section.

CONCLUSION

In this paper, regarding the condition of different components of track in building and

operation of track superstructure which lead to change in track modulus extent, it was

attempted to study the effect of these changes on track modulus extent in field test and

numerical analysis. Result analysis in field test suggests that, under axle load of 20 tons, the

maximum change in sleeper vertical settlement and Track modulus before tamping shows

54% decrease and 337.5% increase, respectively, compared to after track tamping and

stabilization. In numerical analysis method, proposed track superstructure model by the aid of

Ansys software was calibrated based on field test, and track modulus was specified under

different conditions of loading. Analysis of results indicated the extent of effects of various

parameters on track modulus. Generally vertical displacement of rail decreases by increasing

rail bed modulus, decreasing train speed or axle load of rail-borne vehicles. Also, results show

that increasing track modulus with improvement of subgrade quality by 11 to 80% can be

varied, and changes in ballast layer thickness can improve track modulus by 0.93 to 3.77%.

As findings show, type of subgrade quality and ballast layer thickness does not have any main

effect on percent of vertical displacement of rail. It can be said that rail bed modulus varies

by increase in ballast layer thickness and bed layer quality. It increases by increase in bed soil

quality and elastic modulus. Finally regarding obtained results in terms of ballast layer

thickness and bed elastic modulus as two main parameters influencing rail bed modulus, it is

possible to determine track modulus with regard to repair and maintenance conditions as

indicated in field tests.

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