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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, [email protected]; Phone+98-871-3228257


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


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.

Methods of measurement of rail bed modulus

experimental methods

Theoretical-experimental methods

Theoretical methods

Method of Academy of Railway Science of China

AREMA bylaw model

Pyramid model

Method proposed by Talbot Method Nebraska University Beam on elastic subgarde model Method of Technical University of Delft Method USA Transportation Technology Center

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


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

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.

a. Test location

b. base placed in track for performing test

c. Track tamping machine

d. Track stabilizer 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]

Elasticity modulus Materials Type (kg/cm2) poor Subgrade (S1) Fair Subgrade (S2) good Subgrade (S3) Rocky subgrage (R) Ballast Sandy subballast 125 250 800 30000 1300 2000 0.4 0.3 0.3 0.2 0.2 0.3 Poisson's ratio (kg/cm2) 0.15 0.1 0 15 0 0 10 20 30 20 45 35 Adhesion Friction angle

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 Sleeper moment of inertia (cm4) Rail moment of inertia (cm4) Ballast thickness (cm) Subballast thickness (cm) Wheel load (Ton) Sleeper length(cm) Sleeper width(mm) Sleepers spacing (cm) Rail area (cm2) Sub-ballast Poisson's ratio Track system 24200 3950 38 15.2 14.2 259 229 61 86.5 0.3 Parameter Elastic modulus of bed (kg/cm2) Elastic modulus of Subballast (kg/cm2) Elastic modulus of ballast (kg/cm2) Elastic modulus of Sleeper (kg/cm2) Elastic modulus of rail (kg/cm2) Bed Poisson's ratio Ballast layer Poisson's ratio Sleeper Poisson's ratio Rail Poisson's ratio Track system 1240 1260 2490 2.07×105 2.07×106 0.4 0.4 0.3 0.25

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]

Model Field state Theoretical state Stress (kPa) 70 71 Bed surface displacement(mm) 0.85 0.89 Ballast surface strain 0.00155 0.00144

Discrepancy 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.


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

Track system characteristics Before tamping After tamping and stabilization of track 17.20 57.24 Rail bed Modulus (MPa) Sleeper 1 Sleeper 2 23.964 53.62 Sleeper 3 35.06 54.78

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).

Axial load: 16 Tons


Track modulus (MPa)

Axial load: 18 Tons Axial load: 25 Tons

Axial load: 20 Tons R S3

60 50 40


30 20 25 30 35 40 45 50

Ballast layer Thickness (cm)


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 Subgrade 1 to subgrade 2 Subgrade 2 to subgrade 3 Subgrade 3 to subgrade 4 Track modulus increase percent 11.81 28.86 23.62 Type of subgrade change Subgrade 1 to subgrade 3 Subgrade 2 to subgrade 4 Subgrade 1 to subgrade 4 Track modulus increase percent 44.1 59.3 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

Percent average of increase in rail bed modulus





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.

60 55

Track Modulus (MPa)


Ballast thickness: 30 cm


Ballast thickness: 35 cm

40 35

Ballast thickness: 40 cm Ballast thickness: 45 cm Ballast thickness: 50 cm

30 100 1000 10000



Bed Elastic Modulus (kg/cm )

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.

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

Percent of track modulus increase 0 12.5 42.75 78.125 maximum vertical displacement of rail Percent of decrease in maximum (mm) 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 1.27 1.54 1.41 1.76 0 0 0 0 1.23 1.28 1.26 1.57 10.26 10.29 10.16 10.07 0.99 1.11 1.02 1.27 27.69 27.69 27.72 27.72 0.84 0.95 0.78 1.09 38.24 38.18 38.17 38.08

Track modulus 32 36 46 57

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.


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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