Journal of Mechanical Science and Technology 26 (12) (2012) 3885~3892 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-012-0886-5
Field investigation of variation of loading pattern of concrete sleeper due to ballast sandy contamination in sandy desert areas† Jabbar Ali Zakeri1,* and Rauf Abbasi2 1
School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran
2
(Manuscript Received November 9, 2011; Revised May 8, 2012; Accepted July 16, 2012) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract Sleeper is one of the most important components in a railway track system. Thus, for accurate analysis and design of concrete sleepers, knowledge of imposed loading pattern is necessary. Sandy desert areas are critical regions where loading status of concrete sleeper is different from other areas. In these areas, the influence of flowing sand grains between the ballast aggregates increase the stiffness of ballast layer; consequently, rail support modulus increases, so the received share of total axle load subsequently increases on the sleeper which is placed under the wheel load. On the other hand, the pressure distribution underneath the sleeper changes considerably. In this paper, the results of a field investigation about the variation of rail support modulus and also variation of loading pattern of concrete sleeper followed by the variation of bending moment of sleepers in sandy desert regions were presented. Keywords: Field investigation; Railway; Desert areas; Loading pattern; Concrete sleeper; Moving load ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Sleeper is one of the most important components in the railway track system. This structural element has several functions; for example, transmitting the rail load to the ballast layer, providing mechanical resistance in lateral and vertical directions and maintaining track gauge [1]. Awareness of applied forces is the most important task in analysis, design and maintenance of concrete sleepers. Various hypothetical and theoretical opinions about the loading pattern of sleeper have been presented up to now; but, there is a lack of experimental investigations on the load transfer mechanism by the concrete sleepers in different conditions of tracks [2]. Sandy desert areas are one of the critical areas, through which railway track may pass. In these regions, accordingly, the rail support modulus and loading pattern of concrete sleeper change considerably due to influence of flowing sand grains between ballast aggregates, so-called ballast contamination. The investigation presented here was conducted to provide the understanding of variation of the rail support modulus and load transfer mechanism and the resulting variation on bending moments of the sleeper. Also, these results were compared with the similar results in non-sandy areas.
The field tests of this research were as follows: (1) Ballast sampling in different test locations to determine ballast contamination. (2) Determining the rail support modulus in test sites. (3) Determining the rail-seat load and distribution of sleeper-ballast contact pressure. In this paper, first, theoretical background related to the loading pattern of concrete sleeper was presented. Then, ballast layer contamination and determination method of the rail support modulus was described. Next, the process of field tests and the results of them were explained and compared with results of the similar field study related to non-sandy areas.
2. Theoretical basics of applied load to the sleeper In common methods of analysis and design as recommended by AREMA, analysis steps of concrete sleeper include: (1) calculation of dynamic load transferred from wheel to the concrete sleeper, (2) determination of the maximum rail-seat load, (3) determination of pressure distribution status underneath the sleeper, and (4) attainment of bending moment along the sleeper (especially, at the rail seat position and sleeper center) [3].
*
Corresponding author. Tel.: +98 21 7391 3517, Fax.: +98 21 7745 1568 E-mail address:
[email protected] † Recommended by Editor Yeon June Kang © KSME & Springer 2012
2.1 Maximum load at rail seat position Several factors affect axle load distribution on adjacent
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Table 1. Formulas for calculation of maximum rail seat load. Developer
Formula
Awoleye [6]
qr = 0.5P
Australian formula, ASR [7]
qr = 0.43P
AREA (Pre-stressed concrete sleepers at 760 mm centers) [8]
qr = 0.6P
ORE (BR type F pre-stressed concrete sleeper at 760 mm centers) [9]
qr = 0.65P
Watanabe (Finite element analysis) [10]
qr = 0.4P
Iranian code 301 (Pre-stressed concrete sleeper at 600 mm centers) [11]
qr = 0.6P
Clark [12]
qr = suymf
UIC (Concrete sleeper) [13]
qr = Ps(1+γp×γv) γd×γr
Table 2. Hypothetical distributions of sleeper-ballast contact pressure. Distribution of contact pressure underneath the concrete sleeper
2.2 Pressure distribution under the sleeper Under sleeper, stresses are the response of the ballast layer against the applied load from the sleeper. Numerous factors affect the contact pressure distribution underneath the sleeper which includes aggregation quality of ballast, mechanical properties of concrete sleeper (rigidity), quality of track maintenance operations, volume of passing traffic and time passed after tamping operation. After the tamping operation and creating the mass density of ballast in two end sections of the sleeper, the largest share of bearing receives these sections and central part of the sleeper has negligible contribution of the bearing. Over time and with traffic passing, the accumulation of ballast material is reduced at two ends of the sleeper and therefore the pressure distribution gets more uniform underneath the sleeper [1]. In order to analyze and calculate the loading and bending occurred in concrete sleepers, various railway regulations consider a simple form of stress distribution beneath the sleeper. A number of hypothetical distributions of sleeperballast contact pressure are presented in Table 2. For example, AREA proposed that, to calculate the average of contact pressure between the concrete sleeper and ballast layer, the maximum rail-seat load is deemed to double and then the calculated average pressure should be considered for the entire
Developer
Uniform distribution
AREA [8], Talbot [15], Raymond [16]
According to laboratory test
ORE [9], Talbot [17]
Maximum pressure under the rails
ORE, Talbot [15]
Concentration of pressure in sleeper center
Talbot [17]
Tamping effects ORE [9], Talbot and ballast [15], Bartlett compaction in the [18], Clark [19] vicinity of rails
s: sleepers space (mm), u: rail support modulus (MPa), ym: maximum deflection of rail due to wheel load (mm) and f: factor of safety for considering the changes of support conditions due to maintenance operations.
sleepers which include rail support modulus, sleeper distance, weight of rail, characteristics of fastening system, type and dimension of sleepers and quantity and quality of maintenance operations. Among these factors, rail support modulus is more important than other factors because the effects of other factors are hidden within this factor [4, 5]. Table 1 indicates several formulas which have been proposed to determine the maximum rail seat load thus far. In these formulas, qr and P are the rail seat load and wheel load, respectively.
Description
According to field test
Zakeri and Sadeghi [2]
sleeper [14].
3. Rail support modulus and its measurement methods Rail support modulus is defined as the support load being imposed on rail length unit per vertical deflection of rail unit. This parameter is measured in Pa and is indicated by u [20]. Rail support modulus is an important parameter which affects track performance and maintenance costs. A low amount of this modulus causes the track differential settlements and high value of rail support modulus leads to the reduction of displacement and stress in rail support. But, on the other hand, a low amount of rail support modulus causes axle load to be distributed over a fewer number of sleepers and therefore the received share of axle load for any sleeper finally increases [21]. Ballast layer condition such as contamination of ballast is an effective factor for the rail support modulus because the ballast layer stiffness and subsequently rail support modulus increase when the fine grain particles penetrate between ballast aggregates [22]. There are several methods for measuring rail support modulus: theoretical, theoretical-experimental and experimental. Talbot-Wasiutynski method is one of the theoreticalexperimental methods which is accepted for many railroads and has reliable accuracy despite its high costs [1]. This method that was used in this field investigation to determine the rail support modulus in sandy desert areas was provided by the Talbot committee in 1918 [23] and was developed by Wasiutynski twenty years later [24]. According to this method, the rail support displacements should be measured at the locations of several adjacent sleepers; then, considering the vertical
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granular behavior. So, the stiffness of ballast layer and therefore rail support modulus increases. In addition, several other problems may occur in such areas. These problems include chemical reaction of salt and concrete of sleeper leading to concrete corrosion, erosion of rail, fastening system and other metal components of track in the vicinity of salty sands, rail crown crushing and flattening due to reduced track elasticity, increase of maintenance operations costs, switches dysfunction, etc.
5. Methodology of field tests Fig. 1. Rail support displacement under heavy and light load.
equilibrium of a rail, "the rail support modulus, u, is calculated by dividing the sum of the wheel loads ∑P by the area formed between the undeformed and the deformed rail, AR". Noting that p(x) is the pressure which acts on the rail base and p(x) = uw(x), it follows that [1]:
.
(1)
However, field tests have indicated that rail support displacement was is not increasing linearly with increasing the applied load [25]. Thus, according to this fact and considering Fig. 1, the following formula was proposed by Prof. Kerr [1], where h and l correspond to heavy and light wheels, respectively, and a is the distance between sleepers centers and, therefore, denominator is the area formed between the undeformed rail due to heavy wheel load and undeformed rail due to light wheel load [1].
(2)
4. Ballast contamination in desert sandy areas The particles (finer than 9.5 mm) are assumed as the contamination components of ballast layers. This contamination increases with time. Ballast breakage, infiltration from surface, sleeper wear, infiltration from underlying granular layer and subgrade infiltration are the most important sources of ballast contamination [20]. Ballast layer contamination disrupts proper performance of this layer; for example, fine gravel size contamination increases the resilient modulus of ballast layer and, consequently, reduces the track elasticity [26]. Also, tamping operation becomes more difficult when the ballast layer voids are filled with fine particles [20]. Desert sandy areas are one of the most critical areas about ballast layer contamination with fine grain particles. In these regions, flowing sands are transmitted by wind and fill the voids of ballast layer; finally, this layer takes away from the
A series of thorough field experiments were conducted in this investigation. These tests pursued the following objectives: (1) Studying the amount of ballast contamination in sandy desert areas, (2) Calculating the rail support modulus at test locations of desert sandy regions using vertical displacement of rail support and by Talbot-Wasiutynski method, (3) Determining the received share of axle load for the sleeper located underneath the wheel, (4) Determining pressure distribution underneath the concrete sleeper (between the ballast layer and sleeper), (5) Comparing the above results with similar results related to non-sandy areas, (6) Determining the relationship between loading pattern of concrete sleeper and the rail support modulus, and (7) Calculating bending moment of concrete sleeper in the condition of contaminated ballast. The field investigations were conducted in four different locations in a sandy desert block of east district of Iran railway networking. Selection of these four locations was done based on ballast layer granular contamination and another similar field investigation related to non-sandy areas in Iran was selected as the fifth location to compare these results. In the selected straight track, the sleepers were B70 prestressed concrete sleepers, rail was UIC60, sleeper spacing was 60 cm, fastening system was Vossloh, ballast aggregates were Granite with size of 20 to 60 mm and thickness of ballast and sub-ballast layers were 30 and 15 cm respectively. In any test location, three series of measurement were done; (A) Ballast sampling for determining the ballast layer contamination, (B) Measuring rail support displacements due to both heavy and light wheel loads in order to calculate the rail support modulus of test locations; these measurements were done by installing the LVDT equipments at the end of the adjacent sleepers. (C) Installing four load cells at the bottom of a sleeper and putting this sleeper in test locations instead of a track sleeper in order to evaluate the received share of wheel load for the under-load sleeper and to determine the distribution status of contact pressure between the sleeper and ballast layer.
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Table 3. Ballast contamination. No. 5
Test location
No. 1
No. 2
No. 3
No. 4
ballast contamination
%62.7
%50.7
%27.5
%25.9 Trace
Fig. 3. LVDTs’ installation.
Fig. 2. Situation of railway track in the sandy desert area.
5.1 Determining ballast contamination According to ASTM-C136 standard [27], ballast sampling was done in each four test sites and particle size analysis was taken on the samples. The test sites were located in a block of east district of Iran railway networking which was a critical area of the flowing sand. The tests were conducted in four different locations and with different granular contamination of ballast. These locations were selected as ocular and, during location selection; the fine grain amount was not specified in the depth of ballast layer. Track situation in the sandy desert area is shown in Fig. 2. Table 3 indicates the percentage of ballast contamination (particles smaller than 9.5 mm). 5.2 Measuring vertical displacement of rail support LVDTs1 were used in this field investigation to measure the vertical displacement of rail support due to heavy and light loadings. These measurements were necessary to calculate the rail support modulus according to Talbot-Wasiutynski method. LVDTs were placed on the end of adjacent sleepers while being connected to the data logger which was connected to a computer in order to record the vertical displacement of rail support as time history. The data logger recorded these displacements per 0.0005 second. The LVDTs were installed with special steel bases because 1
Linear variable differential transformer
Fig. 4. Load cells layout and installation underneath the sleeper.
these equipments were very sensitive and accurate so they must be installed without any movement. The tip of device that was the sensor part could move inside and outside and it must be placed on the point that the vertical displacements were measured. The special steel bases were buried inside the trench in the vicinity of ballast shoulder and the metal horns located at the end of these bases helped to complete their stabilization inside the soil. Fig. 3 shows the method of LVDTs installation [28]. 5.3 Determining sleeper loading pattern To calculate the received share of the wheel load for the under wheel sleeper and to determine the load distribution pattern under the sleeper, four load cells were installed at the bottom of the sleeper (between the ballast layer and sleeper). Fig. 4 indicates the load cells layout and installation beneath the sleeper. Considering test conditions, the capacity and type of load cells were selected. For these field tests, 3-ton load cells with the accuracy of %0.05 were used. Since it was assumed that the sleeper loading pattern was symmetrical in the straight track, load cells were installed only in one half of the sleeper. The installation places of load cells under the sleeper included load cell No. 1 at the distance center between the end of sleeper and rail-seat point, load cell No. 2 underneath the
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Table 5. Magnitude of loads recorded by load cells (kg).
Table 4. Rail support modulus for test locations. Test location
No. 1
No. 2
No. 3
No. 4
No. 5
Rail support modulus calculated due to both heavy and light wheel loads (MPa)
116
108
96
90
18
rail-seat point, load cell no.3 at the distance center between rail-seat point and sleeper center and load cell no.4 at the sleeper center. The length of the steel plates mounted on the load cells were 30, 40, 40 and 40 cm, respectively. The output signals from the load cells were transferred to a computer using a data logger and software package. The software can obtain data from all load cells simultaneously (10000 data per second) and import them into the Excel program or text file. Calculation of rail support modulus needs two types of loading: heavy and light. Load of 111 tons from a 6-axle GT26CW locomotive as heavy loading (with the speed of 15 km/hr) and load of 4 tons from a 2-axle lightweight wagon as light loading (static load) were applied to the track. Therefore, considering the dynamic load coefficient, the axle loads of heavy and light loading were equal to 19.8 tons and 2 tons, respectively. For the similar field study in the non-sandy area, the static axle load of 13.3 tons from a 4-axle tamping machine was applied [2].
Test location
No. 1
No. 2
No. 3
No. 4
No. 5
Load cell No. 1
1662
1598
1507
1459
861
Load cell No. 2
2290
2319
2195
2196
1294
Load cell No. 3
1330
1216
1362
1421
694
Load cell No. 4
1178
1162
1105
1126
498
Axle load
18500
18500
18500
18500
1300
Table 6. Contact pressure values under the sleeper (kg/m). Test location
No. 1
No. 2
No. 3
No. 4
No. 5
Load cell No. 1
5540
5330
5020
4860
4260
Load cell No. 2
5730
5800
5490
5490
4810
Load cell No. 3
3330
3040
3410
3550
2570
Load cell No. 4
2940
2900
2760
2820
1840
Table 7. Values of rail support modulus and received share of load for sleeper considering ballast contamination. Ballast contamination percentage Rail support modulus (MPa) Received share of axle load for under wheel sleeper Max-Min ratio for under sleeper contact pressure
%62.7 %50.7 %27.5 %25.9 Trace 116
108
96
90
18
%59.3 %57.7 %56.7 %56.9 %46.5 1.94
1.99
1.99
1.95
2.60
6. Results of tests and interpretation Complete analysis was done on the recorded data from the LVDTs and load cells for all test locations with different percentage of ballast layer contamination. Final analytical results could be presented as follows: note that, in these results, the data of similar investigation related to the non-sandy area were assumed as test location No. 5. 6.1 Calculating rail support modulus for test locations According to Talbot-Wasiutynski method and using the recorded data of rail support displacement by LVDTs under heavy and light loading, the rail support modulus was calculated for all test locations. The rail support modulus for test locations is indicated in Table 4. 6.2 Results of sleeper loading pattern The values recorded by the load cells are presented in Table 5. Also, according to the dimensions of the steel plates placed on the load cells, the contact pressure values under the sleeper at load cells’ installation places are given in Table 6.
7. Interpretation of the field test results Useful results can be obtained from these conducted field investigation on rail support modulus variations and sleepers’
loading pattern due to ballast contamination. Also, the relationship between rail support modulus and sleeper loading pattern or sleeper bending moments could be determined. Table 7 indicates the values of the rail support modulus and received share of axle load for under wheel sleeper considering the percentage of ballast contamination. Assuming the symmetry of loading on the sleeper, twice of the total load of the load cells No. 1, 2 and 3 plus the load of load cell No. 4 was equal to the received share of the axle load for the sleeper. Also, this table shows the proportion of the maximum and minimum amounts of the recorded loads by load cells for any test location. The results indicated that the received share of axle load was higher in the sandy areas in comparison with non-sandy one and this share was increasing with the more contamination of the ballast layer. This phenomenon was due to the influence of flowing fine grains between the ballast aggregates and, consequently, increase of the rail support modulus. The maximum amount of pressure underneath the sleeper occurred under the rail-seat point and the minimum amount happened in the middle point of the sleeper. Max-Min ratio of contact pressure for the desert sandy regions was considerably less than the ratio of non-sandy areas; with increasing the ballast contamination, this proportion amount got closer to 1. In other words, the contact pressure distribution underneath the sleeper was more uniform in the track with contaminated bal-
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Location #1
Location #2
Location #3
Location #4
Location #5
Fig. 5. Contact pressure distribution and bending moments for the concrete sleeper.
last layer. Irregularities in these values and also other irregularities related to the under sleeper pressure were justified by under sleeper tamping and disturbance of ballast materials in the upper part of this layer. 7.1 Bending moments of concrete sleepers in sandy desert areas The contact pressure distribution under the sleeper was more uniform in sandy regions and was more gradually uniform due to traffic loads and time away from the tamping
operations; consequently, larger bending stresses were expected in the sleeper and these issues led to faster and more damage to the concrete sleeper used in the sandy desert regions [29]. Therefore, it is essential to pay more attention to track maintenance operations in the sandy desert areas. Fig. 5 illustrates the contact pressure distribution underneath the prestressed B70 sleeper and bending moments along the sleeper considering the contamination of ballast. Note that, in test location No. 5 (non-sandy area), before calculating the bending moment, the load values recorded by load cells increased in the proportion of axle loads (18.5/13.3);
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Table 8. Comparison of maximum bending moments with noncontaminated condition. Test location
No. 1
No. 2
No. 3
No. 4
No. 5
Maximum bending moment (kg.m)
843.9
820.9
774.0
754.8
661.5
Proportion of maximum bending moment to related amount of non-sandy area
1.28
1.24
1.17
1.14
1
these moments can be compared in similar circumstances. The proportions of maximum bending moments (occurring at under rail position) of sandy desert test locations to the maximum value of non-sandy area are presented in Table 8. As can be seen, in location no. 1 that was in a critical situation, %28 increase occurred in the maximum bending moment in comparison with the non-sandy area.
8. Conclusion The results of this field investigation indicated that the influence of fine sandy grains between ballast aggregates increased the stiffness of ballast layer; therefore, the rail support modulus increased in the sandy desert area. The received share of axle load for under wheel sleeper and sleepers bending moments was subsequently higher in such regions; thus, more careful planning was necessary about the elimination of ballast contamination and other maintenance operations. The forces measured by the inserted load cells underneath the sleeper indicated that, with increasing the sandy contamination of ballast, pressure distribution underneath the concrete sleeper gradually was approaching towards being uniform. It should be noted that, the tests of this investigation were done immediately after the insertion of the tested sleeper and handy tamping; therefore, no traffic crossed from the mentioned sleeper location. Passing traffic gradually reduced the pressure concentration beneath the rail-seat and then middle parts of the sleeper attracted a greater amount of contact pressure between the sleeper and ballast. This phenomenon was due to the movement of ballast material from the sides toward the middle part of the sleeper which occurred because of the multiple passes of traffic load. The ratio between the maximum and minimum amounts of under sleeper contact pressure was obtained for test locations. The maximum amount of pressure underneath the sleeper occurred beneath the rail-seat point and the minimum amount happened in the middle point of sleeper. For the desert sandy regions, this ratio was considerably less than the ratio of non-sandy areas and this case demonstrated more uniform distribution of the contact pressure between the sleeper and the ballast layer. Another point about the applied loads to the sleeper is to determine the received share of axle load for under wheel sleeper. In the present paper, pressure distribution under the sleeper was assumed symmetrical because all tests were performed in
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the straight track. The received share of total axle load for the sleeper was considerably greater in desert sandy regions than the non-sandy regions. This issue was due to the influence of flowing sand between the ballast aggregates and thus considerable increase of the rail support modulus. On the other hand, as was expressed before, the contact pressure distribution underneath the sleeper was more uniform in desert sandy regions and, due to the traffic loads, it slowly became more uniform; consequently, larger bending stress was expected in the sleeper. Calculations of bending moments of sleeper indicated that these moments were considerably greater in the condition of contaminated ballast. In track with the contamination of %62.7 (location No. 1), the maximum amount of bending moment which occurred beneath the rail seat position was 28% greater than the similar moment of non-contaminated track. These issues led to more and faster damage to the concrete sleeper in sandy areas. Therefore, more attention to the maintenance of sleepers seems to be necessary in such regions. Thus, the period duration of tamping and ballast cleaning should be shorter in these areas. This can be done according to the sleeper bearing capacity and also the amount of ballast contamination.
Acknowledgment The authors are grateful to the Iranian Railway Research Center for the financial support throughout this study. The authors would like to thank the technical Engineers, Sh. Homavandi and H. Mohammadvand, for their assistance during the course of this project. Also, authors wish to thank Engineers M. Moeeni and H. Mortazavi for their helps and suggestions.
References [1] A. D. Kerr, On the determination of the rail support modulus k, International Journal of Solids and Structures, 37 (2000) 4335-4351. [2] J. A. Zakeri and J. Sadeghi, Field investigation on load distribution and deflections of railway track sleepers, Journal of Mechanical Science and Technology 21 (2007) 1948-1956. [3] AREMA, Manual for railway engineering, American Railway Engineering and Maintenance Way Association, Chapter 5 and Chapter 30, Part 1 (2006) 11-17. [4] J. A. Zakeri, Investigation on railway track maintenance in sandy-dry areas, structure and infrastructure engineering, Volume (8) Issue 2 February (2012) 135-140. [5] J. A. Zakeri and R. Abbasi, Field investigation on distribution of contact pressure between sleeper and saturated ballast with flowing sand, 11th International Conference of Railway Engineering, London, (2011). [6] E. O. A. Awoleye, Ballast type–ballast life predictions, British rail research LRCES122, (1993). [7] M. D. O’Rourke, Critique of conventional track design procedures as applied to heavy axle load conditions, BHP Melb.,
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Lab. Res. Rep. No. MRL/C77/78/27 (1), (BHP MNM H1/TDC/78/053) (1978). [8] AREA, Manual of recommended practice, American Railway Engineering Association, Washington D.C., USA, 1980, 1981. [9] ORE, Stresses in the rails, Report D71/RP8/E, Utrecht (1968). [10] V. A. Profillidis, Railway engineering, Aldershot, Ashgate Publishing Limited (2000). [11] Iranian Railway-Code 301, General-technical properties of ballasted railway track (2005). [12] C. W. Clark, Track loading fundamentals, The Railway Gazette, Part 1, 45-48, Part 2, 103-107, Part 3, 157-163, Part 4, 220-221, and Part 7, 479-488 (1975). [13] International Union of Railway, Design of mono-block concrete sleeper, UIC CODE, 713 R, 1st Edition (2004). [14] AREA, American railway engineering association, Manual of Recommendation, Special Committee on Concrete Ties (2004). [15] Talbot Committee, ASCE-AREA committee on stresses in railroad tracks, Sixth Progress Report, Proceedings AREA, 35 (1933). [16] G. P. Raymond, Railroad wood tie design and behavior. Proc., ASCE, Journal 103, Trans. Eng. [17] A. N. Talbot, Fifth progressive report of special committee on stresses in railroad track. Chairman, Proceeding of the AREA, 30, 34-35. [18] D. L. Bartlett, The stability of long welded rails, Civil eng. And public works review, 55 (649), 1099-1035, (650), 11701171, (651), 1299-1303, (653), 1591-1593 (1960). [19] R. A. Clark and V. P. Lownder, Discrete support track dynamics model, Theory and program guide, British Railway Board Railway Research and Development Division Technical Report TM.TS.95 (1979). [20] E. T. Selig and J. M. Waters, Track geotechnology and substructure management, University of Massachusetts, USA (1994). [21] A. M. Zarembski and J. Palese, Transitions eliminate impact at crossings, Railway Track and Structures, August issue (2003). [22] D. Li and E. T. Selig, Resilient modulus for fine grained subgrade soils, Journal of Geotechnical Engineering, ASC, 120 (6) (1994) 939-957.
[23] Talbot Committee, ASCE-AREA committee on stresses in railroad tracks, First Progress Report, Proceedings AREA, 19 (1918). [24] A. Wasiutynski, Recherches experimentales sur les déformations elastiques et le travail de la superstructure des chemins de fer (Experimantal research on the elastic deformations and stresses in a railroad track, in French), Annales de L’Academie des Sciences Techniques á Varsavie, IV, Dunod, Paris, France (1937). [25] A. M. Zarembski and J. Choros, On the measurement and calculation of vertical track modulus, AREA Bulletin 675, Nonember-Desember (1979) 156-173. [26] B. Indraratna, J. S. Vinod and J. Lackenby, Influence of particle breakage on the resilient modulus of railway ballast, Journal of Géotechnique, 59 (7) (2008) 643-646. [27] ASTM, American society for testing and materials. C13696 a. Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates. [28] J. A. Zakeri and R. Abbasi, Field investigation of variation of rail support modulus in ballasted railway track, Latin American Journal of Solids and Structures, 9 (2) (2012) 643656. [29] J. A. Zakeri, E. Morteza and F. Masoud, Evaluation of humped slab track performance in desert railways, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 225 (6) November (2011) 567-574.
Jabbar Ali Zakeri received his B.S. degree in Civil Engineering and M.Sc. degree in Structural Engineering from Tabriz University in 1992 and 1995, respectively. He then went on to receive his Ph.D. degree in Road and Railway Engineering from Beijing Jiaotong University in 2000. Dr. Zakeri is currently an Associate Professor at the School of Railway Engineering at Iran University of Science and Technology. His research interests are in the area of dynamic analysis of train – track interaction, railway track dynamics, track maintenance, and construction.
