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The contribution of ballast layer components to the lateral resistance of ladder sleeper track
Construction and Building Materials 202 (2019) 796–805
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
The contribution of ballast layer components to the lateral resistance of ladder sleeper track Guoqing Jing 1, Peyman Aela ⇑, Hao Fu School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
h i g h l i g h t s Lateral resistance of ladder sleepers is investigated by the lateral track panel test. The contribution of ballast components to the lateral resistance is obtained. The DEM simulation of a ladder sleeper on the ballast layer was performed.
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Article history: Received 23 September 2018 Received in revised form 29 December 2018 Accepted 3 January 2019
Keywords: Ladder sleeper Ballast Lateral resistance LTPT Shoulder height Shoulder width Crib height DEM
a b s t r a c t The sleeper-ballast interface of railway tracks directly is associated with lateral resistance which plays an important role in the mechanical behavior of ballasted tracks. In a real-case implementation of ballasted track for speeds as high as 400 km/h, sufficient lateral resistance is vital to prevent the lateral movement of the track. In view of the future development, a series of full-scale lateral track panel tests (LTPT) were conducted to evaluate the lateral resistance of ladder sleepers as a substitution of monoblock sleepers. The experimental results revealed that the application of the ladder sleepers caused an increase in lateral resistance of the ballasted track as well as a reduction in the use of ballast aggregates. In addition, the contribution of the ladder sleeper facets to the lateral resistance was investigated by the discrete element method (DEM). In conclusion, crib ballast has the main role in the lateral resistance of ladder sleeper tracks. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Ballast layer is an important component of superstructure used to transmit vertical loads from sleepers to subgrade. Investigating track lateral buckling, caused by temperature changes and moving trains is a continuing concern within continuously welded rails (CWR) and is also a major issue regarding track stability [1]. Lateral resistance of sleepers is one of the most important factors to prevent the lateral movement of ballasted tracks. This concept has been comprehensively investigated by Kish, A [2] studies demonstrating the importance of track stability influenced by vertical loads induced by moving trains and track curvature. According to this research, the type and weight of sleepers, and sleeper spacing ⇑ Corresponding author at: Beijing Jiaotong University, No.3, Shangyuancun, Haidian District, Beijing 100044, China. E-mail addresses: [email protected] (G. Jing), [email protected] (P. Aela). 1 Beijing Jiaotong University, No. 3 Shangyuancun Haidian District, Beijing 100044, China. https://doi.org/10.1016/j.conbuildmat.2019.01.017 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
are important elements which influence the lateral stability of tracks. Ballast layer specifications are other parameters which affect the lateral resistance of the track such as ballast compaction, degradation and the geometry of the ballast layer. For instance, there is about 40–50% reduction in the lateral resistance of the sleeper after ballast tamping due to the disturbance of ballast compaction [3]. In another study, as noted by Kish [6], ballast tamping decreases the lateral movement of the ballasted track by 40–70 %. In terms of the impact of ballast layer components, Le Pen and Powrie [4] reported that the contribution of ballast bed, crib ballast, and shoulder ballast to the lateral resistance under vertical loading condition was in the range of 26–35 %, 37–50%, and 15– 37%, respectively. Thus, friction between ballast and sleeper sides and the base has a higher resistance than passive pressure between sleeper ends and shoulder ballast under vertical loading condition. In contrast, B. Lichtberger [5] proposed the range of 45–50%, 10– 15%, and 35–40% for the resistance of ballast bed, crib, and shoulder ballast, respectively. To sum up, the passive earth pressure of the shoulder ballast and sliding friction of crib ballast have a differ-
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Fig. 1. Components of lateral resistance forces for a) monoblock, b) ladder sleepers.
by Wakui et al [9], and Asanuma, K [10] as it aims to meet the lateral displacement of ballast tracks with the following characteristics: The prolongation of the life of ballast tracks and consequently lengthen maintenance and tamping intervals. Lowering life-cycle cost by minimizing maintenance costs. The reduction of sleeper settlement into the ballast. Increasing the track stability by means of high-mass and continuous support and occupying less track area. An effective alternative to reduce ground vibration induced by moving trains [11].
Fig. 2. PSD for tests.
ent proportion to the lateral resistance governed by the ballast compaction, the friction coefficient between ballast and sleepers, and loading conditions. In recent years, the lateral resistance of tracks has increased with the use of monoblock concrete sleepers widely in railway tracks [6]. Furthermore, there are limited methods to increase lateral resistance regarding ballast material and ballast compaction. Ballast reinforcement using polymeric binders is an innovative method to improve the lateral stability of ballast tracks [7]. Among existing approaches to enrich the lateral resistance of the track, the type and geometry of sleepers have an important impact on the lateral resistance. The use of ladder sleeper tracks is a sustainable solution first proposed by Moses, NK et al. [8] in order to reduce vibrations in high-speed slab tracks, and studied
Although the lateral movement of the ballasted ladder track has been already evaluated [12], previous studies have not dealt with the effect of the geometry of the ballast layer on the lateral displacement of the ladder sleeper. Therefore, with an aim to investigate the lateral resistance of ladder sleeper tracks with the contribution of the base, crib, and shoulder ballast as shown in Fig. 1, a series of lateral track panel test (LTPT) were conducted for a ladder sleeper on the ballast layer. In the next stage, coupled with experimental tests, the DEM simulation of LTPT was developed using PFC3D. Recently investigators have examined the effect of ballast bed conditions on lateral resistance of the ballast layer in PFC. It has been observed that the shoulder width greater than 400 mm and shoulder slope of 1:1.75 provide sufficient lateral resistance against the movement of monoblock sleepers [13]. In another research, Hou, W et al. [14] confirmed the effectiveness of sleeper support conditions on the stress distribution. Therefore, a well-compacted ballast layer is required to minimize the movement of ballast particles. According to previous research [15–17], the ballast particle shape is an important parameter which influences the mechanical behavior of ballast aggregates in DEM simulations. In this regard, Khatibi et al. [18] developed a numerical model in conjunction with experimental studies to evaluate the
Fig. 3. Geometrical characteristics of the ladder sleeper.
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effect of the realistic ballast shape on the reduction of particles movement. So far, no research has been found that surveyed the lateral resistance of ladder track on the ballast layer. This paper considered the lateral resistance of the ladder sleeper by means of lateral track panel tests (LTPT) to examine the effect of shoulder width and crib ballast height on the lateral resistance of the ladder sleeper. In the next section, the DEM simulation of LTPT has been conducted using 3D-laser scanning and PFC3D. After the validation of numerical results of the DEM models via experimental data for various ballast layer conditions, a ballast layer with the shoulder height of 150 mm was simulated to measure the influence of shoulder ballast height on the lateral resistance of ladder sleeper track.
2. Material and method
2.2. Testing procedure In the first step, ballast bed was initially compacted and leveled in three layers using a vibrating plate compactor to provide a layer with the length, width, and thickness of 10000 mm, 3600 mm, and 350 mm. In this stage, preparation of the track could be divided into changes in shoulder width and crib height according to Table 3. Ultimately, a ballast layer with the bulk density of 1650 kg/m3 was prepared. As shown in Fig. 4, the crib ballast in the ladder track system contributes as the passive pressure resistance against sleeper movement while it has the sliding friction resistance in monoblock sleeper track. Thus, the influence of crib height variations were considered in the present research. In case of changes in crib height, ballast was filled and well compacted by the vibrator from the bottom to top of the sleeper surface between longitudinal beams to examine the effect of 0%, 50%,75%, and 100% crib ballast height as shown in Fig. 5. To evaluate the influence of shoulder width, the lateral resistance of the ladder track with the shoulder width of 200, 300, 400, and 500 mm was measured. It should be noted that the ballast layer was tamped by tamper machine VPO-3000 with the weight and frequency of 80 kg and 67 Hz, respectively [19]. In order to apply lateral force, steel bars were positioned in the vicinity of the ballast track to provide a frame as support for applying horizontal force as illustrated in Fig. 6.
2.1. Characteristics of ballast and sleepers 2.3. Lateral resistance tests procedure Ballast material, used in the experimental tests, was crushed basalt aggregates which adequately met China National Standard TBT 2140 requirements, and particle size distribution (PSD) shown in Fig. 2. The geometry and characteristics of sleepers are represented in Fig. 3 and Table 1. In this research, all tests were conducted on a ballast layer with detailed specifications as illustrated in Table 2.
In order to evaluate the behavior of two types of concrete sleepers, lateral panel tests were conducted to investigate the lateral resistance of the ladder sleeper. In this method, the displacement of the sleepers was measured by attaching the two LVDTs with an accuracy of 0.001 mm and amplitude of 30 mm to the end of
Table 1 Ballast layer specifications. Track type
Length (m)
Sleeper space (mm)
Ballast height (mm)
Top width (mm)
Shoulder width (mm)
Shoulder height (mm)
Slope gradient
Monoblock track Ladder sleeper track
100 100
600 _
350 350
3500 3500
500 500
150 0
1:1.75 1:1.75
Table 2 Sleepers specifications. Sleeper type
Monoblock Ladder sleeer
Section height (mm) Rail seat
Mid-section
230 185
185 0
Bottom surface (cm2)
End surfaces (cm2)
Mass (kg)
Length (m)
Width (m)
7720 69,640
590 5500
350 3600
2.6 6
0.32 2
Table 3 The geometrical condition of ballast track samples. Sleeper type
code
Shoulder width (mm)
Shoulder height (mm)
Crib height
Ladder Ladder Ladder Ladder Ladder Ladder Ladder Ladder
SW500 SW400 SW300 SW200 CH100 CH75 CH50 CH0
500 400 300 200 none none none none
0 0 0 0 100% 75% 50% 0
full full full full
sleeper sleeper sleeper sleeper sleeper sleeper sleeper sleeper
SW: shoulder width, CH: crib ballast.
Fig. 4. Variations of shoulder ballast height and width in experiments and numerical modeling.
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Fig. 5. Ladder sleeper track with (a) 0%, (b) 25%, (c) 75%, (d) 100% crib ballast height.
the sleeper. The lateral displacement of different panels, described in Table 3, was recorded using a data logger until the horizontal displacement reached the steady state. In this case, the lateral force at a displacement of 2 mm was determined as the sleeper lateral resistance which was reported in different research [20,21]. It should be mentioned that the mean of the values obtained from LVDTs was recorded as the displacement of the sleeper.
3. Experimental results and discussions 3.1. Effect of shoulder width The effect of shoulder width is extensively investigated by Zakeri JA [22] and Liang, Gao [23]. In this way, Le Pen, L [24] claimed that the the threshold width of a level shoulder for monoblock sleeper track is about 0.75 m. However, far too little attention has been paid to the effect of shoulder ballast width on the lateral resistance of ladder sleeper tracks as illustrated in Fig. 7. In contrast to the contribution of the shoulder width to the resistance of monoblock sleepers, the lateral resistance of the ladder track was fairly steady over the different shoulder ballast width from 200 mm to 500 mm with a slight increment from 17.74 up to 18.66 kN/m. In other words, the lateral resistance measured on the ladder sleeper with the shoulder width of 500 mm was approximately 5% higher than that of the track with the shoulder width of 200 mm. The above findings are important and practical for ladder sleeper application considering that the reduction in the shoulder width in ballasted tracks.
3.2. Effect of crib ballast height As reported by Khatibi, F et al. [18], in previous studies on the contribution of ballast components to the lateral resistance of monoblock sleeper tracks, different proportions have been found to be related to loaded/unloaded condition of tests. In this regard, depending on the loading condition, the contribution of crib ballast differs from 9 to 54% of total lateral resistance. This variation could be related to the crib ballast density and friction coefficient between sleeper and ballast. In order to examine the impact of crib ballast height on the lateral resistance of ladder tracks, four push tests were carried out on the panel with 0, 25%, 50% and 100% of crib ballast in depth (Fig. 8). Accordingly, the lateral resistance was measured at 6.21, 11.46, 13.43, and 14.76 kN/m for ladder track panels respectively. In other words, due the passive pressure act of crib ballast, the lateral resistance of panels with 25%, 50%, and 100% crib ballast increased by 84%, 116%, 137% in comparison to the track with 0% crib ballast, respectively (Fig. 9). According to the above-mentioned results, increasing the ballast shoulder width had a negligible effect on lateral resistance than that of the crib ballast height. Therefore, there is no satisfactory justification for increasing shoulder ballast width in ladder sleeper tracks. These findings agree with finite element analysis reported by Kabo [25]. As noted in the previous sections, the lateral resistance of the ladder sleeper track significantly increased with the crib height increment. This can be attributed to the high
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Fig. 6. The test set up for (a, b) ladder sleeper, and (c) monoblock sleeper.
frictional force in the interface between ladder sleeper and crib ballast. Consequently, the implementation of crib ballast up to the sleeper top surface has been recommended. 4. Numerical modeling In order to measure the lateral resistance of ballast layer components throughout the sleeper movement, DEM simulation of ladder tracks with the shoulder height of 0 mm and 150 mm was
performed in PFC3D. In this way, the shape of particles was generated based on the image analysis method described earlier by Yunlong, G [26]. In order to occupy the generated particle geometry with the sufficient number of pebbles, min/max radius ratio of pebbles and a angle were defined in the range of 0.15–0.4 mm and 0°-120°, respectively. Since many research used linear contact model to simulate the shear behavior of ballast particles [27,28], this method was employed with the allocation of normal and shear contact stiffness. The shape of simulated particles was presented in
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Lateral resistance (kN/m)
20 15 10 SW_200 SW_300 SW_400 SW_500
5 0
(a)
0
0.5
1 Displacement (mm)
1.5
2
18.8
Lateral resistance (kN/m)
18.6 18.4 18.2 18 17.8 17.6
(b)
200
250
300
350
400
450
500
Displacement (mm)
Fig. 7. a) Force – displacement ladder sleeper tracks with various shoulder width, b) Lateral resistance variations regarding shoulder width.
previous research conducted by authors [29]. It is noteworthy that the particle size distribution was determined in accordance with the PSD of experimental tests. As reported by Irazábal, J [30], the variation of Young’s modulus has an insignificant effect on the ballast lateral resistance. Thus, the mechanical characteristics of particles used in previous research by authors have been employed (Table 4). Several studies have attempted to simulate the breakage behavior of particles. For instance, the generation of small discs between balls [31], and polyhedral particle shapes with two plane polyhedron contacts [32] are proposed methods to evaluate irregular particles crushing. However, in this paper, due to the large scale of the model and a time-consuming simulation process, the modeling of ballast breakage has not taken into consideration. 4.1. Modeling procedure The DEM simulation was performed for one sleeper domain with the length, width and height of 6 m, 0.6 m, and 1 m, respectively. Fig. 10 (a) illustrated the geometry of the sleeper imported as the STL file in PFC. To simulate the weight of the ladder sleeper, the wall servo command was considered to apply the translational velocity which is equivalent to the desired force on the sleeper in the z-direction [33]. In the next step, the generation of particles within the domain continued by gravity to achieve the desirable ballast porosity of 0.3 (Fig. 10 (b)). After removing top surface walls, the model was cycled to reach the equilibrium state, so that the final porosity of the ballast layer was 0.32. Fig. 10 (c) shows two panels with the shoulder height of 0 mm and 150 mm before
the lateral movement of the sleeper. It should be noted that in order to measure the porosity of the whole layer, several measurement spheres with the diameter of 330 mm were determined under the ladder sleeper track (Fig. 10 (d)). 4.2. Validation of discrete element models To validate the results obtained from modeling, the simulation of the ladder sleeper track with the shoulder height of 0 mm was compared with those obtained from experiments demonstrated in Fig. 11. The differences in the initial and ultimate lateral forces between the simulation and experimental results (corresponding to the displacement of 0.75 mm and 4 mm) were almost 25% and 7%, respectively. This can be attributed to the spherical shape of particles and higher displacement of the sleeper, particularly in the initial stage. As expected, due to the lower porosity of the simulation, the rate of resistance increment in the simulation was higher than that in the experimental test. In fact, in order to prevent the higher displacement of particles due to the spherical shape of particles in PFC simulation, the porosity of the simulated layer was defined lower than that of the experimental condition. 4.3. Contribution of ladder sleeper components to the lateral resistance of the track The contribution of ladder sleeper components to the lateral resistance was shown in Fig. 12. For this purpose, the contact force between the ladder sleeper and particles was measured in three areas of the sleeper base, external and internal faces of the ladder
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Lateral resistance (kN/m)
Fig. 8. Ladder track with a) 0%, b) 50%, c) 75% and d) 100% crib ballast.
16
CH_0%
14
CH_50%
12
CH_100%
CH_75%
10 8 6 4 2 0 0
0.5
1
1.5
2
Displacement (mm) Fig. 9. Force-displacement curves of panels with different crib ballast height.
sleeper as the contribution of the ballast bed, shoulder ballast, and crib ballast, respectively. The reasons for different proportions of sleeper components to the lateral resistance are as follows.
Table 4 Mechanical parameters adopted for simulation of ladder sleeper track [29]. Parameters
Clump
Sleeper (wall)
Wall
Young’s Modulus (N/m2) Normal stiffness, kn (N/m) Shear stiffness, ks (N/m) Density (kg/m3) Friction
65e9 1.5e9 0.77e8 2700 0.8
_ 1e9 1e9 3500 0.6
_ 1e9 1e9 _ 0.8
(1) As shown in Fig. 13 the contact force between ballast particles and sleeper base in the initial state is higher than that at the displacement of 2 mm. In fact, due to the enormous initial friction between particles and sleeper bottom surface, the maximum lateral resistance of the sleeper base occurs at the displacement of 0.25 mm (equal to 2.15 kN/m) and
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Fig. 10. (a) Generation of track domain and the ladder sleeper, (b) Ballast generation within the domain, (c) The equilibrium state of the panels with SH = 0 and 150 mm, (d) different views of the porosity measurement spheres.
Lateral resistance (kN/m)
20 15 10 DEM_SW500_SH0
5
Test_SW500_SH0 0 0
0.5
1
1.5
2
2.5
3
3.5
4
Displacement (mm) Fig. 11. DEM and experimental results for a panel with SH = 0 mm.
Rb_SH0
Rc_SH0
Rs_SH0
Rb_SH150
Rc_SH150
Rs_SH150
Ballast components resistance (kN)
14 12 10 8 6 4
steadily declined down to 1.74 kN/m corresponding to the displacement of 2 mm. The lower contribution of the bottom surface of the ladder sleeper in the case of with and without shoulder height can be associated with the small area of the sleeper, the frictional nature of sleeper/ballast interaction in comparison with sleeper side facets, and the unloaded condition of the simulated track. Therefore, vertical loading induced by trains has a significant effect on the frictional contact between the sleeper base and ballast bed. (2) As illustrated in Figs. 14 and 4, the presence of crib ballast between longitudinal beams act as passive pressure resistance against the ladder sleeper movement. Consequentely, surrounding crib ballast by longitudinal beams caused the large contribution of the internal faces to the lateral resistance for both panels so that the influence of crib ballast on the resistance increment of ladder sleepers is remarkable (about 62%) compared to monoblock sleepers in the unloaded condition. (3) The resistance of panels with the shoulder height of 0 mm and 150 mm was about 5.2 kN/m and 8.7 kN/m which is a justification for providing a shoulder ballast layer with the adequate height for a 20% increase in the total resistance of the ballast layer. On the other word, adding shoulder ballast has the greater impact on the lateral resistance of ladder tracks due to the uniform distribution of the lateral force along the concrete beams. 5. Conclusions
2 0 0
0.5
1
1.5
2
2.5
3
3.5
4
Displacement (mm)
Fig. 12. The contribution of the sleeper facets to the lateral resistance Rb: Ballast bed resistance, Rc: Crib ballast resistance, Rs: Shoulder ballast resistance.
In this research, a series of lateral panel tests were conducted to study the influence of the shoulder ballast width and crib height to the lateral resistance of ladder sleeper tracks as the substitution of monoblock sleepers. In the next stage, the contribution of ladder sleeper components for panels with SH = 0 mm and 150 mm was
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Fig. 13. The contact force between sleeper base and particles at the displacement of (a) 0 mm, and (b) 2 mm.
Fig. 14. The stress distribution in ladder tracks with (a) SH = 0 mm, and (b) SH = 150 mm.
measured using the discrete element method. According to experimental results, crib ballast has the high proportion to the increment of lateral resistance than changes in the shoulder ballast width due to the passive pressure and confined condition of crib ballast along two longitudinal concrete beams. The resistance characteristics of ladder sleeper components lead to the following conclusions: (1) There was no significant increase in the lateral resistance of the ladder sleeper track associated with the variation of the shoulder ballast width so that the variation of shoulder width from 200 mm to 500 mm has led to 5% increase in the lateral resistance. Therefore, its effect on horizontal load-bearing capacity is ignorable. (2) With respect to experimental tests on panels with different crib ballast height, this component provides a significant contribution to the lateral resistance of the ladder track, so that the increase in the resistance of ladder tracks containing 25%, 50%, and 100% crib ballast is about 84%, 116%, and 137% higher than that of the track without crib ballast, respectively. In fact, due to the passive resistance of crib ballast between two longitudinal beams, a higher amount of crib ballast enhances ballast/sleeper interaction and consequently reduces the lateral movement of the ladder sleeper. (3) Considering the contribution of the ladder sleeper components to the lateral resistance, the sleeper internal facets have shown 62% of lateral load bearing, which was 29% and 9% for sleeper external facets and sleeper base, respectively. It can be concluded that the sleeper/crib ballast interaction provides the high proportion of the lateral resistance in ladder sleeper tracks. Therefore, the application of heavier material as crib ballast could be an efficient solution in order to the improvement of sleeper lateral resistance. Conflict of interest None.
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The contribution of ballast layer components to the lateral resistance of ladder sleeper track Guoqing Jing 1, Peyman Aela ⇑, Hao Fu School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
h i g h l i g h t s Lateral resistance of ladder sleepers is investigated by the lateral track panel test. The contribution of ballast components to the lateral resistance is obtained. The DEM simulation of a ladder sleeper on the ballast layer was performed.
a r t i c l e
i n f o
Article history: Received 23 September 2018 Received in revised form 29 December 2018 Accepted 3 January 2019
Keywords: Ladder sleeper Ballast Lateral resistance LTPT Shoulder height Shoulder width Crib height DEM
a b s t r a c t The sleeper-ballast interface of railway tracks directly is associated with lateral resistance which plays an important role in the mechanical behavior of ballasted tracks. In a real-case implementation of ballasted track for speeds as high as 400 km/h, sufficient lateral resistance is vital to prevent the lateral movement of the track. In view of the future development, a series of full-scale lateral track panel tests (LTPT) were conducted to evaluate the lateral resistance of ladder sleepers as a substitution of monoblock sleepers. The experimental results revealed that the application of the ladder sleepers caused an increase in lateral resistance of the ballasted track as well as a reduction in the use of ballast aggregates. In addition, the contribution of the ladder sleeper facets to the lateral resistance was investigated by the discrete element method (DEM). In conclusion, crib ballast has the main role in the lateral resistance of ladder sleeper tracks. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Ballast layer is an important component of superstructure used to transmit vertical loads from sleepers to subgrade. Investigating track lateral buckling, caused by temperature changes and moving trains is a continuing concern within continuously welded rails (CWR) and is also a major issue regarding track stability [1]. Lateral resistance of sleepers is one of the most important factors to prevent the lateral movement of ballasted tracks. This concept has been comprehensively investigated by Kish, A [2] studies demonstrating the importance of track stability influenced by vertical loads induced by moving trains and track curvature. According to this research, the type and weight of sleepers, and sleeper spacing ⇑ Corresponding author at: Beijing Jiaotong University, No.3, Shangyuancun, Haidian District, Beijing 100044, China. E-mail addresses: [email protected] (G. Jing), [email protected] (P. Aela). 1 Beijing Jiaotong University, No. 3 Shangyuancun Haidian District, Beijing 100044, China. https://doi.org/10.1016/j.conbuildmat.2019.01.017 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
are important elements which influence the lateral stability of tracks. Ballast layer specifications are other parameters which affect the lateral resistance of the track such as ballast compaction, degradation and the geometry of the ballast layer. For instance, there is about 40–50% reduction in the lateral resistance of the sleeper after ballast tamping due to the disturbance of ballast compaction [3]. In another study, as noted by Kish [6], ballast tamping decreases the lateral movement of the ballasted track by 40–70 %. In terms of the impact of ballast layer components, Le Pen and Powrie [4] reported that the contribution of ballast bed, crib ballast, and shoulder ballast to the lateral resistance under vertical loading condition was in the range of 26–35 %, 37–50%, and 15– 37%, respectively. Thus, friction between ballast and sleeper sides and the base has a higher resistance than passive pressure between sleeper ends and shoulder ballast under vertical loading condition. In contrast, B. Lichtberger [5] proposed the range of 45–50%, 10– 15%, and 35–40% for the resistance of ballast bed, crib, and shoulder ballast, respectively. To sum up, the passive earth pressure of the shoulder ballast and sliding friction of crib ballast have a differ-
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Fig. 1. Components of lateral resistance forces for a) monoblock, b) ladder sleepers.
by Wakui et al [9], and Asanuma, K [10] as it aims to meet the lateral displacement of ballast tracks with the following characteristics: The prolongation of the life of ballast tracks and consequently lengthen maintenance and tamping intervals. Lowering life-cycle cost by minimizing maintenance costs. The reduction of sleeper settlement into the ballast. Increasing the track stability by means of high-mass and continuous support and occupying less track area. An effective alternative to reduce ground vibration induced by moving trains [11].
Fig. 2. PSD for tests.
ent proportion to the lateral resistance governed by the ballast compaction, the friction coefficient between ballast and sleepers, and loading conditions. In recent years, the lateral resistance of tracks has increased with the use of monoblock concrete sleepers widely in railway tracks [6]. Furthermore, there are limited methods to increase lateral resistance regarding ballast material and ballast compaction. Ballast reinforcement using polymeric binders is an innovative method to improve the lateral stability of ballast tracks [7]. Among existing approaches to enrich the lateral resistance of the track, the type and geometry of sleepers have an important impact on the lateral resistance. The use of ladder sleeper tracks is a sustainable solution first proposed by Moses, NK et al. [8] in order to reduce vibrations in high-speed slab tracks, and studied
Although the lateral movement of the ballasted ladder track has been already evaluated [12], previous studies have not dealt with the effect of the geometry of the ballast layer on the lateral displacement of the ladder sleeper. Therefore, with an aim to investigate the lateral resistance of ladder sleeper tracks with the contribution of the base, crib, and shoulder ballast as shown in Fig. 1, a series of lateral track panel test (LTPT) were conducted for a ladder sleeper on the ballast layer. In the next stage, coupled with experimental tests, the DEM simulation of LTPT was developed using PFC3D. Recently investigators have examined the effect of ballast bed conditions on lateral resistance of the ballast layer in PFC. It has been observed that the shoulder width greater than 400 mm and shoulder slope of 1:1.75 provide sufficient lateral resistance against the movement of monoblock sleepers [13]. In another research, Hou, W et al. [14] confirmed the effectiveness of sleeper support conditions on the stress distribution. Therefore, a well-compacted ballast layer is required to minimize the movement of ballast particles. According to previous research [15–17], the ballast particle shape is an important parameter which influences the mechanical behavior of ballast aggregates in DEM simulations. In this regard, Khatibi et al. [18] developed a numerical model in conjunction with experimental studies to evaluate the
Fig. 3. Geometrical characteristics of the ladder sleeper.
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effect of the realistic ballast shape on the reduction of particles movement. So far, no research has been found that surveyed the lateral resistance of ladder track on the ballast layer. This paper considered the lateral resistance of the ladder sleeper by means of lateral track panel tests (LTPT) to examine the effect of shoulder width and crib ballast height on the lateral resistance of the ladder sleeper. In the next section, the DEM simulation of LTPT has been conducted using 3D-laser scanning and PFC3D. After the validation of numerical results of the DEM models via experimental data for various ballast layer conditions, a ballast layer with the shoulder height of 150 mm was simulated to measure the influence of shoulder ballast height on the lateral resistance of ladder sleeper track.
2. Material and method
2.2. Testing procedure In the first step, ballast bed was initially compacted and leveled in three layers using a vibrating plate compactor to provide a layer with the length, width, and thickness of 10000 mm, 3600 mm, and 350 mm. In this stage, preparation of the track could be divided into changes in shoulder width and crib height according to Table 3. Ultimately, a ballast layer with the bulk density of 1650 kg/m3 was prepared. As shown in Fig. 4, the crib ballast in the ladder track system contributes as the passive pressure resistance against sleeper movement while it has the sliding friction resistance in monoblock sleeper track. Thus, the influence of crib height variations were considered in the present research. In case of changes in crib height, ballast was filled and well compacted by the vibrator from the bottom to top of the sleeper surface between longitudinal beams to examine the effect of 0%, 50%,75%, and 100% crib ballast height as shown in Fig. 5. To evaluate the influence of shoulder width, the lateral resistance of the ladder track with the shoulder width of 200, 300, 400, and 500 mm was measured. It should be noted that the ballast layer was tamped by tamper machine VPO-3000 with the weight and frequency of 80 kg and 67 Hz, respectively [19]. In order to apply lateral force, steel bars were positioned in the vicinity of the ballast track to provide a frame as support for applying horizontal force as illustrated in Fig. 6.
2.1. Characteristics of ballast and sleepers 2.3. Lateral resistance tests procedure Ballast material, used in the experimental tests, was crushed basalt aggregates which adequately met China National Standard TBT 2140 requirements, and particle size distribution (PSD) shown in Fig. 2. The geometry and characteristics of sleepers are represented in Fig. 3 and Table 1. In this research, all tests were conducted on a ballast layer with detailed specifications as illustrated in Table 2.
In order to evaluate the behavior of two types of concrete sleepers, lateral panel tests were conducted to investigate the lateral resistance of the ladder sleeper. In this method, the displacement of the sleepers was measured by attaching the two LVDTs with an accuracy of 0.001 mm and amplitude of 30 mm to the end of
Table 1 Ballast layer specifications. Track type
Length (m)
Sleeper space (mm)
Ballast height (mm)
Top width (mm)
Shoulder width (mm)
Shoulder height (mm)
Slope gradient
Monoblock track Ladder sleeper track
100 100
600 _
350 350
3500 3500
500 500
150 0
1:1.75 1:1.75
Table 2 Sleepers specifications. Sleeper type
Monoblock Ladder sleeer
Section height (mm) Rail seat
Mid-section
230 185
185 0
Bottom surface (cm2)
End surfaces (cm2)
Mass (kg)
Length (m)
Width (m)
7720 69,640
590 5500
350 3600
2.6 6
0.32 2
Table 3 The geometrical condition of ballast track samples. Sleeper type
code
Shoulder width (mm)
Shoulder height (mm)
Crib height
Ladder Ladder Ladder Ladder Ladder Ladder Ladder Ladder
SW500 SW400 SW300 SW200 CH100 CH75 CH50 CH0
500 400 300 200 none none none none
0 0 0 0 100% 75% 50% 0
full full full full
sleeper sleeper sleeper sleeper sleeper sleeper sleeper sleeper
SW: shoulder width, CH: crib ballast.
Fig. 4. Variations of shoulder ballast height and width in experiments and numerical modeling.
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Fig. 5. Ladder sleeper track with (a) 0%, (b) 25%, (c) 75%, (d) 100% crib ballast height.
the sleeper. The lateral displacement of different panels, described in Table 3, was recorded using a data logger until the horizontal displacement reached the steady state. In this case, the lateral force at a displacement of 2 mm was determined as the sleeper lateral resistance which was reported in different research [20,21]. It should be mentioned that the mean of the values obtained from LVDTs was recorded as the displacement of the sleeper.
3. Experimental results and discussions 3.1. Effect of shoulder width The effect of shoulder width is extensively investigated by Zakeri JA [22] and Liang, Gao [23]. In this way, Le Pen, L [24] claimed that the the threshold width of a level shoulder for monoblock sleeper track is about 0.75 m. However, far too little attention has been paid to the effect of shoulder ballast width on the lateral resistance of ladder sleeper tracks as illustrated in Fig. 7. In contrast to the contribution of the shoulder width to the resistance of monoblock sleepers, the lateral resistance of the ladder track was fairly steady over the different shoulder ballast width from 200 mm to 500 mm with a slight increment from 17.74 up to 18.66 kN/m. In other words, the lateral resistance measured on the ladder sleeper with the shoulder width of 500 mm was approximately 5% higher than that of the track with the shoulder width of 200 mm. The above findings are important and practical for ladder sleeper application considering that the reduction in the shoulder width in ballasted tracks.
3.2. Effect of crib ballast height As reported by Khatibi, F et al. [18], in previous studies on the contribution of ballast components to the lateral resistance of monoblock sleeper tracks, different proportions have been found to be related to loaded/unloaded condition of tests. In this regard, depending on the loading condition, the contribution of crib ballast differs from 9 to 54% of total lateral resistance. This variation could be related to the crib ballast density and friction coefficient between sleeper and ballast. In order to examine the impact of crib ballast height on the lateral resistance of ladder tracks, four push tests were carried out on the panel with 0, 25%, 50% and 100% of crib ballast in depth (Fig. 8). Accordingly, the lateral resistance was measured at 6.21, 11.46, 13.43, and 14.76 kN/m for ladder track panels respectively. In other words, due the passive pressure act of crib ballast, the lateral resistance of panels with 25%, 50%, and 100% crib ballast increased by 84%, 116%, 137% in comparison to the track with 0% crib ballast, respectively (Fig. 9). According to the above-mentioned results, increasing the ballast shoulder width had a negligible effect on lateral resistance than that of the crib ballast height. Therefore, there is no satisfactory justification for increasing shoulder ballast width in ladder sleeper tracks. These findings agree with finite element analysis reported by Kabo [25]. As noted in the previous sections, the lateral resistance of the ladder sleeper track significantly increased with the crib height increment. This can be attributed to the high
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Fig. 6. The test set up for (a, b) ladder sleeper, and (c) monoblock sleeper.
frictional force in the interface between ladder sleeper and crib ballast. Consequently, the implementation of crib ballast up to the sleeper top surface has been recommended. 4. Numerical modeling In order to measure the lateral resistance of ballast layer components throughout the sleeper movement, DEM simulation of ladder tracks with the shoulder height of 0 mm and 150 mm was
performed in PFC3D. In this way, the shape of particles was generated based on the image analysis method described earlier by Yunlong, G [26]. In order to occupy the generated particle geometry with the sufficient number of pebbles, min/max radius ratio of pebbles and a angle were defined in the range of 0.15–0.4 mm and 0°-120°, respectively. Since many research used linear contact model to simulate the shear behavior of ballast particles [27,28], this method was employed with the allocation of normal and shear contact stiffness. The shape of simulated particles was presented in
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Lateral resistance (kN/m)
20 15 10 SW_200 SW_300 SW_400 SW_500
5 0
(a)
0
0.5
1 Displacement (mm)
1.5
2
18.8
Lateral resistance (kN/m)
18.6 18.4 18.2 18 17.8 17.6
(b)
200
250
300
350
400
450
500
Displacement (mm)
Fig. 7. a) Force – displacement ladder sleeper tracks with various shoulder width, b) Lateral resistance variations regarding shoulder width.
previous research conducted by authors [29]. It is noteworthy that the particle size distribution was determined in accordance with the PSD of experimental tests. As reported by Irazábal, J [30], the variation of Young’s modulus has an insignificant effect on the ballast lateral resistance. Thus, the mechanical characteristics of particles used in previous research by authors have been employed (Table 4). Several studies have attempted to simulate the breakage behavior of particles. For instance, the generation of small discs between balls [31], and polyhedral particle shapes with two plane polyhedron contacts [32] are proposed methods to evaluate irregular particles crushing. However, in this paper, due to the large scale of the model and a time-consuming simulation process, the modeling of ballast breakage has not taken into consideration. 4.1. Modeling procedure The DEM simulation was performed for one sleeper domain with the length, width and height of 6 m, 0.6 m, and 1 m, respectively. Fig. 10 (a) illustrated the geometry of the sleeper imported as the STL file in PFC. To simulate the weight of the ladder sleeper, the wall servo command was considered to apply the translational velocity which is equivalent to the desired force on the sleeper in the z-direction [33]. In the next step, the generation of particles within the domain continued by gravity to achieve the desirable ballast porosity of 0.3 (Fig. 10 (b)). After removing top surface walls, the model was cycled to reach the equilibrium state, so that the final porosity of the ballast layer was 0.32. Fig. 10 (c) shows two panels with the shoulder height of 0 mm and 150 mm before
the lateral movement of the sleeper. It should be noted that in order to measure the porosity of the whole layer, several measurement spheres with the diameter of 330 mm were determined under the ladder sleeper track (Fig. 10 (d)). 4.2. Validation of discrete element models To validate the results obtained from modeling, the simulation of the ladder sleeper track with the shoulder height of 0 mm was compared with those obtained from experiments demonstrated in Fig. 11. The differences in the initial and ultimate lateral forces between the simulation and experimental results (corresponding to the displacement of 0.75 mm and 4 mm) were almost 25% and 7%, respectively. This can be attributed to the spherical shape of particles and higher displacement of the sleeper, particularly in the initial stage. As expected, due to the lower porosity of the simulation, the rate of resistance increment in the simulation was higher than that in the experimental test. In fact, in order to prevent the higher displacement of particles due to the spherical shape of particles in PFC simulation, the porosity of the simulated layer was defined lower than that of the experimental condition. 4.3. Contribution of ladder sleeper components to the lateral resistance of the track The contribution of ladder sleeper components to the lateral resistance was shown in Fig. 12. For this purpose, the contact force between the ladder sleeper and particles was measured in three areas of the sleeper base, external and internal faces of the ladder
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Lateral resistance (kN/m)
Fig. 8. Ladder track with a) 0%, b) 50%, c) 75% and d) 100% crib ballast.
16
CH_0%
14
CH_50%
12
CH_100%
CH_75%
10 8 6 4 2 0 0
0.5
1
1.5
2
Displacement (mm) Fig. 9. Force-displacement curves of panels with different crib ballast height.
sleeper as the contribution of the ballast bed, shoulder ballast, and crib ballast, respectively. The reasons for different proportions of sleeper components to the lateral resistance are as follows.
Table 4 Mechanical parameters adopted for simulation of ladder sleeper track [29]. Parameters
Clump
Sleeper (wall)
Wall
Young’s Modulus (N/m2) Normal stiffness, kn (N/m) Shear stiffness, ks (N/m) Density (kg/m3) Friction
65e9 1.5e9 0.77e8 2700 0.8
_ 1e9 1e9 3500 0.6
_ 1e9 1e9 _ 0.8
(1) As shown in Fig. 13 the contact force between ballast particles and sleeper base in the initial state is higher than that at the displacement of 2 mm. In fact, due to the enormous initial friction between particles and sleeper bottom surface, the maximum lateral resistance of the sleeper base occurs at the displacement of 0.25 mm (equal to 2.15 kN/m) and
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Fig. 10. (a) Generation of track domain and the ladder sleeper, (b) Ballast generation within the domain, (c) The equilibrium state of the panels with SH = 0 and 150 mm, (d) different views of the porosity measurement spheres.
Lateral resistance (kN/m)
20 15 10 DEM_SW500_SH0
5
Test_SW500_SH0 0 0
0.5
1
1.5
2
2.5
3
3.5
4
Displacement (mm) Fig. 11. DEM and experimental results for a panel with SH = 0 mm.
Rb_SH0
Rc_SH0
Rs_SH0
Rb_SH150
Rc_SH150
Rs_SH150
Ballast components resistance (kN)
14 12 10 8 6 4
steadily declined down to 1.74 kN/m corresponding to the displacement of 2 mm. The lower contribution of the bottom surface of the ladder sleeper in the case of with and without shoulder height can be associated with the small area of the sleeper, the frictional nature of sleeper/ballast interaction in comparison with sleeper side facets, and the unloaded condition of the simulated track. Therefore, vertical loading induced by trains has a significant effect on the frictional contact between the sleeper base and ballast bed. (2) As illustrated in Figs. 14 and 4, the presence of crib ballast between longitudinal beams act as passive pressure resistance against the ladder sleeper movement. Consequentely, surrounding crib ballast by longitudinal beams caused the large contribution of the internal faces to the lateral resistance for both panels so that the influence of crib ballast on the resistance increment of ladder sleepers is remarkable (about 62%) compared to monoblock sleepers in the unloaded condition. (3) The resistance of panels with the shoulder height of 0 mm and 150 mm was about 5.2 kN/m and 8.7 kN/m which is a justification for providing a shoulder ballast layer with the adequate height for a 20% increase in the total resistance of the ballast layer. On the other word, adding shoulder ballast has the greater impact on the lateral resistance of ladder tracks due to the uniform distribution of the lateral force along the concrete beams. 5. Conclusions
2 0 0
0.5
1
1.5
2
2.5
3
3.5
4
Displacement (mm)
Fig. 12. The contribution of the sleeper facets to the lateral resistance Rb: Ballast bed resistance, Rc: Crib ballast resistance, Rs: Shoulder ballast resistance.
In this research, a series of lateral panel tests were conducted to study the influence of the shoulder ballast width and crib height to the lateral resistance of ladder sleeper tracks as the substitution of monoblock sleepers. In the next stage, the contribution of ladder sleeper components for panels with SH = 0 mm and 150 mm was
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Fig. 13. The contact force between sleeper base and particles at the displacement of (a) 0 mm, and (b) 2 mm.
Fig. 14. The stress distribution in ladder tracks with (a) SH = 0 mm, and (b) SH = 150 mm.
measured using the discrete element method. According to experimental results, crib ballast has the high proportion to the increment of lateral resistance than changes in the shoulder ballast width due to the passive pressure and confined condition of crib ballast along two longitudinal concrete beams. The resistance characteristics of ladder sleeper components lead to the following conclusions: (1) There was no significant increase in the lateral resistance of the ladder sleeper track associated with the variation of the shoulder ballast width so that the variation of shoulder width from 200 mm to 500 mm has led to 5% increase in the lateral resistance. Therefore, its effect on horizontal load-bearing capacity is ignorable. (2) With respect to experimental tests on panels with different crib ballast height, this component provides a significant contribution to the lateral resistance of the ladder track, so that the increase in the resistance of ladder tracks containing 25%, 50%, and 100% crib ballast is about 84%, 116%, and 137% higher than that of the track without crib ballast, respectively. In fact, due to the passive resistance of crib ballast between two longitudinal beams, a higher amount of crib ballast enhances ballast/sleeper interaction and consequently reduces the lateral movement of the ladder sleeper. (3) Considering the contribution of the ladder sleeper components to the lateral resistance, the sleeper internal facets have shown 62% of lateral load bearing, which was 29% and 9% for sleeper external facets and sleeper base, respectively. It can be concluded that the sleeper/crib ballast interaction provides the high proportion of the lateral resistance in ladder sleeper tracks. Therefore, the application of heavier material as crib ballast could be an efficient solution in order to the improvement of sleeper lateral resistance. Conflict of interest None.
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