# Use of Rubber Mat to Improve Deformation Behaviors of Ballastless Tracks Laid on Bridges

Authors: Weiqi Zheng; Xingwang Sheng; Hongqiang He; Hongyi Xu; Ying Yang
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

The deformation behaviors of ballastless tracks have an important influence on their service performance. In this work, rubber mats commonly used in metro traffic were employed in ballastless tracks laid on bridges to improve their deformation behaviors. In order to research the effect of rubber mat for deformation behaviors, a series of static loading tests were carried out based on two full-scale ballastless tracks with different types of isolation layers. Main conclusion include that, for ballastless track with geotextile isolation layers, gaps and voids are formed at interlayers with the increasing static load. However, for ballastless track with rubber mat isolation layer, the maximum tensile deformation in the thickness direction unexceeds the precompression of rubber mat under the deadweight of its upper structures. Interlayer gaps and voids can be eliminated due to the precompression of rubber mat. Besides, the rubber mat isolation layer is still in the linear elasticity stage under the routine service condition, and the interlayer behaviors of the ballastless tracks perform well. It is a feasible way to use a rubber mat isolation layer to improve the deformation behaviors of ballastless tracks laid on bridges.


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## Body

## 1. Introduction

High-speed railway was developed rapidly in recent years; as a typical track structural pattern, ballastless tracks were widely applied in high-speed railways, especially in China [1]. Certainly, higher requirements are put forward for ballastless tracks with the development of high-speed railway technologies [2–5]. A traditional ballastless track generally consists of rails, track slab, self-compacting concrete layer or cement asphalt mortar layer, isolation layer, and base plate (Figure 1). Nowadays, several modifications of traditional ballastless tracks have been developed to obtain a higher bearing capacity system while increasing its durability [6]. As a kind of railway elastic elements, an isolation layer coordinated the deformation between lower structures and ballastless tracks and achieved isolation for facilitating maintenance [7]. Reasonable adjustment of the isolation layer is a way to improve the structural performance of ballastless tracks. The commonly used isolation layers in ballastless tracks included EPDM isolation layer (ethylene propylene diene monomer), geotextile isolation layer, and so on (Figure 2) [8, 9]. Due to lack of thickness, it is difficult for these isolation layers to compress and their elastic properties are not prominent. They mainly play the role of interlayer isolation and have no regulating effect on interlayer deformations. It is of particular importance to identify the effect of using new isolation layers to improve deformation behaviors of ballastless tracks laid on bridges.Figure 1
The structures of a traditional ballastless track.Figure 2
Commonly used isolation layers: (a) EPDM isolation layer; (b) geotextile isolation layer.
(a)(b)With the increase in the rail freight traffic and the train running speed, many countries have incorporated some elastic elements into their railway systems as the standard practice [10–12]. Rubber mats are essential in ballasted tracks at some regions such as tunnels and bridges where the elastic components are necessarily required in the railway structures to reduce the stress on the substructures as well as the vibration and noise levels due to the deformation capacity and mechanical energy dissipation of rubber material [13, 14]. Primarily being applied in ballasted tracks, rubber subballasted mats have been growing as a feasible and effective solution to guarantee the reliable properties of ballasted tracks [15–17]. In this regard, it is an attempt to use the rubber mats as isolation layers in ballastless tracks laid on bridges to improve their deformation behaviors. The reasonable arrangement of the isolation interlayer of the ballastless tracks can reduce the related defects such as gaps and voids at interlayers. It is worthwhile to take the rubber mats commonly used in metro traffic transit as the isolation layers in ballastless tracks to improve their deformation behaviors (Figure 3).Figure 3
Rubber mat used as the isolation layer in ballastless track.In this research, a type of rubber mat is employed in ballastless tracks to achieve interlayer isolation and deformation adjustment of ballastless tracks under routine service conditions. In this context, a series of full-scale laboratory tests are carried out to research the deformation characteristics of the ballastless tracks laid on bridges. Furthermore, the measures to reduce inconsistency of interlayer deformations are explored.


## 2. Full-Scale Laboratory Tests

### 2.1. Test Objects and Materials

In this research, two groups of full-scale static loading tests were conducted to demonstrate the feasibility of using rubber mats to improve ballastless tracks behaviors. The two full-scale ballastless tracks were poured on the concrete bridge deck of a simply supported box girder in a laboratory (Figure4). The structure of the simply supported box girder and the location of these ballastless tracks laid on the simply supported box girder are shown in Figure 5, and more information can be found in [18].Figure 4
Test objects used in this work: (a) simply supported box girder; (b) ballastless tracks cast in place; (c) ballastless track with rubber mat isolation layer; (d) ballastless tracks with geotextile isolation layer.
(a)(b)(c)(d)Figure 5
The simply supported box girder and ballastless tracks: (a) top view (unit: mm); (b) side view (unit: mm); (c) front view (unit: mm).
(a)(b)(c)The structural details of ballastless tracks used in this work are listed in Table1.Table 1
The structural details of ballastless tracks used in this work.
ComponentDimension (mm)Material or typeRailCHN60FastenersWJ7-B constant resistance fastenersTrack slab5920 × 2800 × 260C40 concreteIsolation layer5920 × 2800 × 27 (4)Rubber (geotextile)Base plate5920 × 2800 × 240C40 concreteIt is noteworthy that the types of isolation layer of these two full-scale ballastless tracks are different. One is the geotextile isolation layer, and it is labeled as “standard assembly;” the other is a kind of rubber mat, and it is labeled as “subballasted mat”. The main parameters of the materials of these two isolation layers are listed in Table2.Table 2
The main parameters of two types of isolation layers in this work.
No.IndexUnitLimitsThe material of geotextile isolation layer1Tensile strengthkN/m≥482Elongation%70 ± 203Bursting strengthkN≥8.54Tearing strength by trapezoid methodN≥9005Acid and alkali resistance%Retention rate ≥906Wear resistance%≤25The material of subballasted mat isolation layer1Static stiffnessMN/m3.0 ± 0.52Determination of compression%≤233Tensile strengthMPa≥3.04Elongation%≥1505Fatigue propertyAppearanceNo tearing or breakage occursResidual deformationmm≤16Water resistance%≤1.0At present, the leading concerned indicators of the geotextile materials are the tearing strength, the tensile strength, and so on. However, its compressive performance is rarely considered in practical engineering due to its thin thickness. For the rubber subballasted mat, its material properties are generally measured by the standard testing specimens, which can be guaranteed for the properties of the material itself [19, 20]. However, the corresponding indicators of the rubber subballasted mat cannot be truly reflected only by the standard testing specimens due to its irregular shapes (Figure 6). The commonly used rubber subballasted mats usually have a thickness of 15∼30 mm, whereas their horizontal dimensions depend on the technique developed during the construction. Currently, there are various product specifications depending on the thickness and rigidity of the rubber mats. The subballasted mats are defined by their bedding modulus Cd (N/mm3); a series of rubber mats with a thickness of 27 mm and a design bedding modulus of 0.025 N/mm3 are selected for further research in this work. The rubber subballasted mat used as an isolation layer has an irregular shape in this research, and it is composed of two layers: (i) a distribution layer to uniformly distribute loads; it is a piece of plate-like structure rubber, and its thickness is 10 mm; (ii) an elastic layer to dampen loads; it is a set of evenly arranged circular truncated cone rubber structures, and its thickness is 17 mm. The structure of the rubber subballast mat used in this work is shown in Figure 6.Figure 6
The structure of rubber mat used in this work.


### 2.2. Measuring Method and Sensors Arrangement

In this work, two kinds of measuring sensors are used to measure the interlayer vertical deformation of ballastless tracks, namely, embedment strain gauge and embedment jointmeter. Due to the differences in the measurement range of these measuring sensors, the embedment strain gauges are used to measure the interlayer deformation of ballastless track with geotextile isolation layer, and the embedment jointmeters are used to measure the interlayer deformation of ballastless track with rubber mat isolation layer.Firstly, the lower ends of the measuring sensors are fixed on base plate upper steel bars, and they are kept vertical all the time during the pouring process of concrete base plate. Then, the measuring sensors are vertically passed through the isolation layer. Next, the upper ends of the measuring sensors are placed in a track slab, and they are consolidated with track slab steel bars. Finally, the concrete of track slab is poured so that the high-precision measurements of vertical displacements between layers are achieved. For ballastless track with rubber mat isolation layer, the vertical deformation at interlayers of the ballastless track is large enough to be measured directly by the embedment jointmeters. However, for ballastless track with geotextile isolation layer, the vertical deformation at interlayers is quite small to measure directly. Therefore, the strain at interlayers is measured by the embedment strain gauges, and then, the actual vertical deformations at interlayers can be deduced from the measured strain data. The layout of the embedment strain gauges and the embedment jointmeters is shown in Figure7.Figure 7
The layout of interlayer deformation measuring sensors: layout of the (a) embedment jointmeters and (b) embedment strain gauges.
(a)(b)For the two full-scale ballastless tracks, six embedment strain gauges or six embedment jointmeters are arranged between isolation layers, respectively. Furthermore, both the arrangement and the nomenclature of the measuring sensors of these two full-scale ballastless tracks are the same. The arrangements of interlayer deformation measuring sensors are shown in Figure8.Figure 8
The arrangements of interlayer deformation measuring sensors (unit: mm).In addition, a series of steel strain gauges are attached on the upper and lower steel bars of the base plate and track slab, and a set of concrete strain gauges are arranged near the upper and lower surfaces of the base plate and track slab. Based on this, the stress levels of these two full-scale ballastless tracks with different isolation layers are tested, and the influences on the ballastless tracks can be judged by stress variations. The arrangements of these strain gauges are shown in Figure9.Figure 9
The arrangements of strain gauges (unit: mm): the locations of the (a) concrete strain gauges and (b) steel strain gauges.
(a)(b)


### 2.3. Test Procedure

After the maintenances of these two full-scale ballastless tracks are completed, a series of static loading tests are carried out. Moreover, the static loading tests are divided into two testing conditions: loading at the longitudinal end or the longitudinal center of the ballastless tracks, respectively. Three tests are conducted for each testing condition. The static loading is to simulate the axle load of a high-speed train, and the maximum testing load is 425 kN, which is 2.5 times of the axle load of a train (170 kN). The whole static loading process is divided into ten stages, with an interval of 30 minutes between each stage. The static loading tests are repeated independently for three times of each testing condition. During the static loading test, the hydraulic jack is used to load in stages, and the load cell is arranged between the jack and the reaction frame to reflect the actual loading level in real time. Furthermore, the loading speed during the test does not exceed 1 kN/s. After each loading stage is completed and stabilized for 30 minutes, the values of these measuring sensors are recorded. The static loading procedures and the loading devices are shown in Figure10.Figure 10
The static loading test: (a) static loading devices; (b) static loading procedure.
(a)(b)


## 2.1. Test Objects and Materials

In this research, two groups of full-scale static loading tests were conducted to demonstrate the feasibility of using rubber mats to improve ballastless tracks behaviors. The two full-scale ballastless tracks were poured on the concrete bridge deck of a simply supported box girder in a laboratory (Figure4). The structure of the simply supported box girder and the location of these ballastless tracks laid on the simply supported box girder are shown in Figure 5, and more information can be found in [18].Figure 4
Test objects used in this work: (a) simply supported box girder; (b) ballastless tracks cast in place; (c) ballastless track with rubber mat isolation layer; (d) ballastless tracks with geotextile isolation layer.
(a)(b)(c)(d)Figure 5
The simply supported box girder and ballastless tracks: (a) top view (unit: mm); (b) side view (unit: mm); (c) front view (unit: mm).
(a)(b)(c)The structural details of ballastless tracks used in this work are listed in Table1.Table 1
The structural details of ballastless tracks used in this work.
ComponentDimension (mm)Material or typeRailCHN60FastenersWJ7-B constant resistance fastenersTrack slab5920 × 2800 × 260C40 concreteIsolation layer5920 × 2800 × 27 (4)Rubber (geotextile)Base plate5920 × 2800 × 240C40 concreteIt is noteworthy that the types of isolation layer of these two full-scale ballastless tracks are different. One is the geotextile isolation layer, and it is labeled as “standard assembly;” the other is a kind of rubber mat, and it is labeled as “subballasted mat”. The main parameters of the materials of these two isolation layers are listed in Table2.Table 2
The main parameters of two types of isolation layers in this work.
No.IndexUnitLimitsThe material of geotextile isolation layer1Tensile strengthkN/m≥482Elongation%70 ± 203Bursting strengthkN≥8.54Tearing strength by trapezoid methodN≥9005Acid and alkali resistance%Retention rate ≥906Wear resistance%≤25The material of subballasted mat isolation layer1Static stiffnessMN/m3.0 ± 0.52Determination of compression%≤233Tensile strengthMPa≥3.04Elongation%≥1505Fatigue propertyAppearanceNo tearing or breakage occursResidual deformationmm≤16Water resistance%≤1.0At present, the leading concerned indicators of the geotextile materials are the tearing strength, the tensile strength, and so on. However, its compressive performance is rarely considered in practical engineering due to its thin thickness. For the rubber subballasted mat, its material properties are generally measured by the standard testing specimens, which can be guaranteed for the properties of the material itself [19, 20]. However, the corresponding indicators of the rubber subballasted mat cannot be truly reflected only by the standard testing specimens due to its irregular shapes (Figure 6). The commonly used rubber subballasted mats usually have a thickness of 15∼30 mm, whereas their horizontal dimensions depend on the technique developed during the construction. Currently, there are various product specifications depending on the thickness and rigidity of the rubber mats. The subballasted mats are defined by their bedding modulus Cd (N/mm3); a series of rubber mats with a thickness of 27 mm and a design bedding modulus of 0.025 N/mm3 are selected for further research in this work. The rubber subballasted mat used as an isolation layer has an irregular shape in this research, and it is composed of two layers: (i) a distribution layer to uniformly distribute loads; it is a piece of plate-like structure rubber, and its thickness is 10 mm; (ii) an elastic layer to dampen loads; it is a set of evenly arranged circular truncated cone rubber structures, and its thickness is 17 mm. The structure of the rubber subballast mat used in this work is shown in Figure 6.Figure 6
The structure of rubber mat used in this work.


## 2.2. Measuring Method and Sensors Arrangement

In this work, two kinds of measuring sensors are used to measure the interlayer vertical deformation of ballastless tracks, namely, embedment strain gauge and embedment jointmeter. Due to the differences in the measurement range of these measuring sensors, the embedment strain gauges are used to measure the interlayer deformation of ballastless track with geotextile isolation layer, and the embedment jointmeters are used to measure the interlayer deformation of ballastless track with rubber mat isolation layer.Firstly, the lower ends of the measuring sensors are fixed on base plate upper steel bars, and they are kept vertical all the time during the pouring process of concrete base plate. Then, the measuring sensors are vertically passed through the isolation layer. Next, the upper ends of the measuring sensors are placed in a track slab, and they are consolidated with track slab steel bars. Finally, the concrete of track slab is poured so that the high-precision measurements of vertical displacements between layers are achieved. For ballastless track with rubber mat isolation layer, the vertical deformation at interlayers of the ballastless track is large enough to be measured directly by the embedment jointmeters. However, for ballastless track with geotextile isolation layer, the vertical deformation at interlayers is quite small to measure directly. Therefore, the strain at interlayers is measured by the embedment strain gauges, and then, the actual vertical deformations at interlayers can be deduced from the measured strain data. The layout of the embedment strain gauges and the embedment jointmeters is shown in Figure7.Figure 7
The layout of interlayer deformation measuring sensors: layout of the (a) embedment jointmeters and (b) embedment strain gauges.
(a)(b)For the two full-scale ballastless tracks, six embedment strain gauges or six embedment jointmeters are arranged between isolation layers, respectively. Furthermore, both the arrangement and the nomenclature of the measuring sensors of these two full-scale ballastless tracks are the same. The arrangements of interlayer deformation measuring sensors are shown in Figure8.Figure 8
The arrangements of interlayer deformation measuring sensors (unit: mm).In addition, a series of steel strain gauges are attached on the upper and lower steel bars of the base plate and track slab, and a set of concrete strain gauges are arranged near the upper and lower surfaces of the base plate and track slab. Based on this, the stress levels of these two full-scale ballastless tracks with different isolation layers are tested, and the influences on the ballastless tracks can be judged by stress variations. The arrangements of these strain gauges are shown in Figure9.Figure 9
The arrangements of strain gauges (unit: mm): the locations of the (a) concrete strain gauges and (b) steel strain gauges.
(a)(b)


## 2.3. Test Procedure

After the maintenances of these two full-scale ballastless tracks are completed, a series of static loading tests are carried out. Moreover, the static loading tests are divided into two testing conditions: loading at the longitudinal end or the longitudinal center of the ballastless tracks, respectively. Three tests are conducted for each testing condition. The static loading is to simulate the axle load of a high-speed train, and the maximum testing load is 425 kN, which is 2.5 times of the axle load of a train (170 kN). The whole static loading process is divided into ten stages, with an interval of 30 minutes between each stage. The static loading tests are repeated independently for three times of each testing condition. During the static loading test, the hydraulic jack is used to load in stages, and the load cell is arranged between the jack and the reaction frame to reflect the actual loading level in real time. Furthermore, the loading speed during the test does not exceed 1 kN/s. After each loading stage is completed and stabilized for 30 minutes, the values of these measuring sensors are recorded. The static loading procedures and the loading devices are shown in Figure10.Figure 10
The static loading test: (a) static loading devices; (b) static loading procedure.
(a)(b)


## 3. Test Results

### 3.1. Stress Level of the Ballastless Tracks

The stress values of each component of the ballastless tracks under different loading conditions are recorded separately. The stress distributions of the ballastless tracks are very simple under static loading, and the most unfavorable stress appears at loading positions. In detail, the maximum stress of each component among the testing results is summarized, as shown in Tables3 and 4.Table 3
The maximum values of concrete stress.
Types of the ballastless tracksComponentsLoading at the slab centerLoading at the slab endLongitudinal stress (MPa)Transverse stress (MPa)Longitudinal stress (MPa)Transverse stress (MPa)Standard assemblyTop of track slab−0.65−0.550.330.26Bottom of track slab−0.98−0.87−0.65−0.64Top of base plate−0.65−0.49−0.92−0.81Bottom of base plate−0.40−0.46−0.56−0.42Subballasted matTop of track slab1.601.720.980.90Bottom of track slab−1.30−1.18−1.63−1.67Top of base plate−0.52−0.62−0.74−0.92Bottom of base plate−0.33−0.34−0.52−0.54Table 4
The maximum values of steel stress.
Types of the ballastless tracksComponentsLoading at the slab centerLoading at the slab endLongitudinal stress (MPa)Transverse stress (MPa)Longtudinal stress (MPa)Transverse stress (MPa)Standard assemblyTop of track slab4.003.023.001.96Bottom of track slab−3.20−2.20−2.00−2.60Top of base plate−4.60−3.50−6.40−5.80Bottom of base plate−2.60−2.20−4.75−4.25Subballasted matTop of track slab12.0010.0012.0011.10Bottom of track slab−12.00−10.20−16.00−14.90Top of base plate−5.00−3.80−6.70−6.30Bottom of base plate−2.46−2.55−3.75−3.54As shown in above Tables3 and 4, under these two static test loading conditions, the stress levels of each component of the two full-scale ballastless tracks are very low. The stress level of track slab with rubber mat isolation layer is slightly higher than that with geotextile isolation layer. However, for the concrete base plate, the stress variation law is precisely opposite to that of track slab due to the different arrangements of isolation layers. Under static load, the local compressive deformations of rubber mat isolation layer are more significant than that of geotextile isolation layer. As a result, the track slab above the rubber mat isolation layer is undergoing large bending deformations. Moreover, the bending deformations lead to different stress distributions of ballastless tracks with different isolation layers. Fortunately, ballastless track generally consists of reinforced concrete structures or prestressed reinforced concrete structures, its material strength is high, and it has a particular ability to resist cracking. A little change in stress of ballastless tracks caused by the arrangement of rubber mat isolation layers will not have a significant impact on ballastless tracks, and the structural safety of ballastless tracks can be guaranteed.


### 3.2. Deformation Behaviors of the Ballastless Tracks

The interlayer deformation of ballastless track not only affects the smoothness of high-speed railway but also affects the durability of ballastless tracks. In this work, two static loading conditions are carried out on full-scale ballastless tracks with geotextile isolation layers or rubber mat isolation layers to research the interlayer deformation characteristics. The test results of the two full-scale ballastless tracks under these two static test loading conditions are summarized and analyzed as follows.Condition 1.
static loading at longitudinal end of ballastless tracks.
There is a static loading at longitudinal end of ballastless tracks, which is next to sensor 3-1 and 3-2. The test results of each measuring sensor on the two full-scale ballastless tracks are shown in Figure11, in which negative values represent compressive deformations at interlayers and positive values represent tensile deformations at interlayers.
Figure11 shows the interlayer deformations of ballastless track with geotextile isolation layers or rubber mat isolation layers under static loading at longitudinal end of track slab. The interlayer deformations of these two full-scale ballastless tracks at loading position are large, while those of the ballastless tracks far from the loading position are small. Besides, the interlayer deformations of these two ballastless tracks increase linearly with the increase in the static loadings. For ballastless track with geotextile isolation layer, the interlayer deformation is quite small, which is only 1/10 of the interlayer deformation of ballastless track with rubber mat isolation layer. More importantly, the longitudinal edge of the track slab is more prone to warp. Furthermore, for ballastless track with rubber mat isolation layer, with the increase in static loading, tensile deformations in thickness direction of isolation layer tend to form at the other longitudinal end of track slab which is far from the loading position.Figure 11
Interlayer deformations of the ballastless tracks loading at the slab end: (a) 1-1; (b) 1-2; (c) 2-1; (d) 2-2; (e) 3-1; (f) 3-2.
(a)(b)(c)(d)(e)(f)Condition 2.
static loading at longitudinal center of ballastless tracks.
For the two full-scale ballastless tracks with rubber mat isolation layer or geotextile isolation layer, the static loading test is carried out at longitudinal center of ballastless tracks, which is near sensor 2-1 and 2-2. The deformation results of measuring sensors are shown in Figure12.
From Figure12, the interlayer deformations of ballastless tracks increase linearly with the increase in static loadings. Besides, the deformations of geotextile isolation layers are much small than those of rubber mat isolation layers, and it is hard to judge whether there are gaps or voids formation at interlayers of ballastless track with geotextile isolation layer due to its almost negligible compressive deformations. The rubber mat isolation layer is still in the liner-elastic state, and the deformation characteristics of rubber mat perform well. However, for ballastless track with rubber mat isolation layers, with the increase in static loading, tensile deformation occurred at interlayers of the end of ballastless track which is far from loading position. Whether gaps and voids can be formed or not is related to the precompression of rubber mat under deadweight of its upper structures, which is further analyzed in following sections.Figure 12
Interlayer deformations of the ballastless tracks loading at the slab center: (a) 1-1; (b) 1-2; (c) 2-1; (d) 2-2.
(a)(b)(c)(d)


## 3.1. Stress Level of the Ballastless Tracks

The stress values of each component of the ballastless tracks under different loading conditions are recorded separately. The stress distributions of the ballastless tracks are very simple under static loading, and the most unfavorable stress appears at loading positions. In detail, the maximum stress of each component among the testing results is summarized, as shown in Tables3 and 4.Table 3
The maximum values of concrete stress.
Types of the ballastless tracksComponentsLoading at the slab centerLoading at the slab endLongitudinal stress (MPa)Transverse stress (MPa)Longitudinal stress (MPa)Transverse stress (MPa)Standard assemblyTop of track slab−0.65−0.550.330.26Bottom of track slab−0.98−0.87−0.65−0.64Top of base plate−0.65−0.49−0.92−0.81Bottom of base plate−0.40−0.46−0.56−0.42Subballasted matTop of track slab1.601.720.980.90Bottom of track slab−1.30−1.18−1.63−1.67Top of base plate−0.52−0.62−0.74−0.92Bottom of base plate−0.33−0.34−0.52−0.54Table 4
The maximum values of steel stress.
Types of the ballastless tracksComponentsLoading at the slab centerLoading at the slab endLongitudinal stress (MPa)Transverse stress (MPa)Longtudinal stress (MPa)Transverse stress (MPa)Standard assemblyTop of track slab4.003.023.001.96Bottom of track slab−3.20−2.20−2.00−2.60Top of base plate−4.60−3.50−6.40−5.80Bottom of base plate−2.60−2.20−4.75−4.25Subballasted matTop of track slab12.0010.0012.0011.10Bottom of track slab−12.00−10.20−16.00−14.90Top of base plate−5.00−3.80−6.70−6.30Bottom of base plate−2.46−2.55−3.75−3.54As shown in above Tables3 and 4, under these two static test loading conditions, the stress levels of each component of the two full-scale ballastless tracks are very low. The stress level of track slab with rubber mat isolation layer is slightly higher than that with geotextile isolation layer. However, for the concrete base plate, the stress variation law is precisely opposite to that of track slab due to the different arrangements of isolation layers. Under static load, the local compressive deformations of rubber mat isolation layer are more significant than that of geotextile isolation layer. As a result, the track slab above the rubber mat isolation layer is undergoing large bending deformations. Moreover, the bending deformations lead to different stress distributions of ballastless tracks with different isolation layers. Fortunately, ballastless track generally consists of reinforced concrete structures or prestressed reinforced concrete structures, its material strength is high, and it has a particular ability to resist cracking. A little change in stress of ballastless tracks caused by the arrangement of rubber mat isolation layers will not have a significant impact on ballastless tracks, and the structural safety of ballastless tracks can be guaranteed.


## 3.2. Deformation Behaviors of the Ballastless Tracks

The interlayer deformation of ballastless track not only affects the smoothness of high-speed railway but also affects the durability of ballastless tracks. In this work, two static loading conditions are carried out on full-scale ballastless tracks with geotextile isolation layers or rubber mat isolation layers to research the interlayer deformation characteristics. The test results of the two full-scale ballastless tracks under these two static test loading conditions are summarized and analyzed as follows.Condition 1.
static loading at longitudinal end of ballastless tracks.
There is a static loading at longitudinal end of ballastless tracks, which is next to sensor 3-1 and 3-2. The test results of each measuring sensor on the two full-scale ballastless tracks are shown in Figure11, in which negative values represent compressive deformations at interlayers and positive values represent tensile deformations at interlayers.
Figure11 shows the interlayer deformations of ballastless track with geotextile isolation layers or rubber mat isolation layers under static loading at longitudinal end of track slab. The interlayer deformations of these two full-scale ballastless tracks at loading position are large, while those of the ballastless tracks far from the loading position are small. Besides, the interlayer deformations of these two ballastless tracks increase linearly with the increase in the static loadings. For ballastless track with geotextile isolation layer, the interlayer deformation is quite small, which is only 1/10 of the interlayer deformation of ballastless track with rubber mat isolation layer. More importantly, the longitudinal edge of the track slab is more prone to warp. Furthermore, for ballastless track with rubber mat isolation layer, with the increase in static loading, tensile deformations in thickness direction of isolation layer tend to form at the other longitudinal end of track slab which is far from the loading position.Figure 11
Interlayer deformations of the ballastless tracks loading at the slab end: (a) 1-1; (b) 1-2; (c) 2-1; (d) 2-2; (e) 3-1; (f) 3-2.
(a)(b)(c)(d)(e)(f)Condition 2.
static loading at longitudinal center of ballastless tracks.
For the two full-scale ballastless tracks with rubber mat isolation layer or geotextile isolation layer, the static loading test is carried out at longitudinal center of ballastless tracks, which is near sensor 2-1 and 2-2. The deformation results of measuring sensors are shown in Figure12.
From Figure12, the interlayer deformations of ballastless tracks increase linearly with the increase in static loadings. Besides, the deformations of geotextile isolation layers are much small than those of rubber mat isolation layers, and it is hard to judge whether there are gaps or voids formation at interlayers of ballastless track with geotextile isolation layer due to its almost negligible compressive deformations. The rubber mat isolation layer is still in the liner-elastic state, and the deformation characteristics of rubber mat perform well. However, for ballastless track with rubber mat isolation layers, with the increase in static loading, tensile deformation occurred at interlayers of the end of ballastless track which is far from loading position. Whether gaps and voids can be formed or not is related to the precompression of rubber mat under deadweight of its upper structures, which is further analyzed in following sections.Figure 12
Interlayer deformations of the ballastless tracks loading at the slab center: (a) 1-1; (b) 1-2; (c) 2-1; (d) 2-2.
(a)(b)(c)(d)


## 4. Discussion

### 4.1. Deformation Characteristics of Ballastless Tracks

Concrete base plate is connected with bridge deck by embedded steel bars. The connection between the base plate and the bridge deck is firm and can deform together. However, track slab is formed by pouring concrete directly onto the isolation layer above base plate, and there is no binding force between track slab and base plate, which leads to deformation inconsistency between the two layers, such as gaps and voids.Without considering the deformation of isolation layer, the deformation characteristics of each component of the ballastless track are deduced as follows.The deflectionvx, rotation θx, and curvature ρx of the main bridge or the ballastless tracks can be expressed as follows:(1)vx,θx=v′x,1ρx=v″x.It can be considered that the base plate and the bridge deck are well connected, and the deformation between the base plate and the bridge deck can be coordinated. That is to say,(2)vgx=vbx,vg′x=vb′x,vg″x=vb″x.In Formula (2), g and b are used to represent the main bridge and the concrete base plate, respectively.The deformation of the concrete base plate is consistent with that of the main girder of the bridge, and its deflection equilibrium equation can be expressed as(3)EgIgvg″x=EbIbvb″x=Mgx.The track slab and the concrete base plate are separated entirely by the isolation layers. The deflection equilibrium equation of the track slab can be expressed as(4)EsIsvs″x=Msx.In Formula (4), s is used to represent the track slab.Furthermore, the ballastless tracks laid on bridges are usually discontinuous, and there is a crack at the end of the track slab of a ballastless track, where(5)Msxj≡0.In Formula (5), xj is the position of the crack.However,(6)Mbxj≠0.Considering the bending stiffness of the track slab is0<EsIs≪EgIg, EsIs cannot be ignored; that is to say, EsIs≠0. Because EsIsvs″xj=Msxj≡0, for the track slab, vs″xj≡0 certainly.The deflection of the bridge is a continuous curve, and the curvature equation of the bridge is a continuous function or a piecewise continuous function. Therefore, for the main bridge and the base plate,EgIgvg″xj=EbIbvb″xj=Mgxj≠0, and then, vg″xj≠0, vb″xj≠0. As a result, vs″xj≠vg″xj; besides, vsxj≠vgxj, vs′xj≠vg′xj.In all, the deformation of track slab laid on bridges is not exactly the same as that of main bridge. For ballastless tracks laid on bridges, without considering the compressive deformations of isolation layers, the coordination of the deformations between track slab and main bridge cannot be achieved. That is to say, it is inevitable that there will be gaps and voids formation between track slab and concrete base plate for the ballastless track with geotextile isolation layers.


### 4.2. Deformations at Interlayers of Ballastless Tracks

The reasonable arrangement of isolation layer in ballastless track is an effective way to avoid deformation inconsistency between track slab and main bridge. During the operation process, interlayer tensile deformations under routine service condition do not exceed the precompressions of isolation layers, and the interlayers of ballastless tracks are compactly filled with isolation layers, so as to improve the stress state of ballastless tracks, slow down the deterioration of ballastless tracks, and improve the deformation behaviors of ballastless tracks. For geotextiles or EPDM isolation layers which are commonly used in ballastless tracks on railroad bed, their thickness is very thin (less than 4 mm), and the compressive deformations of these isolation layers can be nearly neglected under the deadweight of its upper structures. When ballastless track with these isolation layers is laid on rigid foundation such as bridge structures, it is highly that there will be gaps and voids formation between track slab and base plate. For the rubber mat used as isolation layer, its thicknesses are always large (15∼30 mm), and compressive stiffness can be accurately obtained according to its bedding modulus. It can be considered that the rubber mat used as isolation layer is in a state of uniform compression, and its precompression is about 0.4 mm under deadweight of upper structures.For high-speed trains in China, the standard train axle load is 170 kN, and the control load of a train axle load acting on substructures is 255 kN (1.5 times of 170 kN). Under the action of the above load levels, the deformations of ballastless tracks are significant. It is considered that these deformations are essential indicators for evaluating the impact on operation of high-speed trains. Thus, the maximum compressive and tensile deformations at interlayers of ballastless tracks are listed in Table5.Table 5
The maximum deformations at interlayers.
Load conditionsLoading at slab endLoading at slab centerLimits [9] (mm)Load values (kN)170255170255Standard assemblyMaximum tensile deformations (mm)0.0030.0040.0010.002≤0Maximum compressive deformations (mm)0.250.350.030.05≤2Subballasted matMaximum tensile deformations (mm)0.170.230.150.22≤0.4Maximum compressive deformations (mm)1.181.700.901.25≤2In Table5, under the standard axle load of 255 kN, the maximum compressive and tensile deformations at interlayers of ballastless track with rubber mat isolation layer are 1.70 mm and 0.23 mm, respectively. The maximum tensile deformation does not exceed the precompression (0.4 mm) of rubber mat isolation layer under deadweight of its upper structures. Besides, the maximum compressive deformation at interlayers also meets the limit of track irregularity (2 mm) [9]. As a result, there will be no gap and void formed at interlayers of ballastless track with rubber mat isolation layer, and this allows for an increase in durability and quality of ballastless tracks. At the same time, the arrangement of rubber mat isolation layer will not have a significant impact on operation of high-speed trains. For ballastless track with geotextile isolation layer, the maximum compressive and tensile deformations at interlayers are tiny. Not surprisingly, the test data of the compressive and tensile deformations at interlayers are discrete.


## 4.1. Deformation Characteristics of Ballastless Tracks

Concrete base plate is connected with bridge deck by embedded steel bars. The connection between the base plate and the bridge deck is firm and can deform together. However, track slab is formed by pouring concrete directly onto the isolation layer above base plate, and there is no binding force between track slab and base plate, which leads to deformation inconsistency between the two layers, such as gaps and voids.Without considering the deformation of isolation layer, the deformation characteristics of each component of the ballastless track are deduced as follows.The deflectionvx, rotation θx, and curvature ρx of the main bridge or the ballastless tracks can be expressed as follows:(1)vx,θx=v′x,1ρx=v″x.It can be considered that the base plate and the bridge deck are well connected, and the deformation between the base plate and the bridge deck can be coordinated. That is to say,(2)vgx=vbx,vg′x=vb′x,vg″x=vb″x.In Formula (2), g and b are used to represent the main bridge and the concrete base plate, respectively.The deformation of the concrete base plate is consistent with that of the main girder of the bridge, and its deflection equilibrium equation can be expressed as(3)EgIgvg″x=EbIbvb″x=Mgx.The track slab and the concrete base plate are separated entirely by the isolation layers. The deflection equilibrium equation of the track slab can be expressed as(4)EsIsvs″x=Msx.In Formula (4), s is used to represent the track slab.Furthermore, the ballastless tracks laid on bridges are usually discontinuous, and there is a crack at the end of the track slab of a ballastless track, where(5)Msxj≡0.In Formula (5), xj is the position of the crack.However,(6)Mbxj≠0.Considering the bending stiffness of the track slab is0<EsIs≪EgIg, EsIs cannot be ignored; that is to say, EsIs≠0. Because EsIsvs″xj=Msxj≡0, for the track slab, vs″xj≡0 certainly.The deflection of the bridge is a continuous curve, and the curvature equation of the bridge is a continuous function or a piecewise continuous function. Therefore, for the main bridge and the base plate,EgIgvg″xj=EbIbvb″xj=Mgxj≠0, and then, vg″xj≠0, vb″xj≠0. As a result, vs″xj≠vg″xj; besides, vsxj≠vgxj, vs′xj≠vg′xj.In all, the deformation of track slab laid on bridges is not exactly the same as that of main bridge. For ballastless tracks laid on bridges, without considering the compressive deformations of isolation layers, the coordination of the deformations between track slab and main bridge cannot be achieved. That is to say, it is inevitable that there will be gaps and voids formation between track slab and concrete base plate for the ballastless track with geotextile isolation layers.


## 4.2. Deformations at Interlayers of Ballastless Tracks

The reasonable arrangement of isolation layer in ballastless track is an effective way to avoid deformation inconsistency between track slab and main bridge. During the operation process, interlayer tensile deformations under routine service condition do not exceed the precompressions of isolation layers, and the interlayers of ballastless tracks are compactly filled with isolation layers, so as to improve the stress state of ballastless tracks, slow down the deterioration of ballastless tracks, and improve the deformation behaviors of ballastless tracks. For geotextiles or EPDM isolation layers which are commonly used in ballastless tracks on railroad bed, their thickness is very thin (less than 4 mm), and the compressive deformations of these isolation layers can be nearly neglected under the deadweight of its upper structures. When ballastless track with these isolation layers is laid on rigid foundation such as bridge structures, it is highly that there will be gaps and voids formation between track slab and base plate. For the rubber mat used as isolation layer, its thicknesses are always large (15∼30 mm), and compressive stiffness can be accurately obtained according to its bedding modulus. It can be considered that the rubber mat used as isolation layer is in a state of uniform compression, and its precompression is about 0.4 mm under deadweight of upper structures.For high-speed trains in China, the standard train axle load is 170 kN, and the control load of a train axle load acting on substructures is 255 kN (1.5 times of 170 kN). Under the action of the above load levels, the deformations of ballastless tracks are significant. It is considered that these deformations are essential indicators for evaluating the impact on operation of high-speed trains. Thus, the maximum compressive and tensile deformations at interlayers of ballastless tracks are listed in Table5.Table 5
The maximum deformations at interlayers.
Load conditionsLoading at slab endLoading at slab centerLimits [9] (mm)Load values (kN)170255170255Standard assemblyMaximum tensile deformations (mm)0.0030.0040.0010.002≤0Maximum compressive deformations (mm)0.250.350.030.05≤2Subballasted matMaximum tensile deformations (mm)0.170.230.150.22≤0.4Maximum compressive deformations (mm)1.181.700.901.25≤2In Table5, under the standard axle load of 255 kN, the maximum compressive and tensile deformations at interlayers of ballastless track with rubber mat isolation layer are 1.70 mm and 0.23 mm, respectively. The maximum tensile deformation does not exceed the precompression (0.4 mm) of rubber mat isolation layer under deadweight of its upper structures. Besides, the maximum compressive deformation at interlayers also meets the limit of track irregularity (2 mm) [9]. As a result, there will be no gap and void formed at interlayers of ballastless track with rubber mat isolation layer, and this allows for an increase in durability and quality of ballastless tracks. At the same time, the arrangement of rubber mat isolation layer will not have a significant impact on operation of high-speed trains. For ballastless track with geotextile isolation layer, the maximum compressive and tensile deformations at interlayers are tiny. Not surprisingly, the test data of the compressive and tensile deformations at interlayers are discrete.


## 5. Conclusions

The reasonable arrangement of isolation layer can improve the deformation behaviors of ballastless tracks laid on bridges. Rubber mats are applied in ballastless tracks laid on high-speed railway bridges as isolation layers to realize interlayer isolation and deformation coordination. The static loading tests of two full-scale ballastless tracks with rubber mat isolation layer or geotextile isolation layer have been carried out. The main conclusions are as follows:(1)
For the slab ballastless tracks laid on rigid foundation such as bridges, without considering the precompressions of isolation layer, gaps and voids can be formed at interlayers of the ballastless tracks.(2)
The application of rubber mats reduces the possibility of gaps and voids formed at interlayers of ballastless tracks. Meanwhile, the application of rubber mat has a slight effect on ballastless track stress distribution, but the safety and reliability of ballastless tracks can be guaranteed.(3)
Under the routine service condition, the rubber mats are still in elastic working state, and the interlayer deformations of ballastless tracks perform well. The tensile and compressive deformations of rubber mat isolation layers are more evident than those of geotextile isolation layers, which still meet the requirements of the specifications concerned.



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*Source: 8821402-2020-08-17.xml*