STUDY ON LONGITUDINAL FORCES CHARACTERISTIC OF LONGITUDINAL CONNECTED SLAB TRACK ON HIGH-SPEED RAILWAY BRIDGE

Qingyuan XU，Qi WEI，Jun DUAN，Xi OU，Ping LOU，Xiaolin ZHOU

School of Civil Engineering，Central South University，Changsha 410075

Abstract：Longitudinal connected slab track has been widely used in several high-speed railways in our country，including Beijing-Shanghai High-speed Railway.In order to study the longitudinal force characteristic of longitudinal connected slab track on high-speed railway bridge，a nonlinear finite element mechanical model for calculating the longitudinal force of longitudinal connected slab track mechanical model was verified by the results of Bogl Company.Taking a 10-span 32 m longitudinal connected slab track on High-speed railway bridge as an example，the longitudinal force characteristics of longitudinal connected slab track on high-speed railway bridge，which are caused by expansion and contraction load of bridge，braking load of vehicle，breaking load of rail，and breaking load of slab，were studied.The results show that the longitudinal force of rail and pier/abutment of longitudinal connected slab track is far less than that of discontinuous slab track，which is favorable to use large resistance fastener and trans-section continuously welded rail to increase safety and speed of train running on High-speed railway bridge，and to reduce construction cost of abutment and pier at the same time.But it is important to ensure construction quality of longitudinal connected slab track to avoid strong longitudinal force transmission among different components of longitudinal connected slab track under slab breaking load.

Keywords：high-speed railway，longitudinal connected slab track，nonlinear finite element method，railway engineering，longitudinal forces，track-bridge interaction

Email：xuqingyuan1972@163.com

1　Introduction

Slab track is a modern railway technology.Compared to ballast track，there are many merits for slab track.For example，stability of track is increased，security of train operation is raised，and maintenance work of track is greatly reduced.With the development of ballastless track technology，it has been widely used in high-speed railway in many foreign countries，such as Japan，Germany and so on.It is also widely used in many high-speed railway lines in our country.

Longitudinal connected slab track on bridge is very different from traditional discontinuous slab track on bridge which is widely used in Japan.Firstly，the former is continuous but the latter is discontinuous.Secondly，a sliding layer is installed between track and bridge to reduce longitudinal force among rail，track and bridge，which is caused by expansion and contraction of bridge.Thirdly，there is an anchor bar connecting track and bridge in order to transmit braking force from rail to bridge pier or abutment.

Because slab track on bridge is longitudinally connected，longitudinal force is one of the controlling design forces of slab track，terminal spine，abutment and pier as well as rail.When Bogl Company transferred its technology to China Ministry of Railway，the design and calculation of longitudinal forces of longitudinal connected slab track on bridge was in important position.

The design and calculation theory of ballastless track is a precondition to design ballastless track.Although many studies have been made on this aspect at home and aboard，most of studies were mainly on spatial mechanical characteristic of discontinuous slab track under vertical train load[1-5].Studies on spatial mechanical characteristic of longitudinal connected slab track on bridge under longitudinal load still lack depth[6].Mechanical characteristic analysis of longitudinal connected slab track on bridge under longitudinal load is very similar to that of traditional bridge and rail interaction[7-11]，but the later mainly studies longitudinal force of rail as well as abutment and pier，and its research achievements cannot be directly used.

In this paper，a nonlinear finite element mechanical model for calculating the longitudinal forces of longitudinal connected slab track on high-speed railway bridge was established by absorbing the calculation theory of Bogl Company and the research achievements of Chinese bridge and rail interaction，and longitudinal force characteristics of longitudinal connected slab track on bridge are studied in depth.

2　Nonlinear FEM Mechanical Model for Calculating Longitudinal Forces of Longitudinal Connected Slab Track on Bridge

Nonlinear FEM mechanical model for calculating the longitudinal forces of longitudinal connected slab track on bridge is shown in Figure 1.Rail，slab，bridge，and friction plate are simulated as beam element respectively.The longitudinal connections between rail and slab，slab and bridge，slab and friction plate，slab and subgrade，bridge and pier/abutment are considered as nonlinear spring element respectively.Friction plate is supposed to be fixed in subgrade.

3　Verification of Model

The nonlinear FEM mechanical model for calculating the longitudinal forces of longitudinal connected slab track on bridge is verified by the calculation results of Bogl Company.

3.1　Calculation condition

Taking the middle 50 spans of 301-span bridge in Beijing-Tianjin Intercity High-speed Railway as object of study，the serial numbers of pier are from 150 to 200 and all spans of bridge are 32 m.The longitudinal stiffness of pier and layout of bridge bearing could be found in Reference[12].Other calculation parameters are shown in Table 1.

Continued Table

3.2　Results and discussion

Longitudinal forces of rail and slab under single-line braking load of vehicle are shown in Figure 2 and Figure 3 respectively.Comparison of calculation results is shown in Table 2.

It can be found from Table 2 that percentage error between results of Bogl Company and results of this paper is smaller than 3％，which illustrates that the mechanical model of longitudinal connected slab track on bridge established in this paper is reasonable.

4　Examples

4.1　Calculation condition

Taking longitudinal connected slab track on a simply-supported bridge as an example，bearing layout and braking load distribution are shown in Figure 4.The span of bridge is 32 m，and the span number of bridge is 10.Anchor bars are set up to connect slab with bridge in the location of fixed support.Other calculation parameters are shown in Table 3.

The following six load cases are calculated.

Case 1：Slab without stiffness reduction，Young’s modulus of slab is 3.5×1010MPa，temperature rising amplitude of bridge is 30 ℃.

Case 2：Slab with stiffness reduction of 70％，Young’s modulus of slab is 1.05×1010MPa，temperature falling amplitude of bridge is 30 ℃.

Case 3：Slab without stiffness reduction，Young’s modulus of slab is 3.5×1010MPa，braking load of vehicle is 16 kN·m-1.

Case 4：Slab with stiffness reduction of 70％，Young’s modulus of slab is 1.05×1010MPa，braking load of vehicle is 16 kN·m-1.

Case 5：Slab with stiffness reduction of 70％，Young’s modulus of slab is 1.05×1010MPa，temperature falling amplitude of bridge is 30 ℃，temperature falling amplitude of slab is 40 ℃，temperature falling amplitude of rail is 60 ℃，rail breaks at the location of 5# pier.

Case 6：Slab with stiffness reduction of 70％，Young’s modulus of slab is 1.05×1010MPa，temperature falling amplitude of bridge is 30 ℃，temperature falling amplitude of slab is 40 ℃，temperature falling amplitude of rail is 60 ℃，slab breaks at the location of 5# pier.

In addition，in order to compare longitudinal forces characteristics of longitudinal connected slab track on bridge to those of discontinuous slab track on bridge under longitudinal loads，the following four load cases for discontinuous slab track on bridge are calculated.

Case 7：Temperature rising amplitude of bridge is 30 ℃.

Case 8：Temperature falling amplitude of bridge is 30 ℃.

Case 9：Braking load of vehicle is 16 kN·m-1.

Case 10：Temperature falling amplitude of bridge is 30 ℃，temperature falling amplitude of rail is 60 ℃，rail breaks at the location of 5# pier.

Continued Table

4.2　Calculation results

Calculation results of longitudinal connected slab track on bridge in different cases are shown in Table 4.Calculation results of discontinuous slab track on bridge in different cases are shown in Table 5.

4.3　Discussion of calculation results

Longitudinal tensile force of slab for longitudinal connected slab track on bridge under expansion and contraction load of bridge is smaller than 200 kN.

Longitudinal force of slab for longitudinal connected slab track on bridge under braking load cannot be neglected.Slab tensile force is 803 kN，and its tensile stress is bigger than 0.7 MPa.Slab compressive force is 877 kN，and its compressive stress is also bigger than 0.7 MPa.

It can be found from Table 4 and 5 that longitudinal forces of rail and pier/abutment for longitudinal connected slab track on bridge，which are caused by expansion and contraction load of bridge，braking load of vehicle and breaking load of rail，are much smaller than those of discontinuous slab track on bridge.For example，under expansion and contraction load of bridge，rail longitudinal force of the former is smaller than 30 kN，but the later is 467 kN.Under braking load of vehicle，rail longitudinal force of the former is smaller than 100 kN，but the later is 462 kN.

When longitudinal connected slab track on bridge is in normal condition，longitudinal force of anchor bar is smaller than 800 kN.But if slab breaks，longitudinal force of anchor bar may reach 2724.6 kN，which may lead anchor bar to fracture.

5　Conclusions

（1）The small value of longitudinal force of rail for longitudinal connected slab track on bridge under expansion and contraction load of bridge or braking load of vehicle is helpful to cancel expansion joint of rail on long span bridge，which is favorable to high-speed of train.Longitudinal force of pier/abutment for longitudinal connected slab track on bridge under expansion and contraction load of bridge or braking load of vehicle is also very small，which is favorable to reduce construction cost of bridge pier/abutment.

（2）Longitudinal force of rail and pier/abutment for longitudinal connected slab track on bridge under breaking load of rail is smaller than that for discontinuous slab track on bridge，which is helpful to use fastener with large resistance for longitudinal connected slab track on bridge，and to reduce rail gap caused by breaking load of rail.

（3）Longitudinal force of longitudinal connected slab track on bridge under breaking load of slab is very large.In order to prevent slab to break suddenly，it is very important to ensure construction quality of slab，and to deal with slab related problems in time.

Acknowledgement

The works described in this paper are supported by the National Natural Science Foundation of China（No.51178469），the Central South University Graduate Students Independently Exploratory Innovative Fund（No.2016zzts 425）and the National Science Joint High Speed Railway Foundation of China（No.U1334203）.

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