STABILITY ANALYSIS OF TRACK STRUCTURE AND ITS COMPONENTS ON SLOPE AND SHARP CURVE
Yu ZHOU，Xiaofeng ZHENG，Miao YU，Difeng KUANG
The Key Laboratory of Roads and Traffic Engineering，Ministry of Education，Tongji
University，Shanghai 201804
Abstract：In this paper the longitudinal and lateral models of four track structures such as the tie-embanked track，ladder track，steel spring and rubber mat floating-slab tracks were established by finite element method（FEM）.The forces loaded on the track at the steep slope of 30‰ and sharp curve of 400 m radius was applied in the models respectively.The mechanical properties and stability of the track structure and the rail on it such as the longitudinal force and displacement of the rail，the longitudinal and lateral displacement of the concrete slab were analyzed.The results show that the longitudinal force and displacement of the rail on the anti-vibration track structure were from-35 kN to 28 kN and 0.20 mm to 0.31 mm respectively.The displacements of the slab on the floating slab track structures were 0.20 mm to 0.36 mm in the longitudinal direction and 2.7 mm to 4.4 mm in the lateral direction which were larger than others.Therefore，the longitudinal stability of the continuous welded rail（CWR）and each slab，the longitudinal shear deformation of the steel spring and rubber mat of the floating slab track structures should be carefully considered and inspected.
Keywords：steep slope，sharp curve，finite element，track structure，anti-vibration track
Email：yzhou2785@tongji.edu.cn
1 Introduction
With the development of urban rail transit in China，there are lots of lines with special alignment condition such as steep slope with more than 25‰ and sharp curve with radius less than 400 m.The track structures and its components on these conditions should be carefully considered for safety operation.Therefore，the analysis of the stability of different of track structures and its components on these line conditions should be necessary for guiding the design and construction of the track structures on steep slope and sharp curve line.
In this paper，the models of four track structures like the tie-embanked track，ladder track，steel spring and rubber mat floating-slab tracks were established by finite element method（FEM），The mechanical properties of the rail and track structures on the conditions of steep slope and sharp curve were analyzed，the suggestions about the design and maintenance of the rail and track were presented.
2 Modeling
According to the characters of these 4 track structures[1]，the longitudinal section and lateral section models of the tie-embanked track，ladder track，steel spring and rubber mat floating-slab tracks were established by FEM.
2.1 Model
The tie-embanked track is composed of rail，fastening，tie and cast-in-place concrete around it，ballast bed slab etc.The fastening connects the rail and tie as the spring and damping（it has the same function in the following；the bottom of the concrete is fully-constrained and connect with foundation）.The type of the cast-in-place concrete is C40.
The steel spring floating slab track is composed of rail，fastening and the floating concrete slab which supported at its bottom by the steel spring.The model is shown in the Figure 1.The function of steel springs is represented by spring and damping.The floating concrete slab is the C40 type concrete.
Figure 1 Model of steel spring floating slab track
The Ladder track is composed of rail，fastening and the ladder-type sleeper，L-shape holder，the cushion rubber，anti-vibration mat，steel tube.The model is shown in the Figure 2.The function of cushion rubber and anti-vibration pad are represented by spring and damping.The ladder-type sleeper is the C35type concrete.
Figure 2 Model of ladder track
The rubber mat floating-slab is composed of rail，fastening，concrete bed slab and lab mat.The model is shown in the Figure 3.
Figure 3 Model of ballast bed anti-vibration pad track
According to these track structure model element and the elements parameters in the references[2]，the longitudinal section track FEM with 60 m long were established.
2.2 Loading
Since the track structures are on the steep slope and sharp curve condition，with the train running on them respectively，the loading on them include the forces along three directions which are the vertical force，the longitudinal horizontal force and lateral horizontal force.
（1）The vertical force：In view of the worst situation，train axle load is 16 t according to the type A vehicle in urban rail transit system，the average weight of single wheel is 8 t，Considering the slope of 30‰，and the dynamic coefficient is 1.5，the vertical force of a single wheel on the rail is 120 kN.
（2）The longitudinal horizontal force：according to the standard[3]，the braking force of train on the slope is 0.25 times of the axle load.Moreover，considering the component force of train gravity along the steep slope.
sin F Gθ=⋅
where，F is the component force of gravity.G is gravity.θ is slope angle（tan=30‰ in this paper）.So，the longitudinal horizontal force was 22.4 kN.
（3）The lateral horizontal force：the horizontal force was designed as 40 kN in sharp curve with radius of 400 m[4].
（4）The form of loading：for the ladder track，steel spring and rubber mat floating-slab tracks，the forces were applied in the form of concentrated force on the basis of total wheel base in one vehicle and rigid wheel base in one bogie.Then，move the force from one side of the track structure to another to simulate the process of a vehicle with two bogies passing a single concrete slab.The tie-embanked track was integral pouring，so it’s not necessary to move the force.
3 Results Analysis
The mechanical properties such as the longitudinal force，the longitudinal and lateral displacement of the concrete slab were simulated.
3.1 Longitudinal force of rail
The rail longitudinal force of the tie-embanked track was shown in the Figure 4.It’s shown that the force was from-17.9 kN to 17.9 kN.
Figure 4 Rail longitudinal force in tie-embanked track
The longitudinal forces of the rail on other track structures were shown in the Figure 5.
Figure 5 Rail longitudinal forces
It can be seen from Figure 5，the longitudinal force of the rail on the ladder track，the steel spring and rubber mat floating-slab tracks were-35 to 12 kN，-30 to 20 kN and-34.5 to 28.4 kN respectively.Comparing Figure 4 and Figure 5 ，it’s shown that the maximum rail longitudinal force were about 1.95 and 1.67，1.59 times on the 3 kinds of anti-vibration track structures than that of on the tie-embanked on the steep slope with 30‰ and sharp curve with radius of 400 m.
3.2 Longitudinal displacement of rail
The longitudinal displacement of the rail in these 4 track structures were shown in the Figure 6.The maximum rail longitudinal displacement of the tie-embanked track，the ladder track，the steel spring and rubber mat floating slab tracks were 0.046 mm，0.20 mm，0.31 mm and 0.21 mm respectively.The rail longitudinal displacement on the anti-vibration track structures was about 4.35 times-6.74times than that of on the tie-embanked track on the steep slope with 30‰ and sharp curve with radius of 400 m.
Figure 6 Longitudinal displacement of rail
3.3 Longitudinal displacement on top of concrete slab
As for the tie-embanked track，the longitudinal displacement on the top of the concrete slab was shown in the Figure 7.The maximum displacement was 0.0008 mm.
Figure 7 Longitudinal displacements on top of concrete slab on tie-embanked track
The maximum displacements on the top of the other 3 types of track structure were shown in the Figure 8.From Figure 8，the longitudinal displacements on the top of the concrete slab of the ladder track，the steel spring and rubber mat floating-slab tracks were 0.25 mm，0.25 mm and 0.22mm respectively.Therefore，the longitudinal displacements on the top of the concrete slabs on these anti-vibration track structures were larger than that of on the tie-embanked track on the steep slope with 30‰and sharp curve with radius of 400 m.
Figure 8 Longitudinal displacements on top of concrete slab
3.4 Longitudinal displacement on bottom of concrete slab
The longitudinal displacement at the bottom of the concrete slab of tie-embanked track can be negligible because the concrete slab was connected with the infrastructure totally.And the maximum longitudinal displacements at the bottom of the slab of the other three track structures were shown in the Figure 9.
Figure 9 longitudinal displacements at bottom of concrete slab
As shown in Figure 9，the maximumlongitudinal displacements at the bottom of the concrete slab of the ladder track，the steel spring and rubber mat floating-slab tracks were 0.23 mm，0.3 mm and 0.36 mm respectively.
3.5 Lateral displacement of concrete slab
The maximum displacements of the concrete slab on the 3 anti-vibration track structures were shown in the Figure 10.They were 0.53 mm，2.7 mm and 4.4 mm on the ladder track the steel spring and rubber mat floating-slab tracks respectively.
Figure 10 Lateral displacement of concrete slab
In summary，the mechanical properties of these four types of track structures were shown in the Table 1.
Table 1 Mechanical properties of track structures
4 Conclusions
With the steep slope of 30‰ and sharp curve of 400 m，the mechanical properties of 4 kinds of track structures were analyzed.The conclusions were shown below：
（1）The longitudinal force and displacement of the rail on the anti-vibration track structure were-35 kN to 28 kN and 0.20 mm to 0.31 mm respectively which were larger than those on the tie-embanked track.Therefore，the longitudinal stability of the CWR on the steep slope should be inspected carefully.Moreover，the fastening with a large clamping force can be applied for CWR stability.
（2）It can be found that the displacements of the slab on the floating slab track structures were 0.20 mm to 0.36 mm in the longitudinal direction and 2.7 mm to 4.4 mm in the lateral direction which were larger than others.0.20 mm to 0.36 mm in the longitudinal direction and 2.7 mm to 4.4 mm in the lateral direction which were larger than others.
（3）The longitudinal shear deformation of the steel spring and rubber mat of the floating slab track structures on should be given attention.The condition of the shear hinge between slabs of the floating slab track should be inspected regularly during the whole life time.
References
[1]Chen P.，2008.Research on Mechanical Characteristics of Ballastless Track in High-Speed Railway[D].Beijing：Beijing Jiaotong University.
[2]Guang Z.Y.，et al.，2001.Continuous Welded Rail[M]Beijing：China Railway Press.
[3]Shanghai Tunnel Engineering＆Rail Transit Design and Research Institute，2003.Urban rail transit design standard[S].
[4]Wang Q.C.，2006.Rail Fastening of the ballastless track[M].Chengdu：Southwest Jiaotong University Press.
ICRE2016-International Conference on Railway Engineering