Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)

ISSN: 2311-9020; ISBN: 978-972-752-165-4

813

ABSTRACT: This paper presents a full-scale physical model test on a ballastless high-speed railway’s dynamic

performance. Both cyclic loading at fixed point at track and simulated train moving loads are used. A portion of

ballastless high-speed railway consisting of track superstructure (rails, slab, concrete base) and track substructure

(roadbed, subbase and subgrade soil) has been built in a model test box (15m*5m*6m) in Zhejiang University. A

sequential loading system composed of eight high-performance hydraulic actuators is developed to exert dynamic

loading on slab track at fasteners’ positions to simulate train’s moving loads. A theoretical model of train-slab track-

subgrade dynamic interaction is applied to determine loads acting on fasteners in the experiments. The resonance

frequency of the ballastless track system and vibration velocities at track structure show good agreement with the

field test. A three-dimensional finite element model is also developed to interpolate the test results from the physical

model testing. The influence of train speed on ballastless slab track’s dynamic behaviors is clearly illustrated.

KEY WORDS: Slab Track; Full-scale model testing; Dynamic behavior; Numerical model.

1 INTRODUCTION

Ballastless slab track has been widely used in high-speed

railway for its high durability, high stability and low whole-

life cost. Meanwhile, it difficult to recover and maintain the

ballastless slab track once damaged [1]. The use of slab track

becomes an apparent trend in high-speed railway development

and it has become the main form of newly-built high-speed

railway in the world. With the train speed increases, the

dynamic responses of track slab correspondingly increases.

To assess the dynamic performance of track slab under

different conditions, the slab dynamic performance analyzed

has been conducted. A.V. Metrikine [2] presented a

theoretical study of the stability of a two-mass oscillator that

moves along a beam on a viscoelastic half-space. Using

Laplace and Fourier integral transforms, expressions for the

dynamic stiffness of the beam are derived in the point of

contact with the oscillator. Takemiya [3] and X.C. Bian [4]

used dynamic substructure method to solve the vibration in

track and ground induced by train passages with due

consideration to dynamic interaction between an

inhomogeneous track system comprising continuous rails and

discrete sleepers, and the underlying viscoelastic layered half

space ground. Blanco-Lorenzo J [5] studied the dynamic

performance of a high speed ballasted track and three different

types of slab tracks by means of numerical simulations in the

time domain of a vehicle running on a straight section of track

at high speed with vertical rail irregularities. Different types

of vehicle–track models have been developed in order to study

the vertical dynamic vehicle–track interaction and a

comprehensive representation of the whole vehicle–track

system, necessary for the study of dynamic phenomena at

high frequencies, has been achieved making use of systematic

methodologies and standard tools offered in a commercial

MBS and in a commercial FEM analysis tool. X.Y. Lei [6]

established continuous elastic double deck beam model to

analyze the impacts of different train speeds ， track

irregularity，and rail pad rigidity and sleeper pad rigidity on

track vibrations to provide the technical data for the

construction works．And the studies show the train speed has

a significant impact on track structure vibrations.

The above-mentioned theoretical analysis are almost simple

the model, which could not indicate realistic dynamic

characteristic of slab. The physical model test could well

reflect the realistic dynamic characteristic. Momoya.Y [7, 8]

built a small-scale physical model of 1:5 size, and 1.68m

length along the track direction. They analyzed the response

of the roadbed under fixed point load and moving loads.

Ishikawa et al. [9] built a small-scale model to study the

roadbed settlement law under the cycle loads. Shaer et al. [10]

and Zhan et al. [11] established small scale rail road models.

The small-scale physical model has some disadvantages,

which could not accurately reflect the actual main features of

the roadbed. Zhejiang University built a full-scale model of a

ballastless railway to study the static and dynamic

characteristics of slab track structure [12]. Based on the full-

scale physical model testing, the author analyzed the dynamic

responses on various places on the track slab.

2 HIGH SPEED RAILWAY SLAB TRACK MODEL

2.1 Physical model

Slab track model test was carried out in a large rigid steel box.

Its size is 16m length and 15m×5m in cross-section. The

reaction force system includes longitudinal beam and cross

beam two parts. And the reaction longitudinal beam connects

with the model case through high-strength bolts, reaction

Model testing on dynamic behaviors of the slab track of high-speed railway

Chong Cheng2, Xuecheng Bian1, Hongguang Jiang1, Jianqun Jiang2

1Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Zhejiang University, Hangzhou

310027, China 2Institute of hydraulic structure and water environment, Zhejiang University, Hangzhou 310058, China

email: bianxc@zju.edu.cn, 10912062@zju.edu.cn

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

814

force crossbeam connect with the longitudinal beam through

high-strength bolts. The finished model is shown in Figure 1.

Physical model was built according to the real high-speed

railway embankment. The part from the top to bottom is rail,

fastener, track slab, CA mortar, concrete base, surface layer,

bottom layer and foundation. The 8 actuators are listed above

the fasteners as shown in Figure 2(b), the maximum amplitude

of actuator is 200kN, and the maximum excitation frequency

is 30Hz.

地基

基床底层

钱塘江粉土

A/B组填料

级配碎石

0.2

0.05

0.3

0.4

2.3

2.5

5.0

1:1.5

15.0

RailTrack slab

Concrete base基床表层Roadbed

Subgrade

Subsoil

Fastener

CA motar CRTSⅠ

Graded gravel

A/B filler

Qiantang River silt

CHN60

C40

Figure 1. Cross section of the slab track-subgrade model.

(a) Fixed point test.

(b) Configuration of the loading system.

Figure 2. Slab track-subgrade dynamic load system.

2.2 Strain sensors installation on track slab

The physical model established dynamic test and detection

system according the dynamic characteristic of slab track.

This paper is mainly focus on the dynamic strain response on

slab surface under the moving train load.

The position that gauges attached is shown in Figure 3:

According to the symmetry of slab, the gauges were attached

on 1#~5# fasteners near places (below the fastener center and

slab middle place) during the test. And at 1#-5# fastener

places attached the longitudinal (along the rail direction)

strain gauge, and on 1#, 3# and 4#fasteners, attached both

longitudinal and lateral gauges.

Figure 3. The photos of layout of the strain sensor.

1 2 3 4 5 6 7 8

Strain4-1

Strain4-2

Strain4-3

Strain4-4

Strain4-5

Slab Strain gauge

5000

2400

Figure 4. Schematic diagram of layout of the strain sensor.

2.3 Model loading system

Figure 2 shows the developed sequential loading device for

simulating train’s moving loads, consisting of reaction frames,

eight hydraulic actuators and eight load distribution girders.

The eight hydraulic actuators were placed corresponding to

the positions of the fasteners, and distribution girders were

installed on each fastener to transfer loads applied by the

actuators to the track slab. Unlike the original track structures,

the rails were no longer continuous in the sequential loading

system. The rail segments were fixed to the track slab with

fasteners at the original positions. This treatment keeps the

load-transferring interface between the fasteners and the track

structure intact.

2.4 Moving train load simulation

The sequential loading device for simulating train varies

speeds, the load frequency and adjacent phase to achieve this.

Assuming the railway has a homogeneous profile in the

track’s direction and that the train runs at a constant speed, the

loading profiles on each fastener in the track’s direction

remain unchanged, but with a certain lag in time.

The fastening spacing along the rail direction is L, train

speed v, load frequency f, adjacent actuator load time interval

δ, train load (one axle/bogie) shared by n fasteners, phase is .

1

vf

n L

，

1360 360 360

1

Lf

T v n

Axle load

The load time history curve could be replaced by an

approximate half sine wave or sine wave under one axle load

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

815

in theoretical. The sequential loading system control as shown

in Table 1 under one axle load.

Bogie load

The fastening system load time history cure is ”M” wave

under one bogie load, and approximately load is shared by 10

fasteners , as shown in Figure 5 , a distributed load of train

speed analog control system as shown in Table 1.

Table 1. Frequency and the phase space of the actuator

associated to the speed.

Train

speed

(km/h)

60 120 180

Frequency

(Hz) 4.41/2.57 8.82/2.57 13.23/7.69

Adjacent

phase(°) 60/36 60/36 60/36

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Lo

ad

sh

ari

ng

rati

o

Time(s)

Figure 5. The loading time history of “M” wave.

Moving train loads

According to the bogie and axle length, combined with M

wave load cure and train speed, the fastener load time history

curve could be given as below:

Car body

Bogie

Wheel2.5

17.5

(a) The length parameter of train.

1 2 3 4 5 6 7 8

0

20

40

60

80

Fas

ten

er l

oad

(k

N)

Time (s)

2.5m

7.5m 17.5m

(b) Fastener load time history.

Figure 6. Schematic diagram of distributed loading simulation

system

Figure 7. Simulate moving train load.

3 SLAB RESPONSES UNDER MOVING TRAIN LOAD

For a detailed analysis of the response of slab under vary

speeds, the train speed increase from 10m/s to 100m/s during

the test, and the train axle load is 17 ton.

3.1 Model result and analysis

The number of strain gauges arranged is very large, in order to

convenient introduce the test results, this paper focuses on 5

longitudinal strain gauges near the central part of the 4th

fastener and 3 transverse strain gauges test results. Defined

along the rail direction is the longitudinal direction. The paper

considers three typical train speeds(10m/s, 50m/s and

100m/s), the results shown in Figure 8 - Figure 10. When train

runs with low speed (10m/s), it would arouse severe strain

response when axle via the fastener. From the Figure 8, it

clearly shows the axle position. When the axle load move

away from the fastener, the strain response near the fastener is

sharply decrease. Refer to 4# fastener, the responses is not

obvious on lateral direction. It indicates that when the train

runs with low speed, the strain difference on slab surface is

slightly. When train runs with medium speed (50m/s), it also

appears a peak strain response when load on the top of

fastener. There is a clear fluctuation, which indicating that

when train runs with medium speed will arouse serious

vibration and significant fluctuations. Figure 9 shows, strain

response time-history response occurs significant fluctuation,

which indicating that when speed increases to 50m/s, the

vibration on slab track structure intense increase. On middle

of slab is mainly longitudinal strain (about 3εμ); near the

bottom of fastener, the compressive strain amplitude is near

6εμ.

Figure 10 shows when the train runs with the speed of

100m/s: Compared with the low speed and medium speed

cases, the amplitude of tensile strain response aroused by

speed of 100m/s reaches 15εμ, and the compressive strain

near the fastener is also increase to 6εμ. The curve clear

shows the schedule violent fluctuate, which indicating that the

train running under high speed arouse dramatic structural

strain changes.

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

816

56 60 64 68 72 76

-4.0x10-6

-2.0x10-6

0.0

2.0x10-6

4.0x10-6

6.0x10-6

8.0x10-6

1.0x10-5

Str

ain

Time (s)

56 60 64 68 72 76

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

Str

ain

Time(s)

B

(a) Position: 4-5. (b) Position: 4-2.

56 60 64 68 72 76

-2.50x10-6

0.00

2.50x10-6

5.00x10-6

7.50x10-6

1.00x10-5

Str

ain

Time(s)56 60 64 68 72 76

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

Str

ain

Time(s)

B

(c) Position: 4-4 (d) Position: 4-1

56 60 64 68 72 76-3.0x10

-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

Str

ain

Time(s)

B

(e) Position: 4-3

Figure 8. Longitudinal strain near 4# fastener under train

speed of 10m/s in full-scale physical model test: (a) and (b) on

the edge of the rail; (c) and (d) under the center of rail; (e) on

the center of the slab.

57 58 59 60

-6.0x10-6

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

Str

ain

Time(s)56.4 57.0 57.6 58.2 58.8 59.4 60.0

-6.0x10-6

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

1.5x10-5

Str

ain

Time(s) (a) Position: 4-5 (b) Position: 4-2

57 58 59 60

-6.0x10-6

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

Str

ain

Time(s)

B

57 58 59 60

-6.0x10-6

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

Str

ain

Time(s) (c) Position: 4-4 (d) Position: 4-1

57 58 59 60

-3.0x10-6

0.0

3.0x10-6

6.0x10-6

9.0x10-6

1.2x10-5

Str

ain

Time(s)

B

(e) Position: 4-3

Figure 9. Longitudinal strain near 4# fastener at train speed of

50m/s in the full-scale physical model test: (a) and (b) on the

edge of the rail; (c) and (d) under the center of rail; (e) on the

center of the slab.

56.5 57.0 57.5 58.0-8.0x10

-6

-4.0x10-6

0.0

4.0x10-6

8.0x10-6

1.2x10-5

1.6x10-5

Str

ain

Time(s)

B

56.5 57.0 57.5 58.0-8.0x10

-6

-4.0x10-6

0.0

4.0x10-6

8.0x10-6

1.2x10-5

1.6x10-5

Str

ain

Time(s) (a) Position: 4-5 (b) Position: 4-2

56.5 57.0 57.5 58.0-8.0x10

-6

-4.0x10-6

0.0

4.0x10-6

8.0x10-6

1.2x10-5

1.6x10-5

Str

ain

Time(s)

B

56.5 57.0 57.5 58.0

-1.0x10-5

-5.0x10-6

0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

Str

ain

Time(s) (c) Position: 4-4 (d) Position: 4-1

56.5 57.0 57.5 58.0

-6.0x10-6

0.0

6.0x10-6

1.2x10-5

1.8x10-5

Str

ain

Time(s)

B

(e) Position: 4-3

Figure 10. Longitudinal strain near 4# fastener at train speed

of 100m/s in the full-scale physical model test: (a) and (b) on

the edge of the rail; (c) and (d) under the center of rail; (e) on

the center of the slab.

Based on the strain responses under different train speeds, it

could plot the typical speed response diagram (near 4#

fastener position), as shown in Figure 11. It can be found that

when the train speed less than 40m/s, the amplitude of the

longitudinal strain is near 8εμ; once train speed exceeds

40m/s, the longitudinal strain increase rapidly. When speed

reaches 100m/s, the longitudinal strain amplitude increases to

14εμ, compared with the low speed and medium speed cases

increases 75.0%. The five longitudinal strain data near 4#

fasteners averaged vertical cross section can be obtained on

the fastener strain rate response map.

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

817

0 100 200 300 400

8

9

10

11

12

13

Str

ain

(10

-6)

Train speed(km/h)

Test results

Fitting curve

0 100 200 300 4008

10

12

14

Str

ain

(1

0-6

)

Train speed(km/h)

Test results

Fitting curve

(a) Position: 4-5 (b) Position: 4-2

0 100 200 300 400

8

9

10

11

12

13

Str

ain

(1

0-6

)

Train speed(km/h)

Test results

Fitting surve

0 100 200 300 400

9

10

11

12

13

14

15

S

train

(1

0-6

)

Train speed(km/h)

Test results

Fitting curve

(c) Position: 4-4 (d) Position: 4-

0 100 200 300 400

10

11

12

13

14

15

Str

ain

(1

0-6

)

Train speed(km/h)

Test results

Fitting surve

0 100 200 300 400

9

10

11

12

13

14

Average of test data

Fitting curve

Str

ain

(1

0-6)

Train speed (km/h) (e) Position: 4-3 (f) Fitting curve

Figure 11. Relationship between dynamic longitudinal strain

and train speed.

According above test data, we can get dynamic

magnification factor Φd [13], as shown in Figure 12. When

the train speed is less than 60km/h, the dynamic amplification

factor 1.45; when the train speeds greater than 60km/h, this

test presents the results shows parabola (combined with

Figure 11(f)) form. When train runs at 360km/h, this test

result obtained is 1.7. China Railway specification is 3.0,

which is far more than this test results.

0 100 200 300 4001.4

1.5

1.6

1.7

dy

nam

icam

pli

ficati

on

facto

r

Train speed (km/h)

Test data

Figure 12. Relationship between dynamic load magnification

factor of slab and train speed

According to the test measured data obtained under

different conditions. As gauge attached on 1#~5# fastener,

select the axle on the 3rd fastener as a typical case, combined

with the test data the strain clouds can be plotted, as Figure 13

shows: on low speed case, strain distribution mainly on the

vicinity of 4# fastener, when the train speed increase to

360km/h, the strain response area increased dramatically, this

can be reasonably interpreted from Figure 11 and Figure 12.

(a) (b)

(a) 36km/h (b) 180km/h

(c) 360km/h

Figure 13. Strain responses on slab surface under varied train

speeds (left) longitudinal strain, (right) lateral strain. (a) c =

36 km/h, (b) c = 180 km/h, (c) c = 360 km/h

3.2 Numerical analysis

As only record the typical position strain response on slab

surface during the test, in order to better describe the dynamic

performance on slab surface under moving train loads and

compared with the physical result, it is necessary to establish

the numerical model, as shown in Figure 14.

4#Lateral

Longitudinal

(Rail direction)

Track slab

Concrete base Fastener

Surface layer

Bottom layer

Figure 14. Slab track embankment model

For comparison with the experimental results, author also

select typical condition on slab surface of FEM: when axle is

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

818

located just above the 4# fastener position. And the whole slab

only has this axle on the slab surface. Take the high-speed

condition (360km/h) as an example. The track slab surface

strain contours as shown in Figure 15. It can be found that at

the edge of the rail appears strain concentration phenomenon,

longitudinal strain diagram Figure 15 (a) are distributed along

rail direction, transverse strain concentrated on the middle of

two fasteners. It appear pear strain value near the 4# fastener,

the vertical and horizontal strain amplitude are 16εμ and 13εμ

separately, fit well with the test results (as shown in Figure

11,14 εμ).

(a) Longitudinal strain cloud (b) Transverse strain cloud

Figure 15. Strain responses on slab surface under train speed

of 360km/h (left) longitudinal strain, (right) lateral strain

4 CONCLUSIONS

Based on physical model test and numerical model analysis

under moving train loads, some conclusions are drawn as

follows:

(1) The full-scale physical model could well simulate high-

speed train moving on track slab under different train

speeds, and record the strain;

(2) When train speed below 150km/h, the strain on central of

slab surface is nearly stayed constant, the amplitude is

around 9εμ. Once the speed exceeds 150km/h, the strain

increases rapidly, the maximum strain is 14εμ under the

speed of 360km/h;

(3) When train speed less than 60km/h, dynamic load

amplification factor calculated is near 1.45; when the

train speed greater than 60km/h, herein test results with a

parabolic increase with speed increases.

ACKNOWLEDGMENTS

Financial supports from the Natural Science Foundation of

China (Grant Nos. 51178418 and 51222803) are gratefully

acknowledged.

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