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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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