Proceedings of the 9th International Conference on Structural Dynamics, EURODYN... Porto, Portugal, 30 June - 2 July 2014

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
Numerical analysis of collision between a car and high-speed railway bridge pier
Kunpeng Cui1, Chaoyi Xia1, He Xia1, Yanhai Liu2
School of Civil Eng., Bridge of Engineering, Beijing Jiaotong University, 100044, Beijing, China
2
School of Civil Eng., Bridge of Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, China
email: [email protected], [email protected], [email protected], [email protected]
1
ABSTRACT: Elevated bridges crossing roadways have a high proportion on high-speed railways, thus the risk of vehicle
collision with piers becomes serious. A Dodge Neon car and railway pier system is established to analyze the collision force
characteristics with the help of finite element software ANSYS LS_DYNA. Different types of elements, such as shell, solid and
beam elements are introduced corresponding to various components of the car and the pier. Four different car speeds, 60km/h,
80km/h, 100km/h and 120km/h are considered to extract the collision force-time histories and analyze the force characteristics.
The result shows that: the intensity of the impact force reaches to several MN, and the loading duration is less than 0.16s; the
impact energy mainly concentrates on the low frequency, and the higher the impact speed, the more component of highfrequency; the equivalent static force exceeds the design value of the Chinese railway code and the Eurocode. This method is
feasible to simulate a vehicle collision with pier and to gain impact force time histories.
KEY WORDS: High-speed railway, bridge pier; car; collision; numerical simulation.
1
INTRODUCTION
With the development of high-speed railways in China, more
and more elevated bridges are constructed. For example, on
the 1,318 km Beijing-Shanghai high-speed railway, the bridge
length accounts for 80.5% of the total. When a bridge crosses
a river, its piers in the river may be collided by vessels or
other floating objects. For a railway bridge that steps across
another roadway, its piers close to the road may be collided by
moving cars. Although these accidents are rare, once
happened, they would cause serious damage to life, property,
society and environment [1-3].
When a collision load acts on a bridge pier, it may cause
dislocation of bearings and beams, uneven deformation or
fracture of expansion joints, or even beam collapse. For highspeed railway bridges, however, even if there is no beam
collapse, the vibration and displacement induced by collision
may deform the track and make it instable, which may further
threaten the running safety of train vehicles. During the
collision, the vehicle on the bridge may derail from the track
in case that the collision is intense and the train’s running
speed is high [4-5].
In the Code for Design of High-speed Railways (TB106212009) [6] issued by the Ministry of Railways in China, it is
stipulated that a vehicle collision force should be considered
in bridge pier design, which is represented by an 1,000-kN
static force if they are not protected by a crashworthy barrier.
The force is applied to the pier horizontally at 1.20m above
the ground, while it is unclear about the origins of the
provision and it does not explain that basis of the design
forces. Eurocode [7] gives the same vehicle collision force on
bridge piers, while it acts at 1.25m above the ground. This
paper discusses this issue and presents the results of detailed
finite element analysis of vehicle-pier collision, to evaluate
the process of vehicle collision with pier.
2
2.1
ANALYSIS MODEL
Vehicle model
To simulate the vehicle collision process more accurately, the
finite element models for vehicles issued by the National
Crash Analysis Center (NCAC, America) [6] are adopted. The
models are established and digitized from the geometry
information of each part of the vehicles, based on a large
number of automobile tests and engineering experience. These
models have received the recognition and development from
the Federal Government for Vehicle Collision Research
Center, therefore, using these models to simulate the car has a
high credibility. More detail information about the vehicle
models and the simulation procedures can be downloaded
from the NCAC’s website.
For the vehicle model, a Dodge neon car with a weight of
1.35t is select as an example to represent the light cars, as
shown in Fig. 1.
Figure 1. FE model of Dodge neon car.
The FE model of the car includes 270,768 elements and
283,859 nodes. Different material models are adopted to
simulate different parts of the car. Elastic material model is
adopted for the engine, transmission and radiator, while a
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
rubber material for the tires. As for the chassis, the front shell,
the compartment and some other parts with inelastic property,
an isotropic elastic-plastic material model is adopted.
Different types of elements, such as shell, solid and beam
elements are introduced corresponding to various components
of the structure. By connecting the various parts with rigid
constraints, a whole model is obtained reflecting the true
condition of the vehicles. More details can be found on the
website of NCAC and Reference [8].
2.2
Pier model
For the pier model, a round-end pier in service is selected,
which can be referenced from the bridge design code for
double track high-speed railway lines of 350 km/h. The pier is
made of C30 reinforced concrete, with the cross section of
760cm×300cm, and the height of 710cm. Detailed geometric
dimensions can be seen in Figure 2.
Firstly, incorporate the established car model and pier
model into a whole K file by Ls_ PrePost software through the
combine file.
Secondly, define the vehicle and bridge pier contact as the
"ASTS" aspects contact. The car collides with the pier
positively at a speed, with the car head as the initiative
collision surface and the pier as the passive collision surface.
It is called the hard collision model, with the feature of that
the collision energy absorbed by the car-body. Cater to the
collision, a standard combine file is established, in which each
different car model and pier model can be quickly
incorporated. The setting calculated time is 0.6s, with the
output of 120 steps.
4
RESULT ANALYSIS
Since the size and the weight of the pier are very big, in a case
of a light car collision, especially with low speed, the damage
of the pier is usually very slight. The collision time history
data are extracted from this simulation course, and the process
and the corresponding laws of vehicle collision with bridge
pier are analyzed.
In the Ls_PrePost software, it is convenient to see the whole
simulated impact process of the Dodge Neon car in four
different speeds. Clearly shown in Figure 3~6 are the
deformation courses of the car hitting on the pier at 120km/h
speed, and the corresponding collision times are shown on the
time-history curve in Fig. 7.
Figure 2. Geometric dimensions of the pier(unit: cm)
The finite element model adopts Solid 164 unit and Brittle
_damage[3,7] models. The constitutive of the Brittle_damage
model is based on damage mechanics theory, which can well
simulate the tensile fracture behavior of concrete. The
constitutive yield relationship function includes the tensile
stress vertical to fracture and the shear stress along the crack,
which can be expressed as:
  f n  kn q  0

   f s  ks q  0
(1)
where, kn  (1  n ) , ks  (1  s ) , q  f n (1  e ) ; ， 
and l* are program internal variables, while n is program
internal constant.
The pier is fixed at the bottom while free at top, namely,
without considering the constraint and gravity action from the
superstructure. The mapping mesh division with a total of 900
elements is adopted.
3
Figure 3. Before collision.
Figure 4. Collision begins.
PARAMETRIC STUDY
The allowance vehicle speed for roadway and highway in
China are respectively 60km/h and 120km/h, so four speeds,
60km/h, 80km/h, 100km/h and 120km/h, are selected for the
study.
The vehicle collision with the pier is simulated with the
following procedures:
Figure 5. Peak force appears at 0.028s.
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
(maximum value) of the collision force increases with the car
speed approximately in linear relationship. The peak collision
forces are 814kN, 1620kN, 2880kN and 4050kN, respectively,
corresponding to the car speeds of 60km/h, 80km/h, 100km/h
and 120km/h. The higher the collision speed is, the earlier the
peak value appears and the narrower the pulse width is.
The frequency spectrum analysis is applied to the collision
force time histories using the Fast Fourier Transform (FFT),
and the spectral density curves corresponding to four car
speeds are shown in Fig. 9.
Figure 6. The biggest deformation.
C
1200
60 km/h
80 km/h
100 km/h
120 km/h
4000
Spectrum [kN/Hz]
Collision force [kN]
1000
3000
2000
1000
800
600
400
200
A
0
0.00
D
B
0.02
0
0.04
0.06
0.08
0.10
0.12
0
50 100 150 200 250 300 350 400 450 500
Frequency [Hz]
Time [s]
Figure 7. Corresponding collision times on the time-history
curve at speed of 120km/h
In the collision force time history curve in Fig. 7, one can
find four characteristic points A, B, C and D. Point A is the
time before car collision with pier. Point B indicates the
beginning of collision. Point C indicates the peak value of the
collision force which is 4050 N appearing at 0.028s. At Point
D, the biggest deformation of the car appears at 0.089s.
There are several peaks appearing in the curve, with each
indicating certain part of the car participated and damaged in
the collision. The first crest of force time history is generated
by collision between the car-engine and pier, while the second
hysteretic crest by collision between car-body and pier.
Illustrated in Figure 8 are the time history curves of the
collision forces of the Dodge Neon car with the pier at four
different speeds.
Collision force [kN]
4000
3000
Peak force 4050 kN, 120 km/h
Figure 9. Spectrum density curves of collision force
From the figure, one can observe that the main impact
energy concentrates in the band of 50Hz. Within the
frequency band lower than 40Hz, the spectral density values
are high, normally more than 200kN/Hz, with the maximum
value close to 1,120kN/Hz appearing at 0Hz. The spectral
densities of 60 km/h is closed to zero at 80Hz, that of 80 km/h
closing to zero in 160Hz, that of 100km/h closing to zero in
240Hz, and that of 120km/h at 380Hz, showing that the higher
the car speed is, the more component the high frequency
contains.
In order to facilitate the process in the structural design, the
dynamic force is often simplified to the equivalent static
force. Equivalent static force means the static force value to
produce the same displacement under the dynamic load at the
same applied point, which depends on the stiffness and
dynamic characteristics of the system [8, 9].
According to Chopra [9], the car-pier collision system is
simplified to a single spring-mass system without damping, as
shown in Fig. 10.
Peak force 2880 kN, 100 km/h
p (t)
m
k
2000
Peak force 1620 kN, 80 km/h
1000
Peak force 814 kN, 60 km/h
0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Figure 10. Single spring-mass systems without damping
The solution of the differential equation of motion is:
mu  ku  p(t )
(2)
Time [s]
Figure 8. Force-time histories of collision forces
It can be seen from the figure that the collision duration is
less than 0.16s, and the curves show the narrow pulse load
form with only about 0.01~0.02s in width. The intensity
which subjects to the initial conditions:
u(0)  u(0)  0
(3)
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
For this case study, the top-pier displacement time history is
selected and treated with FFT, then the spectral response is
obtained, as shown in Fig. 12, which indicates the first order
frequency is 3.564 Hz. So Eq. (7) is suited to calculate the
static force for this case study.
3.564 Hz
0.8
Displacement [mm]
In developing the general solution, p(t) is interpreted as a
sequence of impulses of infinitesimal duration, and the
response of the system to p(t) is the sum of the responses to
individual impulses. These individual responses can
conveniently be written in terms of the response of the system
to a unit impulse.
The shock spectra for three kinds of pulses of rectangular,
half-cycle sine and triangular shapes, each with the same
value of force-integration in time-domain, are presented
together in Fig. 11. Over the range td /Tn＜1/4, the pure
impulse solution is close to the exact response. The two
solutions differ increasingly as td /Tn increases up to 1/2.
0.6
0.4
0.2
0.0
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30
Frequency [Hz]
Figure 12 The spectral response
Table 1 shows the peak collision force values and the
corresponding equivalent static force values.
Figure 11. Shock spectra for three force pulses of equal area
The previous observations suggest that if the pulse duration
is much shorter than the natural period, say td/Tn＜1/4, the
maximum deformation should be essentially controlled by the
pulse area, independent of its shape. Therefore, the range td /Tn
＜1/2 is approximated to calculate the equivalent static force
in this study.
As the pulse duration becomes enough short compared to
the natural period of the system, it becomes a pure impulse of
magnitude:
td
I   p(t )dt
0
(4)
Table 1. Peak collision forces and corresponding equivalent
static forces
Speed(km/h)
Peak force(kN)
Equivalent static force(kN)
60
814
644
80
1620
859
100
2880
1074
120
4050
1288
Shown in Fig. 13 is the comparison among the peak
collision force, equivalent static force and the limited static
force given by the Code of China Design of High-speed
Railways (TB10621-2009) and the Eurocode.
The response of the system to this impulsive force is the
unit impulse response of Eq. (2) times I:
1
sin n t )
mn
(5)
4000
The maximum deformation,
I
I 2π
u0 

mn k Tn
(6)
is proportional to the magnitude of the impulse.
According to equivalent displacement, to generate the same
displacement on dynamic force, it needs the static force Pa,
Pa  ku0 
2πI
 2πIf
Tn
3000
2000
1000
0
60
70
80
90
100
110
120
Speed [km/h]
(7)
where, k and f are, respectively, the stiffness and frequency of
the system.
Usually, the process of car-pier collision is less than 0.16s,
conservatively take td =0.10s, say td/Tn＜1/2, Tn＞0.20s, f＞
5Hz, Eq. (7) can be used to calculate the static force.
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Peak collision force
Equivalent static force
Design force on Code in China and Europe
5000
Force [kN]
u (t )  I (
6000
Figure 13. Comparison of collision force values.
One can see that when the car speed exceeds 100 km/h, the
equivalent static force is beyond the code limit of 1000 kN,
and the peak collision force goes up to more than thousands of
kN, indicating that the collision force given in the code is
insufficient for design of bridge piers. Therefore, it is
necessary to consider the dynamic response of vehicle
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
collision with pier to ensure the safe operation of the highspeed trains.
5
CONCLUSIONS
This paper established a car and pier simulation system by
finite element software ANSYS LS_DYNA to analyze the
collision force characteristics. The force-time histories and the
spectrum densities of the car collision on the pier at different
speeds are gained. The following conclusions can be drawn
from the analysis:
(1) The intensity of car collision force with pier reaches to
several MN, and the pulse duration is short, less than 0.16s.
(2) The higher the car speed, the earlier the peak collision
force appears, and the narrower the pulse width is.
(3) The collision energy concentrates in 50Hz. Within the
frequency band less than 40Hz, the spectral density values are
high, normally more than 200kN/Hz, with the maximum value
close to 1120kN/Hz appearing at 0Hz.
(4) The equivalent static forces exceed the limited static
force in the China High-speed Railway Code and the
Eurocode, so it is necessary to consider the dynamic response
in railway bridge pier design.
This method is feasible to simulate a vehicle collision with
pier and gain an impact force time history as an input
excitation for a further study in the high-speed train and
bridge coupling system.
The collision analysis of vehicle-pier system is a rather
complex problem, which is related with the speed and the
mass of the vehicle, the form and size of the pier, the impact
angle, the acting position, and so on. In this paper, only a
preliminary study is performed, and there need a further
theoretical and experimental research.
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ACKNOWLEDGMENTS
This paper is supported by the Natural Science Foundation of
China (51308035), the Major State Basic Research
Development Program of China (973 Program:
2013CB036203) and the Fundamental Research Funds for the
Central Universities of China (Grant No. 2013YJS059).
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